Scanning protocol design for imaging brain microstructure using diffusion magnetic resonance imaging

Abstract

Accurate characterization of brain tissue microstructure using diffusion MRI (dMRI) data relies on optimal scanning protocols. A framework to optimize dMRI protocols for sophisticated multicompartment tissue models is based on the Cramér-Rao lower bound (CRLB). The framework is capable of capturing features like axonal diameter index and multiple fiber orientations in a voxel. The framework can handle any number of model parameters, including water diffusivities, enhancing estimation fidelity. Leveraging automatic differentiation and parallel computing, the framework is capable of systematically exploring the entire parameter space for comprehensive scanning rotocol optimization. By optimizing the data acquisition, this framework can significantly enhance biophysical modeling accuracy in dMRI, thereby deepening understanding of brain tissue properties in health and disease.

Description

SCANNING PROTOCOL DESIGN FOR IMAGING BRAIN MICROSTRUCTURE USING DIFFUSION MAGNETIC RESONANCE IMAGINGCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Patent Application Serial No. 63 / 697,874, filed on September 23, 2024, and entitled “Scanning Protocol Design for Imaging Brain Microstructure Using Diffusion Magnetic Resonance Imaging." which is herein incorporated by reference in its entirety.STATEMENT OF FEDERALLY SPONSORED RESEARCH

[0002] This invention was made with government support under EB027061 and NS 132207 awarded by the National Institutes of Health. The government has certain rights in the invention.BACKGROUND

[0003] Diffusion magnetic resonance imaging (dMRI) is a non-invasive neuroimaging technique that probes the microstructural properties of biological tissues by quantifying the Brownian motion of water molecules. This technique offers significant potential for investigating subtle alterations in tissue architecture associated with various neurological and pathological conditions. To extract quantitative information about these microstructural features, dMRI data undergoes analysis using biophysical models. These models are mathematical frameworks that incorporate the influence of cellular components, such as axons and myelin sheaths, on the diffusion process. By fitting biophysical models to dMRI data, users can estimate a range of tissue properties, providing valuable insights into tissue health and function.

[0004] Complex biophysical models depict tissue microstructure in greater detail than simpler models by incorporating separate compartments for intra-axonal, extra-axonal, and cerebrospinal fluid (CSF). However, these complex models heavily rely on the specific parameters chosen during the dMRI scan (e.g., pulse sequence, diffusion time, gradient strength) for accuracy. The challenge lies in selecting optimal scanning parameters to ensure the most accurate estimation of these model parameters. Accurate biophysical model parameter estimation requires acquiring multiple dMRI images with varying scanner parameters, which extends scan time. In vivo studies and clinical applications face significant limitations on totalscan time due to factors like participant comfort and safety Therefore, it is crucial to optimize the dMRI acquisition protocol to ensure that the most informative data is collected within a reasonable timeframe.

[0005] Currently, optimal scanning protocols for a particular brain tissue biophysical model are found empirically and iteratively. This involves running multiple scans and iteratively evaluating / analyzing each of them. This is extremely time consuming and suboptimal (as the "best" protocol can easily be missed).SUMMARY OF THE DISCLOSURE

[0006] According to an aspect of the present disclosure, a method for performing a diffusion magnetic resonance imaging (MRI) scan of a subject using an MRI system is provided. The method includes receiving user input data, where the user input data includes a selected diffusion model. The method includes generating Cramer-Rao Lower Bound (CRLB) values with automatic differentiation to determine scanning protocol data for the diffusion MRI scan, where the scanning protocol data includes at least one of acquisition parameters for a pulse sequence used in the diffusion MRI scan and model parameters for the selected diffusion model. The method includes acquiring magnetic resonance data from a subject using the MRI system to perform the pulse sequence using the scanning protocol data. The method includes generating at least one diffusion image from the magnetic resonance data.

[0007] According to another aspect of the present disclosure, a method for optimizing diffusion magnetic resonance imaging (dMRI) acquisition protocols is provided. The method includes selecting a multi-compartment tissue biophysical model. The method includes generating parameter combinations across parameter values for model parameters of the selected multi-compartment tissue biophysical model. The method includes computing Fisher information matrix (FIM) elements for each parameter combination using automatic differentiation. The method includes calculating Cramer-Rao Lower Bound (CRLB) values from the FIM elements. The method includes determining pulse sequence parameters that minimize the CRLB values for the model parameters. The method includes outputting the pulse sequence parameters for use in controlling a magnetic resonance imaging (MRI) system to perform a dMRI acquisition.BRIEF DESCRIPTION OF THE DRAWINGS

[0008] FIG. 1 illustrates an example protocol optimization framework for microstructure imaging. The figure illustrates a framework for optimizing diffusion MRI (dMRI) scans using Pulse Gradient Spin Echo (PGSE) sequences. The objective is to acquire the most informative dMRI signal regarding the tissue microstructure, within a constrained scan time. This optimization process involves: 1) User-defined selection of tissue properties of interest (tissue model selection) and available scanning time, 2) Generation of synthetic dMRI data using a model function, followed by computation of the Cramer-Rao lower bound (CRLB) with automatic differentiation to determine optimal scanning protocol parameters (a). 3) The process involves iterative filtration of the optimized scanning parameters considering scanner hardware limitations and balancing information gained from the signal and SNR, and finally, 4) Fitting of the tissue model to dMRI data, resulting in estimated model parameters (x) with minimal variance for reliable tissue microstructure imaging.

[0009] FIG. 2 illustrates the impact of scanning parameters on water diffusivity estimation. The figure shows the optimal b-values required for estimation of diffusivity values with minimal variance (i.e., minimum CRLB for diffusivities). Each panel (A-D) corresponds to a distinct tissue biophysical model: Diffusion Tensor, Neurite Orientation Dispersion and Density' Imaging (NODDI), ActiveAx, and Ball-and-Three-Sticks, respectively. All subfigures plot the magnitude of the gradient value G on the x-axis (mT.m-1) and the CRLB on the y-axis using a logarithmic scale. The color scheme signifies different diffusivity components: red represents the primary / intrinsic diffusivity along the main fiber / axonal orientationblue depicts the diffusivity' along the secondary' main orientation and greencorresponds to the tertiary diffusion direction (A3).

[0010] FIG. 3 illustrates CRLB for diffusion tensor (DT) model parameters. CRLB variability is shown with multiple gradient directions and b-values, using 1000 unique diffusion tensor orientations at SNR values of 10 and 50. Diffusivities were constrained within the human brain's feasible range (illustrated by FA = 0.68). The sub-figures share a common y-axis, exhibiting log-scale CRLB plots for all the six diffusion tensor model variables. The x-axis show the magnitude of the gradient value G (mT.m-1) with the top two rows featuring different G ranges than the bottom two rows, reflecting variations in the choice of Δ and 8 (ms), b-values are shown in the rightmost figures of the second and third rows. Each column corresponds to three gradient tables featuring 7, 27, and 130 pulse directions, uniformly distributed in q-space shells. Sub-figures show plots for mean CRLB values of model parameters and their sum (traceof the inverse of FIM). with the corresponding-colored shaded areas indicating the 95 percent confidence interval.

[0011] FIG. 4 illustrates an evaluation of NODDI imaging protocols. The figure presents the CRLB analysis for the NODDI model parameters under various imaging protocols. The x-axis represents eight distinct scanning protocols (P1-P9). Details of these protocols are provided in Table 1. replicated from Table 1 of the reference. The y-axis displays the mean CRLB values (in log scale) for each NODDI model parameteras well as their sum (trace of the inverse FIM). The corresponding color-coded shaded areas represent the 95% confidence intervals. The analysis confirms the findings of the original NODDI publication, indicating that protocol P14 exhibits the optimal performance for most of the tissue configuration. To further investigate the influence of individual model parameters on experimental design optimization, eight distinct combinations ofare evaluated. A high number of 256 unique fiber orientations are simulated to account for potential biases introduced by fiber orientation, assuming SNR of 20.

[0012] FIG. 5 illustrates CRLB for NODDI model parameters. CRLB variability is shown with multiple gradient directions and b-values across 36 unique tissue configurations at SNR 20. NODDI parameters were constrained within the human brain’s feasible range. The sub-figures share a common y-axis. displaying log10CRLB plots for all six variables of the NODDI model. The x-axis represents the magnitude of the gradient value G (mT.m'1) with the two columns featuring different separation time, Δ (ms), and duration time, <5 (ms) of the diffusion encoding gradients. Sub-figures show case plots for log-scaled mean CRLB values of model parameters and their sum (trace of the inverse of FIM), with the corresponding-colored shaded areas indicating the 95 percent confidence interval. Each row corresponds to results obtained with 30, 60, and 90 gradient directions. The middle displays b-values plots, highlighting optimal b-values corresponding to the minimum CRLB for each configuration. Maximum curvature points marked with red arrow s are “sweet spots'’ detected by a “kneedie” algorithm with default settings. These points represent optimal trade off at which the relative cost of increasing G or b-values is no longer worth in reducing CRLB.

[0013] FIG. 6 illustrates a comparison of optimal NODDI protocols from this study with those proposed in the original NODDI publication. The figure compares the CRLB of scanning protocols identified in this work with those established in the original NODDI study. The x-axis represents eleven distinct protocols: Two protocols (Pl 3 and P 14) from the original NODDI publication (details in Table 1), and nine novel protocols identified through analysisof FIG. 5. The y-axis displays the log scaled mean CRLB values for each NODDI model parameter. The corresponding color-coded shaded areas represent the 95% confidence intervals. The results indicate that the systematically derived protocols (learned from FIG. 5) achieve comparable performance to the empirically found optimal protocols P14 and Pl 3 from the original NODDI study. This finding generalizes to eight different and extreme combinations of vic, cl and OD. simulated with 256 unique fiber orientations, at SNR 20.

[0014] FIG. 7 illustrates CRLB for ActiveAx model parameters. CRLB analysis of ActiveAx model using 48 unique tissue configurations at SNR = 20 are shown. ActiveAx parameters were constrained within the human brain's feasible range. The sub-figures share a common y-axis, displaying / og10CRLB plots for all six variables of the ActiveAx model. The x-axis represents the magnitude of the gradient value G (mT.m-1) with the two columns featuring different separation time, Δ (ms), and duration time, 8 (ms) of the diffusion encoding gradients. Sub-figures showcase plots for log-scaled mean CRLB values of model parameters and their sum (trace of the inverse of FIM), with the corresponding-colored shaded areas indicating the 95 percent confidence interval. Each row shows results for 30, 60 and 90 gradient directions. The middle row shows b-values plots. The optimal b-values corresponding to the minimum CRLB are shown for each configuration.

[0015] FIG. 8 illustrates the best 15 protocols for an ActiveAx model determined from in an example study. This figure presents the 15 best scanning protocols identified for the ActiveAx model, considering scanner limitations (maximum gradient strength G < 300 mT.m-1and pulse duration to diffusion time ratio (5 / Δ > 0.1). All sub-figures share the x-axis and y-axes. The x-axis displays the log-scale CRLB of the trace of the inverse FIM in ascending order, indicating overall parameter estimation uncertainty (lower is better). The left y-axis shows diffusion time (A) and pulse duration (8) in ms (blue and green, respectively). The right y-axis displays b-values in s.mm-2(red) and gradient strength G mT.m-1(purple), as detailed in the legend. Each sub-figure showcases the corresponding optimal protocol for a specific model parameter, indicated at the top of the sub-figure. The results were obtained using a single diffusion shell with 30 gradient directions, applied to 48 unique tissue configurations and assuming SNR of 20.

[0016] FIG. 9 illustrates CRLB for Ball-and-Three-Sticks model parameters. The figures illustrate optimal CRLB using 648 unique tissue configurations at SNR = 20. Ball and Stick parameters varied within the feasible range of the human brain. A common y-axis exhibits Zog10CRLB plots for the twelve model variables. The x-axis displays the magnitude of thegradient value G mT.m'1with the two columns featuring different G ranges, reflecting variations in the choice of Δ and 6 (ms), b-values corresponding to minimum CRLB are depicted. Plots in the sub-figures display mean CRLB values of model parameters and their sum (trace of the inverse of FIM), with shaded areas indicating the 95 percent confidence interval in corresponding colors. Maximum curvature points, identified by the “kneedie” algorithm with default settings, are denoted by red arrows, representing “sweet spots.” These points indicate optimal trade-offs at which the relative cost of increasing G or b-values is no longer worthwhile for improving CRLB.

[0017] FIG. 10 illustrates parameters of the diffusion tensor model and PGSE. (A) Parameters of the diffusion tensor model include the principal eigenvaluesecondary eigenvalue A2. and tertiary eigenvalue A3(mm2.s-1), represented in red, blue, and green colors, respectively. The corresponding orientation angles 0, <|>, and 0 (rad) are also shown, using the same color code, (B) PGSE parameters, specifically the amplitude of the diffusion gradient (G mT.m-1). separation time, Δ (ms), and duration time, δ (ms) of the diffusion encoding gradients, can be chosen to achieve optimal experimental design in dMRI-based biophysical modeling, (C) The three row s depict outcomes related to the three eigenvalues of the diffusion tensor, following the color code from panel A. The middle column demonstrates the attenuation of the dMRI signal with increasing G values, while the right column presents the log0CRLB plots. Both columns show results for the two extreme combinations of Δ and δ. The results show that the minimum CRLB is linked to b-values approximately reciprocal to the corresponding diffusivity values. This implies that higher diffusivity values yield optimal CRLB at lower b- values, while lower diffusivities require higher b-values for reliable estimation.

[0018] FIG. 11 illustrates example CRLB for lower intrinsic and perpendicular diffusivity values e.g., in gray matter and infant brains using NODDI model. The left column demonstrate the dMRI signal attenuation with increasing G values, while the right column presents the log-scale CRLB plots. The two line types show results related to extreme values of OD as shown in figure legend. Also, the row s show results for the two extreme combinations of Δ and 8 (ms). The results show that the minimum (optimal) CRLB is related to b-values approximately reciprocal to the corresponding diffusivity values while OD values affect the relationship.

[0019] FIG. 12 illustrates example CRLB for lower intrinsic and perpendicular diffusivity values e.g., in gray matter and infant brains using ActiveAx model. The left column demonstrate the dMRI signal attenuation with increasing G values, while the right columnpresents the log-scale CRLB plots. The two line types show results related to extreme values of R as shown in figure legend. Also, the rows show results for the two extreme combinations of Δ and 8 (ms). The key finding is that the minimum (optimal) CRLB is related to the b-values approximately reciprocal to the corresponding diffusivity values while R values. However, the R value only influences this relationship for perpendicular diffusivity A±only.

