A generative model of realistic brain cells with application to numerical simulation of the diffusion-weighted MR signal

A flexible generative algorithm for growing in silico placentas

The placenta is crucial for a successful pregnancy, facilitating oxygen exchange and nutrient transport between mother and fetus. Complications like fetal growth restriction and pre-eclampsia are linked to placental vascular structure abnormalities, highlighting the need for early detection of placental health issues. Computational modelling offers insights into how vascular architecture correlates with flow and oxygenation in both healthy and dysfunctional placentas. These models use synthetic networks to represent the multiscale feto-placental vasculature, but current methods lack direct control over key morphological parameters like branching angles, essential for predicting placental dysfunction. We introduce a novel generative algorithm for creating in silico placentas, allowing user-controlled customisation of feto-placental vasculatures, both as individual components (placental shape, chorionic vessels, placentone) and as a complete structure. The algorithm is physiologically underpinned, following branching laws (i.e. Murray's Law), and is defined by four key morphometric statistics: vessel diameter, vessel length, branching angle and asymmetry. Our algorithm produces structures consistent with in vivo measurements and ex vivo observations. Our sensitivity analysis highlights how vessel length variations and branching angles play a pivotal role in defining the architecture of the placental vascular network. Moreover, our approach is stochastic in nature, yielding vascular structures with different topological metrics when imposing the same input settings. Unlike previous volume-filling algorithms, our approach allows direct control over key morphological parameters, generating vascular structures that closely resemble real vascular densities and allowing for the investigation of the impact of morphological parameters on placental function in upcoming studies.

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.

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.

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.

Random walk diffusion simulations in semi-permeable layered media with varying diffusivity

In this paper we present random walk based solutions to diffusion in semi-permeable layered media with varying diffusivity. We propose a novel transit model for solving the interaction of random walkers with a membrane. This hybrid model is based on treating the membrane permeability and the step change in diffusion coefficient as two interactions separated by an infinitesimally small layer. By conducting an extensive analytical flux analysis, the performance of our hybrid model is compared with a commonly used membrane transit model (reference model). Numerical simulations demonstrate the limitations of the reference model in dealing with step changes in diffusivity and show the capability of the hybrid model to overcome this limitation and to offer substantial gains in computational efficiency. The suitability of both random walk transit models for the application to simulations of diffusion tensor cardiovascular magnetic resonance (DT-CMR) imaging is assessed in a histology-based domain relevant to DT-CMR. In order to demonstrate the usefulness of the new hybrid model for other possible applications, we also consider a larger range of permeabilities beyond those commonly found in biological tissues.

Physical and digital phantoms for validating tractography and assessing artifacts

Fiber tractography is widely used to non-invasively map white-matter bundles in vivo using diffusion-weighted magnetic resonance imaging (dMRI). As it is the case for all scientific methods, proper validation is a key prerequisite for the successful application of fiber tractography, be it in the area of basic neuroscience or in a clinical setting. It is well-known that the indirect estimation of the fiber tracts from the local diffusion signal is highly ambiguous and extremely challenging. Furthermore, the validation of fiber tractography methods is hampered by the lack of a real ground truth, which is caused by the extremely complex brain microstructure that is not directly observable non-invasively and that is the basis of the huge network of long-range fiber connections in the brain that are the actual target of fiber tractography methods. As a substitute for in vivo data with a real ground truth that could be used for validation, a widely and successfully employed approach is the use of synthetic phantoms. In this work, we are providing an overview of the state-of-the-art in the area of physical and digital phantoms, answering the following guiding questions: "What are dMRI phantoms and what are they good for?", "What would the ideal phantom for validation fiber tractography look like?" and "What phantoms, phantom datasets and tools used for their creation are available to the research community?". We will further discuss the limitations and opportunities that come with the use of dMRI phantoms, and what future direction this field of research might take.

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.

