Time-Variant Modeling of Brain Processes

In science and engineering mathematical modeling serves as a tool for the understanding of processes and systems and as a testing bed for several hypotheses, e.g., concerning the testing (prediction) of functional limits by simulations. A brief overview of current modeling strategies in brain research is given, spatial scales ranging from single neuron to large scale activity of and between brain regions are considered. The models are mainly time-invariant. Three time-variant modeling strategies, which enable a model-based signal analysis, are described and applied to large scale signals. The first is derived from adaptive filter theory and covers linear system and linear as well as nonlinear process models. The second is based on modeled brain source signals, i.e., the inverse problem must be solved. The third strategy consists of a generalization of Dynamic Causal Modeling (DCM); DCM is frequently used for analysis of directed interactions between brain structures. Examples are derived from neonatal electroencephalography (EEG) monitoring of preterm and fullterm newborns. A further example is based on high-density recordings of event-related potentials (ERPs) and shows the combination of a time-variant ERP-based source model, as a part of a realistic head model, with a multivariate process model to analyze the time evolution of interactions between source processes before and during the execution of a complex motoric task. In two other examples hemodynamic signals (functional magnetic resonance imaging-fMRI) are utilized for analysis of interactions between brain regions, where nonlinear, multivariate models are used.