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

TL;DR

This paper introduces a novel method combining polynomial chaos expansions and dimension reduction to assess parameter identifiability and sensitivity in complex biomedical PDE models, improving model calibration and experimental design.

Contribution

It develops a new approach using PCEs for sensitivity analysis and formal identifiability assessment in PDE-based biomedical models, addressing limitations of heuristic methods.

Findings

Efficient quantification of time-series sensitivity in pulmonary hemodynamics models.

Formal assessment of parameter identifiability using profile-likelihood confidence intervals.

Demonstrates how experimental design modifications enhance parameter identifiability.

Abstract

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 profile-likelihood confidence intervals to formally assess parameter identifiability, 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.