Hydrophysiology magnetic resonance method

Abstract

A nuclear magnetic resonance (NMR) system measures an effective osmolarity or tonicity and characterizes the effective osmolarity or tonicity's effect on water exchange in a specimen. The NMR system includes a magnetic resonance (MR) device, which has: a magnetic field generator; a magnetic field gradient generator; a radio frequency (RF) transmitter; and a RF receiver. The NMR system also includes a processing system coupled to the MR device. The processing system is configured to: receive sample NMR data from the MR device, the sample NMR data corresponding to the specimen; estimate an exchange rate from the NMR data, the exchange rate corresponding to the water exchange through a semipermeable membrane of the specimen; and estimate the effective osmolarity or tonicity based on the estimated exchange rate.

Description

HYDROPHYSIOLOGY MAGNETIC RESONANCE METHODCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U. S. Provisional Patent Application No.63 / 713,789, filed on October 30, 2024, which is incorporated herein by reference in its entirety.STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] The present invention was made with Government support by the National Institutes of Health, Eunice Kennedy Shriver National Institute of Child Health & Human Development. The Government has certain rights in this invention.BACKGROUND

[0003] Biological homeostasis is a state of steady internal, physical, and chemical conditions maintained by a living organism. Homeostasis involves modulation of different transport processes to maintain relatively constant cell volumes, pressures, transmembrane potentials, and water and ion concentrations, which are coupled through the electrochemical potential. While the steady-state seems static, molecules (including water) are constantly exchanging between the inside and outside of cells, and through the extracellular matrix (ECM), both actively and passively. Indeed, such molecular exchange may not be static, as there can be different exchange rates without there being any net flow. See, e.g., OG Fritz Jr and TJ Swift. The state of water in polarized and depolarized frog nerves: A proton magnetic resonance study. Biophysical Journal, 7( 6):675-687, 1967; and Yajie Zhang, Marie Poirier-Quinot, Charles S Springer Jr, and James A Balschi. Active trans-plasma membrane water cycling in yeast is revealed by nmr. Biophysical journal, 101 (11): 2833 2842, 2011 (the entire contents of each of which are hereby incorporated by reference herein). As can be appreciated, energy expenditure to maintain homeostasis may be quite substantial, even if outwardly, little change is happening. For example, 95% of the brain’s energy budget is devoted to homeostasis, i.e., maintaining steady-state activity levels conducive to normal function. See Marcus E Raichle and Debra A Gusnard.Appraising the brain ’s energy budget. Proceedings of the National Academy of Sciences,99(16): 10237-10239, 2002 (the entire contents of which is hereby incorporated by reference herein).

[0004] Biological homeostasis can also vary in order to alter the cellular physical and chemical conditions, thus, acting as a mechanism to define the physiological state of cellular activity, for instance resting states or active states (e.g., intensive physical or mental activity or intensive physical or mental stimulation). Deviations or perturbations from biological homeostasis, even at the cellular level, can be caused by pathological conditions such as diseases within the organism. Such deviations result in physical and chemical conditions that can feedback to prolong pathological states as part of an injury or disease. In the extreme case, cell death can be characterized by a complete loss of homeostasis, which is consistent with thermodynamic equilibrium. In these ways, states of biological homeostasis are linked to physiological and pathological activities occurring at various levels of the organism (e.g., organelle, cell, tissue, organ, etc.). States of biological homeostasis, particularly related to water homeostatis, can be difficult to detect using conventional analytical techniques.

[0005] In one particular example, diseases that affect the state of the central nervous system (CNS) are difficult to assess due to the difficulty in taking accurate measurements of the CNS. The CNS undergoes changes occurring in disease, development, aging, and trauma. Due to the difficulty in taking accurate measurements of the CNS, diagnosing and understanding these CNS changes presents a problem.

[0006] One such avenue for measuring the state of the CNS is using nuclear magnetic resonance (NMR)-based measurement techniques, such as NMR spectroscopy or magnetic resonance imaging (MRI).

[0007] NMR can measure the rate constant for steady-state transmembrane water exchange, hereafter called the “exchange rate”. Such a measurement involves labeling the protons (1H) on water inside versus outside of the cell, and watching the protons mix. See, e.g., Nathan H Williamson, Rea Ravin, Dan Benjamini, Hellmut Merkle, Melanie Falgairolle, Michael James O 'Donovan, Dvir Blivis, Dave Ide, Teddy X Cai, Nima S Ghorashi, et al. Magnetic resonance measurements of cellular and sub-cellular membrane structures in live and fixed neural tissue. Elife, 8:e51101, 2019 (the entire contents of which is hereby incorporated by reference herein).

[0008] For exchange across cell membranes, i.e. transmembrane exchange, the exchange rate (fc) depends on diffusive permeability (p) and membrane surface-to-volume ratio (SVR) through the relation k = / cdSVR. In this way, the exchange rate is sensitive to membrane permeability, however not quantitatively due to the heterogeneity in cell surface-to-volume ratios, and not specifically due to the sensitivity to other exchange pathways such as between regions inside the cell, i.e. geometric exchange, which exist due to the microstructural heterogeneity of biological tissue. See, Mohammad Khateri, Marco Reisert, Alejandra Sierra, Jussi Tohka, and Valerij G Kiselev. “What does fexi measure? ”, NMR in Biomedicine, 35(12):e4804, 2022 (the entire contents of which are hereby incorporated by reference herein).

[0009] NMR has also been used to measure activation energies (Ea) associated with the temperature dependence of water exchange. Measured values suggest underlying passive and active mechanisms. See, e.g., Gheorghe Benga. Water transport red blood cell membranes. Progress in biophysics and molecular biology), 51(3): 193- -245, 1988; Ingrid Aslund, Agnieszka Nowacka, Markus Nilsson, and Daniel Topgaard. Filter-exchange PGSE NMR determination of cell membrane permeability. Journal of Magnetic Resonance, 200(2):291 - 295, 2009. ISSN 1090-7807; and Nathan H Williamson, Rea Ravin, Teddy X Cai, Melanie Falgairolle, Michael J O ’Donovan, and Peter J Basser. Water exchange rates measure active transport and homeostasis in neural tissue. PNAS nexus, 2(3):pgad056, 2023 (the entire contents of each of which are hereby incorporated by reference herein). While such measurements are interesting, to understand fully the utility of such water exchange measurements, it is important to elucidate the molecular mechanism(s) that drive transmembrane water exchange.

[0010] In the literature, the Na+ / K+-ATPase has been suggested as being important for active exchange. See, e.g., Charles S Springer Jr, XinLi, LuminitaA Tudorica, Karen Y Oh, Nicole Roy, Stephen Y-C Chui, Arpana MNaik, Megan L Holtorf Aneela Afzal, William D Rooney, et al. Intratumor mapping of intracellular water lifetime: metabolic images of breast cancer? NMR in Biomedicine, 27(7):760-773, 2014; William D Rooney, Xin Li, Manoj K Sammi, Dennis N Bourdette, Edward A Neuwelt, and Charles S Springer Jr. Mapping human brain capillary water lifetime: high-resolution metabolic neuroimaging. NMR in Biomedicine, 28(6): 607-623, 2015; Ruiliang Bai, Charles S Springer Jr, Dietmar Plenz, and Peter J Basser. Fast, na+F+ pump driven, steady-state transcytolemmal water exchange in neuronal tissue: Astudy of rat brain cortical cultures. Magnetic Resonance in Medicine, 79(6): 3207- -3217, 2018; Ruiliang Bai, Charles S Springer Jr, Dietmar Plenz, and Peter J Basser. Brain active transmembrane water cycling measured by mr is associated with neuronal activity. Magnetic resonance in medicine, 81(2): 1280- -1295, 2019; Charles S Springer Jr. Using lh2o mr to measure and map sodium pump activity in vivo. Journal of Magnetic Resonance, 291: 110-126, 2018. Charles S Springer Jr, Eric M Baker, Xin Li, Brendan Moloney, Martin MPike, Gregory J Wilson, Valerie C Anderson, Manoj K Sammi, Mark G Garzotto, Ryan P Kopp, et al. Metabolic activity diffusion imaging [madi]: H. non-invasive, high-resolution human brain mapping of sodium pump flux and cell metrics. NMR in Biomedicine, page e4782, 2022; Charles S Springer Jr, Eric M Baker, Xin Li, Brendan Moloney, Gregory J Wilson, Martin M Pike, Thomas M Barbara, William D Rooney, and Jeffrey H Maki. Metabolic activity diffusion imaging [madi]: I. metabolic, cytometric modeling and simulations. NMR in Biomedicine, page e4781, 2022 (the entire contents of each of which is hereby incorporated by reference herein).

[0011] For example, it has been proposed that water may move directly with the ions through the Na+ / K+- ATPase and other transporters downstream of the Na+ / K+- ATPase. A second possible mechanism controlling water exchange is that the Na+ / K+-ATPase creates an osmotic gradient, which pulls water through the membrane. These water co-transport mechanisms were found to exist for the case of water flux, but has not been demonstrated for water exchange. See, e.g., Donald DF Loo, Thomas Zeuthen, Grischa C handy, and Ernest M Wright. Cotransport of water by the na+ / glucose cotransporter. Proceedings of the National Academy of Sciences, 93(23): 13367-13370, 1996. 16. AK Meinild, DA Klaerke, DDF Loo, EM Wright, and T Zeuthen. The human na+-glucose cotransporter is a molecular water pump. The Journal of Physiology, 508 (Pt 1): 15, 1998; Thomas Zeuthen and Nanna MacAulay. Cotransporters as molecular water pumps. International review of cytology, 215:259-284, 2002; Thomas Zeuthen. Watertransporting proteins. Journal of Membrane Biology, 234(2): 57 73, 2010; N MacAulay and T Zeuthen. Water transport between cns compartments: contributions of aquaporins and cotransporters. Neuroscience, 168(4):941-956, 2010 (the entire contents of each of which are hereby incorporated by references herein).

[0012] Yet, despite these interesting proposals, in the state of the art, the exact molecular mechanism for transmembrane exchange remains unknown. In view of the above, newtechniques for characterizing transmembrane and geometric exchange and characterizing homeostasis in various entities are needed. The discussion above regarding the CNS and exchange rates in biological systems are provided, in part, to illustrate a common problem in diagnosing and understanding disease in biological systems. However, in general there is a need for improved analytical techniques and mathematical models for characterizing many systems having transmembrane and geometric exchange. Accordingly, new techniques and models to measure and determine deviations from normal homeostasis are needed. In particular, new non-invasive techniques and models to characterize water exchange through semipermeable membranes and between environments within the biological tissue are needed.SUMMARY

[0013] Aspects of the present disclosure provide methods and systems to characterize a homeostatic steady-state of biological and non-biological systems.

[0014] The present specification provides two models for characterizing such systems. While the models, as a whole, are independent of each other, certain aspects within the models may be complementary or may be utilized in combination to describe certain attributes of a target system. The first model is devised under the assumption that tonicity affects directly transmembrane exchange and that these effects on exchange are not related to changes in the microstructures of the tissue that affects diffusion. This first model is directed to characterizing a system (e.g., biological system) with at least two compartments separated by a semi-permeable membrane. The second model is a multisite exchange model, which is devised under the assumption that all the effects on exchange and diffusion are through effects on tonicity that, in turn, changes the volume ratios between the different compartments that differ generally in their diffusion and exchange characteristics. Because of these changes, the apparent exchange and diffusion changes. The second model is directed to characterizing a system with at least three compartments (or volume fractions), where at least of the two compartments are separated by a semi-permeable membrane between. The first model can be referred to for simplicity as the direct model, and the second model can be referred to for simplicity as the pump-leak model or the multi -site exchange model.

[0015] A first aspect of the present disclosure provides a nuclear magnetic resonance (NMR) system for measuring / estimating an osmolarity or tonicity and characterizing the osmolarity or tonicity’s effect on water exchange in a specimen. The NMR system includes: a magnetic resonance (MR) device, which has: a magnetic field generator; a radio frequency (RF) transmitter; and an RF receiver. The NMR system also includes a processing system coupled to the MR device. The processing system is configured to: receive sample NMR data from the MR device, the sample NMR data corresponding to the specimen; estimate an exchange rate from the NMR data, the exchange rate corresponding to the water exchange through a semipermeable membrane of the specimen; and estimate the osmolarity or tonicity based on the estimated exchange rate.

[0016] According to one implementation, in the NMR system according to any implementation of the first aspect, the magnetic field generator is configured to generate a constant magnetic field, the magnetic field gradient generator is configured to generate a static magnetic field gradient, the RF transmitter is configured to emit RF electromagnetic fields to excite magnetic spins in the specimen, and the RF receiver is configured to receive RF electromagnetic field signals induced by magnetic resonance of spins in the specimen.

[0017] According to one implementation, in the NMR system according to any implementation of the first aspect, the MR device further includes a NMR RF pulse sequence generator that is configured to send pulse signals to an RF transmitter amplifier, which is coupled to the RF transmitter, such that the emitted RF electromagnetic fields correspond to diffusion exchange spectroscopy (DEXSY) encoded signals, and the received sample NMR data is DEXSY data. The processing system is also configured to estimate the exchange rate from the DEXSY data using a mathematical modeling framework that is configured to transform the DEXSY data to an exchange rate value estimate.

[0018] According to one implementation, in the NMR system according to the above implementation of the first aspect, the mathematical modeling framework includes fitting a first-order rate model to the signals as a function of the mixing time.

[0019] According to one implementation, in the NMR system according to the above implementation of the first aspect, the mathematical modeling framework includes fitting anonparametric or parametric distribution of first order rate constants to the signals as a function of mixing time.

[0020] According to one implementation, in the NMR system according to the above implementation of the first aspect, the mathematical modeling framework comprises estimating the exchange rate from a three-point interpolation between signals acquired at short, intermediate and long mixing times. The model assumes that the exchange process is described by a single first order rate constant. Here, short, intermediate, and long mixing times are defined relative to 1 / k, e.g. with short mixing time being much smaller than 1 / k (such that effectively no exchange has occurred), intermediate being similar to 1 / k (for high sensitivity to exchange), and long being much larger than 1 / k (such that effectively all exchange has occurred). The three-point model may use prior knowledge of Ri. Rj may, therefore, be known or measured separately.

[0021] According to one implementation, in the NMR system according to any implementation of the first aspect, the processor system is configured to estimate the osmolarity or tonicity from a polynomial function based on the estimated exchange rate by solving a polynomial equation of the following form:k = Bo+ BI C+B2AC2... +Bncnwhere Ac is the osmotic concentration difference from a reference state, k is the estimated exchange rate, and Bo.1,2 n are coefficients. For instance, a first order polynomial (linear function):Ac = (fc -B0) / Bi,can be used to calculate Ac from a measurement of k once Boandare known or found.

[0022] According to one implementation, in the NMR system according to any implementation of the first aspect, the processor system is configured to estimate the osmolarity or tonicity based on the estimated exchange rate using the following modified Arrhenius model:k = A ’ * exp(~Ea / R. * (1 / T ~1 / TC)),where Eais an activation energy, 7' is an absolute temperature of the specimen, Tcis a crossover temperature at which exchange rates are equal for the system under all states due to the compensation of enthalpic and entropic contributions, and A ’ is an entropy factor.

[0023] In this embodiment, the estimation can be made from:Ac = ln(0) / a.where Ac = ct— c0, and 6 — kt / k0. Here, k0is the exchange rate at a reference osmolarity co, and ktis the exchange rate at an osmolarity ct. Additional variables are given by:a = 6Eat / cRT) - (8St / cRwhere 6Eatand 8Stcan be approximated by a Taylor series about Ac = 0, to first order:« - [Eat] / T - [St],with the two parameters calculated as:andfrom measurements of Eaand A at c=co and ci.

[0024] According to one implementation, in the NMR system according to any implementation of the first aspect, wherein the processing system is configured to process acquired DEXSY data to provide an output on a homeostatic steady-state of the specimen.

[0025] According to one implementation, in the NMR system according to any implementation of the first aspect, the MR device is a portable NMR configured with a probeend in a shape of a wand such that an end of the wand is such that it may be used to move over a human scalp to measure aggregate water exchange in cortical neurons and other cells of the specimen, the specimen being a human.

[0026] According to one implementation, in the NMR system according to any implementation of the first aspect, the MR device is a whole-head low-field magnetic resonance imaging (MRI) system, comprising having an array of RF coils placed on a helmet, along with permanent magnets, which are configured to provide localized imaging of transmembrane water transport in different cortical brain areas of the specimen.

[0027] According to one implementation, in the NMR system according to any implementation of the first aspect, the specimen is a biological specimen including central nervous system (CNS) cells. Also, the processing system is further configured to indicate deviations in steady-state osmotic or tonicity conditions experienced by the CNS cells based on the estimated osmotic concentration difference.

[0028] According to one implementation, in the NMR system according to any implementation of the first aspect, the specimen is a biological specimen, including centralnervous system (CNS) cells, epithelial cells, endothelial cells, kidney cells, liver cells, muscle cells, cardiac cells of an animal (including a human) or plant cells. Also, the processing system includes memory storing statistical data characterizing at least one of homeostatic steady-state conditions, osmolarity, exchange rates, or tonicities for biological specimen (e.g., CNS cells) in at least one of clinically normal physiological states, clinically normal pathological states, clinically diagnosed pathological states, or clinically required physiological states. Clinically diagnosed pathological states may be, for example, clinically diagnosed CNS pathological states caused by at least one of mild traumatic brain injury (mTBI), brain aneurysms, stroke, migraine aura, or cancer. Clinically required physiological states may be caused by at least one of anesthesia, sleep, or wakefulness. Also, the processing system is further configured to compare the estimated osmolarity or tonicity to the statistical data and output a result of the comparison.

[0029] According to one implementation, in the NMR system according to the above implementation of the first aspect, the processing system is configured to output an assessment, based on the result of the comparison, of a physiological state or physiological changes of the biological specimen.

[0030] According to one implementation, in the NMR system according to any of the above two implementations of the first aspect, the processing system controls the MR device to acquire the NMR sample data and outputs the result of the comparison on a display to detect pathological and physiological events as they occur in real-time.

[0031] According to one implementation, in the NMR system according to any implementation of the first aspect, the specimen includes at least two compartments separated by a semipermeable membrane, the water exchange being via the semipermeable membrane.

[0032] According to one implementation, in the NMR system according to any implementation of the first aspect, the specimen is non-biological. For example, in such an implementation, the semipermeable membrane may be a reverse osmosis membrane for filtration.

[0033] According to a second aspect of the present disclosure, a method is provided for non-invasively measuring a transmembrane exchange rate of endogenous water through a semipermeable membrane in a specimen under steady-state or non-steady-state conditions in near-real time. The system includes at least three compartments with at least two compartmentsbeing separated by the semipermeable membrane. The method includes: receiving sample nuclear magnetic resonance (NMR) data corresponding to the specimen; estimating the transmembrane exchange rate from the NMR data, the exchange rate corresponding to the endogenous water exchange through the semipermeable membrane of the specimen; and estimating the osmolarity or tonicity based on the estimated exchange rate.

[0034] According to one implementation, in the method according to the second aspect, the method is performed using a magnetic resonance (MR) device. The MR device may include: a magnetic field generator; a magnetic field gradient generator; a radio frequency (RF) transmitter; a RF receiver; and a NMR RF pulse sequence generator that sends pulse signals to a RF transmitter amplifier, which is coupled to the RF transmitter, such that the emitted RF electromagnetic fields correspond to diffusion exchange spectroscopy (DEXSY) encoded signals. The magnetic field generator generates a constant magnetic field, which is applied to the specimen. The magnetic field generator or a magnetic field gradient generator generates a magnetic field gradient, which is applied to the specimen. The RF transmitter emits RF electromagnetic fields at the specimen to excite magnetic spins in the specimen. The RF receiver receives RF electromagnetic field signals emanating from the specimen. The received sample NMR data is DEXSY data. Also, the method further includes estimating the exchange rate from the DEXSY data using a mathematical modeling framework that is configured to transform the DEXSY data to an exchange rate value estimate.

[0035] According to one implementation, in the method according to the second aspect, the specimen is a biological specimen having central nervous system (CNS) cells. The method further includes comparing the estimated osmolarity or tonicity to statistical data and outputting a result of the comparison. The statistical data includes data characterizing at least one of homeostatic steady-state conditions, osmolarity, exchange rates, or tonicities for CNS cells in at least one of clinically normal physiological states, clinically normal pathological states, clinically diagnosed CNS pathological states caused by at least one of mild traumatic brain injury (mTBI), brain aneurysms, stroke, migraine aura, Alzheimer’s, dementia, or cancer, or clinically required physiological states caused by at least one of anesthesia, sleep, or wakefulness.

[0036] According to one implementation, in the method according to the second aspect, the osmolarity or tonicity is estimated based on the estimated exchange rate by solving the following equation:k = Bo+ Bi c+B2c2... +Bn cnwhere Ac is the osmotic concentration difference from a reference state, ' is the estimated exchange rate, and Bo, 1,2 „ are coefficients. For instance, for a first order polynomial (linear function),Ac = (k - B0) / 5ican be used to calculate Ac from a measurement of k if Boand B±are known or found.

[0037] According to one implementation, in the method according to the second aspect, wherein the osmolarity or tonicity is estimated based on the estimated exchange rate using the following modified Arrhenius model:k = A ’ * exp(-Ea / R. * (1 / T ~1 / TC)),where Eais an activation energy, T is an absolute temperature of the specimen, Tcis a crossover temperature at which exchange rates are equal for the system under all states due to the compensation of enthalpic and entropic contributions, and d ’ is an entropy factor. For instance, Ac = ln(0) / a,where Ac = ct— c0and 6 = kt / k0in which k0is the exchange rate at a reference osmolarity co, and ktis the exchange rate at an osmolarity ct. Additionalya = (8Eat / cRT) - (8St / cR)~where 8Eatand 8Stcan be approximated by a Taylor series about Ac = 0. To first order« « [Eat] / T ~ [St]with the two parameters calculated asandfrom measurements of Eaand A at c=co and cj.

[0038] As would be apparent to those skilled in the art, the above and other aspects and implementations made according to the present disclosure may be variously combined while remaining within the scope of the invention described herein.

[0039] The above and other aspects of the present disclosure are further elucidated in the following description.BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Subject matter of the present disclosure will be described in even greater detail below based on the exemplary figures. All features described and / or illustrated herein can be used alone or combined in different combinations. The features and advantages of various embodiments will become apparent by reading the following detailed description with reference to the attached drawings, which illustrate the following:

[0041] FIG. 1 illustrates a diffusion exchange spectroscopy (DEXSY) pulse sequence using static gradients (SG);

[0042] FIG. 2 illustrates a DEXSY pulse sequence using pulsed gradients (PG);

[0043] FIGS. 3A-3B illustrate aspects of acquiring DEXSY signals with weightings used for isolation of exchange and measurement of exchange;

[0044] FIG. 4 illustrates a method of measuring osmolarities or tonicities and their effect on water exchange through semipermeable membranes;

[0045] FIGS. 5A, 5B, and 6A and 6B illustrate exemplary magnetic resonance (MR) devices / systems for acquiring MR data;

[0046] FIGS. 7A-7J show experimental data illustrating that sodium-potassium pump inhibition with ouabain decreases exchange rates more than apparent diffusion coefficients;

[0047] FIGS. 8 A and 8B show experimental data illustrating that osmolytes recover exchange;

[0048] FIGS. 9A-9H, show experimental data illustrating that exchange rate depends on tonicity;

[0049] FIGS. 10A-10G show experimental data illustrating that temperature dependence of exchange is explained by entropy and enthalpy modulated by tonicity;

[0050] FIGS. 11A-11D show experimental data illustrating that the exchange rate is not directly linked to Na+ / K+-ATPase activity;

[0051] FIGS. 12A-12B show experimental data illustrating that exchange rates are affected by physiological perturbations;

[0052] FIG. 13 shows experimental data illustrating time courses of exchange rate k and ADCy during perturbations involving combinations of sucrose and ouabain;

[0053] FIG. 14 shows experimental data illustrating the effect of osmolarity on metrics related to compartment fractions from diffusion measurements for samples treated and not treated with ouabain;

[0054] FIG. 15 shows experimental data illustrating the effects of osmolarity on metrics from the slope of the long-time signal from diffusion measurements;

[0055] FIG. 16 shows experimental data illustrating the effect of osmolarity on DEXSY metrics;

[0056] FIGS. 17A-17F show correlation plots of various metrics on samples before and after ouabain affected exchange;

[0057] FIGS. 18A-G illustrate the temperature dependence of ADC,

[0058] FIGS. 19A-19G illustrate the temperature dependence of T,

[0059] FIGS. 20A-20G illustrate the temperature dependence of Ry,

[0060] FIG. 21 illustrates time courses of exchange rate k and ADCy during perturbations with AMPA;

[0061] FIG. 22 illustrates a percent change in exchange rate relative to the prior condition;

[0062] FIG. 23 illustrates an exemplary processing system.

[0063] FIGS. 24A-24I are graphs illustrating that sodium-potassium pump inhibition with ouabain has a large effect on exchange rate and simultaneously a smaller effect on ADC,'

[0064] FIGS. 25A-25F are graphs illustrating that exchange rate is not directly linked to ion transport, voltage, or active water cycling;

[0065] FIGS. 26A-26D are graphs illustrating that osmolytes recover exchange rate;

[0066] FIGS. 27A-27F are graphs illustrating that exchange rate depends on tonicity;

[0067] FIGS. 28A-28H are graphs illustrating that tonicity affects activation energies of exchange;

[0068] FIGS. 29A-29D are graphs illustrating that tonicity does not affect activation energies of diffusion;

[0069] FIGS. 30A-30D are graphs that illustrate that exchange rate increasing with activation energy can be explained by a multisite exchange mechanism;

[0070] FIG. 31 illustrates the connection between tonicity and k in the 3 -site model for gray matter;

[0071] FIGS. 32A-32B are graphs illustrating that ADCyand k may be affected by ouabain simultaneously;

[0072] FIGS. 33A-33B are graphs illustrating that a pump-leak model (PLM) implemented according to aspects of the present disclosure provides predictions of cell volume and voltage;

[0073] FIG 34 is a graph illustrating concentration-dependent effects of sucrose and mannitol on ADC of pure aCSF; and

[0074] FIG. 35A-35D are graphs demonstrating a 3 -site model implemented according to aspects of the present disclosure can predict that ADC and k are affected by tonicity through a dependence on extracellular volume fraction.DETAILED DESCRIPTION

[0075] The present disclosure provides methods to measure and characterize transmembrane exchange. In particular, aspects of the present disclosure provide non-invasive (including noncontact) methods to measure osmolarities (and / or characterize tonicity) and their effect on water exchange through semipermeable membranes. The disclosure contained herein, therefore, provides an improved, non-invasive method to characterize homeostasis (e.g., cellular homeostasis) in order to diagnose, identify, record, monitor, map, or image, normal and abnormal homeostatic states of organic systems (e.g., organisms, tissues, cells, etc.) and inorganic systems (i.e., non-living systems with semipermeable membranes).

[0076] As explained above, there exists controversy in the art over what mechanisms drive transmembrane water transport under steady-state conditions (i.e., with no net flow of water). Generally, steady-state water transport is believed to be a function of the permeability and surface area of the membrane. More recently, it has been suggested that there are active and passive water transport components. The active component was believed to be a result of directed movement or co-transport of water with ions.

[0077] The present inventors have investigated whether the “active” component is one that depends primarily on the osmolarity across the membrane and is not associated with co-transportof water with ions. In this regard, the present inventors have developed a model on the basis that water exchange is driven by tonicity.

[0078] Tonicity is the capability of a solution to modify a volume defined by a semipermeable membrane (e.g., a cell) by altering the water content. Put another way, tonicity is a qualitative measure of the osmolarity between two solutions separated by a semipermeable membrane. Tonicity takes into account the semipermeability of the membrane to solutes and is therefore related to the effective osmolarity. The osmolarity, on the other hand, is a quantitative measure of a difference in solute concentration from a reference state. The tonicity of a system may be said to be: (1) hypertonic — external solution has a higher solute concentration; (2) hypotonic — external solution has a lower solute concentration; or (3) isotonic — concentrations are equal. Furthermore, osmolarity directly influences osmotic pressure, which is a measure of the pressure required to prevent water from moving across a semipermeable membrane due to differences in solute concentration. Osmolarity also influences the osmotic pressure gradient, which is the difference in osmotic pressure between two solutions separated by a semipermeable membrane, driving the movement of solvent molecules from an area of lower solute concentration to one of higher solute concentration until equilibrium is reached.

