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VIGRE seminar, fall 2000: Soft Tissue Modeling

Jay Walton, David Dobson
Students enrolled
Sherry O'Rourke (undergraduate bioengineering student); Michael Flanagan, Amie Moch, Haewon Nam, Christopher Romero, Stephen Shauger (graduate mathematics students); Kaibin Fu (graduate aerospace student); Rudolph Gleason, Sungsod Na, Ruchi Singhal, Katherine Smith, Paul Wells (graduate bioengineering students)
A continuation of past VIGRE courses. The topic was soft tissue modeling with two specific applications, the first being a continuation of the arterial tissue modeling and the second involving the lamina cribrosa, a soft plate like structure forming part of the optical disk. The work on the lamina cribrosa was done in collaboration with Theresa Good of the Chemical Engineering Department, who is researching glaucoma.
In particular, it is not well understood why elevated interocular pressure leads to the death of optical nerve cells since some people with elevated pressure experience no vision loss while others with normal interocular pressure suffer from glaucoma symptoms. Based upon her work on mechanically induced death of nerve cells, Good conjectured that deformation of the lamina cribrosa holds the key to understanding the progression to clinical symptoms. The idea is simple; Good showed in the lab that straining axons to a sufficient degree initiates chemical processes within the nerve cell leading to its death. Basically, nerve cells self-destruct when their axons are strained too much. In the eye, the axons from rods and cones in the retina pass out of the eye through the lamina cribrosa forming the optical nerve network going to the brain. The conjecture is that higher fluid pressure in the eye causes the lamina cribrosa to bulge outward thereby straining the axons passing through it to the point that they initiate the self-destruct processes within their associated neuron. A key element of verifying this conjecture is the ability to predict how much bulging the lamina cribrosa undergoes with increased interocular pressure. This is where the soft tissue modeling comes in. The lamina cribrosa is known to be highly anisotropic due to a dense matrix of oriented fibers forming its main structural component.
The class was divided into a group pursuing the arterial modeling and a group attempting to model the lamina cribrosa. The latter group not only had to address of problem of modeling the constitutive properties of the material, but also solve a complicated boundary value problem that attempts to capture in situ boundary conditions. In addition to the mathematics students, the arteries group had students from Humphrey's research group and the lamina cribrosa group had students from Good's research group. The students seemed to benefit from the interdisciplinary interactions. Each group had working models by the end of the semester.
Walton and Wilber (VIGRE-supported postdoc) completed their first paper on nonlinear elasticity models relevant to soft tissue which was started during past VIGRE courses on the same subject.