The principal investigator and colleagues will address two issues in mathematical modeling and analysis of oculomotor reflexes. First, the various published models have not been fully verified by comparison with actual data and comparison with other models. Second, a new and powerful class of dynamic measures has recently been developed in the field of nonlinear dynamics ("chaos theory"). These measures provide a way to assess nonlinearity and determinism in a time series, but the measurements are not always easy to interpret and to relate to the underlying physiology. This research project addresses these issues in two ways. First, the investigators will implement on a computer several mathematical models of reflexive oculomotor control, obtain actual data from the species (cat, turtle, human) for which each model was developed, and use the dynamic measures (correlation dimension, prediction error, fractal structure, and others) to compare the data to simulated data generated by each model. Making allowances for differences between species, the models will be compared with each other in the same manner. In the course of this work the investigators also plan to develop new models of oculomotor control. Second, the models will be modified systematically (by making small parameter changes, changing the form of probability distributions, etc.), and a record will be kept of the effect of each modification on the various dynamic measures. In this way, the project will give insight into the interpretation of the measurements, what physiologic processes might be responsible for their taking on particular values and how pathologic conditions alter the nominal values.