[0079] Under normal homeostasis, the Na+ / K+- ATPase operates in combination with leakage channels to maintain isotonic conditions, a state far from equilibrium. Under pathological conditions involving Na+ / K+-ATPase inhibition, ionic concentrations tend towards Gibbs-Donnan equilibrium. However, the tonicity can be restored while the system is still at equilibrium simply by adding an osmolyte. The present inventors have found that the exchange rate follows the tonicity under these conditions and is independent of ion transport. While the water exchange is not “active” per se, the ability to quantify tonicity absolutely was not possible in the art before, and the present inventors believe that the present inventive concept that enables such quantification has profound consequences.

[0080] Under normal conditions of cellular homeostasis, faster exchange may result from higher effective osmolarities or tonicities generated by ionic gradients. Under pathological conditions, water exchange may be slower due to the equilibration and loss of these gradients. Fast exchange recovers when an osmolyte that does not penetrate the cell is added, although the system is at equilibrium. Water exchange measurements may therefore be used as a proxy forosmolarity (and thus also an osmotic pressure gradient) or tonicity in nonliving and live semipermeable membranes. Importantly, the exchange rate is an absolute and intrinsic measurement, as opposed to a relative measurement, and is therefore an absolute measure of tonicity, not requiring observation of a change or difference. These insights can be used to assess physiological states in cells, tissues, and organs for diagnostic and prognostic applications.

[0081] For example, an aspect of the present disclosure provides a method for nuclear magnetic resonance (NMR)-based measurement of the steady-state water exchange as a proxy for tonicity and osmotic pressure gradients that develop across semipermeable membranes. In biology, this measurement can be used to non-invasively characterize physiological and pathological states of cells and tissues. When there are multiple exchange compartments (e.g., at least three exchanging compartments), this approach reveals the relationship between them. It further utilizes that relationship as a means of quantifying tonicity.

[0082] More specifically with regard to biology applications, aspects of the present disclosure provide a non-invasive, non-contacting method using endogenous water transmembrane transport to measure, monitor, and evaluate deviations in the steady-state osmotic and tonicity conditions experienced by cells in tissue. The disclosed method may be applied to diagnose brain pathologies, including but not limited to mild traumatic brain injury (mTBI), brain aneurysms, stroke, migraine aura, Alzheimer’s, dementia, and various cancers. The disclosed method may also be used to assess normal physiological state and changes therein, including caused by anesthesia, sleep, and wakefulness, especially in the central nervous system (CNS). Thus, aspects of the present disclosure may be used to improve the diagnosis of physiological and pathological states in animal (e.g., human) organs. The disclosed methods may be used to detect pathological and physiological events as they occur in real-time.

[0083] Aspects of the present disclosure, therefore, improve existing magnetic resonance imaging (MRI) scanners and other NMR devices. For example, in one embodiment, MR pulse sequences may be used to measure and map the steady-state water exchange rate in the brain using existing, conventional low-field and high-field MRI scanners. Other aspects of the present disclosure provide improved scanners and imaging devices. For example, an aspect of the present disclosure provides a device based on low-field MR technology, which may be used for measuring the pathological and physiological states in the CNS of humans in vivo, e.g., incortical grey matter. One embodiment is a portable NMR mobile explorer (MOUSE), which may be used to move over the scalp, like an ultrasound wand, to measure aggregate water exchange in cortical neurons, astrocytes, and other cells. Another embodiment is a whole-head low-field MRI system, having an array of radio frequency (RF) coils placed on a helmet, along with permanent magnets, which would provide localized imaging of transmembrane water transport in different cortical brain areas.

[0084] What follows includes an overview of advancements provided in the present disclosure, exemplary embodiments implementing aspects of the present disclosure, and detailed experimental examples conducted in accordance with aspects of the present disclosure. While a majority of the present disclosure is made in reference to a biological cell, aspects of the present disclosure are not so limited, but instead are extendable to systems with water exchange through semipermeable membranes between several compartments. The focus of the present disclosure on an exemplary cell system is done, at least in part, to illustrate a common problem in diagnosing and understanding disease in biological systems, which is of particular consequence in the art.

[0085] The inventors have found that there are multiple pathways for water exchange. At least one pathway is transmembrane (kt) based, and another is geometric (kg). Water exchange k is high and closer to kt in the normal state when the Na+ / K+-ATPase effectively pumps sodium out of the cell to lower the overall intracellular osmolarity relative to the extracellular space and maintain isotonicity. £ is at a minimum and approaches kgwhen the Na+ / K+-ATPase is inhibited semipermeable ions re-partition across the cell and the tissue becomes hypotonic with swollen cells and shrunken extracellular space. High levels of k approaching kt are restored by adding an osmolyte to the bathing media leading to isotonicity or hypertonicity.

[0086] Similarly, the present inventors have found that tonicity may modulate which pathway dominates the overall exchange process within a multisite exchange model. The transmembrane pathway kt is normally faster than the geometric pathway kg. This leads to transmembrane exchange dominating under isotonic and hypertonic conditions. Under hypotonic conditions, the measurement is less sensitive to the transmembrane exchange pathway. 3-compartment modeling suggests that this is because of the reduction in volume fraction of the extracellular space. This leads to the exchange rate k approaching the geometric exchange rate kgfor exchange between regions within cells, which still exists under these conditions. Osmolytes restore the extracellular space and the sensitivity to transmembrane exchange.

[0087] In an alternative explanation, water exchange from inside to outside the cell (or vice versa) is driven by osmotic pressure and can be modeled as ktto= LpSVR(o it). Here, Lpis the filtration coefficient with units [m / (sPa)], SVR is the surface-to-volume ratio, and a is the reflection coefficient, equal to 1 for impermeable solutes. However, this is not traditional osmosis because the system is at steady state, and because the electrochemical potential of water inside and outside of the cell are equal (iwt=wo). Other components of the electrochemical potential form a gradient to balance the osmotic pressure gradient and keep the cell from collapsing, i.e., Apw-s / = An, where Vv- is the partial molar volume of water. Components of R / uw-s could include a hydrostatic pressure gradient AP maintained by the membrane, a mechanical compression by a length A / of components in the cell such macromolecules and organelles with an effective spring constant, chemical reactions within the cell, or an electrical potential A i associated with species with valence zt, which cannot permeate across the membrane ziF ip.

[0088] This last component must obey elecro-neutrality, and in that way will be associated with an osmotic component from counter-ions. These other components of the electrochemical potential drive water exchange back across the membrane from out to in ktoi= LpSVR(v-s / Vw). ktis the product of these two components kt= ktio+ktOi. The passive component can be expressed as the sum of membrane permeability and the surface-to-volume ratio, kp=pSVR.

[0089] In both cases, one way to describe these changes is through a series expansion of the effect of osmolarity or osmotic concentration on exchange. In some ways this is similar to a virial expansion, with the van’t Hoff equation including just the first order effects of concentration.

[0090] Putting this all together leads to a model for exchange:k = Bo+Bi c+B2 c2+... +Bncn(Equation 1)where Ac is the osmotic concentration difference from a reference state, k is the estimated exchange rate, and Bo, 1,2... n are coefficients. For instance, for a first order polynomial (linear function),Ac = (fc — BQ / B (Equation 2)can be used to calculate Ac from a measurement of k if Boand B are known or found. Ac is the difference in osmolarity acting on the membrane relative to a reference state and offers a quantitative definition for the effective osmolarity / tonicity.

[0091] As shown herein, the apparent exchange rate is modulated by an effective osmolarity or tonicity. In the studies of the temperature dependence of exchange, it was found that this osmolarity linearly increased both ln(A) and activation energy (Ea). This is a consequence of entropy-enthalpy compensation (EEC), where A is a factor related to the entropy and Eais related to the enthalpy. EEC is commonly observed in heterogeneous systems where the apparent rate constant involves multiple interconnected steps occurring in parallel or sequence and some factor modulates the appearance or dominance of certain steps. This can occur due to multisite exchange. Here, EEC is seen because tonicity affects the exchange rate by modulating the dominance or appearance of certain exchange pathways. Importantly, the common EEC behavior for the normal, normal + osmolyte, ouabain-treated, and ouabain-treated + osmolyte conditions shows that exchange shares a common mechanism for all conditions (see FIGS. 10A-10D, discussed below).

[0092] Alternatively, tonicity and / or osmolarity can be derived from the exchange rate using a model based on entropy-enthalpy compensation. Here, the exchange rate is related to the tonicity / osmolarity via the exchange rate’s dependence on changes in entropy and enthalpy produced by the concentration of the osmolyte. For example, tonicity can be determined based on a modified Arrhenius model: k = A' * exp(-Ea / R * (1 / T ~1 / TC)). See discussion of FIGS. 10A-10G below. For instance,Ac = ln(0) / a, (Equation 3)where Ac = ct— c0and 6 = kt / k0in which k0is the exchange rate at a reference osmolarity co, and ktis the exchange rate at an osmolarity ct. Additionalya = (8Eat / cRT) - (8St / cR)where SEatand 8Stcan be approximated by a Taylor series about Ac = 0. To first order« - [Eat] / T - [St]with the two parameters calculated asandfrom measurements of Eaand A at c=co and ci. R is the universal gas constant.

[0093] MR hydrophysiology characterizes water homeostasis.

[0094] The approach of the present disclosure is named by the inventors as “MR hydrophysiology.”

[0095] Please note that the following description of the measurement techniques provided in this disclosure are discussed in terms of transmembrane water exchange and geometric water exchange, and more specifically discussed in terms of exchange between environments in which water exhibits a distinct mobility. However, the disclosed techniques are similarly applicable to many other processes, biological and non-biological, that include water exchange between multiple compartments with one or more of those exchange pathways being through the semipermeable membranes. Indeed, any such process or disease related to disruptions in system homeostasis may be measured and analyzed using the aspects of the disclosure provided herein.

[0096] The measurement of homeostasis disclosed herein detects a rate (e.g., a steady-state rate) of transmembrane water exchange. Furthermore, this measurement is used to characterize osmolarity and / or tonicity of the target system. Evaluating osmolarity and / or tonicity in a system that deviates from a normal value (or predetermined value) can indicate a problem within the system, which can lead to earlier detection of the problem as compared to other means presently known in the art.

[0097] For example, the disclosed method may be used to evaluate the normal physiological state of the CNS and possible pathological changes occurring in disease, development, aging or that results from trauma. As such, the disclosed methods can function as a useful biomarker for normal and abnormal CNS activity from development, aging, degeneration, mild traumatic brain injury (mTBI), trauma, Alzheimer’s disease, and physiological states such as sleep, wakefulness, arousal, and any CNS activity in general.

[0098] To this end, aspects of the present disclosure are directed to magnetic resonance (MR) devices and methods for characterizing a water exchange rate, osmolarity, and / or tonicity that is indicative of a state of a system having a semipermeable membrane.

[0099] MR is particularly suited to measure water exchange rate because a proton MR signal derives directly from magnetization of hydrogen atoms on naturally-abundant endogenous watermolecules within a biological sample without a need for dyes or indicators. MR is completely non-invasive and safe for human use. Sensitivity to water, complete non-invasiveness, and a plethora of image contrast mechanisms sensitive to anatomy and pathology make MR ideal for imaging vital organs, such as the brain and spinal cord. The proton magnetization holds a memory of how it was encoded, enabling the measurement of water motion and other processes. Such encoding methods form the basis of MR diffusion measurements and diffusion magnetic resonance imaging (MRI). Membranes impart a difference in the diffusive mobility between water inside and outside the cell, and in this way, diffusion MR methods can detect the intracellular volume fraction and average changes in cell volume.

[0100] Building on diffusion measurements and utilizing the fact that magnetization holds a memory of its encoding, the exchange of water between regions of differing diffusive mobility with diffusion exchange spectroscopy (DEXSY) can be encoded. Traditional DEXSY requires many scans with different encoding combinations and greater than one hour measurement times to resolve exchanging components. Accordingly, to make DEXSY more suitable for biological applications, rapid techniques have been developed to reduce the number of scans, achieving exchange rate measurement times between one and ten minutes (i.e., about one, about two, about 3, about 4, about 5, about 6, about 7, about 8 about 9, about 10 minutes). Such techniques are discussed in Cai et al., Journal of Magnetic Resonance, 297: 17-22 (2018) (the entire disclosure of which is incorporated herein in its entirety). By greatly reducing the measurement time, measuring water exchange disclosed herein is useable for real-time recording in biological samples as the basis of MR hydrophysiology.

[0101] Aspects of the disclosed method may be implemented in existing magnetic resonance imaging (MRI) scanners and other MR devices. Using such MR devices, the method can detect normal conditions as well as pathological and physiological events as they occur in real-time. In certain aspects, MR pulse sequences may be used to measure and map a steady-state water exchange rate in the brain using existing conventional low-field and high-field MRI scanners. In other aspects, a low-field MR device may measure these pathological and physiological states in the CNS of human patients in vivo, for instance in cortical gray matter.

[0102] The following description provides an aspect of a method of characterizing water exchange rate, osmolarity, and / or tonicity within in vivo or ex vivo CNS tissue in near-real time.The disclosed method measures a cellular-scale average of the complete exchange associated with all transmembrane water transport (inside— ^outside plus outside— >inside), which is in contrast to other types of measurements of transmembrane water transport that can only measure non- steady -state net flux (inside— ^outside minus outside— dnside). The disclosed method uses the exchange rate method as the basis for measuring the osmolarity and / or characterizing the tonicity of the system.

[0103] The following portion of the description describes an aspect of a non-invasive measurement of exchange for assessing the homeostatic state in a system with a semipermeable membrane (e.g., living organisms). Aspects of the method can be performed using any non-invasive technique and method within a technique capable of tagging and separating signals from endogenous molecules in the intramembrane and extramembrane (e.g., intracellular and extracellular) spaces based on characteristics of their environments and recording the signals at different times as the molecules exchange between these spaces and impart distinct characteristics in the signal. Within the field of MR, this includes nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR) techniques. Exchange methods within the field of NMR measure signal from non-zero spin-bearing nuclei. This includes molecules containing protons for which relevant endogenous molecules include water and metabolites such as lactate, pyruvate, creatinine, and N-acetylaspartate (NAA). It also includes other endogenous nuclei such as NMR-detectable isotopes of carbon, sodium, phosphorus, fluorine, etc.

[0104] A non-exhaustive list of relevant measurement techniques within NMR include relaxation exchange spectroscopy (REXSY), velocity exchange spectroscopy (VEXSY), exchange spectroscopy (EXSY), relaxation dispersion, single diffusion encoding with variable diffusion time, double diffusion encoding with variable mixing time, and multi- (n>2) diffusion encoding.

[0105] Within the umbrella of single diffusion encoding with variable diffusion times there are several techniques to measure exchange, which all show some commonality to the seminal Karger method (Karger et al., Adv. Magn. Reson., 21: 1-89 (1988)). Techniques to measure exchange with double diffusion encoding with variable mixing time are based off the original diffusion exchange spectroscopy (DEXSY) method (Callaghan & Furo, J. Chem. Phys., 120: 4032-4038 (2004)) and include the filter exchange spectroscopy (FEXSY) (Aslund, etal., J.Magn. Reson. 200(2): 291- -295 (2009)) and Imaging (FEXI) (Lasic, et al., Magn. Reson. Med., 66(2): 356-365 (2011)) techniques, as well as a method herein referred to as the curvature approach (Cai, et al.. Journal of Magnetic Resonance, 297: 17-22 (2018)). Measurements of exchange with multi-diffusion encoding can be based off repeated diffusion encodings such as with a Carr-Purcell-Meiboom-Gill (CPMG) echo train (Carr & Purcell, Phys. Rev., 94: 630 1954) including a technique termed static gradient time incremented echo train acquisition (SG-TIETA) (Cai, J. Chem. Phys., 154: 111105 (2021)). Further, combinations of signals acquired with single, double, or multiple diffusion encoding schemes can be analyzed together to measure exchange. (The entire contents of each of the publications mentioned in this paragraph are expressly incorporated by reference herein).

[0106] In general, NMR methods to measure exchange can be combined with other NMR modalities including magnetic resonance imaging (MRI) methods for exchange rate mapping and imaging, with spectroscopic techniques, such as Fourier transform of the echo signal to spectrally resolve species based on their chemical shift, or with CPMG refocusing to increase signal. Exchange rates can also be analyzed as a distributed property, i.e., as a probability density function (pdf) representing different components with distinct exchange rates. Exchange rate can be combined with other parameters as a multidimensional measurement, e.g., 2-dimensional measurements of ADC-, Ti-k, T2-k, restricted diameter-^, and diffusion anisotropy-^, as well as combinations of these or other MR parameters leading to measurements with 3 dimensions or more.

[0107] NMR methods to measure exchange based on single, double, or multi-diffusion encoding can utilize any means of forming gradient echoes including radiofrequency modulation under a static gradient, pulsed field gradients, radiofrequency pulses which create magnetic gradients, and combinations of radiofrequency pulses and gradient pulses (pulsed gradient spin echo), inter alia.

[0108] The following aspects of the disclosed method describe a method for measuring exchange based on the DEXSY method. This method involves acquiring signals with a DEXSY pulse sequence and fitting an exchange model to the signals. The DEXSY pulse sequence involves two diffusion-encoding periods separated by a mixing time. The DEXSY pulse sequence can be performed with static gradients (SG) or pulsed gradients (PG) and these aspectsare described in FIGS. 1 and 2. An additional stimulated echo DEXSY pulsed gradient version does not include 180° pulses but involves positive and negative gradient lobes which form gradient echoes during diffusion encoding and storage of the signal with two 90° pulses that form a stimulated echo. In general, the DEXSY pulse sequence can take any form which involves two gradient echoes separated by a mixing time and followed by any form of signal acquisition, i.e., encode bi — mixing time — encode Z>2 — acquisition.

[0109] Each diffusion encoding period satisfies the condition that the integral under the effective gradient waveform sums to zero, i.e., the gradient echo condition, which refocuses location-dependent phase shifts. Spins dephase based on their displacement along the direction of the applied gradient during the intervals. Signals hold the correlation between displacements of spins during each interval. Diffusion during each interval is probed by varying the gradient and / or timing characteristics of the diffusion encoding periods. During the mixing time, the magnetization is stored in the longitudinal axis and decays slowly due to spin-lattice relaxation. During this time, spins are able to exchange between different local environments within the sample. Exchange is probed by varying the mixing time. In certain aspects of the disclosed method, the signal may be processed in a certain way to quantify the exchanging fraction at each mixing time. An exchange model is fit to the signal data to estimate the exchange rate.

[0110] Acquisition of DEXSY signals with various weightings necessary for isolation of exchange and measurement of exchange rate is depicted in FIGS. 3A-3B.[OHl] In the DEXSY signal acquisition, the diffusion weightings of the two gradient echoes, bi and Z>2, as well as the exchange weighting and Ti weighting of the mixing time tmare varied independently. Signals are combined to isolate the exchange weighting, normalize for proton density, and cancel the diffusion and Ti weighting. Signals acquired with bi and Z>2 ~ 0 have negligible diffusion weighting. Signals acquired withhave insignificant Ti and exchange weighting. Signals acquired with band b2>0 or Z>2~0 and bi>0 are diffusion weighted but not exchange weighted. Exchange weighting is increased while diffusion weighting is held constant by decreasing b2-bi=ba towards zero while keeping bi + b2=bsconstant. Maximum exchange weighting is achieved with bd =0 and minimum exchange weighting is achieved when bd =+bs. The diffusion weighting is canceled to isolate the exchange weighting by taking the difference between the minimally and maximally exchange-weighted signals acquired with the same bsandtm. This is one way of producing an exchange weighted DEXSY signal. The signal combination is then acquired at multiple tmspanning tm« / k to tm» 1 / k where k is the exchange rate to be measured.

[0112] The exchange rate is estimated by fitting a model to the signals as a function of the mixing time tm. For instance, it may be a first-order rate model.

[0113] The acquisition time per exchange rate is determined by the number of signals needed per measurement, the repetition time, and the number of scans per signal. The minimal number of scans per signal is defined by the phase cycles. The minimum repetition time is defined by the Ti relaxation time. The minimum number of scans per measurement is reduced by fitting the minimally and maximally exchange weighted signals in two steps, assuming that both signals share similar R] relaxation. This involves separately fitting the minimally exchange weighted signal to separately estimate Ri, subtracting the model fit from the maximally exchange signal and then fitting the remaining signal decay to estimate the exchange rate.

[0114] In order to reduce further the number of parameters to fit, the signal at the largest tmcan be baseline subtracted. This assumes that all exchange has occurred at the final mixing time (tm» 1 / k) and does not account for uncertainty in the measurement. With these various options for data reduction, the minimum number of signals per exchange rate measurement can vary from twenty -two to as few as five.

[0115] Data reduction methods are summarized in Table 1. Parameters are estimated by combining the data as specified by the signal equation and then fitting a first-order rate model to the data using least squares minimization of error. Methods 3, 4, and 5 have two steps in which step 1 involves fitting a model of the form S —Methods 4 and 5 also involve subtracting a baseline B equal to the average of the signal at the two longest or the longest mixing time. The estimated R1is used in the Signal Equation for step 2. The model for estimating the exchange rate k in Methods 1 and 2, and step 2 of Method 3 takes the form S = fn(tm) = (So— S∞) exp(— tmk) + S∞where S0are estimates of the signal at tm= 0 and tm= oo. The model for estimating k in step 2 of Methods 4 and 5 takes the form S = (tm) = Soexp(— tmk), as subtracting a baseline B effectively sets Smto 0. Variations of this approach are possible, for instance the data for any method or step can be fit using other parametric models of a specified number of components involving exponentials, stretchedexponentials, or parametric distributions such as the gamma distribution or lognormal distribution.

[0116] It is additionally possible to interpolate between signals acquired with exchange weighting at different mixing times to estimate an exchange rate, or after adjusting for relaxation. Such an interpolation can be performed with three signals, where one signal Sshortis acquired at tmmuch less than \ / k, a second signal Sintis acquired at tmsimilar to \!k, and a third signal Siong is acquired at tmmuch larger than l / k. An example of an interpolation would k =Table 1:

[0117] FIG. 4 provides a depiction of a method for estimating exchange rate, osmolarity, and / or tonicity.

[0118] In a first step (S 101) MR signals (e.g., DEXSY signals) are acquired. The MR signals may be acquired by various methodologies, preferably those described herein, particularly preferably using DESXY signal acquisition. In general, however, the step of acquiring MR signals includes, using an NMR system: a), applying magnetic and radio frequency signals to a target system having transmembrane water exchange; b). receiving an NMR magnetization signal as a radiofrequency signal; and c). sampling and storing the detected NMR magnetization signals.

[0119] In a second step (SI 02), the water exchange weighted signal is isolated from the detected NMR magnetization signals. The isolation may also be done according to variousmethodologies, in a preferred embodiment this isolation may be done on DEXSY acquired signals by, e.g., combining signals and canceling the relaxation weighing. This a preferred way of producing an exchange weighted DEXSY signal. Another way of producing an exchange weighted DESXY signal is to have prior knowledge of Ri and divide DEXSY acquired signals by exp(— tmR1) to cancel the effect of relaxation weighting.

[0120] In a third step (SI 03), the exchange rate is estimated from the exchange weighted isolated signal. In a preferred embodiment, the exchange rate is estimated by fitting a first-order rate model to the signals according to the methodologies disclosed herein.

[0121] In a fourth step (SI 04), the tonicity and / or the osmolarity is estimated and / or characterized based on the estimated exchange rate. The estimation is done using the methodology disclosed herein. Particularly, using Equations 2 or 3, the osmotic gradient An or osmotic concentration Ac is solved for based on the estimated exchange rate k together with the predetermined parameters Boand B, or a. The estimated osmotic gradient or tonicity can be compared to a defined value for isotonicity for the system, which is predetermined or known, e.g. from literature, in order to determine if the system is hypotonic, hypertonic or isotonic.

[0122] In one aspect, the above-described methodologies of measuring water exchange, osmotic gradients, and / or characterizing tonicity may be performed with an MR system involving an inhomogeneous magnetic field that serves as a static gradient. FIG. 1 shows the Static Gradient Diffusion Exchange Spectroscopy (SG-DEXSY) pulse sequence. The echo signal following the second diffusion encoding is refocused and acquired many times in CPMG echo train. The echo train signal is summed together in order to increase the signal -to-noise ratio. The phases of the first 5 RF pulses and the receiver channel are set to the (p values and varied between four steps according to Table 2.Table 2;

[0123] In another aspect, the method of measuring water exchange may be performed using a homogeneous magnetic field and pulsed field gradients. FIG. 2 shows a Pulsed Gradient Diffusion Exchange Spectroscopy (PG-DEXSY) pulse sequence and phase cycles. The echo signal following the second diffusion encoding is brought through an imaging or spectroscopy acquisition scheme including but not limited to Multi-Slice Multi-Echo (MSME), Echo Planar Imaging (EPI), and Single-Voxel Spectroscopy. These DEXSY MRI methods can be used to produce exchange weighted DEXSY images, which can be combined to create an exchange rate map or an effective osmolarity or tonicity map.

[0124] FIGS. 5A and 5B show exemplary MR hardware / systems 500 and 5000 for performing methods according to aspects of the present disclosure, including the method shown in FIG. 4 as well as the methods for acquiring the SG-DEXY signals explained in relation to FIGS. 1, 3A, and 3B.

[0125] In FIG. 5 A, the MR hardware 500 includes a magnet 501 (such as a superconducting magnet, permanent magnet, electro magnet or other magnetic generator), a radio frequency (RF) probe 502 (which may include one or more RF receiver(s) and RF transmitter(s)), an NMR spectrometer or console 503, at least one RF amplifier 504 (where an RF amplifier may be provided for both an RF receiver and RF transmitter), and a computer 507 (also referred to herein as a processing system or control system). In one implementation, the magnet produces an inhomogeneous magnetic field with a static or constant magnetic field gradient. In another implementation (and as shown in FIG. 5A), the MR hardware 500 may include a gradient coil 505, and gradient amplifier 506, which are configured for providing pulsed field gradients (collectively the gradient coil and gradient amplifier may be referred to as a magnetic generator,specifically a magnetic gradient generator). The computer 507 may include memory and one or more processors, with the memory storing instructions (executed by the processors) for operating the MR hardware and / or executing one or more methods described herein, including for determining water exchange, osmolarity, and tonicity.

[0126] In a preferred embodiment, the MR hardware 500 is adapted to provide an NMR system. The NMR system uses the magnet 501 as its means to create a constant magnetic field (constant magnetic generator), and a constant or static magnetic field gradient (static magnetic field gradient generator). A specimen holder may also be provided (see FIG. 6A), which holds a subject specimen within the magnetic field and the magnetic field gradient at a predetermined position.

[0127] The NMR spectrometer 503 is connected to the RF probe 502 and is configured to send and receive RF signals from the RF probe, thereby providing a radiofrequency transmitter that emits radiofrequency electromagnetic fields to excite magnetic spins in the specimen and radiofrequency receiver that measures radiofrequency electromagnetic fields emanating from the specimen. The RF amplifier 504 may provide both a RF transmitter amplifier to adjust the power of the emitted RF signal, and a RF receiver amplifier to adjust the signal strength of the received signal. The spectrometer 503 may be controlled to act as an NMR RF pulse sequence generator that sends signals to the RF transmitter amplifier to acquire spectroscopy data (for example Diffusion Exchange Spectroscopy (DEXSY) data).

[0128] The computer 507 may provide a processing system for the NMR system, and may be configured as one or multiple sub-systems at one or more physical locations). The computer 507 may therefore control each of the NMR system components to operate according to a set of instructions stored in memory (e.g., using one or more processors). The computer 507 can include a recording device that samples and stores an NMR magnetization signal detected by the RF receiver. The computer 507 can further execute one or more mathematical models to transform the recorded magnetization signal to, e.g., DEXSY data, estimate exchange rate from the DEXSY data, and estimate an osmolarity and / or tonicity from the exchange rate and / or DEXSY data.

