Nuclear magnetic resonance methods and systems for non-invasive shear measurments of a material

Abstract

A method and system of characterizing a property of a sample including providing a magnet with a static magnetic field and a constant gradient where at least a portion of the sample defining a sensitive region is in the constant gradient, inducing a shear wave or shear waves in the sample in at least the sensitive region, generating an NMR pulse sequence, acquiring at least one echo from the pulse sequence from the sensitive region, measuring motion-induced phase interference in the NMR signal of the at least one acquired echo, and relating the measured phase interference to a property of the sample. The induced shear wave can be a transient shear wave, with a delay introduced before RF excitation in the NMR pulse sequence. Continuous shear waves can also be induced.

Description

NUCLEAR MAGNETIC RESONANCE METHODS AND SYSTEMS FOR NON-INVASIVE SHEAR MEASURMENTS OF A MATERIALFIELD

[0001] In one of its aspects, the present disclosure relates generally to nuclear magnetic resonance method and system for non-invasive measurements of a material.BACKGROUND

[0002] Magnetic resonance elastography (MRE) is a sophisticated technique that uses conventional phase-contrast magnetic resonance imaging (MRI) sequences, synchronized with harmonic sample displacements, to analyze the mechanical properties of tissues and assess their dynamic properties

[0001] ,

[0003] Elastography is a growing area of research in which certain imaging modalities, such as MRI, are employed to measure the response of materials to an external (typically dynamic) stress allowing for quantitative estimation of viscoelastic properties. This has tremendous potential in a clinical setting, as changes in tissue viscoelasticity can be indicative of myriad health conditions.

[0004] Traditional MRE techniques commonly employ phase-contrast MRI sequences with time-varying magnetic field gradients to measure displacements within submillimeter "voxels," enabling the generation of 2D displacement maps. However, these techniques rely on large and costly clinical MRI scanners, which are often in high demand.SUMMARY

[0005] The present disclosure, in one aspect, relates to a method of using a constant gradient portable magnet array to detect shear waves, where changes in viscoelastic properties influence the velocity distribution and amount of phase interference within a sample in a sensitive volume. In one embodiment, a dependence of a magnetic resonance signal on shear wavelength is used. In another embodiment, a frequencysweep method is used. In another embodiment, direct measurements of dynamic properties are carried out through MR signals modulated by phase interference due to the presence of a velocity distribution.

[0006] The present disclosure, in one aspect, relates to methods which use phase interference in a sensitive region of a constant gradient MR sensor to encode information on the shear wavelength in a sample. A shorter wavelength corresponds to greater phase interference and modulation of MR signal.

[0007] The present disclosure, in another aspect, relates to a method for the detection and characterization of shear waves that employs a portable magnetic resonance instrument to observe the effects of motion-induced phase interference on the detected magnetic resonance signal. In another embodiment, magnetic resonance methods of the present invention can be used for the detection and characterization of shear waves propagating in soft elastic solids. In one embodiment, the present invention includes sample excitation, portable MR instrumentation, and methods for MR data collection and analysis.

[0008] In one aspect, the present disclosure relates to a method and system of characterizing a property of a sample, including providing a magnet with a static magnetic field and a constant gradient where at least a portion of the sample defining a sensitive region is in the constant gradient, inducing a shear wave in the sample in at least the sensitive region, generating an NMR pulse sequence, acquiring at least one echo from the pulse sequence from the sensitive region, measuring change in the NMR signal of the at least one acquired echo, and relating the measured motion-induced change to a property of the sample. In one embodiment, a processing unit is used to process the generated NMR signal, and the processed signals can be displayed on a display unit. In one aspect, the shear wave is a transient shear wave. In another aspect, a delay is introduced before RF excitation in the NMR pulse sequence. In another aspect, a continuous series of shear waves is induced.

[0009] In another aspect, the present disclosure relates to an NMR system including a portable unilateral magnetic having a constant gradient perpendicular to a surface of the magnet.BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Embodiments of the present invention will be described with reference to the accompanying drawings, wherein like reference numerals and reference letters denote like parts, and in which:

[0011] FIG. 1 is a schematic diagram of an MR set-up for use in an aspect of the present disclosure;

[0012] FIG. 2 is an end view schematic diagram of the MR set-up of FIG. 1 with an actuator shown for use in an aspect of the present disclosure;

[0013] FIG. 3 is a schematic diagram of an MR set-up for use in an aspect of the present disclosure for scanning a human foot;

[0014] FIG. 4 are two graphs of particle displacement over position of an actuated sample;

[0015] FIG. 5 is an MR sequence usable in an aspect of the present disclosure;

[0016] FIG. 6 is a graph of first echo magnitude at various tau times and three 60 Hz- wave amplitudes (a computer simulation);

[0017] FIG. 7 is a graph of first echo magnitude at various tau times and three 90 Hz wave amplitudes (a computer simulation);

[0018] FIG. 8 is a graph of first echo magnitude at tau time of 1.8 ms and various frequencies (experiment on an 8% ballistic gel) showing the wavelength-dependent behavior, yielding an approx.140 cm / s wavespeed;

[0019] FIG. 9 is a graph of first echo magnitude at tau time of 1.7 ms and various frequencies (experiment);

