Fluid transport in a tube of variable cross-sectional area by peristaltic waves of dilating amplitude: A mathematical model for investigating impact of hiatus hernia on swallowing Fluid transport in a tube of variable cross-section

Abstract

In order to extract new inferences to help medical intervention, this paper aims to construct a mathematical model to suitably characterize swallowing in an oesophagus which suffers from sliding hiatus hernia. In such a state of dysfunction of oesophagus, the stomach moves upward through the hiatal orifice; due to which, there is a widening above the hiatus.

We make an attempt to mathematical formulate the circumstances created due to herniation, The formulation is in the dimensionless parameters using the long wavelength and low Reynolds number approximations modelling Newtonian flows in tubes, converging and diverging  partially,  or converging somewhere and diverging somewhere else.

The model validates the practical observations and gives some clues of the impact of partial convergence and divergence on pressure distribution. Less pressure is required for flow if the tube diverges but pressure has to be increased if the tube converges. It is further inferred from computer simulation that even if merely the lower part diverges, pressure is affected right from the beginning of flow. In case of sliding hiatal hernia, it is expected, pressure requirement for swallowing will be less due to oesophageal widening near the lower sphincter. It is even an experimental report that hiatus hernia reduces LES pressure. When the oesophagus converges, unlike this, pressure requirement for flow is more. This convergence may be an alarming situation. If hiatus hernia goes unnoticed, it is suspected that the narrowed part is less than the widened part. This inference can also be useful in peristaltically driven engineering applications.