Towards efficient uncertainty quantification in complex and large-scale biomechanical problems based on a Bayesian multi-fidelity scheme
Towards efficient uncertainty quantification in complex and large-scale biomechanical problems based on a Bayesian multi-fidelity scheme
复制标题
DOI：
10.1007/s10237-014-0618-0
复制
发表时间：
2015-06-01
影响因子：
3.5
通讯作者：
Wall, Wolfgang A.
中科院分区：
文献类型：
--
作者：
Biehler, Jonas;Gee, Michael W.;Wall, Wolfgang A.
在心血管过程和疾病的模拟中，患者特定的模型参数（例如本构特性）通常不容易获得。在计算评估中必须考虑这些不确定性，而不是使用群体平均值来执行“患者特定”模拟，从而忽略这些参数中存在的患者间和患者内的变化。然而，由于有限的计算资源和传统不确定性量化方法的一些缺点，建模为随机场的参数不确定性尚未在患者特异性、非线性、大规模和复杂的生物力学应用中得到考虑。因此，本研究的目的是双重的。首先，我们提出了一个基于多保真度采样和贝叶斯公式的不确定性量化框架。该方法的关键特征是能够严格利用和合并来自近似低保真度模型的信息。最重要的是，即使低保真度模型仅提供非常差的近似值，也可以准确地计算相应高保真度模型的响应统计数据。该方法仅要求低保真度模型和相应的高保真度模型共享相似的随机结构，即依赖于随机输入。这使得近似模型的选择具有极大的灵活性。该框架的灵活性和功能通过使用腹主动脉瘤的两个特定于患者的大规模非线性有限元模型进行不确定性量化来证明。动脉瘤动脉壁的一个本构参数被建模为单变量三维、非高斯随机场，从而考虑到该参数的患者间以及患者内的变化。我们使用直接蒙特卡罗来评估所提出的方法，并发现与该参考解决方案非常吻合。此外，所采用的方法大大降低了计算成本，首次使复杂的患者特异性非线性生物力学模型的不确定性量化变得实用。其次，我们还分析了输入参数的不确定性对通常与腹主动脉瘤破裂电位相关的机械量（例如 von Mises 应力、von Mises 应变和应变能）的影响。因此，由于不确定的本构参数，对这些机械量的变异性进行了初步估计，并揭示了在腹主动脉瘤的患者特异性模拟中假设群体平均平均值所造成的潜在误差。此外，在使用 MC 的参数研究中研究了随机场相关长度的影响。
In simulation of cardiovascular processes and diseases patient-specific model parameters, such as constitutive properties, are usually not easy to obtain. Instead of using population mean values to perform "patient-specific" simulations, thereby neglecting the inter- and intra-patient variations present in these parameters, these uncertainties have to be considered in the computational assessment. However, due to limited computational resources and several shortcomings of traditional uncertainty quantification approaches, parametric uncertainties, modeled as random fields, have not yet been considered in patient-specific, nonlinear, large-scale, and complex biomechanical applications. Hence, the purpose of this study is twofold. First, we present an uncertainty quantification framework based on multi-fidelity sampling and Bayesian formulations. The key feature of the presented method is the ability to rigorously exploit and incorporate information from an approximate, low fidelity model. Most importantly, response statistics of the corresponding high fidelity model can be computed accurately even if the low fidelity model provides only a very poor approximation. The approach merely requires that the low fidelity model and the corresponding high fidelity model share a similar stochastic structure, i.e., dependence on the random input. This results in a tremendous flexibility in choice of the approximate model. The flexibility and capabilities of the framework are demonstrated by performing uncertainty quantification using two patient-specific, large-scale, nonlinear finite element models of abdominal aortic aneurysms. One constitutive parameter of the aneurysmatic arterial wall is modeled as a univariate three-dimensional, non-Gaussian random field, thereby taking into account inter-patient as well as intra-patient variations of this parameter. We use direct Monte Carlo to evaluate the proposed method and found excellent agreement with this reference solution. Additionally, the employed approach results in a tremendous reduction of computational costs, rendering uncertainty quantification with complex patient-specific nonlinear biomechanical models practical for the first time. Second, we also analyze the impact of the uncertainty in the input parameter on mechanical quantities typically related to abdominal aortic aneurysm rupture potential such as von Mises stress, von Mises strain and strain energy. Thus, providing first estimates on the variability of these mechanical quantities due to an uncertain constitutive parameter, and revealing the potential error made by assuming population averaged mean values in patient-specific simulations of abdominal aortic aneurysms. Moreover, the influence of correlation length of the random field is investigated in a parameter study using MC.