Research

My group is primarily interested in theoretical and computational biomechanics. In particular, we are developing continuum and multiscale methods to understand the mechanics of biological structures from the molecular and cellular scales upward. Some of our projects are listed below.

Mechanics of viruses and macromolecular assemblies We are developing coarse-grained continuum theories and multiscale simulation methodologies to study the mechanics of macromolecules (proteins and nucleic acids) and macromolecular assemblies. The protein shells (capsids) of viruses are the main focus of our efforts.
Mechanics of biomembranes We are studying the mechanics of lipid bilayer membranes under the influence of externally applied loadings, developing models to account for "realistic" biological complexities such as mixtures of lipids, intermembrane proteins, and interaction with the cytoskeleton.
Continuum Modeling of DNA With Michael Ortiz I've developed a director field model of DNA packaging of viral capsids. Analytical and numerical optimization techniques were employed to identify energy minimizing packaged configurations of viral DNA. Check out my Ph.D. thesis
Cardiac Mechanics With HoHai Van, Stevan Dubljevic, and Alan Garfinkel from UCLA Cardiology, we are developing finite element techniques for coupling electrophysiology with the mechanics of contraction for the human heart. We are working to understand the complex dynamics of fibrilation.
Subdivision Curves and Surfaces I have worked with Gabriel Taubin on subdivision algorithms for generating 3D spline curves and subdivision surfaces based on sets of vertices with positions and normal vectors. We are developing a triangular finite element for nonlinear analysis of thin shells using position- and normal-based subdivision-surface interpolation.
Simulation of Traumatic Head Injury See Alejandro Mota's page on our simulation of fire-arm injuries.