A Riemannian Revisiting of Structure-Function Mapping Based on Eigenmodes

Area of Science:

• Neuroscience
• Computational Biology
• Medical Imaging

Background:

• Understanding brain organization and pathology relies on quantifying the link between brain structure and function.
• Predicting functional connectivity from structural connectivity is a key challenge in neuroscience.
• Functional connectivity data resides in a Riemannian manifold, requiring specialized analytical approaches.

Purpose of the Study:

• To investigate the impact of using an affine invariant Riemannian metric for structure-function mapping.
• To re-evaluate existing structure-function mapping methods using this specialized Riemannian distance.
• To enhance the accuracy of predicting functional brain connectivity from structural data.

Main Methods:

• Employed an affine invariant Riemannian metric for distance calculations within the symmetric positive definite space.
• Revisited and tested established structure-function mapping techniques based on eigendecomposition.
• Utilized data from 100 healthy subjects from the Human Connectome Project.

Main Results:

• The chosen Riemannian distance significantly changes the assessment of functional similarity between subjects.
• Incorporating this Riemannian distance enhances the correlation between structural and functional similarities.
• Mapping brain function from structure within the Riemannian manifold improves predictive performance.

Conclusions:

• The application of a Riemannian-appropriate distance is crucial for accurate structure-function mapping.
• This approach offers superior performance compared to standard methods, potentially surpassing the group average and existing limitations.
• The findings highlight the importance of manifold-aware analysis in neuroimaging research.