Upadhyay Kshitiz, Giovanis Dimitris G, Alshareef Ahmed, Knutsen Andrew K, Johnson Curtis L, Carass Aaron, Bayly Philip V, Shields Michael D, Ramesh K T
Hopkins Extreme Materials Institute, Johns Hopkins University, Baltimore, MD 21218, USA.
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA.
Comput Methods Appl Mech Eng. 2022 Aug 1;398. doi: 10.1016/j.cma.2022.115108. Epub 2022 Jun 21.
Computational models of the human head are promising tools for estimating the impact-induced response of the brain, and thus play an important role in the prediction of traumatic brain injury. The basic constituents of these models (i.e., model geometry, material properties, and boundary conditions) are often associated with significant uncertainty and variability. As a result, uncertainty quantification (UQ), which involves quantification of the effect of this uncertainty and variability on the simulated response, becomes critical to ensure reliability of model predictions. Modern biofidelic head model simulations are associated with very high computational cost and high-dimensional inputs and outputs, which limits the applicability of traditional UQ methods on these systems. In this study, a two-stage, data-driven manifold learning-based framework is proposed for UQ of computational head models. This framework is demonstrated on a 2D subject-specific head model, where the goal is to quantify uncertainty in the simulated strain fields (i.e., output), given variability in the material properties of different brain substructures (i.e., input). In the first stage, a data-driven method based on multi-dimensional Gaussian kernel-density estimation and diffusion maps is used to generate realizations of the input random vector directly from the available data. Computational simulations of a small number of realizations provide input-output pairs for training data-driven surrogate models in the second stage. The surrogate models employ nonlinear dimensionality reduction using Grassmannian diffusion maps, Gaussian process regression to create a low-cost mapping between the input random vector and the reduced solution space, and geometric harmonics models for mapping between the reduced space and the Grassmann manifold. It is demonstrated that the surrogate models provide highly accurate approximations of the computational model while significantly reducing the computational cost. Monte Carlo simulations of the surrogate models are used for uncertainty propagation. UQ of the strain fields highlights significant spatial variation in model uncertainty, and reveals key differences in uncertainty among commonly used strain-based brain injury predictor variables.
人体头部的计算模型是用于估计撞击引起的大脑反应的有前景的工具，因此在创伤性脑损伤的预测中发挥着重要作用。这些模型的基本组成部分（即模型几何形状、材料属性和边界条件）通常与显著的不确定性和变异性相关。因此，不确定性量化（UQ），即量化这种不确定性和变异性对模拟响应的影响，对于确保模型预测的可靠性至关重要。现代生物逼真的头部模型模拟具有非常高的计算成本以及高维的输入和输出，这限制了传统不确定性量化方法在这些系统上的适用性。在本研究中，提出了一种基于数据驱动的流形学习的两阶段框架用于计算头部模型的不确定性量化。该框架在一个二维特定个体头部模型上进行了演示，其目标是在不同脑亚结构的材料属性存在变异性（即输入）的情况下，量化模拟应变场（即输出）中的不确定性。在第一阶段，一种基于多维高斯核密度估计和扩散映射的数据驱动方法被用于直接从可用数据生成输入随机向量的实现。对少量实现的计算模拟提供了输入 - 输出对，用于在第二阶段训练数据驱动的替代模型。替代模型采用基于格拉斯曼扩散映射的非线性降维、高斯过程回归以在输入随机向量和降维解空间之间创建低成本映射，以及几何调和模型用于在降维空间和格拉斯曼流形之间进行映射。结果表明，替代模型在显著降低计算成本的同时，提供了计算模型的高精度近似。替代模型的蒙特卡罗模拟用于不确定性传播。应变场的不确定性量化突出了模型不确定性中的显著空间变化，并揭示了常用的基于应变的脑损伤预测变量之间不确定性的关键差异。
