Diffusion time dependence, power-law scaling, and exchange in gray matter

Linear rotationally invariant kurtosis measures from double diffusion encoding MRI

PURPOSE

To characterize the complete set of linear rotationally invariant kurtosis measures provided by double diffusion encoding (DDE) MRI, show their utility in distinguishing different types of multiple Gaussian compartment (MGC) models, and demonstrate simplified acquisition and analysis schemes for their estimation.

THEORY AND METHODS

The lowest order novel information obtainable with DDE MRI can be encapsulated in a six-dimensional kurtosis tensor. The most basic DDE MRI kurtosis measures are rotational invariants that are linear in this tensor while depending on no other physical quantities. We identify four such invariants and show that any others must be linear combinations of these. The invariants are applied to classify MGC models according to whether they include microscopic anisotropy or intercompartmental water exchange. In addition, they are used to investigate the effect of exchange on estimates of the microscopic fractional anisotropy (μFA). Simplified acquisition and analysis schemes for the invariants are proposed and demonstrated with human brain data obtained at 3 T.

RESULTS

For the considered brain regions, the kurtosis invariants are found to be largely consistent with MGC models having microscopic anisotropy. They also indicate that water exchange in gray matter may affect estimates of μFA.

CONCLUSION

The kurtosis measures can classify MGC models according to whether they have microscopic anisotropy or water exchange, and they can be estimated with simple acquisition and analysis schemes. Measurements of the invariants in brain support the validity of MGC models with microscopic anisotropy and the importance of water exchange for modeling diffusion in gray matter.

In vivo cortical microstructure mapping using high-gradient diffusion MRI accounting for intercompartmental water exchange effects

In recent years, mapping tissue microstructure in the cortex using high gradient diffusion MRI has received growing attention. The Soma And Neurite Density Imaging (SANDI) explicitly models the soma compartment in the cortex assuming impermeable membranes. As such, it does not account for diffusion time dependence due to water exchange in the estimated microstructural properties, as neurites in gray matter are much less myelinated than in white matter. In this work, we performed a systematic evaluation of an extended SANDI model for in vivo human cortical microstructural mapping that accounts for water exchange effects between the neurite and extracellular compartments using the anisotropic Kärger model. We refer to this model as in vivo SANDIX, adapting the nomenclature from previous publications. As in the original SANDI model, the soma compartment is modeled as an impermeable sphere due to the much smaller surface-to-volume ratio compared to the neurite compartment. A Monte Carlo simulation study was performed to examine the sensitivity of the in vivo SANDIX model to sphere radii, compartment fractions, and water exchange times. The simulation results indicate that the proposed in vivo SANDIX framework can account for the water exchange effect and provide measures of intra-soma and intra-neurite signal fractions without spurious time-dependence in estimated parameters, whereas the measured water exchange times need to be interpreted with caution. The model was then applied to in vivo diffusion MRI data acquired in 13 healthy adults on the 3-Tesla Connectome MRI scanner equipped with 300 mT/m gradients. The in vivo results exhibited patterns that were consistent with corresponding anatomical characteristics in both cortex and white matter. In particular, the estimated water exchange times in gray and white matter were distinct and differentiated between the two tissue types. Our results show the SANDIX approach applied to high-gradient diffusion MRI data achieves cortical microstructure mapping of the in vivo human brain with the evaluation of water exchange effects. This approach potentially provides a more appropriate description of in vivo cortical microstructure for improving data interpretation in future neurobiological studies.

Comparison of water exchange measurements between filter-exchange imaging and diffusion time-dependent kurtosis imaging in the human brain

PURPOSE

Filter-exchange imaging (FEXI) and diffusion time (t)-dependent kurtosis imaging (DKI(t)) are two diffusion-based methods that have been proposed for in vivo measurements of water exchange rates. Few studies have directly compared these methods. We aimed to investigate whether FEXI and DKI(t) yield comparable water exchange measurements in the human brain in vivo.

METHODS

Eight healthy volunteers underwent multiple-direction FEXI and DKI(t) acquisitions on a 3T scanner. We performed region of interest (ROI) analysis to determine correlations between FEXI-derived apparent exchange rate (AXR) and DKI(t)-derived reciprocal of exchange time (1 / τ ex $$ 1/{\tau}_{ex} $$ ).

RESULTS

In both white matter (WM) and gray matter (GM), DKI(t) revealed substantial diffusion-time dependence of diffusivity and kurtosis. However, at t ≥ 100 ms, the diffusivity showed weak time dependence. In WM, this time dependence may be due to water exchange between myelin water and "free" water with different T1 values, although other factors, such as remaining restrictive effects from microstructural barriers, cannot be excluded. We found a significant correlation between DKI(t)-derived1 / τ ex $$ 1/{\tau}_{ex} $$ and FEXI-derived AXR in the axial direction within WM. No such correlation was present in GM, although both values showed similar ranges.

CONCLUSION

These results suggest that FEXI and DKI(t) could be sensitive to the same water exchange process only when the diffusion time in DKI(t) is sufficiently long, and only in WM. In both GM and WM, the restrictive effect of microstructure is non-negligible, especially at short diffusion times (<100 ms).

Considerations and recommendations from the ISMRM diffusion study group for preclinical diffusion MRI: Part 2-Ex vivo imaging: Added value and acquisition

The value of preclinical diffusion MRI (dMRI) is substantial. While dMRI enables in vivo non-invasive characterization of tissue, ex vivo dMRI is increasingly being used to probe tissue microstructure and brain connectivity. Ex vivo dMRI has several experimental advantages including higher SNR and spatial resolution compared to in vivo studies, and enabling more advanced diffusion contrasts for improved microstructure and connectivity characterization. Another major advantage of ex vivo dMRI is the direct comparison with histological data, as a crucial methodological validation. However, there are a number of considerations that must be made when performing ex vivo experiments. The steps from tissue preparation, image acquisition and processing, and interpretation of results are complex, with many decisions that not only differ dramatically from in vivo imaging of small animals, but ultimately affect what questions can be answered using the data. This work represents "Part 2" of a three-part series of recommendations and considerations for preclinical dMRI. We describe best practices for dMRI of ex vivo tissue, with a focus on the value that ex vivo imaging adds to the field of dMRI and considerations in ex vivo image acquisition. We first give general considerations and foundational knowledge that must be considered when designing experiments. We briefly describe differences in specimens and models and discuss why some may be more or less appropriate for different studies. We then give guidelines for ex vivo protocols, including tissue fixation, sample preparation, and MR scanning. In each section, we attempt to provide guidelines and recommendations, but also highlight areas for which no guidelines exist (and why), and where future work should lie. An overarching goal herein is to enhance the rigor and reproducibility of ex vivo dMRI acquisitions and analyses, and thereby advance biomedical knowledge.

Measuring the velocity autocorrelation function using diffusion NMR

Molecular self-diffusion in the presence of barriers results in time-dependent displacements that are controlled by barrier characteristics, such as thickness, arrangement, and permeability, which manifests itself in the form of the ensemble-average velocity autocorrelation function (VAF). We describe a direct method to measure the VAF based on a combination of diffusion-weighted nuclear magnetic resonance (NMR) measurements in which two time-shifted diffusion encodings are separated by a longitudinal storage period. The VAF estimated from simulated data is shown to agree with the known expression for impermeable parallel planes. Simulations of diffusion in periodically spaced, permeable planes and connected, box-shaped pores are also presented. We find that scaling of the VAF faster than t-1/2 is indicative of barrier permeation or exchange between domains and that this can be captured by the proposed method. As an experimental proof-of-concept, we present data from an ex vivo neonatal mouse spinal cord studied using a permanent magnet NMR MOUSE system. We report a transition from t-1/2 to t-3/2 scaling at t ≈ 10 ms, consistent perhaps with transmembrane water exchange. Compared to other NMR-based approaches, this method can potentially access several orders of magnitude in time (ms - s), revealing a wealth of VAF behaviors with one experimental paradigm.

Isotropic sampling of tensor-encoded diffusion MRI

PURPOSE

The purpose of this study is to develop a method for selecting uniform wave vectors for double diffusion encoding (DDE) to improve the accuracy and reliability of diffusion measurements.

METHODS

The method relies on identifying orthogonal wave vectors with rotations, and representing these rotations as points on a three-dimensional sphere in four dimensions using quaternions. This enables an electrostatic repulsion algorithm to achieve a uniform distribution of these points. The optimal points are then converted back into orthogonal wave vectors (or rotations).

RESULTS

The method was validated by comparing the distribution of directions to those generated by uniform sampling and by evaluating the error in the powder-averaged signal for various models. Our results demonstrate that the electrostatic repulsion approach effectively achieves a uniform distribution of wave vectors.

CONCLUSION

The proposed method provides a systematic way to generate uniform diffusion directions suitable, for example, for DDE, enhancing the precision of diffusion measurements and reducing potential bias in experimental results. The method is also capable of generating uniform sets of B-tensors, and is thus applicable for general free waveform encoding.

MRI signatures of cortical microstructure in human development align with oligodendrocyte cell-type expression

Neuroanatomical changes to the cortex during adolescence have been well documented using MRI, revealing ongoing cortical thinning and volume loss. Recent advances in MRI hardware and biophysical models of tissue informed by diffusion MRI data hold promise for identifying the cellular changes driving these morphological observations. Using ultra-strong gradient MRI, this study quantifies cortical neurite and soma microstructure in typically developing youth. Across domain-specific networks, cortical neurite signal fraction, attributed to neuronal and glial processes, increases with age. The apparent soma radius, attributed to the apparent radius of glial and neuronal cell bodies, decreases with age. Analyses of two independent post-mortem datasets reveal that genes increasing in expression through adolescence are significantly enriched in cortical oligodendrocytes and Layer 5-6 neurons. In our study, we show spatial and temporal alignment of oligodendrocyte cell-type gene expression with neurite and soma microstructural changes, suggesting that ongoing cortical myelination processes drive adolescent cortical development.

