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.

Perivascular space diffusivity and brain microstructural measures are associated with circadian time and sleep quality.

The glymphatic system is centred around brain cerebrospinal fluid flow and is enhanced during sleep, and the synaptic homeostasis hypothesis proposes that sleep acts on brain microstructure by selective synaptic downscaling. While so far primarily studied in animals, we here examine in humans if brain diffusivity and microstructure is related to time of day, sleep quality and cognitive performance. We use diffusion weighted images from 916 young healthy individuals, aged between 22 and 37 years, collected as part of the Human Connectome Project to assess diffusion tensor image analysis along the perivascular space index, white matter fractional anisotropy, intra-neurite volume fraction and extra-neurite mean diffusivity. Next, we examine if these measures are associated with circadian time of acquisition, the Pittsburgh Sleep Quality Index (high scores correspond to low sleep quality) and age-adjusted cognitive function total composite score. Consistent with expectations, we find that diffusion tensor image analysis along the perivascular space index and orbitofrontal grey matter extra-neurite mean diffusivity are negatively and white matter fractional anisotropy positively correlated with circadian time. Further, we find that grey matter intra-neurite volume fraction correlates positively with Pittsburgh Sleep Quality Index, and that this correlation is driven by sleep duration. Finally, we find positive correlations between grey matter intra-neurite volume fraction and cognitive function total composite score, as well as negative interaction effects between cognitive function total composite score and Pittsburgh Sleep Quality Index on grey matter intra-neurite volume fraction. Our findings propose that perivascular flow is under circadian control and that sleep downregulates the intra-neurite volume in healthy adults with positive impact on cognitive function.

Romer-EPTI: rotating-view motion-robust super-resolution EPTI for SNR-efficient distortion-free in-vivo mesoscale dMRI and microstructure imaging.

Purpose: To overcome the major challenges in dMRI acquisition, including low SNR, distortion/blurring, and motion vulnerability. Methods: A novel Romer-EPTI technique is developed to provide distortion-free dMRI with significant SNR gain, high motion-robustness, sharp spatial resolution, and simultaneous multi-TE imaging. It introduces a ROtating-view Motion-robust supEr-Resolution technique (Romer) combined with a distortion/blurring-free EPTI encoding. Romer enhances SNR by a simultaneous multi-thick-slice acquisition with rotating-view encoding, while providing high motion-robustness through a motion-aware super-resolution reconstruction, which also incorporates slice-profile and real-value diffusion, to resolve high-isotropic-resolution volumes. The in-plane encoding is performed using distortion/blurring-free EPTI, which further improves effective spatial resolution and motion robustness by preventing not only T2/T2*-blurring but also additional blurring resulting from combining encoded volumes with inconsistent geometries caused by dynamic distortions. Self-navigation was incorporated to enable efficient phase correction. Additional developments include strategies to address slab-boundary artifacts, achieve minimal TE for SNR gain at 7T, and achieve high robustness to strong phase variations at high b-values. Results: Using Romer-EPTI, we demonstrate distortion-free whole-brain mesoscale in-vivo dMRI at both 3T (500-µm-iso) and 7T (485-µm-iso) for the first time, with high SNR efficiency (e.g., 25×), and high image quality free from distortion and slab-boundary artifacts with minimal blurring. Motion experiments demonstrate Romer-EPTI's high motion-robustness and ability to recover sharp images in the presence of motion. Romer-EPTI also demonstrates significant SNR gain and robustness in high b-value (b=5000s/mm2) and time-dependent dMRI. Conclusion: Romer-EPTI significantly improves SNR, motion-robustness, and image quality, providing a highly efficient acquisition for high-resolution dMRI and microstructure imaging.

Volume electron microscopy in injured rat brain validates white matter microstructure metrics from diffusion MRI.

Biophysical modeling of diffusion MRI (dMRI) offers the exciting potential of bridging the gap between the macroscopic MRI resolution and microscopic cellular features, effectively turning the MRI scanner into a noninvasive in vivo microscope. In brain white matter, the Standard Model (SM) interprets the dMRI signal in terms of axon dispersion, intra- and extra-axonal water fractions and diffusivities. However, for SM to be fully applicable and correctly interpreted, it needs to be carefully evaluated using histology. Here, we perform a comprehensive histological validation of the SM parameters, by characterizing WM microstructure in sham and injured rat brains using volume (3d) electron microscopy (EM) and ex vivo dMRI. Sensitivity is evaluated by how close each SM metric is to its histological counterpart, and specificity by how independent it is from other, non-corresponding histological features. This comparison reveals that SM is sensitive and specific to microscopic properties, clearing the way for the clinical adoption of in vivo dMRI derived SM parameters as biomarkers for neurological disorders.

