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.