The investigator and his colleagues construct and analyze minimal mathematical models of gamma (30-80 Hz) oscillations in the hippocampus and neocortex. The model networks are composed of synaptically coupled excitatory and inhibitory (single- or multi-compartment) integrate-and-fire neurons. A major aim of the project is a deeper understanding of the persistent gamma oscillations observed in vitro by Eberhard Buhl, Miles Whittington, et al., and computationally simulated, using complex, biophysically realistic models, by Roger Traub et al. The greater simplicity of the models in the present study permits much more extensive computational experimentation, as well as the mathematical analysis of the characteristics of the oscillations. Tools from stochastic dynamics (noise-driven excitable systems) and probability (order statistics) are used in this analysis. The investigator also studies hypothetical roles of gamma oscillations in attentional processes. In this part of the project, the working hypotheses are: 1. Widespread, persistent gamma oscillations with infrequent, irregular participation of individual excitatory cells are a correlate of sustained attention. 2. Ensemble-specific, transient gamma oscillations with frequent participation of individual cells are a correlate of focused attention. Computational simulation and mathematical analysis are used to examine hypothetical functional roles of persistent gamma oscillations in sustained attention (vigilance), and interactions of ensemble-specific transient gamma oscillations with a background of widespread persistent gamma oscillations.
Strong experimental evidence has shown a correlation between attention and gamma frequency oscillations in the brain. However, it is not known how (or even whether) gamma oscillations support attentional processes. This project aims at clarifying this link using mathematical modeling, analysis, and computational simulation. Some experimental studies have indicated abnormalities in gamma frequency oscillations in the brains of patients with schizophrenia or Alzheimer's disease. A deeper understanding of gamma oscillations and their roles in attention may therefore eventually prove important in understanding and treating these diseases. The project also provides training opportunities for undergraduate and graduate students.
