Modelling the biomechanics and control of sphincters

This paper reviews current mathematical models of sphincters and compares them with a new spatial neuromuscular control model based on known physiological properties. Almost all the sphincter models reviewed were constructed as a component of a more extensive model designed to mirror the overall behaviour of a larger system such as the lower urinary tract. This implied less detailed modelling of the sphincter component. It is concluded that current sphincter models are not suitable for mimicking detailed interactions between a neural controller and a sphincter. We therefore outline a new integrated model of the biomechanics and neural control of a sphincter. The muscle is represented as a lumped-mass model, providing the possibility of applying two- or three-dimensional modelling strategies. The neural network is a multi-compartment model that provides neural control signals at the level of action potentials. The integrated model was used to simulate a uniformly activated sphincter and a partially deficient innervation of the sphincter, resulting in a non-uniformly activated sphincter muscle. During the simulation, the pressure in the sphincter lumen was prescribed to increase sinusoidally to a value of 60 kPa. In the uniformly activated situation, the sphincter muscle remains closed, whereas the partially denervated sphincter is stretched open, although the muscle is intact.