Comparative analysis of signal models for microscopic fractional anisotropy estimation using q-space trajectory encoding

Microscopic diffusion anisotropy imaging using diffusion-weighted MRI and multidimensional diffusion encoding is a promising method for quantifying clinically and scientifically relevant microstructural properties of neural tissue. Several methods for estimating microscopic fractional anisotropy (µFA), a normalized measure of microscopic diffusion anisotropy, have been introduced but the differences between the methods have received little attention thus far. In this study, the accuracy and precision of µFA estimation using q-space trajectory encoding and different signal models were assessed using imaging experiments and simulations. Three healthy volunteers and a microfibre phantom were imaged with five non-zero b-values and gradient waveforms encoding linear and spherical b-tensors. Since the ground-truth µFA was unknown in the imaging experiments, Monte Carlo random walk simulations were performed using axon-mimicking fibres for which the ground truth was known. Furthermore, parameter bias due to time-dependent diffusion was quantified by repeating the simulations with tuned waveforms, which have similar power spectra, and with triple diffusion encoding, which, unlike q-space trajectory encoding, is not based on the assumption of time-independent diffusion. The truncated cumulant expansion of the powder-averaged signal, gamma-distributed diffusivities assumption, and q-space trajectory imaging, a generalization of the truncated cumulant expansion to individual signals, were used to estimate µFA. The gamma-distributed diffusivities assumption consistently resulted in greater µFA values than the second order cumulant expansion, 0.1 greater when averaged over the whole brain. In the simulations, the generalized cumulant expansion provided the most accurate estimates. Importantly, although time-dependent diffusion caused significant overestimation of µFA using all the studied methods, the simulations suggest that the resulting bias in µFA is less than 0.1 in human white matter.

Evidence for microscopic kurtosis in neural tissue revealed by correlation tensor MRI

PURPOSE

The impact of microscopic diffusional kurtosis (µK), arising from restricted diffusion and/or structural disorder, remains a controversial issue in contemporary diffusion MRI (dMRI). Recently, correlation tensor imaging (CTI) was introduced to disentangle the sources contributing to diffusional kurtosis, without relying on a-priori multi-gaussian component (MGC) or other microstructural assumptions. Here, we investigated µK in in vivo rat brains and assessed its impact on state-of-the-art methods ignoring µK.

THEORY AND METHODS

CTI harnesses double diffusion encoding (DDE) experiments, which were here improved for speed and minimal bias using four different sets of acquisition parameters. The robustness of the improved CTI protocol was assessed via simulations. In vivo CTI acquisitions were performed in healthy rat brains using a 9.4T pre-clinical scanner equipped with a cryogenic coil, and targeted the estimation of µK, anisotropic kurtosis, and isotropic kurtosis.

RESULTS

The improved CTI acquisition scheme substantially reduces scan time and importantly, also minimizes higher-order-term biases, thus enabling robust µK estimation, alongside K_aniso and K_iso metrics. Our CTI experiments revealed positive µK both in white and gray matter of the rat brain in vivo; µK is the dominant kurtosis source in healthy gray matter tissue. The non-negligible µK substantially were found to bias prior MGC analyses of K_iso and K_aniso .

CONCLUSIONS

Correlation Tensor MRI offers a more accurate and robust characterization of kurtosis sources than its predecessors. µK is non-negligible in vivo in healthy white and gray matter tissues and could be an important biomarker for future studies. Our findings thus have both theoretical and practical implications for future dMRI research.

Mapping complex cell morphology in the grey matter with double diffusion encoding MR: A simulation study

This paper investigates the impact of cell body (namely soma) size and branching of cellular projections on diffusion MR imaging (dMRI) and spectroscopy (dMRS) signals for both standard single diffusion encoding (SDE) and more advanced double diffusion encoding (DDE) measurements using numerical simulations. The aim is to investigate the ability of dMRI/dMRS to characterize the complex morphology of brain cells focusing on these two distinctive features of brain grey matter. To this end, we employ a recently developed computational framework to create three dimensional meshes of neuron-like structures for Monte Carlo simulations, using diffusion coefficients typical of water and brain metabolites. Modelling the cellular structure as realistically connected spherical soma and cylindrical cellular projections, we cover a wide range of combinations of sphere radii and branching order of cellular projections, characteristic of various grey matter cells. We assess the impact of spherical soma size and branching order on the b-value dependence of the SDE signal as well as the time dependence of the mean diffusivity (MD) and mean kurtosis (MK). Moreover, we also assess the impact of spherical soma size and branching order on the angular modulation of DDE signal at different mixing times, together with the mixing time dependence of the apparent microscopic anisotropy (μA), a promising contrast derived from DDE measurements. The SDE results show that spherical soma size has a measurable impact on both the b-value dependence of the SDE signal and the MD and MK diffusion time dependence for both water and metabolites. On the other hand, we show that branching order has little impact on either, especially for water. In contrast, the DDE results show that spherical soma size has a measurable impact on the DDE signal's angular modulation at short mixing times and the branching order of cellular projections significantly impacts the mixing time dependence of the DDE signal's angular modulation as well as of the derived μA, for both water and metabolites. Our results confirm that SDE based techniques may be sensitive to spherical soma size, and most importantly, show for the first time that DDE measurements may be more sensitive to the dendritic tree complexity (as parametrized by the branching order of cellular projections), paving the way for new ways of characterizing grey matter morphology, non-invasively using dMRS and potentially dMRI.