[0020] FIG. 13 illustrates example CRLB for Ball-and-Two-Sticks model. CRLB using 18 unique tissue configurations at SNR = 20 are shown. Ball and Stick parameters were constrained within the human brain's feasible range. The sub-figures share a common y-axis, exhibiting log-scale CRLB plots for all six variables in the model. The x-axis shows the magnitude of the gradient value G (rnT.m-1) with the two columns featuring different G ranges, reflecting variations in the choice of Δ and 8 (ms), b-values corresponding to the optimal CRLB are show n. Sub-figures show plots for mean CRLB values of model parameters and their sum (trace of the CRLB matrix), with the corresponding-colored shaded areas indicating the 95 percent confidence interval. Maximum curvature points shown with red arrows are ‘"sweet spots’’ detected by a "kneedle" algorithm with default settings. The points show optimal trade off at which the relative cost of increasing G or b-values is no longer worth in improvement of CRLB.

[0021] FIG. 14 is a block diagram of an example system for generating optimized scanning protocols (e.g., acquisition parameters, fixed parameters, common tissue model parameters, model-specific parameters) for diffusion MRI acquisitions.

[0022] FIG. 15 is a block diagram of example components that can implement the system of FIG. 14.

[0023] FIG. 16 is a block diagram of an example MRI system that can implement the methods described in the present disclosure.

[0024] FIG. 17 is a flowchart of an example method for performing a dMRI scan of a subject using an MRI system .DETAILED DESCRIPTION

[0025] Described here are systems and methods for generating optimal scanning protocols for diffusion magnetic resonance imaging (dMRI) that improve the characterization of brain tissue microstructure in the acquired dMRI data. Presently, without such protocols, extensive datasets are required to image intricate tissue architecture by fitting complexbiophysical models to dMRI data. This impedes the full realization of dMRI’s potential, particularly in time-constrained clinical scans.

[0026] The disclosed systems and methods address these drawbacks by providing a framework based on the Cramer-Rao lower bound (CRLB) to optimize dMRI protocols for sophisticated multicompartment tissue models, capturing features like axonal diameter index and multiple fiber orientations in a voxel. Unlike previous methods that are limited in model complexity or parameter scope, the framework described in the present disclosure handles all model parameters, including water diffusivities, thereby enhancing estimation fidelity. Leveraging automatic differentiation and parallel computing (e.g., via TensorFlow), the disclosed systems and methods systematically explore the entire parameter space for comprehensive scanning protocol optimization. By optimizing the data acquisition, the disclosed systems and methods can significantly enhance biophysical modeling accuracy in dMRI, thereby deepening understanding of brain tissue properties in health and disease.

[0027] In some implementations, the disclosed systems and methods for computing optimal scanning protocol parameters for dMRI data in tissue microstructure imaging can include computing derivatives of complex biophysical models (functions) using automatic differentiation and subsequently computing the CRLB for experiment design optimization.

[0028] Advantageously, the disclosed systems and methods can be integrated into existing MRI scanners, allowing users to specify the scanning time and the tissue properties they are interested in. The systems and methods will then generate an optimal scanning protocol tailored to the given MRI scanner hardware. In this way, the efficiency of existing commercial scanners can be enhanced, and can enable the use of imaging techniques that currently cannot be done.

[0029] As noted above, the disclosed systems and methods provide a generalized framework that can handle complex, multi-compartment tissue models. This framework allows for optimization across all model parameters, encompassing those related to tissue geometry including water diffusivity. Specifically, the disclosed systems and methods aim to overcome the limitations of previous efforts to find optimal scanning protocols for multicompartment tissue biophysical models by: (1) Extending the focus to complex multi-compartment tissue models capable of detecting intricate brain tissue features like axon diameter, distribution, and multiple fiber orientations; (2) Optimizing over all model parameters relating to tissue geometry, including water diffusivity’ values, to enhanced model parameter estimation fidelity’; (3) Leveraging differentiable programming in TensorFlow. derivative-based Fisherinformation matrix (FIM) calculation methods are employed, enabling efficient optimization through automatic differentiation and parallel computing with GPUs; and (4) Systematically exploring the entire acquisition protocol parameter space, and also span extreme ranges of biologically feasible tissue geometrical features, to ensure comprehensive optimization if scanning protocols.

[0030] As described above. dMRI provides a non-invasive approach for characterizing brain tissue microstructure by measuring the Brownian motion of water molecules within biological tissues. The technique enables investigation of tissue architecture changes associated with neurological conditions and pathological states. Accurate characterization of tissue microstructure using dMRI data may depend on the selection of scanning protocols that maximize information content while operating within practical time constraints. In some cases, suboptimal scanning protocols may lead to extensive data requirements for fitting complex biophysical models to dMRI data, which can limit the practical application of advanced microstructure imaging techniques in clinical settings.

[0031] Traditional approaches to protocol optimization often rely on empirical methods that involve iterative scanning and evaluation processes. These methods may be timeconsuming and may not guarantee identification of globally effective protocols. In some cases, the complexity of multi-compartment biophysical models makes manual optimization challenging, particularly when considering all model parameters simultaneously. The mathematical complexity of these models may make analytical derivative computation impractical for comprehensive protocol optimization.

[0032] A systematic framework for dMRI protocol optimization may address these limitations by employing the CRLB as a theoretical foundation for determining acquisition parameters that minimize parameter estimation variance. The CRLB provides a lower bound on the variance of unbiased estimators, making the bound suitable for evaluating the information content of different scanning protocols. In some cases, minimizing the CRLB may lead to protocols that extract maximum information from dMRI data within given time constraints.

[0033] The framework disclosed herein utilizes automatic differentiation techniques to compute derivatives of complex biophysical model functions with respect to model parameters. Automatic differentiation may enable efficient computation of the Fisher Information Matrix, which forms the basis for CRLB calculations. In some cases, parallel computing capabilities may accelerate the optimization process, allowing systematic exploration of the entireparameter space for comprehensive protocol optimization. The approach may handle multiple model parameters simultaneously, including water diffusivity values, volume fractions, and tissue-specific parameters.

[0034] Protocol optimization using this framework may accommodate various scanner hardware limitations and practical constraints. The system may filter potential protocols based on maximum gradient strength capabilities and pulse sequence timing requirements. In some cases, the optimization process may consider different numbers of gradient directions and signal-to-noise ratio levels to generate protocols suitable for specific imaging scenarios. The framework may also incorporate mechanisms to ensure that only feasible parameter combinations are considered during optimization, maintaining mathematical validity throughout the process.

[0035] FIG. 1 illustrates an example workflow of the optimization framework described in the present disclosure. The protocol optimization framework illustrated in FIG. 1 may demonstrate a systematic workflow that begins with user-defined inputs and progresses through computational optimization to deliver tailored diffusion MRI protocols. The workflow may initiate with scanner time input, where users specify available scan time constraints, and number of gradient directions input, allowing selection from minimal configurations with as few as 7 directions to comprehensive sampling approaches utilizing up to 256 directions. These initial parameters may establish the operational boundaries within which the optimization process operates.

[0036] The framework may incorporate multi -compartment tissue models as fundamental components, including intracellular compartment, extracellular compartment, and CSF compartment representations. These tissue models may define the biophysical parameters of interest through tissue model functions, while users may specify tissue properties of interest such as orientation dispersion and neurite densify index. The scanning protocol component may detail PGSE sequence parameters including echo time, gradient strength, and timing parameters, which serve as the foundation for protocol optimization.

[0037] The computational core of the workflow may employ synthetic data generation processes that create simulated diffusion signals based on the specified tissue models and scanning parameters. This synthetic data may feed into automatic differentiation calculations that compute complex mathematical derivatives required for Fisher Information Matrix analysis. The framework may subsequently calculate CRLBs to establish theoretical minimumvariance limits for parameter estimation, enabling systematic evaluation of protocol performance across different configurations.

[0038] The optimization process may culminate in diffusion MRI data collection simulation and tissue model fitting to dMRI data, ultimately producing estimated model parameters with minimum variance. The final output may include comprehensive parameter distributions for axon density index, axon dispersion index, and parallel diffusivity measurements. The framework may apply hardware constraint integration to filter protocols based on scanner specifications, ensuring compatibility with clinical systems through constraints such as maximum gradient strength thresholds below 300 mT / m and minimum pulse duration ratios above 0.1. The system may generate multiple protocol options ranked by estimation precision metrics, providing users with configurations that balance scan time constraints with measurement accuracy requirements while including protocol validation information such as expected CRLB values and confidence interval estimates.

[0039] By providing a method to optimize dMRI acquisition protocols for complex models, the disclosed systems and methods have the potential to significantly improve the accuracy of biophysical modeling in dMRI. This, in turn, can lead to a better understanding of brain tissue properties in both healthy and diseased states.

[0040] By way of example, the framework elements illustrated in FIG. 1 may operate in a coordinated sequence to perform comprehensive diffusion MRI protocol optimization. In some cases, the process begins with tissue model selection, where users may specify the biophysical model appropriate for the tissue microstructure of interest. The framework may support multiple model types including diffusion tensor models for basic anisotropy characterization, NODDI models for neurite density and dispersion analysis, ActiveAx models for axonal diameter estimation, and Ball-and-Sticks models for multi-fiber orientation detection. Each model may define specific parameter sets that characterize different aspects of tissue microstructure, such as water diffusivity values, volume fractions, fiber orientations, and specialized metrics like axonal diameter index or orientation dispersion parameters.

[0041] Following model selection, the framework may initiate systematic parameter space exploration through Cartesian product operations. In some cases, the framework may generate comprehensive combinations of extreme parameter values within biologically feasible ranges for each model parameter. The framework may establish parameter sets containing minimum and maximum permissible values for volume fractions, orientation angles, and diffusivity measurements across different tissue types. As a non-limiting example, for whitemater characterization, diffusivity ranges may span from 1.74x 1 O'3mm2 / s for parallel diffusion to lower values for perpendicular diffusion components. Gray mater and cerebrospinal fluid applications may utilize different diffusivity ranges appropriate for those tissue characteristics.

[0042] The automatic differentiation engine may compute Fisher Information Matrix elements for each parameter combination using TensorFlow framework capabilities. In some cases, the framework may calculate complex mathematical derivatives of biophysical model functions with respect to all model parameters simultaneously. The parallel computing architecture may distribute these calculations across GPU processing units to handle the computational intensity of derivative calculations for sophisticated multi-compartment models. The framework may ensure that only full-rank Fisher Information Matrices are processed, filtering out parameter combinations that would result in insufficient information content for reliable parameter estimation.

[0043] CRLB calculations may proceed using the computed Fisher Information Matrix elements to determine theoretical minimum variance bounds for parameter estimation. The framework may evaluate CRLB values across different scanning protocol configurations, including variations in gradient strength, diffusion pulse duration, and diffusion time parameters. In some cases, the framework may systematically explore PGSE sequence parameter combinations within hardware-feasible ranges, considering constraints such as maximum gradient strength limitations and pulse duration ratios. The optimization process may identify parameter combinations that minimize CRLB values while maintaining practical implementation feasibility.

[0044] Protocol generation may incorporate curvature-based optimization methods to identify trade-off points between scanning parameters and estimation precision. The framework may employ algorithms such as the kneedie method to detect maximum curvature points in CRLB versus parameter plots, indicating where additional increases in gradient strength or b-values provide diminishing returns in estimation improvement. Multi-shell protocol generation may combine multiple b-value shells with optimized gradient direction distributions to maximize information content within specified scan time constraints. The framework may generate protocols with specific b-value combinations, such as two-shell configurations with first shell values ranging from 700-1300 s / mm2and second shell values from 2100-2300 s / mm2.

[0045] Hardware constraint integration may filter generated protocols based on scanner specifications and practical limitations. In some cases, the framework may apply constraints such as maximum gradient strength thresholds below 300 mT / m and minimum pulse duration ratios above 0.1 to ensure protocol compatibility with clinical scanner capabilities. The framework may accommodate different numbers of gradient directions ranging from minimal configurations with 7 directions to comprehensive sampling with 256 directions, adjusting protocol complexity based on available scan time and desired precision levels. Signal-to-noise ratio (SNR) considerations may influence protocol selection, with the system adapting recommendations for different SNR environments ranging from 10 to 50 or higher values.

[0046] Final protocol output may include comprehensive scanning parameter specifications tailored to the selected tissue model and application requirements. The framework may provide detailed PGSE sequence parameters including optimized gradient strength values, diffusion pulse durations, diffusion times, and b-value distributions. In some cases, the framework may generate multiple protocol options ranked by estimation precision metrics, allowing users to select configurations that balance scan time constraints with desired measurement accuracy. The output may include protocol validation information such as expected CRLB values for each model parameter and confidence interval estimates for the optimized scanning configuration.

[0047] As described above, the framework provides support for multiple biophysical models that characterize different aspects of brain tissue microstructure. Each model offers distinct capabilities for analyzing specific tissue properties and may be selected based on the particular microstructural features of interest in a given study. The multi-model approach allows for the selection of the appropriate mathematical framework that corresponds to specific tissue characterization objectives.

[0048] The Diffusion Tensor model represents one approach for tissue microstructure analysis. This model utilizes six parameters including three mutually perpendicular eigenvectors that represent primary diffusion directions within a voxel. The model incorporates eigenvalues along with rotation parameters that define the spatial orientation of the diffusion tensor. This model provides measurements of tissue anisotropy and diffusion characteristics that form the basis for more complex tissue analysis approaches.

[0049] The Neurite Orientation Dispersion and Density Imaging (NODDI) model extends beyond simple tensor representations to provide detailed analysis of white matter integrity and pathology. This three-compartment tissue model separately analyzes intra-cellularand extra-cellular properties within brain tissue. The model quantifies axonal packing density through the intra-cellular volume fraction parameter and captures spatial dispersion of axons through the orientation dispersion index. The NODDI model signal may be expressed as a combination of three compartments. The model parameters include fiber orientation angles, parallel and perpendicular diffusivity values, intra-cellular volume fraction, and orientation dispersion index, providing comprehensive characterization of tissue microstructure.

[0050] The ActiveAx model offers quantitative evaluation of average axonal diameter within fiber bundles, providing measurements that remain insensitive to fiber orientation variations. This model utilizes a three-compartment approach that separates intra-cellular, extra-cellular, and isotropic diffusion components. The ActiveAx signal representation incorporates cylinder, zeppelin. and dot compartments. The model includes parameters for fiber orientation, parallel and perpendicular diffusivity values, volume fractions for each compartment, and the axonal radius index R measured in micrometers. This approach enables direct assessment of axonal diameter distributions within white matter structures.

