Mathematical Modeling of Gastric Slow Waves During Electrical Field Stimulation.

While neural modulation has been trialed as a therapy for functional gastric motility disorders, a computational model that guides stimulation protocol does not exist. In this work, a mathematical model of gastric slow wave activity, which incorporates the effects of neurotransmitter release during electrical field stimulation (EFS), was developed. Slow wave frequency responses due to the release of acetylcholine and slow wave amplitude responses due to the release of nitric oxide were modeled. The model was calibrated using experimental data from literature. A sensitivity analysis was conducted, which showed that the model yielded stable, periodic solutions for EFS frequencies in the range 0-20 Hz. A 25% increase in the input parameter (EFS frequency) from 5 Hz to 6.25 Hz resulted in a 5.2% increase in slow wave frequency and a 3.2 % decrease in slow wave amplitude. Simulated EFS showed that, for stimulation at 15 Hz, with blocking of the nitrergic neurotransmitter pathway the slow wave increased from the no stimulation scenario in frequency by only 2.4x compared to 2.7x when the nitrergic pathway was not blocked. A 21 % reduction in slow wave amplitude occurred when the cholinergic pathway was blocked, compared to a 46% reduction when no neurotransmitter pathways were blocked. Clinical relevance - This mathematical model is a step towards successful computational modeling of the effects ther-apeutic neural stimulation on the stomach. The model is also a tool for understanding of the physiology of neural stimulation.