Methods for Building and Validating Equations for Physiology-Based Mathematical Models

Abstract

Objectives. Describe steps for deriving and validating equations for physiology processes for use in mathematical models. Illustrate the steps using glucose metabolism and Type 2 diabetes in the Archimedes model. Methods and Results. The steps are as follows: identify relevant variables, describe their relationships, identify data sources that relate the variables, correct for biases in data sources, use curve fitting algorithms to estimate equations, validate the accuracy of curve fitting against empirical data, perform partially and fully independent external validations, examine any discrepancies to determine causes and make corrections, and periodically update and revalidate equations as necessary. Specific methods depend on the available data. Specific data sources and methods are illustrated for equations that represent the cause of Type 2 diabetes and its effect on fasting plasma glucose in the Archimedes model. Methods for validating the equations are illustrated. Applications enabled by including physiological equations in healthcare models are discussed. Conclusions. The methods can be used to derive equations that represent the relationships between physiological variables and the causes of diseases and that validate well against empirical data.