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

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