Diffusion MRI tractography for neurosurgery: the basics, current state, technical reliability and challenges

Diffusion magnetic resonance imaging (dMRI) tractography is currently the only imaging technique that allows for non-invasive delineation and visualisation of white matter (WM) tractsin vivo,prompting rapid advances in related fields of brain MRI research in recent years. One of its major clinical applications is for pre-surgical planning and intraoperative image guidance in neurosurgery, where knowledge about the location of WM tracts nearby the surgical target can be helpful to guide surgical resection and optimise post-surgical outcomes. Surgical injuries to these WM tracts can lead to permanent neurological and functional deficits, making the accuracy of tractography reconstructions paramount. The quality of dMRI tractography is influenced by many modifiable factors, ranging from MRI data acquisition through to the post-processing of tractography output, with the potential of error propagation based on decisions made at each and subsequent processing steps. Research over the last 25 years has significantly improved the anatomical accuracy of tractography. An updated review about tractography methodology in the context of neurosurgery is now timely given the thriving research activities in dMRI, to ensure more appropriate applications in the clinical neurosurgical realm. This article aims to review the dMRI physics, and tractography methodologies, highlighting recent advances to provide the key concepts of tractography-informed neurosurgery, with a focus on the general considerations, the current state of practice, technical challenges, potential advances, and future demands to this field.

Recent Advances in Parameter Inference for Diffusion MRI Signal Models

In this paper, fundamentals and recent progress for obtaining biological features quantitatively by using diffusion MRI are reviewed. First, a brief description of diffusion MRI history, application, and development was presented. Then, well-known parametric models including diffusion tensor imaging (DTI), diffusional kurtosis imaging (DKI), and neurite orientation dispersion diffusion imaging (NODDI) are introduced with several classifications in various viewpoints with other modeling schemes. In addition, this review covers mathematical generalization and examples of methodologies for the model parameter inference from conventional fitting to recent machine learning approaches, which is called Q-space learning (QSL). Finally, future perspectives on diffusion MRI parameter inference are discussed with the aspects of imaging modeling and simulation.

Apparent exchange rate imaging: On its applicability and the connection to the real exchange rate

PURPOSE

Water exchange between the intracellular and extracellular space can be measured using apparent exchange rate (AXR) imaging. The aim of this study was to investigate the relationship between the measured AXR and the geometry of diffusion restrictions, membrane permeability, and the real exchange rate, as well as to explore the applicability of AXR for typical human measurement settings.

METHODS

The AXR measurements and the underlying exchange rates were simulated using the Monte Carlo method with different geometries, size distributions, packing densities, and a broad range of membrane permeabilities. Furthermore, the influence of SNR and sequence parameters was analyzed.

RESULTS

The estimated AXR values correspond to the simulated values and show the expected proportionality to membrane permeability, except for fast exchange (ie, AXR > 20 - 30 s - 1 ) and small packing densities. Moreover, it was found that the duration of the filter gradient must be shorter than 2 · AX R - 1 . In cell size and permeability distributions, AXR depends on the average surface-to-volume ratio, permeability, and the packing density. Finally, AXR can be reliably determined in the presence of orientation dispersion in axon-like structures with sufficient gradient sampling (ie, 30 gradient directions).

CONCLUSION

Currently used experimental settings for in vivo human measurements are well suited for determining AXR, with the exception of single-voxel analysis, due to limited SNR. The detection of changes in membrane permeability in diseased tissue is nonetheless challenging because of the AXR dependence on further factors, such as packing density and geometry, which cannot be disentangled without further knowledge of the underlying cell structure.

