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.
