BB14: Wave phenomena in neural field models of visual cortex and the role of short term plasticity

Project report to follow

Background

Binocular rivalry is the curious visual phenomenon where sufficiently different images when presented to the left and right eyes cause an oscillation in visual perception of the image. Using these kinds of phenomena, we aim to better understand how the visual cortex and perception in general work. Moreover, understanding how large scale collective effects occur in brain tissue could have medical applications for epilepsy and sleep.

Techniques and Challenges

We have primarily used neural fields to study binocular rivalry, since techniques have been developed for analysing the travelling front behaviour of this particular type of partial integro-differential equation, often yielding analytic results. When we have considered noise in these neural field equations, which is certainly present in the underlying biology, we obtain stochastic partial integro-differential equations. We have adapted techniques previously developed for partial differential equations (PDEs) to analytically deal with travelling waves in this context. Numerical simulation of stochastic partial integro-differential equations is often required to justify assumptions that we make while deriving analytical expressions.

Results

As a result of our work, it has now been shown that for travelling waves in binocular rivalry to occur, a symmetry breaking mechanism has to be present. We have also shown that it is possible to describe various experimental observations on travelling waves in real subjects within the context of binocular rivalry. Furthermore, we have also developed a framework for handling noise in stochastic neural field equations. We have used this to show that for one-dimensional neural field equations with constant external input, wave position follows a Brownian motion, whereas for equations with a moving input stimulus, wave position follows an Ornstein-Uhlenbeck process.

The Future

As a next step we aim to combine our work on binocular rivalry with our framework on stochastic neural fields to analyse stochastic wave behaviour. We hope the work yields testable hypotheses that could help determine where noise primarily enters the system in neural field equations, currently an open question.

References

[12/46] Webber M.A., Bressloff P.C.: The effects of noise on binocular rivalry waves a stochastic neural field model

[11/63] Bressloff P.C., Webber M.A.: Front propagation in stochastic neural fields

[11/62] Bressloff P.C., Webber M.A.: Neural field model of binocular rivalry waves, Journal of Computational Neuroscience

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Coombes S., Owen M.R.: Evans functions for integral neural field equations with Heaviside firing rate function, SIAM Journal on Applied Dynamical Systems, 34:574–600, 2004