DeepACSON automated segmentation of white matter in 3D electron microscopy

Tracing the entirety of ultrastructures in large three-dimensional electron microscopy (3D-EM) images of the brain tissue requires automated segmentation techniques. Current segmentation techniques use deep convolutional neural networks (DCNNs) and rely on high-contrast cellular membranes and high-resolution EM volumes. On the other hand, segmenting low-resolution, large EM volumes requires methods to account for severe membrane discontinuities inescapable. Therefore, we developed DeepACSON, which performs DCNN-based semantic segmentation and shape-decomposition-based instance segmentation. DeepACSON instance segmentation uses the tubularity of myelinated axons and decomposes under-segmented myelinated axons into their constituent axons. We applied DeepACSON to ten EM volumes of rats after sham-operation or traumatic brain injury, segmenting hundreds of thousands of long-span myelinated axons, thousands of cell nuclei, and millions of mitochondria with excellent evaluation scores. DeepACSON quantified the morphology and spatial aspects of white matter ultrastructures, capturing nanoscopic morphological alterations five months after the injury.

A simple estimate of axon size with diffusion MRI

Noninvasive estimation of mean axon diameter presents a new opportunity to explore white matter plasticity, development, and pathology. Several diffusion-weighted MRI (DW-MRI) methods have been proposed to measure the average axon diameter in white matter, but they typically require many diffusion encoding measurements and complicated mathematical models to fit the signal to multiple tissue compartments, including intra- and extra-axonal spaces. Here, Monte Carlo simulations uncovered a straightforward DW-MRI metric of axon diameter: the change in radial apparent diffusion coefficient estimated at different effective diffusion times, ΔD_⊥. Simulations indicated that this metric increases monotonically within a relevant range of effective mean axon diameter while being insensitive to changes in extra-axonal volume fraction, axon diameter distribution, g-ratio, and influence of myelin water. Also, a monotonic relationship was found to exist for signals coming from both intra- and extra-axonal compartments. The slope in ΔD_⊥ with effective axon diameter increased with the difference in diffusion time of both oscillating and pulsed gradient diffusion sequences.

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.

Diffusion MRI simulation of realistic neurons with SpinDoctor and the Neuron Module

The diffusion MRI signal arising from neurons can be numerically simulated by solving the Bloch-Torrey partial differential equation. In this paper we present the Neuron Module that we implemented within the Matlab-based diffusion MRI simulation toolbox SpinDoctor. SpinDoctor uses finite element discretization and adaptive time integration to solve the Bloch-Torrey partial differential equation for general diffusion-encoding sequences, at multiple b-values and in multiple diffusion directions. In order to facilitate the diffusion MRI simulation of realistic neurons by the research community, we constructed finite element meshes for a group of 36 pyramidal neurons and a group of 29 spindle neurons whose morphological descriptions were found in the publicly available neuron repository NeuroMorpho.Org. These finite elements meshes range from having 15,163 nodes to 622,553 nodes. We also broke the neurons into the soma and dendrite branches and created finite elements meshes for these cell components. Through the Neuron Module, these neuron and cell components finite element meshes can be seamlessly coupled with the functionalities of SpinDoctor to provide the diffusion MRI signal attributable to spins inside neurons. We make these meshes and the source code of the Neuron Module available to the public as an open-source package. To illustrate some potential uses of the Neuron Module, we show numerical examples of the simulated diffusion MRI signals in multiple diffusion directions from whole neurons as well as from the soma and dendrite branches, and include a comparison of the high b-value behavior between dendrite branches and whole neurons. In addition, we demonstrate that the neuron meshes can be used to perform Monte-Carlo diffusion MRI simulations as well. We show that at equivalent accuracy, if only one gradient direction needs to be simulated, SpinDoctor is faster than a GPU implementation of Monte-Carlo, but if many gradient directions need to be simulated, there is a break-even point when the GPU implementation of Monte-Carlo becomes faster than SpinDoctor. Furthermore, we numerically compute the eigenfunctions and the eigenvalues of the Bloch-Torrey and the Laplace operators on the neuron geometries using a finite elements discretization, in order to give guidance in the choice of the space and time discretization parameters for both finite elements and Monte-Carlo approaches. Finally, we perform a statistical study on the set of 65 neurons to test some candidate biomakers that can potentially indicate the soma size. This preliminary study exemplifies the possible research that can be conducted using the Neuron Module.