Quasi-Diffusion Imaging: Application to Ultra-High b-Value and Time-Dependent Diffusion Images of Brain Tissue

We demonstrate that quasi-diffusion imaging (QDI) is a signal representation that extends towards the negative power law regime. We evaluate QDI for in vivo human and ex vivo fixed rat brain tissue acrossb $$ b $$ -value ranges from 0 to 25,000 s mm-2, determine whether accurate parameter estimates can be acquired from clinically feasible scan times and investigate their diffusion time-dependence. Several mathematical properties of the QDI representation are presented. QDI describes diffusion magnetic resonance imaging (dMRI) signal attenuation by two fitting parameters within a Mittag-Leffler function (MLF). We present its asymptotic properties at low and highb $$ b $$ -values and define the inflection point (IP) above which the signal tends to a negative power law. To show that QDI provides an accurate representation of dMRI signal, we apply it to two human brain datasets (Dataset 1:0 ≤ b ≤ 15,000 $$ 0\le b\le \mathrm{15,000} $$ s mm-2; Dataset 2:0 ≤ b ≤ 17,800 $$ 0\le b\le \mathrm{17,800} $$  s mm-2) and an ex vivo fixed rat brain (Dataset 3:0 ≤ b ≤ 25,000 $$ 0\le b\le \mathrm{25,000} $$  s mm-2, diffusion times17.5 ≤ ∆ ≤ 200 $$ 17.5\le \Delta \le 200 $$  ms). A clinically feasible 4b $$ b $$ -value subset of Dataset 1 (0 ≤ b ≤ 15,000 $$ 0\le b\le \mathrm{15,000} $$  s mm-2) is also analysed (acquisition time 6 min and 16 s). QDI showed excellent fits to observed signal attenuation, identified signal IPs and provided an apparent negative power law. Stable parameter estimates were identified upon increasing the maximumb $$ b $$ -value of the fitting range to near and above signal IPs, suggesting QDI is a valid signal representation within in vivo and ex vivo brain tissue across largeb $$ b $$ -value ranges with multiple diffusion times. QDI parameters were accurately estimated from clinically feasible shorter data acquisition, and time-dependence was observed with parameters approaching a Gaussian tortuosity limit with increasing diffusion time. In conclusion, QDI provides a parsimonious representation of dMRI signal attenuation in brain tissue that is sensitive to tissue microstructural heterogeneity and cell membrane permeability.

Diffusion MRI with double diffusion encoding and variable mixing times disentangles water exchange from transient kurtosis

Double diffusion encoding (DDE) makes diffusion MRI sensitive to a wide range of microstructural features, and the acquired data can be analysed using different approaches. Correlation tensor imaging (CTI) uses DDE to resolve three components of the diffusional kurtosis: isotropic, anisotropic, and microscopic kurtosis. The microscopic kurtosis is estimated from the contrast between single diffusion encoding (SDE) and parallel DDE signals at the same b-value. Another approach is multi-Gaussian exchange (MGE), which employs DDE to measure exchange. Sensitivity to exchange is obtained by contrasting SDE and DDE signals at the same b-value. CTI and MGE exploit the same signal contrast to quantify microscopic kurtosis and exchange, and this study investigates the interplay between these two quantities. We perform Monte Carlo simulations in different geometries with varying levels of exchange and study the behaviour of the parameters from CTI and MGE. We conclude that microscopic kurtosis from CTI is sensitive to the exchange rate and that intercompartmental exchange and the transient kurtosis of individual compartments are distinct sources of microscopic kurtosis. In an attempt to disentangle these two sources, we propose a heuristic signal representation referred to as tMGE (MGE incorporating transient kurtosis) that accounts for both effects by exploiting the distinct signatures of exchange and transient kurtosis with varying mixing time: exchange causes a slow dependence of the signal on mixing time while transient kurtosis arguably has a much faster dependence. We find that applying tMGE to data acquired with multiple mixing times for both parallel and orthogonal DDE may enable estimation of the exchange rate as well as isotropic, anisotropic, and transient kurtosis.

Surface-based Analyses of Diffusional Kurtosis Imaging in Amyotrophic Lateral Sclerosis: Relationship with Onset Subtypes

PURPOSE

Here, we aimed to characterize the cortical and subcortical microstructural alterations in the brains of patients with amyotrophic lateral sclerosis (ALS). In particular, we compared these features between bulbar-onset ALS (b-ALS) and limb-onset ALS (l-ALS).

METHODS

Diffusion MRI data (b = 0, 700, 2000 ms/mm2, 1.7-mm isotropic voxel) from 28 patients with ALS (9 b-ALS and 19 l-ALS) and 17 healthy control subjects (HCs) were analyzed. Diffusional kurtosis imaging (DKI) metrics were sampled at the mid-cortical and subcortical surfaces. We used permutation testing with a nonparametric combination of mean diffusivity (MD), fractional anisotropy (FA), and mean kurtosis (MK) to assess intergroup differences over the cerebrum. We also carried out an atlas-based analysis focusing on Brodmann Area 4 and 6 (primary motor and premotor areas) and investigated the correlation between MRI metrics and clinical parameters.

RESULTS

At both the mid-cortical and subcortical surfaces, b-ALS was associated with significantly greater MD, smaller FA, and smaller MK in the motor and premotor areas than HC. In contrast, the patients with l-ALS showed relatively moderate differences relative to HCs. The ALS Functional Rating Scale-Revised bulbar subscore was significantly correlated with the diffusion metrics in Brodmann Area 4.

CONCLUSION

The distribution of abnormalities over the cerebral hemispheres and the more severe microstructural alteration in b-ALS compared to l-ALS were in good agreement with findings from postmortem histology. Our results suggest the feasibility of surface-based DKI analyses for exploring brain microstructural pathologies in ALS. The observed differences between b-ALS and l-ALS and their correlations with functional bulbar impairment support the clinical relevance of DKI measurement in the cortical and juxtacortical regions of patients with ALS.

In vivo human neurite exchange imaging (NEXI) at 500 mT/m diffusion gradients

Evaluating tissue microstructure and membrane integrity in the living human brain through diffusion-water exchange imaging is challenging due to requirements for a high signal-to-noise ratio and short diffusion times dictated by relatively fast exchange processes. The goal of this work was to demonstrate the feasibility of in vivo imaging of tissue micro-geometries and water exchange within the brain gray matter using the state-of-the-art Connectome 2.0 scanner equipped with an ultra-high-performance gradient system (maximum gradient strength=500 mT/m, maximum slew rate=600 T/m/s). We performed diffusion MRI measurements in 15 healthy volunteers at multiple diffusion times (13-30 ms) and b -values up to 17.5 ms/μm2. The anisotropic Kärger model was applied to estimate the exchange time between intra-neurite and extracellular water in gray matter. The estimated exchange time across the cortical ribbon was around (median±interquartile range) 13±8 ms on Connectome 2.0, substantially faster than that measured using an imaging protocol compatible with Connectome 1.0-alike systems on the same cohort. Our investigation suggested that the NEXI exchange time estimation using a Connectome 1.0 compatible protocol was more prone to residual noise floor biases due to the small time-dependent signal contrasts across diffusion times when the exchange is fast (≤20 ms). Furthermore, spatial variation of exchange time was observed across the cortex, where the motor cortex, somatosensory cortex and visual cortex exhibit longer exchange times compared to other cortical regions. Non-linear fitting for the anisotropic Kärger model was accelerated 100 times using a GPU-based pipeline compared to the conventional CPU-based approach. This study highlighted the importance of the chosen diffusion times and measures to address Rician noise in dMRI data, which can have a substantial impact on the estimated NEXI exchange time and require extra attention when comparing NEXI results between various hardware setups.

Single-shot multi-b-value (SSMb) diffusion-weighted MRI using spin echo and stimulated echoes with variable flip angles

Conventional diffusion-weighted imaging (DWI) sequences employing a spin echo or stimulated echo sensitize diffusion with a specific b-value at a fixed diffusion direction and diffusion time (Δ). To compute apparent diffusion coefficient (ADC) and other diffusion parameters, the sequence needs to be repeated multiple times by varying the b-value and/or gradient direction. In this study, we developed a single-shot multi-b-value (SSMb) diffusion MRI technique, which combines a spin echo and a train of stimulated echoes produced with variable flip angles. The method involves a pair of 90° radio frequency (RF) pulses that straddle a diffusion gradient lobe (GD), to rephase the magnetization in the transverse plane, producing a diffusion-weighted spin echo acquired by the first echo-planar imaging (EPI) readout train. The magnetization stored along the longitudinal axis is successively re-excited by a series of n variable-flip-angle pulses, each followed by a diffusion gradient lobe GD and a subsequent EPI readout train to sample n stimulated-echo signals. As such, (n + 1) diffusion-weighted images, each with a distinct b-value, are acquired in a single shot. The SSMb sequence was demonstrated on a diffusion phantom and healthy human brain to produce diffusion-weighted images, which were quantitative analyzed using a mono-exponential model. In the phantom experiment, SSMb provided similar ADC values to those from a commercial spin-echo EPI (SE-EPI) sequence (r = 0.999). In the human brain experiment, SSMb enabled a fourfold scan time reduction and yielded slightly lower ADC values (0.83 ± 0.26 μm2/ms) than SE-EPI (0.88 ± 0.29 μm2/ms) in all voxels excluding cerebrospinal fluid, likely due to the influence of varying diffusion times. The feasibility of using SSMb to acquire multiple images in a single shot for intravoxel incoherent motion (IVIM) analysis was also demonstrated. In conclusion, despite a relatively low signal-to-noise ratio, the proposed SSMb technique can substantially increase the data acquisition efficiency in DWI studies.

