### abstract ###
A new method is presented for extraction of population firing-rate models for both thalamocortical and intracortical signal transfer based on stimulus-evoked data from simultaneous thalamic single-electrode and cortical recordings using linear multielectrodes in the rat barrel system.
Time-dependent population firing rates for granular, supragranular, and infragranular populations in a barrel column and the thalamic population in the homologous barreloid are extracted from the high-frequency portion of the recorded extracellular signals.
These extracted firing rates are in turn used to identify population firing-rate models formulated as integral equations with exponentially decaying coupling kernels, allowing for straightforward transformation to the more common firing-rate formulation in terms of differential equations.
Optimal model structures and model parameters are identified by minimizing the deviation between model firing rates and the experimentally extracted population firing rates.
For the thalamocortical transfer, the experimental data favor a model with fast feedforward excitation from thalamus to the layer-4 laminar population combined with a slower inhibitory process due to feedforward and/or recurrent connections and mixed linear-parabolic activation functions.
The extracted firing rates of the various cortical laminar populations are found to exhibit strong temporal correlations for the present experimental paradigm, and simple feedforward population firing-rate models combined with linear or mixed linear-parabolic activation function are found to provide excellent fits to the data.
The identified thalamocortical and intracortical network models are thus found to be qualitatively very different.
While the thalamocortical circuit is optimally stimulated by rapid changes in the thalamic firing rate, the intracortical circuits are low-pass and respond most strongly to slowly varying inputs from the cortical layer-4 population.
### introduction ###
Following pioneering work in the 1970s by, e.g., Wilson and Cowan CITATION and Amari CITATION a substantial effort has been put into the investigation of neural network models, particularly in the form of firing-rate or neural field models CITATION.
Some firing-rate network models, in particular for the early visual system, have been developed to account for particular physiological data.
However, for strongly interconnected cortical networks, few mechanistic network models directly accounting for specific neurobiological data have been identified.
Instead most work has been done on generic network models and has focused on the investigation of generic features, such as the generation and stability of localized bumps, oscillatory patterns, traveling waves and pulses and other coherent structures, for reviews see Ermentrout CITATION or Coombes CITATION .
We here present a new method for identification of specific population firing-rate network models from extracellular recordings, apply the method to extract network models for thalamocortical and intracortical signal processing based on stimulus-evoked data from simultaneous single-electrode and multielectrode extracellular recordings in the rat somatosensory system, and analyze and interpret the identified firing-rate models using techniques from dynamical systems analysis.
Our study reveals large differences in the transfer function between thalamus and layer 4 of the barrel column, compared to that between cortical layers, and thus sheds direct light on how whisker stimuli is encoded in population firing-activity in the somatosensory system.
The derivation of biologically realistic, cortical neural-network models has generally been hampered by the lack of relevant experimental data to constrain and test the models.
Single electrodes can generally only measure the firing activity of individual neurons, not the joint activity of populations of cells typically predicted by population firing-rate models.
Kyriazi and Simons CITATION and Pinto et al. CITATION, CITATION thus developed models for the somatosensory thalamocortical signal transformation based on pooled data from single-unit recordings from numerous animals.
By contrast, multielectrode arrays provide a convenient and powerful technology for obtaining simultaneous recordings from all layers of the cerebral cortex, at one or more cortical locations CITATION.
The signal at each low-impedance electrode contact represents a weighted sum of the potential generated by synaptic currents and action potentials of neurons within a radius of a few hundred micrometers of the contact, where the weighting factors depend on the shape and position of the neurons, as well as the electrical properties of the conductive medium CITATION CITATION .
In the present paper we describe a new method for extraction of population firing-rate models for both thalamocortical and intracortical transfer on the basis of data from simultaneous thalamic single-electrode and cortical recordings using linear multielectrodes in the rat barrel system.
With so called laminar population analysis Einevoll et al. CITATION jointly modeled the low-frequency and high-frequency parts of such stimulus-evoked laminar electrode data to estimate the laminar organization of cortical populations in a barrel column, time-dependent population firing rates, and the LFP signatures following firing in a particular population.
These postfiring population LFP signatures were further used to estimate the synaptic connection patterns between the various populations using both current source density estimation techniques and a new LFP template-fitting technique CITATION .
Here we use the stimulus-evoked time-dependent firing rates for the cortical populations estimated using LPA, in combination with single-electrode recordings of the firing activity in the homologous barreloid in VPM, to identify population firing-rate models.
The models are formulated as nonlinear Volterra integral equations with exponentially decaying coupling kernels allowing for a mapping of the systems to sets of differential equations, the more common mathematical representation of firing-rate models CITATION, CITATION .
The population responses were found to increase monotonically both with increasing amplitude and velocity of the whisker flick CITATION, CITATION, CITATION.
A stimulus set varying both the whisker-flicking amplitude and the rise time was found to provide a rich variety of thalamic and cortical responses and thus to be well suited for distinguishing between candidate models.
The optimal model structure and corresponding model parameters are estimated by minimizing the mean-square deviation between the population firing rates predicted by the models and the experimentally extracted population firing rates.
A first focus is on the estimation of mathematical models for the signal transfer between thalamus and the layer-4 population, the population receiving the dominant thalamic input.
For this thalamocortical transfer our experimental data favors a model with fast feedforward excitation, a slower predominantly inhibitory process mediated by a combination of recurrent and feedforward interactions, and a mixed linear-parabolic activation function.
The identified thalamocortical circuits are seen to have a band-pass property, and in the frequency domain the largest responses for the layer-4 population is obtained for thalamic firing rates with frequencies around twenty Hz.
Very different population firing-rate models are identified for the intracortical circuits, i.e., the spread of population activity from layer 4 to supragranular and infragranular layers.
For the present experimental paradigm the extracted firing rates of the various cortical laminar populations are found to exhibit strong temporal correlations and simple feedforward models with linear or mixed linear-parabolic activation function are found to account excellently for the data.
The functional properties of the identified thalamocortical and intracortical network models are thus qualitatively very different: while the thalamocortical circuit is optimally stimulated by rapid changes in the thalamic firing rate, the intracortical circuits are low-pass and respond strongest to slowly varying inputs.
Preliminary results from this project were presented earlier in poster format CITATION .
