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

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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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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Spatiotemporal patterns of cortical microstructural maturation in children and adolescents with diffusion MRI

Neocortical maturation is a dynamic process that proceeds in a hierarchical manner; however, the spatiotemporal organization of cortical microstructure with diffusion MRI has yet to be fully defined. This study characterized cortical microstructural maturation using diffusion MRI (fwe-diffusion tensor imaging [DTI] and neurite orientation dispersion and density imaging [NODDI] multicompartment modeling) in a cohort of 637 children and adolescents between 8 and 21 years of age. We found spatially heterogeneous developmental patterns broadly demarcated into functional domains where NODDI metrics increased, and fwe-DTI metrics decreased with age. By applying nonlinear growth models in a vertex-wise analysis, we observed a general posterior-to-anterior pattern of maturation, where the fwe-DTI measures mean diffusivity and radial diffusivity reached peak maturation earlier than the NODDI metrics neurite density index. Using non-negative matrix factorization, we found occipito-parietal cortical regions that correspond to lower order sensory domains mature earlier than fronto-temporal higher order association domains. Our findings corroborate previous histological and neuroimaging studies that show spatially varying patterns of cortical maturation that may reflect unique developmental processes of cytoarchitectonically determined regional patterns of change.

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.

Spatiotemporal patterns of cortical microstructural maturation in children and adolescents with diffusion MRI

Neocortical maturation is a dynamic process that proceeds in a hierarchical manner; however, the spatiotemporal organization of cortical microstructure with diffusion MRI has yet to be fully defined. This study characterized cortical microstructural maturation using diffusion MRI (fwe-DTI and NODDI multi-compartment modeling) in a cohort of 637 children and adolescents between 8 and 21 years of age. We found spatially heterogeneous developmental patterns broadly demarcated into functional domains where NODDI metrics increased and fwe-DTI metrics decreased with age. Using non-negative matrix factorization, we found cortical regions that correspond to lower-order sensory regions mature earlier than higher-order association regions. Our findings corroborate previous histological and neuroimaging studies that show spatially-varying patterns of cortical maturation that may reflect unique developmental processes of cytoarchitectonically-determined regional patterns of change.

Practical computation of the diffusion MRI signal based on Laplace eigenfunctions: permeable interfaces

The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium such as brain tissue can be modeled by the Bloch-Torrey partial differential equation. The spatial integral of the solution of this equation in realistic geometry provides a gold-standard reference model for the diffusion MRI signal arising from different tissue micro-structures of interest. A closed form representation of this reference diffusion MRI signal, called matrix formalism, which makes explicit the link between the Laplace eigenvalues and eigenfunctions of the tissue geometry and its diffusion MRI signal, was derived 20 years ago. In addition, once the Laplace eigendecomposition has been computed and saved, the diffusion MRI signal can be calculated for arbitrary diffusion-encoding sequences and b-values at negligible additional cost. In a previous publication, we presented a simulation framework that we implemented inside the MATLAB-based diffusion MRI simulator SpinDoctor that efficiently computes the matrix formalism representation for biological cells subject to impermeable membrane boundary conditions. In this work, we extend our simulation framework to include geometries that contain permeable cell membranes. We describe the new computational techniques that allowed this generalization and we analyze the effects of the magnitude of the permeability coefficient on the eigendecomposition of the diffusion and Bloch-Torrey operators. This work is another step in bringing advanced mathematical tools and numerical method development to the simulation and modeling of diffusion MRI.

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

Characterizing neural tissue microstructure is a critical goal for future neuroimaging. Diffusion MRI (dMRI) provides contrasts that reflect diffusing spins’ interactions with myriad microstructural features of biological systems. However, the specificity of dMRI remains limited due to the ambiguity of its signals vis-à-vis the underlying microstructure. To improve specificity, biophysical models of white matter (WM) typically express dMRI signals according to the Standard Model (SM) and have more recently in gray matter (GM) taken spherical compartments into account (the SANDI model) in attempts to represent cell soma. The validity of the assumptions underlying these models, however, remains largely undetermined, especially in GM. To validate these assumptions experimentally, observing their unique, functional properties, such as the b^−1/2 power-law associated with one-dimensional diffusion, has emerged as a fruitful strategy. The absence of this signature in GM, in turn, has been explained by neurite water exchange, non-linear morphology, and/or by obscuring soma signal contributions. Here, we present diffusion simulations in realistic neurons demonstrating that curvature and branching does not destroy the stick power-law behavior in impermeable neurites, but also that their signal is drowned by the soma signal under typical experimental conditions. Nevertheless, by studying the GM dMRI signal's behavior as a function of diffusion weighting as well as time, we identify an attainable experimental regime in which the neurite signal dominates. Furthermore, we find that exchange-driven time dependence produces a signal behavior opposite to that which would be expected from restricted diffusion, thereby providing a functional signature that disambiguates the two effects. We present data from dMRI experiments in ex vivo rat brain at ultrahigh field of 16.4T and observe a time dependence that is consistent with substantial exchange but also with a GM stick power-law. The first finding suggests significant water exchange between neurites and the extracellular space while the second suggests a small sub-population of impermeable neurites. To quantify these observations, we harness the Kärger exchange model and incorporate the corresponding signal time dependence in the SM and SANDI models.

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.