Understanding spiking and bursting electrical activity through piece-wise linear systems
In recent years there has been an increased interest in working with piece-wise linear caricatures of nonlinear models. Such models are often preferred over more detailed conductance based models for their small number of parameters and low computational overhead. Moreover, their piece-wise linear (...
| Main Author: | |
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| Format: | Thesis (University of Nottingham only) |
| Language: | English |
| Published: |
2012
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| Online Access: | https://eprints.nottingham.ac.uk/12512/ |
| _version_ | 1848791516003172352 |
|---|---|
| author | Gheorghe, Ana Maria |
| author_facet | Gheorghe, Ana Maria |
| author_sort | Gheorghe, Ana Maria |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | In recent years there has been an increased interest in working with piece-wise linear caricatures of nonlinear models. Such models are often preferred over more detailed conductance based models for their small number of parameters and low computational overhead. Moreover, their piece-wise linear (PWL) form, allow the construction of action potential shapes in closed form as well as the calculation of phase response curves (PRC). With the inclusion of PWL adaptive currents they can also support bursting behaviour, though remain amenable to mathematical analysis at both the single neuron and network level. In fact, PWL models caricaturing conductance based models such as that of Morris-Lecar or McKean have also been studied for some time now and are known to be mathematically tractable at the network level.
In this work we proceed to analyse PWL neuron models of conductance type. In particular we focus on PWL models of the FitzHugh-Nagumo type and describe in detail the mechanism for a canard explosion. This model is further explored at the network level in the presence of gap junction coupling.
The study moves to a different area where excitable cells (pancreatic beta-cells) are used to explain insulin secretion phenomena. Here, Ca2+ signals obtained from pancreatic beta-cells of mice are extracted from image data and analysed using signal processing techniques. Both synchrony and functional connectivity analyses are performed. As regards to PWL bursting models we focus on a variant of the adaptive absolute IF model that can support bursting. We investigate the bursting electrical activity of such models with an emphasis on pancreatic beta-cells. |
| first_indexed | 2025-11-14T18:29:45Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-12512 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T18:29:45Z |
| publishDate | 2012 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-125122025-02-28T11:19:40Z https://eprints.nottingham.ac.uk/12512/ Understanding spiking and bursting electrical activity through piece-wise linear systems Gheorghe, Ana Maria In recent years there has been an increased interest in working with piece-wise linear caricatures of nonlinear models. Such models are often preferred over more detailed conductance based models for their small number of parameters and low computational overhead. Moreover, their piece-wise linear (PWL) form, allow the construction of action potential shapes in closed form as well as the calculation of phase response curves (PRC). With the inclusion of PWL adaptive currents they can also support bursting behaviour, though remain amenable to mathematical analysis at both the single neuron and network level. In fact, PWL models caricaturing conductance based models such as that of Morris-Lecar or McKean have also been studied for some time now and are known to be mathematically tractable at the network level. In this work we proceed to analyse PWL neuron models of conductance type. In particular we focus on PWL models of the FitzHugh-Nagumo type and describe in detail the mechanism for a canard explosion. This model is further explored at the network level in the presence of gap junction coupling. The study moves to a different area where excitable cells (pancreatic beta-cells) are used to explain insulin secretion phenomena. Here, Ca2+ signals obtained from pancreatic beta-cells of mice are extracted from image data and analysed using signal processing techniques. Both synchrony and functional connectivity analyses are performed. As regards to PWL bursting models we focus on a variant of the adaptive absolute IF model that can support bursting. We investigate the bursting electrical activity of such models with an emphasis on pancreatic beta-cells. 2012-07-19 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en arr https://eprints.nottingham.ac.uk/12512/1/Understanding_spiking_and_bursting_electrical_activity_through_piece-wise_linear_systems.pdf Gheorghe, Ana Maria (2012) Understanding spiking and bursting electrical activity through piece-wise linear systems. PhD thesis, University of Nottingham. |
| spellingShingle | Gheorghe, Ana Maria Understanding spiking and bursting electrical activity through piece-wise linear systems |
| title | Understanding spiking and bursting electrical activity through piece-wise linear systems |
| title_full | Understanding spiking and bursting electrical activity through piece-wise linear systems |
| title_fullStr | Understanding spiking and bursting electrical activity through piece-wise linear systems |
| title_full_unstemmed | Understanding spiking and bursting electrical activity through piece-wise linear systems |
| title_short | Understanding spiking and bursting electrical activity through piece-wise linear systems |
| title_sort | understanding spiking and bursting electrical activity through piece-wise linear systems |
| url | https://eprints.nottingham.ac.uk/12512/ |