Computational Methods for Modeling Muscle Tissue
Ron Fedkiw, Stanford

We begin by discussing a novel approach to finite element simulation that allows one to model degenerate and inverted elements in a smooth fashion even under complex contact and collision scenarios. The method relies on a "polar" singular value decomposition that models potentially inverted elements in a space where the deformation gradient is diagonal. The method is quite versatile and readily extends to treat plastic flow, anisotropic constitutive models, fracture, muscles with active and passive components, etc. Next, we discuss quasistatic simulation and show that inverted elements can be handled for equilibrium problems as well - since our method allows for smooth modeling through degenerate and inverted states. In addition, we propose a new technique that enforces positive definiteness of the global stiffness matrix in an element by element fashion by considering SVD's of a block decomposition of a fourth order tensor for each element. The resulting symmetric positive definite global stiffness matrix can be dealt with via an efficient conjugate gradient iterative technique allowing us to handle rather large simulation meshes. Finally, we apply this simulation framework to facial muscle modeling using patient specific data built from MRI data and laser scans. We propose a new method that takes facial motion capture marker data and computes the solution to an inverse problem to figure out what muscle contractions and jaw articulation parameters were exercised by the subject. This has serious implications for facial surgery and other applications.    

Fedkiw received his Ph.D. in Mathematics from UCLA in 1996 and did postdoctoral studies both at UCLA in Mathematics and at Caltech in Aeronautics before joining the Stanford Computer Science Department. He was awarded a Packard Foundation Fellowship, a Presidential Early Career Award for Scientists and Engineers (PECASE), a Sloan Research Fellowship, an Office of Naval Research Young Investigator Program Award (ONR YIP), a Robert N. Noyce Family Faculty Scholarship, two distinguished teaching awards, etc. Currently he is on the editorial board of the Journal of Scientific Computing, IEEE Transactions on Visualization and Computer Graphics, and Communications in Mathematical Sciences, and he participates in the reviewing process of a number of journals and funding agencies. He has published over 55 research papers in computational physics, computer graphics and vision, as well as a book on level set methods. For the past four years, he has been a consultant with Industrial Light + Magic.