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.

    Breast Cancer Modeling

The breast cancer model is a detailed, continuous time, mathematical model of breast cancer incidence; tumor growth, detection, and spread; survival; and health care processes associated with breast cancer. The model is built primarily using the SEER database and the literature, and is validated against SEER, the Cancer Prevention Study II Nutrition cohort, and the Breast Cancer Surveillance Consortium data. 

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.

    Bladder Cancer Modeling

Bladder cancer, the fourth and eighth most common cancer in men and women, respectively, boasts the largest lifetime per patient treatment costs of any cancer. Currently, I am implementing the first bladder cancer treatment model which describes disease recurrence, progression/worsening, treatments and surveillance. This model will be used to investigate and compare different treatment modalities and surveillance protocols.

    Diabetes Modeling

The type 1 and type 2 diabetes models form one of the core components of the Archimedes model. A a member of the diabetes team, I conducted simulation studies of cardiovascular outcomes for diabetic populations; built a new model of glitazones, a class of medications used to treat type 2 diabetes mellitus; and validated the nephropathy (kidney) complications model.

Postdoctoral Research

  Ions at the liquid-vapor interface

My postdoctoral research investigated the role of ions in heterogeneous environments. Conventional theories for ion solvation predict no ion population at the liquid-vapor interface. This prediction is largely based on electrostatic arguments within dielectric continuum theory and macroscopic surface tension measurements of liquid-vapor interfaces. Yet recent experimental and computational results provide contradictory evidence to conventional theories, highlighting our lack of understanding of ion solvation at interfaces. These studies include second order spectroscopic experiments, e.g., SFG and SHG studies, and molecular dynamics simulations of slabs of aqueous salt solutions. 

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.

    Sum frequency generation spectroscopy

Sum frequency generation (SFG) spectroscopy is emerging as an important tool for studying the molecular structure of interfacial environments. SFG is a second order optical technique, forbidden in bulk media, and thus specific to interfacial signals. Some interpretations of SFG spectra have led to the suggestion of different populations of hydrogen bonding configurations in water. Yet recent findings have concluded that such a multi-state classification is inappropriate, favoring instead a more continuous view of intermolecular arrangements at the interface. Using a set of a simplifying approximations for studying SFG signals based on the proportionality between the hydroxyl stretching frequencies and a specific component of the electric field, I described the nature of water molecule arrangements at the interface. The results of this work can be found on the 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.