Parameters estimation from the diffusion MRI signal using a macroscopic model

2nd International Conference on Mathematical Modeling in Physical Sciences 2013

物理学;数学

Nguyen, H.T.^1 ; Li, J.R.^2 ; Grebenkov, D.S.^3 ; Bihan, D Le^1 ; Poupon, C.^1

Neurospin-CEA Saclay, Gif-sur-Yvette, France^1

INRIA Saclay-Equipe DEFI, CMAP, Ecole Polytechnique, Palaiseau, France^2

LPMC, CNRS-Ecole Polytechnique, Palaiseau, France^3

关键词: Diffusion characteristics;    Diffusion magnetic resonance imaging;    Macroscopic model;    Magnetic field gradient;    Multiple compartments;    Parameters estimation;    Partial differential equations (PDE);    Spatial positions;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/490/1/012117/pdf
DOI  :  10.1088/1742-6596/490/1/012117

来源: IOP

【 摘 要 】

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.