### abstract ###
A neural field model is presented that captures the essential non-linear characteristics of activity dynamics across several millimeters of visual cortex in response to local flashed and moving stimuli.
We account for physiological data obtained by voltage-sensitive dye imaging which reports mesoscopic population activity at high spatio-temporal resolution.
Stimulation included a single flashed square, a single flashed bar, the line-motion paradigm for which psychophysical studies showed that flashing a square briefly before a bar produces sensation of illusory motion within the bar and moving squares controls.
We consider a two-layer neural field model describing an excitatory and an inhibitory layer of neurons as a coupled system of non-linear integro-differential equations.
Under the assumption that the aggregated activity of both layers is reflected by VSD imaging, our phenomenological model quantitatively accounts for the observed spatio-temporal activity patterns.
Moreover, the model generalizes to novel similar stimuli as it matches activity evoked by moving squares of different speeds.
Our results indicate that feedback from higher brain areas is not required to produce motion patterns in the case of the illusory line-motion paradigm.
Physiological interpretation of the model suggests that a considerable fraction of the VSD signal may be due to inhibitory activity, supporting the notion that balanced intra-layer cortical interactions between inhibitory and excitatory populations play a major role in shaping dynamic stimulus representations in the early visual cortex.
### introduction ###
Visual cortical activity does not exclusively mirror visual input but rather reflects the contribution of additional recurrent processes involving lateral and local feedback couplings.
Understanding cortical processing requires a theoretical understanding of the underlying activity dynamics, which can be attained by modeling at various levels of abstraction.
Naturally, the chosen level should match the level at which neuronal recordings are made CITATION.
The activity patterns observed using voltage-sensitive dye imaging reflect population activity at the mesoscopic level CITATION, CITATION.
This suggests the application of mean-field models in which large numbers of neurons are averaged.
Moreover, we are interested in the relation of neuronal dynamics to the spatial dimensions of the cortical sheet.
Neural field models CITATION, CITATION CITATION, in which the efficacy of synaptic coupling depends on the notion of distance between neurons or ensembles of neurons, are therefore our preferred choice.
Here, we show that a minimalistic multiple-layer NF models can simulate mean VSD data in space and time with high accuracy.
The model is an abstract functional description of VSD-recorded dynamics.
Thus, it is in the first place phenomenological.
However, its interpretation in biological terms allows to link its structure and parameters to the neuronal functional architecture.
The imaging data that we model showed: Two stationary stimuli presented in rapid succession produce a pattern that signals propagation of activity across the bar's retinotopic representation in early visual cortex.
ii The obtained pattern was different from activity when the bar was flashed alone, and did not match the simple superposition of activities evoked by individually-presented square and bar stimuli.
iii Rather, we observed propagation of a wave front of activity that was also found when a square stimulus moved physically in visual space CITATION .
Based on the VSD imaging data CITATION, we hypothesized that a two-layer neural field CITATION CITATION model can account for the findings i iii.
If so, this would imply that the feedback from higher brain areas is not a principal requirement to produce motion patterns across primary visual cortex upon presentation of a square and a bar flashed in rapid succession .
Voltage sensitive dye imaging measures relative fluorescence changes that are linearly correlated to changes in membrane potentials CITATION, CITATION.
This technique currently allows recording of in vivo cortical activity at sub- as well as suprathreshold level with at least 10 ms temporal resolution and a spatial resolution of 50 FORMULAm across several millimeters of cortex.
Hence, it is well suited to capture the real-time dynamics of millions of neurons at once.
However, the signal does not distinguish between excitatory or inhibitory contributions to the overall activity.
Therefore, our model explicitly assumes that the VSD signal reflects a mixture of activity from excitatory and inhibitory neuronal populations, and thus contrasts with studies that interpret VSD data as mainly reflecting excitatory activity.
We expect to gain insights about the relative contributions of excitatory and inhibitory activities in the VSD signal, because the model allows separate inspection of its inhibitory and excitatory layers.
In the following, we first describe the underlying data and its preprocessing, our model structure, and our parameter identification procedure.
Then we present the results including the model fit in comparison to further simplified models, the model prediction regarding similar yet novel stimuli, and the results of a standard linear stability analysis of the homogeneous solution of the model.
We then follow with a discussion of the findings in relation to alternative modeling approaches, the physiological interpretation of our model, and the role of excitation and inhibition in the model.
Finally, we consider our results in the context of hypotheses concerning the cortical representation of motion and the origin of the line-motion illusion.
