TY - JOUR
T1 - Quantifying the uncertainty in model parameters using Gaussian process-based Markov chain Monte Carlo in cardiac electrophysiology
AU - Dhamala, Jwala
AU - Arevalo, Hermenegild J.
AU - Sapp, John
AU - Horácek, B. Milan
AU - Wu, Katherine C.
AU - Trayanova, Natalia A.
AU - Wang, Linwei
N1 - Funding Information:
This work was supported by the National Science Foundation CAREER Award under Grant ACI-1350374 ; the National Institute of Heart, Lung, and Blood of the National Institutes of Health under Award R21Hl125998 ; the National Heart, Lung, and Blood Institute of the National Institutes of Health under Grant R01HL103812; and the National Institutes of Health Director's Pioneer Award under Grant DP1-HL123271.
Publisher Copyright:
© 2018 Elsevier B.V.
PY - 2018/8
Y1 - 2018/8
N2 - 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.
AB - 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.
KW - Cardiac electrophysiology
KW - Gaussian process
KW - Markov chain Monte Carlo
KW - Probabilistic local parameter estimation
KW - Uncertainty quantification
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U2 - 10.1016/j.media.2018.05.007
DO - 10.1016/j.media.2018.05.007
M3 - Article
C2 - 29843078
AN - SCOPUS:85047641088
SN - 1361-8415
VL - 48
SP - 43
EP - 57
JO - Medical image analysis
JF - Medical image analysis
ER -