Structural Identifiability and Indistinguishability analyses of Cardiovascular Feedback Models

In pharmaceutical safety testing, mathematical models are used to represent drug effects on hemodynamic variables such as blood pressure and heart rate. Suitably parameterized models can be used for making predictions for effects at different dose levels, or between different species, in order to minimize the amount of animal testing required. While effects on different variables are traditionally modelled separately, there is increasing interest in the use of systems pharmacology models, to represent a drug's effect on different variables, and how the variables affect each other through cardiovascular homeostasis. Increasing model complexity means a greater number of unknown parameters, leading to greater need for a priori testing of model appropriateness. Structural identifiability analysis establishes whether the unknown parameters can be identified from the experimental observations available. In this paper, four hemodynamic models are tested for structural identifiability, leading to insight on their appropriateness for different experimental conditions. Structural indistinguishability analysis between models with different effects is also performed, as a prerequisite to using models for numerically distinguishing different mechanisms of action in novel compounds.