Finsler Geometry in Diffusion MRI Tom Dela Haije Supervisors: Luc Florack Andrea Fuster

Connectomics Mapping out the structure and function of the human brain

Multi-modality, Multi-scale Denk (2004)Feusner (2007) Palm (2010)

Diffusion MRI Wedeen (2012)

Diffusion MRI - Basics Measure diffusion locally Correlated with fiber orientation Free diffusion Restricted diffusion

Diffusion MRI - Basics Stejskal (1965)

Diffusion Tensor Imaging Diffusion modeled with second order positive-definite symmetric tensors Basser (1994)

Diffusion Tensor Imaging Bangera (2007)

Diffusion modeled with second order positive-definite symmetric tensors Introducing a Riemannian metric White Matter as a Riemannian Manifold O’Donnel (2002)

White Matter as a Riemannian Manifold Elegant perspective: Interpolation Affine transformations Tractography Downsides: Incompatible with complex fiber architecture

High Angular Resolution Diffusion Imaging Prčkovska (2009)

Diffusion MRI - Basics

White Matter as a Finsler Manifold Diffusion modeled with a function, homogeneous of degree 2

White Matter as a Finsler Manifold Diffusion modeled with a function Interpret as a Finsler manifold

Riemann-Finsler Geometry Advantages: Same advantages as Riemannian Compatible with complex tissue structure Downsides: More difficult to measure and post-process

Project Motivation for the metric Validity of the DTI Extending the Riemannian case to the Finsler case Relating the Finsler interpretation to existing viewpoints Operational tools for tractography and connectivity analysis