finsler geometry in diffusion mri
DESCRIPTION
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). - PowerPoint PPT PresentationTRANSCRIPT
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 diffusionRestricted 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