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An image‐based finite difference model for simulating restricted diffusion
Author(s) -
Hwang Scott N.,
Chin ChihLiang,
Wehrli Felix W.,
Hackney David B.
Publication year - 2003
Publication title -
magnetic resonance in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.696
H-Index - 225
eISSN - 1522-2594
pISSN - 0740-3194
DOI - 10.1002/mrm.10536
Subject(s) - ellipsoid , diffusion , monte carlo method , computation , current (fluid) , diffusion mri , work (physics) , anisotropy , finite difference method , diffusion equation , biological system , computer science , physics , algorithm , mathematical analysis , mathematics , optics , magnetic resonance imaging , medicine , statistics , economy , radiology , astronomy , biology , economics , thermodynamics , service (business)
Water diffusion in tissues is generally restricted and often anisotropic. Neural tissue is of particular interest, since it is well known that injury alters diffusion in a characteristic manner. Both Monte Carlo simulations and approximate analytical models have previously been reported in attempts to predict water diffusion behavior in the central nervous system. These methods have relied on axonal models, which assume simple geometries (e.g., ellipsoids, cylinders, and square prisms) and ignore the thickness of the myelin sheath. The current work describes a method for generating models using synthetic images. The computations are based on a 3D finite difference (FD) approximation of the diffusion equation. The method was validated with known analytic solutions for diffusion in a cylindrical pore and in a hexagonal array of cylinders. Therefore, it is envisioned that, by exploiting histologic images of neuronal tissues as input model, current method allows investigating the water diffusion behavior inside biological tissues and potentially assessing the status of neural injury and regeneration. Magn Reson Med 50:373–382, 2003. © 2003 Wiley‐Liss, Inc.