[0020] FIG. 10 is a graph of first echo magnitude at tau time of 1.9 ms and various frequencies (experiment);

[0021] FIG. 11 is a graph of simulated effects of pulse arrival on MR signal magnitude for a 100 Hz sinusoidal pulse with an amplitude of 5 m, excited 11.5 cm from the sensitive region. The effects are shown for wave speeds of cm s-1(solid line), 550 cm s-1(dashed line), cm s-1(dash-dot line), and cm s-1(dotted line);

[0022] FIG. 12 is a schematic of the transient portable MR elastometry apparatus according to an aspect of the present disclosure;

[0023] FIG. 13 is an illustration of MR pulse sequence that was employed in experiments of the present disclosure;

[0024] FIG. 14 is a graph comparison of MR signal magnitude vs. delay time, A, for a 100 Hz acoustic pulse excited at a distance of L = 11 .5 cm from the MR sensor when adding 1 (solid line), 2 (dashed line), 4 (dash-dot line), and 8 (dotted line) echoes;

[0025] FIG. 15 is a graph of normalized MR signal magnitude (smoothened by a Savitzky- Golay filter) plotted against delay time for each of the tissue mimicking gels. The gels are plotted in order of decreasing stiffness. The stiffest gel (gel 2) is shown by the solid line, followed by gel 3 (dashed line), gel 4 (dash-dot line), and gel 5 (dotted line);

[0026] FIG. 16 is a graph of optical sensor measurements of displacement vs. time for each of the tissue mimicking gels. Gel 2 is shown by the solid line followed by gel 3 (dashed line), gel 4 (dash-dot line), and gel 5 (dotted line);

[0027] FIG. 17 is a comparison of shear wave speeds as a plot of MR sensor measurements against optical sensor measurements; and FIG. 18 is an image of T2 distributions at various delays for gel 2 excited with a 100 Hz acoustic pulse with a regularization parameter, = 1. Note the disappearance of the main peak that corresponds with the arrival of the shear wave in the sensitive region.DETAILED DESCRIPTION

[0028] Various systems and methods will be described below to provide an example of an embodiment of each claimed invention. No embodiment described below limits any claimed invention and any claimed invention may cover systems or methods that differ from those described below. The claimed inventions are not limited to systems or methods having all of the features of any one system or method described below or to features common to multiple or all of the systems and methods described below. It ispossible that a system or method described below is not an embodiment of any claimed invention. Any invention disclosed in a system or method described below that is not claimed in this document may be the subject matter of another protective instrument, for example, a continuing patent application, and the applicants, inventors or owners do not intend to abandon, disclaim, or dedicate to the public any such invention by its disclosure in this document.

[0029] While the teaching herein includes illustrative embodiments and examples of some aspects of an invention, the description is not intended to be construed in a limiting sense. Thus, various modifications of the illustrative embodiments, as well as other embodiments of the invention, may be apparent to persons skilled in the art upon reference to this description. It is therefore contemplated that the appended claims will cover any such modifications or embodiments.

[0030] All publications, patents, and patent applications referred to herein are incorporated by reference in their entirety to the same extent as if each individual publication, patent, or patent application was specifically and individually indicated to be incorporated by reference in its entirety.

[0031] The present invention, in one embodiment, uses a portable NMR instrument which includes a handheld sensor (a combination of a magnet array and an RF coil) that can be applied to a sample of arbitrary size, and an NMR console to excite and collect NMR signal. An NMR signal is generated from a thin sensitive volume at a distance of, for example, 1 -2 cm from the surface of the magnet array. Unlike an MRI scan covering an extensive area, this is a localized measurement but it carries the same NMR information that can be 1 D-resolved.

[0032] In one embodiment of a set-up according to the present invention, a portable MR instrument includes an array of permanent magnets arranged in a configuration to provide an optimal (constant) magnetic field gradient over a finite sensitive region. The thickness of the excited slice in which the instrument is sensitive to motion is determined by the strength of the magnetic field gradient and the bandwidth of the radiofrequency (RF)probe. The instrument can be capable of providing 1 D spatial resolution in the direction of the magnetic field gradient.

[0033] By inducing shear waves with particle displacement in the direction of the magnetic field gradient using acoustic actuators, the MR signal becomes sensitive to the velocity distribution present in the sensitive region, which in turn is dependent on the shear wave velocity, and therefore, shear modulus of the material. Changes in frequency, and therefore wavelength, lead to changes in the velocity distribution and the amount of phase interference within the sensitive region. This causes an overall modulation of signal magnitude dependent on the shear properties of the sample.

[0034] Through careful control of experimental parameters such as the "spin-echo time", and the amplitude and frequency of vibrations, one can manipulate the effects of the shear waves on the observed signal, therefore allowing for the encoding of the shear wave velocity, and by extension, the shear modulus of the sample.

[0035] Measurements by the present inventors demonstrate the potential of a simple measurement capable of directly measuring the shear wavelength in biological tissues and can already achieve a rough estimate that aligns with expectations. In another embodiment, methods for characterizing shear properties can be combined with conventional MR measurements of relaxation and diffusion, providing an additional layer of information that can be useful in clinical applications.

