Uncertainty Quantification of Cardiac Properties | 95 In this study, we chose importance sampling because it is highly effective for complex high-dimensional models.11 The computational cost of our model was approximately 1000 times higher compared to the calculation of the probability density of a sample drawn from the proposal distribution. Therefore, AMIS was the most suitable variant to optimally reuse all samples.10 Efficiency of AMIS heavily depends on the definition of the proposal distribution.11 A wider proposal distribution ensures to visit the full input space of interest, but is accompanied by a risk of non- converging estimations due to the high number of samples with a low sample weight. On the other hand, a more narrowed search has the risk of finding a local minimum in which the wrong posterior is estimated, or the risk of collapsing when the weight of the found minimum drops to zero. As the number of samples goes to infinity, the sample weight will be equally distributed. However, for the limited number of samples drawn, an optimal balance should be found. We successfully implemented annealed adaptive importance sampling to prevent the model from premature convergence while still being able to narrow the proposal distribution in the later iterations. More research should go into defining the proposal distribution or the initial proposal distribution. In this study, it took approximately 16h per dataset to converge. This time includes generating the proposal distributions, generating samples, running simulations, obtaining the likelihood function, and calculating the sample weights. The total duration mainly depends on the duration of each individual simulation, since the number of iterations in the estimations was equal or close to 500. The duration of each simulation depended on heart rate, numerical stability, and number of beats needed to get a hemodynamically stable solution. Computational time can be reduced in future studies, since AMIS allows parallel calculation of simulations. This reduction in computational time will be essential for clinical application of our method on a larger scale. Uncertainty Quantification in Arrhythmogenic Cardiomyopathy Cardiovascular models are, in general, complex models with a multitude of parameters. To create digital twins with the CircAdapt model, we used a parameter subset that we determined in a previous study.3 This subset includes model parameters related to regional RV contractile function, compliance, and activation delay. This is in line with functional and structural myocardial changes found in AC patients (e.g. fibro-fatty replacement of myocytes6, altered calcium handling34, and fibrosis35) and early generic simulation based hypotheses36. These structural changes might cause abnormal electrical activation observed in patients with AC.37 The RV tissue properties are useful to quantify the substrate, however, the model cannot distinguish the cellular origin of the substrate. The likelihood function was based on our prior knowledge of the pathology. It is not trivial how to include this information as the amount of uncertainty and its dependencies is not known but heavily affects the posterior distribution. In this study, we limited the objectives in the likelihood function to only that information in the longitudinal study that our model can simulate realistically. The main contributor is regional RV strain, as regional deformation abnormalities are found in early stages of the disease.36,38–42 LV strain, RVD, LV EF, and LV EDV are included in the likelihood to personalize geometric properties of the model. Because of the complex geometry of the thin-walled RV, our 2D imaging methods did not provide a comprehensive measure of RV size and wall thickness. In future studies, 3D imaging methods might provide a more comprehensive inclusion of geometric variability of the RV. The RVD 5
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