[0051] The Ball-and-Sticks model decomposes water diffusion into distinct compartments representing different diffusion behaviors within tissue. The model incorporates an isotropic compartment, referred to as the “ball,” which represents unrestricted water diffusion, along with restricted diffusion compartments known as “sticks” that model diffusion constrained along specific fiber orientations. The Ball-and-Three-Sticks variant models three distinct fiber tracts within a single voxel. The model parameters include orientation angles, diffusivity values, and volume fractions for each stick compartment, along with the isotropic volume fraction. This approach provides flexibility for modeling complex fiber crossing patterns and multiple fiber populations within individual voxels.

[0052] Each biophysical model addresses different aspects of tissue microstructure characterization and may be selected based on the specific objectives and tissue properties under investigation. The Diffusion Tensor model provides fundamental anisotropy measurements suitable for basic tissue characterization. The NODDI model offers enhanced sensitivity to microstructural changes associated with neurological conditions through its multi-compartment approach. The ActiveAx model enables direct quantification of axonal diameter properties that relate to tissue development and pathology. The Ball-and-Sticks model accommodates complex fiber architectures including crossing fibers and multiple fiber populations that occur in many brain regions. The framework's support for multiple models allows users to select the appropriate mathematical representation based on their specific tissueanalysis requirements and the level of microstructural detail needed for their particular application.

[0053] The optimization framework may operate across multiple categories of model parameters to provide comprehensive characterization of tissue microstructure properties. Water diffusivity' values represent one category of parameters that may be optimized, encompassing parallel diffusivity along fiber orientations, perpendicular diffusivity across fiber bundles, and isotropic diffusivity in unrestricted compartments. In some cases, the parallel diffusivity values may range from approximately 0.5xl0'3mm2 / s to 2.5 / 10-3mm2 / s depending on tissue type and experimental conditions. The perpendicular diffusivity' values may be derived through tortuosity’ models or estimated independently, while isotropic diffusivity values may be fixed at tissue-appropriate levels such as 3.0x l0-3mm2 / s for in-vivo applications or 2. Ox 10'3mm2 / s for ex-vivo studies.

[0054] Volume fraction parameters constitute another category' that may be simultaneously optimized within the framework. Intracellular volume fractions may represent the proportion of signal originating from restricted diffusion compartments, while extracellular volume fractions may characterize the contribution from hindered diffusion environments. In some cases, isotropic volume fractions may account for cerebrospinal fluid or other free water compartments within the tissue. The framework may enforce constraints such that the sum of all volume fractions equals unity, while individual fractions may vary within biologically plausible ranges. For example, intracellular volume fractions may range from 0. 1 to 0.79, while isotropic volume fractions may be constrained to low values such as 0.01 in white matter regions.

[0055] Fiber orientation parameters may be optimized to characterize the directional properties of tissue microstructure. These parameters may include polar angles 0 and azimuthal angles cp that define the primary fiber orientations within each voxel. In some cases, multiple fiber orientations may be estimated simultaneously for regions containing crossing or branching fiber bundles. The framework may sample orientation parameters uniformly across spherical coordinates to ensure comprehensive coverage of possible fiber directions. Additional rotational parameters such as [3 may be included for models requiring full three- dimensional orientation specification.

[0056] Tissue-specific parameters may provide specialized characterization capabilities for different biophysical models. The axonal diameter index may be optimized to estimate average axon radius within fiber bundles, with values typically ranging from 0.01 to11 micrometers. Orientation dispersion parameters may quantify the degree of fiber coherence within tissue regions, with values ranging from 0.02 for highly coherent bundles to 0.9 for dispersed or crossing configurations. In some cases, tortuosity parameters may be optimized to characterize the geometric complexify of extracellular spaces. The framework may accommodate model-specific parameters such as exchange rates between compartments or relaxation time constants when incorporated into the biophysical models.

[0057] The simultaneous optimization of multiple parameter categories may be achieved through the Fisher Information Matrix calculation that accounts for parameter interdependencies and correlations. The framework may generate parameter combinations using Cartesian product operations across the ranges of each parameter type, ensuring comprehensive exploration of the joint parameter space. In some cases, infeasible parameter combinations may be filtered out based on physical constraints or mathematical requirements such as positive definiteness of diffusion tensors. The optimization process may consider the sensitivity of each parameter type to different aspects of the diffusion-weighted signal, allowing for balanced protocol design that provides adequate information for all parameter categories simultaneously.

[0058] As described above, following model selection, the framework may initiate systematic parameter space exploration through Cartesian product operations. The systematic exploration of parameter space may be accomplished through Cartesian product operations that generate comprehensive combinations of model parameters within biologically feasible ranges. The parameter space exploration process may begin by establishing sets containing extreme permissible values for each model parameter of interest. For example, volume fraction parameters may be defined within a set F = {0.1, 0.79} representing the minimum and maximum biologically feasible volume fractions, while orientation parameters may be encompassed within sets such as 0 = {0, TT / 2} and 0 = {0, TL / 2} representing the allowable extreme values for fiber orientation angles. Diffusivity parameters may be similarly constrained within sets such as D = {1.74xl0‘3, 0.5xl0’3} mm2 / s, representing the range of water diffusivity values observed in different tissue types including white matter and gray matter regions.

[0059] The Cartesian product operation (F x 0 x <5 x ... x D) may yield all possible combinations of parameter values across the defined parameter sets. This mathematical operation may be repeated N times, where N represents the number of compartments or structural components within the biophysical model being analyzed. For multi-compartmentmodels such as Ball-and-Sticks configurations, the Cartesian product may generate combinations that account for multiple fiber orientations, diffusivity values, and volume fractions simultaneously. The systematic nature of this approach may ensure that no feasible parameter combination within the defined ranges is overlooked during the optimization process.

[0060] Following the generation of all possible parameter combinations, filtering mechanisms may be applied to eliminate infeasible configurations that do not conform to physical or biological constraints. Parameter combinations where the sum of volume fractions does not equal unity7may be excluded from further analysis, as such configurations violate the fundamental requirement that all tissue compartments must account for the complete voxel volume. Similarly, combinations where fiber orientations within different compartments are identical or repeated may be filtered out, as such configurations would not represent distinct structural components within the tissue microstructure. Additional filtering may remove combinations that result in non-full-rank Fisher Information Matrices, ensuring that only parameter sets with sufficient information content for reliable estimation are considered.

[0061] The extreme value approach employed in the parameter space exploration may provide comprehensive coverage of the biologically relevant parameter ranges while maintaining computational efficiency. By focusing on extreme parameter values rather than dense sampling across continuous ranges, the method may capture the boundaries of parameter sensitivity while avoiding redundant intermediate values that may not contribute additional information to the optimization process. This approach may be particularly advantageous when dealing with high-dimensional parameter spaces where exhaustive sampling would be computationally prohibitive. The resulting parameter combinations may span the full range of tissue microstructural configurations encountered in both healthy and pathological conditions, enabling the development of robust scanning protocols that perform effectively across diverse biological scenarios.

[0062] As described above, the framework may provide detailed PGSE (Pulse Gradient Spin Echo) sequence parameters including optimized gradient strength values, diffusion pulse durations, diffusion times, and b-value distributions. The optimization process involves systematic adjustment of PGSE sequence parameters to achieve optimal diffusion- eighted imaging protocols. The PGSE sequence parameters include gradient strength (G), diffusion pulse duration (5), and diffusion time (A), which collectively determine the b-value and sensitivity to tissue microstructure. The gradient strength G represents the magnitude of themagnetic field gradient applied during diffusion encoding, typically measured in millitesla per meter (mT / m). The diffusion pulse duration 5 defines the duration of each gradient pulse, while the diffusion time Δ represents the time interval between the onset of the first and second gradient pulses in the PGSE sequence.

[0063] The relationship between these parameters and the resulting b-value follows the equation b = y2G252( Δ - 5 / 3), where y represents the gyromagnetic ratio. This mathematical relationship demonstrates how modifications to any of the three PGSE parameters directly influence the b-value and consequently the diffusion weighting of the acquired signal. In some cases, the optimization process explores different combinations of G, 5, and Δ values to identify parameter sets that minimize the Cramer-Rao lower bound for specific tissue model parameters. The systematic exploration may involve grid search approaches across predefined ranges of each parameter, with constraints applied based on scanner hardware limitations and physiological considerations.

[0064] For example, gradient strength values may be varied within ranges from 10 mT / m to 300 mT / m, reflecting typical clinical scanner capabilities. The diffusion pulse duration 5 may be adjusted between 5 milliseconds and 65 milliseconds, while diffusion time Δ may range from 10 milliseconds to 75 milliseconds. These parameter ranges allow for exploration of b-values spanning from approximately 500 s / mm2to over 14,000 s / mm2, accommodating different tissue types and microstructural features. In some cases, specific parameter combinations such as Δ = 75 ms and 5 = 65 ms may be selected for high diffusion weighting applications, while combinations like Δ = 10 ms and 5 = 5 ms may be used for lower diffusion weighting scenarios.

[0065] The optimization algorithm evaluates each parameter combination by computing the Fisher Information Matrix and corresponding Cramer-Rao lower bound for the tissue model parameters of interest. Parameter combinations that result in singular or ill- conditioned Fisher Information Matrices may be excluded from consideration to ensure reliable parameter estimation. The process may also incorporate constraints such as 5 / Δ ratios greater than 0. 1 to maintain adequate diffusion encoding efficiency while avoiding impractical pulse sequence configurations. In some cases, the optimization identifies multiple parameter combinations that achieve similar Cramer-Rao lower bound values, providing flexibility in protocol selection based on specific experimental requirements or scanner limitations.

[0066] The systematic parameter space exploration enables identification of trade-off points where further increases in gradient strength or diffusion weighting provide diminishingreturns in terms of parameter estimation precision. These trade-off points may be detected using algorithms that identify maximum curvature locations in the Cramer-Rao lower bound versus parameter value curves. For instance, a gradient strength of 150 mT / m with 8 = 30 ms and Δ = 40 ms might represent an optimal balance between signal-to-noise ratio and diffusion sensitivity for certain tissue models. The optimization process may generate lookup tables or parameter maps that associate specific tissue properties with recommended PGSE parameter combinations, facilitating rapid protocol selection for different imaging applications.

[0067] The optimization process incorporates multiple filtering mechanisms to maintain data quality and computational reliability throughout the protocol optimization workflow. These filtering mechanisms operate at various stages of the parameter space exploration to exclude combinations that may lead to unreliable or mathematically invalid results. In some cases, the filtering process begins during the initial parameter combination generation phase, where physically impossible or biologically implausible parameter sets are identified and removed from consideration. The filtering mechanisms may evaluate parameter combinations based on mathematical constraints, biological feasibility criteria, and computational stability requirements to ensure that subsequent optimization calculations produce meaningful and reliable results.

[0068] Parameter combination feasibility assessment may involve multiple validation criteria that examine the mathematical and physical validity of each generated parameter set. In some cases, volume fraction constraints are applied to ensure that the sum of all compartment volume fractions equals unity, as required by the underlying biophysical models. The filtering process may also evaluate fiber orientation parameters to identify and exclude combinations where multiple compartments share identical or nearly identical orientation vectors, which can lead to mathematical degeneracies in the model equations. Additionally, diffusivity value combinations may be assessed to ensure that parallel and perpendicular diffusivity relationships remain within biologically plausible ranges, preventing parameter sets that would represent phy sically impossible tissue configurations.

[0069] Fisher Information Matrix rank assessment constitutes a fundamental component of the filtering mechanisms, ensuring that parameter estimation problems remain well-posed and mathematically solvable. The filtering process may evaluate the rank of the Fisher Information Matrix for each parameter combination to identify cases where the matrix becomes singular or near-singular. In some cases, combinations that result in rank-deficient Fisher Information Matrices are automatically excluded from the optimization analysis, asthese conditions indicate insufficient information content for reliable parameter estimation. The rank assessment may involve numerical evaluation of matrix eigenvalues, condition numbers, or determinant values to quantify the mathematical stability of each parameter combination.

[0070] Gradient direction sufficiency evaluation may form another layer of the filtering process, examining whether the selected number and distribution of diffusion gradient directions provide adequate sampling of the parameter space. The filtering mechanisms may assess the relationship between the number of model parameters and the number of independent measurements to ensure that the optimization problem remains overdetermined. In some cases, parameter combinations that require more independent measurements than available gradient directions are flagged for exclusion or modified to maintain mathematical solvability. The evaluation process may also consider the geometric distribution of gradient directions to ensure adequate angular sampling for accurate parameter estimation across all model compartments.

[0071] Noise level compatibility' assessment may be incorporated into the filtering mechanisms to ensure that parameter combinations remain estimable under realistic signal-to- noise ratio conditions. The filtering process may evaluate the theoretical lower bounds for parameter estimation uncertainty under specified noise conditions, excluding combinations where the expected estimation variance exceeds acceptable thresholds. In some cases, the assessment considers the interaction between parameter values, gradient strengths, and noise levels to identify combinations that would result in parameter estimates dominated by noise rather than true tissue properties. The compatibility evaluation may also account for the propagation of measurement uncertainties through the model equations to ensure that final parameter estimates maintain sufficient precision for practical applications.

[0072] Computational stability criteria may be applied throughout the filtering process to identify parameter combinations that could lead to numerical instabilities during optimization calculations. The filtering mechanisms may evaluate the conditioning of the optimization problem, examining factors such as parameter scaling, gradient magnitudes, and convergence properties. In some cases, combinations that exhibit poor numerical conditioning are excluded to prevent convergence failures or unreliable optimization results. The stability assessment may also consider the sensitivity of the objective function to small perturbations in parameter values, ensuring that the optimization landscape remains well-behaved and conducive to reliable numerical solution methods.

[0073] It is an advantage of the disclosed systems and methods that the framework may accommodate tissue-specific optimization by analyzing different diffusivity ranges characteristic of various brain tissue types. In some cases, the optimization process considers the distinct microstructural properties of white matter, gray matter, and CSF to generate tailored scanning protocols. The framework may evaluate diffusivity' values spanning from high anisotropic regions to isotropic compartments, with white matter typically exhibiting diffusivity values around 1.74x 1 O’3mm2 / s along the primary' fiber direction. Gray matter regions may demonstrate lower diffusivity' values due to increased cellular density' and reduced directional organization compared to white matter tracts. CSF compartments may exhibit higher isotropic diffusivity values reflecting unrestricted water molecule movement.

[0074] The tissue-specific optimization may incorporate fractional anisotropy variations across different brain regions to determine appropriate scanning parameters. In some cases, white matter regions with high fractional anisotropy values may benefit from protocols emphasizing directional sensitivity through specific gradient direction configurations. Gray matter areas with lower fractional anisotropy may utilize protocols optimized for detecting subtle microstructural changes through enhanced signal-to-noise considerations. The framework may adjust b-value selections based on the expected diffusivity ranges, with higher b-values potentially providing improved sensitivity for tissues with lower diffusivity values. CSF regions may utilize lower b-value protocols to avoid signal loss while maintaining adequate contrast for tissue boundary delineation.

