Ion channel models are related to non-equilibrium statistical physics, fluid mechanics and electromagnetism. Some classes of ordinary differential equations that model ion channels can be seen as a limit of finite state-space continuous-time Markov chains. The purpose of this thesis is to qualitatively investigate the numerical results of systems of equations that incorporate ion channels modeled by such Markov chains and an electrical circuit model of a single neuron with isopotential extracellular space. This may be useful for making more detailed micro-physical simulations of neurons. A subset of the Rallpack benchmarks is conducted in order to evaluate the accuracy of the electrical circuit model of the transmembrane voltage propagation. In order to test the tau-leap method employed to simulate the Markov-chain based ion channel models a cylindrical geometry is implemented. Convergence properties are presented in terms of mean interspike intervals of the transmembrane voltages for different time- and spatial discretisations. Accuracy of the tau-leap method is presented in relation to the deterministic versions of the ion channel models. The results show that the method used to simulate the transmembrane voltages is accurate and that while the tau-leap method is convergent in the mean interspike interval sense, it is not conclusive how accurate it is compared to the corresponding ordinary differential equations or how efficient it is.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:uu-222876 |
| Date | January 2014 |
| Creators | Berwald, Emil |
| Publisher | Uppsala universitet, Avdelningen för beräkningsvetenskap |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | UPTEC F, 1401-5757 ; 14011 |
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