Bressloff Research Group
Keener Research Group

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Oral Document: This comprises the plan of work submitted to my thesis committee on November 19, 2007.
Oral Presentation: These are the slides that accompanied my presentation, made with the LaTeX beamer class.

Traveling Pulses in Inhomogeneous Neural Media

When the synaptic weight between neurons in a neural field model is periodically modulated as a means of representing long-range connections of visual cortex, one finds that the overall wavespeed of traveling pulses decreases. As pictured in the above figure, we see that as the period of this modulation increases, wavespeed decreases, as is the same for increasing the amplitude of modulation. The bounds given in the right panel represent the wavespeed of pulses in a homogeneous network with the maximum and minimum weights of the periodically modulated weight.

Aside from slowing the wave and even causing wave propagation failure, inhomogeneous synaptic weights change the profile of the "traveling pulse" so that it is no longer invariant. We now see rippled or multibump solutions whose envelope propagates by the formation of a new bump at the leading edge and the death of a bump at the trailing edge. [Click on the figures below to see the associated movie]

ZP Kilpatrick, SE Folias, and PC Bressloff. Traveling Pulses and Wave Propagation Failure in Inhomogeneous Neural Media. SIAM J. Appl. Dyn. Syst., 7 (2008), pp. 161-185.

Contour Grouping
When a subject attends to a contour in their visual field, recordings from primary visual cortex show that neurons whose receptive fields contain the contour increase their firing rate. Thus, elevated firing rate may be a neural substrate for the conscious perception of a contiguous object. We analyze this phenomenon using a coupled hypercolumn model of visual cortex wherein discrete areas of cortical space contain neurons responding to the full range of orientations. When given a contour and attentional signal as input, we analyze the effect of long range connections between hypercolumns using perturbation theory.