The effects of axonal beading and undulation on axonal diameter estimation from diffusion MRI: Insights from simulations in human axons segmented from three-dimensional electron microscopy.

The increasing availability of high-performance gradient systems in human MRI scanners has generated great interest in diffusion microstructural imaging applications such as axonal diameter mapping. Practically, sensitivity to axon diameter in diffusion MRI is attained at strong diffusion weightings b , where the deviation from the expected 1 / b scaling in white matter yields a finite transverse diffusivity, which is then translated into an axon diameter estimate. While axons are usually modeled as perfectly straight, impermeable cylinders, local variations in diameter (caliber variation or beading) and direction (undulation) are known to influence axonal diameter estimates and have been observed in microscopy data of human axons. In this study, we performed Monte Carlo simulations of diffusion in axons reconstructed from three-dimensional electron microscopy of a human temporal lobe specimen using simulated sequence parameters matched to the maximal gradient strength of the next-generation Connectome 2.0 human MRI scanner ( ≲ 500 mT/m). We show that axon diameter estimation is accurate for nonbeaded, nonundulating fibers; however, in fibers with caliber variations and undulations, the axon diameter is heavily underestimated due to caliber variations, and this effect overshadows the known overestimation of the axon diameter due to undulations. This unexpected underestimation may originate from variations in the coarse-grained axial diffusivity due to caliber variations. Given that increased axonal beading and undulations have been observed in pathological tissues, such as traumatic brain injury and ischemia, the interpretation of axon diameter alterations in pathology may be significantly confounded.

Optimization and Validation of the DESIGNER dMRI preprocessing pipeline in white matter aging.

Various diffusion MRI (dMRI) preprocessing pipelines are currently available to yield more accurate diffusion parameters. Here, we evaluated accuracy and robustness of the optimized Diffusion parameter EStImation with Gibbs and NoisE Removal (DESIGNER) pipeline in a large clinical dMRI dataset and using ground truth phantoms. DESIGNER has been modified to improve denoising and target Gibbs ringing for partial Fourier acquisitions. We compared the revisited DESIGNER (Dv2) (including denoising, Gibbs removal, correction for motion, EPI distortion, and eddy currents) against the original DESIGNER (Dv1) pipeline, minimal preprocessing (including correction for motion, EPI distortion, and eddy currents only), and no preprocessing on a large clinical dMRI dataset of 524 control subjects with ages between 25 and 75 years old. We evaluated the effect of specific processing steps on age correlations in white matter with DTI and DKI metrics. We also evaluated the added effect of minimal Gaussian smoothing to deal with noise and to reduce outliers in parameter maps compared to DESIGNER (Dv2)'s noise removal method. Moreover, DESIGNER (Dv2)'s updated noise and Gibbs removal methods were assessed using ground truth dMRI phantom to evaluate accuracy. Results show age correlation in white matter with DTI and DKI metrics were affected by the preprocessing pipeline, causing systematic differences in absolute parameter values and loss or gain of statistical significance. Both in clinical dMRI and ground truth phantoms, DESIGNER (Dv2) pipeline resulted in the smallest number of outlier voxels and improved accuracy in DTI and DKI metrics as noise was reduced and Gibbs removal was improved. Thus, DESIGNER (Dv2) provides more accurate and robust DTI and DKI parameter maps as compared to no preprocessing or minimal preprocessing.

Eddy current-induced artifact correction in high b-value ex vivo human brain diffusion MRI with dynamic field monitoring.