Double diffusion encoding and applications for biomedical imaging

Diffusion Magnetic Resonance Imaging (dMRI) is one of the most important contemporary non-invasive modalities for probing tissue structure at the microscopic scale. The majority of dMRI techniques employ standard single diffusion encoding (SDE) measurements, covering different sequence parameter ranges depending on the complexity of the method. Although many signal representations and biophysical models have been proposed for SDE data, they are intrinsically limited by a lack of specificity. Advanced dMRI methods have been proposed to provide additional microstructural information beyond what can be inferred from SDE. These enhanced contrasts can play important roles in characterizing biological tissues, for instance upon diseases (e.g. neurodegenerative, cancer, stroke), aging, learning, and development. In this review we focus on double diffusion encoding (DDE), which stands out among other advanced acquisitions for its versatility, ability to probe more specific diffusion correlations, and feasibility for preclinical and clinical applications. Various DDE methodologies have been employed to probe compartment sizes (Section 3), decouple the effects of microscopic diffusion anisotropy from orientation dispersion (Section 4), probe displacement correlations, study exchange, or suppress fast diffusing compartments (Section 6). DDE measurements can also be used to improve the robustness of biophysical models (Section 5) and study intra-cellular diffusion via magnetic resonance spectroscopy of metabolites (Section 7). This review discusses all these topics as well as important practical aspects related to the implementation and contrast in preclinical and clinical settings (Section 9) and aims to provide the readers a guide for deciding on the right DDE acquisition for their specific application.

Challenges for biophysical modeling of microstructure

The biophysical modeling efforts in diffusion MRI have grown considerably over the past 25 years. In this review, we dwell on the various challenges along the journey of bringing a biophysical model from initial design to clinical implementation, identifying both hurdles that have been already overcome and outstanding issues. First, we describe the critical initial task of selecting which features of tissue microstructure can be estimated using a model and which acquisition protocol needs to be implemented to make the estimation possible. The model performance should necessarily be tested in realistic numerical simulations and in experimental data - adapting the fitting strategy accordingly, and parameter estimates should be validated against complementary techniques, when/if available. Secondly, the model performance and validity should be explored in pathological conditions, and, if appropriate, dedicated models for pathology should be developed. We build on examples from tumors, ischemia and demyelinating diseases. We then discuss the challenges associated with clinical translation and added value. Finally, we single out four major unresolved challenges that are related to: the availability of a microstructural ground truth, the validation of model parameters which cannot be accessed with complementary techniques, the development of a generalized standard model for any brain region and pathology, and the seamless communication between different parties involved in the development and application of biophysical models of diffusion.

ConFiG: Contextual Fibre Growth to generate realistic axonal packing for diffusion MRI simulation

This paper presents Contextual Fibre Growth (ConFiG), an approach to generate white matter numerical phantoms by mimicking natural fibre genesis. ConFiG grows fibres one-by-one, following simple rules motivated by real axonal guidance mechanisms. These simple rules enable ConFiG to generate phantoms with tuneable microstructural features by growing fibres while attempting to meet morphological targets such as user-specified density and orientation distribution. We compare ConFiG to the state-of-the-art approach based on packing fibres together by generating phantoms in a range of fibre configurations including crossing fibre bundles and orientation dispersion. Results demonstrate that ConFiG produces phantoms with up to 20% higher densities than the state-of-the-art, particularly in complex configurations with crossing fibres. We additionally show that the microstructural morphology of ConFiG phantoms is comparable to real tissue, producing diameter and orientation distributions close to electron microscopy estimates from real tissue as well as capturing complex fibre cross sections. Signals simulated from ConFiG phantoms match real diffusion MRI data well, showing that ConFiG phantoms can be used to generate realistic diffusion MRI data. This demonstrates the feasibility of ConFiG to generate realistic synthetic diffusion MRI data for developing and validating microstructure modelling approaches.

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We present ConFiG, a biologically motivated numerical phantom generator for white matter.

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ConFiG produces phantoms with state-of-the-art density and realistic microstructure.

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Diffusion MRI simulations in ConFiG phantoms are comparable to real dMRI signals.

