Assessing parameter identifiability of a hemodynamics PDE model using spectral surrogates and dimension reduction

Computational inverse problems for biomedical simulators suffer from limited data and relatively high parameter dimensionality. This often requires sensitivity analysis, where parameters of the model are ranked based on their influence on the specific quantities of interest. This is especially important for simulators used to build medical digital twins, as the amount of data is typically limited. For expensive models, such as blood flow models, emulation is employed to expedite the simulation time. Parameter ranking and fixing using sensitivity analysis are often heuristic, though, and vary with the specific application or simulator used. The present study provides an innovative solution to this problem by leveraging polynomial chaos expansions (PCEs) for both multioutput global sensitivity analysis and formal parameter identifiability. For the former, we use dimension reduction to efficiently quantify time-series sensitivity of a one-dimensional pulmonary hemodynamics model. We consider both Windkessel and Structured Tree boundary conditions. We then use PCEs to construct univariate profile-likelihood confidence intervals and show how changes in experimental design improve identifiability. Our work presents a novel approach to determining parameter identifiability and leverages a common emulation strategy for enabling profile-likelihood analysis in problems governed by partial differential equations.Author summary: The calibration of biophysical models is often ill-posed, with the parameter dimensionality typically larger than available data for parameter inference. In addition, these models often employ parameters that are clinically or experimentally interpretable, hence a unique set of estimated parameters are necessary for interpreting biophysical processes. Sensitivity analysis is a necessary tool for reducing the parameter dimensionality by “fixing” noninfluential parameters, yet choosing the cutoff for parameter fixing is problem dependent. Identifiability methods like profile-likelihood are computationally expensive, and have traditionally been reserved for relatively fast simulators. We show that emulation, using polynomial chaos, provides a framework for a two-in-one analysis of model sensitivity and parameter identifiability. Using a pulmonary hemodynamics simulator, we show how this framework allows for a more formal analysis of the model and its parameters. Our approach allows us to examine how different measurement modalities affect the ability to infer biophysical parameters, and is a step forward in developing data-specific models for understanding cardiovascular disease.