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.