[0075] The optimization process may generate distinct protocol recommendations for pediatric and adult brain studies based on age-related diffusivity' differences. In some cases, developing brain tissue may exhibit different diffusivity characteristics compared to mature tissue, requiring adjusted scanning parameters to achieve comparable measurement precision. The framework may account for regional variations in tissue properties within the same subject, allowing for multi-region optimization strategies. White matter tract-specific protocols may be generated to enhance detection of axonal integrity measures, while cortical gray matter protocols may focus on detecting cellular density variations. The tissue-specific approach may enable users to select protocols tailored to particular clinical applications.

[0076] The framework may evaluate tissue-specific parameter combinations through systematic exploration of biologically relevant ranges for each tissue ty pe. In some cases, the optimization considers the relationship between tissue microstructure and optimal scanning parameters to maximize information content for specific biomarkers. The approach mayincorporate prior knowledge about tissue properties to constrain the parameter space exploration, reducing computational requirements while maintaining optimization effectiveness. Different tissue types may exhibit varying sensitivity' to specific scanning parameters, with the framework identifying these relationships through comprehensive analysis. The tissue-specific optimization may provide guidance for multi-contrast studies where different tissue types are examined within the same imaging session.

[0077] Referring now to FIG. 17, an example method for performing a dMRI scan of a subject using an MRI system is illustrated. The method begins at step 1702 where user input data is received, wherein the user input data includes a selected diffusion model. The selected diffusion model may include various microstructure models such as multi-compartment tissue models that characterize intracellular, extracellular, and cerebrospinal fluid compartments. In some embodiments, the user input data may further include constraints such as available scan time, number of gradient directions, and specific tissue properties of interest for optimization.

[0078] At step 1704, CRLB values are generated using automatic differentiation to determine scanning protocol data for the diffusion MRI scan. The scanning protocol data includes at least one of acquisition parameters for a pulse sequence used in the diffusion MRI scan and model parameters for the selected diffusion model. The automatic differentiation process may enable efficient computation of parameter sensitivities and optimization of the scanning protocol to minimize parameter estimation variance. The acquisition parameters may include b-values, gradient directions, echo times, and repetition times, while the model parameters may correspond to tissue-specific characteristics such as axon density index, axon dispersion index, and parallel diffusivity.

[0079] The method proceeds to step 1706 where magnetic resonance data is acquired from a subject using the MRI system to perform the pulse sequence using the scanning protocol data. The pulse sequence may include a PGSE sequence with optimized timing parameters including gradient duration and separation time. The acquisition may be performed using the determined optimal scanning parameters to collect diffusion-weighted images with enhanced signal-to-noise characteristics and improved parameter estimation precision.

[0080] At step 1708, at least one diffusion image is generated from the magnetic resonance data. The diffusion image may include parametric maps representing various microstructural properties derived from the selected diffusion model. In some aspects, the generated images may include quantitative measures of tissue microstructure such as fractionalanisotropy, mean diffusivity', or model-specific parameters that provide insights into the underlying tissue architecture and pathological conditions.

[0081] The experiment design optimization problem aims to find the optimal acquisition parameters, a (explained below) such that the precision of the estimated model parameters, % (description follows) is maximized. In other words, the process seeks to minimize the sum of the standard errors associated with each model parameter in x.

[0082] Eq. 1 minimizes the trace of the inverse Fisher Information Matrix (FIM) with respect to scanning protocol parameters in a. The FIM, denoted as F, depends on both parameter vectors a and x. This minimization enhances the precision of estimating model parameters (x). as the trace represents the sum of variances (diagonal elements) - the Cramer- Rao Lower Bounds (CRLB) for x. Minimizing the objective function with respect to acquisition parameters a ensures that dMRI data obtained under these scanning parameters yields model parameter (x) estimates with minimal uncertainty.

[0083] This objective function can be derived as follows.

[0084] Let model predicted MR signal attenuation beand w be additive Gaussian noise with zero mean and variance = o2, measured MR signal attenuation y can be given as:

[0085] Likelihood function with the Gaussian noise assumption:

[0086]

[0087]

[0088] First derivative with respect to x:

[0089] Second derivative with respect to x:

[0090] Taking the expected value of:

[0091] Fisher information matrix F

[0092]

[0093] It is an aim to minimize the sum of the coefficients of variation of the model parameters x. To optimize acquisition parameters a, sum of standard errors of each model parameter x can be minimized:

[0094] Where skis the variance of klh model parameter. Since skare unknown.CRLBs can be used in their place. CRLBs are estimated by inverse of Fisher information matrix. F:

[0095] The objective function can be written as:

[0096] CRLB for model parameters x are the diagonal elements of F-1

[0097] The disclosed framework aims to identify the optimal parameters for single diffusion encoding (SDE) within the Pulse Gradient Spin Echo (PGSE) sequence for biophysical modeling applications using dMRI data. As illustrated in FIG. 10. notable PGSE parameters for SDE include: 1) Gradient strength (G): magnetic field gradient magnitude ( mT.m -1 ). 2) Diffusion pulse duration (δ): duration of the diffusion-sensitizing pulse (ms), and3) Diffusion lime (A): interval between the diffusion gradients (ms). Therefore, the set of independent parameters, denoted by a, is defined as: a = {G, A, 8} (2)

[0098] The three independent parameters collectively define the diffusion weighting factor b (s.mm-2), calculated as:

[0099] where y represents the gyromagnetic ratio = 267.515 x 106rad-s^-T"1.

[0100] Gradient directions'. A single unit vector, g = [gx; gy; gz], defines a spatial direction in 3D for the PGSE sequence. Depending on the available scanning time, a set of L such gradient directions can be employed. These can be represented as a matrix, g e RLx3, where each row is a unit vector like g. In some embodiments, the disclosed systems and methods leverage a toolbox from INRIA to acquire a set of L directions uniformly distributed across q -space shells.

[0101] Gyromaznetic ratio M: This constant relates magnetic field strength to nuclear precession frequency with a value of approximately 267.515 x 106rad-s-1-T-1.

[0102] This section details the common parameters used in the model functions representing tissue compartments within the disclosed framework for optimizing scanning protocols for dMRI. Model-specific functions and additional parameters are described in more detail later.

[0103] Volume fi' actions (fd: The volume fraction of the ithcompartment, where i = 1,2, ... , N. These fractions sum to unity’ across all compartments:

[0104] Fiber orientation vector (nd: Defined by using the followingequation: nf= [cos

[0105] Parallel diffusivity, denoted as Ay, signifies thediffusivity along the direction parallel to the fiber orientation vector (nd, commonly referred to as intrinsic free diffusivity7. This parameter is frequently constrained to specific values, such as 0.6 x 103mm2, s’1for ex-vivo and 1.7 x 103mm2. s’1for in-vivo brain tissues. Conversely, perpendicular diffusivity, denoted as characterizes the diffusion perpendicular to nf. It isderived from the parallel diffusivity using a tortuosity' model. Isotropic diffusivity,describes the unrestricted diffusion of w'ater molecules, and is fixed to 2.0 x 103mm2.s-1for ex-vivo and 3.0 x 103mm2. s’1for in-vivo brain tissues. Therefore, in some embodiments, thediffusivity values may not be fixed except for isotropic diffusivity and instead the CRLB can be provided for all diffusivity values in the models.

[0106] In addition to the common model parameters outlined above, this section elaborates on model-specific parameters that can be included for a comprehensive definition of the parameter set x in the optimization problem given in Eq. 1. Below, a brief overview of the commonly utilized biophysical models in brain tissue microstructure imaging is provided. Subsequently, the complete set of model parameters x is provided within the context of each model.

[0107] Diffusion tensor'. Normalized estimated diffusion MRI signal yDTwith diffusion tensor model:

[0108] is the diffusion tensor with dependent modelp where A, are the eigen values of the diffusion tensor and0, 4>, P give rotation of DT around x, y, and z-axis respectively (FIG. 10, Panel A).

[0109] NODDI'. The estimated dMRI signal y oDDi includes the normalized signals from the following three compartments:

[0110] Here, yicand yecdenote the normalized signals from the intra-cellular and extra-cellular compartments of NODDI model, respectively, as outlined by Zhang et al. (13). The isotropic dMRI signal function ydotcan be found in supplementary information of Farooq et al. (53). The NODDI model is parameterized by a set of dependent variables x =wherein vicsignifies the intra-cellular volume fraction, visorepresents the isotropic volume fraction, and OD denotes the neurite orientation dispersion index (13).

[0111] ActiveAx: The estimated dMRI normalized signal using ActiveAx model (14) VActiveAx is assumed to originate from the following three compartments:

[0112] Where, vic, vec, and visoare intra-, extra-and isotropic volume fractions of the dMRI signal such that vic+ vec+ viso= 1. Model functions forand yrlotcan be found in (14, 54) and also in the supplementary information of (53). The ActiveAx model has model parameters s where R denotes axon radius index (in fim).

[0113] Ball-and-Sticks'. The normalized estimated dMRI signal from Ball-and-N-sticks can be expressed as follows:JV

[0114] is the diffusivity values along stick i. Model functions for ystickand can be found in (75) and also in the supplementary information of (03). For ball-and-Three-Sticks. model parameters

[0115] To systematically explore the parameter space and devise an optimal scanning protocol, sets containing the extreme permissible values for each model parameter are established. For instance, let F = {0.1, 0.79} denote the range of volume fractions, 0 = {0, rr / 2} encompass the allowable extreme values of δ, = {0, rr / 2} represents the minimum and maximum possible values for Φ, and D = {1.74, 0.5} represent the range of diffusivity values. To generate all possible combinations of parameter values across these sets, the Cartesian product operation can be employed. The Cartesian product ( F x 0 x <J x ... x D ) yields all possible combinations of parameter values. This product is repeated N times, where N represents the number of compartments, such as the number of sticks in the Ball-and-Sticks model. This process results in a comprehensive set of all possible combinations of model parameters. Subsequently, infeasible combinations are filtered out. For instance, combinations where the sum of volume fractions does not equal one, or where the fiber orientation within a compartment is repeated or identical, are eliminated. This rigorous approach ensures that only physically permissible parameter combinations are considered in the experiments, facilitating a thorough exploration of the model parameter space.

[0116] Biophysical models in diffusion MRI can characterize tissue microstructure, including axonal radius index, density, and orientation distribution. However, the power of these models comes at the cost of complexity . These models rely on intricate mathematical formulations to describe the diffusion process within tissues. Analyzing these models and optimizing MRI sequences based on them necessitates the calculation of derivatives (including CRLB) with respect to various (or all the) model parameters.

[0117] Manual computation of these gradients proves challenging due to the inherent complexity of the models. The intricate nature of mathematical expressions translates to a timeconsuming and laborious differentiation process, inherently prone to errors. While analyticalsolutions exist for simpler models, they become impractical for more intricate biophysical models.

[0118] Differentiable programming offers a solution by treating the entire model as a differentiable entity. This concept unlocks powerful optimization and analysis techniques through automatic differentiation. Automatic differentiation leverages the chain rule to efficiently compute the derivatives of complex functions, ensuring both accuracy by minimizing errors through automation and efficiency by significantly reducing computation time compared to calculating analytical derivatives.

[0119] In some embodiments, biophysical models can be implemented in the TensorFlow framework to capitalize on its capabilities in automatic differentiation and GPU acceleration. It enables the exploitation of automatic differentiation benefits in computing the CRLB for parameters of biophysical models, while also harnessing GPU computational power for accelerated derivative computations.

[0120] A full-rank FIM is advantageous for the disclosed systems and methods, indicating that the information content is sufficient for parameter estimation without redundancy. Three factors can contribute to achieving a full-rank FIM. One example factor is the choice of model parameters. Selecting a diverse set of parameters that comprehensively capture various aspects of the tissue microstructure is advantageous. This heterogeneity helps ensure the FIM is full rank and avoids parameter redundancy. Another example factor is the diffusion gradient directions. In diffusion MRI experiments, applying magnetic field gradients along multiple directions allows for probing the tissue microstructure from various angles. This multi-angular scanning enriches the information content, contributing to a full-rank FIM. Still another factor is the measurement noise. While ideally minimized, a small amount of noise in the data can positively impact the FIM’s rank. Noise can disrupt potential symmetries or degeneracies within the data that might otherwise lead to a non-full-rank FIM.

[0121] In an example study, the reliable recovery' of water diffusivity values in brain tissue was established by optimizing dMRI scanning parameters using the systems and methods described in the present disclosure. These results were achieved by optimizing dMRI scanning parameters across four distinct tissue biophysical models: Diffusion Tensor, Neurite Orientation Dispersion and Density Imaging (NODDI), ActiveAx, and Ball-and-Three-Sticks. Subsequently, each model was analyzed, encompassing all model parameters, including diffusivity values, to identify the optimal overall combination of scanning parameters.

[0122] FIG. 2 illustrates the relationship between water diffusivity and the optimal b- values (refer to Methods section for details on b-values / scanning parameters) essential for their estimation with minimal variance (i.e., minimum Cramer-Rao lower bound, CRLB). Each

[0123] Diffusion Tensor'. FIG. 2 Panel A addresses the diffusion tensor model, a simple yet widely used approach for dMRI microstructure evaluation. The model incorporates six parameters, including three mutually perpendicular eigenvectors that represent the primary diffusion directions within a voxel (see supplementary FIG. SI for details). Human braindistinct eigenvalues within the human brain's feasible range. For clarity, only three perfectly aligned pulse gradient directions with the model’s eigenvectors and an ideal SNR of 50 were used.

[0124] The three sub-figures in FIG. 2 Panel A depict the CRLB for each eigenvalue, revealing an optimal b-value around the reciprocal of the diffusivity value. This aligns with studies comparing Apparent Diffusion Constant (ADC) with b-values. For instance, an optimal b-value, when multiplied by tissue ADC, can be selected to be close to 1.

[0125] These findings underscore the dependence of optimal scanning protocols on specific diffusivity values. Estimating multiple brain tissue diffusivities necessitates protocols incorporating multiple b-values. The challenge of estimating lower diffusivities is evident, as they require high b-values for optimal CRLB. For example, in FIG. 2 Panel A, the rightcombinations. Additionally, these results maintain their consistency irrespective of the selections made for the rotation parameters of the diffusion tensor, namely. 0, <ty and (rad).

[0126] NODDT. The model offers valuable insights into white matter integrity and pathology. It leverages a three-compartment tissue model to separately analyze intricate intra-and extracellular properties. NODDI details two key aspects of axonal pathology: axonal packing density within white matter, quantified by the intracellular volume fraction (vic), and the spatial dispersion of axons, captured by the orientation dispersion index (OD).

