Date of Award

Spring 1990

Document Type

Dissertation

Degree Name

Doctor of Engineering Science in Electrical Engineering

Department

Electrical and Computer Engineering

First Advisor

Stanley S. Reisman

Second Advisor

Walter N. Tapp

Third Advisor

Peter Engler

Fourth Advisor

Joseph Frank

Fifth Advisor

Denis L. Blackmore

Abstract

Biological rhythms are an important phenomenon and feature of physiologic systems. Indirect means have to be employed for their description and exploration due to the unclear internal nature of the system. This study analyzed and developed several possible mathematical models using single or multidimensional nonlinear differential equations to approach the experimental circadian data. The numerical solutions of the models were obtained by computer simulation and the simulated and experimental acquired circadian data were analyzed in both the time and frequency domains. Phase plane plots, phase response curves and power spectrum analysis were employed to determine the nonlinearity of the system and its relation to the harmonic structure while bispectrum analysis showed the relation between the harmonics. Dynamic spectrum and frequency demodulation techniques were used to explore the dynamic transient process of the circadian rhythms when a stimulus is applied. The coherence function was examined to explore the frequency correlation between two different circadian rhythms: temperature and activity of the same subject. The study showed that a two dimensional coupled nonlinear oscillator model can be used to describe the circadian rhythm better and a model with relatively large nonlinearity closely approximated the experimental data. The research revealed the harmonic structure of circadian rhythms. This structure related to the nonlinearity of the system with the 2nd harmonic of experimental data representing bimodality in the time series. All the models developed in this research reflected this important feature. The effects of a nonperiodic stimulus to the circadian system were simulated in the model and an "overshoot" phenomenon was found during the frequency transient process. High values of coherence were found at the fundamental and third harmonics while no phase relation was found between harmonics of the experimental data using the bispectrum method.

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