PURPOSE: To investigate whether spatiotemporal magnetic field monitoring can correct pronounced eddy current-induced artifacts incurred by strong diffusion-sensitizing gradients up to 300 mT/m used in high b-value diffusion-weighted (DW) EPI. METHODS: A dynamic field camera equipped with 16 1 H NMR field probes was first used to characterize field perturbations caused by residual eddy currents from diffusion gradients waveforms in a 3D multi-shot EPI sequence on a 3T Connectom scanner for different gradient strengths (up to 300 mT/m), diffusion directions, and shots. The efficacy of dynamic field monitoring-based image reconstruction was demonstrated on high-gradient strength, submillimeter resolution whole-brain ex vivo diffusion MRI. A 3D multi-shot image reconstruction framework was developed that incorporated the nonlinear phase evolution measured with the dynamic field camera. RESULTS: Phase perturbations in the readout induced by residual eddy currents from strong diffusion gradients are highly nonlinear in space and time, vary among diffusion directions, and interfere significantly with the image encoding gradients, changing the k-space trajectory. During the readout, phase modulations between odd and even EPI echoes become non-static and diffusion encoding direction-dependent. Superior reduction of ghosting and geometric distortion was achieved with dynamic field monitoring compared to ghosting reduction approaches such as navigator- and structured low-rank-based methods or MUSE followed by image-based distortion correction with the FSL tool "eddy." CONCLUSION: Strong eddy current artifacts characteristic of high-gradient strength DW-EPI can be well corrected with dynamic field monitoring-based image reconstruction.

Universal Sampling Denoising (USD) for noise mapping and noise removal of non-Cartesian MRI.

Random matrix theory (RMT) combined with principal component analysis has resulted in a widely used MPPCA noise mapping and denoising algorithm, that utilizes the redundancy in multiple acquisitions and in local image patches. RMT-based denoising relies on the uncorrelated identically distributed noise. This assumption breaks down after regridding of non-Cartesian sampling. Here we propose a Universal Sampling Denoising (USD) pipeline to homogenize the noise level and decorrelate the noise in non-Cartesian sampled k-space data after resampling to a Cartesian grid. In this way, the RMT approaches become applicable to MRI of any non-Cartesian k-space sampling. We demonstrate the denoising pipeline on MRI data acquired using radial trajectories, including diffusion MRI of a numerical phantom and ex vivo mouse brains, as well as in vivo $T_2$ MRI of a healthy subject. The proposed pipeline robustly estimates noise level, performs noise removal, and corrects bias in parametric maps, such as diffusivity and kurtosis metrics, and $T_2$ relaxation time. USD stabilizes the variance, decorrelates the noise, and thereby enables the application of RMT-based denoising approaches to MR images reconstructed from any non-Cartesian data. In addition to MRI, USD may also apply to other medical imaging techniques involving non-Cartesian acquisition, such as PET, CT, and SPECT.

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.

The influence of axonal beading and undulation on axonal diameter mapping.

We consider the effect of non-cylindrical axonal shape on axonal diameter mapping with diffusion MRI. Practical sensitivity to axon diameter is attained at strong diffusion weightings b, where the deviation from the 1/b scaling yields the finite transverse diffusivity, which is then translated into axon diameter. While axons are usually modeled as perfectly straight, impermeable cylinders, the local variations in diameter (caliber variation or beading) and direction (undulation) have been observed in microscopy data of human axons. Here we quantify the influence of cellular-level features such as caliber variation and undulation on axon diameter estimation. For that, we simulate the diffusion MRI signal in realistic axons segmented from 3-dimensional electron microscopy of a human brain sample. We then create artificial fibers with the same features and tune the amplitude of their caliber variations and undulations. Numerical simulations of diffusion in fibers with such tunable features show that caliber variations and undulations result in under- and over-estimation of axon diameters, correspondingly; this bias can be as large as 100%. Given that increased axonal beading and undulations have been observed in pathological tissues, such as traumatic brain injury and ischemia, the interpretation of axon diameter alterations in pathology may be significantly confounded.

Eddy current-induced artifacts correction in high gradient strength diffusion MRI with dynamic field monitoring: demonstration in ex vivo human brain imaging.

