Parameters estimation from the diffusion MRI signal using a macroscopic model

Diffusion magnetic resonance imaging (dMRI) probes the diffusion characteristics of a sample via the application of magnetic field gradient pulses. The dMRI signal from a heterogeneous sample includes the water proton magnetization from all spatial positions in a voxel. If the voxel consists of different diffusion compartments with weak exchange, while the duration of the diffusion-encoding gradient pulses is short compared to the diffusion time (the narrow pulse approximation), the dMRI signal can be approximated by the Karger model. A new macroscopic ODE model for the dMRI signal was recently derived mathematically from the microscopic multiple compartments Bloch-Torrey partial differential equation (PDE) without the narrow pulse restriction. We illustrate by numerical simulations that this ODE model accurately approximates the dMRI signal in a domain containing spherical cells of various sizes, and show preliminary results on solving the inverse problem to estimate the cellular volume fraction and surface area.