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Mathematical Modeling of the Human Brain

From Magnetic Resonance Images to Finite Element Simulation

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  • Open Access
  • © 2022

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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)

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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.

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Table of contents (7 chapters)


“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)

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

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