Structure-Function Network Mapping and Its Assessment via Persistent Homology

Area of Science:

• Network neuroscience
• Computational neuroscience
• Brain connectomics

Background:

• Understanding the brain's structure-function relationship is crucial in network neuroscience.
• Current methods for mapping brain structure to function face challenges with large datasets and complex relationships.

Purpose of the Study:

• To develop a general method for whole-brain structure-function mapping.
• To introduce a novel network similarity measure for assessing mapping quality.
• To uncover direct and indirect structural paths predicting functional connectivity.

Main Methods:

• Formulated structure-function mapping as a topological mapping using matrix functions.
• Employed regularization procedures to handle large matrices.
• Introduced a network similarity measure based on persistent homology.

Main Results:

• The developed approach successfully predicts functional connectivity using structural paths.
• The novel network similarity measure outperforms existing methods.
• Demonstrated a nonlinear structure-function relationship, emphasizing direct and indirect connections.

Conclusions:

• The proposed method provides a stable and effective approach for whole-brain structure-function mapping.
• Persistent homology offers a robust tool for comparing network topological changes.
• The findings underscore the complex interplay between structural connectivity and resting-state functional connectivity.