Several measures of dynamical behavior, particularly the correlation dimension and Lyapunov exponents, have been used in the analysis of biological signals. The long-term objective of these investigations is to identify the dynamical structure of the systems generating these signals and to study transitions from normal behavior to clinically observed failures of physiological control systems. It is now clear that these measures are not robust to misapplication. Many of the dynamical analyses in the biological literature, particularly claims for the existence of chaotic behavior, are almost certainly spurious. The objective of the first part of this project is to undertake systematic investigations to produce guidelines for the application of dynamical measures to biological data with an emphasis on simpler measures that are more robust when used with noisy data. The following measures will be investigated: a variant of the correlation dimension, the pointwise dimension, the Lyapunov exponent, the local intrinsic dimension, tests for deterministic structure, tests for nonlinear predictability, coarse grained entropy, algorithmic complexity and epsilon-machines. Theoretical studies will also investigate embedding methods, compare different procedures for testing nonlinearity, and search for noise reduction procedures that will not distort the results of dynamical analysis. The second phase of the project will focus on the dynamical analysis of biological data. The database is now archived in our laboratory. No funds are requested for new experimental studies. The dynamical analysis will stress the comparison of signals obtained in two or more contrasting physiological conditions. The following data will be analyzed as part of this project: human electromyograms (normal, neuropathic, myopathic), rat cortical unit spike trains obtained before and during focal seizures, EEGs obtained from normal human subjects at rest and during different cognitive tasks, event related potentials from normal human subjects performing an auditory oddball task, electrocorticograms obtained from chronically implanted electrodes in rats during normal behaviors and during seizures.
| Rapp, P E; Schmah, T (1996) Complexity measures in molecular psychiatry. Mol Psychiatry 1:408-16 |
| Theiler, J; Rapp, P E (1996) Re-examination of the evidence for low-dimensional, nonlinear structure in the human electroencephalogram. Electroencephalogr Clin Neurophysiol 98:213-22 |
| Rapp, P E (1994) A guide to dynamical analysis. Integr Physiol Behav Sci 29:311-27 |