[0129] FIG. 5B shows an exemplary magnetic resonance imaging (MRI) system. The system 5000 includes a controller / interface 5002 that may be configured to apply selected magnetic fields,such as constant or pulsed field gradients, to a subject 5030 or other specimen. An axial magnet controller 5004 is in communication with an axial magnet 5006 that is generally configured to produce a substantially constant magnetic field Bo. A gradient controller 5008 is configured to apply a constant or time-varying magnetic field gradient in one or more selected directions or in a set of directions using magnet coils 5010-5012 to produce respective magnetic field gradient vector components Gx, Gy, G or combinations thereof to produce the gradients Gi, G2, G3 that are associated with b-matrices and / or tensors. A radiofrequency (RF) generator 5014 is configured to deliver one or more RF pulses to a specimen using a transmitter coil 5015. An RF receiver 5016 is in communication with a receiver coil 5018 and is configured to detect or measure net magnetization of spins. Typically, the RF receiver includes an amplifier 5016A and an analog-to-digital convertor 5016B that detect and digitized received signals to obtain the signals S(B). Slice selection gradients may be applied with the same hardware used to apply, e.g., diffusion gradients. The gradient controller 5008 may be configured to produce pulses or other gradient fields along one or more axes as needed for the application.

[0130] For imaging, specimens are divided into volume elements (voxels) and MR signals for a plurality of gradient directions are acquired as discussed above, but signals may be acquired for one or only a few specimen voxels. In typical examples, signals are obtained for some or all voxels of interest.

[0131] A computer 5024 or other processing system such as a personal computer, a workstation, a personal digital assistant, laptop computer, smart phone, and / or a networked computer may be provided for acquisition, control, and / or analysis of specimen data. The computer 5024 generally includes permanent storage (e.g., a hard disk), a removable storage medium (e.g., flash drive or CD), and / or other memory such as random access memory (RAM). Data may also be transmitted to and from a network using cloud-based processors and storage. Data may be uploaded to the “cloud” or stored elsewhere. Computer-executable instructions for, e.g., data acquisition or control, b-matrix computations, such as random selected of directions and random selected of b-magnitudes as well as determining the associated b-matrices, and tensors and distribution estimations may be provided on storage medium or delivered to the computer 5024 via a local area network, the Internet, or other network. Signal acquisition, instrument control, and signal analysis may be performed locally or with distributed processing. For example, signalacquisition and signal analysis may be performed at different locations. Signal evaluation may be performed remotely from signal acquisition by communicating stored data to a remote processor. In general, control and data acquisition with the MRI system may be provided with a local processor, or via instruction and data transmission via a network.

[0132] FIG. 6A depicts a 3D technical drawing (top) of an NMR device 600 configured in accordance with an aspect of the present disclosure for ex vivo analysis. In FIG. 6A, the NMR device 600 includes a test plate 601 that may be positioned and attached to a test housing 602 at a surface 603 at a predetermined test plane. At the top of FIG. 6A, the test plate 601 is also provided in an enlarged view.

[0133] The test plate 601 includes a test chamber 604 (also called a specimen holder), which is depicted as wet / dry chamber that can be flooded with liquid and / or gas. For example, the chamber 604 may be flooded with aCSF via aCSF inlet / outlets 605 via supply lines (indicated as aCSF in / out). The chamber 604 may be filled with gas (e.g., oxygen) via the gas inlet / outlet 606 via gas supply lines (indicated as gas in / out). A solenoid RF coil 607 is contained within the test chamber (also shown in an enlarged view in FIG. 6A). A test subject is placed within the solenoid RF coil 607 (e.g., a mouse spinal cord). The test chamber may flood the test subject with, for example, aCSF and oxygen for creating conditions simulating a live environment for the sample tissue (e.g., live ex vivo tissue such as a mouse spinal cord). Water inlets and outlets are also provided on the test plate 601 to provide temperature controlled water to maintain a constant test temperature.

[0134] The lift and magnet housing 602 encloses a magnet (e.g., permanent magnet) 609 positioned under the surface 603. The magnet 609 is arranged on a lift 610, which can controllably adjust the distance between the magnet 609 and the surface 603. The magnet 609 provides a magnetic field Bo, which in a preferred embodiment is designed to be constant along an x-z plane parallel to the magnet’s surface and to decrease rapidly and linearly in the y-direction perpendicular to the magnet’s surface, providing a strong static magnetic field gradient. Using the lift 610, the magnet can be raised and / or lowered to position the magnetic field gradient at a target depth within the test sample. The test housing 602 may be mounted on an anti -vibration table 611 in order to avoid disrupting the measurements.

[0135] The solenoid RF coil 607 is coupled to an RF circuit 612 via an RF cable. The RF circuit 612 is controlled by a computer 613, which may also control the entire NMR device 600 (including, e.g., the lift 610 and magnet 109) and processes the signals. The NMR device 600 can be controlled to perform the methods and calculations described herein, practically to perform the DEXSY measurements and estimate the osmolarity and / or tonicity within the sample.

[0136] FIG. 6B depicts technical drawing of an NMR device 600B configured in accordance with an aspect of the present disclosure for in vivo analysis. In FIG. 6B, the NMR device 600B includes a test chamber 60 IB that may be positioned and attached to a test housing 602B at a surface 603B at a predetermined test plane.

[0137] The test chamber 60 IB includes a test chamber 604 (also called a specimen holder), which is depicted as an enclosable chamber that can be flooded with gas (e g., anesthetic gas). For example, the chamber 601B may be flooded with isoflurane via inlet / outlets 605B via supply lines. A solenoid RF coil 607B is contained within the test chamber. A (live) test subject is placed adjacent to the solenoid RF coil 607B (e g., a live mouse). Water inlets and outlets are also provided on a test plate at the bottom of the test chamber 601B to provide temperature controlled water to maintain a constant test temperature. A vitals lead 614B may pass into the test chamber 601B for connecting sensors coupled to the test subject to a vitals monitor.

[0138] The lift and magnet housing 602B encloses a magnet (e.g., permanent magnet) 609B positioned under the surface 603B. The magnet 609B is arranged on a lift 610B, which can controllably adjust the distance between the magnet 609B and the surface 603B. The magnet 609B provides a magnetic field Bo, which in a preferred embodiment is designed to be constant along an x-z plane parallel to the magnet’s surface and to decrease rapidly and linearly in the y-direction perpendicular to the magnet’s surface, providing a strong static magnetic field gradient. Using the lift 610B, the magnet can be raised and / or lowered to position the magnetic field gradient at a target depth within the test sample. The test housing 602B may be mounted on an anti -vibration table 61 IB in order to avoid disrupting the measurements.

[0139] The solenoid RF coil 607B is coupled to an RF circuit 612B via an RF cableB. The RF circuit 612B is controlled by a computer 613B, which may also control the entire NMR device 600 (including, e.g., the lift 610B and magnet 609B) and processes the signals. The NMRdevice 600B can be controlled to perform the methods and calculations described herein, practically to perform the DEXSY measurements and estimate the effective osmolarity and / or tonicity within the sample.

[0140] A person of ordinary skill in the art would recognize that the MR devices described herein are merely exemplary embodiments, and that various alterations and variations of such devices may be made to suit the application.

[0141] For example, an MR device and operation may be configured to vary the gradient strength g and tune the dephasing length lgbased on the intended system of study. In particular, a length scale of the measurement may be adapted based on a change in the dephasing length lgbecause the length scale of restrictions which the measurement is sensitive to is roughly equal to the dephasing length, lg= (Do / yg)1 3, where Do is the self-diffusion coefficient of water or molecular substance of interest at the target temperature, y is the gyromagnetic ratio of the nuclei, and g is the gradient strength.

[0142] A person of ordinary skill in the art would further be capable of adapting the variables of operation of the MR devices based on the particular application, without undue experimentation.

[0143] For example, with respect to the gradient strength g, a person of ordinary skill in the art would recognize that the physical lower limit is g = 0, where the exchange experiment becomes a T2-T2 or Relaxation Exchange Spectroscopy (REXSY) experiment, where we are able to see exchange between environments of different T2 or spin-spin relaxation. Callaghan and Washbum provide one seminal reference for REXSY. K. E. Washburn andP. T. Callaghan, Phys. Rev. Lett. 97, 175502, October 2006 (the entire contents of which is hereby incorporated by reference). However, the preferred approach used by the present inventors provides advances over that of Washburn and Callagan, e.g., by reducing the data requirements. See, e.g., N.Williamson et. al, Real-time measurement of diffusion exchange rate in biological disuse, Journal of Magnetic Resonance. 2020 Aug; 317: 106782 (Where present inventors comment on the effect of T2-T2 exchange being present in the DEXSY measurement (the entire contents of which is hereby incorporated by reference herein). This approach to REXSY is sensitive to tonicity if the water on either side of the membrane experiences a different 'E relaxation.

[0144] The effect of diffusion becomes significant and hence the measurement becomes a true DEXSY measurement when the gradient is strong enough to reach significant diffusion encoding in a time that is shorter than the T2 relaxation time, while still providing enough time for encoding of diffusion and exchange before magnetization is lost to Ti relaxation.

[0145] The upper end (in many applications) for the diffusion encoding time of a DEXSY measurement is approximately 100 ms. The diffusion encoding strength is b=ZI2g2v, where y= 42.58 MHz / T is the proton gyromagnetic ratio. Significant diffusion encoding is defined as b*D > 1. For water, the inventors have found an optimum at roughly b=2 ms / μm2. When the above equation is re-arranged to solve for g, the equation becomes: g= (b / (2 / 3 y2?3)). Plugging in values, the inventors have found that g=0.04 T / m gradient strength as an approximate minimum gradient strength needed to be sensitive to diffusion exchange of protons on water at 25° C. This will change if other nuclei with different gyromagnetic ratios or molecular substances with different effective diffusion coefficients (D) are of interest, but the determination of the minimum g would follow the same logic.

[0146] The upper end of gradient strength may be characterized by a significant fraction of molecules leaving the slice of interest during the measurement. The slice thickness z is proportional to the frequency bandwidth of the excitation radiofrequency pulses / and inversely proportional to the gradient strength and gyromagnetic ratio and is z =f / (yg). The diffusion length in one dimension is defined as ld=^l ZDt. Setting z = Id and solving for g, we have g=f / / 2Dt). Using an upper limit of / = 1 MHz for typical state-of-the-art RF technology, this leads to g = 260 T / m. However, in general the maximum g being produced and used for NMR applications is approximately g = 180 T / m.

[0147] Using the devices and methodologies disclosed herein, one skilled in the art will be able to characterize a homeostatic steady-state (e.g., by its estimated osmotic gradient and / or tonicity) of an entity comprising a semipermeable membrane having transmembrane exchange (particularly biological systems, more particularly CNS cells). For example, those skilled in the art could create compendium of characterizations on such systems with a known steady-state. A relatively small range of values could then be used as a “control” to compare against future unknown samples. For example, one skilled in the art could test samples of normal, healthy spinal cord tissue to determine the range of osmotic gradients for a particular homeostatic steady-state of the normal, healthy tissue. When other samples are tested in the future, values above or below the known values would indicate an unhealthy or pathological state, or an altered physiological state of the same type of biological entity.

[0148] Thus a diagnosis methodology of the present disclosure may include the operations of: a) obtaining first sample(s) of estimated osmotic gradients at a first known state; b) obtaining a second sample of an estimated osmotic gradient at a second, unknown state; c) comparing the first sample(s) to the second sample; and d) making an observation about the state based on the comparison.

[0149] The diagnosis methodology may also use machine learning to classify the estimated osmotic gradients of a system. For example, an Al clustering model (such as a convolutional neural network or graph neural network) may be trained to characterize a state of a system comprising a semipermeable membrane with transmembrane water exchange based on exchange rate isolated DEXSY signals.

[0150] The training dataset may include experimental results from a target system (or systems) at known states with the corresponding exchange rate isolated DEXSY signals (and / or corresponding estimated tonicity, osmolarity, or osmotic gradients). Additional metrics may also be used for training (and classification), for example, ADC, spin-lattice relaxation rate (Ri), spinspin relaxation rate (R2), and compartment fractions ( / ). The known states could include homeostatic or pathological states of various cell and tissue systems. Thus, the training data may comprise sets of metrics and corresponding homeostatic of pathological states. The Al model can also be trained using simultaneous real-time recordings of these metrics combined with microscopy metrics, such as Intrinsic Optical Signal (IOS), intracellular calcium, and voltage during drug (ouabain, AMP A, etc.) and / or media (mannitol, sucrose, KC1, etc.) perturbations on different types of ex vivo tissue, cell culture, and organelle systems.

[0151] After training, the Al model can receive, for example, an exchange rate isolated DEXSY signal (or one or more of the metrics named above) for a system of the target type, and make a prediction as to the state of the system (i.e., classify the system based on its “fingerprint”). The output can include a determination of the types of cells or tissue, the microstructural characteristics, and the homeostatic state of the system.

[0152] This Al diagnostic model has many useful applications, including for medical diagnostics, research in neuroscience, pharmacological testing and biotechnology. For example, in medical diagnostics, this model can be applied to diagnose various conditions by identifying deviations from normal physiological states in tissues (such as spinal cord tissue).

[0153] Thus, the present inventors have provided a methodology to measure osmolarity and / or tonicity, and ratios between different compartment fractions affecting an exchange rate in order to establish as an absolute, intrinsic measure of system (e.g., cellular) function and viability, and these findings lay the groundwork for developing the osmolarity, tonicity, and exchange rates as potential imaging biomarkers as a proxy for homeostasis, viability, and overall tissue state during normal function, disease, development, aging and trauma.

[0154] This is in contrast to the present state of the art where diffusion -weighted imaging (DWI) is the gold-standard for identifying stroke because it can capture the apparent diffusion coefficient (ADC) decrease in affected areas minutes after stroke due to cytotoxic edema (Moseley, et al., Magnetic Resonance in Medicine, 14(2): 330-346 (1990), Baird, et al., Journal of Cerebral Blood Flow & Metabolism, 18(6): 583-609 (1998)). However, the diffusion coefficient alone cannot differentiate recoverable tissue from permanently damaged tissue (Pierpaoli, et al., Journal of Cerebral Blood Flow & Metabolism, 16(5): 892-905 (1996), Beaulieu, et al., Annals of Neurology: Official Journal of the American Neurological Association and the Child Neurology Society, 46(4): 568-578 (1999), Ueda, et al., American Journal of Neuroradiology, 20(6): 983-989 (1999)). DWI shows similarly reduced diffusivities throughout an ischemic area, masking the heterogeneous effects on tissue metabolism (Nicoli, et al., Stroke, 34(7): e82-e87 (2003), Guadagno, et al., Neurology, 67(5): 824-829 (2006)). The ADC of a lesion begins to normalize during the first few days following a stroke, sometimes indicating tissue recovery (Baird, et al., Journal of Cerebral Blood Flow & Metabolism, 18(6): 583-609 (1998)). However, in many cases that the tissue is actually damaged, the ADC will appear to recover or “pseudo-normalize” and will even increase to values higher than the surrounding normal tissue due to necrosis and loss of membrane integrity (Baird, et al., Journal of Cerebral Blood Flow & Metabolism, 18(6): 583-609 (1998), Takahashi, et al., Magnetic Resonance in Medicine, 30(4): 485-488 (1993), Pierpaoli, et al., Radiology, 189(2): 439-448 (1993)). The time course of ADC during oxygen and glucose deprivation (OGD) recapitulates invivo findings — it decreases initially upon switching to OGD, and pseudo-normalizes and sometimes overshoots baseline values during recovery — thus confirming that ADC is not specific to tissue damage. (The entire contents of each of the articles mentioned in this paragraph are expressly incorporated by reference herein).

[0155] In contrast, time courses of exchange rates during OGD, stability tests, and rundown show trends consistent with the exchange rate measuring viability. In other words, water exchange rate is an absolute (as opposed to a relative) metric. Further, the water exchange rate lies within a well-defined range (e.g., of about 150 s'1for normal conditions in many systems pertinent to the present disclosure). The value of the exchange rate itself, and not the difference, can be used to determine the state of the system as being normal or pathological. This is unique among quantitative NMR and MRI metrics and contrasts, where typically one is looking at the change or difference, e.g. the difference between a pathological lesion and a normal -appearing brain region, or the difference between more and less active regions of the brain. The water exchange rate’s absolute nature indicates that a normal exchange rate is a vital sign for homeostasis. As shown herein, the exchange rate can be used as a proxy (and to estimate) the osmolarity and / or tonicity that is actively influencing the cellular homeostatic state. Thus, osmolarity and tonicity are also useful measurements for evaluating the state of a system.

[0156] Thus, the present disclosures enabling of a non-invasive measurement of osmolarity and / or tonicity — and their effect on water exchange through semiperm eable membranes — is a way to determine the effectiveness of clinically-relevant treatment protocols and neuroprotectants.

[0157] Surprisingly, physicians do not have a clear way to identify whether a patient’s brain has been permanently damaged by stroke or if the affected tissue will recover over time. Mean ADC mapping with Diffusion MRI is the gold standard for stroke lesion delineation, however it is primarily sensitive to structural changes, in particular to cellular swelling, and not tissue viability. Diagnostic techniques to grade tissue viability would inform treatment plans and ultimately improve patient outcomes. While cells have mechanisms of maintaining homeostasis during brief periods of hypoxia and ischemia, eventually they can no longer hold on. This critical point defines when cells have been damaged permanently.

[0158] Many studies looking at different collective aspects of this energetic failure show that the critical point is when the cells lose their homeostatic ability. This can be confirmed directly, by measuring many aspects of homeostasis at once. Literature shows that this “pseudonormalization” of the ADC is due to cellular necrosis and loss of membrane integrity rather than recovery, often confounding radiological evaluation of stroke and stroke recovery. These results provide a detailed look into cellular function and structure changes during stroke. The present disclosure can help to advance this study.

[0159] Ketamine and osmolytes (e g., sucrose or mannitol) have been effective as neuroprotective treatments in ex vivo and animal models (Balestrino, et al., Brain Research, 838(1-2): 37-44 (1999), Hudetz & Pagel, Journal of cardiothoracic and vascular anesthesia, 24(1): 131-142 (2010)) but their mechanisms of action are not completely understood and their use clinically has shown mixed results (Bereczki, et al., Cochrane Database of Systematic Reviews, (3): 2007)). While ketamine has a known neuroprotective effect by blocking NMDA receptors, this may not be the entire story. Interestingly, both osmolytes and ketamine increase the fraction of extracellular water (Xie, et al., Science, 342(6156): 373-377 (2013)), which brings the system towards a more neuroprotective state. Restoring water homeostasis may be a critical aspect of osmolytes’ and ketamine’s neuroprotective mechanisms.

[0160] Accordingly, the capability to monitor tissue viability and loss of viability in real time using methods of an aspect of the invention provides a powerful means to test the effectiveness of neuroprotectants. For example, in real time, it can be seen whether therapeutics can help maintain or perhaps recover viability during these perturbations, as well as at what timepoints they need to be administered.

[0161] Although aspects of this disclosure entail measuring water protons exchanging between compartments or pools within a medium (i.e., cell of a biological system), in view of this disclosure, one can imagine following diffusion exchange of protons residing on biomolecules and metabolites, such as phosphocreatine, lactate, pyruvate, etc. by filtering with chemical spectroscopic NMR methods. Moreover, using aspects of the disclosure provided herein, measurements of diffusion exchange in spin-labelled solvent species, such as D2O, and measurements of exchange of various isotopes, such as13carbon (13C),23sodium (23Na),3phosphorus (31P) or19fluorine (19F) may be obtained.

[0162] An aspect of the present disclosure provides methods to determine a homeostatic steady-state of a biological entity. In another aspect, the invention provides methods to determine a loss of homeostatic steady-state of a biological entity. As used herein, a “homeostatic steadystate” refers to a state that is steady or maintained for a period of time. The homeostatic steadystate can be a healthy or normal state in the biological entity. There can be multiple ideal steadystates within a biological entity. Divergence from the ideal steady-states would be non-ideal steady states that can indicate a not-desirable state for the biological entity to be in (e.g., dying). Homeostatic steady-states include physiological states (e.g., sleeping, awake, stimulated, intense thinking, intensive activity). As used herein, “a loss of homeostatic steady-state” refers to state that is not steady. The “loss of homeostatic steady-state” can indicate a pathological state or unhealthy state in the biological entity, but can also indicate adjustment / movement to another physiological steady-state.

[0163] In an aspect, the present disclosure further provides methods to determine a homeostatic steady-state of a biological entity, the method comprising a magnetic resonance (MR) system, the MR system comprising: a. a means to create a static or pulsed magnetic field gradient; b. a means to create a constant magnetic field; c. a means to hold a biological entity within the constant magnetic field and the static or pulsed magnetic field gradient; d. a radiofrequency transmitter; e. a radiofrequency receiver that measures radiofrequency electromagnetic fields; f. a radiofrequency transmit amplifier; g. a MR radiofrequency pulse sequence generator that sends signals to the radiofrequency transmit amplifier to acquire Diffusion Exchange Spectroscopy (DEXSY) data; h. a recording device to sample and store a MR magnetization signal detected by the radiofrequency receiver; and i. a mathematical modeling framework to transform the recorded magnetization signal DEXSY data, wherein interpretation of the DEXSY data provides a homeostatic steady-state of a biological entity. In a further aspect, a biological entity is placed in the means to hold the biological entity. In an aspect, the means to hold the biological entity can be determined by one of skill in the art. It should be an appropriate size to adequately contain the biological entity within the magnetic field, gradient field, and radiofrequency field. The MR system can be a Nuclear Magnetic Resonance (NMR) system or a Magnetic Resonance Imaging (MRI) system.

[0164] An aspect of the invention provides a MR system, the MR system comprising: a. a means to create a static or pulsed magnetic field gradient; b. a means to create a constant magnetic field; c. a means to hold a biological entity within the constant magnetic field and the static or pulsed magnetic field gradient; d. a radiofrequency transmitter; e. a radiofrequency receiver that measures radiofrequency electromagnetic fields; f. a radiofrequency transmit amplifier; g. a MR radiofrequency pulse sequence generator that sends signals to the radiofrequency transmit amplifier to acquire Diffusion Exchange Spectroscopy (DEXSY) data; h. a recording device to sample and store a MR magnetization signal detected by the radiofrequency receiver; and i. a mathematical modeling framework to transform the recorded magnetization signal DEXSY data.

[0165] The pathological state can arise from disease, development, aging, or trauma.Pathological states include infectious and non-infectious diseases. Infectious diseases include those caused by infectious organisms (e.g., bacteria, viruses, parasites, protozoa). Non-infectious diseases include autoimmune disorders, allergies, cancers, Alzheimer’s, Parkinson’s, etc. In an aspect, the pathological state is a stroke, brain aneurysm, traumatic brain injury, migraine aura. In an aspect, the pathological state is caused by a spreading depolarization (SD). In a further aspect, the pathological state is characterized by a rapid and near-complete loss of transmembrane potential that depresses neuronal activity. In an aspect, the pathological state is a stroke.

[0166] In an aspect, the biological entity is a molecule, group of molecules, cell, tissue, or organ. In an aspect of the invention, the biological entity is a cell. The cell can be any cell, e.g., a plant, animal, bacteria, protozoa, etc. In an aspect, the cell is an animal cell. The cell can also be a mammal cell. As used herein, the term “mammal” refers to any mammal, including, but not limited to, mammals of the order Rodentia, including mice and hamsters, mammals of the order Lagomorpha, including rabbits, mammals from the order Carnivora, including Felines (cats) and Canines (dogs), mammals from the order Artiodactyla, including Bovines (cows) and Swine (pigs), mammals from the order Perissodactyla, including Equines (horses), mammals of the order Primates, Ceboids, or Simoids (monkeys), and mammals of the order Anthropoids (humans and apes). An especially preferred mammal is the human.

[0167] In an aspect, the cell is part of a tissue or organ. The tissue can be epithelial tissue, connective tissue, muscle tissue, or nervous tissue. The organs can be cardiovascular (e.g., heart, blood, and blood vessels), lymphatic (e.g., lymph, lymph nodes, and lymph vessels), digestive (e g., mouth, salivary glands, esophagus, stomach, liver, gallbladder, pancreas, intestines), endocrine (e.g., pituitary, pineal, thyroid, parathyroid, pancreas, adrenals, tests, ovaries), integumentary (e.g., skin, hair, and nails), muscular (e.g., skeletal, cardiac, and smooth muscle), nervous (e.g., brain, spinal cord, nerves, sensory organs - eyes, ears, tongue, skin, and nose), reproductive (e.g., fallopian tubes, uterus, ovaries, mammary glands, testes, vas deferens, etc.), respiratory (e.g., mouth, nose, pharynx, larynx, trachea, bronchi, lungs, and diaphragm), skeletal (e.g., bones, cartilage joints, tendons, and ligaments), urinary (e.g., kidneys, ureters, bladder, and urethra), and immune (e.g., leukocytes, tonsils, adenoids, thymus, and spleen). In an aspect, the cell is a cell of the central nervous system. In an aspect, the cell is a spinal cord cell. In a further aspect, the cell is a neuronal or glial cell in white and / or grey matter.

[0168] In an aspect, the biological entity is an organelle. As used herein, an “organelle” is a specialized subunit of the cell that has a specific function. The organelle can be a space within the cell that is bound by lipid bilayers, although some are “membraneless”. In an aspect, the organelle can be a chloroplast, endoplasmic reticulum, Golgi apparatus, mitochondria, nucleus, or vacuole.

[0169] In another aspect, the biological entity is living. In a further aspect, the biological entity is no longer living (e.g., fixed cells and tissues).

[0170] An aspect of the invention provides methods to determine a homeostatic steady-state of a biological entity, the method comprising: acquiring signals with Nuclear Magnetic Resonance (NMR) from the biological entity; and b. fitting an exchange model to the signals. In another aspect, the invention provides methods to determine a homeostatic steady-state of a biological entity, the method comprising: a. acquiring signals with Nuclear Magnetic Resonance (NMR) from the biological entity; and b. isolating exchange weighted signal; and c. estimating the exchange rate.

[0171] In another aspect, the invention provides methods to determine a loss of homeostatic steady-state of a biological entity, the method comprising: a. acquiring signals with Nuclear Magnetic Resonance (NMR) from the biological entity; b. fitting an exchange model to thesignals; and c. observing an abnormal deviation in estimated exchange model parameters. In another aspect, the invention provides methods to determine a loss of homeostatic steady-state of a biological entity, the method comprising: a. acquiring signals with Nuclear Magnetic Resonance (NMR) from the biological entity; and b. isolating exchange weighted signal; and c. estimating the exchange rate, and establishing it is abnormal.

[0172] Any of the NMR methods mentioned herein can be utilized. In an aspect, the NMR is diffusion exchange spectroscopy (DEXSY). In a further aspect, the NMR is low-field, high-gradient (DEXSY).

[0173] In an aspect, the system is a NMR system. In a further aspect, the system is a unilateral, single-sided, or one-sided NMR profiling system. In a NMR system, static magnetic fields are used. In a further aspect, the MR system is a MRI scanner system. In the MRI scanner system, pulsed magnetic gradients are used.

[0174] In an aspect, the radiofrequency receiver measures radiofrequency electromagnetic fields emanating from the biological entity. In a further aspect, the radiofrequency transmitter emits radiofrequency electromagnetic fields to excite magnetic spins in the biological entity.

[0175] In an aspect, the invention further provides a mathematical means to estimate the steady state water exchange rate of endogenous water from the DEXSY NMR data.

[0176] In a further aspect, methods of an aspect of the invention use steady state water exchange rate as a proxy for normal water homeostasis. In another aspect, steady-state water exchange rate is replaced by a steady-state exchange rate spectrum or distribution.

[0177] In an aspect, the biological entity is living human tissue. In a further aspect, the living human tissue is ischemic.

[0178] In another aspect, the invention provides methods to quantify an exchange rate between a plurality of compartments (e.g., at least two compartments according to the direct model or at least three compartments according to the multi-site exchange model) in a biological system. At least two compartments are separated by a semipermeable membrane, for example, by a biological membrane such as a lipid bilayer.

[0179] In an aspect, the exchange rate is used to determine neuroprotectant efficacy.

[0180] In a further aspect, the exchange rate is used to determine a homeostatic steady-state of the biological system. In an aspect, the exchange rate is used to determine a loss ofhomeostatic steady-state of the biological system. A loss of homeostatic steady-state of the biological system may indicate a homeostatic non-steady state. A homeostatic non-steady state may include a pathological state.

