text_figures_tables.zip from Predicting left ventricular contractile function via Gaussian process emulation in aortic-banded rats

Cardiac contraction is the result of integrated cellular, tissue and organ function. Biophysical <i>in silico</i> cardiac models offer a systematic approach for studying these multi-scale interactions. The computational cost of such models is high, due to their multi-parametric and nonlinear nature. This has so far made it difficult to perform model fitting and prevented global sensitivity analysis (GSA) studies. We propose a machine learning approach based on Gaussian process emulation of model simulations using probabilistic surrogate models, which enables model parameter inference via a Bayesian history matching (HM) technique and GSA on whole-organ mechanics. This framework is applied to model healthy and aortic-banded hypertensive rats, a commonly used animal model of heart failure disease. The obtained probabilistic surrogate models accurately predicted the left ventricular pump function (R² = 0.92 for ejection fraction). The HM technique allowed us to fit both the control and diseased virtual bi-ventricular rat heart models to magnetic resonance imaging and literature data, with model outputs from the constrained parameter space falling within 2 SD of the respective experimental values. The GSA identified Troponin C and cross-bridge kinetics as key parameters in determining both systolic and diastolic ventricular function.This article is part of the theme issue ‘Uncertainty quantification in cardiac and cardiovascular modelling and simulation’.

心脏收缩是细胞、组织与器官协同功能共同作用的结果。生物物理计算机模拟（in silico）心脏模型为研究这类多尺度相互作用提供了系统性方法。由于此类模型兼具多参数与非线性特性，其计算成本极高，这使得模型拟合难以开展，同时也阻碍了全局敏感性分析（GSA）相关研究的推进。我们提出了一种基于概率替代模型的机器学习方法，通过对模型仿真进行高斯过程仿真，可借助贝叶斯历史匹配（HM）技术实现模型参数推断，并可开展全器官力学层面的全局敏感性分析。本框架被应用于健康大鼠与主动脉结扎高血压大鼠（一类常用的心力衰竭动物模型）的建模工作。所得到的概率替代模型可精准预测左心室泵血功能（射血分数的决定系数R²=0.92）。借助HM技术，我们可将对照与患病虚拟双心室大鼠心脏模型拟合至磁共振成像与文献数据，约束参数空间下的模型输出结果均落在对应实验值的±2倍标准差范围内。全局敏感性分析结果显示，肌钙蛋白C与横桥动力学是决定心室收缩与舒张功能的关键参数。本文属于‘心脏与心血管建模及仿真中的不确定性量化’专题栏目的一部分。