Mathematical Modeling of the Human Brain: From Magnetic Resonance Images to Finite Element Simulation (Simula SpringerBriefs on Computing Book 10)

"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."--Provided by publisher Series Foreword 6 Foreword 7 Preface 10 Contents 13 Chapter 1 Introduction 15 1.1 A model problem 17 1.2 On reading this book 18 1.3 Datasets and scripts 19 1.4 Other software 19 1.5 Book outline 20 Chapter 2 Working with magnetic resonance images of the brain 21 2.1 Human brain anatomy 21 2.2 Magnetic resonance imaging 23 2.2.1 Structural MRI: T1- and T2-weighted images 24 2.2.2 Diffusion-weighted imaging and diffusion tensor imaging 25 2.3 Viewing and working with MRI datasets 27 2.3.1 The DICOM file format 27 2.3.2 Working with the contents of an MRI dataset 27 2.4 From images to simulation: A software ecosystem 29 2.4.1 FreeSurfer for MRI processing and segmentation 30 2.4.2 NiBabel: A python tool for MRI data 32 2.4.3 SVM-Tk for volume mesh generation 33 2.4.4 The FEniCS Project for finite element simulation 33 2.4.5 ParaView and other visualization tools 34 2.4.6 Meshio for data and mesh conversion 34 2.4.7 Testing the software pipeline 35 Chapter 3 Getting started: from T1 images to simulation 36 3.1 Generating a volume mesh from T1-weighted MRI 36 3.1.1 Extracting a single series from an MRI dataset 37 3.1.2 Creating surfaces from T1-weighted MRI 37 3.1.3 Creating a volume mesh from a surface 39 3.2 Improved volume meshing by surface preprocessing 41 3.2.1 Remeshing a surface 41 3.2.2 Smoothing a surface file 43 3.2.3 Preventing surface intersections and missing facets 45 3.3 Simulation of diffusion into the brain hemisphere 46 3.3.1 Research question and model formulation 47 3.3.2 Numerical solution of the diffusion equation 49 3.3.3 Implementation using FEniCS 50 3.3.4 Visualization of solution fields 55 3.4 Advanced topics for working with larger cohorts 55 3.4.1 Scripting the extraction of MRI series 56 3.4.2 More about FreeSurfer's recon-all 58 Chapter 4 Introducing heterogeneities 60 4.1 Hemisphere meshing with gray and white matter 60 4.1.1 Converting pial and gray/white surface files to STL 61 4.1.2 Creating the gray and white matter mesh 62 4.1.3 More about defining SVM-Tk subdomain maps 64 4.2 Separating the ventricles from the gray and white matter 67 4.2.1 Extracting a ventricular surface from MRI data 67 4.2.2 Removing the ventricular volume 73 4.3 Combining the hemispheres 75 4.3.1 Repairing overlapping surfaces 76 4.3.2 Combining surfaces to create a brain mesh 77 4.4 Working with parcellations and finite element meshes 79 4.4.1 Mapping a parcellation onto a finite element mesh 79 4.4.2 Mapping parcellations respecting subdomains 83 4.5 Refinement of parcellated meshes 89 4.5.1 Extending the Python interface of DOLFIN/FEniCS 89 4.5.2 Refining certain regions of parcellated meshes 90 Chapter 5 Introducing directionality with diffusion tensors 94 5.1 Extracting mean diffusivity and fractional anisotropy 95 5.1.1 Extracting and converting DTI data 95 5.1.2 DTI reconstruction with FreeSurfer 95 5.1.3 Mean diffusivity and fractional anisotropy 97 5.2 Finite element representation of the diffusion tensor 98 5.2.1 Preprocessing the diffusion tensor data 99 5.2.2 Representing the DTI tensor in FEniCS 104 5.2.3 A note on co-registering DTI and T1 data 106 Chapter 6 Simulating anisotropic diffusion in heterogeneous brain regions 110 6.1 Molecular diffusion in one dimension 110 6.1.1 Analytical solution 111 6.1.2 Numerical solution and handling numerical artifacts 111 6.2 Anisotropic diffusion in 3D brain regions 113 6.2.1 Regional distribution of gadobutrol 114 6.2.2 Accuracy and convergence of computed quantities 115 Chapter 7 Concluding remarks and outlook 121 References 123 Index 128