A Mathematical Model for Multiphase Flow in the Antroduodenum with the Consideration of the Neurohumoral Regulation

摘要

This paper focuses on improvements made into a multiphase flow model in the antroduodenum, which was developed previously. The first phase is a multi-component liquid with components (enzymes and nutrients) dissolved at the molecular level. Food particles of different sizes were assumed as separate liquid phases. In this paper we considered the neurohumoral regulation of the digestive processes in the antroduodenal part of the digestive tract. New hormonal elements of the model were introduced: gastrin, somatostatin, motilin, secretin, and cholecystokinin. Also, the influence exerted by the central and enteric nervous systems was taken into account. Within the framework of conceptual statement of the problem we proposed a system of interrelations between components in the multiphase media and neurohumoral elements. The mathematical statement of the problem includes the mass and momentum conservation equations for phases and components, ordinary differential equations for the dynamic change in the regulation elements, and moving boundary conditions. One of the main challenges is to identify numerous parameters of the developed model. At this moment we have identified parameters which describe the rates of enzymes reactions and intensity of mass sources due to components secretion. In some scenarios of computational simulation we analyzed the influence exerted by neurohumoral disorders on the flow characteristics.