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Mathematical Modeling of the Human Brain
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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.
This book is included in DOAB.
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Keywords
- applied mathematics
- Calculus & mathematical analysis
- finite element methods
- Magnetic Resonance Imaging
- mathematical modeling
- mathematical modelling
- Mathematics
- Mathematics & science
- Maths for scientists
- medicine
- mesh generation
- Numerical analysis
- Physiology
- Pre-clinical medicine: basic sciences
- Science: general issues
- scientific computing
- thema EDItEUR::M Medicine and Nursing::MF Pre-clinical medicine: basic sciences::MFG Physiology
- thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKS Numerical analysis
- thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics::PBWH Mathematical modelling
- thema EDItEUR::P Mathematics and Science::PD Science: general issues::PDE Maths for scientists
Links
DOI: 10.1007/978-3-030-95136-8Editions