Introducing µGUIDE for quantitative imaging via generalized uncertainty-driven inference using deep learning

This work proposes µGUIDE: a general Bayesian framework to estimate posterior distributions of tissue microstructure parameters from any given biophysical model or signal representation, with exemplar demonstration in diffusion-weighted magnetic resonance imaging. Harnessing a new deep learning architecture for automatic signal feature selection combined with simulation-based inference and efficient sampling of the posterior distributions, µGUIDE bypasses the high computational and time cost of conventional Bayesian approaches and does not rely on acquisition constraints to define model-specific summary statistics. The obtained posterior distributions allow to highlight degeneracies present in the model definition and quantify the uncertainty and ambiguity of the estimated parameters.

Tuned exchange imaging: Can the filter exchange imaging pulse sequence be adapted for applications with thin slices and restricted diffusion?

Filter exchange imaging (FEXI) is a double diffusion-encoding (DDE) sequence that is specifically sensitive to exchange between sites with different apparent diffusivities. FEXI uses a diffusion-encoding filtering block followed by a detection block at varying mixing times to map the exchange rate. Long mixing times enhance the sensitivity to exchange, but they pose challenges for imaging applications that require a stimulated echo sequence with crusher gradients. Thin imaging slices require strong crushers, which can introduce significant diffusion weighting and bias exchange rate estimates. Here, we treat the crushers as an additional encoding block and consider FEXI as a triple diffusion-encoding sequence. This allows the bias to be corrected in the case of multi-Gaussian diffusion, but not easily in the presence of restricted diffusion. Our approach addresses challenges in the presence of restricted diffusion and relies on the ability to independently gauge sensitivities to exchange and restricted diffusion for arbitrary gradient waveforms. It follows two principles: (i) the effects of crushers are included in the forward model using signal cumulant expansion; and (ii) timing parameters of diffusion gradients in filter and detection blocks are adjusted to maintain the same level of restriction encoding regardless of the mixing time. This results in the tuned exchange imaging (TEXI) protocol. The accuracy of exchange mapping with TEXI was assessed through Monte Carlo simulations in spheres of identical sizes and gamma-distributed sizes, and in parallel hexagonally packed cylinders. The simulations demonstrate that TEXI provides consistent exchange rates regardless of slice thickness and restriction size, even with strong crushers. However, the accuracy depends on b-values, mixing times, and restriction geometry. The constraints and limitations of TEXI are discussed, including suggestions for protocol adaptations. Further studies are needed to optimize the precision of TEXI and assess the approach experimentally in realistic, heterogeneous substrates.

Age-related alterations in human cortical microstructure across the lifespan: Insights from high-gradient diffusion MRI

The human brain undergoes age-related microstructural alterations across the lifespan. Soma and Neurite Density Imaging (SANDI), a novel biophysical model of diffusion MRI, provides estimates of cell body (soma) radius and density, and neurite density in gray matter. The goal of this cross-sectional study was to assess the sensitivity of high-gradient diffusion MRI toward age-related alterations in cortical microstructure across the adult lifespan using SANDI. Seventy-two cognitively unimpaired healthy subjects (ages 19-85 years; 40 females) were scanned on the 3T Connectome MRI scanner with a maximum gradient strength of 300mT/m using a multi-shell diffusion MRI protocol incorporating 8 b-values and diffusion time of 19 ms. Intra-soma signal fraction obtained from SANDI model-fitting to the data was strongly correlated with age in all major cortical lobes (r = -0.69 to -0.60, FDR-p < 0.001). Intra-soma signal fraction (r = 0.48-0.63, FDR-p < 0.001) and soma radius (r = 0.28-0.40, FDR-p < 0.04) were significantly correlated with cortical volume in the prefrontal cortex, frontal, parietal, and temporal lobes. The strength of the relationship between SANDI metrics and age was greater than or comparable to the relationship between cortical volume and age across the cortical regions, particularly in the occipital lobe and anterior cingulate gyrus. In contrast to the SANDI metrics, all associations between diffusion tensor imaging (DTI) and diffusion kurtosis imaging metrics and age were low to moderate. These results suggest that high-gradient diffusion MRI may be more sensitive to underlying substrates of neurodegeneration in the aging brain than DTI and traditional macroscopic measures of neurodegeneration such as cortical volume and thickness.

Robust, fast and accurate mapping of diffusional mean kurtosis

Diffusional kurtosis imaging (DKI) is a methodology for measuring the extent of non-Gaussian diffusion in biological tissue, which has shown great promise in clinical diagnosis, treatment planning, and monitoring of many neurological diseases and disorders. However, robust, fast, and accurate estimation of kurtosis from clinically feasible data acquisitions remains a challenge. In this study, we first outline a new accurate approach of estimating mean kurtosis via the sub-diffusion mathematical framework. Crucially, this extension of the conventional DKI overcomes the limitation on the maximum b-value of the latter. Kurtosis and diffusivity can now be simply computed as functions of the sub-diffusion model parameters. Second, we propose a new fast and robust fitting procedure to estimate the sub-diffusion model parameters using two diffusion times without increasing acquisition time as for the conventional DKI. Third, our sub-diffusion-based kurtosis mapping method is evaluated using both simulations and the Connectome 1.0 human brain data. Exquisite tissue contrast is achieved even when the diffusion encoded data is collected in only minutes. In summary, our findings suggest robust, fast, and accurate estimation of mean kurtosis can be realised within a clinically feasible diffusion-weighted magnetic resonance imaging data acquisition time.

Restriction-induced time-dependent transcytolemmal water exchange: Revisiting the Kӓrger exchange model

The Kӓrger model and its derivatives have been widely used to incorporate transcytolemmal water exchange rate, an essential characteristic of living cells, into analyses of diffusion MRI (dMRI) signals from tissues. The Kӓrger model consists of two homogeneous exchanging components coupled by an exchange rate constant and assumes measurements are made with sufficiently long diffusion time and slow water exchange. Despite successful applications, it remains unclear whether these assumptions are generally valid for practical dMRI sequences and biological tissues. In particular, barrier-induced restrictions to diffusion produce inhomogeneous magnetization distributions in relatively large-sized compartments such as cancer cells, violating the above assumptions. The effects of this inhomogeneity are usually overlooked. We performed computer simulations to quantify how restriction effects, which in images produce edge enhancements at compartment boundaries, influence different variants of the Kӓrger-model. The results show that the edge enhancement effect will produce larger, time-dependent estimates of exchange rates in e.g., tumors with relatively large cell sizes (>10 μm), resulting in overestimations of water exchange as previously reported. Moreover, stronger diffusion gradients, longer diffusion gradient durations, and larger cell sizes, all cause more pronounced edge enhancement effects. This helps us to better understand the feasibility of the Kärger model in estimating water exchange in different tissue types and provides useful guidance on signal acquisition methods that may mitigate the edge enhancement effect. This work also indicates the need to correct the overestimated transcytolemmal water exchange rates obtained assuming the Kärger-model.

The Diffusion Exchange Ratio (DEXR): A minimal sampling of diffusion exchange spectroscopy to probe exchange, restriction, and time-dependence

Water exchange is increasingly recognized as an important biological process that can affect the study of biological tissue using diffusion MR. Methods to measure exchange, however, remain immature as opposed to those used to characterize restriction, with no consensus on the optimal pulse sequence (s) or signal model (s). In general, the trend has been towards data-intensive fitting of highly parameterized models. We take the opposite approach and show that a judicious sub-sample of diffusion exchange spectroscopy (DEXSY) data can be used to robustly quantify exchange, as well as restriction, in a data-efficient manner. This sampling produces a ratio of two points per mixing time: (i) one point with equal diffusion weighting in both encoding periods, which gives maximal exchange contrast, and (ii) one point with the same total diffusion weighting in just the first encoding period, for normalization. We call this quotient the Diffusion EXchange Ratio (DEXR). Furthermore, we show that it can be used to probe time-dependent diffusion by estimating the velocity autocorrelation function (VACF) over intermediate to long times (∼2-500ms). We provide a comprehensive theoretical framework for the design of DEXR experiments in the case of static or constant gradients. Data from Monte Carlo simulations and experiments acquired in fixed and viable ex vivo neonatal mouse spinal cord using a permanent magnet system are presented to test and validate this approach. In viable spinal cord, we report the following apparent parameters from just 6 data points: τk=17±4ms, fNG=0.72±0.01, Reff=1.05±0.01μm, and κeff=0.19±0.04μm/ms, which correspond to the exchange time, restricted or non-Gaussian signal fraction, an effective spherical radius, and permeability, respectively. For the VACF, we report a long-time, power-law scaling with ≈t-2.4, which is approximately consistent with disordered domains in 3-D. Overall, the DEXR method is shown to be highly efficient, capable of providing valuable quantitative diffusion metrics using minimal MR data.

Diffusion magnetic resonance imaging of cerebrospinal fluid dynamics: Current techniques and future advancements

Cerebrospinal fluid (CSF) plays a critical role in metabolic waste clearance from the brain, requiring its circulation throughout various brain pathways, including the ventricular system, subarachnoid spaces, para-arterial spaces, interstitial spaces, and para-venous spaces. The complexity of CSF circulation has posed a challenge in obtaining noninvasive measurements of CSF dynamics. The assessment of CSF dynamics throughout its various circulatory pathways is possible using diffusion magnetic resonance imaging (MRI) with optimized sensitivity to incoherent water movement across the brain. This review presents an overview of both established and emerging diffusion MRI techniques designed to measure CSF dynamics and their potential clinical applications. The discussion offers insights into the optimization of diffusion MRI acquisition parameters to enhance the sensitivity and specificity of diffusion metrics on underlying CSF dynamics. Lastly, we emphasize the importance of cautious interpretations of diffusion-based imaging, especially when differentiating between tissue- and fluid-related changes or elucidating structural versus functional alterations.

