A population density approach that facilitates large-scale modeling of neural networks: Analysis and an application to orientation tuning

We explore a computationally efficient method of simulating realistic netwo rks of neurons introduced by Knight, Manin, and Sirovich (1996) in which in tegrate-and-fire neurons are grouped into large populations of similar neur ons. For each population, we form a probability density that represents the distribution of neurons over all possible states. The populations are coup led via stochastic synapses in which the conductance of a neuron is modulat ed according to the firing rates of its presynaptic populations. The evolut ion equation for each of these probability densities is a partial different ial-integral equation, which we solve numerically. Results obtained for sev eral example networks are tested against conventional computations for grou ps of individual neurons. We apply this approach to modeling orientation tuning in the visual cortex. Our population density model is based on the recurrent feedback model of a hypercolumn in cat visual cortex of Somers et al. (1995). We simulate the response to oriented flashed bars. As in the Somers model, a weak orientati on bias provided by feed-forward lateral geniculate input is transformed by intracortical circuitry into sharper orientation tuning that is independen t of stimulus contrast. The population density approach appears to be a viable method for simulatin g large neural networks. Its computational efficiency overcomes some of the restrictions imposed by computation time in individual neuron simulations, allowing one to build more complex networks and to explore parameter space more easily. The method produces smooth rate functions with one pass of th e stimulus and does not require signal averaging. At the same time, this mo del captures the dynamics of single-neuron activity that are missed in simp le firing-rate models.