Analytical and numerical study of the apparent diffusion coefficient in diffusion MRI at long diffusion times and low b-values

Jing-Rebecca Li 1 Denis Le Bihan 2 Thong Quoc Nguyen 1 Denis Grebenkov 3 Cyril Poupon 2 Houssem Haddar 1
1 DeFI - Shape reconstruction and identification
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR7641
Abstract : Diffusion magnetic resonance imaging provides a measure of the average distance travelled by water molecules in a medium and can give useful information on cellular structure and structural change when the medium is biological tissue. In this paper, two approximate models for the apparent diffusion coefficient at low b-values and long diffusion times are formulated and validated. The first is a steady-state partial differential equation model that gives the steady-state (infinite time) effective diffusion tensor for general cellular geometries. For nearly isotropic diffusion where the intra-cellular compartment consists of non-elongated cells, a second approximate model is provided in the form of analytical formulae for the eigenvalue of the steady-state effective diffusion tensor. Both models are validated by numerical simulations on a variety of cells sizes and shapes.
Type de document :
Pré-publication, Document de travail
2012
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  • HAL Id : hal-00763885, version 1

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Jing-Rebecca Li, Denis Le Bihan, Thong Quoc Nguyen, Denis Grebenkov, Cyril Poupon, et al.. Analytical and numerical study of the apparent diffusion coefficient in diffusion MRI at long diffusion times and low b-values. 2012. 〈hal-00763885〉

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