Interactive simulation of the human body is a crucial issue in medical computer sciences. There are many approaches to reach this goal. Reducing the computation time is the leitmotiv of a large number of efforts in recent years. For researches which use physical models derived from continuum mechanics for the simulation of deformable objects, it is primarily the internal forces and their derivatives which are the subject of study for improving computation time.

We chose to develop the Tensor Mass Method, a physical model often used for its good computation time vs accuracy trade-off. Our first contribution is the use of computer algebra to generate the internal forces and their derivatives. Our second contribution is the parallelization of this physical model by computing the generated equations on the GPU. Our third contribution is an extension of this physical model to other elements: triangle, quandrangle, hexahedron, prism and pyramid.

Considering deformations to use the most effective constitutive law in terms of computation time whenever possible is a good strategy that we started developing. In the same idea, we take the geometry of the simulated model into account to introduce more complex elements, albeit in reduced numbers. To use these strategies, we have developed mixed models in constitutive laws and elements. Our research was performed in the framework of the ETOILE project, to develop a biomechanical model of the respiratory system.

Keywords:

Tensor Mass Method, interactive simulation, phyiscal model, constituive law, element, mixed model, GPU, parallelization, respiratory system