Research at Archimedes The Archimedes Model is a full-scale simulation model of human physiology, diseases, behaviors, interventions, and healthcare systems. These components, expressed as mathematical equations and algorithms, work together to represent real people in real health care systems. Read more. My current responsibilities include the breast cancer and bladder cancer models. I have also worked on the diabetes model, including nephropathy complications and diabetes interventions. Recently, I used the model was used to perform a cost-effectiveness study of the chemopreventive use of tamoxifen, resulting in a reversal of previous findings. See the press release, or go to the paper on my publications page. My current focus is building a comprehensive treatment model for early breast cancer (Stages 1, 2 and DCIS). This model will incorporate breast conserving surgery, radiation therapy, and adjuvant chemo- and endocrine (hormone) therapies with the physiology of breast cancer progression. The goals of the model include aiding clinical decision making for designing therapeutic regimens and allowing for direct comparisons between specific chemotherapy and hormone therapy agents for different patient populations.
Postdoctoral Research A number of physical features may contribute to charged solutes preferring the interface to the bulk solvent in molecular dynamics simulations. I conducted a series of careful molecular dynamics studies of ions in water and ions in ideal polar fluids (Stockmayer fluids) in order to identify the essential physics of ion solvation. For the results of this work, please see my publications page.
Doctoral Research For my graduate work, I used a diagrammatic formulation of the kinetic theory of fluctuations in equilibrium classical fluids to develop approximations for the memory function and to calculate various time correlation functions. Developed by Hans C. Andersen, the diagrammatic theory is a formally exact renormalized kinetic theory that allows us to explicitly express memory functions and correlation functions in terms of diagrams.These diagrams are similar to those that appear in the Mayer cluster diagrams in the equilibrium theory of liquids and can be written mathematically as multidimensional integrals. Moreover, we can use a physical interpretation of the diagrams to aid our understanding of the physical properties of various approximations. Here is an example of some of the diagrams included in a representative binary collision approximation. For my thesis project, I have developed a series of approximations for the memory function for density fluctuations in atomic liquids. The system of interest is a monatomic Lennard-Jones liquid at the triple point density and a range of temperatures. All of these approximations share the central characteristic that only the physics of binary collisions are included. These binary collisions are either purely repulsive, include repulsive and attractive forces, or also include the effect of the surroundings as modeled by Krook-type collisions. For the results of this work, please see my publications. |