[0127] The results presented remain consistent regardless of the specific diffusivity values chosen, though a range from 1.74 to 0.5 x 10'3mm2.s-1was adopted for the study. The analysis employed two perfectly aligned gradient directions, one along the fiber orientation and the other perpendicular, corresponding to parallel and perpendicular diffusivities. Additionally, the impact of OD on diffusivity estimation was examined using extreme values of 0.2 and 0.9. To ensure balanced signal contribution from intra- and extracellular compartments, the intracellular volume fraction (vic) was fixed at 0.5.

[0128] In FIG. 2, panel B shows the minimum achievable CRLB for various intrinsic / parallel and perpendicular diffusivity values. The two subfigures in Panel B correspond to low ( Δ = 10 ms, 8 = 5 ms) and high ( Δ = 75 ms, δ = 65 ms) diffusion-weighting parameters of the Pulse Gradient Spin Echo, PGSE. The results reveal that optimal b-values, marked by minimal CRLB, are roughly reciprocal to diffusivity values, irrespective of A and δ choices. However, OD values affect optimal CRLB or b-values. In regions with minimal axonal dispersion OD = 0.02), both intrinsic and perpendicular diffusivities achieve optimal CRLB at b-values roughly reciprocal to their respective diffusivity values. Conversely, under high orientation dispersion (OD = 0.9), indicative of more isotropic diffusion, parallel diffusivities necessitate relatively higher b-values, while perpendicular diffusivities achieve optimal CRLB at relatively lower b-values. This observation aligns with the anticipated lower parallel diffusivity and higher perpendicular diffusivity in an isotropic diffusion scenario. Similar results, concerning lower diffusivity values such as those found in gray matter and the infant brain.

[0129] ActiveAx: The ActiveAx model offers a quantitative approach to evaluate average axonal diameter within fiber bundles. This method is particularly advantageous as it is insensitive to fiber orientation. However, reliable estimation of model parameters necessitates the use of multishell acquisition protocols. Additionally, recent studies have established correlations between water diffusivity values and axonal radius, whereas the original ActiveAx work employed fixed diffusivity values. Therefore, the relationship between the minimum achievable CRLB and the intrinsic / parallel and perpendicular diffusivity values was investigated. The results of this analysis are shown in FIG. 2, Panel C. The selected diffusivity range aligns with previous research, detailed further in the Discussion section. The analysisutilizes two perfectly aligned gradient directions, the first parallel to the intrinsic diffusivity and the second along the perpendicular diffusivity. To evaluate the impact of diffusivity estimation on CRLB, the axonal radius index (R) is varied across extreme values (0.01 and 11 pm), with a fixed intracellular volume fraction (vic) of 0.5.

[0130] FIG. 2, Panel C, presents results for higher diffusivity regimes, characteristic of white matter. The two sub-figures in the Panel C correspond to distinct diffusion-weighting parameter sets: low weighting with Δ = 10 ms, 8 = 5 ms, and high weighting with A = 75 ms, 8 = 65 ms. Analysis reveals an inverse proportionality (approximately reciprocal relationship) between optimal b-values (at the minimum CRLB) and diffusivity values. This trend persists regardless of the chosen diffusion-weighting parameters ( Δ and 8) or the axonal radius index (R). Interestingly, the R value significantly influences signal attenuation only for the perpendicular diffusivity component, not the parallel component. This behavior can be attributed to the inherent diffusion properties within cylindrical compartments like axons. Parallel diffusivity within these compartments exhibits minimal dependence on the cylinder's radius. Conversely, a larger cylinder radius is likely to elevate perpendicular diffusivity values, potentially leading towards an isotropic diffusion scenario.

[0131] Ball-and-Three-Sticks'. The Ball-and-Stick model decomposes water diffusion into two distinct compartments: an isotropic compartment, which signifies unrestricted water diffusion, commonly referred to as the ’‘ball,” and restricted diffusion compartments, representing diffusion constrained along specific fiber orientations, known as ‘‘sticks.” These sticks correspond to perfectly linear diffusion compartments, suitable for modeling white matter fiber tracts. Here, three stick compartments to model three distinct fiber tracts within a voxel were employed, and a ball was incorporated to capture the isotropic diffusion. Additionally, three gradient pulses precisely aligned with the three stick compartments were(low weighting). The optimal b-value (at minimum CRLB) for achieving the lowest variance in diffusivity estimates is approximately the reciprocal of the corresponding diffusivity value. This observation aligns with findings from other biophysical models, such as the diffusion tensor, NODDL and ActiveAx models.

[0132] Diffusion Tensor '. FIG. 3 explains the impact of pulse gradient directions and signal-to-noise ratio (SNR) on the accurate estimation of all six model parameters of the diffusion tensor. To simulate a diverse array of axonal fiber orientations, the orientation angles were uniformly sampled within the range of [0.01, π ] (rad). This involved ten samples for the three orientation angles of diffusion tensor, resulting in a total of 1000 unique diffusion tensor orientations.

[0133] In a prior study focusing on SNR analysis across various brain regions in dMRI data, SNR values between 10 and 50 were revealed. Consequently, Rician noise at these two SNR levels was introduced into the simulated dMRI data. Additionally, diffusivity' values were constrained within the feasible range of the human brain, resulting in FA = 0.68, distinct from the diffusivity values in FIG. 2 Panel A. In F1G.3, the sub-figures share a common y-axis. presenting log10CRLB plots for all six variables of the diffusion tensor model. The sub-figures also share x-axis, displaying the magnitude of the gradient value G; however, the top two rows feature different ranges of G values compared to the bottom two rows. This variation arises from the need to cover the entire space of PGSE variables. Specifically, two pairs of separation time and gradient duration, similar to those in FIG. 2 (i.e., Δ = 10 ms, 8 = 5 ms for the upper two rows, and Δ = 75 ms, δ = 65 ms for the lower tw o row s), were set. For reference purposes, plots representing b-values are shown in the rightmost figures of the second and third rows, with the b-values scale indicated on the right y-axis.

[0134] Each column in FIG. 3 displays results associated with three distinct gradient tables, each featuring 7, 27, and 130 pulse directions, respectively. The number of pulse gradient directions were chosen to compare the results w ith previous works and to demonstrate how limited scanning time impacts the precision of model parameter estimation (please see Methods section for further discussion). These directions were obtained using a toolbox from INRIA, which provides uniformly distributed directions in q-space shells.

[0135] Each sub-figure in FIG. 3 displays plot lines representing mean values of the CRLB for all parameters of the model, encompassing six model parameters, as well as the sum, i.e., diagonal elements and the trace of the CRLB matrix. The corresponding-colored shaded area for each plot line illustrates the 95 percent confidence interval. Notably, for a smaller number of pulse gradient directions (i.e., 7), the mean CRLB exhibits higher values. Specifically, orientation angles associated with low diffusivity values, i.e., Φ and β, show the highest mean CRLBs with a broad confidence interval. All subfigures are annotated with optimal b-values for the primary diffusivity and the trace of the inverse of FIM. It is evident,particularly from the rightmost column, that an increase in pulse gradient directions leads to reduced confidence intervals for all parameters, with a particular impact on orientation angles associated with low diffusivity values c|t and p (rad), which pose the greatest challenge in terms of estimation. Additionally, the results indicate that with a low SNR of 10, the noise floor is reached earlier. For instance, in the top-right sub-figure, the minimum trace of the CRLB is observed at a b-value of 822 (s.mm-2). Conversely, when maintaining the same configuration but with an SNR of 50 (second row, rightmost column), the optimal CRLB value is achieved at a higher b-value of 902 (s.mm-2). To accurately estimate lower diffusivities and their corresponding orientation angles, employing a greater number of pulse gradient directions and achieving higher SNR is important. In a broad sense, b-values ranging from 900 to 1000 (s.mm’2) are deemed optimal for estimating all six parameters of the diffusion tensor, which is already the standard for clinical diffusion weighted imaging.

[0136] Summary' of optimal diffusion tensor model experiment design results is as follows: (1) Diffusivity significantly influences optimal b-value selection, displaying an inverse relationship. Lower diffusivities necessitate higher b-values, increased SNR, and a greater number of gradient directions; (2) More pulse gradient directions enhance parameter estimation accuracy by reducing CRLB and minimizing confidence interval. However, low SNR can compromise accuracy, even with a substantial number of directions, reaching the noise floor earlier; (3) Optimal scanning protocols vary’ based on tissue properties and objectives. For example, in white matter where anisotropic diffusion dominates, higher b- values may’ yield inaccurate results; (4) For the diffusion tensor model, achieving the minimum CRLB is influenced by b-values, theoretically irrespective of the specific choices for G (mT.m’ ' ). A, and δ (ms). However, practical parameter selection is limited by the hardware constraints.

[0137] NODDI'. Building upon the scanning protocols proposed by Zhang et al. for the NODDI model, this work evaluated their performance using experiment design optimization. FIG. 4 presents a comparison of these protocols, replicating the experimental settings from the original study. To account for potential biases introduced by fiber orientation distribution, a high number of 256 unique axonal fiber orientations sampled uniformly over a sphere was employed. Additionally, eight distinct combinations of NODDI model parameters were investigated to assess variations in the results due to model parameter values. The b-values are denoted in s.mm-2, with the number of sampled orientations for each b-value displayed in parentheses. Building upon the insights from FIG. 5, nine alternative protocols (P 09 2I to P 13 22) are introduced. These protocols are characterized by lower maximum b-values yetmaintaining comparable CRLB with the empirically identified optimal protocol (P 14) in the NODDI publication, as illustrated in FIG. 6.Table 1. Imaging Protocols for the NODDI ModelProtocol Settings

[0138] The results demonstrate the superiority of two-shell protocols over single-shell protocols. Notably, protocol P 14 consistently achieved the best performance for six out of eight tissue configurations. This study arrives at the same conclusion through experiment design optimization, offering advantages in terms of implementation ease and flexibility'. Also, the approach described in the present disclosure readily adapts to vary ing scanning time constraints and allow s for the exploration of a broader range of model parameters of interest. For example, this study considers variable diffusivity values, whereas the original work employed fixed values, enabling to account for diffusivity variations on NODDI parameter estimates.

[0139] The methodology' outlined above can be extended to identify the optimal scanning protocol for the NODDI model. FIG. 5 demonstrates the dependency of the CRLB of the NODDI model parameters on the acquisition parameters such as G (mT.m-1). Δ, δ (ms), and the number of gradient directions. The x-axis of the figure represents the gradient strength, G (mT.m-1), wi th tw o columns corresponding to different ranges of G values determined by the choice of diffusion time and diffusion weighting factor, as indicated atop each column. Thecorresponding b-value distributions for these ranges are depicted in the middle row. The y-axis displays the log scaled CRLB for all sixNODDI model parameters. Each plot exhibits different colored lines representing the CRLB for each model parameter, with color-coded shaded areas indicating the 95% confidence interval. The rows of plots display results for different numbers of gradient directions: 30, 60, and 90. The NODDI model parameters adhere to established human brain ranges, with 36 distinct tissue configurations generated using the Cartesian product of extreme parameter values to maximize variability in the results (see methods section). Unlike previous analyses, diffusivity values are not fixed, showcasing that CRLB for model parameters decreases with increasing scanning time (or number of gradient directions). However, optimal b-values in all cases remain approximately 2200 s.mm-2, as indicated by the gray arrow, while the point of maximum curvature varies between 900 and 1300 s.mm-2. The points of maximum curvature points are marked with red arrows, identified by the "kneedle" algorithm with default settings, signifying the optimal trade-off between G I b-value and CRLB, beyond which further increase in G yield minimal improvement in CRLB.

[0140] Using b-values from maximum curvature and minimum CRLB points from FIG. 5, a series of efficient two-shell protocols are outlined for the NODDI model as detailed in Table 1. Notably, the proposed protocols were compared with those identified as optimal through empirical means. Table 1 provides a comprehensive overview of both sets. FIG. 6 presents the log scaled CRLB for all six NODDI model parameters across the eleven protocols. As evident from the figure, the proposed protocols, derived from the analysis in FIG. 5, achieve comparable CRLB performance to the established NODDI protocols. However, the proposed protocols require low er maximum b-values which can be easy to achieve in clinical settings.

[0141] ActiveAx: FIG. 7 shows the relationship between the CRLB of ActiveAx model parameters and the acquisition parameters, similar to the experiment configuration detailed in FIG. 5 for NODDI model. Here, 48 distinct tissue configurations generated through the Cartesian product of extreme model parameter values were employed to enhance result variability. It can be observed from FIG. 7 that minimizing CRLB in the ActiveAx model relies not only on b-values but also on the choice of G (mT.m'1). A, and 8 (ms). The figure highlights that the parameter R (axon radius index measured in pm) consistently exhibits the highest CRLB, indicating the most challenging parameter to estimate accurately. Moreover, it suggests the presence of potential optimal combinations of G, A. and 8 values within the unexplored ranges depicted in two columns of the figure. To explore these combinations, a grid search across the three PGSE parameters (6, A, and 5) within the ranges depicted in FIG. 7 wasperformed. The search utilized a resolution of 100 points for each parameter, resulting in a total of 106potential configurations. However, points where 8 exceeded Δ (infeasible scenarios) were excluded from the analysis. This filtering yielded 56632 points with full-rank FIM, representing valid combinations of scanning parameters.

[0142] FIG. 8 visually represents partial results from the grid search. The x-axis illustrates the trace of the inverse FIM. serving as a measure of the overall parameter estimation uncertainty. The left y-axis displays the corresponding Δ and 8 values for each point, while the two righty-axes depict the resulting b-values and G values. Each subfigure showcases the best 15 identified protocols, ranked by CRLB of the corresponding model parameter (displayed at the top of each subfigure). These plots facilitate the selection of optimal multishell protocols for ActiveAx-based axon diameter estimation experiments. By considering scanner limitations and desired scan time constraints, informed choices can be made regarding acquisition parameters. This systematic approach ultimately leads to more accurate estimates of ActiveAx model parameters, particularly the axon diameter index.

[0143] Ball-and-Three-Sticks'. FIG. 9 analyzes the Ball-and-Three-Sticks model. Here, all twelve parameters associated with the three sticks, including diffusivity values, orientation angles, and volume fractions, were freely estimated. To explore combinations of extreme yet biologically plausible parameter values, 648 unique tissue configurations were generated. The plots in FIG. 9 reveal that diffusivity values are generally more challenging to estimate than the orientation angles and volume fractions of the sticks. Increasing the gradient strength (C) and b-values typically leads to a decrease in CRLB. However, the optimal b-value range falls within approximately 5.000 to 7.000 s.mm2. which presents challenges for clinical DWI protocols. Fortunately, the points with the maximum curvature on the Tr FIM 'L) for all variables represent an optimal trade-off between b-value selection and achieving a low CRLB. The optimal value in this case is found to be around 3,000 s.mm2. suggesting that reliable estimation of the three-stick model parameters can be obtained without requiring any prior knowledge or assumptions regarding the diffusivity values.