The Diffusion Exchange Ratio (DEXR): A minimal sampling of diffusion exchange spectroscopy to probe exchange, restriction, and time-dependence

Water exchange is increasingly recognized as an important biological process that can affect the study of biological tissue using diffusion MR. Methods to measure exchange, however, remain immature as opposed to those used to characterize restriction, with no consensus on the optimal pulse sequence(s) or signal model(s). In general, the trend has been towards data-intensive fitting of highly parameterized models. We take the opposite approach and show that a judicious sub-sample of diffusion exchange spectroscopy (DEXSY) data can be used to robustly quantify exchange, as well as restriction, in a data-efficient manner. This sampling produces a ratio of two points per mixing time: (i) one point with equal diffusion weighting in both encoding periods, which gives maximal exchange contrast, and (ii) one point with the same total diffusion weighting in just the first encoding period, for normalization. We call this quotient the Diffusion EXchange Ratio (DEXR). Furthermore, we show that it can be used to probe time-dependent diffusion by estimating the velocity autocorrelation function (VACF) over intermediate to long times (~ 2-500 ms). We provide a comprehensive theoretical framework for the design of DEXR experiments in the case of static or constant gradients. Data from Monte Carlo simulations and experiments acquired in fixed and viable ex vivo neonatal mouse spinal cord using a permanent magnet system are presented to test and validate this approach. In viable spinal cord, we report the following apparent parameters from just 6 data points:τ k = 17 ± 4 m s ,f N G = 0.71 ± 0.01 ,R e f f = 1.10 ± 0.01 μ m , andκ eff = 0.21 ± 0.06 μ m / m s , which correspond to the exchange time, restricted or non-Gaussian signal fraction, an effective spherical radius, and permeability, respectively. For the VACF, we report a long-time, power-law scaling with ≈ t - 2.4 , which is approximately consistent with disordered domains in 3-D. Overall, the DEXR method is shown to be highly efficient, capable of providing valuable quantitative diffusion metrics using minimal MR data.

Comprehensive characterization of tumor therapeutic response with simultaneous mapping cell size, density, and transcytolemmal water exchange

Early assessment of tumor therapeutic response is an important topic in precision medicine to optimize personalized treatment regimens and reduce unnecessary toxicity, cost, and delay. Although diffusion MRI (dMRI) has shown potential to address this need, its predictive accuracy is limited, likely due to its unspecific sensitivity to overall pathological changes. In this work, we propose a new quantitative dMRI-based method dubbed EXCHANGE (MRI of water Exchange, Confined and Hindered diffusion under Arbitrary Gradient waveform Encodings) for simultaneous mapping of cell size, cell density, and transcytolemmal water exchange. Such rich microstructural information comprehensively evaluates tumor pathologies at the cellular level. Validations using numerical simulations and in vitro cell experiments confirmed that the EXCHANGE method can accurately estimate mean cell size, density, and water exchange rate constants. The results from in vivo animal experiments show the potential of EXCHANGE for monitoring tumor treatment response. Finally, the EXCHANGE method was implemented in breast cancer patients with neoadjuvant chemotherapy, demonstrating its feasibility in assessing tumor therapeutic response in clinics. In summary, a new, quantitative dMRI-based EXCHANGE method was proposed to comprehensively characterize tumor microstructural properties at the cellular level, suggesting a unique means to monitor tumor treatment response in clinical practice.

The Larmor frequency shift of a white matter magnetic microstructure model with multiple sources

Magnetic susceptibility imaging may provide valuable information about chemical composition and microstructural organization of tissue. However, its estimation from the MRI signal phase is particularly difficult as it is sensitive to magnetic tissue properties ranging from the molecular to the macroscopic scale. The MRI Larmor frequency shift measured in white matter (WM) tissue depends on the myelinated axons and other magnetizable sources such as iron-filled ferritin. We have previously derived the Larmor frequency shift arising from a dense medium of cylinders with scalar susceptibility and arbitrary orientation dispersion. Here, we extend our model to include microscopic WM susceptibility anisotropy as well as spherical inclusions with scalar susceptibility to represent subcellular structures, biologically stored iron, and so forth. We validate our analytical results with computer simulations and investigate the feasibility of estimating susceptibility using simple iterative linear least squares without regularization or preconditioning. This is done in a digital brain phantom synthesized from diffusion MRI measurements of an ex vivo mouse brain at ultra-high field.

MRI signatures of cortical microstructure in human development align with oligodendrocyte cell-type expression

Neuroanatomical changes to the cortex during adolescence have been well documented using MRI, revealing ongoing cortical thinning and volume loss with age. However, the underlying cellular mechanisms remain elusive with conventional neuroimaging. Recent advances in MRI hardware and new biophysical models of tissue informed by diffusion MRI data hold promise for identifying the cellular changes driving these morphological observations. This study used ultra-strong gradient MRI to obtain high-resolution, in vivo estimates of cortical neurite and soma microstructure in sample of typically developing children and adolescents. Cortical neurite signal fraction, attributed to neuronal and glial processes, increased with age (mean R2 fneurite=.53, p<3.3e-11, 11.91% increase over age), while apparent soma radius decreased (mean R2 Rsoma=.48, p<4.4e-10, 1% decrease over age) across domain-specific networks. To complement these findings, developmental patterns of cortical gene expression in two independent post-mortem databases were analysed. This revealed increased expression of genes expressed in oligodendrocytes, and excitatory neurons, alongside a relative decrease in expression of genes expressed in astrocyte, microglia and endothelial cell-types. Age-related genes were significantly enriched in cortical oligodendrocytes, oligodendrocyte progenitors and Layer 5-6 neurons (pFDR<.001) and prominently expressed in adolescence and young adulthood. The spatial and temporal alignment of oligodendrocyte cell-type gene expression with neurite and soma microstructural changes suggest that ongoing cortical myelination processes contribute to adolescent cortical development. These findings highlight the role of intra-cortical myelination in cortical maturation during adolescence and into adulthood.

In vivo mapping of cellular resolution neuropathology in brain ischemia with diffusion MRI

Noninvasive mapping of cellular pathology can provide critical diagnostic and prognostic information. Recent advances in diffusion magnetic resonance imaging enabled in vivo examination of tissue microstructures well beyond the imaging resolution. Here, we proposed to use diffusion time-dependent diffusion kurtosis imaging (tDKI) to simultaneously assess cellular morphology and transmembrane permeability in hypoxic-ischemic (HI) brain injury. Through numerical simulations and organoid imaging, we demonstrated the feasibility of capturing effective size and permeability changes using tDKI. In vivo MRI of HI-injured mouse brains detected a shift of the tDKI peak to longer diffusion times, suggesting swelling of the cellular processes. Furthermore, we observed a faster decrease of the tDKI tail, reflecting increased transmembrane permeability associated with up-regulated water exchange or necrosis. Such information, unavailable from a single diffusion time, can predict salvageable tissues. Preliminary applications of tDKI in patients with ischemic stroke suggested increased transmembrane permeability in stroke regions, illustrating tDKI's potential for detecting pathological changes in the clinics.

Anesthesia-related brain microstructure modulations detected by diffusion magnetic resonance imaging

Recent studies have shown significant changes to brain microstructure during sleep and anesthesia. In vivo optical microscopy and magnetic resonance imaging (MRI) studies have attributed these changes to anesthesia and sleep-related modulation of the brain's extracellular space (ECS). Isoflurane anesthesia is widely used in preclinical diffusion MRI (dMRI) and it is therefore important to investigate if the brain's microstructure is affected by anesthesia to an extent detectable with dMRI. Here, we employ diffusion kurtosis imaging (DKI) to assess brain microstructure in the awake and anesthetized mouse brain (n = 22). We find both mean diffusivity (MD) and mean kurtosis (MK) to be significantly decreased in the anesthetized mouse brain compared with the awake state (p < 0.001 for both). This effect is observed in both gray matter and white matter. To further investigate the time course of these changes we introduce a method for time-resolved fast DKI. With this, we show the time course of the microstructural alterations in mice (n = 5) as they transition between states in an awake-anesthesia-awake paradigm. We find that the decrease in MD and MK occurs rapidly after delivery of gas isoflurane anesthesia and that values normalize only slowly when the animals return to the awake state. Finally, time-resolved fast DKI is employed in an experimental mouse model of brain edema (n = 4), where cell swelling causes the ECS volume to decrease. Our results show that isoflurane affects DKI parameters and metrics of brain microstructure and point to isoflurane causing a reduction in the ECS volume. The demonstrated DKI methods are suitable for in-bore perturbation studies, for example, for investigating microstructural modulations related to sleep/wake-dependent functions of the glymphatic system. Importantly, our study shows an effect of isoflurane anesthesia on rodent brain microstructure that has broad relevance to preclinical dMRI.

DIMOND: DIffusion Model OptimizatioN with Deep Learning

Diffusion magnetic resonance imaging is an important tool for mapping tissue microstructure and structural connectivity non-invasively in the in vivo human brain. Numerous diffusion signal models are proposed to quantify microstructural properties. Nonetheless, accurate estimation of model parameters is computationally expensive and impeded by image noise. Supervised deep learning-based estimation approaches exhibit efficiency and superior performance but require additional training data and may be not generalizable. A new DIffusion Model OptimizatioN framework using physics-informed and self-supervised Deep learning entitled "DIMOND" is proposed to address this problem. DIMOND employs a neural network to map input image data to model parameters and optimizes the network by minimizing the difference between the input acquired data and synthetic data generated via the diffusion model parametrized by network outputs. DIMOND produces accurate diffusion tensor imaging results and is generalizable across subjects and datasets. Moreover, DIMOND outperforms conventional methods for fitting sophisticated microstructural models including the kurtosis and NODDI model. Importantly, DIMOND reduces NODDI model fitting time from hours to minutes, or seconds by leveraging transfer learning. In summary, the self-supervised manner, high efficacy, and efficiency of DIMOND increase the practical feasibility and adoption of microstructure and connectivity mapping in clinical and neuroscientific applications.

