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

• Published in: Medical image analysis 2018-08, Vol.48, p.43-57
• Main Authors: Dhamala, Jwala, Arevalo, Hermenegild J., Sapp, John, Horácek, B. Milan, Wu, Katherine C., Trayanova, Natalia A., Wang, Linwei
• Format: Article
• Language: English
• Subjects: Acceptance; Accuracy; Algorithms; Approximation; Cardiac Catheterization; Cardiac electrophysiology; Computer Simulation; Conditional probability; Data processing; Distribution functions; Electrocardiography; Electrophysiologic Techniques, Cardiac; Electrophysiology; Excitability; Gaussian process; Heart; Heterogeneity; Humans; Image Interpretation, Computer-Assisted - methods; Image processing systems; Magnetic Resonance Imaging; Markov chain Monte Carlo; Markov Chains; Medical imaging; Models, Cardiovascular; Monte Carlo Method; Monte Carlo simulation; Myocardial Infarction - diagnostic imaging; Normal distribution; Parameter estimation; Parameter identification; Parameter uncertainty; Probabilistic local parameter estimation; Process parameters; Representations; Sampling; Statistical analysis; Tomography, X-Ray Computed; Uncertainty; Uncertainty quantification
• ISSN: 1361-8415; 1361-8423
• DOI: 10.1016/j.media.2018.05.007

•A framework to quantify the uncertainty in estimated values of model parameters.•Active construction of Gaussian process surrogate of the posterior distribution.•Accelerated Metropolis-Hastings sampling by using the Gaussian process surrogate.•Studies on estimating tissue excitability in cardiac electrophysiological model.•Posterior distribution shows non-identifiability and correlation among parameters. 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, pa