[0181] In an aspect, the invention provides methods to quantify an exchange rate between multiple compartments (e.g., at least two compartments or at least three compartments) in a biological system, wherein the method comprises a MR system comprising: a. a means to create a static or pulsed magnetic field gradient; b. a means to create a constant magnetic field; c. a means to hold a biological entity within the constant magnetic field and the static or pulsed magnetic field gradient; d. a radiofrequency transmitter; e. a radiofrequency receiver that measures radiofrequency electromagnetic fields; f. a radiofrequency transmit amplifier; g. a MR radiofrequency pulse sequence generator that sends signals to the radiofrequency transmit amplifier to acquire Diffusion Exchange Spectroscopy (DEXSY) data; h. a recording device to sample and store a MR magnetization signal detected by the radiofrequency receiver; and i. a mathematical modeling framework to transform the recorded magnetization signal DEXSY data. In a further aspect, the exchange rate is used to determine neuroprotectant efficacy. In another aspect, the exchange rate is used to determine a homeostatic steady-state of the biological entity. In an aspect, the homeostatic non-steady state is a pathological state.

[0182] The means to create a static magnetic field gradient can be determined by one skilled in the art and any suitable means to create a static magnetic field gradient may be used. The means to create a pulsed magnetic field gradient can be determined by one skilled in the art and any suitable means to create a pulsed magnetic field gradient may be used. The means to create a constant magnetic field can be determined by one skilled in the art and any suitable means to create a constant magnetic field may be used.

[0183] In another aspect, the invention provides Nuclear Magnetic Resonance (NMR) methods to characterize physiological water transport.

[0184] In aspects of the invention, the methods do not require exogenous contrast agents in order to visualize the homeostatic steady-state of a biological entity. In an aspect, the methods explicitly exclude exogenous contrast agents.

[0185] In another aspect, the invention provides methods for non-invasively measuring exchange rates between different compartments of endogenous water in biological systems understeady-state or non-steady-state conditions in near-real time, in accordance with embodiments of the disclosure provided herein. In an aspect, the method detects an exchange rate which is an intrinsic metric or parameter that is used as a quantitative imaging biomarker to measure the physiological or pathological state of the biological system.

[0186] In an aspect, the methods utilize existing MRI devices, existing NMR devices, or new devices that will be developed specifically for this approach to measure the physiological or pathological state in vivo. In an aspect, the method further comprises utilizing modification of existing NMR and MRI pulse sequences and associated methods.

[0187] In another aspect, the methods are used on any endogenous molecular species containing nuclei with non-zero spin.

[0188] An aspect of the invention provides methods to determine a homeostatic steady-state of a biological entity, the method comprising the use of a magnet, a gradient coil, a radiofrequency probe, a gradient amplifier, a spectrometer, a radiofrequency amplifier, and a computer.

[0189] An aspect of the invention provides an experimental set up according to FIGS. 5A, 5B, and / or FIGS. 6A or 6B.

[0190] In an aspect of the invention, the magnet is used to produce a static gradient in the magnetic field. In another aspect of the invention, the magnet is a single-sided permanent magnet. In a further embodiment, the magnet is a homogeneous magnet.

[0191] As used herein, “non-invasive” refers to not having to enter the biological entity with a physical object, not having to deposit a clinically-significant amount of energy, and / or not having to subject the entity to a clinically-significant amount of radiation.

[0192] Aspects, including embodiments, of the subject matter described herein may be beneficial alone or in combination, with one or more other aspects or embodiments. Without limiting the foregoing description, certain non-limiting aspects of the disclosure numbered 1-17 are provided below. As will be apparent to those of skill in the art upon reading this disclosure, each of the individually numbered aspects may be used or combined with any of the preceding or following individually numbered aspects. This is intended to provide support for all such combinations of aspects and is not limited to combinations of aspects explicitly provided below:

[0193] The following examples further illustrate the invention but, of course, should not be construed as in any way limiting its scope.Examples

[0194] The following experimental examples demonstrate that the “active” component of water exchange across a semipermeable membrane is one that depends primarily on the osmolarity and / or tonicity which affects the osmotic pressure on the membrane and is not associated with co-transport of water with ions. Additionally, the examples demonstrate that steady-state water exchange depends on the tonicity. Furthermore, the examples demonstrate that tonicity can be quantified and characterized by non-invasive methodologies. As such, the examples include the non-invasive measurement of the exchange of water (e.g., the steady-state exchange of water into and out) of a system with a semipermeable membrane.

[0195] Experimental Design

[0196] Sample preparation and materials

[0197] All experiments were performed on Swiss Webster wild type mice (Taconic Biosciences, Rensselaer, NY, USA) between postnatal day 1 to 4. The mouse spinal cords were isolated in a dissecting chamber perfused with low-calcium, high-magnesium artificial cerebrospinal fluid (aCSF). After dissection, the spinal cord was placed in the sample chamber in normal calcium aCSF bubbled with 95% O2 and 5% CO2. Bubbled aCSF circulated through the chamber at 7 ml / min. Perturbations were performed with ouabain, AMPA (a-amino-3 -hydroxy -5-methyl-4-isoxazolepropionic acid), sucrose, and 0 NaCl media by either adding the drug to circulating reservoir or washing with the new media. The 0 NaCl media was made following the same recipe as normal aCSF, but replacing the 128.35 mM NaCl with 256.7 mM sucrose.

[0198] Hardware, setup, and experimental conditions

[0199] NMR experiments were performed with a single-sided permanent magnet (PM 10 NMR MOUSE, Magritek, Aachen Germany) at Bo = 0.3239 T and g =15.3 T / m. See e.g., G Eidmann, R Savelsberg, Peter Blümler, and Bernhard Blümich. The nmr mouse, a mobile universal surface explorer. Journal of Magnetic Resonance, 122: 104- 109, 1996; and Nathan H Williamson, Rea Ravin, Teddy X Cai, Dan Benjamini, Melanie Falgairolle, Michael JO ’Donovan, and Peter J Basser. Real-time measurement of diffusion exchange rate in biologicaltissue. Journal of Magnetic Resonance, 317:106782, 2020 (the entire contents of each of which is hereby incorporated by reference herein). A test chamber and radiofrequency (RF) probe with a solenoid coil were specially built to maintain live sample

[0200] viability and maximize signal to noise ratio (SNR). Sample temperature was maintained at 25° C.

[0201] Experimental protocols involved looping through sets of diffusion NMR experiments and rapid water exchange experiments. Diffusion experiments were performed using a standard spin echo sequence. See D. G. Rata, F. Casanova, J. Perlo, D. E. Demco, and B. Blümich. Selfdiffusion measurements by a mobile single-sided nmr sensor with improved magnetic field gradient. Journal of Magnetic Resonance, 180(2):229 - 235, 2006. ISSN 1090-7807.doi: https: / / doi.org / 10.1016 / j.jmr.2006.02.015 (the entire contents of which is hereby incorporated by reference herein). Each set took 11 minutes to acquire.

[0202] The diffusion time, r of the spin echo was varied linearly from 0.05 to 3.3 ms over 22 steps with 4 scans per T. This corresponds to b-values ranging from 0.001 to 400 ms / μm2where b = 2 / 3γ2g2τ3. See Erwin L Hahn. Spin echoes. Physical review, 80(4):580, 1950 (the entire contents of which is hereby incorporated by reference herein). Points two through four (T = 0.2048 to 0.5143 ms, b = 0.096 to 1.5 ms / μm2) of diffusion data were fit with I(b) = I₀ exp(-bD̄C) to estimate the Apparent Diffusion Coefficient and Io. For measurements on spinal cords, the term ADCyis used, acknowledging that diffusion may be anisotropic but was measured only in the y direction, perpendicular to the cord.

[0203] Rapid exchange experiments were performed using a DEXSY sequence involving two spin echoes separated by a mixing time tm. Experiments were performed with (n, T2) combinations (τ, T₂) = (0.200, 0.735), (0.593, 0.580) and 8 scans per combination. The tmvalues were [0.2, 1, 2, 4, 7, 10, 20, 40, 80, 160, 300] ms. The signal from (n, T2) = (0.200, 0.735) was fit with I(tm) = I₀(ω₁ exp(-tm / τ₁) + (1 - ω₁) exp(-tm / τ₁)). The resulting model was subtracted from the signal from (n, T2) = (0.593, 0.580) and the remaining signal was fit with I(tm) = I₀ exp(-tmk) + B to estimate the exchange rate, k.

[0204] Additional details aspects of some of the methods used herein can be found in Williamson, et al., Elife, 8: e51101 (2019) and Williamson, et al., Journal of Magnetic Resonance, 317: 106782 (2020).

[0205] Statistical Analysis

[0206] Hypothesis tests on whether MR metrics were affected by perturbations were performed using paired-sample t-tests, with p < 0.05.

[0207] Results

[0208] Sodium-potassium pump inhibition with ouabain has a large effect on exchange rate and simultaneously a smaller effect on ADC. First, results are provided real-time simultaneous measurements of water diffusion in the y-direction, perpendicular to the orientation of the spinal cord and transmembrane water exchange during perturbations with ouabain.

[0209] Ouabain is a specific inhibitor of the Na+ / K+- ATPase. There are multiple Na+ / K+-ATPase isoforms in mouse brain and spinal cord, which are characterized as having low ouabain affinity (1 isoform) or high ouabain affinity (2 and 3 isoform). Ouabain half-maximal inhibitory concentration (IC50) values were reported for rodent 1, 2 and 3 isoforms to be 48 pM, 59 nM, and 7 nM respectively. Based on this, the effects of a 100 pM ouabain dose expected to maximally inhibit all isoforms were investigated, as well the effects of 2 and 10 pM ouabain doses expected to inhibit the 2 and 3 isoforms but not the 1 isoform (FIGS. 7A-7J). See, e.g., Gustavo Blanco and Robert W Mercer. Isozymes of the na-k-atpase: heterogeneity’ in structure, diversity in function. American Journal of Physiology-Renal Physiology, 275(5): F633-F650, 1998; Michael J Marks and Nicholas W Seeds. A heterogeneous ouabain-atpase interaction in mouse brain. Life sciences, 23 (27 -28): 2735- -2744, 1978; Ian J Edwards, Gareth Bruce, Charlotte Law renson, Laura Howe, Steven J Clapcote, Susan A Deuchars, and Jim Deuchars. Na+ / k+ atpase al and a 3 isoforms are differentially expressed in a-and y-motoneurons. Journal of Neuroscience, 33(24):9913- 9919, 2013; and William J Obrien, Jerry B Lingrel, and Earl T Wallick. Ouabain binding kinetics of the rat alpha two and alpha three isoforms of the sodiumpotassium adenosine triphosphate. Archives of Biochemistry and Biophysics, 310(l):32- -39, 1994 (the entire contents of each of which are hereby incorporated by references herein).

[0210] Ouabain simultaneously decreases the apparent diffusion coefficient (ADCf) and exchange rate (k) (FIGS. 7A, 7B, 7D, and 7E). The effect is irreversible and occurs within the first measurement set (within 11 minutes) after adding 100 pM ouabain (FIGS. 7A and 7D), but is delayed at lower doses (FIGS. 7B, 7E, 7G, and 7H). After the effect has occurred, increasing the dosage has no additional effect (FIGS. 7B and 7E). ADCyand k remain stable until the startof an effect which occurs over less than 11 minutes (FIGS. 7B, 7E, and 7G). Ouabain affects ADCy in a dose-dependent manner. (FIGS. 7C and 7F). 2, 10 and 100 pM ouabain decrease ADCy by 5.3±2.8%, 8.3±2.2%, and 10.5±2.2% percent respectively. On the other hand, ouabain decreases A; in a roughly dose-independent manner, by 72±8% (averaged across the three groups).

[0211] Simultaneous real-time measurements were used to test for correlations between the metrics ADCy, k and f (restricted water fraction). ADCy and / both arise from diffusion measurements. ADCymeasures the average mobility of all water molecules in the sample on the timescales of diffusion encoding (here between 0.20 and 0.51 ms). / measures localization or motional averaging of water near surfaces on the length scale of the gradient dephasing length lg. Here, with the extremely strong g= 15.3 T / m static gradient produced by the low-field singlesided magnet, lg= 0.8 pm (at 25° C). ADC is a standard measurement used clinically (although with longer diffusion timescales between 20 and 100 ms), whereas / requires gradient strengths not currently accessible with the pulsed gradients of clinical systems.

[0212] Correlations between ADC and / have not been studied before, although they are often inferred in two-component models for ADC. (The present experiment was limited to the initial slope of the signal attenuation, where various components can be described as roughly Gaussian.) Such models may include a hindered component and a restricted component with apparent diffusion coefficients Di and D2 respectively, leading to ADC = (1 - / )Di + / D2.Hindrances reduce Di below the diffusion coefficient of freely diffusing water, D₀ = 2.15 μm2 / ms at 25° C. Water that is restricted on length scales similar to or smaller than lgwill have D2 « Di, leading to ADC = (1-f)D₁ in the limit that D₂ = 0 (29).

[0213] Correlations between k and / also have not been studied before. It may be expected that would be correlated with / given that k is related to cell membrane permeability (P) and membrane surface-to-volume ratio (SVR) through k = P *SVR and / is positively correlated to SVR.

[0214] All measurement data was split into two groups based on whether or not exchange had been affected by ouabain. The two groups overlap when ADCy is plotted vs. / , suggesting a similar underlying relationship (Figs 71). ADCyand f were strongly correlated, with correlation coefficients cc = -0.64 before the effect of ouabain and cc = -0.87 after ouabain took effect.Linear fits yielded ADCy= -1.82 / +1.22 μm2 / ms before ouabain took effect, and ADCy= “2.72 / +1.37 pm2 / ms after ouabain took effect.

[0215] The idealized two-component model discussed above has a slope and intercept equal to the apparent diffusivity of the hindered component. Slopes and y-intercepts are similar to or slightly smaller than Do consistent with the model. The high degree of correlation between ADCyand / indicates some redundancy in the information they hold, as shown by the simple model. This suggests that both ADCyand / report cellular swelling and shrinking. In contrast, the two groups do not overlap when k is plotted vs. / (FIG. 7J). k and / were weakly correlated with cc= -0.29 before the effect of ouabain, and not significantly correlated (p=0.081) after ouabain took effect. Weak and different correlations between the group suggest that k provides distinct information from / Furthermore, given the sensitivity of / to cellular swelling, k differences between groups are not due to cellular swelling.

[0216] FIGS. 7A-7J, referenced above, show that sodium-potassium pump inhibition with ouabain decreases exchange rates much more than apparent diffusion coefficients, and in an all-or-none, dose-independent fashion.

[0217] Representative real-time recordings on individual samples show how ouabain in high (100 pM) concentrations (see FIGS. 7A and 7D) and low (2 i / M) concentrations (see FIGS. 7B and 7E) affects apparent diffusion coefficient in the y-direction (presented as percent change from baseline, A4ZX / ) (see FIGS. 7A and 7B), and affects the exchange rate (k) (see FIGS. 7D and 7E).

[0218] In FIGS. 7D and 7E, arrows with text show the first measurement for which k significantly decreased and the time from ouabain addition to the effect.

[0219] In FIG. 7C, bar graphs of ADCyshow the mean across all measurements (bar height), 95% CI of the mean (whiskers), and mean values from each sample (open symbols) for 2, 10, and 100 pM ouabain after the effect was observed ( / / = 7, 8, and 5 respectively). As is shown, 2 pM ouabain significantly reduced _ ADCyby 5.3+2.8% (mean ± SD) (p < 0.001). Also, 10 and 100 pM ouabain reduced ADCyby 8.3+2.2% and 10.5+2.2% percent respectively, with the effects of 10 pM being more than 2 pM (p < 0.001), and the effects of 100 / / M being more than 10 pM (p = 0.0017).

[0220] FIG. 7D shows bar graphs of k. k was 130±20 s-1under normal conditions ( = 18) and dropped significantly (p < 0.001), to 44.0±8.2 after adding 2 z / M ouabain. 10 and 100 z / M ouabain dropped the exchange rate to 34.9±8.4, and 31.6±11.3 s-1respectively. These values are not significantly different from one-another (p = 0.23), but are significantly lower than k of samples treated with 2 zM ouabain (p < 0.001).

[0221] FIG. 7G shows mean (solid lines) and standard deviation (shaded regions) of realtime exchange rate measurements from a control group under normal conditions (green) and groups treated with 2, 10, and 100 / / M ouabain (lightest to darkest colors) plotted against the time after addition of ouabain.

[0222] FIG. 7H shows a bar chart of the time from ouabain addition to the time at which k dropped below 60 s-1compared between dosages. Times to effect were significantly different between dosages (p < 0.001).

[0223] FIGS. 71 and 7J respectively show correlation plots of ADCyvs. / (restricted volume fraction) and k vs. / In these plots, data was grouped based on whether measurements occurred before or after ouabain affected the exchange rate. In FIG. 71, the data is significantly correlated for both groups (p < 0.001) with Pearson correlation coefficients cc=-0.64 before ouabain effect and cc=-0.87 after ouabain effect. In FIG. 7J, the data is significantly correlated before ouabain effect (p < 0.001), but not after (p = 0.081), and with cc=-0.29 and 0.22 respectively.

[0224] Osmolytes recover exchange rates.

[0225] The effect of an osmolyte (sucrose) on exchange and diffusion was studied under normal conditions and after exchange was affected by ouabain. Sucrose does not penetrate cell membranes and hence adds a tonicity or effective osmotic pressure gradient. For dilute solutions the relationship between osmotic pressure n and concentration c is linear and well-approximated by the van’t Hoff equation, π = cRT, where R is the ideal gas constant and T is the absolute temperature. For reference, +100 mOsm at 25° C equates to +240 kPa. Two experiments were performed.

[0226] In the first experiment, the effect of 100 mOsm was observed on the same sample before and after adding 5 pM ouabain (see FIGS. 8 A and 8B). ADCy followed trends expected for cellular shrinking and swelling. It increased in the 100 mOsm hypertonic conditions, recovered in normal hypotonic media, and decreased slightly when ouabain took effect (see FIG.8A). Exchange rate followed similar trends, however osmolytes had a much larger effect after the sample was treated with ouabain (see FIGS. 8 A and 8B). Starting from the normal condition, 100 mOsm increased A by 39±31%. k recovered when washing back to normal isotonic media. After ouabain took effect, 100 mOsm increased k much more, by 239±94%. k dropped back down when washing back to normal media in the presence of ouabain.

[0227] FIGS. 8A and 8B, referenced above, illustrate that osmolytes recover exchange. FIG.8A shows real-time measurements of the exchange rate (blue circles, with values shown on the left y-axis) and percent change in ADCy(open triangles, with values shown on the right y-axis) during perturbations with 100 mM sucrose (an osmolyte) and 5 pM ouabain. FIG. 8B shows bar graphs showing the statistics across 3 samples for each condition.

[0228] In the second experiment, effects of sucrose dosages in the range of 10 to 200 mOsm were studied on normal samples (see FIG. 9A) and on separate samples treated with 10 pM ouabain (see FIG. 9B). On normal samples, incremental dosages from 10 to 100 mOsm had no effect on ADCyand k (see FIGS. 9C and 9F). On normal samples, ADCyand k significantly increased at 200 mOsm (see FIGS. 9C and 9F). AADCy and k did not recover when washing back to normal media (see FIG. 9A). For ouabain-treated samples, 30 mOsm and higher significantly increased AADCy and k, and 200 mOsm had no additional effect (see FIGS. 9C and 9F). At 0 mOsm, ADCyand k of ouabain-treated samples were significantly less than that of normal samples, and at 100 mOsm they were similar between sample groups. At 200 mOsm, k of ouabain-treated samples was significantly less than that of normal samples (see FIG. 9F) but ADCywas similar between sample groups (see FIG. 9C).

[0229] FIGS. 9A-9H, referenced above illustrate that exchange rate depends on tonicity.

[0230] Real-time measurements during perturbations with sucrose (an osmolyte) concentrations 0, 10, 30, 50, 100, 200 mM and back to 0 mM are shown in FIG. 9A for a sample starting from normal conditions and shown in FIG. 9B for a sample after adding 10 pM ouabain and observing its effect.

[0231] In Figs 9C-9H, illustrate the mean (symbols) and standard deviations (error bars) of parameter estimates from measurements under each condition on n = 3 samples starting from the normal condition (darker leftward-pointing triangles), and n=3 samples after adding 10 pM ouabain (lighter rightward-pointing triangles), plotted as a function of the change in osmolarity.

[0232] Figs 9C-9E illustrate certain structural parameters. FIG. 9C illustrates the apparent diffusion coefficient from diffusion measurements. FIG. 9D shows the inverse of the fraction of non-Gaussian water pools ( / ^1). FIG. 9E shows the fraction of steady-state exchange (^ss) from DEXSY measurements.

[0233] FIG. 9F shows the effect of osmolarity on exchange rate. FIG. 9G showsfrom the roots ofss=Under normal conditions, Ad / X), k and / did not significantly increase for osmolarities in the range of 10 to 100 mM (one-way ANOVA, p > 0.05), but did increase for 200 mM (p = 0.003, p < 0.001, and p = 0.018 respectively). After the effect of ouabain, 10 mM did not significantly affect Ad / X) or k (p = 0.99 and p = 0.98 respectively), but did affect (p = 0.03). All three parameters significantly increased for doses 30 mM (p = 0.009, p < 0.001, and p < 0.001 respectively) and higher (p < 0.001). Models of the form y = mx mOsm+B was fit to the data. For / -1of samples post-ouabain treatment, the fit yielded m = 0.0062 mM-1 and B=1.38.

[0234] In FIG. 9H, k[o=fk with values associated with the left-hand y-axis, and permeability P, assuming a 1, 2, or 3 dimensional (D) model (dashed, dot-dashed, and dotted 1 / Dlines, respectively) of the form P = kofi f / (2D) where the characteristic length scale f is set equal tog= 0.8 pm, with values associated with the right-hand y-axis. Correlations between metrics are presented in FIG. 17.

[0235] When the results are compared between the first experiment (see FIGS. 8A-8B) and the second experiment (see FIGS. 9A-9H), overall trends were consistent. Osmolytes have a much stronger effect on ouabain-treated samples than on normal samples.

[0236] Differences arise when the effects of osmolytes on normal samples are compared between experiments. 100 mOsm had an effect in the first experiment when it was added in a single step, whereas it had no effect in the second experiment when the concentration was brought from 50 mOsm to 100 mOsm (see FIGS. 8A-8B). When samples were washed back to normal media (+0 mOsm), ADCy and k recovered in the first experiment when washed from 100 mOsm, but did not recover in the second experiment when washed from 200 mOsm. AA / )( and k for normal samples depend on the size of the osmotic step change in addition to the final concentration. These experiments illicit different responses because they had different effects on volume regulation.

[0237] DEXSY measurements provide additional structural information. The fraction of nonGaussian water pools ( m) provides another metric for restricted water fraction (see FIG. 9D). The fraction of steady-state exchange (fss) provides a measure of the relative sizes of the local exchanging pools (see FIG. 9E). The intracellular fraction (f) can be found from the roots of / ss= 2 / (1- / ) (see FIG. 9G). Since both roots add to 1, / + / > = 1, and > 0.5 under normal conditions, f was taken as the larger of the two roots, except for the case of samples treated with ouabain and 200 mM sucrose, where the smaller root was taken due to the cells shrinking to / < 0.5. / = 0.68±0.02 under normal conditions. The associated / = 0.32±0.02 can be compared to extracellular volume fractions 0.36 to 0.41 measured in the cortical gray matter of 2 to 3-day old rats using tetramethylammonium iontophoresis. See A Lehmenkiihler, E Sykovd, J Svoboda, K Zilles, and Ch Nicholson. Extracellular space parameters in the rat neocortex and subcortical white matter during postnatal development determined by diffusion analysis. Neuroscience, 55(2):339 351, 1993 (the entire contents of which is hereby incorporated by reference herein), f did not change significantly when sucrose was added to the normal media. Inhibition of the Na+ / K+-ATPase caused / to decrease from 0.68±0.02 to 0.73±0.01. After ouabain, / decreased significantly with the addition of 10 mOsm and continued to decrease for dosages up to 200 mOsm. The associated ff1showed a linear dependence on sucrose concentration. The equilibration of osmolarity between an extracellular space and intracellular space suggests a model in which the concentration of the osmolyte added to the bath (c) plus the concentration or tonicity of osmolytes in the extracellular space (c0) is equal to the concentration of impermeable components within the cell c + c0= ci. The intracellular concentration of impermeable components is equal to the number of moles n, divided by the cell volume Vo = Fr * / where K is a representative volume element of the tissue. This leads to c + c0= «i / (Er* / ), which can be rearranged to a linear model: ff1=fn(c) = Vfn (c + co). From the slope and intercept of the linear fit, c = 219 mM and c0= 211 mM (see FIG. 9G). Overall, structural metrics from DEXSY (see FIGS. 9D, 9E, 9G, and 9H) show a consistent picture to t±ADCy(see FIG. 9C); changes with osmolarity are insignificant under normal conditions but become significant after inhibiting the Na+ / K+-ATPase.

[0238] Given that osmolarity induced cellular shrinkage in ouabain-treated samples, it was necessary to rule out whether structural changes could account for the increasing exchange. Todo so, first kio values were estimated using k and / ,' estimates (see FIG. 9H). Then changes in apparent permeability were estimated assuming P =SVRi*£i0, using 1-D, 2-D, or 3-D models for SVRi of the intracellular compartment. In all cases, apparent permeability increases with osmolarity and hence structural changes cannot account for the effect of osmolarity on exchange rates.

[0239] Temperature dependence confirms osmolytes recover exchange rates

[0240] The various pathways that water can take to exchange across the membrane can involve different energy barriers. These can be probed by observing exchange under different temperatures. The dependence of k on the absolute temperature T can be modeled with the Arrhenius equation k = A exp(~Ea / RT). The activation energy A, is related to the enthalpy and the pre-exponential factor^ is related to the entropy, and hence both can provide information about the thermodynamics of exchange. See, e.g., Hiroyuki Sugimoto, Tsunehisa Miki, Kozo Kanayama, andMisato Norimoto. Dielectric relaxation of water adsorbed on cellulose. Journal of Non-Crystalline Solids, 354(27):3220- -3224, 2008 (the entire contents of which is hereby incorporated by reference herein). Conditions with similar Eaand A likely involve similar pathways for water exchange. Different Eaand A may suggest different exchange pathways, although not necessarily, as the conditions may change the dynamics or Gibbs free energy of the water and hence the driving forces for exchange. In such a situation, it would be expected that the natural log of A and Eawould change linearly due the shared dependence of entropy S and enthalpy Hon the Gibbs free energy G = H - TS. See, e.g., Tatiana Psurek, Christopher L Soles, Kirt A Page, Marcus T Cicerone, and Jack F Douglas. Quantifying changes in the high-frequency dynamics of mixtures by dielectric spectroscopy. The Journal of Physical Chemistry B, 112(50): 15980-15990, 2008 (the entire contents of which is hereby incorporated by reference herein). This phenomenon appears commonly for the Arrhenius behavior of rate and time constants in many systems and is referred to as entropy-enthalpy compensation (EEC). See, e.g., D Daoukaki-Diamanti, P Pissis, and G Boudouris. Depolarization thermocurrents in frozen aqueous solutions of mono-and di-saccharides. Chemical physics, 91(2):315-325, 1984;Wendell Q Sun. Dielectric relaxation of water and water-plasticized biomolecules in relation to cellular water organization, cytoplasmic viscosity, and desiccation tolerance in recalcitrant seed tissues. Plant Physiology, 124(3):1203-1216, 2000; A Anopchenko, Tatiana Psurek, DavidVanderHart, Jack F Douglas, and Jan Obrzut. Dielectric study of the antiplasticization of trehalose by glycerol. Physical Review E, 74(3):031501, 2006; and Marcus T Cicerone and Jack F Douglas. (3 -relaxation governs protein stability in sugar glass matrices. Soft Matter, 8(10):2983- -2991, 2012 (the entire contents of each of which are hereby incorporated by reference herein).

[0241] Normal samples and samples treated with 10 pM ouabain were studied with and without 100 mM sucrose, leading to four condition total. For each condition, k was recorded at 25° C and 7° C, and re-recorded at 25° C to test for sample recovery (see FIG. 10A and 10B). k recovered when re-recorded at 25° C (one-way ANOVA, p > 0.05). Arrhenius model fits (see FIG. 10C), were used to estimate A and Ea(see FIG. 10D and 10E) The temperature dependence of k, and A and Eavalues are similar between the normal samples, normal +100 mOsm samples, and ouabain-treated +100 mOsm samples. This suggests that the pathways for water exchange are the same in these three conditions. A and Eavalues are lower for ouabain-treated samples. These results together confirm that exchange depends on tonicity.

