Manica, Evandro
(2009)
Effects of coupling and heterogeneity in the pre-Botzinger complex cells using first return maps.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
The preBotzinger complex located at the ventrolateral medulla in the brainstem is believedto have an important role in generating the respiratory rhythm in mammals, specially theinspiratory process [56]. Keeping this in mind, we will study a small network of such cellsby means of a minimal model suggested and experimentally tested by Butera et al [6, 7]. Athorough analysis of the Butera model was done for two very small networks of pre-Botzingercells: a self coupled single cell and a network of two coupled cells [5]. In order to understandthe role of coupling and heterogeneity in these two particular networks we reduce the selfcoupled single cell network to a one dimensional map using a similar approach as in [37].Using this one dimensional map, some analytical conditions for switching from one regime toanother are determined and numerical results are shown. Using the same idea as for the selfcoupled single cell case, two identical coupled cells are reduced to a two dimensional iteratedmap which is a composition of many one dimensional maps. Using the form of these maps,mechanisms for the transition between previously observed regimes [5] are determined andlinear analysis is performed for a particular set of parameters.Introducing heterogeneity on the network of two coupled identical cells, for a fixed levelof synaptic input, shows that depending on the level of the synaptic input some differentbehaviors arise which were not previously observed in a network of homogenous cells [5].These results suggest that introducing heterogeneity can increase the range in the parameterspace for which cells are bursting. This is desirable, since from experiments it is observedthat bursting is associated with the inspiratory rhythm of respiration.
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| Item Type: |
University of Pittsburgh ETD
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| Status: |
Unpublished |
| Creators/Authors: |
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| ETD Committee: |
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| Date: |
28 January 2009 |
| Date Type: |
Completion |
| Defense Date: |
2 December 2008 |
| Approval Date: |
28 January 2009 |
| Submission Date: |
9 December 2008 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Dietrich School of Arts and Sciences > Mathematics |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
inspiration; bifurcation analysis; fast/slow decomposition |
| Other ID: |
http://etd.library.pitt.edu/ETD/available/etd-12092008-161303/, etd-12092008-161303 |
| Date Deposited: |
10 Nov 2011 20:09 |
| Last Modified: |
15 Nov 2016 13:54 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/10252 |
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