Traversing Scales of Brain and Behavioral Organization III: Theoretical Modeling

In coordinated movements typically several states related to different behavioral patterns can be found, e.g. different gaits of horses (Collins and Stewart 1993, Schoner et al. 1990) or different configurations among the joints for trajectory formation tasks (Buchanan et al. 1997, Kelso et al. 1991). These states have different stabilities dependent on external or internal control parameters. When such control parameters are manipulated, coordination states may become unstable and the system exhibits a transition from one state to another. These phenomena have intensively been investigated experimentally and theoretically and mathematical models have been set up reproducing the experimentally observed coordination behavior as well as predicting new effects (see (Haken 1996, Kelso 1995) for reviews). On the other hand, recent MEG and EEG experiments (Kelso et al. 1992, Wallenstein et al. 1995) have investigated the spatiotemporal brain dynamics during coordination of finger movements with external periodic stimuli. To accommodate these results, a mathematical phenomenological model was developed describing the on-going brain activity (Jirsa et al. 1994). In (Jirsa and Haken 1996a, 1996b) [Jirsa and Haken 1996a, Jirsa and Haken 1996b] a neurophysiologically motivated field theory of the spatiotemporal brain dynamics was elaborated which combined properties of neural ensembles, including their short- and long-range connections in the cortex, in addition to describing the interaction of functional units embedded into the neural sheet. This approach was applied to the brain-coordination experiment (Kelso et al. 1992) where the subject’s task was to coordinate rhythmic behavior of a finger with an external acoustic stimulus. During the experiment the MEG of the subject was recorded. Complex systems, such as the brain, have the general property that they perform low-dimensional behavior during transitions from one macroscopic state to another (Cross and Hohenberg 1993, Haken 1983, 1987). This type of behavior has also been found in the analyses (Fuchs et al. 1992, Jirsa et al. 1995) of the brain data from the coordination experiment in (Kelso et al. 1992). On the basis of these analyses the phenomenological model in (Jirsa et al. 1994) describing the brain activity was derived qualitatively from the neurophysiologically motivated theory in (Jirsa and Haken 1996a, 1997).