Classification of fMRI Brain Activation Maps by Using Space Filling Curves

Functional magnetic resonance imaging or functional MRI (fMRI) is a brain imaging technique which is used to measure brain activity by detecting changes associated with the blood flow and oxygenation, which are indirect measures of neural activity. When participants perform a task and/or have some stimuli during their fMRI scans, fMRI data helps us to obtain brain activation maps, which have three spatial dimensions (3D). 3D activation maps need to be converted (ordered, or vectorized) to 1D vectors for further analyses such as localization and classification of activations and/or participants. Traditionally, the 3D to 1D conversion has been done using linear ordering, which loses most of the information about the spatial structure of the brain. Instead, one can use space-filling curves (SFC) for vectorization, such as a 3D Hilbert curve, which can better preserve the structure of the brain; however, it is still far from being optimal. Finding an SFC which is adaptive to human brain can better preserve the structure of the human brain in 3D-to-1D ordering. The problem of finding an adaptive optimal SFC is inherently a modified traveling salesman problem (TSP). In this work, we obtained an approximation of the SFC practically using a heuristic solution to the modified TSP. We used completely de-identified fMRI brain activation maps from schizophrenia fMRI experiment participants. We first applied a Hilbert SFC to obtain features and apply deep learning and other machine learning algorithms to classify participants from their brain activation maps and to fine-tune algorithm parameters. We also used an approximation of the optimal SFC using a TSP heuristic, converted the brain maps to 1D and obtained features for classification. The classification based on the heuristic approximations of adaptive SFC’s orderings yielded comparable or better classification accuracies than those of linear ordering and Hilbert ordering.