Superficial white matter microstructural imaging method based on time-space fractional-order diffusion

Objective. Microstructure imaging based on diffusion magnetic resonance signal is an advanced imaging technique that enablesin vivomapping of the brain's microstructure. Superficial white matter (SWM) plays an important role in brain development, maturation, and aging, while fewer microstructure imaging methods address the SWM due to its complexity. Therefore, this study aims to develop a diffusion propagation model to investigate the microstructural characteristics of the SWM region.Approach. In this paper, we hypothesize that the effect of cell membrane permeability and the water exchange between soma and dendrites cannot be neglected for typical clinical diffusion times (20 ms Collapse

Key Words

• anomalous diffusion
• diffusion magnetic resonance imaging
• fractional diffusion equation
• microstructure imaging
• superficial white matter

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MESH Headings Collapse

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Affiliation(s)

Jianglin He School of Health Science and Engineering, University of Shanghai for Science and Technology, Shanghai 200093, People's Republic of China
Yuanjun Wang School of Health Science and Engineering, University of Shanghai for Science and Technology, Shanghai 200093, People's Republic of China

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Diffusion MRI with free gradient waveforms on a high-performance gradient system: Probing restriction and exchange in the human brain

The dependence of the diffusion MRI signal on the diffusion time carries signatures of restricted diffusion and exchange. Here we seek to highlight these signatures in the human brain by performing experiments using free gradient waveforms designed to be selectively sensitive to the two effects. We examine six healthy volunteers using both strong and ultra-strong gradients (80, 200 and 300 mT/m). In an experiment featuring a large set of 150 gradient waveforms with different sensitivities to restricted diffusion and exchange, our results reveal unique and different time-dependence signatures in grey and white matter. Grey matter was characterised by both restricted diffusion and exchange and white matter predominantly by restricted diffusion. Exchange in grey matter was at least twice as fast as in white matter, across all subjects and all gradient strengths. The cerebellar cortex featured relatively short exchange times (115 ms). Furthermore, we show that gradient waveforms with tailored designs can be used to map exchange in the human brain. We also assessed the feasibility of clinical applications of the method used in this work and found that the exchange-related contrast obtained with a 25-minute protocol at 300 mT/m was preserved in a 4-minute protocol at 300 mT/m and a 10-minute protocol at 80 mT/m. Our work underlines the utility of free waveforms for detecting time dependence signatures due to restricted diffusion and exchange in vivo, which may potentially serve as a tool for studying diseased tissue.

A simulation-driven supervised learning framework to estimate brain microstructure using diffusion MRI

We propose a framework to train supervised learning models on synthetic data to estimate brain microstructure parameters using diffusion magnetic resonance imaging (dMRI). Although further validation is necessary, the proposed framework aims to seamlessly incorporate realistic simulations into dMRI microstructure estimation. Synthetic data were generated from over 1,000 neuron meshes converted from digital neuronal reconstructions and linked to their neuroanatomical parameters (such as soma volume and neurite length) using an optimized diffusion MRI simulator that produces intracellular dMRI signals from the solution of the Bloch-Torrey partial differential equation. By combining random subsets of simulated neuron signals with a free diffusion compartment signal, we constructed a synthetic dataset containing dMRI signals and 40 tissue microstructure parameters of 1.45 million artificial brain voxels. To implement supervised learning models we chose multilayer perceptrons (MLPs) and trained them on a subset of the synthetic dataset to estimate some microstructure parameters, namely, the volume fractions of soma, neurites, and the free diffusion compartment, as well as the area fractions of soma and neurites. The trained MLPs perform satisfactorily on the synthetic test sets and give promising in-vivo parameter maps on the MGH Connectome Diffusion Microstructure Dataset (CDMD). Most importantly, the estimated volume fractions showed low dependence on the diffusion time, the diffusion time independence of the estimated parameters being a desired property of quantitative microstructure imaging. The synthetic dataset we generated will be valuable for the validation of models that map between the dMRI signals and microstructure parameters. The surface meshes and microstructures parameters of the aforementioned neurons have been made publicly available.

Probing brain tissue microstructure with MRI: principles, challenges, and the role of multidimensional diffusion-relaxation encoding

Diffusion MRI uses the random displacement of water molecules to sensitize the signal to brain microstructure and to properties such as the density and shape of cells. Microstructure modeling techniques aim to estimate these properties from acquired data by separating the signal between virtual tissue 'compartments' such as the intra-neurite and the extra-cellular space. A key challenge is that the diffusion MRI signal is relatively featureless compared with the complexity of brain tissue. Another challenge is that the tissue microstructure is wildly different within the gray and white matter of the brain. In this review, we use results from multidimensional diffusion encoding techniques to discuss these challenges and their tentative solutions. Multidimensional encoding increases the information content of the data by varying not only the b-value and the encoding direction but also additional experimental parameters such as the shape of the b-tensor and the echo time. Three main insights have emerged from such encoding. First, multidimensional data contradict common model assumptions on diffusion and T2 relaxation, and illustrates how the use of these assumptions cause erroneous interpretations in both healthy brain and pathology. Second, many model assumptions can be dispensed with if data are acquired with multidimensional encoding. The necessary data can be easily acquired in vivo using protocols optimized to minimize Cramér-Rao lower bounds. Third, microscopic diffusion anisotropy reflects the presence of axons but not dendrites. This insight stands in contrast to current 'neurite models' of brain tissue, which assume that axons in white matter and dendrites in gray matter feature highly similar diffusion. Nevertheless, as an axon-based contrast, microscopic anisotropy can differentiate gray and white matter when myelin alterations confound conventional MRI contrasts.

Frequency-dependent diffusion kurtosis imaging in the human brain using an oscillating gradient spin echo sequence and a high-performance head-only gradient

Measuring the time/frequency dependence of diffusion MRI is a promising approach to distinguish between the effects of different tissue microenvironments, such as membrane restriction, tissue heterogeneity, and compartmental water exchange. In this study, we measure the frequency dependence of diffusivity (D) and kurtosis (K) with oscillating gradient diffusion encoding waveforms and a diffusion kurtosis imaging (DKI) model in human brains using a high-performance, head-only MAGNUS gradient system, with a combination of b-values, oscillating frequencies (f), and echo time that has not been achieved in human studies before. Frequency dependence of diffusivity and kurtosis are observed in both global and local white matter (WM) and gray matter (GM) regions and characterized with a power-law model ∼Λ*fθ. The frequency dependences of diffusivity and kurtosis (including changes between fmin and fmax, Λ, and θ) vary over different WM and GM regions, indicating potential microstructural differences between regions. A trend of decreasing kurtosis over frequency in the short-time limit is successfully captured for in vivo human brains. The effects of gradient nonlinearity (GNL) on frequency-dependent diffusivity and kurtosis measurements are investigated and corrected. Our results show that the GNL has prominent scaling effects on the measured diffusivity values (3.5∼5.5% difference in the global WM and 6∼8% difference in the global cortex) and subsequently affects the corresponding power-law parameters (Λ, θ) while having a marginal influence on the measured kurtosis values (<0.05% difference) and power-law parameters (Λ, θ). This study expands previous OGSE studies and further demonstrates the translatability of frequency-dependent diffusivity and kurtosis measurements to human brains, which may provide new opportunities to probe human brain microstructure in health and disease.

Time-dependent diffusion MRI using multiple stimulated echoes

PURPOSE

To develop a time-efficient pulse sequence that acquires multiple diffusion-weighted images with distinct diffusion times in a single shot by using multiple stimulated echoes (mSTE) with variable flip angles (VFA).

METHODS

The proposed diffusion-weighted mSTE with VFA (DW-mSTE-VFA) sequence begins with two 90° RF pulses that straddle a diffusion gradient lobe (GD ) to excite and restore one half of the magnetization into the longitudinal axis. The restored longitudinal magnetization was successively re-excited by a series of RF pulses with VFA, each followed by another GD , to generate a set of stimulated echoes. Each of the multiple stimulated echoes was acquired with an EPI echo train. As such, the train of multiple stimulated echoes produced a set of diffusion-weighted images with varying diffusion times in a single shot. This technique was experimentally demonstrated on a diffusion phantom, a fruit, and healthy human brain and prostate at 3 T.

RESULTS

In the phantom experiment, the mean ADC measured at different diffusion times using DW-mSTE-VFA were highly consistent (r = 0.999) with those from a commercial spin-echo diffusion-weighted EPI sequence. In the fruit and brain experiments, DW-mSTE-VFA exhibited similar diffusion-time dependence to a standard diffusion-weighted stimulated echo sequence. The ADC showed significant time dependence in the human brain (p = 0.003 in both white matter and gray matter) and prostate tissues (p = 0.003 in both peripheral zone and central gland).

CONCLUSION

DW-mSTE-VFA offers a time-efficient tool for investigating the diffusion-time dependency in diffusion MRI studies.

