The importance of an inter-compartmental delay in a model for human gastric acid secretion

In this work we re-examine an existing model of gastric acid secretion. The model is a 2-compartment model of the human stomach accounting for regions where relevant cells (D, G, ECL and parietal cells) and proteins and acid they secrete (somatostatin, gastrin, histamine, and gastric acid, respectively) are found. These proteins compose a positive and negative feedback system that controls the secretion of gastric acid by parietal cells. The original model consists of 18 ordinary differential equations and yields a stable 3-period limit cycle solution. We modify the existing model by introducing a delay into the system and assuming that the cell populations are in steady state over a short-time window (<300 h) and are able to reduce the system to an 8-equation delay differential equation model. In addition to demonstrating congruency between the two models, we also show that a similar stability is only reproducible when the delay in gastrin transport is approximately 30 min. This suggests that gastric acid secretion homeostasis likely depends strongly on the delay in gastrin transport from the antrum to the corpus.