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Extending firing rate models to include ionic effects

Li, Tianke (2019) Extending firing rate models to include ionic effects. Undergraduate Thesis, University of Pittsburgh. (Unpublished)

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Abstract

Spiking models have been widely used to describe single neuron oscillation behaviors. However, these models can be quite complex so that in order to incorporate them in networks, one approach is to use so-called firing rate models where the dynamics of the neuron are reduced to the rate at which it fires when presented with a constant stimulus. In pathological conditions such as epilepsy or when the neurons are driven too strongly, they can stop firing due to a phenomenon known as depolarization block, which can come about due to the accumulation of potassium ions in the intracellular space. In the project, we used a well-known Wang-Buzsaki (WB) spiking model but also included an additional equation considering extracellular potassium effects. Given that the extracellular potassium effects is slow and synapses can be reasonably assumed as slow, we applied a slow-fast technique on the WB model and derived a firing rate model describing the synapse-potassium system qualitatively. The bifurcation of the reduced model suggests that the depolarization block threshold can be viewed as the homoclinic bifurcation in the synapse-potassium system, which would be depended upon the potassium sensitivity and the drift rate. In addition, we implement our firing rate model into a two-nearest neighbor spatial model. The spatial-temporal plots suggest our model behavior is consistent with experimental results. The synaptic connectivity has positive effects on seizure propagation and somewhat negative effects on synchronization. On the other hand, the potassium diffusion has a positive influence on synchronization. However, the influence of potassium sensitivity might be more complex. While the neurons under normal physiological conditions can be driven into the seizure-like oscillations in the network, the neurons under depolarization block seem to be a little bit more complicated and require further explanation.


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Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Li, Tianketil41@pitt.edutil41
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairErmentrout, Bardbard@pitt.edu
Committee MemberNeilan, Rachael Millermillerneilanr@duq.edu
Committee MemberWheeler, Jeffrey Pauljwheeler@pitt.edu
Committee MemberRubin, Jonathanjonrubin@pitt.edu
Date: 28 August 2019
Date Type: Publication
Defense Date: 25 July 0019
Approval Date: 28 August 2019
Submission Date: 1 August 2019
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 37
Institution: University of Pittsburgh
Schools and Programs: University Honors College
Dietrich School of Arts and Sciences > Mathematics
Degree: BPhil - Bachelor of Philosophy
Thesis Type: Undergraduate Thesis
Refereed: Yes
Uncontrolled Keywords: Firing Rate Model; Extracellular Potassium; Seizure
Date Deposited: 28 Aug 2019 19:11
Last Modified: 28 Aug 2019 19:11
URI: http://d-scholarship.pitt.edu/id/eprint/37252

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