[0036] The behaviour of an MR signal when a shear wave propagates through a sensitive region (also sometimes referred to as a sensitive volume) is described as follows. For a plane wave propagating in an isotropic, homogeneous, and linear viscoelastic medium:Displacement:

[0037] Attenuation coefficient and shear wave speed depend on the shear storage and loss modulus:Shear wave speed Attenuation(Eq. 2)

[0038] An integrated MR signal is described as:where A is wavelength, A is amplitude, G is gradient strength, is one half of echo duration, co is cyclic frequency, and [3 is phase angle changing from 0 to 2KL / , with L equal to the sensitive volume size in the direction of the wave propagation.

[0039] In one embodiment, the present invention utilizes a portable magnetic resonance instrument and leverages the phenomenon of phase-interference, typically minimized in conventional MRI. Instead of collecting 2D spatially resolved measurements from numerous voxels, this approach acquires signals by integrating over a finite sensitive region. The thickness of this region is inversely proportional to the strength of the magnetic field gradient and the bandwidth of radiofrequency excitation. In one embodiment of the present invention, assumptions include a short echo time (compared to vibration period) and negligible attenuation (within the sensitive volume).

[0040] Referring to FIG. 1 and FIG. 2, an MR set-up for use in an embodiment of the present invention is depicted. The set-up includes a configuration of several smallpermanent magnets 6 which are be optimized to provide a region 3 (outlined in dashed lines in FIG. 1 and as a solid rectangle in FIG. 2) of constant gradient. The set-up also includes a radio frequency coil (RF coil) 2. Region 3 is also referred to as a sensitive volume or sensitive region and serves as an integrator and carries information on the spatial distribution of velocities within the region of interest. Consider a linear viscoelastic homogenous medium with a plane wave propagating through the MR sensitive region. The displacement (perpendicular to the propagation of the wave) is dependent on the shear wave speed and attenuation coefficient, which in turn are dependent on the viscoelastic properties of the material. An actuator 1 is placed at a fixed distance from the NMR sensor in FIG. 2.

[0041] Uses for the present invention include improving clinical outcomes by offering additional means for detecting and characterizing changes in the mechanical properties of biological tissues, including near-surface tissues, which can be indicative of various health conditions. Examples include characterizing and detecting diabetic foot ulcers and assessing liver stiffness. In another embodiment, methods of the present invention can be applied to any NMR-sensitive material where bulk measurements of shear properties are desired from regions of interest 1 -2 cm beneath a surface.

[0042] The set-up of FIG. 2 can be used as a point-of-care system to take a scan of a foot 16 as depicted in FIG. 3 by using shear wave propagation through the tissue of foot 16: wave propagates the foot 16 while the tissue of foot 16 is being shaken in the perpendicular direction by actuator 1 to induce shear waves. Shear waves have slow wave speeds in tissues (1-10 m / s), the wave speeds strongly vary in response to changes in the tissue, making them a sensitive probing tool. The whole setup is designed as a step-on device with, for example, 15-20 minutes per location, aiming at probing 3-4 locations in a 1 -hour appointment. In one embodiment of the present invention, the measurement of foot 16 is a near-surface measurement.

[0043] In one embodiment of the present invention, to sensitize an MR signal to elasticity, one can directly measure the displacement waveforms with portable MR using the MR signal phase. For the shear wave detection, a faster measurement approach can be usedin one embodiment by exploring the shear wave propagation along foot 16 (sensitive volume). The slow wave speeds mean that the sensitive volume extent along foot 16 becomes comparable with the wavelength (FIG.4), resulting in a distribution of the displacement-dependent MR signal phase over the sensitive volume extent, and the integrated signal dependence on the wavelength and the foot 16 tissue’s elastic modulus (the so-called “phase interference”). In another embodiment, a measurement approach uses the phase interference in combination with a pulsed acoustic excitation that can further reduce measurement time.

[0044] In another embodiment, the present invention relates to a portable MR elastometer for a spot measurement of tissue stiffness (or elasticity) and fluid content in one embodiment in a 4-cm3location. Portable MR is hundreds of times less expensive to build than an MRI scanner, and it can fit in a doctor’s office. Its sensor in one embodiment is the size of a brick, where the foot is placed on the sensor in various positions for foot examination (heel pad, toe pad, etc.) to detect and quantify lesion grade and its relationship to increased stiffness of the skin tissue in the vicinity of the lesion. In one embodiment, the magnet array generates a 40-60 G / cm gradient through a 15-20 mm wide, 8 - 12 mm-deep sensitive volume, permitting a 1 D-resolved depth measurement. In another embodiment, the measurement time is 15-20 min per location, probing 3-4 locations in a 1 hour-appointment. Portable NMR devices usable in the present invention can use simple spin-echo sequences (FIG. 5), such as a variation of the “CPMG sequences”, with signal intensity and decay reporting information on the sample amount and structure. Several acquisition schemes are possible including Fixed T , fixed amplitude, variable frequency, Fixed T, fixed frequency, variable amplitude, Variable T, fixed frequency, fixed amplitude, and Fixed T, variable frequency, variable amplitude.

