School of Mathematics and Statistics, University of Glasgow, Glasgow, UK.
Biomech Model Mechanobiol. 2022 Jun;21(3):953-982. doi: 10.1007/s10237-022-01571-8. Epub 2022 Apr 4.
Personalized computational cardiac models are considered to be a unique and powerful tool in modern cardiology, integrating the knowledge of physiology, pathology and fundamental laws of mechanics in one framework. They have the potential to improve risk prediction in cardiac patients and assist in the development of new treatments. However, in order to use these models for clinical decision support, it is important that both the impact of model parameter perturbations on the predicted quantities of interest as well as the uncertainty of parameter estimation are properly quantified, where the first task is a priori in nature (meaning independent of any specific clinical data), while the second task is carried out a posteriori (meaning after specific clinical data have been obtained). The present study addresses these challenges for a widely used constitutive law of passive myocardium (the Holzapfel-Ogden model), using global sensitivity analysis (SA) to address the first challenge, and inverse-uncertainty quantification (I-UQ) for the second challenge. The SA is carried out on a range of different input parameters to a left ventricle (LV) model, making use of computationally efficient Gaussian process (GP) surrogate models in place of the numerical forward simulator. The results of the SA are then used to inform a low-order reparametrization of the constitutive law for passive myocardium under consideration. The quality of this parameterization in the context of an inverse problem having observed noisy experimental data is then quantified with an I-UQ study, which again makes use of GP surrogate models. The I-UQ is carried out in a Bayesian manner using Markov Chain Monte Carlo, which allows for full uncertainty quantification of the material parameter estimates. Our study reveals insights into the relation between SA and I-UQ, elucidates the dependence of parameter sensitivity and estimation uncertainty on external factors, like LV cavity pressure, and sheds new light on cardio-mechanic model formulation, with particular focus on the Holzapfel-Ogden myocardial model.
个体化计算心脏模型被认为是现代心脏病学中的一种独特而强大的工具，它将生理学、病理学和力学基本定律的知识集成在一个框架中。它们有可能改善心脏病人的风险预测，并有助于开发新的治疗方法。然而，为了将这些模型用于临床决策支持，重要的是要正确量化模型参数摄动对预测感兴趣量的影响以及参数估计的不确定性，其中第一项任务是先验的（即独立于任何特定的临床数据），而第二项任务是后验的（即在获得特定的临床数据之后）。本研究针对一种广泛使用的被动心肌本构模型（ Holzapfel-Ogden 模型）来解决这些挑战，使用全局敏感性分析（SA）来解决第一个挑战，并使用逆不确定性量化（I-UQ）来解决第二个挑战。SA 是在一系列不同的左心室（LV）模型输入参数上进行的，利用计算效率高的高斯过程（GP）代理模型来代替数值正向模拟器。然后，将 SA 的结果用于为所考虑的被动心肌本构模型进行低阶重新参数化。在具有观察到的噪声实验数据的逆问题的上下文中，然后使用 I-UQ 研究来量化这种参数化的质量，该研究再次使用 GP 代理模型。I-UQ 以贝叶斯方式使用马尔可夫链蒙特卡罗（MCMC）进行，这允许对材料参数估计进行全面的不确定性量化。我们的研究揭示了 SA 和 I-UQ 之间的关系，阐明了参数敏感性和估计不确定性对外部因素（如 LV 腔压力）的依赖关系，并为心脏力学模型的制定提供了新的视角，特别关注 Holzapfel-Ogden 心肌模型。
