Mathematical Modeling of the Human Brain: From Magnetic Resonance Images to Finite Element Simulation

ISBN-13: 9783030951351 / Angielski / Miękka / 2022 / 136 str.

Kent-André Mardal;Marie E. Rognes;Travis B. Thompson

Opis

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.

Recenzje

"The book represents an excellent introduction and hands-on guide to this important and exciting field, for applied mathematicians and image processing practitioners ... . It is, perhaps, most beneficial, to electrical and computer science majors who wish to rapidly immerse themselves in the field, in a manner that is mathematically correct and sound, yet also practical." (Emil Saucan, zbMATH 1501.92001, 2023)

Spis treści

Introduction.- Working with magnetic resonance images of the brain.- From T1 images to numerical simulation.- Introducing heterogeneities.- Introducing directionality with diffusion tensors.- Simulating anisotropic diffusion in heterogeneous brain regions.- Concluding remarks and outlook.- References.- Index.