A Model of Gastric Mucosal pH Regulation: Extending Sensitivity Analysis Using Sobol' Indices to Understand Higher Moments

Abstract

Several recent theoretical studies have indicated that a relatively simple secretion control mechanism in the epithelial cells lining the stomach may be responsible for maintaining a neutral (healthy) pH adjacent to the stomach wall, even in the face of enormous electrodiffusive acid transport from the interior of the stomach. Subsequent work used Sobol' Indices (SIs) to quantify the degree to which this secretion mechanism is "self-regulating" i.e. the degree to which the wall pH is held neutral as mathematical parameters vary. However, questions remain regarding the nature of the control that specific parameters exert over the maintenance of a healthy stomach wall pH. Studying the sensitivity of higher moments of the statistical distribution of a model output can provide useful information, for example, how one parameter may skew the distribution towards or away from a physiologically advantageous regime. In this work, we prove a relationship between SIs and the higher moments and show how it can potentially reduce the cost of computing sensitivity of said moments. We define $\gamma$ -indices to quantify sensitivity of variance, skewness, and kurtosis to the choice of value of a parameter, and we propose an efficient strategy that uses both SIs and $\gamma$ -indices for a more comprehensive sensitivity analysis. Our analysis uncovers a control parameter which governs the "tightness of control" that the secretion mechanism exerts on wall pH. Finally, we discuss how uncertainty in this parameter can be reduced using expert information about higher moments, and speculate about the physiological advantage conferred by this control mechanism.

Keywords: Electrodiffusion; Gastric mucus; Sensitivity analysis; Sobol indices; Systems biology.