Optimisation in the Modelling of Digestive Tract Electrical Signals

Spontaneous electrical rhythms have been recorded in many parts of the digestive tract in animals and humans. The signals contain a low frequency regular oscillation which varies in frequency and waveshape between parts of the tract and between species. A mathematical model postulated for these rhythms comprises a set of mutually coupled Van der Pol oscillators. For the human small and large intestines where signals are nearly sinusoidal the method of harmonic balance is used to obtain analytical results for amplitude, phase and entrained frequency. The non-linear algebraic equations are solved using hill-climbing methods due to Rosenbrock, Powell and Fletcher-Reeves. Algorithms requiring first derivatives of the minimised functions have been found significantly faster than the Rosenbrock method.

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