[0045] In a simulated example, consider a shear wave that propagates through a sensitive volume of size, L = 2 cm, with a speed, c = 150 cm / s. Complete decay only occurs when the wavelength occupies the full sensitive volume. Amplitude determines the frequency (in tau space) of magnitude oscillations. FIG. 6 and FIG. 7 show computer- simulated dependence of the first echo magnitude on T at three wave amplitudes ascalculated for wave frequencies of 60 and 90 Hz, respectively. FIG.8 presents an experimentally measured first echo magnitude vs the wave frequency at ? of 1.8 ms, demonstrating the NMR magnitude dependence on the wavelength size and yielding the wave speed of approx.140 cm / s (in agreement with the expected wave speeds in the 8% ballistic gel used in measurements). FIG. 9 and FIG. 10 show experimental data acquired at T of 1 .7 and 1 .9 ms, respectively.

[0046] Since the data are acquired in the presence of the constant gradient, echo shapes can be used to generate a simple one-dimensional imaging (profile) across the sensitive volume. One-shot profiling measurements through the sensitive volume can non- invasively acquire spatially resolved data on fluid content, diffusion, and MR properties from biological samples including human skin.

[0047] Instead of measuring velocity distributions directly using spatially resolved measurements, methods of the present invention employ equations for velocity distributions in the MR signal equations. This enables the prediction of the MR signal response, which is dependent on the material's shear mechanical properties. As a result, this method offers an efficient and cost-effective alternative to traditional MRE, as it enables the assessment of elastic properties using a portable device and novel signal processing techniques.

[0048] Most portable NMR devices get information from a thin, approximately 1 mm-thick sensitive volume. The thickness is determined by a stray magnetic field gradient and an RF coil size and pulse duration. In one embodiment, the reduction of the gradient from, for example, 250 G / cm to, for example, 50 G / cm leads to a proportional extension of the sensitive volume from 1.8 mm to 8 mm. This also enhances the signal from fluids in the sample due to the reduction in the diffusive attenuation. Both changes are beneficial to the measurement: extending the sensitive volume means a deeper reach, the enhanced signal from liquids leads to greater sensitivity to fluids in for example edemas, and the increase in signal-to-noise ratio results in a shorter measurement time.

[0049] A prominent feature of an instrument according to an embodiment of the present invention is that the data collected during the acoustic activation carries information simultaneously on three distinct facets of the tissue under investigation. First, the elasticity encoded in the signal phase. Second, tissue parameters (fluid amount; structure- related info) is encoded in the signal decay (intensity; T1 , T2 relaxation times). Third, the data is spatially resolved across the sensitive volume, enabling a simple 1 D-profiling of the elasticity and NMR parameters. Collecting and analyzing the data leads to a better understanding of the correlation between the tissue’s NMR and mechanical properties, and to a better diagnosis.Wave Propagation

[0050] Exciting a sample with an acoustic pulse results in the generation of both longitudinal and shear wave components. In longitudinal waves, the displacements of particles are parallel to the direction of wave propagation (and the direction of applied stress). In a linearly elastic thin rod under a 1 D stress, the longitudinal wave speed is given by the following equation,where E is the Young’s modulus, and p is the density of the material. Longitudinal waves propagate significantly faster than shear waves; therefore, they have longer wavelengths at the same frequency.

[0051] Because shear waves have shorter wavelengths, they cause more phase interference and have a greater influence on the magnitude of an MR signal. The shear wave speed is given by the following expression,where G is the shear modulus of the material. The longitudinal and shear modulus are related through the Poisson ratio, v, (a measure of the ratio between transverse and axial strain) of the material as follows;E = 2G(1 + v) (Eq. 6)

[0052] See FIG. 11 for a graph of the effects of pulse arrival on MR signal magnitude. If the material has a significant viscous component, the wave speed becomes dependent on frequency. For a homogeneous isotropic Kelvin-Voigt body, the shear wave speed is given as follows,where r) is the shear viscosity of the sample.

[0053] Given that in one embodiment of the present invention the MR sensitive region is close to the surface of the sample, it is also important to consider the effects of Rayleigh (surface) waves. Rayleigh waves contain both longitudinal and transverse components and have amplitudes that decay exponentially with depth [2], The surface wave velocity is related to the shear modulus of a material as follows,0.87 + 1.12 / / G l)~ TT V 7 (Eq. 8)

[0054] For a Poisson ratio, v = 0.5, this simplifies to, CR = 0.95 3cs. (Eq. 9)

[0055] Therefore, the shear wave is followed by a Rayleigh wave. In the present embodiment, the present inventors are only concerned with the shear wave arrival.METHODSAcoustic Excitation

[0056] An experimental setup according to an embodiment of the present invention is depicted in FIG. 12. The present inventors employed an electromagnetic actuator 20, which in the present embodiment is a 2007E mini electromagnetic shaker (The Modal Shop, OH) with a built-in power amplifier to excite samples with acoustic pulses. Actuator 20 is suspended approximately 30 cm above the surface of the sample 22 and is connected to an excitation stinger 24, with end 26 of stinger 24 in contact with the surface of sample 22. Actuator 20 is connected to stinger 24 for two main reasons. First, it reduces side loads, ensuring that pulses are excited in a single direction. Second, it allows actuator 20, which is magnetic, to be positioned a safe distance from magnet array 28 while transmitting vibrations without significant losses.

