The flow of visual information from the eye (retina) to the areas of the brain (cerebral cortex) necessary for visual perception is routed through a brain structure known as the thalamus. Part of the thalamus called the lateral geniculate nucleus (LGN) serves as a "relay station" between the retina and visual cortex. Current research indicates that the LGN plays an important role in visual processing and should be thought of as a "dynamic filter" as opposed to a "relay."

Computational neuroscience research in the Smith lab focuses on the functional role of the inhibitory mechanisms of the LGN (and nearby brain areas). Of particular interest is the possibility that inhibitory neurons are involved in "filtering out" retinal information that is not required by the cerebral cortex.  After constructing a biophysically and anatomically detailed mathematical models of the important subsets of the LGN neuronal network, numerical experiments quantify the input/output properties of the simulated neural circuitry. These neuronal models are subsequently used to predict the influence of inhibitory mechanisms on the relay of retinal information to visual cortex.

Because the LGN is the most extensively studied thalamic relay nuclei, it is a good system in which to study the role of inhibition in sensory processing by thalamus. This study of a sensory thalamic relay may suggest approaches to investigating the role of the thalamus in intracortical communication, a fundamental aspect of brain function.

(see CV for reprints)

Fourier analysis of sinusoidally driven thalamocortical relay neurons and a minimal integrate-and-fire-or-burst model

I have developed a minimal model of the burst and tonic response properties of thalamocortical relay cells observed during sinusoidal current injection in a cat thalamic slice preparation. This ``integrate-and-fire-or-burst'' (IFB) neuron model is constrained using Fourier analysis of both experimental and theoretical firing patterns. The IFB model has many features in agreement with experimental observations such as 1) mixed burst and tonic responses for some stimulus parameters, 2) linearity of tonic responses, and 3) increased phase advance for the nonlinear burst responses. Characterizing the response properties of this minimal model has given insights regarding the stimulus-dependence of burst vs. tonic response mode in TC neurons [with Charles L Cox (Univ of Illinois), S. Murray Sherman (SUNY, Stony Brook) and John Rinzel (NYU)].

Spike frequency adaptation in thalamocortical relay neurons and simplified firing rate models

  With J Rinzel, CL Cox, and SM Sherman, I have developed a firing-rate description of TC cell activity that includes burst responses as well as spike-frequency adaption observed during tonic spiking. In this work I have followed XJ Wang's quantitative theory of temporal spike-frequency adaptation, originally developed for cortical pyramidal cells [J. Neurophysiol., 79(3):1549-1566, 1998]. The simplicity of such firing-rate neuron models makes them good candidates for large scale network simulations.

Mode-locking in a periodically forced integrate-and-fire-or-burst neuron model

  Here we present an exact analysis of such mode-locking in the integrate-and-fire-or-burst model under the influence of arbitrary periodic forcing that includes sinusoidally-driven responses as one case.  In this analysis, the instabilities of mode-locked states are identified as both smooth bifurcations of an associated firing time map and non-smooth bifurcations of the underlying discontinuous flow.  The explicit construction of borders in parameter space that define the instabilities of mode-locked zones is used to build up the Arnold tongue structure for the model.  The zones for mode-locking are shown to be in excellent agreement with numerical simulations and are used to explore the observed stimulus dependence of burst versus tonic response of the IFB neuron model [with S Coombes and M R Owen (both from Loughborough University)].

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