Quantifying the uncertainty in model parameters using Gaussian process-based Markov chain Monte Carlo in cardiac electrophysiology

Abstract

Model personalization requires the estimation of patient-specific tissue properties in the form of model parameters from indirect and sparse measurement data. Moreover, a low-dimensional representation of the parameter space is needed, which often has a limited ability to reveal the underlying tissue heterogeneity. As a result, significant uncertainty can be associated with the estimated values of the model parameters which, if left unquantified, will lead to unknown variability in model outputs that will hinder their reliable clinical adoption. Probabilistic estimation of model parameters, however, remains an unresolved challenge. Direct Markov Chain Monte Carlo (MCMC) sampling of the posterior distribution function (pdf) of the parameters is infeasible because it involves repeated evaluations of the computationally expensive simulation model. To accelerate this inference, one popular approach is to construct a computationally efficient surrogate and sample from this approximation. However, by sampling from an approximation, efficiency is gained at the expense of sampling accuracy. In this paper, we address this issue by integrating surrogate modeling of the posterior pdf into accelerating the Metropolis-Hastings (MH) sampling of the exact posterior pdf. It is achieved by two main components: (1) construction of a Gaussian process (GP) surrogate of the exact posterior pdf by actively selecting training points that allow for a good global approximation accuracy with a focus on the regions of high posterior probability; and (2) use of the GP surrogate to improve the proposal distribution in MH sampling, in order to improve the acceptance rate. The presented framework is evaluated in its estimation of the local tissue excitability of a cardiac electrophysiological model in both synthetic data experiments and real data experiments. In addition, the obtained posterior distributions of model parameters are interpreted in relation to the factors contributing to parameter uncertainty, including different low-dimensional representations of the parameter space, parameter non-identifiability, and parameter correlations.

Deep learning-based reduced order models in cardiac electrophysiology

“…The architecture used to perform all the numerical tests is the one reported in the S2 Appendix. To solve the optimization problem (13) and (14) we use the ADAM algorithm [47] with a starting learning rate equal to η = 10 −4 . Moreover, we perform cross-validation by splitting the data in training and validation and following a proportion 8:2 and we implement an early-stopping regularization technique to reduce overfitting [44].…”

“…To evaluate the performance of the DL-ROM, we use the loss function (14) and an error indicator defined as…”

“…with ω h 2 [0, 1]. The per-example loss function (14) combines the reconstruction error (that is, the error between the FOM solution and the DL-ROM approximation) and the error between the intrinsic coordinates and the output of the encoder. The architecture of DL-ROM is the one shown in Fig 1. The encoder function is used only during the training and validation steps; it is instead discarded during the testing phase.…”

Mathematical Modeling and Characterization of the Spread of Chikungunya in Colombia

“…In particular, we use the proposed Chikungunya mathematical model to perform a fitting process to real data of Colombia. Additionally, we used bootstrapping and Markov chain Monte Carlo techniques in order to do analysis of the parameters' identifiability [34][35][36][37][38][39][40]. Finally, important policies and insights are provided that could help government health institutions in lowering the infected cases with the Chikungunya virus in Colombia.…”

Visualization of Myocardial Strain Pattern Uniqueness with Respect to Activation Time and Contractility: A Computational Study

“…However, finding the best model representation of measured values by the fitting procedure is not useful when the model is complex, nonlinear [17][18][19], and the measurement errors are large; and in STE measurements the error margins are substantial [20,21]. In general, the drawback is that there could be more than one solution to fitting, and these solutions could even have drastically different parameter sets causing system degeneracy [22][23][24].…”