[0057] Alternative methods of acoustic excitation, such as piezoelectric and pneumatic actuators, were considered; however, the present inventors found that the electromagnetic actuator 20 was most reliable for exciting pulses with sufficient amplitudes at a range of frequencies.

[0058] Using signal generator 30, actuator 20 is driven using the burst function on a 33522A 30 MHz arbitrary waveform generator (Agilent, CA). In operation, in one embodiment, pulses were excited consisting of 1 cycle of a sinusoidal waveform with a frequency of 100 Hz, corresponding to a pulse duration of 10 ms. In one embodiment, the pulses were repeated every 500 ms, allowing enough time for the attenuation of the reflected waves which also interfere with the MR signal.Portable MR Instrumentation

[0059] In the present embodiment, unilateral three-magnet array 28 with a constant gradient of 2.54 Tm-1perpendicular to surface 32 was used to acquire the MR signal [3], A 2x2 cm surface RF coil 34 consisting of four turns of copper wire was attached approximately 2 cm from surface 32 of magnet array 28 and tuned to a frequency of 5.26MHz, corresponding to a static magnetic field strength of 0.1235 T. FR coil 34 had a quality factor of 60, measured using the reflection mode method [4], In the present embodiment, the MR sensor including magnet array 28 and RF coil 34 was suspended at a fixed distance, D = 11 .5 cm, from the point of acoustic excitation.

[0060] The present inventors connected the RF tuning and matching network to a duplexer, with the transmit end connected to a 250 W RF pulse amplifier (Tomco, AU), and the receive end to the input of a pre-amplifier (Miteq, NY). The output of the preamplifier was connected through a 10.7 MHz low-pass filter to a LapNMR console (Tecmag, TX).

[0061] While the MR sensor is very portable and can be carried in the hand of a user, the accompanying electronics such as NMR console 36 and RF amplifier are significantly larger and must be setup on a tabletop or cart. In other embodiments, these components are miniaturized [5],Optical Sensor

[0062] In the present embodiment, the present inventors used a KDP-300 retro-reflective optical sensor (MTI Instruments, NY) sensitive to sub-micrometer displacements to provide an additional comparison of the MR measurements of shear wave speed. The sensor was suspended above the surface of the sample at the same position as the MR sensor. The oscilloscope traces were acquired with 16 averages and converted to displacement vs. time curves using calibration curves from the manufacturer. Although useful as a comparison, the optical sensor only provides information on the response at the surface of the sample, compared to the MR instrument which is capable of measurements 1 -2 cm below the surface, making it particularly useful for characterization of stratified samples.MR Acquisition Procedure

[0063] The present inventors programmed pulse sequences using NTNMR pulse programming software (Tecmag, TX). The sequence was triggered by the external trigger function on the signalgenerator simultaneously with the acoustic excitation pulse. A series of 200 delays, incremented by 0.25 ms, was inserted in the pulse sequence immediately after the external trigger prior to the excitation of RF pulses. The present inventors determined the 90° pulse width using a quadrature echo sequence, ensuring that the magnitudes of the first three echoes were in a 1 :1.5: 1.5 ratio [6], 3.9 s pulses were attenuated by 17 and 11 dB to generate 90° and 180° pulses, respectively. In these experiments, the shear wave propagated in the horizontal x-direction along the sensitive region of extent, L = 2 cm. The thickness of the region in the y-direction, determined by the gradient strength and the duration of the RF pulse, was 2.4 mm. The shear wave displacement in the y-direction never exceeded 10 m, being contained entirely within the slice. This eliminated the possibility of a partial excitation recently reported in experiments in which signal modulation in response to mechanical vibrations was due to amplitudes greater than the thickness of the excited slice [7],

[0064] The present inventors used a variation of a Carr Purcell Meiboom Gill (CPMG) echo train (depicted in FIG. 13) to acquire the MR signal [8], The first spin echo was acquired with an echo time (TE = 2r) of 2 ms, long enough to be sensitive to the arrival of the wave in the sensitive region. FIG. 13 is an MR pulse sequence that was employed in all experiments. The sequence was triggered externally at the moment of acoustic excitation. A variable delay, A, was introduced to allow the acoustic wave sufficient time to propagate to the sensitive region before RF excitation. The delay A spanned 200 values evenly spaced by 0.25 ms. The first echo was acquired with an echo time of 2T1 = 1 ms, followed by acquisition of subsequent echoes (n = 256) at an echo time of 2T2 = 0.2 ms. The sequence was repeated for N = 16 signal averages at each delay.

[0065] Subsequent echoes (n = 128) were acquired with the shortest possible echo time of 0.2 ms (restricted by the dead time of the RF probe) and added together in signal processing. The present inventors add echoes for two reasons. First, adding echoes is an effective method for enhancing the SNR [9], Second, modulation of magnitude is more prominent in subsequent echoes due to additional coherence pathways that lead to the destruction of magnetization, making it easier to identify the arrival of the pulse. Furthermore, the echo trains carry information on the T2 relaxation time and the selfdiffusion coefficient. FIG. 14 shows a comparison of signal magnitude versus delay timeusing 1 , 2, 4, and 8 echoes for a 100 Hz pulse excited at a distance of 11 .5 cm from the MR sensor. The change in magnitude using only the first echo is significant; however, adding as few as two echoes can provide substantial improvement, making it easier to identify the arrival time.Tissue Mimicking Phantoms

[0066] The present inventors used synthetic medical gels (Humimic, SC) to test the transient elastometry technique. Tissue-mimicking gel samples were positioned on a vibration-isolating elastomer. Acoustic pulses were delivered to the samples through a 30.48 cm excitation stinger connected to an electromagnetic actuator suspended above. The signal generator simultaneously sent pulses to electromagnetic actuator 20 and NMR console 36 in Figure 12.

