Computational models of the human head are promising tools for estimating the impact-induced response of brain, and thus play an important role in the prediction of traumatic brain injury. Modern biofidelic head model simulations are associated with very high computational cost, and high-dimensional inputs and outputs, which limits the applicability of traditional uncertainty quantification (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 strain fields highlight significant spatial variation in model uncertainty, and reveal key differences in uncertainty among commonly used strain-based brain injury predictor variables.
翻译:人类头部的计算模型是估算大脑撞击引起的反应的有希望的工具,因此在预测创伤性脑损伤方面起着重要作用。现代生物化头型模拟与非常高的计算成本和高维投入和产出相关,这限制了传统不确定性量化方法在这些系统中的适用性。在本研究中,为UQ计算头型模型提出了一个由数据驱动的双阶段多重学习框架。这个框架在2D具体主题的脑部模型上展示,该模型的目标是量化模拟变异领域(即产出)的不确定性。考虑到不同脑下层结构(即输入)的物质特性的变异性,现代生物化头型模型与高维度投入投入和产出。在第一阶段,基于多维测量的内核内核密集度估算和传播图的数据驱动方法被用来直接实现输入随机矢量模型。在第二个阶段,对模拟变异性模型(即模拟产出)的变异性进行了量化,在模拟变异性模型中将数据模型的变异性化模型(即模拟)中,在高基级的变异性演算中,在使用高基级演算模型中,在使用低的变变变后模型中,在降低空间演算中,在低的演算中进行非演算中,在降低的演算中,在降低空间演算中,在使用非演算中,在降低的演算中,在不断变变变化中,在降低空间演算中,在不断变变变变化中,在不断算中进行。