Dear Colleagues,

We continue our COLLOQUIUM.

Yongzhi Xu,

University of Tennessee at Chattanooga

Tuesday, February 11, Metro 161, 2:00pm.

Free Boundary Problem Model of Ductal carcinoma in situ

Abstract. In this talk we will present analytical and numerical results
of our ongoing research in mathematical modeling of Ductal carcinoma in
situ (DCIS).

DCIS refers to a specific diagnosis of breast cancer that is isolated
within the breast duct, and has not spread to other parts of the
breast. In a recent talk Mary Edgerton of Vanderbilt University
described two special patterns  found in DCIS: one lining up like baby
trees and one spreading out evenly. We modify  a model proposed by Byrne
and Chaplain  for the growth of a tumor  consisting of live  cells
(nonnecrotic tumor) to describe the homogeneous growth inside a rigid
cylinder, a model mimicking the growth of a ductal carcinoma. The model
is in the  form of a free  boundary problem. The analysis of stationary
solutions of the problem shows  that this model has five tumor patterns
that mimic some typical patterns of DCIS, including the types described
by Edgerton. The analysis shows that there may be two other kinds of
patterns that resemble the non-growing tumor. We also show for the solid
DCIS case (one-dimensional case) that the stationary solution is
unstable.

This talk presents a typical example of mathematical modeling, analysis
and computational bio-engineering. Students with basic calculus will be
able to understand the problem, the ideas and the computational results,
though some mathematical analysis may require knowledges of
multivariable calculus (Math 255), differential equations (Math 245) and
more advanced mathematics.