State-space analysis of a myocybernetic model of the lower urinary tract

To study the control of the lower urinary tract, the state space of the myocybernetic model by Bastiaanssen et al. (1996) is analysed. This model is able to respond to input signals from a neural network and includes descriptions of the muscle dynamics of both the detrusor in the bladder wall and the urethral sphincter. The equilibrium states of the model for constant input signals were found by evaluation of the roots of calculated flow curves. Two types of equilibrium states could be distinguished: (i) the inflow and the outflow of the bladder are both equal to zero and (ii) the bladder in- and outflow are both equal to a prescribed small constant flow from the ureters into the bladder. The first type of equilibrium features a very high bladder pressure, which in vivo could result in a reflux of urine into the ureters. The second type shows a constant loss of urine. For different combinations of constant input signals, several stable equilibrium states of both types were found. The neural controller should avoid these states so that the lower urinary tract fulfils either its storage or its voiding function. Therefore, the trajectory through the state space of a simulated normal filling and micturition event was evaluated here. It appeared that equilibrium states were avoided by rapid changes of the input signals. The behaviour of the model outside the normal trajectory is compared with neurologic urinary tract disorders. Several pathological behaviours are in qualitative agreement with the model predictions.