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.
Citation: 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[J]. Mathematical Biosciences and Engineering, 2021, 18(5): 4961-4970. doi: 10.3934/mbe.2021252
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.
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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[J]. Mathematical Biosciences and Engineering, 2021, 18(5): 4961-4970. doi: 10.3934/mbe.2021252
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