My interests lie in the general area of mathematical and computational biology aimed particularly towards problems in neuroscience. Following lists some of my current research areas.

Dynamics of Neuronal Networks

It is known that certain modes in the firing activity of neurons in the brain are correlated with behavior and cognition. These modes include for example synchronous firing, persistent neural activity, and oscillatory activity. I am interested in understanding the cellular, synaptic and network mechanisms behind these states and how they relate to functions such as learning, memory, attention and perception. My strategy is to combine mathematical analysis of reduced models with numerical simulations of more complex but biophysically more faithful models. The biophysical models allow for a more direct comparison to experiments while the reduced models can help pinpoint the salient features responsible for the pertinent behaviors. Some of my current projects include: i) Synchronous oscillations induced by gap junctions in the Locus Coeruleus; ii) Enhanced signal propagation due to synchrony in cortex; iii) Spiking neuron models of binocular rivalry and other competitive cortical oscillations; iv) Mechanisms for persistent activity in networks of spiking neurons.

Posture Control

The human postural control system is highly evolved and complex. Even during quiet stance the body continually moves about in a stochastic manner. The mean square amplitude of the motion of the center-of-pressure under the feet exhibits motion that can be modeled with by a flexible string or polymer under tension, elastically pinned to a given location and driven by noise. Recently, we have found experimental evidence that the postural control system obeys the Fluctuation-Dissipation Theorem indicating that the system can be well described by the model we have proposed. This implies that the dynamic response to external perturbations are connected to the noisy movements. These studies could have clinical applications in assessing and characterizing an individual's ability to stand upright, both quietly and in response to external disturbances. I am currently trying to use these observations to develop measures for the early detection of neurological disorders such as Parkinson's disease from data obtained during quiet standing.

Acute Inflammation

The acute inflammatory response is a cascade of cellular and molecular events that takes place in the body after an infection or traumatic injury. This response which involves the immune and endocrine systems, aims to eliminate damaging agents and restore the body back to equilibrium. The clinical manifestation is called the systemic inflammatory response syndrome (SIRS) or sepsis in the case of infection. Sepsis is a serious health concern in the world. If unabated, it can lead to major organ failure and death. Although much has been learned in the last several years on the molecular and cellular mechanisms of sepsis, this knowledge has not translated into much improved outcome prediction or treatments. A reason may be that a good understanding of the global dynamical behavior of the acute inflammatory response remains lacking. I am currently developing computational models of the inflammatory response.