Purpose: To demonstrate the advantages of spatiotemporal magnetic field monitoring to correct eddy current-induced artifacts (ghosting and geometric distortions) in high gradient strength diffusion MRI (dMRI). Methods: A dynamic field camera with 16 NMR field probes was used to characterize eddy current fields induced from diffusion gradients for different gradients strengths (up to 300 mT/m), diffusion directions, and shots in a 3D multi-shot EPI sequence on a 3T Connectom scanner. The efficacy of dynamic field monitoring-based image reconstruction was demonstrated on high-resolution whole brain ex vivo dMRI. A 3D multi-shot image reconstruction framework was informed with the actual nonlinear phase evolution measured with the dynamic field camera, thereby accounting for high-order eddy currents fields on top of the image encoding gradients in the image formation model. Results: Eddy current fields from diffusion gradients at high gradient strength in a 3T Connectom scanner are highly nonlinear in space and time, inducing high-order spatial phase modulations between odd/even echoes and shots that are not static during the readout. Superior reduction of ghosting and geometric distortion was achieved with dynamic field monitoring compared to ghosting approaches such as navigator- and structured low-rank-based methods or MUSE, followed by image-based distortion correction with eddy. Improved dMRI analysis is demonstrated with diffusion tensor imaging and high-angular resolution diffusion imaging. Conclusion: Strong eddy current artifacts characteristic of high gradient strength dMRI can be well corrected with dynamic field monitoring-based image reconstruction, unlike the two-step approach consisting of ghosting correction followed by geometric distortion reduction with eddy.

High-fidelity, high-spatial-resolution diffusion magnetic resonance imaging of ex vivo whole human brain at ultra-high gradient strength with structured low-rank echo-planar imaging ghost correction.

Diffusion magnetic resonance imaging (dMRI) of whole ex vivo human brain specimens enables three-dimensional (3D) mapping of structural connectivity at the mesoscopic scale, providing detailed evaluation of fiber architecture and tissue microstructure at a spatial resolution that is difficult to access in vivo. To account for the short T2 and low diffusivity of fixed tissue, ex vivo dMRI is often acquired using strong diffusion-sensitizing gradients and multishot/segmented 3D echo-planar imaging (EPI) sequences to achieve high spatial resolution. However, the combination of strong diffusion-sensitizing gradients and multishot/segmented EPI readout can result in pronounced ghosting artifacts incurred by nonlinear spatiotemporal variations in the magnetic field produced by eddy currents. Such ghosting artifacts cannot be corrected with conventional correction solutions and pose a significant roadblock to leveraging human MRI scanners with ultrahigh gradients for ex vivo whole-brain dMRI. Here, we show that ghosting-correction approaches that correct for either polarity-related ghosting or shot-to-shot variations in a separate manner are suboptimal for 3D multishot diffusion-weighted EPI experiments in fixed human brain specimens using strong diffusion-sensitizing gradients on the 3-T Connectom MRI scanner, resulting in orientationally biased dMRI estimates. We apply a recently developed advanced k-space reconstruction method based on structured low-rank matrix (SLM) modeling that handles both polarity-related ghosting and shot-to-shot variation simultaneously, to mitigate artifacts in high-angular resolution multishot dMRI data acquired in several fixed human brain specimens at 0.7-0.8-mm isotropic spatial resolution using b-values up to 10,000 s/mm2 and gradient strengths up to 280 mT/m. We demonstrate the improved mapping of diffusion tensor imaging and fiber orientation distribution functions in key neuroanatomical areas distributed across the whole brain using SLM-based EPI ghost correction compared with alternative techniques.

Mapping the human connectome using diffusion MRI at 300 mT/m gradient strength: Methodological advances and scientific impact.

Tremendous efforts have been made in the last decade to advance cutting-edge MRI technology in pursuit of mapping structural connectivity in the living human brain with unprecedented sensitivity and speed. The first Connectom 3T MRI scanner equipped with a 300 mT/m whole-body gradient system was installed at the Massachusetts General Hospital in 2011 and was specifically constructed as part of the Human Connectome Project. Since that time, numerous technological advances have been made to enable the broader use of the Connectom high gradient system for diffusion tractography and tissue microstructure studies and leverage its unique advantages and sensitivity to resolving macroscopic and microscopic structural information in neural tissue for clinical and neuroscientific studies. The goal of this review article is to summarize the technical developments that have emerged in the last decade to support and promote large-scale and scientific studies of the human brain using the Connectom scanner. We provide a brief historical perspective on the development of Connectom gradient technology and the efforts that led to the installation of three other Connectom 3T MRI scanners worldwide - one in the United Kingdom in Cardiff, Wales, another in continental Europe in Leipzig, Germany, and the latest in Asia in Shanghai, China. We summarize the key developments in gradient hardware and image acquisition technology that have formed the backbone of Connectom-related research efforts, including the rich array of high-sensitivity receiver coils, pulse sequences, image artifact correction strategies and data preprocessing methods needed to optimize the quality of high-gradient strength diffusion MRI data for subsequent analyses. Finally, we review the scientific impact of the Connectom MRI scanner, including advances in diffusion tractography, tissue microstructural imaging, ex vivo validation, and clinical investigations that have been enabled by Connectom technology. We conclude with brief insights into the unique value of strong gradients for diffusion MRI and where the field is headed in the coming years.