[0067] Synthetic gels are not water based; therefore, they are shelf-stable, and their elastic properties do not change over time. Synthetic gels also generate significantly more MR signal compared to water-based gels. Furthermore, they can be easily melted and recast repeatably. The gels also have tabulated elastic properties reported by the manufacturer, which serve as an additional verification for the measurement (see Table 1 ).Sample Tissue E (MPa) P o Un32 Skin 0.22-0.29 9673 Uterus 0.16-0.21 8574 Breast 0.13-0.16 9355 Brain 0.09-0.12 1119TABLE 1 Tissue mimicking phantoms used in transient portable MR elastometry experiments.

[0068] Only the Young’s modulus, E, was reported by the manufacturer. The shear modulus, G, was calculated using Equation 6, assuming that the Poisson ratio, v = 0.5. According to the manufacturer, the exact values of the elastic modulus of the samplescan vary by up to ±0.25 MPa due to variations in the preparation conditions; therefore, they do not serve as an exact comparison for experimental measurements and instead are used to provide an estimate of the variations in arrival times between samples.RESULTSWave Speed Measurements

[0069] FIG. 15 shows a normalized MR signal magnitude plotted against the delay time for each of the tissue mimicking gels of Table 1. A Savitzky-Golay filter was used to smoothen the data to facilitate the identification of arrival times. The present inventors shifted the magnitude curves in time by 5.8 ms to account for the delay between triggering of the MR acquisition and peak of the acoustic excitation. The shear wave speed was calculated using the time at which the MR signal magnitude reaches the first local minimum.

[0070] The present inventors applied the same methods to identify arrival times and calculate shear wave speeds in optical sensor measurements (shown in FIG. 16).

[0071] FIG. 17 presents a comparison of shear wave speeds as a plot of MR sensor measurements against optical sensor measurements. The data is fitted to a straight line to gauge the differences between measurement techniques. The line has a slope of 1 .12, and an intercept of -40 cm s-1 .

[0072] Temporal resolution is the largest source of uncertainty in these measurements. Other factors, such as uncertainty in the measured distance, contribute; however, there are no significant variations in arrival times between repeated measurements. The uncertainty was characterized by calculating the shear wave speed half a time step above and below each data point. Note that the method can distinguish slower shear wave speeds with greater precision.7~2 Relaxation and Acoustic Excitation

[0073] The present inventors analyzed the effects of pulse arrival on the T2 distribution of gel 2 using an inverse Laplace transform on the CPMG echo train (r = 0.1 ms) following the first echo (r = 1 ms) consisting of 512 echoes using openly available processing scripts with a regularization parameter, = 1

[0010] , The present inventors measured the echo train at 50 different delays after acoustic excitation separated by 0.5 ms (fewer echoes in the 2D measurement were used due to memory constraints).

[0074] FIG. 18 shows the T2 distribution obtained using the CPMG echo train at each delay. Note that the T2 distribution is identical to the stationary case before the pulse arrives in the sensitive region. After the pulse arrives, the signal decays more rapidly and the distribution shifts to lower apparent T2 values for the duration of the pulse transit.Discussion and Conclusions

[0075] The present inventors can draw several observations from transient MR elastometry measurements (FIG. 15). Firstly, as expected, the arrival times of the pulses vary significantly and show a strong dependence on the stiffness of the gels. This variation in arrival times underscores the sensitivity of MR measurements to mechanical properties, particularly stiffness, which directly influences shear wave speed.

[0076] Secondly, the present inventors observe a clear correlation between the width of each signal dip and the stiffness (and therefore shear wave speed) of the sample. A wider dip indicates slower pulse propagation through the sensitive region. In one embodiment of the present invention, increasing the temporal resolution of the measurement allows for shear wave speed characterization using only the width, provided the exact dimensions of the sensitive region are known. These findings are crucial because they demonstrate a quantitative method for assessing material stiffness, which can be particularly useful in applications such as tissue characterization in medical diagnostics.

[0077] Finally, the present inventors notice differences in the intensities of the first local minima. Note the agreement between FIGs 15 and 16, where the amplitude of theresponse in gel 5 is lower than in all other samples. This agreement between optical and MR measurements enhances the validity of our findings and suggests that MR can be reliably used alongside or instead of optical methods in certain contexts. In one embodiment of the present invention, the amplitude of the response (or the intensity of the first minimum in MR signal magnitude) can be used to probe resonance of the sample (by varying the frequency of excitation and measuring the response) and to measure the attenuation coefficient (by measuring the response at several different tracking locations).

