My current research in Applied Mathematics is focused on modeling and understanding certain bio-chemical processes inherent to the disease atherosclerosis. Cardiovascular disease continues to be the primary cause of adult mortality in the US (and most of the West), and mathematical modeling is another tool we have in our quest to understand and combat disease. My work is primarily concerned with the effect of lipoprotein deposits (both LDL and HDL cholesterol) within the arterial wall on the function of certain immune cells (macrophages) and the role of these immune cells in initiation and progression of disease.
Prior to 2006, my research was at the intersection of chemical engineering and applied mathematics. The focus of that research was on the process of polymerization by self propagating high temperature reaction waves. As with my work in mathematical medicine, the kinetics involved give rise to primarily parabolic differential equations (reaction-diffusion). I found that solutions, defined by families of integral equations, could be used to determine whether a reaction would initiate or not.
- Frontal Polymerization
- Integral Equations
- Mathematical Biology
- Cardiovascular disease