SANDI: A compartment-based model for non-invasive apparent soma and neurite imaging by diffusion MRI

This work introduces a compartment-based model for apparent cell body (namely soma) and neurite density imaging (SANDI) using non-invasive diffusion-weighted MRI (DW-MRI). The existing conjecture in brain microstructure imaging through DW-MRI presents water diffusion in white (WM) and gray (GM) matter as restricted diffusion in neurites, modelled by infinite cylinders of null radius embedded in the hindered extra-neurite water. The extra-neurite pool in WM corresponds to water in the extra-axonal space, but in GM it combines water in the extra-cellular space with water in soma. While several studies showed that this microstructure model successfully describe DW-MRI data in WM and GM at b ​≤ ​3,000 ​s/mm² (or 3 ​ms/μm²), it has been also shown to fail in GM at high b values (b≫3,000 ​s/mm² or 3 ​ms/μm²). Here we hypothesise that the unmodelled soma compartment (i.e. cell body of any brain cell type: from neuroglia to neurons) may be responsible for this failure and propose SANDI as a new model of brain microstructure where soma of any brain cell type is explicitly included. We assess the effects of size and density of soma on the direction-averaged DW-MRI signal at high b values and the regime of validity of the model using numerical simulations and comparison with experimental data from mouse (b_max ​= ​40,000 ​s/mm², or 40 ​ms/μm²) and human (b_max ​= ​10,000 ​s/mm², or 10 ​ms/μm²) brain. We show that SANDI defines new contrasts representing complementary information on the brain cyto- and myelo-architecture. Indeed, we show maps from 25 healthy human subjects of MR soma and neurite signal fractions, that remarkably mirror contrasts of histological images of brain cyto- and myelo-architecture. Although still under validation, SANDI might provide new insight into tissue architecture by introducing a new set of biomarkers of potential great value for biomedical applications and pure neuroscience.

Revisiting double diffusion encoding MRS in the mouse brain at 11.7T: Which microstructural features are we sensitive to?

Brain metabolites, such as N-acetylaspartate or myo-inositol, are constantly probing their local cellular environment under the effect of diffusion. Diffusion-weighted NMR spectroscopy therefore presents unparalleled potential to yield cell-type specific microstructural information. Double diffusion encoding (DDE) consists in applying two diffusion blocks, where gradient's direction in the second block is varied during the course of the experiment. Unlike single diffusion encoding, DDE measurements at long mixing time display some angular modulation of the signal amplitude which reflects microscopic anisotropy (μA), while requiring relatively low gradient strength. This angular dependence has been formerly used to quantify cell fiber diameter using a model of isotropically oriented infinite cylinders. However, how additional features of the cell microstructure (such as cell body diameter, fiber length and branching) may also influence the DDE signal has been little explored. Here, we used a cryoprobe as well as state-of-the-art post-processing to perform DDE acquisitions with high accuracy and precision in the mouse brain at 11.7 ​T. We then compared our results to simulated DDE datasets obtained in various 3D cell models in order to pinpoint which features of cell morphology may influence the most the angular dependence of the DDE signal. While the infinite cylinder model poorly fits our experimental data, we show that incorporating branched fiber structure in our model allows more realistic interpretation of the DDE signal. Lastly, data acquired in the short mixing time regime suggest that some sensitivity to cell body diameter might be retrieved, although additional experiments would be required to further support this statement.

The dot-compartment revealed? Diffusion MRI with ultra-strong gradients and spherical tensor encoding in the living human brain

The so-called “dot-compartment” is conjectured in diffusion MRI to represent small spherical spaces, such as cell bodies, in which the diffusion is restricted in all directions. Previous investigations inferred its existence from data acquired with directional diffusion encoding which does not permit a straightforward separation of signals from ‘sticks’ (axons) and signals from ‘dots’. Here we combine isotropic diffusion encoding with ultra-strong diffusion gradients (240 ​mT/m) to achieve high diffusion-weightings with high signal to noise ratio, while suppressing signal arising from anisotropic water compartments with significant mobility along at least one axis (e.g., axons). A dot-compartment, defined to have apparent diffusion coefficient equal to zero and no exchange, would result in a non-decaying signal at very high b-values (b≳7000s/mm2). With this unique experimental setup, a residual yet slowly decaying signal above the noise floor for b-values as high as 15000s/mm2 was seen clearly in the cerebellar grey matter (GM), and in several white matter (WM) regions to some extent. Upper limits of the dot-signal-fraction were estimated to be 1.8% in cerebellar GM and 0.5% in WM. By relaxing the assumption of zero diffusivity, the signal at high b-values in cerebellar GM could be represented more accurately by an isotropic water pool with a low apparent diffusivity of 0.12 μm2/ms and a substantial signal fraction of 9.7%. The T2 of this component was estimated to be around 61ms. This remaining signal at high b-values has potential to serve as a novel and simple marker for isotropically-restricted water compartments in cerebellar GM.

