Mathematical Modeling of the Human Brain
From Magnetic Resonance Images to Finite Element Simulation
Author(s)
Mardal, Kent-André
Rognes, Marie E.
Thompson, Travis B.
Valnes, Lars Magnus
Language
EnglishAbstract
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.
Keywords
magnetic resonance imaging; Mesh generation; mathematical modeling; finite element methods; scientific computingISBN
9783030951368Publisher
Springer NaturePublisher website
http://www.springernature.com/oabooksPublication date and place
Cham, 2022Imprint
SpringerSeries
Simula SpringerBriefs on Computing,Classification
Mathematical modelling
Maths for scientists
Physiology
Numerical analysis