Coveney Sam, Clayton Richard H
Insigneo Institute for in-silico Medicine and Department of Computer Science, University of Sheffield, Sheffield, United Kingdom.
Front Physiol. 2020 Apr 23;11:364. doi: 10.3389/fphys.2020.00364. eCollection 2020.
Biophysically detailed cardiac cell models reconstruct the action potential and calcium dynamics of cardiac myocytes. They aim to capture the biophysics of current flow through ion channels, pumps, and exchangers in the cell membrane, and are highly detailed. However, the relationship between model parameters and model outputs is difficult to establish because the models are both complex and non-linear. The consequences of uncertainty and variability in model parameters are therefore difficult to determine without undertaking large numbers of model evaluations. The aim of the present study was to demonstrate how sensitivity and uncertainty analysis using Gaussian process emulators can be used for a systematic and quantitive analysis of biophysically detailed cardiac cell models. We selected the Courtemanche and Maleckar models of the human atrial action potential for analysis because these models describe a similar set of currents, with different formulations. In our approach Gaussian processes emulate the main features of the action potential and calcium transient. The emulators were trained with a set of design data comprising samples from parameter space and corresponding model outputs, initially obtained from 300 model evaluations. Variance based sensitivity indices were calculated using the emulators, and first order and total effect indices were calculated for each combination of parameter and output. The differences between the first order and total effect indices indicated that the effect of interactions between parameters was small. A second set of emulators were then trained using a new set of design data with a subset of the model parameters with a sensitivity index of more than 0.1 (10%). This second stage analysis enabled comparison of mechanisms in the two models. The second stage sensitivity indices enabled the relationship between the L-type current and the action potential plateau to be quantified in each model. Our quantitative analysis predicted that changes in maximum conductance of the ultra-rapid channel would have opposite effects on action potential duration in the two models, and this prediction was confirmed by additional simulations. This study has demonstrated that Gaussian process emulators are an effective tool for sensitivity and uncertainty analysis of biophysically detailed cardiac cell models.
生物物理详细的心脏细胞模型重建了心肌细胞的动作电位和钙动力学。它们旨在捕捉电流通过细胞膜中的离子通道、泵和交换器的生物物理学，并且非常详细。然而，由于模型既复杂又非线性，因此难以建立模型参数与模型输出之间的关系。因此，如果不进行大量的模型评估，就很难确定模型参数不确定性和变异性的后果。本研究的目的是证明如何使用高斯过程模拟器进行敏感性和不确定性分析，以对生物物理详细的心脏细胞模型进行系统和定量分析。我们选择了人类心房动作电位的Courtemanche和Maleckar模型进行分析，因为这些模型描述了一组相似的电流，但公式不同。在我们的方法中，高斯过程模拟了动作电位和钙瞬变的主要特征。模拟器使用一组设计数据进行训练，该数据包括来自参数空间的样本和相应的模型输出，最初从300次模型评估中获得。使用模拟器计算基于方差的敏感性指数，并针对参数和输出的每种组合计算一阶和总效应指数。一阶和总效应指数之间的差异表明参数之间相互作用的影响很小。然后使用一组新的设计数据对第二组模拟器进行训练，该数据包含敏感性指数大于0.1（10%）的模型参数子集。第二阶段分析能够比较两个模型中的机制。第二阶段敏感性指数能够量化每个模型中L型电流与动作电位平台期之间的关系。我们的定量分析预测，超快速通道最大电导的变化将对两个模型中的动作电位持续时间产生相反的影响，并且这一预测通过额外的模拟得到了证实。这项研究表明，高斯过程模拟器是对生物物理详细的心脏细胞模型进行敏感性和不确定性分析的有效工具。
