Comparison of time stepping schemes on the cable equation
Electrical propagation in excitable tissue, such as nerve fibers and heart muscle, is described by a parabolic PDE for the transmembrane voltage $V(x,t)$, known as the cable equation, $$ frac{1}{r_a}frac{partial^2V}{partial x^2} = C_mfrac{partial V}{partial t} + I_{m ion}(V,t) + I_{m stim}(t)...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2010-09-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/conf-proc/19/l1/abstr.html |
| _version_ | 1824021569574273024 |
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| author | Chuan Li Vasilios Alexiades |
| author_facet | Chuan Li Vasilios Alexiades |
| author_sort | Chuan Li |
| collection | DOAJ |
| description | Electrical propagation in excitable tissue, such as nerve fibers and heart muscle, is described by a parabolic PDE for the transmembrane voltage $V(x,t)$, known as the cable equation, $$ frac{1}{r_a}frac{partial^2V}{partial x^2} = C_mfrac{partial V}{partial t} + I_{m ion}(V,t) + I_{m stim}(t) $$ where $r_a$ and $C_m$ are the axial resistance and membrane capacitance. The source term $I_{m ion}$ represents the total ionic current across the membrane, governed by the Hodgkin-Huxley or other more complicated ionic models. $I_{m stim}(t)$ is an applied stimulus current. |
| first_indexed | 2024-12-19T01:47:58Z |
| format | Article |
| id | doaj.art-1130303539bb4bf992f5ce2061c487e3 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-19T01:47:58Z |
| publishDate | 2010-09-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-1130303539bb4bf992f5ce2061c487e32022-12-21T20:41:32ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912010-09-01201019189196Comparison of time stepping schemes on the cable equationChuan LiVasilios AlexiadesElectrical propagation in excitable tissue, such as nerve fibers and heart muscle, is described by a parabolic PDE for the transmembrane voltage $V(x,t)$, known as the cable equation, $$ frac{1}{r_a}frac{partial^2V}{partial x^2} = C_mfrac{partial V}{partial t} + I_{m ion}(V,t) + I_{m stim}(t) $$ where $r_a$ and $C_m$ are the axial resistance and membrane capacitance. The source term $I_{m ion}$ represents the total ionic current across the membrane, governed by the Hodgkin-Huxley or other more complicated ionic models. $I_{m stim}(t)$ is an applied stimulus current.http://ejde.math.txstate.edu/conf-proc/19/l1/abstr.htmlExplicit schemessuper time steppingadaptive Runge KuttaDufort Frankelaction potentialLuo-Rudy ionic models |
| spellingShingle | Chuan Li Vasilios Alexiades Comparison of time stepping schemes on the cable equation Electronic Journal of Differential Equations Explicit schemes super time stepping adaptive Runge Kutta Dufort Frankel action potential Luo-Rudy ionic models |
| title | Comparison of time stepping schemes on the cable equation |
| title_full | Comparison of time stepping schemes on the cable equation |
| title_fullStr | Comparison of time stepping schemes on the cable equation |
| title_full_unstemmed | Comparison of time stepping schemes on the cable equation |
| title_short | Comparison of time stepping schemes on the cable equation |
| title_sort | comparison of time stepping schemes on the cable equation |
| topic | Explicit schemes super time stepping adaptive Runge Kutta Dufort Frankel action potential Luo-Rudy ionic models |
| url | http://ejde.math.txstate.edu/conf-proc/19/l1/abstr.html |
| work_keys_str_mv | AT chuanli comparisonoftimesteppingschemesonthecableequation AT vasiliosalexiades comparisonoftimesteppingschemesonthecableequation |