[0242] Estimates of Eaand the natural log of A for all samples share a common linear dependence, as expected for EEC (see FIG. 10F). This implies that all systems can be described by a modified Arrhenius model with a crossover temperature Tcat which the exchange rates are equal for the system under all states due to the compensation of enthalpic and entropic contributions (see FIG. 10G). Indeed, the modified Arrhenius model with an estimated Tc= -17.3 C is capable of describing the temperature-dependence of A; for all systems. This is considered an important test for EEC phenomena. Tccould not be reached because it is less than 0° C. Importantly, the EEC phenomena suggests common mechanisms for exchange exist under all conditions and that the addition of an osmolyte to ouabain-treated samples activates the same shared set of transport pathways which are present under normal conditions.

[0243] Temperature dependence of ADCy, Ti, and R2 was also measured (see FIGS. 18A- 18G, 19A-19G and 20A-20G). In each case, Eaand A values were similar between conditions and significantly smaller than those found for k (in FIGS. 10D and 10E). The low and similar values of Eafor ADCy, Ti, and R2 are consistent with translational and rotational water selfdiffusion being hindered by the tissue microstructure. ADCy, Ti, and R2 do not depend on tonicity in the way that k does.

[0244] FIGS. 10A-10G, referenced above illustrate that temperature dependence of exchange is explained by entropy and enthalpy modulated by tonicity.

[0245] FIG. 10A illustrates a representative experiment in which temperature-dependent data for the ouabain + 100 mOsm condition was collected, k (blue circles) and ADCy(open triangles) were collected on a sample while adding first 10 pM ouabain, then 100 mM sucrose, and then varying the temperature from 25° C, 11° C, and back to 25° C.

[0246] FIG. 10B shows results of k recorded at 25° C and 11° C, and then re-recorded at 25° C on samples under normal conditions (n = 4), after addition of 100 mM sucrose (n = 3), after the effect of 10 pM ouabain (n = 3), and after the combined effect of 10 pM ouabain and 100 mM sucrose (n = 3).

[0247] FIG. 10C shows and Arrhenius plot of the inverse of the absolute temperature T1versus the average exchange for each condition. Solid lines show average fits of k =Aexp(-Ea / RT), where on the semi-log plot the slopes are proportional to activation energy estimates Eaand the intercepts are pre-exponential factor estimates A, and R is the ideal gas constant.

[0248] FIG. 10D is a bar graph of the natural log of pre-exponential factor. Fig 10E is a bar graph of activation energy estimates.

[0249] FIG. 10F shows activation energies plotted versus the natural log of pre-exponential factors for each sample show a linear dependence with slope m = 0.470 In (s1 / (kJ / mol) (95% CI = 0.447, 0.493) and y-intercept In A' = 2.18 Ins1(95% CI =1.30, 3.06) a sign of entropyenthalpy compensation and a common crossover temperature Tc= 1 / (m x R) - 273.15 = -17.3° C (-29.1,-4.3). Estimates suggest the modified Arrhenius model k = A' * exp(-Ea / R. * (1 / T -1 / Tc)).

[0250] FIG. 10G shows a model plotted for a range of Eavalues (grey dashed lines) along with the data and fits from FIG. 10C.

[0251] Similar analyses for ADCy, Ti, and R2 are shown in FIGS. 18A-18G, 19A-19G, and 20A-20G.

[0252] Exchange depends on tonicity and not on ion transport.

[0253] Previous studies of active water flux report mechanisms involving water transport linked to ion transport. See, e.g., Thomas Zeuthen. Water-transporting proteins. Journal ofMembrane Biology, 234(2):57- -73, 2010 (the entire contents of which is hereby incorporated by reference herein). Similarly, previous researchers hypothesized that water exchange was linked to Na+ / K+ pump activity because of water actively cycling with ions. This was tested for by using aCSF media in which the major ionic component, 128.35 mM NaCl, was replaced with 257 mM sucrose (see FIGS. 11 A-l ID). Note that while these media have equal osmolarities, the 0 NaCl, 257 mM sucrose media has a greater tonicity due to the membranes being semi-permeable to Na+ and Cl- but impermeable to sucrose. The higher tonicity of the 0 NaCl, 257 mM sucrose media caused ADCyto increase by 2.1±1.3%, indicative of cellular shrinkage (see FIGS. 11 A and 11C). If water exchange was linked to ion transport, then k was expected to decrease when washing to 0 NaCl, 257 mM sucrose media. Instead, k increased with the increased tonicity (see FIGS. 11 A and 1 ID). While Na+ / K+-ATPase activity should be inhibited by the lack of Na+, ouabain was used for assurance. 10 pM ouabain added on top of 0 NaCl, 257 mM sucrose media did not significantly affect k (see FIGS. HA and 1 ID). Additionally, the 0 NaCl, 257 mM sucrose media recovered k from the effect of ouabain, while the ouabain was still present (see FIGS. 1 IB and 1 ID). Therefore, k is linked to tonicity and not ion transport or Na+ / K+ pump activity.

[0254] Under normal conditions, ions partition by Na+ / K+ pump activity creating an osmotic gradient which increases the exchange rate. Inhibiting the Na+ / K+ pump causes the osmotic gradient to eventually drop, which in turn lowers k. Washing to high-tonicity media reestablishes an osmotic gradient which recovers k.

[0255] Figs 11 A-l ID, referenced above, shows osmolytes recover the exchange rate even when there is no NaCl.

[0256] FIGS. 11A and 10B show representative recording of the exchange rate (blue circles) and percent change in ADCy(open triangles). FIG. 11 A illustrates recording during experiments involving washing the sample from normal media to media in which NaCl was replaced with equimolar concentration of sucrose (257 mM), and then adding 10 pM ouabain. FIG. 1 IB illustrates recording while adding 10 pM ouabain on top of normal medial, waiting for the effect, and then washing to 0 NaCl, 257 mM sucrose in the presence of 10 pM ouabain.

[0257] FIGS. 10C and 10D respectively show box plots of A4£)CVand exchange rate under the various conditions.

[0258] Exchange rates are relevant to physiological processes.

[0259] Ouabain induces a pathological state, and 100 mM sucrose would not be encountered naturally. AMPA (a-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid) is used to demonstrate the physiological relevance of water exchange. AMPA is a specific agonist of AMPA receptors, initiating glutamate release and neuronal excitation. In electrophysiological experiments on the neonatal mouse spinal cord model, ionic currents decreased when 5 pM AMPA was added, began to recover in the presence of AMPA, and completely recovered when the drug was washed away. See, e.g., Melanie Falgairolle and Michael J O’Donovan.Pharmacological investigation of fluoro-gold entry into spinal neurons. PloS one, 0(6):e0131430, 2015 (the entire contents of which is hereby incorporated by reference herein).

[0260] Recovery in the presence of AMPA was attributed to the cells becoming conditioned to AMPA through recycling of receptors, k decreases when 5 pM AMPA is added, and k recovers when AMPA is washed out (see FIGS. 12A-12B). A second dose of AMPA has less of an effect and a higher 10 pM dose has no additional effect (see FIGS. 12A-12B and FIG. 22). These findings suggest that tonicity can vary with the physiological state of the system and that k can measure these states.

[0261] FIGS. 12A-12B, referenced above, show that exchange rates are affected by physiological perturbations.

[0262] FIG. 12A illustrates a representative sample that shows that addition of 5 pM AMPA causes a substantial decrease of the exchange rate, but the effect is reversible when washing back to normal aCSF. A second dose of 5 pM AMPA has less effect and increasing the dose to 10 pM has no further effect. ADCy (open triangles with values associated with the right y-axis) changes similarly to exchange rate, although to a lesser degree.

[0263] FIG. 12B provides bar graphs that show consistent behavior across 5 samples, although the values to which the exchange rates decrease vary between samples. (Open circles show the mean of measurements at each condition for each sample.) The first dose of 5 pM AMPA significantly decreases exchange from 136±10 s-1 to 78±38 s1(p = 0.01). Realtime data for each of the five samples are presented in FIG. 21. Bar graphs of the percentage change in exchange rate relative to the prior condition are shown in FIG. 22.

[0264] Comments on Results

[0265] As discussed herein, in experiments on biological systems, osmotic perturbations from 30 to 100 mOsm increased the Apparent Diffusion Coefficient (ADC) and k in ouabain-treated samples, but 200 mOsm had no additional effect (see FIG. 9C and 9F, discussed above). The linearity of the inverse of the restricted volume fraction ( / j-1) from 0 to 200 mOsm on ouabain-treated biological samples would suggest that sucrose continues to act as an osmolyte at 200 mOsm and does not penetrate (see FIG. 9G, discussed above). ADC would be expected to increase as cells shrink and the extracellular volume fraction increases while its tortuosity decreases. This is the major effect up to 100 mOsm, but the inventors consider that the increased viscosity at 200 mOsm affected ADC more than the additional change in volume fraction f. k would be expected to increase linearly with osmotic concentration by the van’t Hoff law, but the inventors consider that the system deviates from ideality at concentrations above 100 mM sucrose (or above 3.4 wt%). The inventors consider that this phenomenon should be similar to one which occurs in fdtration processes such as ultrafiltration, where the Staverman equation can be applied at low solute concentrations, but higher solute concentrations (e.g. above 1 wt%) lead to the formation of a boundary layer, effectively increasing the resistance to flow. Additionally, the inventors consider that component forces no longer act independently at higher concentrations. See, e.g., CJ Geankoplis. Transport Processes and Unit Operations, 3rd edition. Prentice Hall International Inc, 1993 (the entire contents of which is hereby incorporated by reference herein).

[0266] Low-field high-gradient DEXSY measures k > 100 s~l, faster than was previously reported or measured). However, this can be because low-field high-gradient DEXSY can access exchange on smaller length scales than previously possible, and this length scale happens to be well-tuned to the sample. The neonatal mouse spinal cord is mostly composed of gray matter. See, e.g., Nathan H Williamson, Velencia J Witherspoon, Teddy X Cai, Rea Ravin, Ferenc Horkay, and Peter J Basser. Lo -field, high-gradient nmr shows diffusion contrast consistent with localization or motional averaging of water near surfaces. Magnetic Resonance Letters, 2023; Alex M Henry and John G Hohmann. High-resolution gene expression atlases for adult and developing mouse brain and spinal cord. Mammalian genome, 23(9-10):539- -549, 2012; Gulgun Sengul, Ralph B Pu chaiski, and CharlesWatson. Cytoarchitecture of the spinal cord of the postnatal (p4) mouse. The Anatomical Record: Advances in Integrative Anatomy andEvolutionary Biology, 295(5):837- -845, 2012 (the entire contents of each of which is hereby incorporated by reference herein).

[0267] High gradients provide greater sensitivity to exchange across the sub-micron membranes of neuronal and glial processes, which comprise the majority of gray matter tissue by volume and are seen in high proportions in fluorescent images of the mouse spinal cord. See selectively labeled astrocytes in FIG. 1 in Hui-His Tsai, Huiliang Li, Luis C Fuentealba, Anna V Molofsky, Raquel Taveira-Marques, Helin Zhuang, April Tenney, Alice T Murnen, Stephen PJ Fancy, Florian Merkle, et al. Regional astrocyte allocation regulates cns synaptogenesis and repair. Science, 337(6092):358-362, 2012; and dye-loaded motoneurons and interneurons in FIG. 4 in Dvir Blivis, Melanie Falgairolle, and Michael J O 'Donovan. Dye-coupling between neonatal spinal motoneurons and interneurons revealed by prolonged back-filling of a ventral root with a low molecular weight tracer in the mouse. Scientific Reports, 9(1): 1 9, 2019; see also Ileana O Jelescu, Alexandre de Skowronski, Franqoise Geffroy, Marco Palombo, and Dmitry S Novikov. Neurite exchange imaging (next): A minimal model of diffusion in gray matter with inter -compartment water exchange. NeuroImage, 256:119277, 2022 (the entire contents of each of which is hereby incorporated by reference herein).

[0268] While k values can vary between studies simply due to measurement and system length scales, activation energy Eaand membrane permeability p are intended to be independent of these length scales. (Note that while membrane permeability accounts for these length scales in the relationship p = k / SVR, it depends on the model used to calculate SVR which can be ambiguous in a heterogeneous system, and it assumes exchange to be entirely passive.) Previous studies of passive water exchange report an inverse relationship between permeability and Ea. Lipid bilayers have relatively lower permeability but higher Eabecause permeability depends on membrane fluidity, which varies strongly with temperature. See, e.g., AS Verkman. Water permeability measurement in living cells and complex tissues. The Journal of membrane biology, 173(2):73- -87, 2000 (the entire contents of which is hereby incorporated by reference herein).

[0269] For instance, Ea= 40 kJ / mol and p « 2 pm / s (at 25° C) was found for Baker’s Yeast in which permeability was low and presumed to be primarily across the lipid bilayer. Aqueous channels across cell membranes such as aquaporins increase permeability but reduce Eatowards that of water self-diffusion (Ea= 18 - 20 kJ / mol). For instance, Eaand p values near 25 kJ / moland 40 pm / s (at 25° C) were consistently reported for red blood cells believed to be one of the most permeable plasma membranes due to the high expression of aquaporins. See, e.g., Mills. Self-diffusion in normal and heavy water in the range 1-45. deg. The Journal of Physical Chemistry, 77(5):685-688, 1973; J Bernard Heymann, Peter Agre, and Andreas Engel. Progress on the structure and function of aquaporin 1. Journal of structural biology, 121(2): 191-206, 1998; and Philip W Kuchel and Gheorghe Benga. Why does the mammalian red blood cell have aquaporins? Biosystems, 82(2):189-196, 2005 (the entire contents of each of which are hereby incorporated by reference herein).

[0270] For ouabain-treated samples, it was found that Ea= 25.2±0.8 kJ / mol (see FIG. 10E, discussed above) and p = 3, 5, or 8 pm / s (for 3D, 2D or ID SVR models at 25° C, see FIG. 9H, discussed above), consistent with permeability by diffusion through water channels. In comparison, it was previously found that fixed spinal cords are roughly twice as permeable and have similar Ea= 21=1=8 kJ / mol, which was attributed to pores opened during fixation.

[0271] Unlike the trends for passive systems, it was found that tonicity increased both the permeability (or k) and activation energy Ea).

[0272] The Eavalues for normal (42.6 ± 6.4 kJ / mol), normal + osmolyte (43.2 ± 2.8 kJ / mol), and ouabain-treated + osmolyte conditions (38.5 ± 1.6 kJ / mol) were similar to one-another, but significantly higher than the ouabain-treated condition (see FIG. 10, discussed above). These values are similar to what the inventors previously reported for live (normal) spinal cords, Ea= 36 ± 7 kJ / mol. Values can also be compared to Ealive = 46 kJ / mol reported by Fritz and Swift (1967) for water exchange in ex vivo frog sciatic nerve under normal conditions measured using a contrast agent-based NMR method. Similar to the present disclosure, they found that both the exchange rate and Ea. live decreased when cells were depolarized. Additionally, normal, normal + osmolyte, and ouabain-treated + osmolyte samples had higher permeabilities than ouabain-treated samples without osmolyte, but still less permeable than red blood cells (see FIG. 10H, discussed above).

[0273] Activation energies of ADCy, Ti, and T were similar between conditions and less than values reported for bulk water (see FIGS. 18A-18G, 19A-19G, and 20A-20G, discussed below). See, e.g., JC Hindman, A Svirmickas, and M Wood. Relaxation processes in water, a study of the proton spin-lattice relaxation time. The Journal of Chemical Physics, 59(3): 1517-1522, 1973 (the entire contents of which is hereby incorporated by reference herein). This is consistent with these metrics being sensitive to microstructure but not sensitive to tonicity.

[0274] The passive component present in ouabain-treated samples is present in all conditions. Adding an osmolyte to the ouabain-treated samples reactivates k while the system remains near equilibrium. This adds a caveat to previous findings of “active” water exchange defined as exchange linked to the non-equilibrium metabolic state of the tissue. It is true under normal conditions in which the tonicity of semipermeable ions is maintained in a nonequilibrium state, but it is not true when impermeable solutes are added.

[0275] The inventors have found that the exchange rate does not directly measure Na+ / K+-ATPase activity. When inhibiting the Na+ / K+-ATPase with ouabain, exchange rates reduced to a similar level roughly independent of dosage (see FIG. 7, discussed above). These dosages spanned below and above IC50 of the low ouabain affinity Na+ / K+-ATPase isoform, k would be expected to depend on ouabain dosage if it measured Na+ / K+-ATPase activity. Sucrose recovered exchange while Na+ / K+-ATPase activity was inhibited by ouabain (see FIGS. 2 and 3, discussed above) or the absence of Na+ (see FIG. 11, discussed above). While k measures tonicity resulting from Na+ / K+-ATPase activity, it does not measure water cycling with ions directly through Na+ / K+-ATPase and downstream transporters. Indeed, in the case of AMPA addition (see FIG. 12, discussed above), the exchange rate went down, likely because the ionic gradients were being used for action potentials faster than they could be restored by Na+ / K+-ATPase activity. AMPA elevates extracellular K+, which would be expected to increase (and not decrease) Na+ / K+-ATPase activity. See, e.g., Lydia Vargovd, Pavla Jendelovd, Alexandr Chvdtal, and Eva Sykovd. Glutamate, nmda, and ampa induced changes in extracellular space volume and tortuosity in the rat spinal cord. Journal of Cerebral Blood Flow & Metabolism, 21(9): 1077-1089, 2001 (the entire contents of which is hereby incorporated by reference herein).

[0276] These results distinctly reject the previous hypothesized mechanism that water exchange measures water co-transporting with ions. The proposed hypothesis that water exchange is linked to tonicity provides an alternative explanation for why water exchange is linked to activity.

[0277] The electrochemical potential is so-named for the inseparable influences of the electrical (charge) and chemical (osmotic) components. Here we have a measure of how the total chemical component influences water. It is difficult to imagine another direct measure of the total tonicity. The total electrical component can be characterized via membrane potential, an important measurement in electrophysiology.

[0278] Membrane potential is expected to change hand-in-hand with the exchange rate. To examine this expectation, the present inventors have considered the effects of ouabain in CNS cells. The present inventors have found that ouabain induced an all-or-none dose-independent drop of the exchange rate (see FIGS. 7F and 7G). The effect was similar for all dosages, but the time to effect was delayed at lower dosages. The observations the present inventors made for the present disclosure are reminiscent of the all-or-none, dose-independent effects of ouabain on membrane potential (termed spreading depression-like depolarization) in hippocampal slices reported by Balestrino et al. See Maurizio Balestrino, Jacob Young, and Peter Aitken. Block of (na+, k+) atpase with ouabain induces spreading depression-like depolarization in hippocampal slices. Brain research, 38(1 -2): 37 44, 1999 (the entire contents of which is hereby incorporated by reference herein).

[0279] Ouabain is considered a model for spreading depolarization (anoxic terminal spreading depolarization) because it invokes the quintessential “all-or-none”, nearly complete CNS cell depolarization. Terminal spreading depolarization is accompanied by massive ion and water redistribution between extracellular space (ECS) and intracellular space (ICS), hypotonicity, cell swelling, and dramatic ECS shrinkage. From their observations, the inventors have concluded that similarities between the effect of ouabain on k and its effect on membrane potential support the conclusion that k and membrane potential may be linked.

[0280] MR hydrophysiology characterizes water homeostasis.

[0281] As discussed above, the approach of the present disclosure is named “MR hydrophysiology.” MR hydrophysiology enables, inter alia, characterizing ADCyand k.

[0282] ADCy measures swelling and shrinking (e.g., cellular swelling and shrinking) induced by net water influx or efflux (see FIG. 71 and FIGS. 17A-17F, discussed herein), k measures steady-state water movement which is linked to the overall tonicity. fmand / , from DEXSY measurements trend differently from ADCyand k during osmotic perturbations, indicating to theinventors that they also hold distinct structural information (see FIGS. 7A-7J and FIGS. 17A- 17F, discussed herein).

[0283] An insight of the present disclosure is that k differences between normal and ouabain-treated samples were not due to cellular swelling or shrinking (see FIG. 7J and FIG. SI 1C and SI ID, discussed below), and k recovery with osmolytes could not be explained by microstructural changes (see FIG. 9H, discussed below). Additionally, different treatments, which have similar effects on k, can have different effects on ADCy. This was the case for the effects of different dosages of ouabain (see FIG. 1, discussed below), as well as different numbers of osmotic steps adding to 100 mOsm (compare a single step in FIG. 2 to multiple steps in FIG. 3).

[0284] Additionally, in relation to the present disclosure, it was demonstrated that 100 pM ouabain and 70 min of oxygen and glucose deprivation (OGD), both of which effectively inhibit the Na+ / K+-ATPase, had similar effects on k, but different effects on ADCy. Further, ADCy can be affected without changes in k. For instance, in relation to the present disclosure, it was observed oxygen and glucose deprivation affected ADCy prior to exchange. These results show that cells can independently regulate their volume and tonicity.

[0285] Results of osmotic perturbations clearly showed that ADCyand k are stable when the Na+ / K+-ATPase is active (see FIGS.2 and 3, discussed below). This suggests that cells tightly regulate their volume and tonicity. This is in contrast to electrophysiology and MRI studies reporting that cell volume of isolated neurons behave as perfect osmometers. See, e.g., FJ Alvarez-Leefmans, SM Gamino, and L Reuss. Cell volume changes upon sodium pump inhibition in helix aspersa neurons. The Journal of Physiology, 458(l):603- -619, 1992; and Edward W Hsu, Nanci R Aiken, And Stephen J Blackband. Nuclear magnetic resonance microscopy of single neurons under hypotonic perturbation. American Journal of Physiology-Cell Physiology), 271(6): C1895 C1900, 1996 (the entire contents of each of which is hereby incorporated by reference herein).

[0286] In relation to the present disclosure, it was also found that ouabain caused ADCyto decrease, which is consistent with in vivo MRI findings, but in contrast to reports that isolated neurons transiently swell but then shrink in response to ouabain. See, e.g., Helene Benveniste, Laurence W Hedlund, and G Allan Johnson. Mechanism of detection of acute cerebral ischemiain rats by diffusion-weighted magnetic resonance microscopy. Stroke, 23(5):746- -754, 1992 (the entire contents of which is hereby incorporated by reference herein). Likely, the tissue as a whole is more capable of maintaining homeostasis than cellular components in isolation. In particular, glia may be compensating for the osmotic changes and regulating the extracellular environment under normal conditions. See, e.g., Stephen J Blackband, Jeremy J Flint, Brian Hansen, Timothy M Shepherd, ChoongHLee, Wolfgang J Streit, and John R F order. On the origins of diffusion mri signal changes in stroke. Frontiers in Neurology, 11:549, 2020; and Nanna MacAulay. Molecular mechanisms ofk+ clearance and extracellular space shrinkage — glia cells as the stars. Glia, 68(11):2192 2211, 2020 (the entire contents of each of which is hereby incorporated by reference herein).Additional Experimental Data

[0287] FIG. 13 illustrates time courses of exchange rate k and A DCyduring perturbations involving combinations of sucrose and ouabain. Realtime recordings of k (circles, left-hand y-axis) and ADCy(triangles, right-hand y-axis) involving perturbations with combinations of 100 mM sucrose (osmolyte) and 5 or 10 pM ouabain on n = 8 samples. Text in top right-hand corner of each plot shows the value of the Pearson’s correlation coefficient (cc) for the correlation between exchange rates and ADCy values as well as the postnatal day (e.g., p2) of the mouse sample upon dissection. Arrows point to the first exchange rate for which the all-or-none effect was observed. Text next to the arrows show the time it took for the ouabain to take effect.

[0288] FIG. 14 illustrates the effect of osmolarity on metrics related to compartment fractions from diffusion measurements for samples treated and not treated with ouabain.Subscript 12 indicates that points 12-22 were fit. Subscript 6 indicates that points 6-22 were fit.

[0289] FIG. 15 illustrates the effect of osmolarity on metrics from the slope of the long-time signal from diffusion measurements for samples treated and not treated with ouabain.

[0290] FIG. 16 illustrates the effect of osmolarity on DEXSY metrics for samples treated and not treated with ouabain.

[0291] FIGS. 17A-17F illustrate correlation plots of various metrics on samples before (green) and after (pink) ouabain affected exchange from experiments involving perturbations with sucrose either added as 100 mM in a single dose (squares and circles) or added in increments up to 200 mM total (left and rightward-pointing triangles). Dark green and pink linesshow linear fits of the correlated normal and ouabain-treated data (respectively), and are dashed for fits of the single 100 mM dose experiments and solid for the incremental dose experiments.

[0292] FIG. 17A shows that f and ADCyare significantly correlated (p < 0.001). Correlation coefficients and fit slopes (pi) and intercepts (b) for the 100 mM perturbations are cc = -0.92, m = -2.00, b = 1.29 for normal and cc = -0.89, m = -1.84, b = 1.25 for ouabain-treated, and for the incremental dose experiments they are cc = -0.58, m = -1.66, b = 1.23 for normal and cc = -0.86, m = -2.15, b = 1.26 for ouabain treated. Slope and intercept values have units pm2 / ms and are comparable to those found from Fig. 71.

[0293] FIG. 17B illustrates f and ADCyare not significantly correlated for the 100 mM sucrose perturbation on normal samples (p = 0.11) but are significantly correlated for the other conditions (p < 0.001). Correlation coefficients and fit slopes (m) and intercepts (Z>) for the 100 mM perturbations on ouabain-treated samples are cc = -0.64, m = -0.344, 6 = 1.16, and for the incremental dose experiments they are cc = -0.73, m = -3.44, b = 3.33 for normal and cc = -065, m = -0.61, b = 1.33 for ouabain-treated.

[0294] In FIGS. 17B-17F, parameter correlations are different between normal and ouabain treated samples. They are not significant (p > 0.05) in the case of normal condition for the 100 mM perturbations in FIGS. 17C, 17D, 17E, and 17F, and for the incremental dose experiments in 17D and 17F. Correlations are significant (p < 0.05) for the other cases including all cases for ouabain-treated conditions. These results suggest that these metrics may hold distinct information, particularly about homeostasis.

[0295] FIGS. 18A-G illustrate the temperature dependence of ADCy.

[0296] FIG. 18A illustrates a representative experiment in which temperature-dependent data for the ouabain + 100 mOsm condition was collected, k (blue circles) and AADCy(open triangles) were collected on a sample while adding first 10 pM ouabain, then 100 mM sucrose, and then varying the temperature from 25° C, 11° C, and back to 25° C.

[0297] FIG. 18B illustrates results of ADCyrecorded at 25° C and 11° C, and re-recorded at 25° C on samples under normal conditions (n = 4), after addition of 100 mM sucrose (n = 3), after the effect of 10 pM ouabain (p = 3), and after the combined effect of 10 pM ouabain and 100 mM sucrose (n = 3).

[0298] FIG. 18C is an Arrhenius plot of the inverse of the absolute temperature / '1versus the average exchange for each condition. Solid lines show average fits of ADCy= Aexp( Ea / RT), where on the semi-log plot the slopes are proportional to activation energy estimates Eaand the intercepts are preexponential factor estimates A, and R is the ideal gas constant.

[0299] FIG. 18D is a bar graph of the natural log of pre-exponential factor.

[0300] FIG. 18E is a bar graph of activation energy estimates.

[0301] FIG. 18F shows activation energies of ADCyplotted versus the natural log of preexponential factors. Samples show a linear dependence with slope m = 0.437 ln(pm2 / ms / (kJ / mol) (95% CI = 0.380, 0.495) and y-intercept In A’ = -0.366 In pm2 / ms (95% CI =-0.889, 0.158), however over a small range. This leads to a fit for a common crossover temperature Tc=1 1 (m x R) - 273.15 = 1.96° C (43.5 - 30.1) with poor parameter estimates.

[0302] FIG. 18G illustrates a modified Arrhenius model ADCy= A ’ * exp( EaR * (1 / T -1 / c)) is plotted for a range of Eavalues (grey dashed lines) along with the data and fits from FIG. 18C. From this, it is clear that the modified model does not fit the data, and therefore the ADCyin the system does not fit all the requirements for entropy-enthalpy compensation.

[0303] FIGS. 19A-19G illustrate the temperature dependence of spin lattice relaxation rate Ti.

