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oapen-20.500.12657-533622022-03-16T02:56:33Z Mathematical Modeling of the Human Brain Mardal, Kent-André Rognes, Marie E. Thompson, Travis B. Valnes, Lars Magnus magnetic resonance imaging Mesh generation mathematical modeling finite element methods scientific computing bic Book Industry Communication::P Mathematics & science::PB Mathematics::PBW Applied mathematics::PBWH Mathematical modelling bic Book Industry Communication::P Mathematics & science::PD Science: general issues::PDE Maths for scientists bic Book Industry Communication::M Medicine::MF Pre-clinical medicine: basic sciences::MFG Physiology bic Book Industry Communication::P Mathematics & science::PB Mathematics::PBK Calculus & mathematical analysis::PBKS Numerical analysis This open access book bridges common tools in medical imaging and neuroscience with the numerical solution of brain modelling PDEs. The connection between these areas is established through the use of two existing tools, FreeSurfer and FEniCS, and one novel tool, the SVM-Tk, developed for this book. The reader will learn the basics of magnetic resonance imaging and quickly proceed to generating their first FEniCS brain meshes from T1-weighted images. The book's presentation concludes with the reader solving a simplified PDE model of gadobutrol diffusion in the brain that incorporates diffusion tensor images, of various resolution, and complex, multi-domain, variable-resolution FEniCS meshes with detailed markings of anatomical brain regions. After completing this book, the reader will have a solid foundation for performing patient-specific finite element simulations of biomechanical models of the human brain. 2022-03-15T07:53:44Z 2022-03-15T07:53:44Z 2022 book ONIX_20220314_9783030951368_61 9783030951368 https://library.oapen.org/handle/20.500.12657/53362 eng Simula SpringerBriefs on Computing application/pdf n/a 978-3-030-95136-8.pdf https://link.springer.com/978-3-030-95136-8 Springer Nature Springer 10.1007/978-3-030-95136-8 10.1007/978-3-030-95136-8 6c6992af-b843-4f46-859c-f6e9998e40d5 2ec6bf1f-cf1b-4684-9be9-36e9eb1b2485 9783030951368 Springer 10 118 Cham [grantnumber unknown] open access
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This open access book bridges common tools in medical imaging and neuroscience with the numerical solution of brain modelling PDEs. The connection between these areas is established through the use of two existing tools, FreeSurfer and FEniCS, and one novel tool, the SVM-Tk, developed for this book. The reader will learn the basics of magnetic resonance imaging and quickly proceed to generating their first FEniCS brain meshes from T1-weighted images. The book's presentation concludes with the reader solving a simplified PDE model of gadobutrol diffusion in the brain that incorporates diffusion tensor images, of various resolution, and complex, multi-domain, variable-resolution FEniCS meshes with detailed markings of anatomical brain regions. After completing this book, the reader will have a solid foundation for performing patient-specific finite element simulations of biomechanical models of the human brain.
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