Quasi-periodic spatiotemporal models of brain activation in single-trial MEG experiments

Magneto-encephalography (MEG) is an imaging technique which measures neuronal activity in the brain. Even when a subject is in a resting state, MEG data show characteristic spatial and temporal patterns, resulting from electrical current at specific locations in the brain. The key pattern of interest is a 'dipole', consisting of two adjacent regions of high and low activation which oscillate over time in an out-of-phase manner. Standard approaches are based on averages over large numbers of trials in order to reduce noise. In contrast, this article addresses the issue of dipole modelling for single trial data, as this is of interest in application areas. There is also clear evidence that the frequency of this oscillation in single trials generally changes over time and so exhibits quasi-periodic rather than periodic behaviour. A framework for the modelling of dipoles is proposed through estimation of a spatiotemporal smooth function constructed as a parametric function of space and a smooth function of time. Quasi-periodic behaviour is expressed in phase functions which are allowed to evolve smoothly over time. The model is fitted in two stages. First, the spatial location of the dipole is identified and the smooth signals characterizing the amplitude functions for each separate pole are estimated. Second, the phase and frequency of the amplitude signals are estimated as smooth functions. The model is applied to data from a real MEG experiment focusing on motor and visual brain processes. In contrast to existing standard approaches, the model allows the variability across trials and subjects to be identified. The nature of this variability is informative about the resting state of the brain.