[0304] FIG. 19A shows a representative experiment in which temperature-dependent data for the ouabain + 100 mOsm condition was collected, k (blue circles) and Ti (open triangles) were collected on a sample while adding first 10 pM ouabain, then 100 mM sucrose, and then varying the temperature from 25° C, 11° C, and back to 25°C.

[0305] FIG. 19B shows results of Ti recorded at 25° C and 11°C, and re-recorded at 25° C on samples under normal conditions (zz=4), after addition of 100 mM sucrose (w=3), after the effect of 10 pM ouabain ( = 3), and after the combined effect of 10 pM ouabain and 100 mM sucrose (« = 3).

[0306] FIG. 19C is an Arrhenius plot of the inverse of the absolute temperature / '1versus the Ti for each condition. Solid lines show average fits of Ti = A exp(-EERT), where on the semi-log plot the slopes are proportional to activation energy estimates Eaand the intercepts are pre-exponential factor estimates A, and R is the ideal gas constant.

[0307] FIG. 19D is a bar graph of the natural log of pre-exponential factor.

[0308] FIG. 19E is a Bar graph of activation energy estimates.

[0309] FIG. 19F shows activation energies of Ti plotted versus the natural log of preexponential factors for each sample. Samples show a linear dependence with slope m = 0.418 In (5 / (kJ / mol) (95% CI = 0.403, 0.4322) and y-intercept lnA ’ = -0.043 In 5 (95% CI =-0.139, 0.225), however over a small range. This leads to a fit for a common crossover temperature Tc= l / (m x R) -273.15 = 14.8° C (25.3, 5.1) with poor parameter estimates. Also shown are the best-fit lines of Eaversus log(A) for the k data (dashed pink line, from FIGS. 10A-10G) and for the ADCy data (dotted blue line, from FIGS. 18A-18G). From this, it is seen that the EEC behavior of ADCy and Ti are similar to each other but different from the EEC behavior of k.

[0310] FIG. 19G shows a modified Arrhenius model Ti =A’ * exp( EaR * (1 / T~1 / TC)) is plotted for a range of Eavalues (grey dashed lines) along with the data and fits from FIG. 19C.From this, it is clear that the modified model does not fit the data, and therefore the system may not fit all the requirements for entropy-enthalpy compensation.

[0311] FIGS. 20A-20G illustrate the temperature dependence of R2.

[0312] FIG. 20A illustrates a representative experiment in which temperature-dependent data for the ouabain + 100 mOsm condition was collected, k (blue circles) and Ri (open triangles) were collected on a sample while adding first 10 pM ouabain, then 100 mM sucrose, and then varying the temperature from 25° C, 11° C, and back to 25° C.

[0313] FIG. 20B illustrates the results of R2 recorded at 25° C and 11° C, and re-recorded at 25° C on samples under normal conditions («=4), after addition of 100 mM sucrose («=3), after the effect of 10 pM ouabain (n = 3), and after the combined effect of 10 pM ouabain and 100 mM sucrose (n = 3).

[0314] FIG. 20C shows an Arrhenius plot of the inverse of the absolute temperature 7'1versus the average R2 for each condition. Solid lines show average fits of R2 = A exp(~Ea / RT), where on the semi-log plot the slopes are proportional to activation energy estimates Eaand the intercepts are pre-exponential factor estimates A, and A is the ideal gas constant.

[0315] FIG. 20D shows a bar graph of the natural log of pre-exponential factor.

[0316] FIG. 20E shows a bar graph of activation energy estimates.

[0317] FIG. 20F shows activation energies plotted versus the natural log of pre-exponential factors for each sample show a linear dependence with slope m = 0.4046 In (,s '7(kJ / mol ) (95%CI = 0.3803, 0.4289) and y-intercept In^ ’ = 2.13 In.s1(95% CI =2.034, 2.226), however over a small range. This leads to a fit for a common crossover temperature Tc= I / (m x R) - 273.15 = 24.1° C (43.1,7.269) with poor parameter estimates. Also shown are the best-fit lines of Eaversus log(A) for the k data (dashed pink line, from FIGS. 10A-10G) and for the ADCydata (dotted blue line, from FIGS. 18A-18G). From this, it is seen that the EEC behavior of k and Ri are similar to each other but different from the EEC behavior of ADCy.

[0318] FIG. 20G shows a modified Arrhenius model R2 = A' * exp( Ea / R * (1 / T~1 / TC)) is plotted for a range of Eavalues (grey dashed lines) along with the data and fits from FIG. 20C. From this, it is clear that the modified model does not fit the data, and therefore the system may not fit all the requirements for entropy-enthalpy compensation.

[0319] FIG. 21 illustrates time courses of exchange rate k and ADCyduring perturbations with AMPA. Realtime recordings of k (blue circles, left-hand y-axis) and ADCy(red triangles, right-hand y-axis) involving two perturbations with AMPA on n = 3 samples. Text in top righthand comer of each plot shows the postnatal day (e.g., p2) of the mouse sample upon dissection.

[0320] FIG. 22 illustrates a percentage change in exchange rate relative to the prior condition. Both the first and second additions of 5 pM AMPA significantly decreased the exchange rate from the initial and second normal conditions prior to their addition (one-sample t-test p = 0.04 and 0.03 respectively). The first and second washes to normal media did not significantly increase exchange from the APMPA conditions prior (p = 0.17 and 0.28 respectively), and 10 pM APMPA did had no additional effect from that of the 5 pM AMPA prior (p = 0.57).Processing System

[0321] Referring to FIG. 23, a processing system 2300 can include one or more processors 2302, memory 2304, one or more input / output devices 2306, one or more sensors 2308, one or more user interfaces 2310, and one or more actuators 2312. Processing system 2300 can be representative of each computing / processing system disclosed herein. At a minimum however, the term “processing system” as used in the claims requires at least one hardware processor.

[0322] Processors 2302 can include one or more distinct processors, each having one or more cores. Each of the distinct processors can have the same or different structure. Processors 2302can include one or more central processing units (CPUs), one or more graphics processing units (GPUs), circuitry (e.g., application specific integrated circuits (ASICs), digital signal processors (DSPs), and the like. Processors 2302 can be mounted to a common substrate or to multiple different substrates. Unless clearly defined to the contrary, reference to one processor executing one or more processes includes one or more processors executing (collectively or individually) each of the processes named, and vice versa.

[0323] Processors 2302 are configured to perform a certain function, method, or operation (e g., are configured to provide for performance of a function, method, or operation) at least when one of the one or more of the distinct processors is capable of performing operations embodying the function, method, or operation. Processors 2302 can perform operations embodying the function, method, or operation by, for example, executing code (e.g., interpreting scripts) stored on memory 2304 and / or trafficking data through one or more ASICs. Processors 2302, and thus processing system 2300, can be configured to perform, automatically, any and all functions, methods, and operations disclosed herein. Therefore, processing system 2300 can be configured to implement any of (e.g., all of) the protocols, devices, mechanisms, systems, and methods described herein.

[0324] For example, when the present disclosure states that a method or device performs task “X” (or that task “X” is performed), such a statement should be understood to disclose that processing system 2300 can be configured to perform task “X”. Processing system 2300 is configured to perform a function, method, or operation at least when processors 2302 are configured to do the same.

[0325] Memory 2304 can include volatile memory, non-volatile memory, and any other medium capable of storing data. Each of the volatile memory, non-volatile memory, and any other type of memory can include multiple different memory devices, located at multiple distinct locations and each having a different structure. Memory 2304 can include remotely hosted (e.g., cloud) storage.

[0326] Examples of memory 2304 include a non-transitory computer-readable media such as RAM, ROM, flash memory, EEPROM, any kind of optical storage disk such as a DVD, a Blu-Ray® disc, magnetic storage, holographic storage, a HDD, a SSD, any medium that can be used to store program code in the form of instructions or data structures, and the like. Any and all ofthe methods, functions, and operations described herein can be fully embodied in the form of tangible and / or non-transitory machine-readable code (e.g., interpretable scripts) saved in memory 2304.

[0327] Input-output devices 2306 can include any component for trafficking data such as ports, antennas (i.e., transceivers), printed conductive paths, and the like. Input-output devices 2306 can enable wired communication via USB®, DisplayPort®, HDMI®, Ethernet, and the like. Input-output devices 2306 can enable electronic, optical, magnetic, and holographic, communication with suitable memory 2306. Input-output devices 2306 can enable wireless communication via WiFi®, Bluetooth®, cellular (e g., LTE®, CDMA®, GSM®, WiMax®, NFC®), GPS, and the like. Input-output devices 2306 can include wired and / or wireless communication pathways.

[0328] Sensors 2308 (e.g., RF sensors) can capture physical measurements of environment and report the same to processors 2302. User interface 23100 can include displays, physical buttons, speakers, microphones, keyboards, and the like. Actuators 2312 can enable processors 2302 to control mechanical forces (e.g., turn on / off magnetic field, move lift, turn on gas, etc.).

[0329] Processing system 2300 can be distributed. For example, some components of processing system 2300 can reside in a remote hosted network service (e.g., a cloud computing environment) while other components of processing system 2300 can reside in a local computing system. Processing system 2300 can have a modular design where certain modules include a plurality of the features / functions shown in FIG. 23. For example, VO modules can include volatile memory and one or more processors. As another example, individual processor modules can include read-only-memory and / or local caches.Pump-leak model

[0330] As explained above, another aspect of the present disclosure provides a “pump-leak model”, which may also be described as a multisite exchange model, which is based on capturing effects on exchange and diffusion as dependent on effects on tonicity, which in turn changes volume ratios between the different compartments that differ in their diffusion and exchange. This portion of the present disclosure is focused on this pump-leak model and includes additional aspects beyond what was provided above. Nevertheless, it must be appreciated that certainaspects discussed above are implementable in combination with the pump-leak model. For example, the disclosed Al diagnostic analysis, MR system, and Processing System are readily extendable, mutatis mutandis, for implementing the pump-leak model alone or in combination with aspects of the direct model. For the sake of sectional clarity and consistency, it should be noted that to the extent any portions of the following discussion on the pump-leak model suggest an inconsistency with the direct model, that the discussions when taken independently are consistent, and should be read as such. Also, any perceived repetitiveness in the following discussion of the pump-leak model is done for the purpose of completeness of this section of the disclosure.

[0331] The present inventors have found that data and modeling indicate there may be a multisite exchange mechanism in which tonicity modulates the dominant apparent exchange pathway between fast transmembrane pathways and slow intracellular pathways. The transmembrane pathway has a high activation energy but does not require ions, indicating it is not mediated through channels or cotransporters but through lipid bilayers.

[0332] The permeability of membranes necessitates that molecules, including water, are always exchanging between inside and outside the cell, even at steady-state (i.e., when there is no net flux). This is quantified by the rate constant for apparent steady-state water exchange, which is referred to herein as the “exchange rate”, k. While the apparent value can vary depending on measurement parameters (e.g., gradient strengths and timings / durations), in isolated cells, k has been shown to depend on diffusive permeability p and the membrane surface to to-volume ratio SVR through the relation: / c=pSVR. (Al)

[0333] Research has been on-going to understand the determinants of k in heterogeneous and metabolically-active tissues such as central nervous system (CNS) gray matter.Nonetheless, from the prevalence of dentrites, unmyelinated axons, and glial cell processes with sub-micron diameter plasma membranes composed of polyunsaturated lipids and cholesterol, it is expected that:SVR > 1 / / m-l; andp ^ IOO / / m s.

[0334] The present inventors have also made the prediction that k could be greater than 100 s ' in gray matter.

[0335] Nuclear magnetic resonance (NMR) can characterize diffusion and the steady-state exchange of water noninvasively. Magnetic field gradients can be used to encode for molecular displacements along the direction of the gradient and to measure the apparent diffusion coefficient (ADC). Differences in diffusion properties within the intracellular and extracellular environments can be observed on timescales where water on average has felt the effect of plasma membranes but has not yet permeated them. On these timescales, water inside cells is less mobile because it is bounded and restricted by membranes, whereas water outside is more mobile because it can diffuse through a tortuous and narrow but connected extracellular space (ECS). In this way the ADC may be used as a proxy for cell volume, but not necessarily quantitatively due to the structural heterogeneity. In particular, the heterogeneity of cell sizes and orientations of cellular processes can lead to water in some intracellular domains appearing more mobile than others. Exchange between environments where water mobility differs can be measured by encoding the same water at two instances separated by a mixing time where the water can communicate between environments. In this way, the exchange rate is sensitive to membrane permeability, however not quantitative due to the heterogeneity in cell surface-to-volume ratios, and not specific due to the sensitivity to other exchange pathways such as between regions inside the cell.

[0336] The temperature dependence of water exchange rates have been used to measure activation energies (Ea). While most studies report Eavalues agreeing with those expected for membrane permeability, an additional mechanism may explain reports of Eavarying with cellular state. Sensitivity of the exchange rate to pharmacological inhibitors and cellular energetics suggested a second mechanism involving active transporters, in particular the Na+ / K+-ATPase.

[0337] The present inventors have recognized that elucidating transport mechanisms that govern water exchange will advance the understanding of cellular homeostasis in the CNS and highlight the potential utility of NMR-based water exchange measurements as indicators of cell status.

[0338] The present disclosure demonstrates, inter alia, in ex vivo CNS gray matter that water is not moving with ions through transporters in the steady-state. Instead, the tonicity created by the transporters is affecting k. Data and modeling indicates that k may be sensitive to at least twocompeting pathways for water exchange, which may be modulated by tonicity. A fast pathway that dominates under isotonic and hypertonic conditions is associated with a high activation energy, but does not require NaCl. This fast exchange pathway can be interpreted to transport across the lipid bilayer, as it is not through cotransporters that involve ions or channels or aqueous media which would produce a lower activation energy. A slow pathway has a lower activation energy value similar to water self-diffusion and dominates during hypotonic conditions. This pathway can be interpreted to be between environments within the cell, such as between cell bodies and processes or along branching processes. With additional information from the ADC, the present inventors have found signatures of homeostatic osmotic / volume regulation as cells resist tonicity changes. This allows for the differentiation of normal and inactive samples regardless of the tonicity. The present inventors have found that exchange rates may offer a potentially impactful quantitative functional imaging biomarker, which has the potential for profound consequences in the understanding of cell status in health and disease.

[0339] Methods

[0340] Mouse spinal cord sample preparation and experimental conditions. The following experiments were performed on Swiss Webster wild type mice (Taconic Biosciences, Rensselaer, NY, USA) between postnatal day 1 to 4. The mouse spinal cords were isolated in a dissecting chamber perfused with low-calcium, high-magnesium artificial cerebrospinal fluid (aCSF), with the same composition as normal aCSF (listed below) but 0.5 mM CaCF 2H O and 6 mM MgSO4 7H2O, bubbled with 95% 02 / 5% CO2. After dissection, the spinal cord was placed in the sample chamber in normal calcium aCSF, composed of 128.35 NaCl, 4 KC1, 1.5 CaCh -2H2O, 1 MgSO4 • 7H2O, 0.58 NaFbPCh ’FbO, 21 NaHCOs, 30 D-glucose (concentrations in mM), bubbled with 95% O2 and 5% CO2 aCSF flowed through the chamber at 7 mL / min. Chemical perturbations performed in this study included adding the pharmacological inhibitor ouabain (European Pharmacopeia Reference Standard), adding the osmolytes sucrose and mannitol (Sigma Aldrich), and switching between media in which the 128.35 mM NaCl was re- placed with 256.7 mM sucrose or 128.35 mM sodium gluconate (Sigma Aldrich). Switching between media involved washing in an open loop with 100 m of new media. Sample temperature was monitored by a fiber optic sensor (PicoM, Opsens Solutions Inc., Quebec, Canada) and was controlled by water circulating through heatexchangers connected to a chiller. The sample temperature was maintained at 25 ± 0.2"C by manually regulating the temperature of the chiller. Temperature perturbations were performed by rapidly (5 min equilibration) switching between 25 ± 0.2”C and 11 ± using three-way valves upstream and downstream of the chamber connected to two chillers set at different temperatures.

[0341] NMR hardware, experimental protocol, and analysis methods. NMR experiments were performed with a single- sided permanent magnet 38 (PM10 NMR MOUSE, Magritek, Aachen Germany) at magnetic field strength Bo = 0.3239 T and gradient strength g = 15.3 T / m. A test chamber and radio frequency (RF) probe with a solenoid coil were specially built to maintain live sample viability and maximize filling factor and SNR.

[0342] NMR experimental protocols involved looping through sets of diffusion experiments, rapid diffusion exchange experiments, and Ti saturation recovery experiments. Each set took 11 minutes to acquire. Diffusion experiments were performed using a standard spin echo sequence and 4-step phase cycle. The diffusion encoding time, T of the spin echo was varied linearly from 0.05 to 3.3 ms over 22 steps with 4 scans per T. This corresponds to b-values ranging from.001 to 400 ms / / zm2 where b = ICy2^3and y is the gyromagnetic ratio. Points two through four (r = 0.2048 to 0.5143 ms, b = 0.096 to 1.5 ms / / / m2) of diffusion data were fit with 1(b) = / o exp (-b ADC) to estimate the ADC and Zo, the MR signal in the absence of diffusion weighting. For measurements on spinal cords, the term ADCyis used, acknowledging that diffusion may be anisotropic but was measured only along they direction, perpendicular to the cord. Rapid diffusion exchange experiments were performed following the Diffusion Exchange Ratio (DEXR) method using a diffusion exchange spectroscopy (DEXSY) sequence involving two spin echoes separated by a mixing time tmin the presence of a static magnetic field gradient and a 4-step phase cycle. Experiments were performed with (n, I) combinations (0.200, 0.735) ms and (0.593, 0.580) ms, and 8 scans per combination. The tmvalues were [0.2, 1, 2, 4, 7, 10, 20, 40, 80, 160, 300] ms. The signal from (TI, T ) = (0.200, 0.735) was fit with I(tm) = Io(w exp (— tmRl) +(1 — wi) exp (— tmR2). The resulting model was subtracted from the signal from the (TI, T2) =(0.593, 0.580) experiment and the remaining signal was fit with I(tm) = Io exp (tmk) + B to estimate the exchange rate, k.

[0343] Experimental design and statistical analysis. Tests of whether MR metrics were affected by perturbations were performed using paired-sample t-tests, with p < 0.05 deemed as significant.

[0344] Simulation methods. The pump-leak model (PLM) of cell volume maintenance was used to predict how perturbations affect cell volume and transmembrane potential. See, e.g., AlanR Kay. How cells can control their size by pumping ions. Frontiers in cell and developmental biology, 5:41, 2017 ( the entire contents of which are hereby incorporated by references herein). The PLM approximates intracellular ion concentration and volume changes over time from the active flux of Na+and K+by the Na / K -ATPase pump and passive fluxes of Na+, K+, and Cl". The model assumes electroneutrality and zero transmembrane osmolarity gradient. The Na+ / K+“PUMP ON” rate was chosen to maintain a transmembrane voltage V= - 48 mV under normal conditions, based on intracellular recording from motoneurons in the neonatal mouse spinal cord. The simulated cell contains a set amount of negatively-charged intracellular impermeant species and is isolated in a bathing media. The normal media condition was defined as Nao = 128 mM, Ko = 4 mM, and CL = Nao +Ko = 132 mM based on the aCSF composition but neglecting divalent cations and glucose. Concentrations for other conditions are provided in captions of supplementary figures. Values of volume and transmembrane voltage were taken once the system reached steady-state. However, in normal media and with the PUMP OFF condition, the PLM predicts cell volume to increase towards infinity and voltage to decrease towards zero without reaching steady-state due to the imbalanced osmotic pressure from intracellular impermeants.

[0345] A three-site exchange model was developed to predict how perturbations affect the extracellular space (ECS) fraction ( / □), ADC, and k. This model improves on the PLM by including an osmotic pressure from trapped ECS impermeants and a fixed total extracellular space + intracellular space volume (ECS + ICS = Wtot). This effectively accounts for the hydrostatic pressure imposed by the dura surrounding the spinal cord which holds the tissue together. These improvements lead to a stable cell volume with the PUMP OFF due to the ECS osmotic pressure increasing as the cell swells and the ECS shrinks. However, it is a steady-state model and assumes the voltage to be a fixed specified value. The model involves first setting aninitial fo for the normal cell condition. Here, 75 = 0.3 was chosen based on tetramethylammonium real-time iontophoresis measurements of 0.27 in the P8-10 mouse spinal cord slice model and the trend towards larger ECS fraction in younger animals. Then, an analytical equation based on an osmolarity balance was used to predict fofor the media and PUMP ON / OFF conditions (Eq. SI - discussed more below).

[0346] A three-site exchange model associated with an ECS compartment, a more mobile ICS compartment, and a less mobile ICS compartment were used to predict ADC and k. ADC was modeled as the sum of the ADCs of each compartment multiplied by their relative volume fractions (assuming no exchange), k was modeled by simulating DEXR data using an operator formalism and then fitting the exchange model discussed above. The model included a transmembrane exchange rate between ECS and both ICS components (kt) and geometric exchange rate between ICS components (kg). Transmembrane and geometric exchange rates were determined by the Arrhenius model (Eq. A3 — discussed below) with Ea= 52 kJ / mol for transmembrane, Ea= 22 kJ / mol for geometric, and A values defined by the EEC function (Eq. A4 — discussed below) with In (A.') = 2.18 In (s-1) and Tc= 17.1 C presented in Fig. 30A.

[0347] FIG. 3OA-3OD are graphs illustrating that exchange rate increasing with activation energy is explained by a multisite exchange mechanism. FIG. 30A shows experimental activation energies plotted vs. the natural log of preexponential factors for all samples show a linear dependence described by Eq. A4 with slope m = 0.470 In (s^J / kJ / mol) (95% CI = 0.447, 0.493) and.y-intercept In^') = 2.18 In s ') (95% CI =1.30, 3.06). This is a sign of entropyenthalpy compensation and suggests a common crossover temperature Tc= \ / (m x R) - 273.15 = -17.1 °C (-29, -4.3). FIG. 30B shows a semi-log plot of Eq. A5 for a range of Ea along with the data from FIG. 28F. FIG. 30C shows 3-site model simulations of Ea vs. ln / 4) using the predictions from FIG. 30D. FIG. 30D shows 3-site model predictions of k at temperatures between 25 and +25°C with the Na K PUMP ON or OFF and without or with the addition of100 mOsm. (see legend in FIG. 30C). The modified Arrhenius model (Eq. A5) shows a common crossover temperature at Tc = -15°C (-20, -9.2).

[0348] Results

[0349] Sodium-potassium pump inhibition with ouabain has a large effect on exchange rate and simultaneously a smaller effect on ADC. First, the results of simultaneous real time NMR hydrophysiology measurements o\' ADCs obtained in the j-di recti on (ADC,. which is perpendicular to the orientation of the spinal cord, and water exchange rates (k) during perturbations with ouabain are demonstrated. Ouabain is a specific inhibitor of the Na+ / K+-ATPase.

[0350] FIGS. 24A-24I are graphs illustrating that sodium-potassium pump inhibition with ouabain has a large effect on exchange rate and simultaneously a smaller effect on ADC. FIGS.24A, 24B, 24D, and 24E are representative real-time recordings on individual samples and show how ouabain in (FIG. 24 A, FIG. 24 D) high (100 / zM) and (FIG. 24B, FIG. 24E) low (2 / zM) concentrations affects (FIG. 24 A, FIG. 24B) ADC in the y-di recti on (presented as percent change from baseline, ADCy ) and (FIG. 24D, FIG. 24E) exchange rate (k). In FIG. 24D and FIG. 24E, arrows and text show when k decreased below 60 s ' and the time from ouabain addition to the effect. FIGS. 24C and 24F are bar graphs of FIG. 24C (A4£> Cy) and FIG. 24F (k), showing the mean across all measurements (bar height), 95% CI of the mean (whiskers), and mean values from each sample (open symbols) for the normal condition, 2, 10, and 100 «M ouabain (n =33, 7, 16, and 5 respectively). For ouabain conditions, data was compiled from the first 3 to 5 measurements after an effect was observed and did not incorporate data from additional treatments or doses. F-inset) The correlation between AADCy and for all measurements in the 2, 10, and 100 uM ouabain-treated groups (right-pointing triangles, circles, and up-pointing triangles, respectively). FIG. 24G shows mean (solid lines) and standard deviation (shaded regions) of realtime exchange rate measurements from a control group under normal conditions (green) and groups treated with 2, 10, and 100 / zM ouabain (lightest to darkest colors) plotted against the time after addition of ouabain. FIG. 24H shows a bar chart of the time from ouabain addition to the time at which k dropped below 60 s '. FIG. 241 is a correlation plot of ADCy vs. k. Data was grouped based on whether measurements occurred before (normal) or after 2, 10, and 100 z M ouabain affected k (see legend).

[0351] FIGS. 32A-32B are graphs illustrating that ADCyand k may be affected by ouabain simultaneously. In particular, FIG. 32A shows mean (solid lines) and standard deviation (shaded regions) of realtime ADCy measurements from a control group under normal conditions (green) and groups treated with 2, 10, and 100ouabain (lightest to darkest colors) plotted against the time after addition of ouabain. Dotted lines show the mean of k for each group, scaled to the maximum and minimum of the mean of ADCy for comparison. FIG. 32B is a histogram of the shift between the drop in ADCy relative to the drop in k from a cross-correlation analysis of 26 out of 28 samples for which there was a significant correlation between ADCy and k (cc > 0.2, p < 0.05. Each set was 11 minutes to acquire and ADCy measurements preceded k measurements. Analysis shows that ADCy dropped either during the same set or the following set after k dropped, showing that ADCy and Z: both dropped within 11 minutes of each other.

[0352] Thus, as demonstrated in FIGS. 24A-24I and 32A-32B, the present inventors investigated the effects of 100, / / M ouabain, which is expected to maximally inhibit the Na+ / K+-ATPase, as well as the effects of 2 and 10, / / M ouabain, which are expected to result in partial inhibition. Ouabain simultaneously decreased ADCy and k (see FIG. 24A, 24 B, 24 D, 24 E; and see also FIGS. 32A-32B). ADCy and k WK affected within 10 minutes after the addition of 100 / / M ouabain (see FIGS. 24A, 24D, 24G, and 24H) and did not recover when the drug was washed out (see FIGS. 24A and 24D). The effect was precipitous, dropping over a duration of 10 minutes or less, limited by temporal resolution of the real time recording (see FIGS. 24D, 24G and 24H). At 10 / / M ouabain, the effect was delayed but still precipitous (see FIGS. 24G and 24H). At 2 / / M ouabain, the effect was delayed even further, but always occurred within 200 min of addition (see FIGS. 24B, 24E, 24G and 24H). The effect was precipitous in some cases (see FIGS. 24B and 24E) but less so overall (see FIG. 24G). Subsequent exposure to higher ouabain concentrations did not produce any further effect (see FIG. 24B and 24E). Nevertheless, the impact of the initial dose of ouabain on ADCy was influenced by the concentration (see FIG. 24C). 2, 10 and 100ouabain decreased ADCy by 5.6 ± 3.1%, 8.6 ± 1.8%, and 10.5 ± 2.2%, respectively (significantly different between groups, p < 0.001, see FIG. 24C). In comparison, k was much more affected by ouabain, but it depended less on the dosage, k is 131 19 s’1under normal conditions. Ouabain reduced k by 72 7% (aver- aged across the three concentrationgroups, FIG. 24F). 2 / / M ouabain reduced k to 43.8 6.8 s-1(significantly different from the other concentration groups, p < 0.001). 10 and 100 / ; M ouabain reduced k to 35.2 6.0 and 35.6 8.2 s-1respectively (not significantly different, p = 0.857). The similar precipitous but delayed effect across dosages (with only a small difference at the lowest 2 / / M concentration) is reminiscent of an “all-or-none” effect. The coincident effect onADCy suggests that cells were swelling when the drop in k occurred. Simulations also predict turning the Na+ / K+ pump off to cause cell swelling as well as membrane depolarization due to the redistribution of ions (see also FIGS. 33A-33B).

[0353] FIGS. 33A-33B are graphs illustrating that a pump-leak model (PLM) implemented according to aspects of the present disclosure provides predictions of cell volume and voltage. In particular, FIG. 33A shows percent change in cell volume and 33B shows voltage predicted with the Na+ / K+ATPase ON or OFF under various media conditions when the PLM runs to steadystate (if applicable). Under the normal condition with Na+ / K+ATPase OFF, the cell continues to swell and does not reach a steady-state. Addition of an osmolyte (+100 mOsm) reduces the volume and hyperpolarizes the cell under normal conditions with Na+4C+ATPase ON, and stabilizes the volume but does not recover the voltage with Na+ / K+ATPase OFF. Replacing NaCl with either sucrose or sodium gluconate reduce the cell volume to a similar level regardless of whether the Na+ / K+ATPase is ON or OFF. However, in the case of voltage, while Na+ / K+ATPase OFF has little effect when NaCl is replaced with sucrose, it causes full depolarization to V = 0 when NaCl is replaced with sodium gluconate.

