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Finsler Geometry in Diffusion MRI

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).

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Finsler Geometry in Diffusion MRI

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  1. Finsler Geometry in Diffusion MRI Tom DelaHaije Supervisors: Luc Florack Andrea Fuster

  2. Connectomics • Mapping out the structure and function of the human brain

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

  4. Diffusion MRI Wedeen (2012)

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

  6. Diffusion MRI - Basics Stejskal (1965)

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

  8. Diffusion Tensor Imaging Bangera (2007)

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

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

  11. High Angular Resolution Diffusion Imaging Prčkovska(2009)

  12. Diffusion MRI - Basics

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

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

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

  16. 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

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