Academic Journal
A second order asymptotic model for diffusion MRI in permeable media
| Title: | A second order asymptotic model for diffusion MRI in permeable media |
|---|---|
| Authors: | Marwa Kchaou, Jing-Rebecca Li |
| Contributors: | Sciences, EDP |
| Source: | ESAIM: Mathematical Modelling and Numerical Analysis. 57:1953-1980 |
| Publisher Information: | EDP Sciences, 2023. |
| Publication Year: | 2023 |
| Subject Terms: | Radiology, Nuclear Medicine and Imaging, Finite element method, Inverse Problems in Mathematical Physics and Imaging, Permeability (electromagnetism), Asymptotic analysis, Structural engineering, higher-order diffusion tensor, [MATH] Mathematics [math], Mechanics, 01 natural sciences, Mathematical analysis, Biochemistry, Diffusion MRI, diffusion MRI, Diffusion, 03 medical and health sciences, 0302 clinical medicine, Differential equation, Engineering, Health Sciences, FOS: Mathematics, Multiscale Methods for Heterogeneous Systems, Homogenization (climate), 0101 mathematics, Anisotropic Water Diffusion, Biology, Mathematical Physics, Homogenization, Ecology, Physics, Membrane, Partial differential equation, Biodiversity, Asymptotic homogenization, Upscaling Techniques, Transverse plane, Chemistry, Diffusion Magnetic Resonance Imaging, Computational Theory and Mathematics, Bloch–Torrey equation, FOS: Biological sciences, Computer Science, Physical Sciences, Medicine, Thermodynamics, Multiscale Methods, Mathematics, Ordinary differential equation |
| Description: | Starting from a reference partial differential equation model of the complex transverse water proton magnetization in a voxel due to diffusion-encoding magnetic field gradient pulses, one can use periodic homogenization theory to establish macroscopic models. A previous work introduced an asymptotic model that accounted for permeable interfaces in the imaging medium. In this paper we formulate a higher order asymptotic model to treat higher values of permeability. We explicitly solved this new asymptotic model to obtain a system of ordinary differential equations that can model the diffusion MRI signal and we present numerical results showing the improved accuracy of the new model in the regime of higher permeability. |
| Document Type: | Article Other literature type |
| File Description: | application/pdf |
| ISSN: | 2804-7214 2822-7840 |
| DOI: | 10.1051/m2an/2023043 |
| DOI: | 10.60692/eqjnw-ekv08 |
| DOI: | 10.60692/02x6s-df486 |
| Rights: | CC BY |
| Accession Number: | edsair.doi.dedup.....80b8b97c54ece9e6f73f2a00cc4af77c |
| Database: | OpenAIRE |
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