[0144] FIGS. 11-13 illustrate additional data from the example study described above. FIG. 11 illustrates example CRLB for lower intrinsic and perpendicular diffusivity values e.g., in gray matter and infant brains using NODDI model. The left column demonstrate the dMRI signal attenuation with increasing G values, while the right column presents the log-scale CRLB plots. The two line types show results related to extreme values of OD as shown in figure legend. Also, the rows show results for the two extreme combinations of Δ and 8 (ms).The results show that the minimum (optimal) CRLB is related to b-values approximately reciprocal to the corresponding diffusivity values while OD values affect the relationship. FIG. 12 illustrates example CRLB for lower intrinsic and perpendicular diffusivity values e.g., in gray matter and infant brains using ActiveAx model. The left column demonstrate the dMRI signal attenuation with increasing G values, while the right column presents the log-scale CRLB plots. The two line types show results related to extreme values of R as shown in figure legend. Also, the rows show results for the two extreme combinations of Δ and δ (ms). The key finding is that the minimum (optimal) CRLB is related to the b-values approximately reciprocal to the corresponding diffusivity values while R values. However, the R value only influences this relationship for perpendicular diffusivityonly. FIG. 13 illustrates example CRLB for Ball-and-Two-Sticks model. CRLB using 18 unique tissue configurations at SNR = 20 are shown. Ball and Stick parameters were constrained within the human brain's feasible range. The sub-figures share a common y-axis, exhibiting log-scale CRLB plots for all six variables in the model. The x-axis shows the magnitude of the gradient value G (mT.m-1) with the two columns featuring different G ranges, reflecting variations in the choice of Δ and 8 (ms), b-values corresponding to the optimal CRLB are shown. Sub-figures show plots for mean CRLB values of model parameters and their sum (trace of the CRLB matrix), with the corresponding-colored shaded areas indicating the 95 percent confidence interval. Maximum curvature points shown with red arrows are "sw eet spots” detected by ’kneedle’ algorithm with default settings. The points show' optimal trade off at which the relative cost of increasing G or b-values is no longer w orth in improvement of CRLB.

[0145] Fitting the diffusion tensor model to dMRI data, the diffusion tensor imaging (DTI), is widely employed to explain brain tissue microstructure due to its simplicity and reproducibility. Over the past two decades, a multitude of studies has investigated optimizing scanning protocols for DTI. These investigations have looked into the influence of factors such as the number of gradient directions, parameters of the PGSE, and noise on the accurate estimation of tissue biomarkers derived from DTI. Furthermore, research has illuminated the impact of specific tissue properties on the precise estimation of tissue microstructure using the model and tailored scanning protocols.

[0146] Optimal b-valuc. The b-value in diffusion-weighted imaging is measured in s.mm-2. the reciprocal of diffusivity units for anisotropic diffusion or the ADC matrix in isotropic diffusion. Higher b-values increase degree of diffusion-weighting, causing signal intensity loss. Similarly, elevated diffusivity' values lead to more dMRI signal loss, indicatinggreater diffusion. Previous studies suggest a simple rule of thumb for selecting optimal b-value i.e., b-value when multiplied by the ADC of the tissue under investigation should be close to 1 or approximately 1.1. Also, previous work shows that for DTI, optimal b-values range from 900 to 1000. The results in FIG. 2 Panel A align with the previous literature, however, derived solely from CRLB for the diffusion tensor model.

[0147] Number of gradient directions’. Ideally, for the estimation of the six parameters of the diffusion tensor, employing at least six non-collinear diffusion encoding directions along with one minimally T2 -weighted low b-image (b = 0 s.mm-2) can be sufficient. On the other hand, other studies have shown that for the estimation of all parameters of the diffusion tensor, approximately 30 gradient directions serve as a practical compromise between image quality and scanning time. They also observed that increasing the number of orientations beyond 30 did not lead to improved tensor orientation estimation. Another study, suggested that, for estimating fiber orientation, an acquisition scheme utilizing as many directions as possible and only one b-value produces the best results in terms of accuracy and stability. In the example study involving 7, 27, and 130 gradient orientations, a higher number of orientations was found to enhance fiber orientation estimates.

[0148] Tissue properties’. The example study demonstrated that the optimal acquisition b-value for DTI can be influenced by the specific tissue type and its physiological or pathological characteristics under investigation. Diffusivity values, which vary in white matter, gray matter, cerebrospinal fluid (CSF), and in diseased tissues, may have optimal b-values that deviate from the widely accepted clinical standard of b=1000 (s.mm-2). Following are examples from previous studies that highlight optimal b-values for DTI specific to various tissue types: (1) Discriminating High-Grade and Low-Grade Gliomas: A higher b-value of 3000 (s.mm-2) proves more beneficial than b = 1000 (s.mm-2) for distinguishing between high-grade and low- grade gliomas; (2) Peripheral Nerves Imaging: The optimum tissue-specific b-value in peripheral nerves is capped at approximately 700 (s.mm-2): (3) Multiple Sclerosis-Related Hippocampal Microstructural Alteration: To investigate the impact of multiple sclerosis on gray matter in a mouse model, only DTI with the highest tested b-value (2700 s.mm-2) revealed dendritic loss. Thus, achieving biologically meaningful gray matter DTI metrics necessitates high b-values and an adequate number of gradient directions.

[0149] NODDI is one of the most widely used multi-compartment brain tissue biophysical models due to its short scan times and availability of multiple models fitting tools. The systems and methods described in the present disclosure introduce a systematic frameworkfor identifying optimal NODDI scanning protocols using CRLB analysis (FIG. 5), offering flexibility for different tissue types and scan time constraints.

[0150] Simplifying assumptions on tissue microstructure'. NODDI simplifies the process of model parameter estimation by making several assumptions about tissue architecture and diffusion properties. These include the presence of a single dominant fiber orientation per voxel, a fixed intrinsic parallel diffusivity value, estimation of perpendicular diffusivity using a tortuosity model, negligible water exchange between compartments, and a low volume fraction of isotropic diffusion, particularly in white matter. These simplifications enable the model parameters to be efficiently and reliably estimated from the dMRI signal.

[0151] Several studies have explored the impact of predefined parallel diffusivity

[0152] Based on the findings from FIG. 2 Panel B in the example study, it can be suggested that tissue diffusivity values could potentially be estimated via NODDI when b- values are approximately the reciprocal of diffusivity values. However, two conditions should be met for this estimate: Low OD, typically found in white matter, as high OD can impede accurate diffusivity estimation. Additionally, diffusion gradient directions should be aligned with principal diffusion directions, which is achievable by maximizing the number of diffusion directions within scan time constraints.

[0153] Optimal b-values'. Studies have focused on optimizing NODDI scanning protocols to achieve a practical balance between scan time and the reproducibility of estimated parameters. This optimization process involves finding the best combination of the diffusion weighting factors (b-values) and the number of diffusion directions to acquire reliable data while minimizing scan time.

[0154] One approach to protocol optimization involves evaluating the empirical reproducibility of NODDI metrics based on different b-value and diffusion sampling schemes. One study investigated this concept and suggested that for estimating the intracellular volume fraction (vic), a b-value of 2500 s.mm-2was optimal. In contrast, for orientation dispersion(OD), a b-value of 2500 / 3000 s.mm-2was found to be the most suitable, with a requirement for a total number of diffusion directions exceeding 128. Another study used the same scanning protocol and applied a test-retest approach to assess the reproducibility and reliability of NODDI biomarkers from both pediatric and adult subjects. Beyond in-vivo studies, ex-vivo investigations have also contributed to protocol optimization. A study using mouse brain data concluded that a 3-shell dataset with b-values of 1000. 4000, and 8000 s.mm-2produced model parameter estimates close to those obtained using a 6-shell protocol with b-values of 500, 1000, 2000, 4000, 6000, and 8000 s.mm-2.

[0155] The observations in FIG. 5 partially agree with the prior investigations. The figure indicates that the optimal b-value for estimating orientation dispersion (OD) lies around 4000 s.mm-2, a value higher than the 3000 s.mm-2. FIG. 5 demonstrates that increasing b-values could potentially reduce the CRLB further, thus reducing variability in parameter estimates. Additionally, in ex vivo brain studies, tissue exhibits lower diffusivity compared to in vivo settings. Therefore, higher b-values may be essential for accurately estimating model parameters in ex vivo studies.

[0156] The results presented in this study remain independent of the model fitting algorithms utilized. Nonetheless, it is essential to recognize that investigations assessing the reproducibility of NODDI metrics, as discussed above, utilize diverse model fitting techniques encompassing DMT. CuDIMOT, AMICO, and the NODDI MATLAB toolbox. This may also impact the accuracy of parameter fitting, alongside considerations such as b-values, gradient directions, and fixed diffusivity values. Subsequent research endeavors for assessing reproducibility using empirical methods should endeavor to standardize fitting methods for more uniform comparisons across studies.

[0157] Axon diameter is a critical characteristic of brain white matter, directly impacting conduction speed and influencing action potential firing rates. These processes are fundamental for evaluating brain function. Consequently, the ability to measure axon diameter accurately, non-invasively, and in vivo using dMRI data holds immense value for investigating various brain diseases and healthy development.

[0158] The ActiveAx technique addresses this need by employing a biophysical model known as the Minimal Model of White Matter Diffusion (MMWMD). This model leverages dMRI data to estimate the axonal radius index (R) within a voxel, representing the main fiber bundle. The MMWMD characterizes the intra-axonal space as a compartment with restricted water diffusion confined to a bundle of cylinders with uniform radii. Conversely, the extra-axonal space is modeled as a compartment exhibiting hindered water displacement perpendicular to the axons. Additionally, the model can be optimized for in vivo or ex vivo applications by incorporating compartments for cerebrospinal fluid and stationary water.

[0159] The ActiveAx model offers a valuable tool for estimating axon diameter index, but it relies on certain assumptions that may limit its accuracy. One assumption is the presence of a single fiber orientation within a voxel. Additionally, the model treats diffusivities as fixed values. One study demonstrated the potential of using the PGSE sequence to estimate both parallel diffusivity (λII) and perpendicular diffusivitywithin a voxel and then use the estimated to infer axon radius index index (R). Furthermore, several studies have reported a proportional relationship between increasing monotonically as R increases.

[0160] The findings in FIG. 2 Panel C support this connection. The CRLB of theis influenced by variations in the R. Conversely, the CRLB of theremains largely unaffected by changes in R. This observation confirms thatare indeed interrelated and that variations in R can influence the accuracy ofestimation.

[0161] FIG. 7 comprehensively explores how the CRLB of the ActiveAx model parameters is impacted by utilizing a wide range of the model parameter values. FIG. 7 examines how varying these parameters across their extreme extents influences the minimum achievable variance in the estimates of the model parameters. One takeaway is that the R consistently exhibited the highest CRLB across all scenarios, suggesting it is the most challenging parameter to estimate accurately. In contrast to models like DT, NODDI, and Balls-and-Stick that rely solely on b-values for scanning protocol optimization, the accuracy of ActiveAx estimations depends on a combination of PGSE parameters: G (mT.m-1), Δ, and δ (ms). Therefore, to identify optimal acquisition protocols, a grid search over the PGSE parameter range was conducted. The results, presented in FIG. 8, demonstrate that the optimal protocols identified through the grid search can be further filtered based on specific scanner constraints. For instance, the figure showcases optimal protocols for all model parameters considering a maximum G-value of 300 mT.m-1and a δ / Δ ratio greater than 0.1. These constraints can be tailored to specific scanner capabilities and experimental requirements.

[0162] The Ball-and-Stick model provides a simplified representation of white matter microstructure, conceptualizing axons as impermeable cylinders with negligible radius and assuming isotropic diffusion in the surrounding extracellular space. Initially introduced within a Bayesian framework for ball-and-one-stick estimation and fractography, this model has been widely adopted to implement probabilistic approach in fractography toolsets within prominentsoftware packages such as FSL and FreeSurfer / TRACULA for tractography analysis. However, challenges emerge when dealing with voxels containing crossing fibers, as highlighted by recent studies indicating inaccuracies in fiber parameter estimation within such scenarios. This issue is particularly significant given the prevalence of crossing fibers, with estimates suggesting that 60-90% of white matter voxels exhibit this complex geometry'.

[0163] To tackle this challenge, a simplified version of the Ball-and-Stick model was previously proposed. Moreover, another study introduced model specific fitting techniques employing an Expectation-Maximization algorithm to enhance model parameters estimation accuracy(52). The disclosed systems and methods focus on mitigating the issue of inaccurate parameter estimation of the Ball-and-Stick model, when applied to complex fiber geometries, by identifying optimal scanning protocols specifically tailored for the ball-and-two-sticks and ball-and-three-sticks models. FIG. 9 illustrates the relationship between b-values, the number of gradient directions, and the CRLB for both the models. It is show n that higher b-values and a greater number of gradient directions result in lower CRLB values. These findings suggest that estimating the Ball-and-Stick model in scenarios involving fiber crossings, such as those with two or three sticks, is challenging when using scanning protocols that include a single low b-value of 1000 s.mm-2and only 60 gradient directions.

[0164] The findings suggest that, for fixed diffusivity' values and two fiber orientations / sticks, a two-shell protocol with low b-value of 700 s.mm-2and high b-value ranging from 4000 to 7000 s.mm-2is recommended, with at least 30 to 60 directions in each shell. Similarly, for the ball-and-three-sticks model, with variable diffusivities in each stick, lower b-value of 3000 s.mm-2and higher b-value ranging from 5000 to 7000 s.mm-2is recommended, along with 30 to 60 directions in each shell.

[0165] In summary’, the present disclosure provides a method to optimize dMRI data acquisition for specific scan time constraints and tissue properties. This can be achieved by leveraging advances in automatic differentiation and parallel computing to enable efficient implementation of complex biophysical tissue models. This approach offers a generalizable and scalable framework applicable to any tissue modeling technique utilizing dMRI data for imaging.

[0166] FIG. 14 shows an example of a system 1400 for generating optimized scanning protocols for dMRI acquisitions in accordance with some embodiments described in the present disclosure. As shown in FIG. 14, a computing device 1450 can receive one or more types of data (e.g., scanning protocol data) from data source 1402. In some embodiments, computingdevice 1450 can execute at least a portion of a dMRI scan protocol optimization system 1404 to generate optimized scanning protocol data (e.g.. acquisition parameters, fixed parameters, common tissue model parameters, model-specific parameters) from data received from the data source 1402.

