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A bloch-Torrey Equation for Diffusion in a Deforming Media

Prolate Coordinates


Damien Rohmer and Grant T. Gullberg
A bloch-Torrey Equation for Diffusion in a Deforming Media.
Lawrence Berkeley National Laboratory, Report LBNL-61295, 2006
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The Diffusion Tensor Magnetic Resonance Imaging (DTMRI) technique enables the measurement of diffusion parameters and therefore provides information on the structure of the biological tissue. This technique has been applied with success to static organs such as the brain. However, diffusion measurement of dynamically deformable organs such as the in-vivo heart remains a complex problem, which holds great potential in determining cardiac health. In order to understand the behavior of the magnetic resonance (MR) signal in a deforming media, the Bloch-Torrey equation that defines the MR behavior is expressed in general curvilinear coordinates. These coordinates enable us to follow the heart geometry and deformations through time. The equation is finally discretized and presented in a numerical formulation using implicit methods in order to derive a stable scheme that can be applied to any smooth deformations.

keywords: MRI, Diffusion, Bloch-Torrey, PDE, Heart, Deforming Media


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