An analytical and comparative study of swallowing in a tumor-infected oesophagus: a mathematical model

Abstract

This study discusses non-steady effects encountered in peristaltic flows in oesophagus. The purpose of this communication is to evolve a mechanism to diagnose tumor in an oesophagus mathematically. The tumor is modelled by generic bump function of certain height and width. The method of solution follows long wavelength and low-Reynolds number approximations for unsteady flow, while integrations have been performed numerically in order to plot graphs, which reveal various characteristics of the flow. The goal is to assess how pressure varies across the tumor's width. The spatial, as well as temporal, dependence of pressure has been studied in the laboratory frame of reference. The pressure distribution for tumor-infected oesophagus is compared with that of normal oesophagus. An intensified pressure is obtained in the presence of tumor. The interruption while swallowing through benign oesophageal tumor is confirmed by an abrupt pressure rise across the tumor's width. Tumor position also plays a significant role whether it is at contraction or relaxation of walls. Additionally, wall-shear-stress, volumetric flow rate and streamlines have also been described and compared with that without tumor growth. The expressions corresponding to all the physical quantities are computed numerically. Further, this model may also be implemented to the two-dimensional channel flow for an industrial application.

Keywords: Benign tumor; Dysphagia; Epigastric; Leiomyoma; Peristalsis; Progressive transversal wave.