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The “dot-compartment” is conjectured in diffusion MRI to represent e.g. cell bodies.

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We combine isotropic encoding with ultra-strong gradients to study the dot-compartment.

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A slowly decaying signal for high b-values was seen in cerebellar GM.

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An apparent diffusivity of 0.12 and signal fraction of 9.7% were estimated.

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The signal could serve as a novel and simple marker for spherical compartments.

Monte Carlo Simulations of Water Exchange Through Myelin Wraps: Implications for Diffusion MRI

Diffusion magnetic resonance imaging (dMRI) yields parameters sensitive to brain tissue microstructure. A structurally important aspect of this microstructure is the myelin wrapping around the axons. This paper investigated the forward problem concerning whether water exchange via the spiraling structure of the myelin can meaningfully contribute to the signal in dMRI. Monte Carlo simulations were performed in a system with intra-axonal, myelin, and extra-axonal compartments. Diffusion in the myelin was simulated as a spiral wrapping the axon, with a custom number of wraps. Exchange (or intra-axonal residence) times were analyzed for various number of wraps and axon diameters. Pulsed gradient sequences were employed to simulate the dMRI signal, which was analyzed using different methods. Diffusional kurtosis imaging analysis yielded the radial diffusivity (RD) and radial kurtosis (RK), while the two-compartment Kärger model yielded estimates the intra-axonal volume fraction ( ν _ic ) and exchange time ( τ ). Results showed that τ was on the sub-second level for geometries with axon diameters below 1.0 μ m and less than eight wraps. Otherwise, exchange was negligible compared to typical experimental durations, with τ of seconds or longer. In situations where exchange influenced the signal, estimates of RK and ν _ic increased with the number of wraps, while RD decreased. τ estimates from simulated signals were in agreement with predicted ones. In conclusion, exchange through spiraling myelin permits sub-second τ for small diameters and low number of wraps. Such conditions may arise in the developing brain or in neurodegenerative disease, and thus the results could aid the interpretation of dMRI studies.

Automated 3D Axonal Morphometry of White Matter

Axonal structure underlies white matter functionality and plays a major role in brain connectivity. The current literature on the axonal structure is based on the analysis of two-dimensional (2D) cross-sections, which, as we demonstrate, is precarious. To be able to quantify three-dimensional (3D) axonal morphology, we developed a novel pipeline, called ACSON (AutomatiC 3D Segmentation and morphometry Of axoNs), for automated 3D segmentation and morphometric analysis of the white matter ultrastructure. The automated pipeline eliminates the need for time-consuming manual segmentation of 3D datasets. ACSON segments myelin, myelinated and unmyelinated axons, mitochondria, cells and vacuoles, and analyzes the morphology of myelinated axons. We applied the pipeline to serial block-face scanning electron microscopy images of the corpus callosum of sham-operated (n = 2) and brain injured (n = 3) rats 5 months after the injury. The 3D morphometry showed that cross-sections of myelinated axons were elliptic rather than circular, and their diameter varied substantially along their longitudinal axis. It also showed a significant reduction in the myelinated axon diameter of the ipsilateral corpus callosum of rats 5 months after brain injury, indicating ongoing axonal alterations even at this chronic time-point.

Challenges in diffusion MRI tractography - Lessons learned from international benchmark competitions

Diffusion MRI (dMRI) fiber tractography has become a pillar of the neuroimaging community due to its ability to noninvasively map the structural connectivity of the brain. Despite widespread use in clinical and research domains, these methods suffer from several potential drawbacks or limitations. Thus, validating the accuracy and reproducibility of techniques is critical for sound scientific conclusions and effective clinical outcomes. Towards this end, a number of international benchmark competitions, or "challenges", has been organized by the diffusion MRI community in order to investigate the reliability of the tractography process by providing a platform to compare algorithms and results in a fair manner, and evaluate common and emerging algorithms in an effort to advance the state of the field. In this paper, we summarize the lessons from a decade of challenges in tractography, and give perspective on the past, present, and future "challenges" that the field of diffusion tractography faces.