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We develop a general analytical and numerical framework for estimating intra- and extra-neurite water fractions and diffusion coefficients, as well as neurite orientational dispersion, in each imaging voxel. By employing a set of rotational…

The problem of surface effects at a fluid/force field boundary is investigated. A classical simple fluid with a locally introduced field simulating a solid is considered. For the case of a hard-core field, rigid, exponential, realistic, and…

Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a…

We present DeepTract, a deep-learning framework for estimating white matter fibers orientation and streamline tractography. We adopt a data-driven approach for fiber reconstruction from diffusion weighted images (DWI), which does not assume…

Diffusion models have emerged as powerful generative models, inspiring extensive research into their underlying mechanisms. One of the key questions in this area is the loss functions these models shall train with. Multiple formulations…

Cortical thickness measurements from magnetic resonance imaging, an important biomarker in many neurodegenerative and neurological disorders, are derived by many tools from an initial voxel-wise tissue segmentation. White matter (WM)…

In the analysis of binary longitudinal data, it is of interest to model a dynamic relationship between a response and covariates as a function of time, while also investigating similar patterns of time-dependent interactions. We present a…

Many theoretical and experimental results show that solute transport in heterogeneous porous media exhibits multi-scaling behaviors. To describe such non-Fickian diffusions, this work provides a distributed order Hausdorff diffusion model…

Most brain disorders are very heterogeneous in terms of their underlying biology and developing analysis methods to model such heterogeneity is a major challenge. A promising approach is to use probabilistic regression methods to estimate…

The lack of analytical models describing diffusion time dependence at intermediate time scales in complex tissue microstructure limits the accurate quantification of extracellular diffusivity and tissue microstructure. We introduce TRACED,…

Diffusion MRI (dMRI) streamline tractography, the gold standard for in vivo estimation of brain white matter (WM) pathways, has long been considered indicative of macroscopic relationships with WM microstructure. However, recent advances in…

We perform the linear stability analysis for a new model for poromechanical processes with inertia (formulated in mixed form using the solid deformation, fluid pressure, and total pressure) interacting with diffusing and reacting solutes…

Diffusion magnetic resonance imaging (dMRI) tractography is an advanced imaging technique that enables in vivo mapping of the brain's white matter connections at macro scale. Over the last two decades, the study of brain connectivity using…

In the high-dimensional landscape, addressing the challenges of covariance regression with high-dimensional covariates has posed difficulties for conventional methodologies. This paper addresses these hurdles by presenting a novel approach…

Purpose: To propose a deep learning-based reconstruction framework for ultrafast and robust diffusion tensor imaging and fiber tractography. Methods: We propose SuperDTI to learn the nonlinear relationship between diffusion-weighted images…

Tractography traces the peak directions extracted from fiber orientation distribution (FOD) suffering from ambiguous spatial correspondences between diffusion directions and fiber geometry, which is prone to producing erroneous tracks while…

Measuring fibre dispersion in white matter with diffusion magnetic resonance imaging (MRI) is limited by an inherent degeneracy between fibre dispersion and microscopic diffusion anisotropy (i.e., the diffusion anisotropy expected for a…

Background and Objective: This proof of concept study investigates mathematical modelling of blood flow and oxygen transport in cerebral microcirculation, focusing on understanding hemodynamic responses. By coupling oxygen transport models…

Lateral diffusion of molecules on surfaces plays a very important role in various biological processes, including lipid transport across the cell membrane, synaptic transmission and other phenomena such as exo- and endocytosis, signal…

Human brain maturation is characterized by the prolonged development of structural and functional properties of large-scale networks that extends into adulthood. However, it is not clearly understood which features change and which remain…