Overview of Mathematical Computer Models of Striated Sphincter Muscles

The present paper compares current mathematical striated sphincter models. Current models are subdivided in four categories: (1) simple models, (2) implementations of the urethral resistance relation, (3) models with realistic muscle dynamics and (4) finite element models. In our research group a neural network model, representing Onuf' nucleus, the spinal motor nucleus that innervates the external urethral and anal sphincters, was developed. A realistic sphincter model is needed to test the neural network. To decide whether or not a model is applicable in our research two requirements should be fulfilled: (1) the presence of realistic muscle dynamics preferably by implementation of a Huxley type muscle model and (2) the model should consist of more than one muscle unit to form a more dimensional model. Reviewing the literature, if a myogenic sphincter is modelled, mainly the Hill-equation is applied. Moreover, single muscle unit models are published. In general a multi-unit muscle model of the sphincter is lacking, prohibiting the study of the inherent properties of sphincter muscles, which could give information on the realistic behaviour of elements in circular muscles. It is concluded that the functionality of current sphincter models is limited for our purpose.