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

Bibliographic Details
Main Author: Mardal, Kent-André.
Other Authors: Rognes, Marie E., Thompson, Travis B., Valnes, Lars Magnus.
Format: eBook
Language:English
Published: Cham : Springer International Publishing AG, 2022.
Edition:1st ed.
Series:Simula SpringerBriefs on Computing Series
Subjects:
Electronic books.
Online Access:Click to View
Table of Contents:
  • Intro
  • Series Foreword
  • Foreword
  • Preface
  • Contents
  • Chapter 1 Introduction
  • 1.1 A model problem
  • 1.2 On reading this book
  • 1.3 Datasets and scripts
  • 1.4 Other software
  • 1.5 Book outline
  • Chapter 2 Working with magnetic resonance images of the brain
  • 2.1 Human brain anatomy
  • 2.2 Magnetic resonance imaging
  • 2.2.1 Structural MRI: T1- and T2-weighted images
  • 2.2.2 Diffusion-weighted imaging and diffusion tensor imaging
  • 2.3 Viewing and working with MRI datasets
  • 2.3.1 The DICOM file format
  • 2.3.2 Working with the contents of an MRI dataset
  • 2.4 From images to simulation: A software ecosystem
  • 2.4.1 FreeSurfer for MRI processing and segmentation
  • 2.4.2 NiBabel: A python tool for MRI data
  • 2.4.3 SVM-Tk for volume mesh generation
  • 2.4.4 The FEniCS Project for finite element simulation
  • 2.4.5 ParaView and other visualization tools
  • 2.4.6 Meshio for data and mesh conversion
  • 2.4.7 Testing the software pipeline
  • Chapter 3 Getting started: from T1 images to simulation
  • 3.1 Generating a volume mesh from T1-weighted MRI
  • 3.1.1 Extracting a single series from an MRI dataset
  • 3.1.2 Creating surfaces from T1-weighted MRI
  • 3.1.3 Creating a volume mesh from a surface
  • 3.2 Improved volume meshing by surface preprocessing
  • 3.2.1 Remeshing a surface
  • 3.2.2 Smoothing a surface file
  • 3.2.3 Preventing surface intersections and missing facets
  • 3.3 Simulation of diffusion into the brain hemisphere
  • 3.3.1 Research question and model formulation
  • 3.3.2 Numerical solution of the diffusion equation
  • 3.3.3 Implementation using FEniCS
  • 3.3.4 Visualization of solution fields
  • 3.4 Advanced topics for working with larger cohorts
  • 3.4.1 Scripting the extraction of MRI series
  • 3.4.2 More about FreeSurfer's recon-all
  • Chapter 4 Introducing heterogeneities.
  • 4.1 Hemisphere meshing with gray and white matter
  • 4.1.1 Converting pial and gray/white surface files to STL
  • 4.1.2 Creating the gray and white matter mesh
  • 4.1.3 More about defining SVM-Tk subdomain maps
  • 4.2 Separating the ventricles from the gray and white matter
  • 4.2.1 Extracting a ventricular surface from MRI data
  • 4.2.2 Removing the ventricular volume
  • 4.3 Combining the hemispheres
  • 4.3.1 Repairing overlapping surfaces
  • 4.3.2 Combining surfaces to create a brain mesh
  • 4.4 Working with parcellations and finite element meshes
  • 4.4.1 Mapping a parcellation onto a finite element mesh
  • 4.4.2 Mapping parcellations respecting subdomains
  • 4.5 Refinement of parcellated meshes
  • 4.5.1 Extending the Python interface of DOLFIN/FEniCS
  • 4.5.2 Refining certain regions of parcellated meshes
  • Chapter 5 Introducing directionality with diffusion tensors
  • 5.1 Extracting mean diffusivity and fractional anisotropy
  • 5.1.1 Extracting and converting DTI data
  • 5.1.2 DTI reconstruction with FreeSurfer
  • 5.1.3 Mean diffusivity and fractional anisotropy
  • 5.2 Finite element representation of the diffusion tensor
  • 5.2.1 Preprocessing the diffusion tensor data
  • 5.2.2 Representing the DTI tensor in FEniCS
  • 5.2.3 A note on co-registering DTI and T1 data
  • Chapter 6 Simulating anisotropic diffusion in heterogeneous brain regions
  • 6.1 Molecular diffusion in one dimension
  • 6.1.1 Analytical solution
  • 6.1.2 Numerical solution and handling numerical artifacts
  • 6.2 Anisotropic diffusion in 3D brain regions
  • 6.2.1 Regional distribution of gadobutrol
  • 6.2.2 Accuracy and convergence of computed quantities
  • Chapter 7 Concluding remarks and outlook
  • References
  • Index.

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