Mathematical modeling and qualitative analysis of insulin therapies
Catherine
Lloyd
Auckland Bioengineering Institute, University of Auckland
Model Status
This CellML version of the model has been checked in COR and OpenCell and is known to be valid CellML. The units are consistent and the model runs to recreate the published results.
Model Structure
ABSTRACT: A model of the rabbit sinoatrial action potential is introduced, based on a model by Morris and Lecar. One cell is described by two nonlinear first-order ordinary differential equations, with ten constant parameters. The model is much simpler than most other models in use, but can reproduce perfectly experimentally recorded action potentials. The dynamics of two coupled cells, with and without the presence of periodic acetylcholine pulses, shows examples of bifurcations and strange attractors, mathematical phenomena characterizing chaotic motion. It remains to be clarified whether such dynamics is actually observed, for example in the small irregular variations of the normal heart rate.
model diagram
Schematic diagram of the cell model
The original paper reference is cited below:
Chaos in weakly-coupled pacemaker cells, Lars Petter Endresen, 1997, Journal of Theoretical Biology, 184, 41-50. PubMed ID: 9039399
$\frac{d V}{d \mathrm{time}}=\frac{-(\mathrm{i\_s}+\mathrm{i\_K}+\mathrm{i\_K\_ACh}+\mathrm{i\_j})}{\mathrm{Cm}}$
$\mathrm{i\_s}=\frac{1}{2}\mathrm{g\_s}(1+\tanh \left(\frac{V-\mathrm{V\_1}}{\mathrm{V\_2}}\right))(V-\mathrm{V\_s})$
$\mathrm{i\_K}=\mathrm{g\_K}w(V-\mathrm{V\_K})$
$\frac{d w}{d \mathrm{time}}=\mathrm{lambda\_w}\cosh \left(\frac{V-\mathrm{V\_3}}{2\mathrm{V\_4}}\right)(\frac{1}{2}(1+\tanh \left(\frac{V-\mathrm{V\_3}}{\mathrm{V\_4}}\right))-w)$
$\mathrm{i\_K\_ACh}=1\times 0.27u(V+90)$
$\mathrm{alpha}=\frac{0.012332}{1+\frac{4.2E-6}{\mathrm{ACh}}}\mathrm{beta}=0.01e^{0.0133(V+40)}\frac{d u}{d \mathrm{time}}=\mathrm{alpha}(1-u)-\mathrm{beta}u$
$\mathrm{i\_j}=\mathrm{g\_j}(V-\mathrm{V\_B})$
2007-09-11T00:00:00+00:00This model is known to run in COR and PCEnv 0.2 and reproduces the published results.LarsEndresenPam1123.59039399PennyNobleJ1996-01-07 00:00Oxford UniversityDept of Physiology, Anatomy & GeneticsOxford UniversityThis file is a CellML description of Endresen's 1996 model of the rabbit sinoatrial action potential from the paper "Chaos in Weakly-coupled Pacemaker Cells"penny.noble@dpag.ox.ac.ukJames Lawsoncardiacelectrophysiologyrabbit50Chaos in Weakly-coupled Pacemaker Cells184(1)41James LawsonkeywordJournal of Theoretical Biology