Event Abstract Back to Event Diffusion MRI modelling from first principles Magnus Herberthson1, Carl-Fredrik Westin2 and Hans Knutsson3* 1 Linköping University, Department of Mathematics, Sweden 2 Harvard Medical School, Brigham and Women’s Hospital, United States 3 Linköping University, Medical Informatics, Department of Biomedical Engineering. CMIV, Center for Medical Image Science and Visualisation. , Sweden We present a spatially based matrix method for simulation of diffusion under the influence of an external magnetic field. The method is based on first principles, and models the physical process directly rather then referring to a derived PDE such as the Bloch-Torrey equation. By partitioning the compartment into small units, the magnetization is expressed as a vector, and the diffusion process is represented by a matrix so that the time evolution is simulated by repetitive matrix multiplications. The use of first principles means that the construction of the matrices is quick, and that the matrices become sparse. In a sense, we use a trivial spatial basis, so that there is no need for e.g. eigenfunctions to the Laplace equation over the region of interest. This gives a flexible method that allows for general compartment geometries and general gradient sequences. Among the advantages is that Cartesian grids are not needed and the boundary conditions are naturally captured by the formalism. The method is exemplified and validated by comparing with known exact solutions. For validation we solve the Bloch-Torrey equation for simple geometries with a constant (in time) gradient field for a segment (1D) and a disc (2D). In these cases, the solution is expanded in a series of eigenfunction to the spatial part of the Bloch-Torrey equation. This gives a more natural expansion than in Laplace eigenfunctions, in particular the so called edge effect is apparent. We also give more general examples in two and three dimensions. Keywords: Diffusion, MRI, dMRI, multidimensional, diffusion encoding Conference: New dimensions in diffusion encoding, Fjälkinge, Sweden, 11 Jan - 14 Jan, 2016. Presentation Type: Oral presentation Topic: New Dimensions in Diffusion Encoding Citation: Herberthson M, Westin C and Knutsson H (2016). Diffusion MRI modelling from first principles. Front. Phys. Conference Abstract: New dimensions in diffusion encoding. doi: 10.3389/conf.FPHY.2016.01.00021 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 07 Jul 2016; Published Online: 07 Jul 2016. * Correspondence: Prof. Hans Knutsson, Linköping University, Medical Informatics, Department of Biomedical Engineering. CMIV, Center for Medical Image Science and Visualisation., Linköping, 58185, Sweden, knutte@imt.liu.se Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Magnus Herberthson Carl-Fredrik Westin Hans Knutsson Google Magnus Herberthson Carl-Fredrik Westin Hans Knutsson Google Scholar Magnus Herberthson Carl-Fredrik Westin Hans Knutsson PubMed Magnus Herberthson Carl-Fredrik Westin Hans Knutsson Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.
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