CAREER: Enabling Efficient Non-Linearities in Biomechanical Simulations

在任何复杂的生物力学模拟中，都存在大量的非线性。当人的手折叠成拳头时，非线性接触和物质力会产生特有的凸起和折叠。当红细胞挤入毛细血管时，平流和接触的非线性会导致它们碰撞和旋转。这些基本动力学也是模拟中的主要计算挑战。本项目研究这些和其他生物力学非线性的有效模拟。它专门研究投影物理方法，也被称为模型简化方法，众所周知，这些方法可以将模拟速度加快数个数量级，但也存在纳入任意非线性的困难。研究小组探索了各种有前景的方法，包括多维立方体、指数积分器和向量分割。源代码通常会发布到公共领域。该项目由两个主要应用程序驱动。第一种是高质量的虚拟人，可以用于手术模拟和培训，以及视觉媒体。第二种是模拟血液流动中的柔性微粒，帮助设计有效的形状，将辐射有效载荷输送到癌症部位。这项研究的可视化结果对非专业人士来说是高度可访问的，因此它们被打包成一个公开可用的应用程序，用于吸引本科生研究人员，并在高中推广期间使用，以鼓励参与科学和工程领域。

Non-linearities abound in any complex biomechanical simulation. As a human hand folds into a fist, non-linear contact and material forces give rise to characteristic bulges and folds. As red blood cells crowd down a capillary, advection and contact non-linearities cause them to bump and twirl. These essential dynamics are also the main computational challenges in a simulation.This project investigates the efficient simulation of these and other biomechanical non-linearities. It specifically investigates projected physics methods, also known as model reduction methods, which have been known to accelerate simulations by multiple orders of magnitude, but also have trouble incorporating arbitrary non-linearities. The research team explores a variety of promising approaches, including multidimensional cubature, exponential integrators, and vector partitioning. Source code is routinely released into the public domain.The project is driven by two main applications. The first is high-quality, virtual humans, which can be used in surgical simulation and training, as well as visual media. The second is simulating flexible micro-particles in blood flow, which assists in designing effective shapes that deliver radiation payloads to cancer sites. The visual results of this research are highly accessible to non-specialists, so they are packaged into a publicly available app that is used to engage undergraduate researchers, and used during high school outreach to encourage involvement in science and engineering.