Abstract
Rhythmic signals from physiological systems usually have memory and long term correlation. They can be modeled as fractional Brownian motion or fractional Gaussian noise depending on if the signals are derived from cumulative effects of nerves and muscles. That is, they can be treated as signals with fractional dimension and the value of its fractal dimension (FD) can be used to characterize the intensity of physiological signals. In this study, a novel method of dimension estimation based on the calculation of spectral distribution function (SDF) of discrete-time fractional Gaussian noise using Legendre polynomials (LPs) as basis set is proposed. The dimension estimation is statistically consistent and its standard deviation is small when the system is under positive correlation. Hence, this estimator is especially suitable for investigating synergic physiological functions. Due to SDF, two indicators, FD and spectral frequency, can be obtained simultaneously. These two indicators can be applied in illustrating the synergic behavior of detrusor of the bladder and external urethral sphincter (EUS) during micturition. Another application of these two indicators is the dynamical performance evaluation of the pharmacological effects on micturition in spinal-cord-injury (SCI) rats. Capsaicin and resiniferatoxin (RTX) are administered and their effects are compared. Results indicate that the synergy of micturition using RTX is better than that of capsaicin. It is believed that this methodology would be useful in the assessing of other synergic physiological functions and studying functional effects of pharmacology for animals under dynamical diseases.