### Abstract

An outstanding problem in computational neuroscience is how to use population density function (PDF) methods to model neural networks with realistic synaptic kinetics in a computationally efficient manner. We explore an application of two-dimensional (2-D) PDF methods to simulating electrical activity in networks of excitatory integrate-and-fire neurons.We formulate a pair of coupled partial differential-integral equations describing the evolution of PDFs for neurons in non-refractory and refractory pools. The population firing rate is given by the total flux of probability across the threshold voltage. We use an operator-splitting method to reduce computation time. We report on speed and accuracy of PDF results and compare them to those from direct, Monte-Carlo simulations.We compute temporal frequency response functions for the transduction from the rate of postsynaptic input to population firing rate, and examine its dependence on background synaptic input rate. The behaviors in the1-D and 2-D cases-corresponding to instantaneous and non-instantaneous synaptic kinetics, respectively-differ markedly from those for a somewhat different transduction: from injected current input to population firing rate output (Brunel et al. 2001; Fourcaud & Brunel 2002).We extend our method by adding inhibitory input, consider a 3-D to 2-D dimension reduction method, demonstrate its limitations, and suggest directions for future study.

Original language | English (US) |
---|---|

Pages (from-to) | 373-418 |

Number of pages | 46 |

Journal | Network: Computation in Neural Systems |

Volume | 17 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 2006 |

### Fingerprint

### Keywords

- Network models

### ASJC Scopus subject areas

- Neuroscience(all)

### Cite this

**Population density methods for stochastic neurons with realistic synaptic kinetics : Firing rate dynamics and fast computational methods.** / Apfaltrer, Felix; Ly, Cheng; Tranchina, Daniel.

Research output: Contribution to journal › Article

*Network: Computation in Neural Systems*, vol. 17, no. 4, pp. 373-418. https://doi.org/10.1080/09548980601069787

}

TY - JOUR

T1 - Population density methods for stochastic neurons with realistic synaptic kinetics

T2 - Firing rate dynamics and fast computational methods

AU - Apfaltrer, Felix

AU - Ly, Cheng

AU - Tranchina, Daniel

PY - 2006/12/1

Y1 - 2006/12/1

N2 - An outstanding problem in computational neuroscience is how to use population density function (PDF) methods to model neural networks with realistic synaptic kinetics in a computationally efficient manner. We explore an application of two-dimensional (2-D) PDF methods to simulating electrical activity in networks of excitatory integrate-and-fire neurons.We formulate a pair of coupled partial differential-integral equations describing the evolution of PDFs for neurons in non-refractory and refractory pools. The population firing rate is given by the total flux of probability across the threshold voltage. We use an operator-splitting method to reduce computation time. We report on speed and accuracy of PDF results and compare them to those from direct, Monte-Carlo simulations.We compute temporal frequency response functions for the transduction from the rate of postsynaptic input to population firing rate, and examine its dependence on background synaptic input rate. The behaviors in the1-D and 2-D cases-corresponding to instantaneous and non-instantaneous synaptic kinetics, respectively-differ markedly from those for a somewhat different transduction: from injected current input to population firing rate output (Brunel et al. 2001; Fourcaud & Brunel 2002).We extend our method by adding inhibitory input, consider a 3-D to 2-D dimension reduction method, demonstrate its limitations, and suggest directions for future study.

AB - An outstanding problem in computational neuroscience is how to use population density function (PDF) methods to model neural networks with realistic synaptic kinetics in a computationally efficient manner. We explore an application of two-dimensional (2-D) PDF methods to simulating electrical activity in networks of excitatory integrate-and-fire neurons.We formulate a pair of coupled partial differential-integral equations describing the evolution of PDFs for neurons in non-refractory and refractory pools. The population firing rate is given by the total flux of probability across the threshold voltage. We use an operator-splitting method to reduce computation time. We report on speed and accuracy of PDF results and compare them to those from direct, Monte-Carlo simulations.We compute temporal frequency response functions for the transduction from the rate of postsynaptic input to population firing rate, and examine its dependence on background synaptic input rate. The behaviors in the1-D and 2-D cases-corresponding to instantaneous and non-instantaneous synaptic kinetics, respectively-differ markedly from those for a somewhat different transduction: from injected current input to population firing rate output (Brunel et al. 2001; Fourcaud & Brunel 2002).We extend our method by adding inhibitory input, consider a 3-D to 2-D dimension reduction method, demonstrate its limitations, and suggest directions for future study.

KW - Network models

UR - http://www.scopus.com/inward/record.url?scp=33845394008&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33845394008&partnerID=8YFLogxK

U2 - 10.1080/09548980601069787

DO - 10.1080/09548980601069787

M3 - Article

VL - 17

SP - 373

EP - 418

JO - Network: Computation in Neural Systems

JF - Network: Computation in Neural Systems

SN - 0954-898X

IS - 4

ER -