Uncovering the Topology of Time-Varying fMRI Data using Cubical Persistence

in our paper we’re dealing with functional magnetic resonance imaging or fmri for short this method results in a 3d view of a person’s brain but the data are actually 4d because the state of the brain varies over time so we get a volume of those voxels and we can take a look inside the brain by clipping away some parts of course this remains a 3d volume that we can rotate we model each time step of such a volume as a cubical complex the voxels are becoming the vertices of the cubes and edges connect adjacent voxels we now start tracking topological features such as connected components cycles and voids as we filtrate this cubical complex according to the fmri activation function values from this we obtain a persistence diagram that is a descriptor containing information about the creation and destruction of each topological feature in the data by calculating a summary statistic over the time axis we can summarize the topological activity of each input sample we use this to predict the age of participants in our data set for instance next to such summaries we can also calculate brain state trajectories for cohorts in our data set such as adults or children we observe that their topological activity is markedly different while watching the same movie indicating that adults and children process the same stimuli quite differently to learn more about how topological features can uncover characteristics of fmri data sets please visit our poster or read our paper thank you very much for your attention .