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 can be used to characterize the intensity of physiological signals. In this communication, a novel method of dimension estimation based on the calculation of spectral distribution function of discrete-time fractional Gaussian noise using Legendre polynomials as basis set is proposed. The effectiveness of this proposed method is demonstrated in the dynamic behavior of detrusor of the bladder and external urethral sphincter during micturition.
In normal humans, the bladder is supposed to empty by a synergistic contraction of the detrusor and relaxation of the sphincter during micturition. By contrast, suprasacral spinal cord injury (SCI) patients usually will have both of them contract simultaneously and result in the so-called detrusor-sphincter dyssynergia. In this study, the cystometrograms of the detrusor and the electromyograms of external urethral sphincter of intact and SCI female Wistar rats are used to investigate the detrusor-sphincter synergia and dyssynergia during micturition. Due to the statistical self-similarity of the waveforms, the cystometrogram is modeled as discrete-time fractional Brownian motion and the electromyogram as discrete-time fractional Gaussian noise. Fractal dimensions of both of them are calculated and used as indices in the investigation of synergia. Results indicate that, for intact rats, the sphincter muscle is not only active but also recruited in a synchronous fashion with the detrusor. Furthermore, clear-cut measure using the fractal dimensions can be used to diagnose detrusor-sphincter synergia and dyssynergia.
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