This Demonstration shows the interaction between an eyeball and two of the muscles connected to it. Muscles deform as the eyeball rotates (see Details section for more information about the deformation).
Traditionally muscle deformations were modeled as a controlled solid deformation process; the calculations here are based on the finite-element method (FEM). While FEM is computationally expensive, we have developed an alternative strategy to model muscle contraction (and the interaction between the muscles and eyeball) by approximating the shape changes with a family of closed 3D parametric surfaces.
The muscle shape function is a 3D parametric surface that can be written in closed form, with parameters controlling the shapes. Each time the eyeball rotates, the shape parameters are recalculated such that:
1. The muscle will wrap over the eyeball without penetrating into it. This is achieved by creating a kidney-shaped cross section by changing the shape parameters so that the surface's radius of curvature equals the radius of the eyeball at the muscle-eyeball tangential contact.
2. The entire muscle thickens and shortens when contracted (and thins and lengthens when extended) by constraining the volume to be constant.
3. The muscle cross section is gradually transformed from a kidney shape into an ellipse moving away from the eyeball.
This Demonstration is based on my summer internship with Dr. Mike Paulin (Department of Zoology, University of Otago) in 2006.