Phase and Amplitude Modulation in a Neural Oscillatory Model of the Orientation Map

The traditional approach to characterization of orientation maps as they were expounded by Hubel and Wiesel treats them as static representations. Only the magnitude of a neuron's firing response to orientation is considered and the neuron with the highest response is said to be "tuned" to that response. But the neuronal response to orientation is a time-varying spike train and, if the response of an entire cortical area that potentially responds to orientations in a given part of the visual field is considered, the response must be considered as a spatio-temporal wave. We propose a neural field model consisting of FitzHugh-Nagumo neurons, that generates such a wave. Reflecting the dynamics of a single FitzHugh-Nagumo neuron, the neural field also exhibits excitatory and oscillatory regimes as an offset parameter is increased. We consider the question of the manner in which the input orientation is coded in the response of the neural field and discovered that two different codes - Amplitude Modulation and Phase Modulation - are present. Whereas for smaller offset values, when the model is in excitatory regime the orientation is coded in terms of amplitude, for larger offset values when the model is in the oscillatory regime, the orientation is coded in terms of phase.