Accounting for approximation errors using surrogate-based parameter estimation of cardiac mechanics digital twins

BACKGROUND AND OBJECTIVE: Parameter estimation for complex physics-based cardiac models is computationally demanding. Surrogate models can be used to speed up model evaluations and improve the feasibility of estimation and uncertainty quantification. However, the use of surrogates introduces additional sources of error that, if neglected, can cause bias or overconfidence in inferences. Here, we present a general approach to account for such model errors when carrying out surrogate-based parameter estimation and uncertainty quantification. METHODS: We use the Bayesian approximation error approach to develop a general framework that systematically accounts for modelling errors and uncertainties induced from the use of a surrogate model. We detail and implement this approach for the task of estimating cardiac stiffness from in-silico 3D left ventricle passive deformation data. We use a finite element model of cardiac mechanics with a neural network-based surrogate, and compare the results with those obtained from a simple regression approach. RESULTS: We show that, despite the sophistication of the neural network, neglecting model errors in the estimation stage leads to biased and overconfident estimates. We demonstrate that our proposed framework allows for simple model-error corrections that provide substantially better inferences. We also demonstrate that our approach can decrease the required number of forward simulations and computational cost for training a neural network by augmenting a low-complexity neural network with a Bayesian approximation error model. CONCLUSIONS: We have developed a framework for augmenting surrogate models that improves inference and decreases training time. This has potential for use in the clinical estimation of cardiac stiffness as a biomarker of disease, where efficiency is required at the point of care.