Much of my research spans topics in the general area of activity patterns in neuronal systems . I explore complex dynamics, particularly bursting, in single neuron models, as well as the interaction of intrinsic dynamics and connectivity properties in the generation of neuronal network dynamics, using tools from dynamical systems including geometric singular perturbation theory. Application areas of interest include thalamic activity in sleep, pathological oscillations in the parkinsonian basal ganglia, respiratory rhythms, and locomotor rhythms. In respiration in particular, I consider questions of how bursting emerges from coupled heterogeneous networks of neurons endowed with multiple bursting mechanisms and how this output depends on connectivity patterns among the neurons involved. These investigations are done in collaboration with several other experimentalists and computational researchers. I am also interested in optimization of inputs to elicit particular neuronal outputs, reduction of neuronal models, spike timing-dependent synaptic plasticity, and synchronization, clustering, and traveling waves in neuronal media. This work has been supported in part by the National Science Foundation under a Postdoctoral Research Fellowship and under Grants No. 0108857, 0414023, 0716936, and 1021701.
I also work on problems in inflammation and critical care medicine. This work focuses on abstracted models that capture primary responses in acute inflammation, transient dynamics relevant to the inflammatory response, multi-compartmental models for blood/tissue and organ/blood/organ iteractions, as well as questions related to the practical use of physiological models to inform the differential diagnosis process performed by physicians attending to critically ill patients with cardiovascular issues.