Mapping tissue microstructure across the human brain on a clinical scanner with soma and neurite density image metrics

Soma and neurite density image (SANDI) is an advanced diffusion magnetic resonance imaging biophysical signal model devised to probe in vivo microstructural information in the gray matter (GM). This model requires acquisitions that include b values that are at least six times higher than those used in clinical practice. Such high b values are required to disentangle the signal contribution of water diffusing in soma from that diffusing in neurites and extracellular space, while keeping the diffusion time as short as possible to minimize potential bias due to water exchange. These requirements have limited the use of SANDI only to preclinical or cutting-edge human scanners. Here, we investigate the potential impact of neglecting water exchange in the SANDI model and present a 10-min acquisition protocol that enables to characterize both GM and white matter (WM) on 3 T scanners. We implemented analytical simulations to (i) evaluate the stability of the fitting of SANDI parameters when diminishing the number of shells; (ii) estimate the bias due to potential exchange between neurites and extracellular space in such reduced acquisition scheme, comparing it with the bias due to experimental noise. Then, we demonstrated the feasibility and assessed the repeatability and reproducibility of our approach by computing microstructural metrics of SANDI with AMICO toolbox and other state-of-the-art models on five healthy subjects. Finally, we applied our protocol to five multiple sclerosis patients. Results suggest that SANDI is a practical method to characterize WM and GM tissues in vivo on performant clinical scanners.

Incorporating interface permeability into the diffusion MRI signal representation while using impermeable Laplace eigenfunctions

Objective. The complex-valued transverse magnetization due to diffusion-encoding magnetic field gradients acting on a permeable medium can be modeled by the Bloch-Torrey partial differential equation. The diffusion magnetic resonance imaging (MRI) signal has a representation in the basis of the Laplace eigenfunctions of the medium. However, in order to estimate the permeability coefficient from diffusion MRI data, it is desirable that the forward solution can be calculated efficiently for many values of permeability.Approach. In this paper we propose a new formulation of the permeable diffusion MRI signal representation in the basis of the Laplace eigenfunctions of the same medium where the interfaces are made impermeable.Main results.We proved the theoretical equivalence between our new formulation and the original formulation in the case that the full eigendecomposition is used. We validated our method numerically and showed promising numerical results when a partial eigendecomposition is used. Two diffusion MRI sequences were used to illustrate the numerical validity of our new method.Significance.Our approach means that the same basis (the impermeable set) can be used for all permeability values, which reduces the computational time significantly, enabling the study of the effects of the permeability coefficient on the diffusion MRI signal in the future.

In vivo Mapping of Cellular Resolution Neuropathology in Brain Ischemia by Diffusion MRI

Non-invasive mapping of cellular pathology can provide critical diagnostic and prognostic information. Recent developments in diffusion MRI have produced new tools for examining tissue microstructure at a level well below the imaging resolution. Here, we report the use of diffusion time ( t )-dependent diffusion kurtosis imaging ( t DKI) to simultaneously assess the morphology and transmembrane permeability of cells and their processes in the context of pathological changes in hypoxic-ischemic brain (HI) injury. Through Monte Carlo simulations and cell culture organoid imaging, we demonstrate feasibility in measuring effective size and permeability changes based on the peak and tail of t DKI curves. In a mouse model of HI, in vivo imaging at 11.7T detects a marked shift of the t DKI peak to longer t in brain edema, suggesting swelling and beading associated with the astrocytic processes and neuronal neurites. Furthermore, we observed a faster decrease of the t DKI tail in injured brain regions, reflecting increased membrane permeability that was associated with upregulated water exchange upon astrocyte activation at acute stage as well as necrosis with disrupted membrane integrity at subacute stage. Such information, unavailable with conventional diffusion MRI at a single t, can predict salvageable tissues. For a proof-of-concept, t DKI at 3T on an ischemic stroke patient suggested increased membrane permeability in the stroke region. This work therefore demonstrates the potential of t DKI for in vivo detection of the pathological changes in microstructural morphology and transmembrane permeability after ischemic injury using a clinically translatable protocol.

Higher order diffusion imaging as a putative index of human sleep-related microstructural changes and glymphatic clearance

The brain has a unique macroscopic waste clearance system, termed the glymphatic system which utilises perivascular tunnels surrounded by astroglia to promote cerebrospinal-interstitial fluid exchange. Rodent studies have demonstrated a marked increase in glymphatic clearance during sleep which has been linked to a sleep-induced expansion of the extracellular space and concomitant reduction in intracellular volume. However, despite being implicated in the pathophysiology of multiple human neurodegenerative disorders, non-invasive techniques for imaging glymphatic clearance in humans are currently limited. Here we acquired multi-shell diffusion weighted MRI (dwMRI) in twenty-one healthy young participants (6 female, 22.3 ± 3.2 years) each scanned twice, once during wakefulness and once during sleep induced by a combination of one night of sleep deprivation and 10 mg of the hypnotic zolpidem 30 min before scanning. To capture hypothesised sleep-associated changes in intra/extracellular space, dwMRI were analysed using higher order diffusion modelling with the prediction that sleep-associated increases in interstitial (extracellular) fluid volume would result in a decrease in diffusion kurtosis, particularly in areas associated with slow wave generation at the onset of sleep. In line with our hypothesis, we observed a global reduction in diffusion kurtosis (t15=2.82, p = 0.006) during sleep as well as regional reductions in brain areas associated with slow wave generation during early sleep and default mode network areas that are highly metabolically active during wakefulness. Analysis with a higher-order representation of diffusion (MAP-MRI) further indicated that changes within the intra/extracellular domain rather than membrane permeability likely underpin the observed sleep-associated decrease in kurtosis. These findings identify higher-order modelling of dwMRI as a potential new non-invasive method for imaging glymphatic clearance and extend rodent findings to suggest that sleep is also associated with an increase in interstitial fluid volume in humans.

Detection of grey matter microstructural substrates of neurodegeneration in multiple sclerosis

Multiple sclerosis features complex pathological changes in grey matter that begin early and eventually lead to diffuse atrophy. Novel approaches to image grey-matter microstructural alterations in vivo are highly sought after and would enable more sensitive monitoring of disease activity and progression. This cross-sectional study aimed to assess the sensitivity of high-gradient diffusion MRI for microstructural tissue damage in cortical and deep grey matter in people with multiple sclerosis and test the hypothesis that reduced cortical cell body density is associated with cortical and deep grey-matter volume loss. Forty-one people with multiple sclerosis (age 24-72, 14 females) and 37 age- and sex-matched healthy controls were scanned on a 3 T Connectom MRI scanner equipped with 300 mT/m gradients using a multi-shell diffusion MRI protocol. The soma and neurite density imaging model was fitted to high-gradient diffusion MRI data to obtain estimates of intra-neurite, intra-cellular and extra-cellular signal fractions and apparent soma radius. Cortical and deep grey-matter microstructural imaging metrics were compared between multiple sclerosis and healthy controls and correlated with grey-matter volume, clinical disability and cognitive outcomes. People with multiple sclerosis showed significant cortical and deep grey-matter volume loss compared with healthy controls. People with multiple sclerosis showed trends towards lower cortical intra-cellular signal fraction and significantly lower intra-cellular and higher extra-cellular signal fractions in deep grey matter, especially the thalamus and caudate, compared with healthy controls. Changes were most pronounced in progressive disease and correlated with the Expanded Disability Status Scale, but not the Symbol Digit Modalities Test. In multiple sclerosis, normalized thalamic volume was associated with thalamic microstructural imaging metrics. Whereas thalamic volume loss did not correlate with cortical volume loss, cortical microstructural imaging metrics were significantly associated with thalamic volume, and not with cortical volume. Compared with the short diffusion time (Δ = 19 ms) achievable on the Connectom scanner, at the longer diffusion time of Δ = 49 ms attainable on clinical scanners, multiple sclerosis-related changes in imaging metrics were generally less apparent with lower effect sizes in cortical and deep grey matter. Soma and neurite density imaging metrics obtained from high-gradient diffusion MRI data provide detailed grey-matter characterization beyond cortical and thalamic volumes and distinguish multiple sclerosis-related microstructural pathology from healthy controls. Cortical cell body density correlates with thalamic volume, appears sensitive to the microstructural substrate of neurodegeneration and reflects disability status in people with multiple sclerosis, becoming more pronounced as disability worsens.

Multi-tensor diffusion abnormalities of gray matter in an animal model of cortical dysplasia

Focal cortical dysplasias are a type of malformations of cortical development that are a common cause of drug-resistant focal epilepsy. Surgical treatment is a viable option for some of these patients, with their outcome being highly related to complete surgical resection of lesions visible in magnetic resonance imaging (MRI). However, subtle lesions often go undetected on conventional imaging. Several methods to analyze MRI have been proposed, with the common goal of rendering subtle cortical lesions visible. However, most image-processing methods are targeted to detect the macroscopic characteristics of cortical dysplasias, which do not always correspond to the microstructural disarrangement of these cortical malformations. Quantitative analysis of diffusion-weighted MRI (dMRI) enables the inference of tissue characteristics, and novel methods provide valuable microstructural features of complex tissue, including gray matter. We investigated the ability of advanced dMRI descriptors to detect diffusion abnormalities in an animal model of cortical dysplasia. For this purpose, we induced cortical dysplasia in 18 animals that were scanned at 30 postnatal days (along with 19 control animals). We obtained multi-shell dMRI, to which we fitted single and multi-tensor representations. Quantitative dMRI parameters derived from these methods were queried using a curvilinear coordinate system to sample the cortical mantle, providing inter-subject anatomical correspondence. We found region- and layer-specific diffusion abnormalities in experimental animals. Moreover, we were able to distinguish diffusion abnormalities related to altered intra-cortical tangential fibers from those associated with radial cortical fibers. Histological examinations revealed myelo-architectural abnormalities that explain the alterations observed through dMRI. The methods for dMRI acquisition and analysis used here are available in clinical settings and our work shows their clinical relevance to detect subtle cortical dysplasias through analysis of their microstructural properties.

