A free boundary problem consists of a system of partial differential equations (PDEs) which
are to be solved in a domain whose boundary is unknown and has to be determined together with
a solution of the PDEs.
Biomedical examples of free boundary problems include the growth of a solid
tumor, the healing of a wound, abdominal aorta aneurysm, and granulomas in
tuberculosis and sarcoidosis. In this talk I will focus on atherosclerosis,
a disease where a plaque develops in the artery, causing potentially a
heart attack or a stroke. The risk factor for the disease depends on the
cholesterol levels of LDL and HDL (the "good" and "bad"
cholesterols). I will present a mathematical model, by a system of PDEs and
present a "risk map" which predicts whether a small plaque will
grow or shrink depending on the levels of LDL and HDL in the blood. I will
then describe rigorous mathematical results for a simplified model, and
open problems. Finally, I will briefly mention other free boundary problems
associated with biomedical processes.
Webmaster University of Houston
Last modified: April 11 2016 - 18:14:43