CAREER: Enabling Efficient Non-Linearities in Biomechanical Simulations

在任何复杂的生物力学模拟中，非线性都比比皆是。当人手折叠成拳头时，非线性接触和物质力会产生特征性的凸起和折叠。当红细胞沿着毛细血管聚集时，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，也称为模型简化方法，已知这些方法可以将模拟加速多个数量级，但也难以纳入任意非线性。研究小组探索了各种有前途的方法，包括多维体积，指数积分器和向量分割。源代码定期发布到公共领域。该项目由两个主要应用程序驱动。首先是高质量的虚拟人，可用于手术模拟和培训以及视觉媒体。第二个是模拟血流中的柔性微粒，这有助于设计有效的形状，将辐射有效载荷传递到癌症部位。这项研究的视觉结果对非专业人士来说是非常容易获得的，因此它们被打包成一个公开的应用程序，用于吸引本科研究人员，并在高中推广期间使用，以鼓励参与科学和工程。

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.