Spatio-temporal brain activities with variable delay detectable in resting-state functional magnetic resonance imaging (rs-fMRI) give rise to highly reproducible structures, termed cortical lag threads, that can propagate from one brain region to another. Using a computational topology of data approach, we found that Betti numbers that are cycle counts and the areas of vortex cycles covering brain activation regions in triangulated rs-fMRI video frames make it possible to track persistent, recurring blood oxygen level dependent (BOLD) signals. Our findings have been codified and visualized in what are known as persistent barcodes. Importantly, a topology of data offers a practical approach in coping with and sidestepping massive noise in neuro data, such as unwanted dark (low intensity) regions in the neighbourhood of non-zero BOLD signals. A natural outcome of a topology of data approach is the tracking of persistent, non-trivial BOLD signals that appear intermittently in a sequence of rs-fMRI video frames. The end result of this tracking of changing lag structures is a persistent barcode, which is a pictograph that offers a convenient visual means of exhibiting, comparing and classifying brain activation patterns.
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