[0078] Most importantly, the two measurement techniques agree consistently on the relative measurements of the shear wave speed, as indicated by the slope of the fitted line (see FIG. 17) which is close to 1. In a direct comparison, the MR measurements consistently overshoot the optical sensor measurements, more significantly at higher wave speeds. In addition to being attributed to the temporal resolution of the measurement, the distance used to calculate the wave speed from the arrival time might not be accurate given the finite size of the MR sensor. This can be resolved by calibrating the measurements using a standard elasticity reference or multiple detection locations to correct for systematic errors.

[0079] The portable MR elastometry technique according to an embodiment of the present invention has two main advantages over a simple optical method. First, the MR measurement is capable of characterizing the response of a material to acoustic excitation below the surface, whereas the optical measurement is limited solely to surface measurements. This ability to probe beneath the surface is especially valuable in medical applications, such as imaging of internal organs or tissues where non-invasive techniques are required. Second, MR relaxation measurements can be combined with transient elastometry measurements of shear wave speed. Comparing the T2 distribution for a stationary gel with the T2 distribution acquired at different delays after acoustic excitation (FIG. 18), we see that T2 is the same when the pulse is not present in the sensitive region and shifts to lower values upon arrival. Note that we are not observing a change in the actual T2 of the sample (displacements would have to occur at the molecular level), but rather an apparent change caused by the loss in signal magnitude. This opens thepossibility of characterizing the chemical composition of a tissue simultaneously with measurements of shear wave speed. For example, the relative fat / water content of a tissue could be characterized through its relative T2 components and directly correlated with the shear wave speed measured using the transient technique.

[0080] Having established the fundamentals of the technique and demonstrated proof-of- concept on idealized phantoms, in another embodiment the aim is to enhance its efficiency and robustness through modifications inspired by the extensive literature on transient ultrasound elastography. Other embodiments include minimizing systematic errors by collecting signals from multiple locations, either by manually positioning the sensor or by employing multiple RF coils.

[0081] Still further embodiments of the present invention exploit the advantages of magnetic resonance by using a new portable magnet with a weaker magnetic field gradient (0.5 T m-1) to examine thicker slices of samples (1-2 cm). This advancement enables the application of transient elastometry techniques to stratified samples, thereby investigating depth-dependent changes in elasticity. For instance, this technology can simultaneously assess elasticity in skin and deeper tissues such as fat and muscles. Furthermore, integrating conventional MR measurements of relaxation and diffusion can provide complementary insights into tissue composition.

[0082] The present invention does not aim to replace MRE with its detailed 3D maps of tissue stiffness. Instead, it aims at complementing it where localized, well-defined measurements of tissue stiffness are required, to reduce patient waiting time, and provide an opportunity for disease monitoring. The simplicity of the measurement and a low cost and portability of the instrumentation have potential for implementing it in virtually every clinic for basic diagnostics and monitoring.

[0083] While the teaching herein includes illustrative embodiments and examples of some aspects of an invention, the description is not intended to be construed in a limiting sense. Thus, various modifications of the illustrative embodiments, as well as other embodiments of the invention, may be apparent to persons skilled in the art uponreference to this description. It is therefore contemplated that the appended claims will cover any such modifications or embodiments.

[0084] One or more methods described herein can be implemented by computer program instructions or code, which can be executed on a computer. For example, the code can be implemented by one or more digital processors (e.g., microprocessors or other processing circuitry), and can be stored on a computer program product including a non-transitory computer-readable medium (e.g., storage medium), e.g., a magnetic, optical, electromagnetic, or semiconductor storage medium, including semiconductor or solid state memory, magnetic tape, a removable computer diskette, a random access memory (RAM), a read-only memory (ROM), flash memory, a rigid magnetic disk, an optical disk, a solid-state memory drive, etc.

[0085] The program instructions can also be contained in, and provided as an electronic signal, for example in the form of software as a service (SaaS) delivered from a server (e.g., a distributed system and / or a cloud computing system). Alternatively, one or more methods can be implemented in hardware (logic gates, etc.), or in a combination of hardware and software. Example hardware can be programmable processors (e.g. Field-Programmable Gate Array (FPGA), Complex Programmable Logic Device), general purpose processors, graphics processing units (or GPUs) Application Specific Integrated Circuits (ASICs), and the like. One or more methods can be performed as part of or component of an application running on the system, or as an application or software running in conjunction with other applications and operating system.

[0086] One or more methods described herein can be run as a program in an NMR device or as a standalone program connected to an NMR device. Although the description has been described with respect to particular implementations thereof, these particular implementations are merely illustrative, and not restrictive. Concepts illustrated in the examples may be applied to other examples and implementations. Note that the functional blocks, operations, features, methods, devices, and systems described in the present disclosure may be integrated or divided into different combinations of systems, devices, and functional blocks as would be known to those skilled in the art. Any suitableprogramming language and programming techniques may be used to implement the routines and processing of particular implementations. Different programming techniques may be employed, e.g., procedural or object-oriented. The routines may execute on a single processing device or multiple processors. Although the steps, operations, or computations may be presented in a specific order, the order may be changed in different particular implementations. In some implementations, multiple steps or operations shown as sequential in this specification may be performed at the same time.