Ultra-strong diffusion-weighted MRI reveals cerebellar grey matter abnormalities in movement disorders

Structural brain MRI has proven invaluable in understanding movement disorder pathophysiology. However, most work has focused on grey/white matter volumetric (macrostructural) and white matter microstructural effects, limiting understanding of frequently implicated grey matter microstructural differences. Using ultra-strong spherical tensor encoding diffusion-weighted MRI, a persistent MRI signal was seen in healthy cerebellar grey matter even at high diffusion-weightings (b ​≥ 10,000 s/mm2). Quantifying the proportion of this signal (denoted fs), previously ascertained to originate from inside small spherical spaces, provides a potential proxy for cell body density. In this work, this approach was applied for the first time to a clinical cohort, including patients with diagnosed movement disorders in which the cerebellum has been implicated in symptom pathophysiology. Five control participants (control group 1, median age 24.5 years (20-39 years), imaged at two timepoints, demonstrated consistency in measurement of all three measures - MD (Mean Diffusivity) fs, and Ds (dot diffusivity)- with intraclass correlation coefficients (ICC) of 0.98, 0.86 and 0.76, respectively. Comparison with an older control group (control group 2 (n = 5), median age 51 years (43-58 years)) found no significant differences, neither with morphometric nor microstructural (MD (p = 0.36), fs (p = 0.17) and Ds (p = 0.22)) measures. The movement disorder cohort (Parkinson's Disease, n = 5, dystonia, n = 5. Spinocerebellar Ataxia 6, n = 5) when compared to the age-matched control cohort (Control Group 2) identified significantly lower MD (p < 0.0001 and p < 0.0001) and higher fs values (p < 0.0001 and p < 0.0001) in SCA6 and dystonia cohorts respectively. Lobar division of the cerebellum found these same differences in the superior and inferior posterior lobes, while no differences were seen in either the anterior lobes or with Ds measurements. In contrast to more conventional measures from diffusion tensor imaging, this framework provides enhanced specificity to differences in restricted spherical spaces in grey matter (including small cells) by eliminating signals from cerebrospinal fluid and axons. In the context of human and animal histopathology studies, these findings potentially implicate the cerebellar Purkinje and granule cells as contributors to the observed signal differences, with both cell types having been implicated in several neurological disorders through both postmortem and animal model studies. This novel microstructural imaging approach shows promise for improving movement disorder diagnosis, prognosis, and treatment.

Diffusion MRI with free gradient waveforms on a high-performance gradient system: Probing restriction and exchange in the human brain

The dependence of the diffusion MRI signal on the diffusion time carries signatures of restricted diffusion and exchange. Here we seek to highlight these signatures in the human brain by performing experiments using free gradient waveforms that are selectively sensitive to the two effects. We examine six healthy volunteers using both strong and ultra-strong gradients (80, 200 and 300 mT/m). In an experiment featuring a large set of gradient waveforms with different sensitivities to restricted diffusion and exchange (150 samples), our results reveal unique time-dependence signatures in grey and white matter, where the former is characterised by both restricted diffusion and exchange and the latter predominantly exhibits restricted diffusion. Furthermore, we show that gradient waveforms with independently varying sensitivities to restricted diffusion and exchange can be used to map exchange in the human brain. We consistently find that exchange in grey matter is at least twice as fast as in white matter, across all subjects and all gradient strengths. The shortest exchange times observed in this study were in the cerebellar cortex (115 ms). We also assess the feasibility of future clinical applications of the method used in this work, where we find that the grey-white matter exchange contrast obtained with a 25-minute 300 mT/m protocol is preserved by a 4-minute 300 mT/m and a 10-minute 80 mT/m protocol. Our work underlines the utility of free waveforms for detecting time-dependence signatures due to restricted diffusion and exchange in vivo, which may potentially serve as a tool for studying diseased tissue.

Measuring water exchange on a preclinical MRI system using filter exchange and diffusion time dependent kurtosis imaging

PURPOSE

Filter exchange imaging (FEXI) and diffusion time (t)-dependent diffusion kurtosis imaging (DKI(t)) are both sensitive to water exchange between tissue compartments. The restrictive effects of tissue microstructure, however, introduce bias to the exchange rate obtained by these two methods, as their interpretation conventionally rely on the Kärger model of barrier limited exchange between Gaussian compartments. Here, we investigated whether FEXI and DKI(t) can provide comparable exchange rates in ex vivo mouse brains.

THEORY AND METHODS

FEXI and DKI(t) data were acquired from ex vivo mouse brains on a preclinical MRI system. Phase cycling and negative slice prewinder gradients were used to minimize the interferences from imaging gradients.

RESULTS

In the corpus callosum, apparent exchange rate (AXR) from FEXI correlated with the exchange rate (the inverse of exchange time, 1/τex ) from DKI(t) along the radial direction. In comparison, discrepancies between FEXI and DKI(t) were found in the cortex due to low filter efficiency and confounding effects from tissue microstructure.

CONCLUSION

The results suggest that FEXI and DKI(t) are sensitive to the same exchange processes in white matter when separated from restrictive effects of microstructure. The complex microstructure in gray matter, with potential exchange among multiple compartments and confounding effects of microstructure, still pose a challenge for FEXI and DKI(t).

Temporal Diffusion Ratio (TDR) for imaging restricted diffusion: Optimisation and pre-clinical demonstration

Temporal Diffusion Ratio (TDR) is a recently proposed dMRI technique (Dell'Acqua et al., proc. ISMRM 2019) which provides contrast between areas with restricted diffusion and areas either without restricted diffusion or with length scales too small for characterisation. Hence, it has a potential for informing on pore sizes, in particular the presence of large axon diameters or other cellular structures. TDR employs the signal from two dMRI acquisitions obtained with the same, large, b-value but with different diffusion gradient waveforms. TDR is advantageous as it employs standard acquisition sequences, does not make any assumptions on the underlying tissue structure and does not require any model fitting, avoiding issues related to model degeneracy. This work for the first time introduces and optimises the TDR method in simulation for a range of different tissues and scanner constraints and validates it in a pre-clinical demonstration. We consider both substrates containing cylinders and spherical structures, representing cell soma in tissue. Our results show that contrasting an acquisition with short gradient duration, short diffusion time and high gradient strength with an acquisition with long gradient duration, long diffusion time and low gradient strength, maximises the TDR contrast for a wide range of pore configurations. Additionally, in the presence of Rician noise, computing TDR from a subset (50% or fewer) of the acquired diffusion gradients rather than the entire shell as proposed originally further improves the contrast. In the last part of the work the results are demonstrated experimentally on rat spinal cord. In line with simulations, the experimental data shows that optimised TDR improves the contrast compared to non-optimised TDR. Furthermore, we find a strong correlation between TDR and histology measurements of axon diameter. In conclusion, we find that TDR has great potential and is a very promising alternative (or potentially complement) to model-based approaches for informing on pore sizes and restricted diffusion in general.

Loss of aquaporin-4 results in glymphatic system dysfunction via brain-wide interstitial fluid stagnation

The glymphatic system is a fluid transport network of cerebrospinal fluid (CSF) entering the brain along arterial perivascular spaces, exchanging with interstitial fluid (ISF), ultimately establishing directional clearance of interstitial solutes. CSF transport is facilitated by the expression of aquaporin-4 (AQP4) water channels on the perivascular endfeet of astrocytes. Mice with genetic deletion of AQP4 (AQP4 KO) exhibit abnormalities in the brain structure and molecular water transport. Yet, no studies have systematically examined how these abnormalities in structure and water transport correlate with glymphatic function. Here, we used high-resolution 3D magnetic resonance (MR) non-contrast cisternography, diffusion-weighted MR imaging (MR-DWI) along with intravoxel-incoherent motion (IVIM) DWI, while evaluating glymphatic function using a standard dynamic contrast-enhanced MR imaging to better understand how water transport and glymphatic function is disrupted after genetic deletion of AQP4. AQP4 KO mice had larger interstitial spaces and total brain volumes resulting in higher water content and reduced CSF space volumes, despite similar CSF production rates and vascular density compared to wildtype mice. The larger interstitial fluid volume likely resulted in increased slow but not fast MR diffusion measures and coincided with reduced glymphatic influx. This markedly altered brain fluid transport in AQP4 KO mice may result from a reduction in glymphatic clearance, leading to enlargement and stagnation of fluid in the interstitial space. Overall, diffusion MR is a useful tool to evaluate glymphatic function and may serve as valuable translational biomarker to study glymphatics in human disease.

In vivo quantification of brain soma and neurite density abnormalities in multiple sclerosis

BACKGROUND

Soma and neurite density imaging (SANDI) is a new biophysical model that incorporates soma in addition to neurite density, thus possibly providing more specific information about the complex pathological processes of multiple sclerosis (MS).

PURPOSE

To discriminate the pathological abnormalities of MS white matter (WM) lesions, normal-appearing (NA) WM and cortex and to evaluate the associations among SANDI-derived measures, clinical disability, and conventional MRI variables.

METHODS

Twenty healthy controls (HC) and 23 MS underwent a 3 T brain MRI. Using SANDI on diffusion-weighted sequence, the fractions of neurite (fneurite) and soma (fsoma) were assessed in WM lesions, NAWM, and cortex.

RESULTS

Compared to HC WM, MS NAWM showed lower fneurite (false discovery rate [FDR]-p = 0.011). In MS patients, WM lesions showed lower fneurite and fsoma compared to both HC and MS NAWM (FDR-p < 0.001 for all). In the cortex, MS patients had lower fneurite and fsoma compared to HC (FDR-p ≤ 0.009). Compared to both HC and RRMS, PMS patients had lower fneurite in NAWM (vs HC: FDR-p < 0.001; vs RRMS: FDR-p = 0.003) and cortex (vs HC: FDR-p < 0.001; vs RRMS: p = 0.031, not surviving FDR correction), and lower cortical fsoma (vs HC: FDR-p < 0.001; vs RRMS: FDR-p = 0.009). Compared to HC, PMS also showed a higher fsoma in NAWM (FDR-p = 0.015). Fneurite and fsoma in the different brain compartments were correlated with age, phenotype, disease duration, disability, WM lesion volumes, normalized brain, cortical, and WM volumes (r from - 0.761 to 0.821, FDR-p ≤ 0.4).

