Uncertainty Quantification of Cardiac Properties | 81 INTRODUCTION Computational models of the cardiovascular system are widely used to simulate cardiac (dys) function and related clinical application of therapies for cardiac disease.1. Various attempts to generate a digital twin of the human heart have been made.2 Previously, we proposed a framework to create a digital twin3 for quantification of the disease substrate underlying abnormal tissue deformation in patients with arrhythmogenic cardiomyopathy (AC).4 Inheritable AC primarily affects the right ventricle (RV) and predisposes to ventricular arrhythmias and sudden cardiac death in young individuals.5,6 Therefore, early disease detection is important. We previously determined an in silico disease substrate with decreased regional RV contractility and compliance, with the potential to predict disease progression on a patientspecific level.4 This method was, however, not able to include uncertainty present in both measurement and model. Uncertainty will inevitably play a role in comparing estimated properties and thus Bayesian inference methods should be used to estimate the posterior distribution of model parameters, rather than only providing point estimates. Cardiovascular computational models are in general complex, meaning that the posterior distribution cannot be calculated analytically. Various techniques have been proposed to solve this problem, in which Markov chain Monte Carlo (MCMC) methods are often used.7–9 Adaptive multiple importance sampling (AMIS) is an important alternative to MCMC since it enables estimation of the posterior distribution in a model with a relatively high number of input parameters.10,11 In this study, we apply AMIS to quantify parameter uncertainties in digital twins based on echocardiographic deformation imaging. We validate the methodology based on both in silico generated virtual data and datasets obtained from patients with AC and mutation positive family-members at risk of developing the disease. Furthermore, we use longitudinal series of echocardiograms in two AC patients to validate clinical applicability of this methodology. MATERIALS AND METHODS This section and Figure 1 elucidate the methodology used to estimate parameters and related uncertainties using the CircAdapt model. First, we elaborate the mathematical basis and implementation of AMIS, which is generally applicable. Secondly, we describe the mathematical problem and introduce the included clinical measurements and the computational model used for the likelihood function. Finally, we explain the simulation protocol. The source code as well as the virtual patient datasets are available. 5
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