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

• Superior document: Simula SpringerBriefs on Computing Series ; v.10
• Author: Mardal, Kent-André.
• TeilnehmendeR: Rognes, Marie E.; Thompson, Travis B.; Valnes, Lars Magnus.
• Place / Publishing House: Cham : : Springer International Publishing AG,, 2022.; {copy}2022.
• Year of Publication: 2022
• Edition: 1st ed.
• Language: English
• Series: Simula SpringerBriefs on Computing Series
• Physical Description: 1 online resource (129 pages)

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.