Fourier Representation of the Diffusion MRI Signal Using Layer Potentials

نویسندگان

چکیده

The diffusion magnetic resonance imaging (MRI) signal arising from biological tissues can be numerically simulated by solving the Bloch–Torrey partial differential equation. Numerical simulations facilitate investigation of relationship between MRI signals and cellular structures. With rapid advance available computing power, community has begun to employ numerical for model formulation validation, as well sequence optimization. Existing simulation frameworks use finite difference method, element or Matrix Formalism method solve We propose a new based on efficient evaluation layer potentials. In this paper, mathematical framework implementation are described. demonstrate convergence our via experiments analyze errors linked various parameters. Since provides Fourier-type representation signal, it potentially physical interpretations in future.

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ژورنال

عنوان ژورنال: Siam Journal on Applied Mathematics

سال: 2023

ISSN: ['0036-1399', '1095-712X']

DOI: https://doi.org/10.1137/21m1439572