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Research Abstracts Online
January - December 2011

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University of Minnesota Twin Cities
Medical School
Department of Urologic Surgery

PI: Carl S. Smith

Renal Pelvic and Calyceal Dynamics as Excitable Media

Renal pelvic and calyceal dynamics constitute the processes that transport urine in the upper urinary tract. These processes include the proximal pacemaker system, propagation of urine flow within the renal pelvis, and the initiation of ureteral peristalsis. Modeling these processes is a complex task. Past models recognized the use of coupled oscillators to explain their integration. On close examination however, past models lacked structural realism in two and three dimensions and failed to address calyceal synchrony. The ability of renal pelvic tissue to spontaneously contract indicates that this tissue is an excitable media and can be described mathematically by the FitzHugh-Nagumo equations. An unexpected outcome of solving these equations is the creation of traveling waves, specifically spiral waves that radiate from the source, have constant velocity and display other nonlinear patterns. The goal of this project is to use established programs for spiral wave generation and scroll wave creation to simulate data obtained from a physiologic animal study. Calyceal synchrony is investigated separately with physiologic data and Hilbert transforms. It is hoped that phase transitions from wave to particle-like behavior will be detected in the simulation to support ureteral peristalsis as soliton-like behavior. To conclude, the processes in the upper urinary tract comprise a stable, robust, self-organizing system that allows construction of a plausible theoretic model that simplifies our understanding of urinary transport.