Pitt Logo LinkContact Us

Firing Rate Analysis for an Integrate-and-Fire Neuronal Model

O'Grady, Ryan (2011) Firing Rate Analysis for an Integrate-and-Fire Neuronal Model. Doctoral Dissertation, University of Pittsburgh.

[img] PDF - Primary Text
Restricted to University of Pittsburgh users only until 29 September 2016.

Download (1806Kb) | Request a copy

    Abstract

    We investigate a stochastic linear integrate-and-fire (IF) neuronal model and use the corresponding Fokker-Planck equation (FPE) to study the mean firing rate of a population of IF neurons. The firing rate(or emission rate) function, is given in terms of an eigenfunction expansion solution of the FPE. We consider two parameter regimes of current input and prove the existence of infinitely many branches of eigenvalues and derive their asymptotic properties. We use the eigenfunction expansion solution to prove asymptotic properties of the firing rate function. We also perform a numerical experiment of 10,000 IF neurons and show that our simulation is in agreement with our theoretical results. Finally, we state several open problems for future research.


    Share

    Citation/Export:
    Social Networking:

    Details

    Item Type: University of Pittsburgh ETD
    ETD Committee:
    ETD Committee TypeCommittee MemberEmail
    Committee ChairTroy, Williamtroy@math.pitt.edu
    Committee MemberDoiron, Brentbdoiron@pitt.edu
    Committee MemberCaginalp, Gunduzcaginalp@pitt.edu
    Committee MemberIyengar, Satishssi@pitt.edu
    Title: Firing Rate Analysis for an Integrate-and-Fire Neuronal Model
    Status: Unpublished
    Abstract: We investigate a stochastic linear integrate-and-fire (IF) neuronal model and use the corresponding Fokker-Planck equation (FPE) to study the mean firing rate of a population of IF neurons. The firing rate(or emission rate) function, is given in terms of an eigenfunction expansion solution of the FPE. We consider two parameter regimes of current input and prove the existence of infinitely many branches of eigenvalues and derive their asymptotic properties. We use the eigenfunction expansion solution to prove asymptotic properties of the firing rate function. We also perform a numerical experiment of 10,000 IF neurons and show that our simulation is in agreement with our theoretical results. Finally, we state several open problems for future research.
    Date: 29 September 2011
    Date Type: Completion
    Defense Date: 22 April 2011
    Approval Date: 29 September 2011
    Submission Date: 15 August 2011
    Access Restriction: 5 year -- Restrict access to University of Pittsburgh for a period of 5 years.
    Patent pending: No
    Institution: University of Pittsburgh
    Thesis Type: Doctoral Dissertation
    Refereed: Yes
    Degree: PhD - Doctor of Philosophy
    URN: etd-08152011-120630
    Uncontrolled Keywords: eigenfunction expansion; integrate-and-fire; mean firing rate; neuronal model; sde
    Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
    Date Deposited: 10 Nov 2011 14:59
    Last Modified: 14 Feb 2012 16:17
    Other ID: http://etd.library.pitt.edu/ETD/available/etd-08152011-120630/, etd-08152011-120630

    Actions (login required)

    View Item

    Document Downloads