A computational method for the covariance matrix associated with extracellular diffusivity on disordered models of cylindrical brain axons

This study developed a method to approximate the covariance matrix associated with the simulation of water molecular diffusion inside the brain tissue. The computation implements the Discontinuous Galerkin method of the diffusion equation. A physically consistent numerical flux is applied to model t...

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Autores principales:	Daniel Cervantes, Miguel angel Moreles, Joaquin Peña, Alonso Ramirez-Manzanares
Formato:	article
Lenguaje:	EN
Publicado:	AIMS Press 2021
Materias:	extracellular diffusivity covariance matrix numerical flux discontinuous galerkin Biotechnology TP248.13-248.65 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/58e7dc922d6f4e95852a71180f5bde95
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spelling	oai:doaj.org-article:58e7dc922d6f4e95852a71180f5bde952021-11-08T02:55:51ZA computational method for the covariance matrix associated with extracellular diffusivity on disordered models of cylindrical brain axons10.3934/mbe.20212521551-0018https://doaj.org/article/58e7dc922d6f4e95852a71180f5bde952021-06-01T00:00:00Zhttps://www.aimspress.com/article/doi/10.3934/mbe.2021252?viewType=HTMLhttps://doaj.org/toc/1551-0018This study developed a method to approximate the covariance matrix associated with the simulation of water molecular diffusion inside the brain tissue. The computation implements the Discontinuous Galerkin method of the diffusion equation. A physically consistent numerical flux is applied to model the interaction between the axon walls and extracellular regions. This numerical flux yields an efficient GPU-CUDA implementation. We consider the two-dimensional case of high axon pack density, valid, for instance, in the brain's corpus callosum region.Daniel CervantesMiguel angel MorelesJoaquin PeñaAlonso Ramirez-ManzanaresAIMS Pressarticleextracellular diffusivitycovariance matrixnumerical fluxdiscontinuous galerkinBiotechnologyTP248.13-248.65MathematicsQA1-939ENMathematical Biosciences and Engineering, Vol 18, Iss 5, Pp 4961-4970 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	extracellular diffusivity covariance matrix numerical flux discontinuous galerkin Biotechnology TP248.13-248.65 Mathematics QA1-939
spellingShingle	extracellular diffusivity covariance matrix numerical flux discontinuous galerkin Biotechnology TP248.13-248.65 Mathematics QA1-939 Daniel Cervantes Miguel angel Moreles Joaquin Peña Alonso Ramirez-Manzanares A computational method for the covariance matrix associated with extracellular diffusivity on disordered models of cylindrical brain axons
description	This study developed a method to approximate the covariance matrix associated with the simulation of water molecular diffusion inside the brain tissue. The computation implements the Discontinuous Galerkin method of the diffusion equation. A physically consistent numerical flux is applied to model the interaction between the axon walls and extracellular regions. This numerical flux yields an efficient GPU-CUDA implementation. We consider the two-dimensional case of high axon pack density, valid, for instance, in the brain's corpus callosum region.
format	article
author	Daniel Cervantes Miguel angel Moreles Joaquin Peña Alonso Ramirez-Manzanares
author_facet	Daniel Cervantes Miguel angel Moreles Joaquin Peña Alonso Ramirez-Manzanares
author_sort	Daniel Cervantes
title	A computational method for the covariance matrix associated with extracellular diffusivity on disordered models of cylindrical brain axons
title_short	A computational method for the covariance matrix associated with extracellular diffusivity on disordered models of cylindrical brain axons
title_full	A computational method for the covariance matrix associated with extracellular diffusivity on disordered models of cylindrical brain axons
title_fullStr	A computational method for the covariance matrix associated with extracellular diffusivity on disordered models of cylindrical brain axons
title_full_unstemmed	A computational method for the covariance matrix associated with extracellular diffusivity on disordered models of cylindrical brain axons
title_sort	computational method for the covariance matrix associated with extracellular diffusivity on disordered models of cylindrical brain axons
publisher	AIMS Press
publishDate	2021
url	https://doaj.org/article/58e7dc922d6f4e95852a71180f5bde95
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A computational method for the covariance matrix associated with extracellular diffusivity on disordered models of cylindrical brain axons

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