Quantifying the uncertainty in model parameters using Gaussian process-based Markov chain Monte Carlo in cardiac electrophysiology.
Quantifying the uncertainty in model parameters using Gaussian process-based Markov chain Monte Carlo in cardiac electrophysiology.
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DOI：
10.1016/j.media.2018.05.007
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发表时间：
2018-08
影响因子：
10.9
通讯作者：
Wang L
中科院分区：
文献类型：
--
作者：
Dhamala J;Arevalo HJ;Sapp J;Horácek BM;Wu KC;Trayanova NA;Wang L
模型个性化需要从间接和稀疏的测量数据中以模型参数的形式估计患者特定的组织属性。此外，需要参数空间的低维表示，这通常具有揭示潜在组织异质性的有限能力。因此，很大的不确定性可能与模型参数的估计值有关，如果不量化，将导致模型输出的未知变异性，这将阻碍其可靠的临床采用。然而，模型参数的概率估计仍然是一个悬而未决的挑战。参数的后验分布函数(PDF)的直接马尔可夫链蒙特卡罗(MCMC)采样是不可行的，因为它涉及对计算昂贵的模拟模型的重复评估。为了加速这一推断，一种流行的方法是构造一个计算高效的代理并根据该近似进行样本。然而，通过从近似抽样，以牺牲抽样精度为代价来获得效率。在本文中，我们通过将后验pdf的代理建模与加速后验pdf的Metropolis-Hastings(MH)采样相结合来解决这个问题。它由两个主要部分实现：1)通过主动选择训练点来构造精确的后验概率PDF的高斯过程(GP)代理，该训练点允许良好的全局逼近精度，并集中在后验概率较高的区域；以及2)在MH采样中使用GP代理来改进建议分布，以提高接受率。在合成数据实验和真实数据实验中，该框架对心脏电生理模型的局部组织兴奋性进行了评估。此外，还解释了模型参数的后验分布与引起参数不确定性的因素的关系，包括参数空间的不同低维表示、参数不可辨识性和参数相关性。
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.
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