[0167] Additionally or alternatively, in some embodiments, the computing device 1450 can communicate information about data received from the data source 1402 to a server 1452 over a communication network 1454, which can execute at least a portion of the dMRI scan protocol optimization system 1404. In such embodiments, the server 1452 can return information to the computing device 1450 (and / or any other suitable computing device) indicative of an output of the dMRI scan protocol optimization system 1404.

[0168] In some embodiments, computing device 1450 and / or server 1452 can be any suitable computing device or combination of devices, such as a desktop computer, a laptop computer, a smartphone, a tablet computer, a wearable computer, a server computer, a virtual machine being executed by a physical computing device, and so on. The computing device 1450 and / or server 1452 can also reconstruct images from the data.

[0169] In some embodiments, data source 1402 can be any suitable source of data (e.g., measurement data, images reconstructed from measurement data, processed image data, scan protocol data including acquisition parameters, fixed parameters, common tissue model parameters, model-specific parameters, etc.), such as an MRI system, another computing device (e.g., a server storing measurement data, images reconstructed from measurement data, processed image data, scan protocol data including acquisition parameters, fixed parameters, common tissue model parameters, model-specific parameters, etc.), and so on. In some embodiments, data source 1402 can be local to computing device 1450. For example, data source 1402 can be incorporated with computing device 1450 (e.g.. computing device 1450 can be configured as part of a device for measuring, recording, estimating, acquiring, or otherwise collecting or storing data). As another example, data source 1402 can be connected to computing device 1450 by a cable, a direct wireless link, and so on. Additionally or alternatively, in some embodiments, data source 1402 can be located locally and / or remotely from computing device 1450, and can communicate data to computing device 1450 (and / or server 1452) via a communication network (e.g., communication network 1454).

[0170] In some embodiments, communication network 1454 can be any suitable communication network or combination of communication networks. For example, communication network 1454 can include a Wi-Fi network (which can include one or morewireless routers, one or more switches, etc.), a peer-to-peer network (e.g., a Bluetooth network), a cellular network (e.g., a 3G network, a 4G network, etc., complying with any suitable standard, such as CDMA, GSM, LTE, LTE Advanced, WiMAX, etc.), other types of wireless network, a wired network, and so on. In some embodiments, communication network 1454 can be a local area network, a wide area network, a public network (e.g., the Internet), a private or semi-private network (e.g., a corporate or university intranet), any other suitable type of network, or any suitable combination of networks. Communications links shown in FIG. 14 can each be any suitable communications link or combination of communications links, such as wired links, fiber optic links, Wi-Fi links, Bluetooth links, cellular links, and so on.

[0171] Referring now to FIG. 15, an example of hardware 1500 that can be used to implement data source 1402. computing device 1450, and server 1452 in accordance with some embodiments of the systems and methods described in the present disclosure is shown.

[0172] As shown in FIG. 15, in some embodiments, computing device 1450 can include a processor 1502, a display 1504, one or more inputs 1506, one or more communication systems 1508, and / or memory 1510. In some embodiments, processor 1502 can be any suitable hardware processor or combination of processors, such as a central processing unit (CPU), a graphics processing unit (GPU), and so on. In some embodiments, display 1504 can include any suitable display devices, such as a liquid crystal display (LCD) screen, a light-emitting diode (LED) display, an organic LED (OLED) display, an electrophoretic display (e.g., an “e- ink" display), a computer monitor, a touchscreen, a television, and so on. In some embodiments, inputs 1506 can include any suitable input devices and / or sensors that can be used to receive user input, such as a keyboard, a mouse, a touchscreen, a microphone, and so on.

[0173] In some embodiments, communications systems 1508 can include any suitable hardware, firmware, and / or software for communicating information over communication network 1454 and / or any other suitable communication networks. For example, communications systems 1508 can include one or more transceivers, one or more communication chips and / or chip sets, and so on. In a more particular example, communications systems 1508 can include hardware, firmware, and / or software that can be used to establish a Wi-Fi connection, a Bluetooth connection, a cellular connection, an Ethernet connection, and so on.

[0174] In some embodiments, memory 1510 can include any suitable storage device or devices that can be used to store instructions, values, data, or the like, that can be used, forexample, by processor 1502 to present content using display 1504, to communicate with server 1452 via communications system(s) 1508, and so on. Memory 1510 can include any suitable volatile memory, non-volatile memory, storage, or any suitable combination thereof. For example, memory 1510 can include random-access memory (RAM), read-only memory (ROM), electrically programmable ROM (EPROM), electrically erasable ROM (EEPROM), other forms of volatile memory, other forms of non-volatile memory, one or more forms of semi -volatile memory, one or more flash drives, one or more hard disks, one or more solid state drives, one or more optical drives, and so on. In some embodiments, memory 1510 can have encoded thereon, or otherwise stored therein, a computer program for controlling operation of computing device 1450. In such embodiments, processor 1502 can execute at least a portion of the computer program to present content (e.g., images, user interfaces, graphics, tables), receive content from server 1452, transmit information to server 1452, and so on. For example, the processor 1502 and the memoiy' 1510 can be configured to perform the methods described herein (e.g., the method illustrated in FIG. 1).

[0175] In some embodiments, server 1452 can include a processor 1512, a display 1514, one or more inputs 1516, one or more communications systems 1518, and / or memory 1520. In some embodiments, processor 1512 can be any suitable hardware processor or combination of processors, such as a CPU, a GPU, and so on. In some embodiments, display 1514 can include any suitable display devices, such as an LCD screen, LED display, OLED display, electrophoretic display, a computer monitor, a touchscreen, a television, and so on. In some embodiments, inputs 1516 can include any suitable input devices and / or sensors that can be used to receive user input, such as a keyboard, a mouse, a touchscreen, a microphone, and so on.

[0176] In some embodiments, communications systems 1518 can include any suitable hardware, firmware, and / or software for communicating information over communication network 1454 and / or any other suitable communication networks. For example, communications systems 1518 can include one or more transceivers, one or more communication chips and / or chip sets, and so on. In a more particular example, communications systems 1518 can include hardware, firmware, and / or software that can be used to establish a Wi-Fi connection, a Bluetooth connection, a cellular connection, an Ethernet connection, and so on.

[0177] In some embodiments, memory’ 1520 can include any suitable storage device or devices that can be used to store instructions, values, data, or the like, that can be used, forexample, by processor 1512 to present content using display 1514. to communicate with one or more computing devices 1450, and so on. Memory 1520 can include any suitable volatile memory, non-volatile memory, storage, or any suitable combination thereof. For example, memory 1520 can include RAM, ROM, EPROM, EEPROM, other types of volatile memory, other types of non-volatile memory, one or more types of semi-volatile memory, one or more flash drives, one or more hard disks, one or more solid state drives, one or more optical drives, and so on. In some embodiments, memory 1520 can have encoded thereon a server program for controlling operation of server 1452. In such embodiments, processor 1512 can execute at least a portion of the server program to transmit information and / or content (e.g., data, images, a user interface) to one or more computing devices 1450, receive information and / or content from one or more computing devices 1450, receive instructions from one or more devices (e.g., a personal computer, a laptop computer, a tablet computer, a smartphone), and so on.

[0178] In some embodiments, the server 1452 is configured to perform the methods described in the present disclosure. For example, the processor 1512 and memory 1520 can be configured to perform the methods described herein (e.g.. the method illustrated in FIG. 1).

[0179] In some embodiments, data source 1402 can include a processor 1522, one or more data acquisition systems 1524, one or more communications systems 1526, and / or memory 1528. In some embodiments, processor 1522 can be any suitable hardware processor or combination of processors, such as a CPU, a GPU, and so on. In some embodiments, the one or more data acquisition systems 1524 are generally configured to acquire data, images, or both, and can include an MRI system. Additionally or alternatively, in some embodiments, the one or more data acquisition systems 1524 can include any suitable hardware, firmware, and / or software for coupling to and / or controlling operations of an MRI system. In some embodiments, one or more portions of the data acquisition system(s) 1524 can be removable and / or replaceable.

[0180] Note that, although not show n, data source 1402 can include any suitable inputs and / or outputs. For example, data source 1402 can include input devices and / or sensors that can be used to receive user input, such as a keyboard, a mouse, a touchscreen, a microphone, a trackpad, a trackball, and so on. As another example, datasource 1402 can include any suitable display devices, such as an LCD screen, an LED display, an OLED display, an electrophoretic display, a computer monitor, a touchscreen, a television, etc., one or more speakers, and so on.

[0181] In some embodiments, communications systems 1526 can include any suitable hardware, firmware, and / or software for communicating information to computing device 1450(and, in some embodiments, over communication network 1454 and / or any other suitable communication networks). For example, communications systems 1526 can include one or more transceivers, one or more communication chips and / or chip sets, and so on. In a more particular example, communications systems 1526 can include hardware, firmware, and / or software that can be used to establish a wired connection using any suitable port and / or communication standard (e.g., VGA, DVI video, USB, RS-232, etc.), Wi-Fi connection, a Bluetooth connection, a cellular connection, an Ethernet connection, and so on.

[0182] In some embodiments, memory 1528 can include any suitable storage device or devices that can be used to store instructions, values, data, or the like, that can be used, for example, by processor 1522 to control the one or more data acquisition systems 1524, and / or receive data from the one or more data acquisition systems 1524; to generate images from data; present content (e g., data, images, a user interface) using a display; communicate with one or more computing devices 1450; and so on. Memory 1528 can include any suitable volatile memory, non-volatile memory. storage, or any suitable combination thereof. For example, memory 1528 can include RAM, ROM. EPROM, EEPROM, other types of volatile memory, other types of non-volatile memory, one or more types of semi-volatile memory, one or more flash drives, one or more hard disks, one or more solid state drives, one or more optical drives, and so on. In some embodiments, memory 1528 can have encoded thereon, or otherwise stored therein, a program for controlling operation of data source 1402. In such embodiments, processor 1522 can execute at least a portion of the program to generate images, transmit information and / or content (e.g., data, images, a user interface) to one or more computing devices 1450, receive information and / or content from one or more computing devices 1450, receive instructions from one or more devices (e.g., a personal computer, a laptop computer, a tablet computer, a smartphone, etc.), and so on.

[0183] The dMRI scan protocol optimization system 1404 may implement the methods described in the detailed description through coordinated operation of its distributed computing components. In some embodiments, the computing device 1450 may receive user input data specifying a selected diffusion model, tissue properties of interest, scan time constraints, and desired number of gradient directions through its inputs 1506. The processor 1502 may execute portions of the dMRI scan protocol optimization system 1404 stored in memory 1510 to initiate the protocol optimization workflow. The system may generate parameter combinations across extreme values of model parameters for the selected multi-compartment tissue biophysical model, such as NODDI. ActiveAx. or Ball-and-Sticks models, using Cartesian productoperations to ensure comprehensive exploration of the parameter space. Additionally or alternatively, the server 1452 may receive the user input data and, through its processor 1512 may execute portions of the optimization system 1404 to initiate the protocol optimization workflow.

[0184] The automatic differentiation and FIM calculations may be performed using the computational resources of either the computing device 1450 or the server 1452, depending on the system configuration. In some embodiments, the processor 1502 or 1512 may leverage GPU acceleration capabilities to compute complex mathematical derivatives of biophysical model functions with respect to all model parameters simultaneously. The system may implement the biophysical models in differentiable programming frameworks such as TensorFlow. enabling efficient computation of CRLB values through automatic differentiation. The parallel computing architecture may distribute these calculations across available processing units to handle the computational intensity required for sophisticated multicompartment models while filtering out parameter combinations that result in non-full-rank FIMs.

[0185] The dMRI scan protocol optimization system 1404 may determine optimal pulse sequence parameters by systematically exploring PGSE sequence, or other pulse sequence, parameter combinations including gradient strength, diffusion pulse duration, and diffusion time within hardware-feasible ranges. The dMRI scan protocol optimization system 1404 may apply curvature-based optimization methods to identify trade-off points between scanning parameters and estimation precision, using algorithms such as the kneedie method to detect maximum curvature points in CRLB versus parameter plots. The communications systems 1508, 1518, and 1526 may facilitate data exchange between components, allowing the server 1452 to return optimized scanning protocol data to the computing device 1450 or directly to the data source 1402 when configured as an MRI system. The resulting optimized protocols may include specific b-value combinations, gradient direction distributions, and PGSE (or other pulse sequence) timing parameters that minimize parameter estimation variance while accommodating scanner hardware limitations and scan time constraints specified in the user input data.

[0186] In some embodiments, any suitable computer-readable media can be used for storing instructions for performing the functions and / or processes described herein. For example, in some embodiments, computer-readable media can be transitory’ or non-transitory. For example, non-transitory computer-readable media can include media such as magneticmedia (e.g., hard disks, floppy disks), optical media (e.g., compact discs, digital video discs, Blu-ray discs), semiconductor media (e.g.. RAM, flash memory, EPROM. EEPROM), any suitable media that is not fleeting or devoid of any semblance of permanence during transmission, and / or any suitable tangible media. As another example, transitory' computer- readable media can include signals on networks, in wires, conductors, optical fibers, circuits, or any suitable media that is fleeting and devoid of any semblance of permanence during transmission, and / or any suitable intangible media.

[0187] As used herein in the context of computer implementation, unless otherwise specified or limited, the terms “component,” “system,” “module,” “framework,” and the like are intended to encompass part or all of computer-related systems that include hardware, software, a combination of hardware and software, or software in execution. For example, a component may be, but is not limited to being, a processor device, a process being executed (or executable) by a processor device, an object, an executable, a thread of execution, a computer program, or a computer. By way of illustration, both an application running on a computer and the computer can be a component. One or more components (or system, module, and so on) may reside within a process or thread of execution, may be localized on one computer, may be distributed between two or more computers or other processor devices, or may be included within another component (or system, module, and so on).

[0188] In some implementations, devices or systems disclosed herein can be utilized or installed using methods embodying aspects of the disclosure. Correspondingly, description herein of particular features, capabilities, or intended purposes of a device or system is generally intended to inherently include disclosure of a method of using such features for the intended purposes, a method of implementing such capabilities, and a method of installing disclosed (or otherwise known) components to support these purposes or capabilities. Similarly, unless otherwise indicated or limited, discussion herein of any method of manufacturing or using a particular device or system, including installing the device or system, is intended to inherently include disclosure, as embodiments of the disclosure, of the utilized features and implemented capabilities of such device or system.

