Estimation of Velocity Fields and Propagation on Non-Euclidian Domains: Application to the Exploration of Cortical Spatiotemporal Dynamics

Better understanding of the interrelationship between the brain’s structural architecture and functional processing is one of the leading questions in today’s integrative neuroscience. Non-invasive imaging techniques have revealed as major contributing tools to this endeavor, which obviously requires the cooperation of space and time-resolved experimental evidences. Electromagnetic brain mapping using magnetoand electro-encephalography (M/EEG) source estimation is so far the imaging method with the best trade-off between spatial and temporal resolution (∼1 cm and <1ms respectively, [4,5]). Combined with individual anatomical information from Magnetic Resonance Imaging (MRI) and statistical inference techniques [35], M/EEG source estimation has now reached considerable maturity and may indeed be considered as a true functional brain imaging technique. With or without considering the estimation of M/EEG generators as a priority, the analysis of M/EEG data is classically motivated by the detection of salient features in the time course of surface measures either/both at the sensor or/and cortical levels. These features of interest may be extracted from waveform peaks and/or their related time latencies, band-specific oscillatory patterns surging from a time-frequency decomposition of the data or regional activation blobs at the cortical level. By nature, the extraction of such features usually results from an extremely reductive – though pragmatic – point of view on the spatio-temporal dynamics of brain responses. It is pragmatic because it responds to a need for the reduction in the information mass from the original data. It is reductive