[0354] Cell swelling could reduce membrane S VR and thereby reduce k through their relationship to permeability (Eq. Al). It was tested whether the effect of ouabain on k could be explained by SVR changes alone by examining correlations between k anAADCy. The present inventors have considered that ADC may be sensitive to cell volume and thereby can be a proxy for SVR changes. First, the relative change from baseline of AAIX'y and AA are plotted for all measurements in the ouabain treated groups (see FIG. 24 F inset). The correlation is significant, but weak (correlation coefficient cc = 0.45, / ? < 0.001) and is insignificant when the 2 yM data is omitted (p = 0.7). A linear fit of the data yields A£ = 1.05x / \ADCy -63.0 %. The slope being near 1 is consistent with Eq. Al and suggests that some of the k variation within groups may be described bySVR variation, measured proximally via ADCy. However, the / '-intercept is shifted well below 0, indicating that SVR changes cannot account for the effect of ouabain on k.

[0355] Second, the data is grouped based on whether k has been affected by ouabain and correlations between the absolute values of ADCy and k are presented. The two groups do not share the same correlation (see FIG. 24 I). ADCy and k showed a weak positive correlation before the effect of ouabain (cc = 0.32, / ? < 0.001) and a weak negative correlation after ouabain took effect (cc = -0.21, p = 0.03). Note that the correlation seen when plotting the percent changes from baseline appears much different when plotting the absolute values (compare FIG. 24 F inset to FIG. 24 I). Weak and different correlations between the groups (i.e., with or without ouabain) indicate the underlying tissue properties affect k wiAADCy differently. The present inventors have found that this could be explained by more complicated microstructural effects since activity and microstructure are interlinked normally and are both affected by Na+ K+-ATPase inhibition.

[0356] Exchange rate is not directly linked to ion transport, voltage, or active water cycling. Certain cotransporters have been shown to cotransport water with ions. A similar mechanism involving water actively cycling along with ions through cotransporters downstream of the Na+ / K+- ATPase was proposed to explain the effect of ouabain on k. The effects of activity independent from microstructure were studied by the inventors. Since cells pump ions to control tonicity and cell volumes under normal conditions, this requires compensating for tonicity with an osmolyte. To do so, an aCSF media was used in which the major ionic component, 128.35 mM NaCl, was replaced with 256.7 mM sucrose (see FIGS. 24A and 24B). The present inventors developed this media recipe based on electrophysiology studies which use 0 NaCl, high sucrose media to maintain viability of adult animal brain slices. Compared to normal aCSF, the 0 NaCl, 256.7mM sucrose media has an equal osmolarity but a higher tonicity (smaller predicted cell volume) because while sucrose remains in the ECS, Na+ and Cl- are not completely partitioned to the ECS normally (see also FIG. 35A-35D discussed below).

[0357] FIGS. 35A-35D illustrate that a 3 -site model predicts ADC and k are affected by tonicity through a dependence on extracellular volume fraction. In particular FIG. 35A shows ECS volume fraction (fo), FIG. 35B shows ADC, FIG. 35C shows k, and FIG. 35D shows the correlation between ADC and k predicted using a 3-compartment model and 3-site exchangemodel when an osmolyte is added to the normal media with Na+ / K+ATPase ON (thinner lines) and OFF (thicker lines).

[0358] FIGS. 25A-25F are graphs illustrating that exchange rate is not directly linked to ion transport, voltage, or active water cycling. In particular, FIGS. 25A-25D show representative recordings of k (blue circles) and percent change in ADCy (open triangles) during experiments involving (FIGS. 25 A and 25C) washing the sample from normal media to media in which NaCl was replaced with equimolar concentration of (FIG. 25 A) sucrose (257 mM) or (FIG. 25C) sodium gluconate (128 mM), and then adding 10 pM ouabain, and (FIGS. 25B and 25D) adding 10 uM ouabain on top of normal medial, waiting for the effect, and then washing to (FIG. 25B) 0 NaCl, 257 mM sucrose media or (FIG. 25D) sodium gluconate media in the presence of 10 uM ouabain. FIGS. 25E and 25F are box plots of (FIG. 25E) AADCy and (FIG. 25F) k under the various conditions.

[0359] As demonstrated in these figures, the 0 NaCl, 257 mM sucrose media caused AADCy to increase by 2.1 ± 1.3% due to the higher tonicity causing cells to shrink slightly (see FIGS. 25A and 25E). If water actively cycles along with ions, then k would decrease when washing to 0 NaCl, 257 mM sucrose media and it should be affected directly by Na+ / K+pump activity. Instead, k increased by 27 ± 24% with the increased tonicity of the 0 NaCl, 257 mM sucrose media, and 10 z / M ouabain had no additional effect (see FIGS. 25 A and 25F). When ouabain was added first, the 0 NaCl, 257 mM sucrose media recovered k (see FIGS.25B and 25F). Therefore, k is not linked to ion transport or Na+ K+ pump activity per se, but rather to the tonicity which is established by its activity.

[0360] In a related experiment, normal aCSF media was washed to media in which the 128.35 mM NaCl was replaced with 128.35 mM sodium gluconate. Gluconate is a monovalent anion and does not pass through the plasma membrane. Due to electroneutrality, for every anion of gluconate in the ECS there will also be a cation (ignoring divalent cations). Therefore, 128.35 mM sodium gluconate adds 256.7 mOsm of osmotic pressure. The resulting pressure is similar to replacing 128.35 mM NaCl with 256.7 mM sucrose. Simulations predict that the cell can maintain voltage polarization with this media, but to depolarize without a change in volume when the Na+ / K+pump is off (see FIGS. 33A-33B discussed below). In this way, the use of sodium gluconate media can help distinguish effects related to voltage from effects related to cellvolume. Washing to sodium gluconate media had no significant effect on ADCy or k (see FIGS. 2.5C, 25E, and 25F).

[0361] Adding 10, / / M ouabain on top of sodium gluconate media caused ADCy to increase, indicating cellular shrinkage. It also caused k to increase to values similar to those obtained under 0 NaCl, 257 mM sucrose media conditions. This is expected based on the similar osmolarities of these medias, but it further implies that cells were regulating volume while the Na / K -ATPase was still active during the sodium gluconate media condition. There was also some increase in the data variability which could be due to slow changes occurring during the measurement and the system not being at a true steady-state. Similar results were obtained when ouabain was added before washing to sodium gluconate media (see FIGS. 25D, 25E, and 25F). Overall, these results indicate that k is related to volumetric conditions or tonicity, but is not directly linked to ion transport, voltage, or active water cycling.

[0362] Exchange rate depends on tonicity. The effects of osmolytes (sucrose and mannitol) on ADCy and Sunder nor mal conditions, as well as after ouabain administration, were studied. The van’t Hoff equation predicts a linear relation- ship between osmotic pressure n and osmolyte concentration c:7T = cRT Q42)

[0363] where R is the ideal gas constant and T is the absolute temperature. This relationship is valid for the dilute sucrose concentrations studied. For reference, the Van’t Hoff equation predicts +100 mOsm at 25°C (or 298.15°K) to increase osmotic pressure by +240 kPa.

[0364] FIGS. 26A-26D are graphs illustrating that osmolytes recover exchange rate. In particular, FIGS 26A and 26C are realtime measurements of (FIG. 26A) percent change in ADCy and (FIG. 26C) k during perturbations with 100 mM sucrose (an osmolyte) before and after the addition of 10 pM ouabain on a representative sample. The presence of 10 pM ouabain is shown by the solid-black line. FIGS. 26B ad 26D are bar graphs showing the statistics across n = 5 samples.

[0365] As shown int these figures, the effect of 100 mOsm sucrose was observed on the same sample before and after adding 10 / / M ouabain. ADCy followed trends expected for cellular shrinking and swelling; it increased in the 100 mOsm hypertonic conditions, recoveredin normal isotonic media, and decreased slightly when ouabain took effect (see FIGS. 26A and 26B). k followed similar trends, although osmolytes were seen to have a much larger effect after the sample was treated with ouabain (see FIGS. 26C and 26D). Starting from the normal condition, 100 mOsm increased k slightly but not significantly, by 14 ± 25%. After ouabain took effect, 100 mOsm increased k much more, by 233 ± 68%. k dropped back down when the osmolyte was washed away in the presence of ouabain (see FIGS. 26C and 26D).

[0366] FIGS. 27A-27F are graphs illustrating that exchange rate depends on tonicity. FIGS.27A, 27B, and 27D are realtime measurements of k (lefty-axis) and AADCy (righty-axis) during osmotic perturbations with (FIGS. 27A and 27B) sucrose or (FIGS. 27D) mannitol concentrations 0, 10, 30, 50, 100, 200 mM and back to 0 mM on representative samples (FIGS.27A) starting from normal and (FIGS. 27B and 27D) in the presence of 10 yM ouabain (shown by solid-back line). FIGS. 27C and 27E show the effect of osmolarity on the mean (symbols) and standard deviations (error bars) of (FIG. 27C) ADCy and (FIG. 27E) k when adding sucrose to samples under normal conditions (n = 3), and when adding sucrose (n = 3) or mannitol (H = 3) to samples treated with 10 «M ouabain (see legend in C). Data from FIGS. 26A-26D involving the addition of 100 mM sucrose in a single step pre-ouabain treatment and post-ouabain treatment are also shown. FIG. 27F shows the correlation between ADCy and Ak for all measurements performed on all samples in each group (see legend). Predicted means (solid lines) and 99% CI (broken lines) were found by regression of 1storder (combined normal samples) and 5thorder (combined ouabain-treated samples) polynomials, with the latter being compared to a sigmoidal logistics function (aqua blue line).

[0367] The above figures demonstrate the effects of sucrose dosages in the range of 10 to 200 mOsm were studied on normal samples and on separate samples treated with 10,uM ouabain (see FIG. 27A and 27B). On normal samples, ADCy and k increased only slightly; the effect was insignificant for dosages up to 100 mOsm but became significant at 200 mOsm (see FIG.27C and 27E). For ouabain-treated samples, ADCy and k increased significantly for doses between 30 mOsm and 100 mOsm. The trend changed at 200 mOsm, with ADCy and k decreasing slightly, although not significantly (see FIGS. 27C and 27E). Comparing ADCy and k between the normal and ouabain-treated groups, both values were significantly lower forouabain-treated samples at 0 mOsm and similar between groups at 100 mOsm. At 200 mOsm, k of ouabain-treated samples was significantly less than that of normal samples (see FIGS. 27E) but AADCy remained similar between sample groups (See FIG. 27C). The effects of mannitol were also studied on ouabain-treated samples (see FIG. 27D). Mannitol (MW= 182 g / mol) is a smaller molecule than sucrose (MW= 342 g / mol) and is also used as a cellular osmolyte. Mannitol and sucrose increased ADCy to similar values at each concentration (see FIG. 27C). This is in spite of sucrose reducing the ADC of pure aCSF media to a greater degree than mannitol due to its greater effect on fluid viscosity (see also FIG. 34). Thus, the compounds’ osmotic effects (cell shrinkage increasing ADCy) are greater than their effects on viscosity (reducing ADC in the extracellular space). Their effects on the ECS diffusivity may become apparent at higher concentrations, e.g. at 200 mM, where the average ADC of samples treated with sucrose is less than those treated with mannitol, although not significantly. Mannitol and sucrose also increased k similarly across concentrations (see FIG. 27E). This indicates that their effect on k is osmotic in nature.

[0368] FIG 34 is a graph illustrating concentration-dependent effects of sucrose and mannitol on ADC of pure aCSF. Spin echo diffusion measurements were performed on aCSF at varying concentrations of sucrose (pink rightward-pointing triangles) or mannitol (aqua upward-pointing triangles) at 25 °C without media circulation. At least three measurements were performed at each concentration using 8 r values spaced linearly from r = 105 to 435 zs (b = 0.0129 to 0.9159ms / / zm2), TR=2 s, and 2000 echoes, all other parameters were the same as standard diffusion measurements performed on spinal cords. Sucrose affects diffusion of water more than mannitol because it is a larger molecule (increased obstruction) and affects viscosity more (increased hydrodynamic interactions).

[0369] It was tested whether the effects of osmolytes were similar or different between normal and ouabain-treated groups by examining correlations between AADCy and A / c (see FIG. 27F). The two groups have different correlations and occupy distinct regions of the plot (see distinct model fits and 95% CI). Data from normal samples appears clustered due to osmolytes having very little effect. For ouabain-treated samples, ADCy and k show a sigmoidal relationship, being highly correlated at intermediate ADCy and weakly correlated at low andhigh ADCy. This behavior is not due to insensitivity to lower and higher exchange rates because, lower exchange rates for ouabain-treated samples were reported at 11°C (see FIG. 28E discussed below) and previously higher exchange rates were reported for normal samples at 35°C (see Fig. I B of Nathan H Williamson, Rea Ravin, Teddy X Cai, Melanie Falgairolle, Michael JO 'Donovan, and Peter J Basser. Water exchange rates measure active transport and homeostasis in neural tissue. PNAS nexus, 2(3):pgad 056, 2023, the entire contents of which are hereby incorporated by reference herein). To completely recover k after ouabain-treatment requires that ADCy increase above baseline.

[0370] The osmotic experiments yielded consistent results overall (see FIGS. 27C and 27E). Differences were observed during the wash from hypertonic media to normal media on samples not treated with ouabain, k recovered when washed from +100 mOsm, but not when washed from +200 mOsm (compare FIG. 26C to FIG. 27A). The inventors have found it likely that the samples maintained viability and ability to maintain and regulate cell volume and exchange rate during the wash in the first case but not in the second. The inventors have also found that this could be because of the larger osmotic change in combination with the longer experiment time and potentially penetration of sucrose during that time, with the wash occurring at roughly 120 minutes in the first case and at roughly 300 minutes in the second case.

[0371] Increasing tonicity reduces cell volume and also SVR. This alone will increase k (see Eq. Al). Activation energies measured from the temperature dependence of k can indicate whether this is the major effect of osmolytes after Na+ / K+- ATPase inhibition because, unlike rate constants, activation energies are independent of the membrane SVR.

[0372] Tonicity affects activation energies of exchange but not of diffusion. The energy barriers of the various water exchange pathways can be probed by observing k at different temperatures.

[0373] FIGS. 28A-28H are graphs illustrating that tonicity affects activation energies of exchange. FIGS 28A-28D illustrate realtime measurements of k (blue circles) and / SADCy (open triangles) during temperature perturbation from 25 °C to 11°C back to 25 °C under (FIG. 28 A) normal, (FIG. 28B) +100 mM sucrose, (FIG. 28C) 10 «M ouabain, (FIG. 28D) andouabain + 100 mM sucrose conditions. FIG. 28E shows results of k recorded at 25°C, 11°C, and again at 25 °C on samples under normal (n = 4), + 100 mOsm (n = 3), 10 zzM ouabain (n = 3), and10 «M ouabain + 100 mOsm (n = 4) conditions. FIG. 28F shows an Arrhenius plot of the inverse of the absolute temperature T1vs. the average k for each condition. Solid lines show average fits of the Arrhenius model (Eq. A3). The slope of the line on the semi-log plot is proportional to Ea. FIGS. 28G and 28H are bar graphs of (FIG. 28G) the natural log of pre-exponential factor A and (FIG. 28H) activation energy Ea estimated from Arrhenius model fits.

[0374] Here, samples were studied under normal conditions, treated with 10 «M ouabain, treated with 100 mM sucrose, and treated with 10 «M ouabain and 100 mM sucrose. For each condition, k was recorded at 25°C and 11°C, and re-recorded at 25°C to test for sample recovery (see FIGS. 28A-28E). k recovered when re-recorded at 25°C (one-way ANOVA, / ? > 0.05). The dependence of k on the absolute temperature T is modeled with the Arrhenius equationk = Aexp(-Ea / RT) (A3)[$375] where A is the pre-exponential factor, Eais the activation energy, and R is the ideal gas constant (see FIG. 28F). Eavalues are similar between the normal samples (Ea= 42.6 ± 6.4 kj / mol) and normal +100 mOsm samples (43.2 ± 2.8 kj / mol), but different from the ouabain-treated samples (25.2 ± 0.8 kj / mol, FIGS. 28G and 28H). Earecovers to 38.5 ± 1.6 kj / mol when +100 mOsm is added to ouabain-treated samples, indicating that the recovery is related to tonicity but not directly related to Na / K -ATPase activity. Since Eavalues are independent of SVR, this also indicates that the major effect of tonicity on k is not through SVR changes. Faster k is associated with higher Ea(compare FIGS. 28E and 28H). This surprising result will be explained later.

[0376] FIGS. 29A-29D are graphs illustrating that tonicity does not affect activation energies of diffusion. In particular, FIG. 29A shows results of ADCy recorded at 25°C and 11°C and rerecorded at 25 °C on samples under normal conditions (n = 4), after addition of 100 mM sucrose (w = 3), after the effect of 10 uM ouabain (w = 3), and after the combined effect of 10,z / M ouabain and 100 mM sucrose (n = 3). FIG. 29B is an Arrhenius plot of the inverse of the absolute temperature T-l vs. the average ADCy for each condition. Solid lines show average fits of the Arrhenius model (similar form to Eq. A3). FIG. 29C is a bar graph of the natural log of pre-exponential factor estimates. FIG. 29D is a bar graph of activation energy estimates.

[0377] FIGS. 29A-29D demonstate that, in contrast to k, the Arrhenius analysis of ADCyyielded similar Eavalues between conditions. Eavalues were lower than the value found for water self-diffusion in artificial cerebrospinal fluid (18 kj / mol) likely due to water in the tissue experiencing more hindrances during the encoding time as its mobility increased with temperature.

[0378] Exchange rate increasing with activation energy is explained by a multisite exchange mechanism. Ea and k increasing together is perhaps surprising. One might expect the opposite case, that a higher energy barrier would be associated with a slower transport rate.However, behavior such as this is commonly seen in heterogeneous systems when the overall rate depends on multiple competing processes with different activation energies and when the relative contributions of these processes can be modulated by and additional component. One signature of this behavior is a common linear dependence between Eaand the natural log of A across conditions:In (A) = m x Ea+ In (A ). (A4)

[0379] This is termed entropy-enthalpy compensation (EEC) because the activation energy Eaand the pre-exponential factor A are related to the enthalpy and entropy of the rate process. EEC implies that the system under any condition can be described by a modified Arrhenius model of the form:k = A ' exp (—Ea / R ( 1 / T - 1 / Tc)) (A5)

[0380] with a common crossover temperature Tc= l / (m R) at which the rate constants are equal to A'.

[0381] FIGS. 30A-30D are graphs that illustrate that exchange rate increasing with activation energy can be explained by a multisite exchange mechanism. FIG. 30A show experimental activation energies plotted vs. the natural log of pre-exponential factors for all samples show a linear dependence described by Eq. A4 with slope m = 0.470 In (s ') (kJ mol) (95% CI = 0.447, 0.493) and y-intercept ln( / l ') = 2.18 In (s1) (95% CI =1.30, 3.06). This is a sign of entropyenthalpy compensation and suggests a common crossover temperature Tc = \ / (m * R) - 273.15 = -17.1 °C (-29, -4.3). FIG. 30B is a semi-log plot of Eq. A5 for a range of Ea along with the data from FIG. 28F. FIG. 30C show 3-site model simulations of Ea vs. In(4) using the predictions from FIG. 30D. FIG. 30D show 3-site model predictions of k at temperatures between -25 and+25°C with the Na K PUMP ON or OFF and without or with the addition of 100 mOsm. (see legend in FIG. 30C). The modified Arrhenius model (Eq. A5) shows a common crossover temperature at Tc = -15°C (-20, -9.2).

[0382] Consistent with EEC, across all conditions the Eaand ln(A) values were linearly related through Eq. A4 (see FIG. 30A). This led to estimates of Tc= 17°C and A' = 9.5 s’1which, when put into Eq. A5, describes the temperature-dependence of k for all systems (see FIG. 30B). Importantly, the EEC phenomena suggests a common mechanism exists under all conditions. In this heterogeneous tissue the mechanism may involve the modulation of multisite exchange pathways by tonicity. Consistent with this mechanism, the present inventors found that the 3 -site model predicts the EEC behavior and a similar Tcand A' (see FIG. 30C and 30D). While samples could not be studied at temperatures down to Tcbeing that it is less than 0°C, simulations did show the exchange rates converging at Tc.

[0383] Elucidating the pump-leak model

[0384] Cells evolved semipermeable membranes to partition solutes while permitting water transport. These membranes enable cells to establish and control their electrochemical potential which is in turn used to maintain homeostasis and perform cellular functions. Part of ion and water homeostasis involves maintaining isotonicity and regulating volumes of intra- and extracellular spaces (ICS and ECS). Here the present inventors have demonstrated how the tonicity alone influences apparent steady-state water exchange. This tonicity dependence was observed regardless of the (non)equilibrium state of the tissue. It was seen when tonicity was established by the cells actively pumping and partitioning ions. It was also seen when tonicity was controlled by adding osmolytes while active ion transport was inhibited. This tonicity dependence does not involve water actively cycling with ions; it was seen even when the majority of the ions were replaced by osmolytes. The inventors have found that passive water transport (i.e., diffusive permeability) can entirely explain how the exchange rate is (indirectly) related to cellular activity.

[0385] Spinal cords under various tonicity conditions showed Arrhenius behavior consistent with entropy-enthalpy compensation (EEC). EEC is commonly found in heterogeneous systems where the apparent rate constant involves multiple inter- connected steps occurring in parallel or sequence and some factor modulates the appearance or dominance of certain steps. In the spinalcord, EEC indicated the existence of multisite exchange. It further indicated that tonicity affects k by modulating the dominance of certain exchange pathways. These results suggested that the mechanism involves aspects related to the heterogeneity of the tissue microstructure.

[0386] The neonatal mouse spinal cord consists mostly of gray matter and little myelinated white matter. Gray matter microstructure is characterized by the presence of branching cellular processes with sub-micron radii, and cell bodies (soma) with radii ranging from a few microns to tens of microns. Recently, Khateri et al. demonstrated with Monte Carlo (MC) simulations that in such a heterogeneous microstructure, DEXSY could be sensitive not uniquely to transmembrane exchange but also to various types of geo- metric exchange such as along branching processes. See Mohammad Khateri, Marco Reisert, Alejandra Sierra, Jussi Tohka, and Valerij G Kiselev. What does fexi measure? NMR in Biomedicine, 35(12):e4804, 2022 (the entire contents of which are hereby incorporated by reference herein). This arises from DEXSY distinguishing exchange between compartments based on water translational mobility in the direction of the magnetic field gradient and not specifically based on location in the ECS or ICS. The distinguishing feature is the length scale of membranes surrounding the water relative to the dephasing length, Jg= (Do / yg)13. Jgis set by the gradient strength g and the self-diffusion coefficient Do and is here approximately 0.8 «m for water at 25°C. Water within membrane structures which are a similar size or smaller than Jgwill appear less mobile than water in larger structures. Water diffusing within sub-micron processes running perpendicular to the gradient direction may appear less mobile on the timescale of diffusion encoding. Water diffusing in larger soma and in processes running parallel to the gradient direction may appear more mobile. Water in the ECS may also appear more mobile due to the space being narrow and tortuous but connected. This motivated a three- site exchange model with exchange between a less mobile ICS compartment (a), a more mobile ICS compartment (b), and an ECS compartments (c), depicted in FIG. 31.

[0387] FIG. 31 illustrates the connection between tonicity and k in the 3 -site model for gray matter. In FIG. 31, compartment a represents cellular processes oriented perpendicular to the gradient direction, compartment b represents cell bodies and processes oriented parallel to the gradient direction, and Compartment c represents the ECS. Water in compartment a is less mobile in the gradient direction due to the diameter of cellular processes being similar to or smaller than the dephasing length, I'g. Water in compartments b and c is more mobile in the gradient direction due tothe membrane length scales in that dimension being larger than kg. Transmembrane exchange kt occurs between the ECS and ICS compartments: a-c and b-c. Geometric exchange kg occurs between ICS compartments: a-b. In this model, k is modulated by tonicity affecting the fraction of ECS compartment c and the relative proportion of water seen exchanging with that compartment.

[0388] Here, the compartment mobility is referring to the average mobility of water within the compartment on the timescale of encoding. It has been ignored that there can be some portion of the water in soma and the ECS which could appear less mobile due to localization near membrane surfaces oriented perpendicular to the gradient direction.

[0389] Diffusion exchange measurements are only sensitive to exchange between compartments with distinct water mobilities. Sensitivity increases as the compartment mobilities shift further apart. Sensitivity to exchange with a compartment also depends on the fraction of the sample volume taken up by that compartment. If there are multiple compartments exchanging with one another, sensitivity to exchange pathways involving a certain compartment will depend on the compartment’s volume fraction and its mobility relative to the other compartments. In this 3-site exchange model for gray matter (see FIG. 31), the apparent k is most sensitive tcrexchange between compartments a and c and to geometric exchange between compartments a and b because these compartment pairs have the most disparate mobilities. A is less sensitive to transmembrane exchange between compartments b and c because these compartments have similar mobilities. Under normal and hypertonic conditions when there is significant ECS, the faster transmembrane exchange pathway (a-c) dominates over the slower geometric exchange pathway (a- b). Hypotonicity shifts water from the ECS (compartment c) to ICS (compartments a and b). This leads to the measurement being less sensitive to transmembrane exchange (a-c) and more sensitive to geometric exchange (a-b). This model provides an explanation for how k could depend on tonicity.

[0390] Previous studies of transmembrane water exchange in cellular systems generally suggest an inverse relationship between diffusive permeability ( / ?) and Ea. Cells devoid of water channels tend to have relatively lower / ? but higher Eabecause permeability depends on membrane fluidity which varies strongly with temperature. For instance, Ka ~ 2 / zm / s (at 25°C) and Ea= 40 kJ / mol were found for Baker’s Yeast in which permeability was low and presumed to be primarily across the lipid bilayer. Aqueous channels across cell membranes such as aquaporins increase permeability but reduce Eatowards that of water self-diffusion Ea= 18 - 20 kj / mol). For instance, Ka and Eavalues near 40 / / m / s (at 25°C) and 25 kJ / mol were consistently reported for red blood cells which have highly permeable plasma membranes due to the high expression of aquaporins. In essence, this trend is due to the presence of water channels altering the dominant mechanism by which water crosses the membrane.

[0391] In contrast to the above trend, the present inventors found a positive relationship between Aand Ea. The k (at 25°C) and Eavalues for isotonic or hypertonic conditions (normal, normal + osmolyte, and ouabain-treated + osmolyte conditions) were around 140-170 s ' and 38-43 kJ / mol respectively and significantly higher than found for hypotonic (ouabain- treated) condition (36 ± 8 s ' and 25.2 ± 0.8 kJ / mol), (see FIGS. 28B and 28D). The trend is consistent with what has been previously reported when comparing normal spinal cords (140 ± 16 s ' and 36 ± 7 kJ mol) to fixed spinal cords (87 ± 10 s ' and 21 ± 8 kJ / mol) which are expected to have minimal ECS. Also consistent with this trend, Fritz and Swift (1967) found using a contrast agent-based NMR method to study water exchange in ex vivo frog sciatic that k = 6.8 s ' and Ea= 46 kJ / mol under normal conditions but decreased below resolution after depolarization with either KC1 or electrical stimulation. See, OG Fritz Jr and TJ Swift. The state of water in polarized and depolarized frog nerves: A proton magnetic resonance study. Biophysical Journal, 7(6):675-687, 1967 (the entire contents of which is hereby incorporated by reference herein). The positive relationship between k and Eawas explained by a multisite exchange mechanism and EEC (see FIG. 30A). The 3 -site model for gray matter (see FIG. 31) was capable of predicting this behavior (see FIG. 30B). The hypotonic (ouabain-treated) condition yielded Eavalues similar to that of water self-diffusion, consistent with geometric exchange involving self-diffusion though the aqueous ICS solution. Further, exchange rate values were roughly consistent with MC simulation findings that soma-process exchange and exchange along branching processes in gray matter may become significant at times greater than 20 ms. The isotonic and hypertonic conditions yielded higher Eavalues consistent with transmembrane exchange through the lipid bilayer.