Connectome 2.0: Developing the next-generation ultra-high gradient strength human MRI scanner for bridging studies of the micro-, meso- and macro-connectome.

The first phase of the Human Connectome Project pioneered advances in MRI technology for mapping the macroscopic structural connections of the living human brain through the engineering of a whole-body human MRI scanner equipped with maximum gradient strength of 300 mT/m, the highest ever achieved for human imaging. While this instrument has made important contributions to the understanding of macroscale connectional topology, it has also demonstrated the potential of dedicated high-gradient performance scanners to provide unparalleled in vivo assessment of neural tissue microstructure. Building on the initial groundwork laid by the original Connectome scanner, we have now embarked on an international, multi-site effort to build the next-generation human 3T Connectome scanner (Connectome 2.0) optimized for the study of neural tissue microstructure and connectional anatomy across multiple length scales. In order to maximize the resolution of this in vivo microscope for studies of the living human brain, we will push the diffusion resolution limit to unprecedented levels by (1) nearly doubling the current maximum gradient strength from 300 mT/m to 500 mT/m and tripling the maximum slew rate from 200 T/m/s to 600 T/m/s through the design of a one-of-a-kind head gradient coil optimized to minimize peripheral nerve stimulation; (2) developing high-sensitivity multi-channel radiofrequency receive coils for in vivo and ex vivo human brain imaging; (3) incorporating dynamic field monitoring to minimize image distortions and artifacts; (4) developing new pulse sequences to integrate the strongest diffusion encoding and highest spatial resolution ever achieved in the living human brain; and (5) calibrating the measurements obtained from this next-generation instrument through systematic validation of diffusion microstructural metrics in high-fidelity phantoms and ex vivo brain tissue at progressively finer scales with accompanying diffusion simulations in histology-based micro-geometries. We envision creating the ultimate diffusion MRI instrument capable of capturing the complex multi-scale organization of the living human brain - from the microscopic scale needed to probe cellular geometry, heterogeneity and plasticity, to the mesoscopic scale for quantifying the distinctions in cortical structure and connectivity that define cyto- and myeloarchitectonic boundaries, to improvements in estimates of macroscopic connectivity.

Removal of partial Fourier-induced Gibbs (RPG) ringing artifacts in MRI.

PURPOSE: To investigate and remove Gibbs-ringing artifacts caused by partial Fourier (PF) acquisition and zero filling interpolation in MRI data. THEORY AND METHODS: Gibbs ringing of fully sampled data, leading to oscillations around tissue boundaries, is caused by the symmetric truncation of k-space. Such ringing can be removed by conventional methods, with the local subvoxel shifts method being the state-of-the-art. However, the asymmetric truncation of k-space in routinely used PF acquisitions leads to additional ringings of wider intervals in the PF sampling dimension that cannot be corrected solely based on magnitude images reconstructed via zero filling. Here, we develop a pipeline for the Removal of PF-induced Gibbs ringing (RPG) to remove ringing patterns of different periods by applying the conventional method twice. The proposed pipeline is validated on numerical phantoms, demonstrated on in vivo diffusion MRI measurements, and compared with the conventional method and neural network-based approach. RESULTS: For PF = 7/8 and 6/8, Gibbs-ringings and subsequent bias in diffusion metrics induced by PF acquisition and zero filling are robustly removed by using the proposed RPG pipeline. For PF = 5/8, however, ringing removal via RPG leads to excessive image blurring due to the interplay of image phase and convolution kernel. CONCLUSIONS: RPG corrects Gibbs-ringing artifacts in magnitude images of PF acquired data and reduces the bias in quantitative MR metrics. Considering the benefit of PF acquisition and the feasibility of ringing removal, we suggest applying PF = 6/8 when PF acquisition is necessary.

Quantitative Macromolecular Proton Fraction Mapping Reveals Altered Cortical Myelin Profile in Schizophrenia Spectrum Disorders.

