Practical Identifiability and Uncertainty Quantification of a Pulsatile Cardiovascular Model

Mathematical models of the circulation continue to be an essential tool to study how the cardiovascular (CV) system maintains homeostasis. The utility of these models is ultimately limited by how much we can trust the accuracy of their predictions. The predictive capability of a model can be measured by uncertainty quantification (UQ). A challenge in implementing UQ procedures is that many published methods require that the model be identifiable. An identifiable model is one with a one-to-one mapping from the parameter space to the model output. In this paper we use a novel and reproducible methodology to calibrate a lumped-parameter CV model to left ventricular pressure and volume time series data from rats. Key steps in our methodology include using (1) literature and available data to define a set of nominal parameter values specific to each rat; (2) sensitivity analysis and subset selection to determine a set of identifiable parameters; (3) optimization to find a point estimate for identifiable parameters; and (4) both frequentist and Bayesian UQ methods to assess the predictive capability of the model.