Connectomics

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 Palm (2010)

Feusner (2007) Denk (2004) 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)

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

White Matter as a Riemannian Manifold Elegant perspective: Interpolation

Affine transformations Tractography

Downsides: Incompatible with complex fiber architecture High Angular Resolution Diffusion Imaging

Prkovska (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