Mathematical Modeling of the Human Brain

This is the 10th volume in the Simula SpringerBriefs series and provides a solid foundation for performing patient-specific finite element simulations of biomechanical models of the human brain.

The Simula SpringerBriefs on Computing aims to provide introductions to select areas of research in computing. Each volume aims to provide an introduction to, and overview over, research fields that can otherwise be inaccessible. This is the 10th volume in this series.

Mathematical Modeling of the Human Brain: From Magnetic Resonance Images to Finite Element Simulation by Kent-André Mardal, Marie E. Rognes, Travis B. Thompson, and Lars Magnus Valnes is now available for download. 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.

Open access

Mathematical Modeling of the Human Brain is now available for download. As with all the Simula SpringerBriefs on Computing, this volume is open access under a CC BY 4.0 license and was published by SpringerOpen.

About the authors

Kent-André Mardal is a professor of mechanics at the University of Oslo and an adjunct research scientist at Simula Research Laboratory. He has published more than 100 journal publication, and co-authored/co-edited five books, including the book about the FEniCS project, for which he was a core developer for many years. Research interests include computational modeling of neuroscience applications, including the recently proposed glymphatic system, along with robust and accurate methods.

Marie E. Rognes is Chief Research Scientist and Research Professor in Scientific Computing and Numerical Analysis at Simula Research Laboratory, Oslo, Norway and Professor II at the Department of Mathematics, University of Bergen, Norway. Her current research focus is on mathematical modelling and numerical methods for brain mechanics. She won the 2015 Wilkinson Prize for Numerical Software, the 2018 Royal Norwegian Society of Sciences and Letters Prize for Young Researchers within the Natural Sciences, and was a Founding Member of the Young Academy of Norway.

Travis Thompson is an applied and computational mathematician. He has published on a wide range of topics relevant to the mathematical modeling of neurodegenerative diseases; from novel finite element methods for poroelasticity, generalized poroelasticity, and computational fluid dynamics to network neurodegeneration models for Alzheimer’s disease. Dr. Thompson’s research encompasses numerical analysis, scientific computing, machine learning and the mathematical modeling of soft tissue and the prion-like evolution of neurodegenerative disease proteopathy.

Lars Magnus Valnes is an applied and computational mathematician with active research interests in scientific computing, patient-specific modeling, MRI brain analysis and the mathematical modeling of soft tissue and neurodegenerative disease pathology.