My research centers around increasing our understanding of the mechanisms underlying diseases. Currently, I am focusing on cardiovascular diseases, such as cardiac arrhythmias. For many cardiovascular diseases, the mechanisms underlying the pathologies seen at the organ level lie at the molecular and cellular levels. Therefore, biophysically detailed models of cardiovascular diseases are highly complicated because they must span a wide range of spatial and temporal scales. However, the disparities in spatial and temporal scales present in biophysically detailed models make such models amenable to reductions through mathematical techniques. In my work, I use a combination of biophysically detailed and idealized, reduced models to uncover the key cellular processes and conditions underlying disease states.
In my research, I frequently mathematical techniques such as singular perturbation analysis, analysis based on dynamical systems theory, and numerical simulations of differential equations.