TDA applied to fMRI

Certain types of imaging data, like fMRI, naturally lend themselves to analysis using topological methods. The acquisition of an fMRI signal breaks a region of interest up into three-dimensional voxels. This voxel structure can be used to model the region by a cubical complex, a topological object which is amenable to efficient homological calculations. This space acquires a natural filtration via the fMRI signal, and so the methods of topological data analysis are readily available. Using this set-up, we are currently working on understanding how task modulation in the ACC can be understood using fMRI through the lens of persistent homology. This project has several thrusts, which are joint with Vaibhav Diwadkar, Sam Rizzo, Peter Bubenik, Andrew Salch, Adam Regalski, Hassan Abdallah, and Raviteja Suryadevara.