Mapping Heritability of Large-Scale Brain Networks with a Billion Connections {\em via} Persistent Homology

TL;DR

This paper introduces a scalable method for constructing large-scale voxel-level brain networks using persistent homology, enabling heritability analysis with over 25,000 voxels despite small sample sizes.

Contribution

A novel scalable sparse network model using cross-correlations that overcomes computational bottlenecks in voxel-level brain network construction.

Findings

Successfully built large-scale voxel-level brain networks.

Analyzed heritability of functional brain networks using twin fMRI.

Demonstrated the method's efficiency and scalability.

Abstract

In many human brain network studies, we do not have sufficient number (n) of images relative to the number (p) of voxels due to the prohibitively expensive cost of scanning enough subjects. Thus, brain network models usually suffer the small-n large-p problem. Such a problem is often remedied by sparse network models, which are usually solved numerically by optimizing L1-penalties. Unfortunately, due to the computational bottleneck associated with optimizing L1-penalties, it is not practical to apply such methods to construct large-scale brain networks at the voxel-level. In this paper, we propose a new scalable sparse network model using cross-correlations that bypass the computational bottleneck. Our model can build sparse brain networks at the voxel level with p > 25000. Instead of using a single sparse parameter that may not be optimal in other studies and datasets, the computational speed gain enables us to analyze the collection of networks at every possible sparse parameter in a coherent mathematical framework via persistent homology. The method is subsequently applied in determining the extent of heritability on a functional brain network at the voxel-level for the first time using twin fMRI.