Numerical modeling of acidity distribution in antroduodenum aimed at identifying anomalous zones at consuming drinks with different pH level

The article focuses on describing mathematical model of a multi-phase flow in antroduodenum and its application for predicting digestive process features, including pH level detection. The suggested sub-model representing antroduodenal area of gastrointestinal tract is being developed within the frameworks of mathematical multilevel model depicting evolution of damage to critical organs and systems under exposure to risk factors. We introduced damages as per three functions (motor, secretory and absorbing one) to several gastrointestinal tract zones (body of stomach, antrum, and duodenum) and to pancreas and liver, into the sub-model. Mathematical problem statement includes records of mass and impulse conservation equations for mixture of liquid incompressible phases; ratios for mass flow intensity vector due to diffusion processes; ratios for mass sources due to reactions, secretion and components absorption, food dissolution, initial and terminal conditions. We obtained numeric experiment results when drinks with various pH level (2.3; 3.5; 7) were consumed; they revealed that anomalous considerable increase in acidity occurred in pyloric opening zone and duodenal cap zone when a drink with pH level equal to 2.3 was consumed. The results presented in this work make a considerable contribution into mathematical modeling development used to describe multiphase flows in biological channels with variable form. We showed that obtained acidity levels in various antroduodenum zones correspond to experimental data given in the works of other researchers. In future the model can be applied to predict risks of duodenum damages evolvement together with detecting areas of their localization under exposure to negative factors.