Diffusion MRI enables us to non-invasively probe the microstructure of biological tissues. It is of the utmost importance to design powerful biomarkers for studying neurological disorders. Combined with functional MRI, it has also started to shed new light on the anatomo-functional networks of the human brain. However, the complexity of the data and the need for adequate mathematical models raise many theoretical and computational challenges.
I will present a series of mathematical concepts and computational tools based on differential geometry, partial differential equations, front propagation and spherical data analysis for the processing of Diffusion Tensor Images (DTI) and High Angular Resolution Diffusion Images (HARDI). I will discuss problems such as the cerebral connectivity mapping, the segmentation of DTI/HARDI and the registration of DTI. I will show how the fusion of structural MRI and fMRI with DTI can provide exquisite insights into the architecture of the human motor and visual systems. Finally, I will describe how manifold learning techniques can help quantifying the non-uniform complexity of the cerebral white matter from HARDI.
Audio (MP3 File, Podcast Ready)
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