1. Fractal and Rhythms in Urodynamics 張翔 教授 國立清華大學電機系

2. Table of Contents Introduction Materials and methods Results Discussion Conclusion Appendix A. Fractional Brownian motion Appendix B. Calculation of fractal dimension

3. Introduction The function of micturition is mainly regulated by bladder and external urethral sphincter.

4. Introduction The detrusor of bladder consists of smooth muscles and is innervated by sympathetic and parasympathetic nerves.

5. Introduction The external urethral sphincter consists of striated muscles and is innervated by somatic nerves.

6. Introduction Our current understanding of human and animal micturition involves relaxation of the external urethral sphincter (EUS) while the detrusor of the bladder is active (Cheng et al., 1995, 1997; Kruse et al.,1993; Walsh et al., 1998; Williams et al., 1995).

7. Introduction To successfully empty the bladder, the detrusor and EUS cannot be active simultaneously.

8. Introduction To investigate the question if the detrusor and EUS will work synergistically to facilitate voiding. To find out the quantitative measures that can characterize the synergism

9. Materials and methods A total of 39 micturition experiments were performed on four intact and four spinalized (SCI) adult female Wistar rats (250–400 g).

10. Materials and methods The cystometrogram (CMG) of detrusor and EMG of EUS are invoked. Based on the data records, the waveform of EMG exhibits statistical self-similarity while that of the CMG indicates the cumulative force generated by smooth muscles of the detrusor. Therefore, the EMG can be modeled as the discrete-time fractional Gaussian noise (DFGN) and the CMG as discrete-time fractional Brownian motion (DFBM), respectively.

11. Materials and methods The fractal dimensions of CMG and EMG are then combined with the spectral information to investigate the synergistic behavior during micturition.

12. Results

17. Discussion Firstly, they have temporal fractal structure. Secondly, they are rhythmic but with fluctuations.

18. Discussion A) a temporal “coherent” fractal structure B) synchronization of rhythms

19. In the urodynamics of lower urinary tract in female Wistar rats The rhythms of detrusor of the bladder and external urethral sphincter are synchronized around 7Hz. Their fractal dimensions as functions of time are temporally “coherent” under 1.5 during voiding in order to facilitate the concerted process.

21. Synergistic concept of voiding This is different from conventional textbook. It can be considered as an emergent property of a high degree of accordance between detrusor and EUS

22. Dyssynergia of SCI patients The dyssynergia of SCI patients may be categorized by the fact that either the temporal coherence of fractal dimensions or the synchronization of rhythms is impaired, weakened, or absent.

23. Conclusion These results have promoted our understanding in the synergistic concerted actions They have potential implications in the diagnosis of the so-called “dynamical” diseases.