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  • Open Access
  • © 2022

Mathematical Modeling of the Human Brain

From Magnetic Resonance Images to Finite Element Simulation

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  • This book is open access, which means that you have free and unlimited access.

  • Includes a step-by-step guide to constructing anatomical finite element brain meshes

Part of the book series: Simula SpringerBriefs on Computing (SBRIEFSC, volume 10)

Buying options

Softcover Book
USD 37.99
Price excludes VAT (USA)

Table of contents (7 chapters)

  1. Front Matter

    Pages i-xvi
  2. Introduction

    • Kent-André Mardal, Marie E. Rognes, Travis B. Thompson, Lars Magnus Valnes
    Pages 1-6Open Access
  3. Working with magnetic resonance images of the brain

    • Kent-André Mardal, Marie E. Rognes, Travis B. Thompson, Lars Magnus Valnes
    Pages 7-21Open Access
  4. Getting started: from T1 images to simulation

    • Kent-André Mardal, Marie E. Rognes, Travis B. Thompson, Lars Magnus Valnes
    Pages 23-46Open Access
  5. Introducing Heterogeneities

    • Kent-André Mardal, Marie E. Rognes, Travis B. Thompson, Lars Magnus Valnes
    Pages 47-80Open Access
  6. Introducing Directionality with Diffusion Tensors

    • Kent-André Mardal, Marie E. Rognes, Travis B. Thompson, Lars Magnus Valnes
    Pages 81-96Open Access
  7. Simulating Anisotropic Diffusion in Heterogeneous Brain Regions

    • Kent-André Mardal, Marie E. Rognes, Travis B. Thompson, Lars Magnus Valnes
    Pages 97-107Open Access
  8. Concluding Remarks and Outlook

    • Kent-André Mardal, Marie E. Rognes, Travis B. Thompson, Lars Magnus Valnes
    Pages 109-110Open Access
  9. Back Matter

    Pages 111-118

About this book

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

  • Open Access
  • magnetic resonance imaging
  • Mesh generation
  • mathematical modeling
  • finite element methods
  • scientific computing

Authors and Affiliations

  • Department of Mathematics, University of Oslo, Lysaker, Norway

    Kent-André Mardal

  • Biocomp CBC 1-2118, Simula Research Laboratory, Fornebu, Norway

    Marie E. Rognes

  • Mathematical Institute, Oxford University, Oxford, UK

    Travis B. Thompson

  • Rikshospitalet, Oslo University Hospital, Oslo, Norway

    Lars Magnus Valnes

Bibliographic Information

Buying options

Softcover Book
USD 37.99
Price excludes VAT (USA)