We address here the use of EEG and fMRI, and their combination, in order to estimate the full spatiotemporal patterns of activity on the cortical surface in the absence of any particular assumptions on this activity such as stimulation times. For handling such a high-dimension inverse problem, we propose the use of (1) a global forward model of how these measures are functions of the “neural activity” of a large number of sources distributed on the cortical surface, formalized as a dynamical system, and (2) adaptive filters, as a natural solution to solve this inverse problem iteratively along the temporal dimension. This estimation framework relies on realistic physiological models, uses EEG and fMRI in a symmetric manner, and takes into account both their temporal and spatial information. We use the Kalman filter and smoother to perform such an estimation on realistic artificial data and demonstrate that the algorithm can handle the high dimensionality of these data and that it succeeds in solving this inverse problem, combining efficiently the information provided by the two modalities (this information being naturally predominantly temporal for EEG and spatial for fMRI). It performs particularly well in reconstructing a random temporally and spatially smooth activity spread over the cortex. The Kalman filter and smoother show some limitations, however, which call for the development of more specific adaptive filters. First, they do not cope well with the strong nonlinearity in the model that is necessary for an adequate description of the relation between cortical electric activities and the metabolic demand responsible for fMRI signals. Second, they fail to estimate a sparse activity (i.e., presenting sharp peaks at specific locations and times). Finally their computational cost remains high. We use schematic examples to explain these limitations and propose further developments of our method to overcome them.

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