CONCLUSIONS

SANDI may represent a clinically relevant model to discriminate different neurodegenerative phenomena that gradually accumulate through MS disease course.

Metabolic activity diffusion imaging (MADI): II. Noninvasive, high-resolution human brain mapping of sodium pump flux and cell metrics

We introduce a new ¹ H₂ O magnetic resonance approach: metabolic activity diffusion imaging (MADI). Numerical diffusion-weighted imaging decay simulations characterized by the mean cellular water efflux (unidirectional) rate constant (k_io ), mean cell volume (V), and cell number density (ρ) are produced from Monte Carlo random walks in virtual stochastically sized/shaped cell ensembles. Because of active steady-state trans-membrane water cycling (AWC), k_io reflects the cytolemmal Na⁺ , K⁺ ATPase (NKA) homeostatic cellular metabolic rate (^c MR_NKA ). A digital 3D "library" contains thousands of simulated single diffusion-encoded (SDE) decays. Library entries match well with disparate, animal, and human experimental SDE decays. The V and ρ values are consistent with estimates from pertinent in vitro cytometric and ex vivo histopathological literature: in vivo V and ρ values were previously unavailable. The library allows noniterative pixel-by-pixel experimental SDE decay library matchings that can be used to advantage. They yield proof-of-concept MADI parametric mappings of the awake, resting human brain. These reflect the tissue morphology seen in conventional MRI. While V is larger in gray matter (GM) than in white matter (WM), the reverse is true for ρ. Many brain structures have k_io values too large for current, invasive methods. For example, the median WM k_io is 22s^-1 ; likely reflecting mostly exchange within myelin. The k_io •V product map displays brain tissue ^c MR_NKA variation. The GM activity correlates, quantitatively and qualitatively, with the analogous resting-state brain ¹⁸ FDG-PET tissue glucose consumption rate (^t MR_glucose ) map; but noninvasively, with higher spatial resolution, and no pharmacokinetic requirement. The cortex, thalamus, putamen, and caudate exhibit elevated metabolic activity. MADI accuracy and precision are assessed. The results are contextualized with literature overall homeostatic brain glucose consumption and ATP production/consumption measures. The MADI/PET results suggest different GM and WM metabolic pathways. Preliminary human prostate results are also presented.

Diffusion MRI with pulsed and free gradient waveforms: Effects of restricted diffusion and exchange

Monitoring time dependence with diffusion MRI yields observables sensitive to compartment sizes (restricted diffusion) and membrane permeability (water exchange). However, restricted diffusion and exchange have opposite effects on the diffusion-weighted signal, which can lead to errors in parameter estimates. In this work, we propose a signal representation that incorporates the effects of both restricted diffusion and exchange up to second order in b-value and is compatible with gradient waveforms of arbitrary shape. The representation features mappings from a gradient waveform to two scalars that separately control the sensitivity to restriction and exchange. We demonstrate that these scalars span a two-dimensional space that can be used to choose waveforms that selectively probe restricted diffusion or exchange, eliminating the correlation between the two phenomena. We found that waveforms with specific but unconventional shapes provide an advantage over conventional pulsed and oscillating gradient acquisitions. We also show that parametrization of waveforms into a two-dimensional space can be used to understand protocols from other approaches that probe restricted diffusion and exchange. For example, we found that the variation of mixing time in filter-exchange imaging corresponds to variation of our exchange-weighting scalar at a fixed value of the restriction-weighting scalar. The proposed signal representation was evaluated using Monte Carlo simulations in identical parallel cylinders with hexagonal and random packing as well as parallel cylinders with gamma-distributed radii. Results showed that the approach is sensitive to sizes in the interval 4-12 μm and exchange rates in the simulated range of 0 to 20 s - 1 , but also that there is a sensitivity to the extracellular geometry. The presented theory constitutes a simple and intuitive description of how restricted diffusion and exchange influence the signal as well as a guide to protocol design capable of separating the two effects.

What does FEXI measure?

Filter-exchange imaging (FEXI) has already been utilized in several biomedical studies for evaluating the permeability of cell membranes. The method relies on suppressing the extracellular signal using strong diffusion weighting (the mobility filter causing a reduction in the overall diffusivity) and monitoring the subsequent diffusivity recovery. Using Monte Carlo simulations, we demonstrate that FEXI is sensitive not uniquely to the transcytolemmal exchange but also to the geometry of involved compartments: complex geometry offers locations where spins remain unaffected by the mobility filter; moving to other locations afterwards, such spins contribute to the diffusivity recovery without actually permeating any membrane. This exchange mechanism is a warning for those who aim to use FEXI in complex media such as brain gray matter and opens wide scope for investigation towards crystallizing the genuine membrane permeation and characterizing the compartment geometry.

Improving MR cell size imaging by inclusion of transcytolemmal water exchange

The goal of the current study is to include transcytolemmal water exchange in MR cell size imaging using the IMPULSED model for more accurate characterization of tissue cellular properties (e.g., apparent volume fraction of intracellular space v in ) and quantification of indicators of transcytolemmal water exchange. We propose a heuristic model that incorporates transcytolemmal water exchange into a multicompartment diffusion-based method (IMPULSED) that was developed previously to extract microstructural parameters (e.g., mean cell size d and apparent volume fraction of intracellular space v in ) assuming no water exchange. For t diff ≤ 5 ms, the water exchange can be ignored, and the signal model is the same as the IMPULSED model. For t diff ≥ 30 ms, we incorporated the modified Kärger model that includes both restricted diffusion and exchange between compartments. Using simulations and previously published in vitro cell data, we evaluated the accuracy and precision of model-derived parameters and determined how they are dependent on SNR and imaging parameters. The joint model provides more accurate d values for cell sizes ranging from 10 to 12 microns when water exchange is fast (e.g., intracellular water pre-exchange lifetime τ in ≤ 100 ms) than IMPULSED, and reduces the bias of IMPULSED-derived estimates of v in , especially when water exchange is relatively slow (e.g., τ in &gt; 200 ms). Indicators of transcytolemmal water exchange derived from the proposed joint model are linearly correlated with ground truth τ in values and can detect changes in cell membrane permeability induced by saponin treatment in murine erythroleukemia cancer cells. Our results suggest this joint model not only improves the accuracy of IMPULSED-derived microstructural parameters, but also provides indicators of water exchange that are usually ignored in diffusion models of tissues.

Estimating axial diffusivity in the NODDI model

To estimate microstructure-related parameters from diffusion MRI data, biophysical models make strong, simplifying assumptions about the underlying tissue. The extent to which many of these assumptions are valid remains an open research question. This study was inspired by the disparity between the estimated intra-axonal axial diffusivity from literature and that typically assumed by the Neurite Orientation Dispersion and Density Imaging (NODDI) model (d_∥=1.7μm²/ms). We first demonstrate how changing the assumed axial diffusivity results in considerably different NODDI parameter estimates. Second, we illustrate the ability to estimate axial diffusivity as a free parameter of the model using high b-value data and an adapted NODDI framework. Using both simulated and in vivo data we investigate the impact of fitting to either real-valued or magnitude data, with Gaussian and Rician noise characteristics respectively, and what happens if we get the noise assumptions wrong in this high b-value and thus low SNR regime. Our results from real-valued human data estimate intra-axonal axial diffusivities of ∼2-2.5μm²/ms, in line with current literature. Crucially, our results demonstrate the importance of accounting for both a rectified noise floor and/or a signal offset to avoid biased parameter estimates when dealing with low SNR data.

Neurite Exchange Imaging (NEXI): A minimal model of diffusion in gray matter with inter-compartment water exchange

Biophysical models of diffusion in white matter have been center-stage over the past two decades and are essentially based on what is now commonly referred to as the "Standard Model" (SM) of non-exchanging anisotropic compartments with Gaussian diffusion. In this work, we focus on diffusion MRI in gray matter, which requires rethinking basic microstructure modeling blocks. In particular, at least three contributions beyond the SM need to be considered for gray matter: water exchange across the cell membrane - between neurites and the extracellular space; non-Gaussian diffusion along neuronal and glial processes - resulting from structural disorder; and signal contribution from soma. For the first contribution, we propose Neurite Exchange Imaging (NEXI) as an extension of the SM of diffusion, which builds on the anisotropic Kärger model of two exchanging compartments. Using datasets acquired at multiple diffusion weightings (b) and diffusion times (t) in the rat brain in vivo, we investigate the suitability of NEXI to describe the diffusion signal in the gray matter, compared to the other two possible contributions. Our results for the diffusion time window 20-45 ms show minimal diffusivity time-dependence and more pronounced kurtosis decay with time, which is well fit by the exchange model. Moreover, we observe lower signal for longer diffusion times at high b. In light of these observations, we identify exchange as the mechanism that best explains these signal signatures in both low-b and high-b regime, and thereby propose NEXI as the minimal model for gray matter microstructure mapping. We finally highlight multi-b multi-t acquisition protocols as being best suited to estimate NEXI model parameters reliably. Using this approach, we estimate the inter-compartment water exchange time to be 15 - 60 ms in the rat cortex and hippocampus in vivo, which is of the same order or shorter than the diffusion time in typical diffusion MRI acquisitions. This suggests water exchange as an essential component for interpreting diffusion MRI measurements in gray matter.