December 5, 2001

3:05 pm JWB 208

Title:An overview of population density methods for the large-scale modelling of neuronal networks in the brain and applications.

Speaker: Evan Haskell, Department of Mathematics, University of Utah

Abstract: Population density methods provide promising time-saving alternatives to direct Monte-Carlo simulations of neuronal network activity, in which one tracks the state of thousands of individual neurons and synapses. A population density method was found to be roughly a hundred times faster than direct simulation for various test networks of integrate-and-fire model neurons with instantaneous excitatory and inhibitory post-synaptic conductances (Nykamp and Tranchina, 2000a). In this method, neurons are grouped into large populations of similar neurons. For each population, one calculates the evolution of a probability density function (PDF) which describes the distribution of neurons over state space. The population firing rate is then given by the total flux of probability across the threshold voltage for firing an action potential. The method is more accurate than the mean-field method in the steady state, where the mean-field approximation works best, and also under dynamic-stimulus conditions. The method is much faster than direct simulations. In this talk, I will present the development of a population density method in a very simplified setting. Then I will give an overview of how this method has been applied in modeling the brain, focusing on applications to vision. Some references: Brunel N. and Hakim V. Fast global oscillations in networks of integrate-and-fire neurons with low firing rates. Neural Computation 11:1621-1671, 1999. Casti AR, Omurtag A. Sornborger A. Sirovich L. Knight BW. Kaplan E. and Victor J. A Dynamic population model of the neuronal pathway from the retina to the primary visual cortex. Society for Neuroscience abstracts, 2001. Haskell E. Nykamp DQ and Tranchina D. Population density methods for large-scale modelling of neuronal networks with realistic synaptic kinetics: cutting the dimension down to size. Network 12:141-174, 2001. Knight BW. Omurtag A. and Sirovich L. The approach of a neuron population firing rate to a new equilibrium: An exact theoretical result. Neural Computation 12:1045-1055, 2000. Knight BW. Dynamics of encoding in a population of neurons. J. Gen. Physiol. 59:767-778, 1972. Knight BW. Dynamics of encoding in neuron populations: Some general mathematical features. Neural Computation 12:473-518, 2000. Nykamp DQ and Tranchina D. A population density approach that facilitates large-scale modeling of neural networks: Analysis and an application to orientation tuning. Journal of Computational Neuroscience 8:19-50, 2000. Nykamp DQ and Tranchina D. A population density approach that facilitates large-scale modeling of neural networks: Extension to slow inhibitory synapses Neural Computation 13:511-46, 2001. Omurtag A. Knight BW and Sirovich L. On the simulation of large populations of neurons. Journal of Computational Neuroscience 8:51-63, 2000. Omurtag A. Kaplan E. Knight BW and Sirovich L. A population approach to cortical dynamics with an application to orientation tuning. Network 11:247-60, 2000. Sirovich L. Knight BW and Omurtag A. Dynamics of neuronal populations: The equilibrium solution. SIAM J. Appl. Math. 60:2009-2028, 2000.

For more information contact J. Keener, 1-6089