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估计大脑撞击引起的反应的有前途的工具，因此在预测创伤性脑损伤中发挥着重要作用。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）通常与显着的不确定性和可变性相关。因此，不确定性量化 (UQ) 涉及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变得至关重要。现代生物逼真头部模型模拟与非常高的计算成本和高维输入和输出相关，这限制了传统 UQ 方法在这些系统上的适用性。在本研究中，为计算头模型的 UQ 提出了一个两阶段、数据驱动的流形学习框架。该框架在 2D 特定主题头部模型上进行了演示，其目标是在给定不同大脑子结构（即输入）材料特性的可变性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，基于多维高斯核密度估计和扩散图的数据驱动方法用于直接从可用数据生成输入随机向量的实现。少量实现的计算模拟为第二阶段训练数据驱动的代理模型提供输入输出对。代理模型采用使用格拉斯曼扩散图的非线性降维、高斯过程回归以在输入随机向量和缩减解空间之间创建低成本映射，以及用于在缩减空间和格拉斯曼流形之间映射的几何调和模型。事实证明，替代模型提供了计算模型的高精度近似，同时显着降低了计算成本。代理模型的蒙特卡罗模拟用于不确定性传播。应变场的 UQ 突出了模型不确定性的显着空间变化，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。