Population Density Methods and Applications in Large-Scale Modeling of Neural Networks

New York University, New York NY

Investigators

Abstract

Computational models of networks of neurons in the brain usually are based on following the details of activity patterns in large numbers of individually explicit neuronal elements and their synapses. Simulations of activity in functional units based on hundreds or even thousands of such neural units, such as a column within the sensory cortex, can take hours of computer time to model seconds of real time. The goal of this project is to develop new techniques to facilitate large-scale modeling of neural networks in the mammalian brain. The theory of probability (population) density function, borrowed from the field of statistical mechanics, uses large numbers of elements to advantage. In the population density method, similar neurons are lumped together in a population, and one tracks the distribution of neurons over 'state space' in each population. The state of a neuron is determined by the dynamic variables in the underlying single-neuron model, to allow deriving a population firing rate from a flux of probability across a particular surface in state space, taking into account coupling between neurons by excitatory and inhibitory input events at stochastic synapses. The present project will extend the population density theory by incorporating realistic synaptic kinetics. This consequent increased computational complexity will lead to developing and testing new simulation methods to compare with conventional direct simulations for accuracy and speed. Population density methods will be applied to the well known primary visual cortex, including interactions among cortical layers and columns, to account for physiologically known features such as sensitivity to orientation of visual bar stimuli, and the relation of responses to stimulus contrast levels. Results will have an impact on visual neuroscience as well as computational neuroscience, and on understanding information processing in the brain in general. These new methods could accelerate network simulations by orders of magnitude, with the promise of applications in computer and information sciences. Cross-disciplinary graduate training is an important added feature of this project.