[0087] It will be appreciated that the various operations, processes, and methods disclosed herein can be embodied in a machine-readable medium and / or a machine accessible medium compatible with a data processing system (e.g., a computer system), and can be performed in any order (e.g., including using means for achieving the various operations). Accordingly, the specification and drawings are to be regarded in an illustrative rather than a restrictive sense. In some embodiments, the machine-readable medium can be a non-transitory form of machine-readable medium.References[1] Muthupillai, R. et al., Science 269 (1995).[2] Achenbach J D. Wave propagation in elastic solids. North Holland; 1975.[3] Garc'ia-Naranjo Juan C., Mastikhin Igor V., Colpitts Bruce G., Balcom Bruce J. A unilateral magnet with an extended constant magnetic field gradient. Journal of Magnetic Resonance. 2010;207(2):337-344.[4] Mispelter Jo"el, Lupu Mihaela, Briguet Andr'e. NMR Probeheads for Biophysical and Biomedical Experiments. Imperial College Press; 2015.[5] Zalesskiy Sergey S., Danieli Ernesto, Blu’ mich Bernhard, Ananikov Valentine P.. Miniaturization of NMR Systems: Desktop Spectrometers, Microcoil Spectroscopy, and “NMR on a Chip” for Chemistry, Biochemistry, and Industry. Chemical Reviews. 2014;114(11 ):5641-5694.[6] Benson T.B., Mcdonald P.J. Profile Amplitude Modulation in Stray-Field Magnetic- Resonance Imaging. Journal of Magnetic Resonance, Series A. 1995; 112(1 ): 17-23.[7] Lucas-Oliveira Everton, Marassi Agide Gimenez, Arau'jo-Ferreira Arthur Gustavo, et al. Mechanically oscillating sample under magnetic field gradients: MOS-NMR. Journal of Magnetic Resonance Open. 2022; 12-13: 100084.[8] Meiboom S., Gill D.. Modified Spin-Echo Method for Measuring Nuclear Relaxation Times. Review of Scientific Instruments. 1958;29(8):688-691 .[9] Casanova F., Perlo J., Blu’ mich B., Kremer K.. Multi-echo imaging in highly inhomogeneous magnetic fields. Journal of Magnetic Resonance. 2004;166(1):76- 81.

[0010] Afrough Armin, Mokhtari Rasoul, Feilberg Karen L.. Simple MATLAB and Python scripts for multi-exponential analysis. Magnetic Resonance in Chemistry. 2024

Claims

WE CLAIM:(a) A method of characterizing a property of a sample comprising: i) providing a magnet with a static magnetic field and a constant gradient where at least a portion of the sample defining a sensitive region is in the constant gradient; ii) inducing a shear wave in the sample in at least the sensitive region; iii) generating an NMR pulse sequence; iv) acquiring at least one echo from the pulse sequence from the sensitive region v) measuring motion-induced change in the NMR signal of the at least one acquired echo; and vi) relating the measured motion-induced change to a property of the sample.

2. The method of claim 1 , where in step ii), the shear wave is a transient shear wave, and further comprising in step iii) introducing a delay before RF excitation in theNMR pulse sequence.

3. The method of claim 2, further comprising varying the delay.

4. The method of claim 3, further comprising repeating steps iv) to vi).

5. The method of claim 1 , where in step ii), a continuous series of shear waves is induced.

6. The method of any one of claims 1 to 5, wherein the magnet is a unilateral magnet array.

7. The method of any one of claims 1 to 5, wherein the echoes from the pulse sequence are acquired from a slice in at least a portion of the sample.

8. The method of any one of claims 1 to 7, wherein the sheer waves are induced by an actuator inducing movement in the sample.

9. The method of any one of claims 1 to 8, wherein the pulse sequence is a Carr- Purcell-Meiboom-Gill sequence.

10. The method of any one of claims 1 to 9, wherein the sample is human tissue.11 . The method of claim 10, wherein the human tissue is human foot tissue.

12. The method of any one of claims 1 to 11 , wherein the property is tissue elasticity or fluid content.

13. The method of any one of claims 1 to 12, further comprising calculating the shear wave speed using the time at which an MR signal magnitude reaches a first local minimum.

14. The method of claim 13, further comprising deriving the elastic modulus from the wave speed.

15. An MR system comprising: a portable unilateral magnetic having a constant gradient perpendicular to a surface of the magnet; an inducer adjacent the magnet for inducing a shear wave in a sample; a radio frequency; and an NMR console operably connected to the radio frequency coil.

16. The NMR system of claim 15, wherein the MR console comprises a radio frequency generator and a radio frequency detector both operably connected to the radio frequency coil, and a computer system operably connected to the radio frequency detector.

17. The NMR system of claim 16, wherein the computer system comprising computer program instructions for computer implemented steps comprisinggenerating an NMR pulse sequence; acquiring at least one echo from the pulse sequence from the sensitive region; and measuring motion-induced phase interference in the NMR signal of the at least one acquired echo.

18. The NMR system of claim 16, wherein the shear wave is a transient shear wave, and further comprising introducing a delay before RF excitation in the NMR pulse sequence.

19. The NMR system of claim 18, further comprising varying the delay.

20. The NMR system of claim 15, wherein the shear wave is a continuous series of shear waves.

21. The NMR system of any one of claims 15 to 20, wherein the sample is human tissue.

22. The NMR system of claim 21 , wherein the human tissue is human foot tissue.

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