Mathematical Modeling of the Human Brain by Kent-André Mardal
Mathematical Modeling of the Human Brain - Table of Contents
1. Introduction
2. Working with Magnetic Resonance Images of the Brain
3. Getting Started: from T1 Images to Simulation
4. Introducing Heterogeneities
5. Introducing Directionality with Diffusion Tensors
6. Simulating Anisotropic Diffusion in Heterogeneous Brain Regions
7. Concluding Remarks and Outlook
What You Will Learn in Mathematical Modeling of the Human Brain
The book "Mathematical Modeling of the Human Brain: From Magnetic Resonance Images to Finite Element Simulation" by Kent-André Mardal, Marie E. Rognes, Travis B. Thompson, Lars Magnus Valnes provide a bridge between common tools in medical imaging and neuroscience, and the numerical solution of PDEs that can arise in brain modeling. More specifically, our work focuses on the use of two existing tools, Free Surfer and FEniCS, and one novel tool, the SVM-Tk, developed for this book.
A central, and practical, problem preventing a more widespread interest in the mathematical modeling of the human brain is that of anatomical mesh generation. Generating physiological finite element meshes of the brain is not an easy task. The sulcal and gyral folds of the cortex are intricate, and the extracellular diffusion tensor, dictated largely by axonal white-matter bundles, is an isotropic and tortuous. Nevertheless, such features are essential for even the simplest, patient-specific PDE models of brain structural deformation and fluid dynamics. The ability to accurately capture anatomical features could help us address many human problems, particularly when it comes to under standing the mechanisms underlying neurodegenerative pathology evolution. This book stands at the gateway of these pressing problems.
Book Details & Specifications
Title:
Mathematical Modeling of the Human Brain by Kent-André Mardal
Publisher:
Springer
Year:
2022
Pages:
136
Type:
PDF
Language:
English
ISBN-10 #:
3030951359
ISBN-13 #:
978-3030951351
License:
CC BY 4.0
Amazon:
Amazon
About the Author: Kent-André Mardal
The author
Kent-André Mardal
is Professor of Mathematics at Department of Mathematics, University of Oslo, Oslo, Norway Travis B. Thompson, Mathematical Institute, University of Oxford, Oxford, UK
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