[0189] Referring particularly now to FIG. 16, an example of an MRI system 1600 that can implement the methods described here is illustrated. The MRI system 1600 includes an operator workstation 1602 that may include a display 1604, one or more input devices 1606 (e.g., a keyboard, a mouse), and a processor 1608. The processor 1608 may include a commercially available programmable machine running a commercially available operatingsystem. The operator workstation 1602 provides an operator interface that facilitates entering scan parameters into the MRI system 1600. The operator workstation 1602 may be coupled to different servers, including, for example, a pulse sequence server 1610, a data acquisition server 1612, a data processing server 1614, and a data store server 1616. The operator workstation 1602 and the servers 1610, 1612, 1614. and 1616 may be connected via a communication system 1640, which may include wired or wireless network connections.

[0190] The pulse sequence server 1610 functions in response to instructions provided by the operator workstation 1602 to operate a gradient system 1618 and a radiofrequency (“RF”) system 1620. Gradient waveforms for performing a prescribed scan are produced and applied to the gradient system 1618. which then excites gradient coils in an assembly 1622 to produce the magnetic field gradientsthat are used for spatially encoding magnetic resonance signals. The gradient coil assembly 1622 forms part of a magnet assembly 1 24 that includes a polarizing magnet 1626 and a whole-body RF coil 1 28.

[0191] RF waveforms are applied by the RF system 1620 to the RF coil 1628, or a separate local coil to perform the prescribed magnetic resonance pulse sequence. Responsive magnetic resonance signals detected by the RF coil 1628. or a separate local coil, are received by the RF system 1620. The responsive magnetic resonance signals may be amplified, demodulated, filtered, and digitized under direction of commands produced by the pulse sequence server 1610. The RF system 1620 includes an RF transmitter for producing a wide variety of RF pulses used in MRI pulse sequences. The RF transmitter is responsive to the prescribed scan and direction from the pulse sequence server 1610 to produce RF pulses of the desired frequency, phase, and pulse amplitude waveform. The generated RF pulses may be applied to the whole-body RF coil 1628 or to one or more local coils or coil arrays.

[0192] The RF system 1620 also includes one or more RF receiver channels. An RF receiver channel includes an RF preamplifier that amplifies the magnetic resonance signal received by the coil 1628 to which it is connected, and a detector that detects and digitizes the I and Q quadrature components of the received magnetic resonance signal. The magnitude of the received magnetic resonance signal may, therefore, be determined at a sampled point by the square root of the sum of the squares of the I and Q components:

[0193] and the phase of the received magnetic resonance signal may also be determined according to the following relationship:

[0194] The pulse sequence server 1610 may receive patient data from a physiological acquisition controller 1630. By way of example, the physiological acquisition controller 1630 may receive signals from a number of different sensors connected to the patient, including electrocardiograph (ECG) signals from electrodes, or respiratory signals from a respiratory bellows or other respiratory' monitoring devices. These signals may be used by the pulse sequence server 1610 to synchronize, or “gate,” the performance of the scan with the subjects heart beat or respiration.

[0195] The pulse sequence server 1610 may also connect to a scan room interface circuit 1632 that receives signals from various sensors associated with the condition of the patient and the magnet system. Through the scan room interface circuit 1632, a patient positioning system 1634 can receive commands to move the patient to desired positions during the scan.

[0196] The digitized magnetic resonance signal samples produced by the RF system 1620 are received by the data acquisition server 1612. The data acquisition server 1612 operates in response to instructions downloaded from the operator workstation 1602 to receive the realtime magnetic resonance data and provide buffer storage, so that data is not lost by data overrun. In some scans, the data acquisition server 1612 passes the acquired magnetic resonance data to the data processor server 1614. In scans that require information derived from acquired magnetic resonance data to control the further performance of the scan, the data acquisition server 1612 may be programmed to produce such information and convey it to the pulse sequence server 1610. For example, during pre-scans, magnetic resonance data may be acquired and used to calibrate the pulse sequence performed by the pulse sequence server 1610. As another example, navigator signals may be acquired and used to adjust the operating parameters of the RF system 1620 or the gradient system 1618. or to control the view order in which k-space is sampled. In still another example, the data acquisition server 1612 may also process magnetic resonance signals used to detect the arrival of a contrast agent in a magnetic resonance angiography (“MRA”) scan. For example, the data acquisition server 1612 may acquire magnetic resonance data and processes it in real-time to produce information that is used to control the scan.

[0197] The data processing server 1614 receives magnetic resonance data from the data acquisition server 1612 and processes the magnetic resonance data in accordance withinstructions provided by the operator workstation 1602. Such processing may include, for example, reconstructing two-dimensional or three-dimensional images by performing a Fourier transformation of raw k-space data, performing other image reconstruction algorithms (e.g., iterative or backproj ection reconstruction algorithms), applying filters to raw k-space data or to reconstructed images, generating functional magnetic resonance images, or calculating motion or flow images.

[0198] Images reconstructed by the data processing server 1614 are conveyed back to the operator workstation 1602 for storage. Real-time images may be stored in a data base memory cache, from which they may be output to operator display 1602 or a display 1636. Batch mode images or selected real time images may be stored in a host database on disc storage 1638. When such images have been reconstructed and transferred to storage, the data processing server 1614 may notify the data store server 1616 on the operator workstation 1602. The operator workstation 1602 may be used by an operator to archive the images, produce films, or send the images via a network to other facilities.

[0199] The MRI system 1600 may also include one or more networked workstations 1642. For example, a networked workstation 1642 may include a display 1644, one or more input devices 1646 (e.g., a keyboard, a mouse), and a processor 1648. The networked workstation 1642 may be located within the same facility as the operator workstation 1602, or in a different facility, such as a different healthcare institution or clinic.

[0200] The networked workstation 1642 may gain remote access to the data processing server 1614 or data store server 1616 via the communication system 1640. Accordingly, multiple networked workstations 1642 may have access to the data processing server 1614 and the data store server 1616. In this manner, magnetic resonance data, reconstructed images, or other data may be exchanged between the data processing server 1614 or the data store server 1616 and the networked workstations 1642, such that the data or images may be remotely processed by a networked workstation 1642.

[0201] The scan protocol optimization described herein may be implemented in various configurations to accommodate different computational requirements and system architectures. In some embodiments, the dMRI scan protocol optimization system 1404 may be executed locally within the MRI system 1600 environment, where the computing device 1450 may be integrated with or directly connected to the operator workstation 1602. In such local implementations, the processor 1502 of computing device 1450 may perform the automatic differentiation calculations and Fisher Information Matrix computations using available CPUand GPU resources, with the optimization algorithms and biophysical models stored in memory 1510. The operator may input the selected diffusion model, tissue properties of interest, and scan constraints through inputs 1506 or through the input devices 1606 of the operator workstation 1602, and the dMRI scan protocol optimization system 1404 may execute the CRLB minimization process locally. The optimized scanning protocol data may then be communicated directly to the pulse sequence server 1610, enabling immediate implementation of the optimized sequence parameters without requiring external network connectivity.

[0202] Alternatively, the scan protocol optimization may be implemented as a cloudbased service where the computationally intensive optimization algorithms are executed on server 1452 located remotely from the MRI system 1600. In such embodiments, the operator workstation 1602 or computing device 1450 may collect user input data specifying the diffusion model selection, scan time constraints, and tissue properties of interest, then transmit this information to server 1452 over communication network 1454. The server 1452 may leverage high-performance processors 1512, including specialized CPUs and GPUs optimized for parallel computing, to perform the comprehensive parameter space exploration and automatic differentiation calculations required for CRLB optimization. The server’s memory 1520 may store extensive libraries of biophysical model implementations, pre-computed optimization results for common tissue ty pes and scanner configurations, and continuously- updated optimization algorithms that benefit from aggregated data across multiple MRI installations.

[0203] When the optimization is performed on server 1452, the resulting scan protocol parameters may be managed through various storage and transmission mechanisms to control MRI system operations. In some embodiments, the optimized scanning protocol data, including specific gradient strength values, diffusion pulse durations, diffusion times, b-value distributions, and gradient direction specifications, may be stored in the server’s memory 1520 for future reference and reuse with similar optimization requests. The server 1452 may maintain comprehensive databases of optimized protocols indexed by tissue model ty pe, scanner hardware specifications, and user-defined constraints to enable rapid retrieval and customization. The server may transmit the optimized protocol parameters back to the MRI system 1600 through communications systems 1518 and communication network 1454, where they may be received by the operator workstation 1602 or computing device 1450. The protocol parameters may then be formatted and communicated to the pulse sequence server 1610, which may implement the optimized pulse sequence parameters by controlling the gradient system1618 and RF system 1620. for example, to execute the prescribed diffusion- weighted imaging acquisition with the optimized timing, gradient strengths, and directional sampling schemes.

[0204] In some cases, the optimized scan protocol parameters generated by server 1452 may be transmitted to the MRI system 1600 as encrypted file formats to ensure data security and seamless integration with existing clinical workflows. In some embodiments, the server 1452 may package the optimized scanning protocol data, including gradient strength values, diffusion pulse durations, diffusion times, b-value distributions, and gradient direction specifications, into encrypted file formats such as encrypted XML, JSON, or proprietary binary formats that incorporate authentication and integrity verification mechanisms. The communications systems 1518 may transmit these encrypted protocol files over communication network 1454 using secure transmission protocols such as HTTPS or encrypted VPN connections to the operator workstation 1602. Upon receipt, the processor 1608 of the operator workstation 1602 may automatically decrypt and parse the protocol files using preinstalled decryption keys and protocol interpretation software stored in the memory of the workstation 1602. The operator workstation 1602 may then automatically populate the scan parameter fields in its user interface and prepare the optimized protocol parameters for transmission to the pulse sequence server 1610, enabling seamless implementation of the cloud-optimized dMRI acquisition protocols without requiring manual parameter entry' by the operator.

[0205] The present disclosure has described one or more preferred embodiments, and it should be appreciated that many equivalents, alternatives, variations, and modifications, aside from those expressly stated, are possible and within the scope of the invention.

Claims

CLAIMS1. A method for performing a diffusion magnetic resonance imaging (MRI) scan of a subject using an MRI system, the method comprising: receiving user input data, wherein the user input data comprises a selected diffusion model; generating Cramer-Rao Lower Bound (CRLB) values with automatic differentiation to determine scanning protocol data for the diffusion MRI scan, wherein the scanning protocol data comprises at least one of acquisition parameters for a pulse sequence used in the diffusion MRI scan and model parameters for the selected diffusion model; and acquiring magnetic resonance data from a subject using the MRI system to perform the pulse sequence using the scanning protocol data; and generating at least one diffusion image from the magnetic resonance data.

2. The method of claim 1. wherein generating the CRLB values comprises minimizing a trace of a Fisher information matrix (F1M) based on at least one of acquisition parameters for a pulse sequence used in the diffusion MRI scan and model parameters for at least one diffusion model.

3. The method of claim 2. wherein the FIM is computed using automatic differentiation of biophysical model functions with respect to the model parameters.

4. The method of claim 1, wherein the user data further comprises at least one of tissue properties of interest, a scan time setting, or a number of diffusion gradient directions.

5. The method of claim 1, wherein the user input data further comprises at least one of tissue properties of interest, a scan time constraint, or a number of diffusion gradient directions.

6. The method of claim 5, wherein the tissue properties of interest comprise at least one of axonal diameter index, neurite density index, or fiber orientation dispersion.

7. The method of claim 1. wherein the selected diffusion model comprises a multi-compartment tissue model selected from the group consisting of: Diffusion Tensor model, Neurite Orientation Dispersion and Density Imaging (NODDI) model, ActiveAx model, and Ball-and-Sticks model.

8. The method of claim 7. wherein the multi-compartment tissue model comprises separate compartments for intra-axonal, extra-axonal, and cerebrospinal fluid components.

9. The method of claim 1. wherein the acquisition parameters comprise at least one of gradient strength, diffusion pulse duration, diffusion time, b-values, or gradient directions.

10. The method of claim 9. wherein the gradient strength ranges from 10 mT / m to 300 mT / m.

11. The method of claim 9, wherein the b-values are optimized based on water diffusivity7values of tissue being imaged.

12. The method of claim 1. wherein the model parameters comprise at least one of water diffusivity values, volume fractions, fiber orientation parameters, or tissue-specific parameters.

13. The method of claim 12, wherein the water diffusivity values comprise parallel diffusivity, perpendicular diffusivity7, and isotropic diffusivity'.

14. The method of claim 1, wherein the pulse sequence comprises a pulse gradient spin echo (PGSE) sequence.

15. The method of claim 14, wherein the PGSE sequence parameters are optimized through systematic exploration of parameter combinations within hardware- feasible ranges.

16. The method of claim 1. further comprising a step of filtering parameter combinations to exclude configurations that result in non-full-rank FIMs.

17. The method of claim 1, wherein generating the CRLB values comprises using parallel computing via Graphics Processing Units (GPUs) to accelerate derivative computations.

18. A method for optimizing diffusion magnetic resonance imaging (dMRI) acquisition protocols, comprising: selecting a multi-compartment tissue biophysical model using a computer system; generating, with the computer system, parameter combinations across parameter values for model parameters of the selected multi-compartment tissue biophysical model; computing, with the computer system, Fisher information matrix (FIM) elements for each parameter combination using automatic differentiation; calculating, with the computer system, Cramer-Rao Lower Bound (CRLB) values from the FIM elements; determining, with the computer system, pulse sequence parameters that minimize the CRLB values for the model parameters; and outputting, with the computer system, the pulse sequence parameters for use in controlling a magnetic resonance imaging (MRI) system to perform a dMRI acquisition.

19. The method of claim 18, wherein the model parameters comprise at least one of water diffusivity values, volume fractions, fiber orientation parameters, and tissue-specific parameters.

20. The method of claim 19, wherein the water diffusivity values comprise parallel diffusivity, perpendicular diffusivity, and isotropic diffusivity.

21. The method of claim 19, wherein the tissue-specific parameters comprise at least one of axonal diameter index and orientation dispersion index.

22. The method of claim 18, wherein generating parameter combinations comprises establishing sets containing permissible values for each model parameter and applying Cartesian product operations to generate combinations of parameter values.

23. The method of claim 22, further comprising filtering infeasible parameter combinations based on physical constraints and mathematical requirements.

24. The method of claim 18, wherein the pulse sequence parameters comprise gradient strength, diffusion pulse duration, and diffusion time.

25. The method of claim 24, wherein determining pulse sequence parameters comprises identifying parameter combinations that achieve minimum CRLB values while satisfying hardware constraints of the MRI system.

26. The method of claim 18, wherein outputting the pulse sequence parameters with the computer system comprises transmitting the pulse sequence parameters from the computer system to the MRI system.

27. The method of claim 18, wherein the computer system forms a part of the MRI system and outputting the pulse sequence parameters with the computer system comprises controlling a pulse sequence server of the MRI system using the pulse sequence parameters to perform the dMRI acquisition.

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