Myelin abnormalities have been reported in schizophrenia spectrum disorders (SSD) in white matter. However, in vivo examinations of cortical myeloarchitecture in SSD, especially those using quantitative measures, are limited. Here, we employed macromolecular proton fraction (MPF) obtained from quantitative magnetization transfer imaging to characterize intracortical myelin organization in 30 SSD patients versus 34 healthy control (HC) participants. We constructed cortical myelin profiles by extracting MPF values at various cortical depths and quantified their shape using a nonlinearity index (NLI). To delineate the association of illness duration with myelin changes, SSD patients were further divided into 3 duration groups. Between-group comparisons revealed reduced NLI in the SSD group with the longest illness duration (>5.5 years) compared with HC predominantly in bilateral prefrontal areas. Within the SSD group, cortical NLI decreased with disease duration and was positively associated with a measure of spatial working memory capacity as well as with cortical thickness (CT). Layer-specific analyses suggested that NLI decreases in the long-duration SSD group may arise in part from significantly increased MPF values in the midcortical layers. The current study reveals cortical myelin profile changes in SSD with illness progression, which may reflect an abnormal compensatory mechanism of the disorder.

Realistic Microstructure Simulator (RMS): Monte Carlo simulations of diffusion in three-dimensional cell segmentations of microscopy images.

BACKGROUND: Monte Carlo simulations of diffusion are commonly used as a model validation tool as they are especially suitable for generating the diffusion MRI signal in complicated tissue microgeometries. NEW METHOD: Here we describe the details of implementing Monte Carlo simulations in three-dimensional (3d) voxelized segmentations of cells in microscopy images. Using the concept of the corner reflector, we largely reduce the computational load of simulating diffusion within and exchange between multiple cells. Precision is further achieved by GPU-based parallel computations. RESULTS: Our simulation of diffusion in white matter axons segmented from a mouse brain demonstrates its value in validating biophysical models. Furthermore, we provide the theoretical background for implementing a discretized diffusion process, and consider the finite-step effects of the particle-membrane reflection and permeation events, needed for efficient simulation of interactions with irregular boundaries, spatially variable diffusion coefficient, and exchange. COMPARISON WITH EXISTING METHODS: To our knowledge, this is the first Monte Carlo pipeline for MR signal simulations in a substrate composed of numerous realistic cells, accounting for their permeable and irregularly-shaped membranes. CONCLUSIONS: The proposed RMS pipeline makes it possible to achieve fast and accurate simulations of diffusion in realistic tissue microgeometry, as well as the interplay with other MR contrasts. Presently, RMS focuses on simulations of diffusion, exchange, and T1 and T2 NMR relaxation in static tissues, with a possibility to straightforwardly account for susceptibility-induced T2* effects and flow.

The impact of realistic axonal shape on axon diameter estimation using diffusion MRI.

To study axonal microstructure with diffusion MRI, axons are typically modeled as straight impermeable cylinders, whereby the transverse diffusion MRI signal can be made sensitive to the cylinder's inner diameter. However, the shape of a real axon varies along the axon direction, which couples the longitudinal and transverse diffusion of the overall axon direction. Here we develop a theory of the intra-axonal diffusion MRI signal based on coarse-graining of the axonal shape by 3-dimensional diffusion. We demonstrate how the estimate of the inner diameter is confounded by the diameter variations (beading), and by the local variations in direction (undulations) along the axon. We analytically relate diffusion MRI metrics, such as time-dependent radial diffusivity D⊥(t)and kurtosis K⊥(t),to the axonal shape, and validate our theory using Monte Carlo simulations in synthetic undulating axons with randomly positioned beads, and in realistic axons reconstructed from electron microscopy images of mouse brain white matter. We show that (i) In the narrow pulse limit, the inner diameter from D⊥(t)is overestimated by about twofold due to a combination of axon caliber variations and undulations (each contributing a comparable effect size); (ii) The narrow-pulse kurtosis K⊥|t→∞deviates from that in an ideal cylinder due to caliber variations; we also numerically calculate the fourth-order cumulant for an ideal cylinder in the wide pulse limit, which is relevant for inner diameter overestimation; (iii) In the wide pulse limit, the axon diameter overestimation is mainly due to undulations at low diffusion weightings b; and (iv) The effect of undulations can be considerably reduced by directional averaging of high-b signals, with the apparent inner diameter given by a combination of the axon caliber (dominated by the thickest axons), caliber variations, and the residual contribution of undulations.