[0392] It should be noted that varying the lipid bilayer composition can strongly affect its permeability. Polyunsaturated lipids tend to increase permeability whereas cholesterol tends to decrease permeability. Plasma membranes in the CNS contain around 50% cholesterol and the remaining phospholipids are mostly unsaturated. While reported permeability values can vary by over an order of magnitude between labs and techniques, Fluster et al. reported Kd (at 25°C)between 70-400 m s and Ea~ 40 kJ / mol for a range of polyunsaturated lipid bilayers, and Mathai et al. found 40% cholesterol to reduce permeability by 50%. See Daniel Hnster, Albert J Jin, Klaus Arnold, and Klaus Gawrisch. Water permeability of polyunsaturated lipid membranes measured by 17o nmr. Biophysical Journal, 73(2):855— 864, 1997; and John C Mathai, Stephanie Tristram-Nagle, John F Nagle, and Mark L Zeidel. Structural determinants of water permeability through the lipid membrane. The Journal of general physiology, 131(1):69- -76, 2008 (the entire contents of each of which are hereby incorporated by reference herein). Altogether this suggests that K of some lipid bilayers in the CNS could be around 100 / / m s. With the SVR > 1 / / nr1for plasma membranes in gray matter, Eq. Al suggests that A; values greater than 100 s ' are conceivable. The high Eaindicates that aquaporin water channels are not a major pathway.

[0393] While perhaps a high Eacould result from active transport, Eawas also high for the case that active transport was inhibited but tonicity was maintained (ouabain- treated + osmolyte condition). After eliminating transporters and channels, the only transmembrane exchange pathway which remains is the lipid bilayer.

[0394] Ouabain is considered a model for spreading depolarization because it invokes the quintessential “all-or-none” nearly complete CNS cell depolarization accompanied by massive ion and water redistribution between ICS and ECS, hypotonicity, cell swelling, and dramatic ECS shrinkage. The present inventors found ouabain to cause an all-or-none drop of k and ADCy, indicating that these observations are a consequence of spreading depolarization (see FIGS. 24A-24I). The similarity between the effect of ouabain on k in the study and its effect on membrane potential in Balestrino et al. suggested that k and membrane potential may be linked, however, combining perturbations with ouabain and sodium gluconate media indicated that they are only indirectly linked through the effect of membrane potential on tonicity under normal conditions when the media contains chloride (FIGS. 25A-25F). See Maurizio Balestrino, Jacob Young, and Peter Aitken. Block of (na+, k+) atp-ase with ouabain induces spreading depressionlike depolarization in hippocampal slices. Brain research, 838(l-2):37- -44, 1999 (the entire contents of which is hereby incorporated by reference herein). The larger effect of ouabain on k relative to its effect onADCy can be explained by a multisite model (see FIG. 35A-35D), where k is related to the exchange rates of the pathways and ADC is the weighted average over allcompartments. These findings indicate that exchange rate measurements can be a biomarker for spreading depolarization, more sensitive and specific than ADC measurements alone. Results indicate that the mechanism involves the sensitivity of to the hypotonic shift, and the three-site exchange model further suggests that its specifically measuring the dramatic ECS shrink- age during spreading depolarization.

[0395] The present inventors found that the EEC model can describe the data under a range of tonicity conditions (FIGS. 30A-30D). This suggested to the inventors that there exists an EEC -based model to predict tonicity as a function of k. The present inventors derived a model for the enhancement of k at a tonicity (kt) relative to a state of minimum (hypo)tonicity (9 = kt / ko). (See below for more details). After rearranging, the final result is:Ac = In (0) / a, (A6)

[0396] where Ac = Ct - co is defined as the change in effective osmolarity of solutes acting on the membrane, excluding the contribution from naturally-occurring permanently trapped ECS and ICS impermeants. Additionally:a = (8Eat / AcRT) -(5St / AcR),(A7)

[0397] where 6Eat and 6St are the enhancement of the activation energy and entropy by the tonicity at Ac. These can be expanded in a Taylor series about Ac = 0. To first order:a« [Eat] / T -[St], (A8)

[0398] where [Eat] and [St] are related to the first virial coefficients for the entropy and enthalpy of activation. While true only in the limit of Ac -> 0, the two parameters are calculated using \Eat\ = (Ea(c=c ) Ea(c=c )) / (ci co)R and [&] = In (AC= / AC=CQ ) / (ci co) from measurements of Ej and A at c = co and ci.

[0399] For the system of this disclosure, by comparing Eaand A between the ouabain condition and the ouabain + 100 mOsm condition, it was found that [E, / ] = 16.1 °K / mM and [S] = 0.0686 l / 'mM, leading to a ~ 0.0146 1 / mM at 25°C. Based on k and ko from the normal and ouabain conditions respectively, it was found that 6 = 130 / 35 = 3.7, and Eq. A6 predicts Ac = 90 mOsm. This value is consistent with the osmolarity which recovered k of ouabain-treated samples back to normal values (130 x1), found to be 82 mOsm by fitting a linear model to k at sucrose concentrations between 0-100 mM for the ouabain-treated data in FIG. 27E. The presentinventors consider that this ability to quantify tonicity from exchange rate measurements forms the basis for a quantitative biomarker of cell status.

[0400] The MR hydrophysiology methods involved simultaneously collecting ADCyand k. These metrics share a dependence on tonicity, but they also add some distinct information not predicted by changes in ECS fraction alone (compare correlation in FIG. 27F to the 3-site model prediction in FIG. 35D). This added information arises from the inherent differences between the two measurements. Both measurements have the sameand similar diffusion encoding times (r ~ 0.5 ms, corresponding to a diffusion length =TDo ~ 1at25°C). Hence, they similarly encode a blurred landscape of tissue compartments based on water’s t / -di recti onal diffusive mobility on length scales around (g0.8 / / m. However, the exchange rate measurement probes a window of mixing times (tm= 0.2-300 ms corresponding to diffusion lengths ~ 0.7- 25 / / m). The ADCy is averaged over all water compartments in the tissue. In contrast, the exchange rate is sensitive to water which appears to exchange between compartments with different mobility within the mixing time window. They provide different views of the heterogeneous tissue microstructure. The added information can be related to a number of factors including differing sensitivities to pathway permeabilities, non-exchanging compartments, or water compartmental mobilities. Changes in pathway permeabilities will affect k more than ADCy. Changes in the fraction or mobility of water which does not exchange within the mixing time window will affect ADCybut not k. Changes in mobility of water in certain compartments will affect the ADCy, but will also affect how sensitive k is to certain exchange pathways. Alternatively, or in addition to compartments, effects like localization may be considered. The sigmoidal relationship between ADCyand k observed for ouabain-treated tissues at osmolarities from 0 to 200 mOsm. indicates that tonicity affects these factors in a very repeatable way.

[0401] While k of ouabain-treated tissues recovered to normal values with the addition of osmolytes, the combined information from ADCyallowed for differentiating these two tissue states (see FIG. 27F). This indicates that the added information includes some physiologically-regulated tissue properties. When normal tissue was treated with osmolytes, Ak stayed relatively constant whereas AADCyvaried more. It appears that k is related to more tightly regulated tissue properties than AADCy. This is consistent with previous findings of differing behavior between ADCyand k during a stroke model involving insult and recovery from oxygen and glucose deprivation. ADCywasaffected within 10 minutes of initiating OGD and 20 to 30 minutes before & was affected. ADCyrecovered when restoring oxygen and glucose while k remained suppressed.

[0402] Part of this mechanism may involve homeostatic regulation. Cells have mechanisms for maintaining isotonicity under osmotic changes. For instance, regulatory volume decrease mechanisms are activated to compensate for increased osmolarity. Most of these mechanisms utilize ionic gradients established by the Na+ / K+-ATPase and are blocked by ouabain. The weak effect of osmolytes on ADCyand k of normal samples compared to ouabain-treated samples is consistent with the effect of regulatory volume decrease mechanisms (see FIG. 27F). The lack of effect seen when washing to sodium gluconate media despite its higher osmolarity, and the increase in ADC and k when ouabain was added implicates a subset of regulatory volume decrease mechanisms which do not involve chloride (see FIGS. 25C, 25E, and 25F).

[0403] The addition of a third compartment and second exchange pathway provided a minimal model for experimental observations which two-site exchange could not easily explain. The heterogeneity of gray matter tissue, however, leads to many more than three exchanging tissue microenvironments, potentially also deviating from first-order kinetics. In this view of multicompartment tissue heterogeneity, the sensitivity to tissue compartments and exchange pathways can be determined by the experimental parameters such as gradient strengths, durations, and timings. This can explain why reported exchange rates and times for gray matter essentially span the entire range of NMR-accessible timescales.

[0404] According to an implementation, model diffusion in gray matter can further consider multisite exchange’s effect on the time and length scales of the MRI measurement, and what type of exchange (transmembrane or geometric) is being measured (if any). Parsimonious biolphysical models of tissue microstructure and function can be provided.

[0405] The present inventors have demonstrated that k may depend on tonicity and not directly on activity. Entropy-enthalpy compensation indicates the mechanism involves multisite exchange. A three-site exchange model incorporating transmembrane and within-cell (geometric) pathways shows that the exchange rate can be modulated by the effect of tonicity on extracellular space. Transmembrane exchange across the plasma membranes of cell processes in CNS gray matter is fast > 100 s-1. In contrast, geometric exchange is slow, around 40 s-1. This may include exchange between soma and cell processes or along branching processes. Water channelsand potential water cotransporters do not play a significant role in transmembrane exchange, suggesting that the primary pathway is through the lipid bilayer. Results indicate exchange rates can be used to quantify tonicity, and added information from ADC can help to differentiate normal tissue from inactive tissue under all tonicities. Combined water exchange and diffusion measurements can be used as a proxy homeostasis, tonicity, and overall tissue state during normal function, disease, development, aging and trauma.

[0406] Further details on an embodiment of the pump-leak model

[0407] According to an aspect of the present disclosure, a pump-leak model (PLM) model uses the finite difference method to approximate ion fluxes from their governing differential equations for mass conservation. Na+and K+transport actively with a 3:2 stoichiometry. Na+, K+, and Cl’ transport passively based on their electrochemical potential. The net charge of the intracellular impermeants is z = 1. Water permeability is assumed to be much higher than ion permeability and is not modeled directly. Instead, the cell changes volume so that the intracellular osmolarity matches the extracellular osmolarity at the end of each timestep. Voltage is modeled based on the net charge of the intracellular ions and the (constant) capacitance of the membrane. Unless stated otherwise, simulation parameters were the same as in Kay (2017). See Alan R Kay. How cells can control their size by pumping ions. Frontiers in cell and developmental biology, 5:41, 2017 (the entire contents of which is incorporated by reference herein.). Volumes and voltages were taken as the values obtained at the final timestep. This time was sufficiently long for systems to reach steady-state (if there existed a stable steady-state), as determined by volume and voltage not changing when total time was increased by a factor of 10.

[0408] An analytical equation for the steady-state ECS fraction ( □) was developed based on an osmotic balance which includes the contribution of an uncharged, trapped ECS osmolyte (0):

[0409] where x;is number of moles of intracellular impermeants, n is the concentration of small osmolytes in the ECS, Cl0is the concentration of extracellular chloride, F is the Faraday constant, R is the ideal gas constant, and T is the absolute temperature, TC and Cloare assumed equal to that of the bathing media. The ECS and ICS volumes sum to a fixed total volume,M. This equation does not model ion flux and instead assumes a value for the voltage (F). Thepresent inventors used -48 mV for PUMP ON conditions and -10 mV for the PUMP OFF conditions. First, wtot was set using the PUM to find the steady-state cell volume predicted with the PUMP ON but xo= 0 and fo = 0.3. Then xowas arbitrarily set to 1 / 50th of the moles of intracellular impermeants xt. This caused the ECS volume fraction to increase slightly with the PUMP ON. Then the equation, (Eq. SI) was used to predict ECS fraction o at varying osmolarities for the PUMP ON and PUMP OFF conditions (see, e.g., FIG. 35A-35D).

[0410] A 3-compartment model associated with two ICS compartments (a and b) and an ECS compartment (c) was developed for predicting ADC and k (see FIG. 31). Eq. SI was used to define fc=fo. For simplicity, the fractions of the two ICS compartments were set equal, / * =fa= (1 / 2, so that the exchange matrix (defined below) naturally satisfied the detailed balance. The ECS compartment and a more mobile ICS compartment were both given ADCc= ADCb = 1 ms / m2. A less mobile ICS compartment was given ADCa= 0.1 ms / m2. Varying ADC values of the compartments affected the overall ADC, the size of effects on ADC, and the correlation between ADC and k (see FIGS. 35A-35D) but had little effect on overall interpretations. It did not affect the EEC relationship (see FIG. 30C). ADC was modeled as the sum of the ADCs of each compartment multiplied by their volume fraction, ADC =fcADCc+ fbADCb + faADCa. k was modeled by simulating data from the DEXSY experiment and then fitting the exchange model to the data. DEXSY signals were modeled using an operator formalism S = [1, 1, 1] * ODz * OE * OD\ * So, ignoring relaxation. This involved multiplication of matrix exponentials which used the function expm() in MATLAB 2024a. Here, the operators for the first and second diffusion encoding blocks were ODi,z = expm(-&i,2 * D) with D = [ADCc, ADCb, ADCa\~'. * 7(3), where 7(3) is a 3 x 3 identity matrix. Equilibrium magnetization was So = \fc, fb,fa\'. The exchange operator was OE = expm(- / mX) with exchange matrix:

[0411] The exchange matrix included transmembrane exchange ktand geometric exchange kgpathways. Exchange rates were determined by the Arrhenius model (Eq. A3) with T= 298.15 K unless specified otherwise, using Ea= 22 kJ mol and In (A) = 12.52 s ' for kt and Ea= 52 kJ / mol and In (A) = 26.62 s ' for kg. In (A) values were chosen for each Eausing Eq. A4 and the slope and intercept values presented in the caption of FIGS. 30A-30D. Parameters (timings, gradient,b and b protocol, mixing times, etc.) were set based on values used experimentally, k values were estimated using the same analysis method described with respect to the above-discussed NMR hardware, experimental protocol, and analysis methods.

[0412] Derivation of EEC-based model to predict tonicity

[0413] A model is derived relating the exchange rate to tonicity. The model is based on an application of transition state theory to the dynamics of mixtures. First, the enhancement of exchange with tonicity is defined relative to a state of minimum (hypo)tonicity as 0 = kt / ko.Within transition state theory, 6 = exp (-6GtRT') where 3Gt= |G« Go| is the change in Gibbs free energy associated with the difference in osmolarity of impermeable solutes in the extracellular space which increase the tonicity (hence the subscript t). Changes in Gibbs free energy can be decomposed into enthalpic and entropic contributions by its thermodynamic definition 6Gt= 3Eat - T6St. Then:,8St^,-8Eat= expM exp (— ^)K Ki

[0414] To become the Arrhenius model, the present inventors explicitly defined the connections between the change in entropy and the preexponential factors exp (3S R) = At / Ao, and between the change in enthalpy and the activation energies bEat= EatEM. Here, Atand Eatare tonicity-dependent and Ao and EM are evaluated when the system is at a state of minimum (hypo)tonicity, defining c = 0. Then:

[0415] Now the effect of tonicity on exchange can be considered in terms of its separate effect on bEat and bSt. The analytical functions for bEatand bSrwith respect to the osmotic concentration can be obtained by Taylor expansions:

[0416] where < (Ac2) +... refer to second- and higher-order terms and \c^o refers to the term being evaluated in the limit of Ac — 0, i.e., Ct —> co. A first-order approximation was used as a limit so that a two-parameter model can be obtained, but with the downside that the model loses validity as Ac increases above dilute concentrations. The evaluated symbol was dropped for brevity (although still implied). Then:5Eat ~ dEat / dc Ac5St ~ dSt / dc Ac. (S5)

[0417] These two parameters can be calculated from measurements of Eaand A at c = co and ci with Ac = ci by using the relations dEatdc = (Ea(c=ci) - Ea(c=c0)) / Ec and dSt / dc = In (Ac=d / Ac- =co) R / c. These are related to virial coefficients for the entropy and enthalpy of activation by [Eat\ = (dEatdc R and [ ] = (dSt / dcyR. These definitions are combined with Eq. S2 to obtain the final relationship:9= exp(-aAc) (86)

[0418] where:

[0419] From this model, it is also possible to calculate the tonicity Ac as:Ac = In (9) / a (S3)

[0420] According to a system of the present disclosure, by comparing Eaand A of samples after treatment with ouabain to samples after treatment with ouabain and 100 mM sucrose (c = co and c = ci, respectively), it was found that [Eat\ = 16.1 K-mM and [S] = 0.0686 1 / mM, leading to a ~ 0.0146 1 mM at 25°C. Based on E under normal and k from ouabain-treated conditions 6 = 130 / 35, and Eq. S8 predicts Ac = 90 mOsm.

[0421] The use of the terms “a” and “an” and “the” and “at least one” and similar referents in the context of describing the invention (especially in the context of the following claims) are tobe construed to cover both the singular and the plural, unless otherwise indicated herein or clearly contradicted by context. The use of the term “at least one” followed by a list of one or more items (for example, “at least one of A and B”) is to be construed to mean one item selected from the listed items (A or B) or any combination of two or more of the listed items (A and B), unless otherwise indicated herein or clearly contradicted by context. The terms “comprising,” “having,” “including,” and “containing” are to be construed as open-ended terms (i.e., meaning “including, but not limited to,”) unless otherwise noted. Recitation of ranges of values herein are merely intended to serve as a shorthand method of referring individually to each separate value falling within the range, unless otherwise indicated herein, and each separate value is incorporated into the specification as if it were individually recited herein. All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The use of any and all examples, or exemplary language (e.g., “such as”) provided herein, is intended merely to better illuminate the invention and does not pose a limitation on the scope of the invention unless otherwise claimed. No language in the specification should be construed as indicating any non-claimed element as essential to the practice of the invention.

[0422] While preferred implementations of the present disclosure are described herein, variations and combinations of those preferred implementations should be apparent to those of ordinary skill in the art upon reading the foregoing description. The inventors expect skilled artisans to employ such variations as appropriate, and the inventors intend for the aspects of the present disclosure to be practiced beyond those specific implementations that are described herein. Accordingly, the invention of this disclosure includes all modifications and equivalents of the subject matter recited in the claims appended hereto as permitted by applicable law.Moreover, any combination of the above-described elements in all possible variations thereof is encompassed by the present invention unless otherwise indicated herein or otherwise clearly contradicted by context.

[0423] All references, including publications, patent applications, and patents, cited herein are hereby incorporated by reference to the same extent as if each reference were individually and specifically indicated to be incorporated by reference and were set forth in its entirety herein. Including the following background information: Donald DF Loo, Thomas Zeuthen, GrischaChandy, and Ernest M Wright. Cotransport of water by the na+ / glucose cotransporter.Proceedings of the National Academy of Sciences, 93(23): 13367-13370, 1996; AKMeinild, DA Klaerke, DDF Loo, EM Wright, and T Zeuthen. The human na+ -glucose cotransporter is a molecular water pump. The Journal of Physiology, 508(Pt 1):15, 1998; and Thomas Zeuthen and N anna Mac Aulay. Cotransporters as molecular water pumps. International review of cytology, 215:259 284, 2002; GregJStanisz. Diffusion mr in biological systems: tissue compartments and exchange. Israel Journal of chemistry, 43(l-2):33-44, 2003.

Claims

CLAIM(S):

1. A nuclear magnetic resonance (NMR) system for measuring an effective osmolarity / tonicity and characterizing the osmolarity’s effect on water exchange in a specimen, the NMR system comprising:a magnetic resonance (MR) device, the MR device comprising:a magnetic field generator;a radio frequency (RF) transmitter; andan RF receiver; anda processing system coupled to the MR device, the processing system being configured to:receive sample NMR data from the MR device, the sample NMR data corresponding to the specimen;estimate an exchange rate from the NMR data, the exchange rate corresponding to the water exchange through a semipermeable membrane of the specimen; andestimate the effective osmolarity / tonicity based on the estimated exchange rate.

2. The NMR system according to claim 1,wherein magnetic field generator comprises magnetic field gradient generator that is configured to generate at least one of a static magnetic field gradient or a pulsed magnetic field gradient,wherein the RF transmitter is configured to emit RF electromagnetic fields to excite spins in the specimen, andwherein the RF receiver is configured to receive RF electromagnetic field signals emanating from the specimen.

3. The NMR system according to claim 2,wherein the MR device further comprises a pulse sequence generator that is configured to send pulse signals to a RF transmitter amplifier, which is coupled to the RF transmitter, such thatthe sample NMR data corresponds to diffusion exchange spectroscopy (DEXSY) encoded signals,wherein the received sample NMR data is DEXSY data, andwherein processing system is configured to estimate the exchange rate from the DEXSY data using a mathematical modeling framework that is configured to transform the DEXSY data to an exchange rate value estimate.

4. The NMR system according to claim 3,wherein the DEXSY data comprise exchange weighted DEXSY signals, and wherein the mathematical modeling framework comprises estimating the exchange rate from a three-point interpolation between the exchange weighted DEXSY signals acquired at short, intermediate and long mixing times.

5. The NMR system according to claim 3,wherein the processor system is configured to estimate the effective osmolarity / tonicity based on the following equation:Ac = ln(0) / a,where Ac is an osmotic concentration difference from a reference state and is given by Ac = ct— c0, 0 = kt / k0in which k0is the exchange rate at a reference osmolarity co, and ktis the exchange rate at an osmolarity ct, and where a is given by:« « [Eat\ / T ~ ]where:where Eais an activation energy, Tis an absolute temperature of the specimen, R is the universal gas constant, and A is an entropy factor.

6. The NMR system according to claim 3,wherein the processing system is configured to process the DEXSY data to provide an output on a homeostatic steady state exchange rate of the specimen.

7. The NMR system according to claim 1,wherein the MR device is a portable NMR configured with a probe-end in a shape of a wand such that an end of the wand is configured such that it is usable to move over a human scalp to measure aggregate water exchange rate in cortical neurons and other cells of the specimen, the specimen being a human.

8. The NMR system according to claim 1,wherein the MR device is a whole-head low-field magnetic resonance imaging (MRI) system, comprising having an array of RF coils placed on a helmet, along with permanent magnets, which are configured to provide localized imaging of transmembrane water transport in different cortical brain areas of the specimen.

9. The NMR system according to claim 1,wherein the specimen is a biological specimen comprising central nervous system (CNS) cells,wherein the processing system is further configured to indicate deviations in steady-state osmotic or tonicity conditions experienced by the CNS cells based on the estimated effective osmolarity / tonicity.

10. The NMR system according to claim 1,wherein the specimen is a biological specimen comprising central nervous system (CNS) cells,wherein the processing system comprises memory storing statistical data characterizing at least one of homeostatic steady-state conditions, osmolarities, exchange rates, or tonicities for CNS cells in at least one of clinically normal physiological states, clinically abnormal pathological states, clinically diagnosed CNS pathological states caused by at least one of mildtraumatic brain injury (mTBI), brain aneurysms, stroke, migraine aura, or cancer, or clinically required physiological states caused by at least one of anesthesia, sleep, or wakefulness, and wherein the processing system is further configured to compare the estimated osmotic gradient to the statistical data and output a result of the comparison.

11. The NMR system according to claim 10,wherein the processing system is configured to output an assessment, based on the result of the comparison, of a physiological state or physiological changes of the biological specimen.

12. The NMR system according to claim 10,wherein the MR device is a magnetic resonance imaging (MR1) device, and wherein the processing system controls the MRI device to acquire the NMR sample data and to output the result of the comparison on a display as a tonicity map or as an exchange rate map to detect pathological and physiological events as they occur.

13. The NMR system according to claim 1, wherein the exchange rate is estimated by modeling the specimen as having at least two compartments separated by the semipermeable membrane, the water exchange being via the semipermeable membrane.

14. The NMR system according to claim 1, wherein the exchange rate is estimated by modeling the specimen as a multi-site exchange model modeling at least three compartments, with at least two of the compartments separated by the semipermeable membrane, the water exchange being via the semipermeable membrane.

15. The NMR system according to claim 1, wherein the specimen is non-biological.

16. The NMR system according to claim 1, wherein the semipermeable membrane of the specimen comprises a reverse osmosis membrane for filtration17. A method for non-invasively measuring a transmembrane exchange rate of endogenous water through a semipermeable membrane in a specimen under steady-state or non-steady-state conditions in near-real time, the specimen comprising a plurality of compartments, with at least two of the compartments being separated by the semipermeable membrane, the method comprising:receive sample nuclear magnetic resonance (NMR) data corresponding to the specimen; estimate the transmembrane exchange rate from the NMR data, the exchange rate corresponding to the endogenous water exchange through the semipermeable membrane of the specimen; andestimate a value characterizing an effective osmolarity or tonicity based on the estimated exchange rate.

18. The method of claim 17, wherein the method is performed using a magnetic resonance (MR) device, the MR device comprising:a magnetic field generator;a radio frequency (RF) transmitter;a RF receiver; anda pulse sequence generator that sends pulse signals to a RF transmitter amplifier, which is coupled to the RF transmitter, such that the emitted RF electromagnetic fields correspond to diffusion exchange spectroscopy (DEXSY) encoded signals,wherein the magnetic field generator generates a static magnetic field gradient or a pulsed magnetic field gradient t, which are applied to the specimenwherein the RF transmitter is configured to emit RF electromagnetic fields at the specimen to excite magnetic spins in the specimen, andwherein the RF receiver is configured to receive RF electromagnetic field signals emanating from the specimen.wherein the received sample NMR data is DEXSY data, andwherein the method further comprises estimating the exchange rate from the DEXSY data using a mathematical modeling framework that is configured to transform the DEXSY data to an exchange rate value estimate.

19. The method of claim 17,wherein the specimen is a biological specimen comprising central nervous system (CNS) cells,wherein the method further comprises comparing the estimated osmotic gradient to statistical data and outputting a result of the comparison, andwherein the statistical data comprises data characterizing at least one of homeostatic steady-state conditions, osmolarities, exchange rates, or tonicities for CNS cells in at least one of clinically normal physiological states, clinically abnormal pathological states, clinically diagnosed CNS pathological states caused by at least one of mild traumatic brain injury (mTBI), brain aneurysms, stroke, migraine aura, or cancer, or clinically required physiological states caused by at least one of anesthesia, sleep, or wakefulness, or varying degrees of sensory relaxation or stimulation.

20. The method according to claim 17,wherein the effective osmolarity or tonicity is estimated based on the following equation:Ac = ln(0) / a,where Ac is an osmotic concentration difference from a reference state and is given by Ac = ct— c0, 6 = kt / k0in which k0is the exchange rate at a reference osmolarity co, and ktis the exchange rate at an osmolarity ct, and where a is given by:« - [Eat] / T ~ [St]where:where A’ais an activation energy, T is an absolute temperature of the specimen, R is the universal gas constant, and A is an entropy factor.

21. The method of claim 17, wherein estimating the value characterizing the effective osmolarity or tonicity comprises estimating a value of an osmotic gradient.

22. A method for non-invasively measuring an exchange ratio of endogenous water between at least three compartments or at least three volume fractions of a specimen under steady-state ornon- steady -state conditions in near-real time, the specimen comprising a semipermeable membrane, the method comprisingreceive sample nuclear magnetic resonance (NMR) data corresponding to the specimen; estimate the exchange rate from the NMR data, the exchange rate corresponding to a transmembrane exchange of the endogenous water through the semipermeable membrane of the specimen and / or to geometric exchange of the endogenous water between compartments and / or volume fractions of the specimen; andestimate a value characterizing an effective osmolarity or tonicity based on the estimated exchange rate.

23. A method for non-invasively measuring a volume ratio between at least three compartments or at least three volume fractions of a specimen under steady-state or non-steadystate conditions in near-real time, the specimen comprising a semipermeable membrane, the method comprisingreceive sample nuclear magnetic resonance (NMR) data corresponding to the specimen; estimate the exchange rate from the NMR data, the exchange rate corresponding to a transmembrane exchange of endogenous water through the semipermeable membrane of the specimen and / or to geometric exchange of the endogenous water between compartments and / or volume fractions of the specimen; andestimate the volume ratio based on the estimated exchange rate.

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