- Author:
- Catherine Lloyd <c.lloyd@auckland.ac.nz>
- Date:
- 2009-09-30 09:51:10+13:00
- Desc:
- removed rest of paper link.
- Permanent Source URI:
- https://models.cellml.org/workspace/aslanidi_atrial_model_2009/rawfile/e087e8ab00085c42cebbd536273ab346f068ff17/aslanidi_atrial_model_2009_LindbladCa_corrected.cellml
<?xml version="1.0" encoding="utf-8"?>
<!--
This CellML file was generated on 21/09/2009 at 15:12:58 using:
COR (0.9.31.1319)
Copyright 2002-2009 Dr Alan Garny
http://cor.physiol.ox.ac.uk/ - cor@physiol.ox.ac.uk
CellML 1.0 was used to generate this model
http://www.cellml.org/
-->
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<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Optimal velocity and safety of discontinuous conduction through the heterogeneous Purkinje-ventricular junction
</title>
<author>
<firstname>Penny</firstname>
<surname>Noble</surname>
<affiliation>
<shortaffil>University of Oxford</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This CellML version of the model has been checked in both PCEnv and COR and it runs to recreate the published results. The units have been checked and they balance. We would like to thank the original model author Oleg Aslanidi for his help in the final stages of model curation.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: Experimental evidence suggests that regional differences in action potential (AP) morphology can provide a substrate for initiation and maintenance of reentrant arrhythmias in the right atrium (RA), but the relationships between the complex electrophysiological and anatomical organization of the RA and the genesis of reentry are unclear. In this study, a biophysically detailed three-dimensional computer model of the right atrial tissue was constructed to study the role of tissue heterogeneity and anisotropy in arrhythmogenesis. The model of Lindblad et al. for a rabbit atrial cell was modified to incorporate experimental data on regional differences in several ionic currents (primarily, I(Na), I(CaL), I(K1), I(to), and I(sus)) between the crista terminalis and pectinate muscle cells. The modified model was validated by its ability to reproduce the AP properties measured experimentally. The anatomical model of the rabbit RA (including tissue geometry and fiber orientation) was based on a recent histological reconstruction. Simulations with the resultant electrophysiologically and anatomically detailed three-dimensional model show that complex organization of the RA tissue causes breakdown of regular AP conduction patterns at high pacing rates (>11.75 Hz): as the AP in the crista terminalis cells is longer, and electrotonic coupling transverse to fibers of the crista terminalis is weak, high-frequency pacing at the border between the crista terminalis and pectinate muscles results in a unidirectional conduction block toward the crista terminalis and generation of reentry. Contributions of the tissue heterogeneity and anisotropy to reentry initiation mechanisms are quantified by measuring action potential duration (APD) gradients at the border between the crista terminalis and pectinate muscles: the APD gradients are high in areas where both heterogeneity and anisotropy are high, such that intrinsic APD differences are not diminished by electrotonic interactions. Thus, our detailed computer model reconstructs complex electrical activity in the RA, and provides new insights into the mechanisms of transition from focal atrial tachycardia into reentry.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
Mechanisms of transition from normal to reentrant electrical activity in a model of rabbit atrial tissue: interaction of tissue heterogeneity and anisotropy, Oleg V. Aslanidi, Mark R. Boyett, Halina Dobrzynski, and Henggui Zhang, 2009, <emphasis>Biophysical Journal</emphasis>, 96, 798-817. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=19186122&dopt=Abstract">PubMed ID: 19186122</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
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<title>schematic diagram</title>
</objectinfo>
<imagedata fileref="aslanidi_2009b.png"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram describing the atrial cell model.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
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<apply>
<eq/>
<ci>E10</ci>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_d_L</ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt_second">16.72</cn>
</apply>
<ci>E0_alpha_d_L</ci>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>E0_alpha_d_L</ci>
<apply>
<minus/>
<cn cellml:units="millivolt">2.5</cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt_second">50</cn>
</apply>
<ci>E10</ci>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>E10</ci>
<apply>
<minus/>
<cn cellml:units="millivolt">4.808</cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_d_L</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_second">4.48</cn>
<ci>E0_beta_d_L</ci>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>E0_beta_d_L</ci>
<cn cellml:units="millivolt">2.5</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>d_L_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>E10</ci>
<cn cellml:units="millivolt">0.95</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">6.6</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_d_L</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>alpha_d_L</ci>
<ci>beta_d_L</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>d_L</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>d_L_infinity</ci>
<ci>d_L</ci>
</apply>
<ci>tau_d_L</ci>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_channel_f_L_gate">
<variable name="f_L" units="dimensionless" initial_value="0.99981" public_interface="out"/>
<variable name="E0_f_L" units="millivolt"/>
<variable name="alpha_f_L" units="per_second"/>
<variable name="beta_f_L" units="per_second"/>
<variable name="f_L_infinity" units="dimensionless" public_interface="out"/>
<variable name="tau_f_L" units="second"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>E0_f_L</ci>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">18</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_f_L</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_second">8.49</cn>
<ci>E0_f_L</ci>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>E0_f_L</ci>
<cn cellml:units="millivolt">4</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_f_L</ci>
<apply>
<divide/>
<cn cellml:units="per_second">67.922</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<ci>E0_f_L</ci>
<apply>
<minus/>
<cn cellml:units="millivolt">4</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>f_L_infinity</ci>
<apply>
<divide/>
<ci>alpha_f_L</ci>
<apply>
<plus/>
<ci>alpha_f_L</ci>
<ci>beta_f_L</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_f_L</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>alpha_f_L</ci>
<ci>beta_f_L</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>f_L</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>f_L_infinity</ci>
<ci>f_L</ci>
</apply>
<ci>tau_f_L</ci>
</apply>
</apply>
</math>
</component>
<component name="T_type_Ca_channel">
<variable name="i_Ca_T" units="picoA" public_interface="out"/>
<variable name="g_Ca_T" units="nanoS" initial_value="0.006"/>
<variable name="E_Ca_T" units="millivolt" initial_value="38"/>
<variable name="time" units="second" public_interface="in" private_interface="out"/>
<variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
<variable name="d_T" units="dimensionless" private_interface="in"/>
<variable name="f_T" units="dimensionless" private_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Ca_T</ci>
<apply>
<times/>
<ci>g_Ca_T</ci>
<ci>d_T</ci>
<ci>f_T</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Ca_T</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="T_type_Ca_channel_d_T_gate">
<variable name="d_T" units="dimensionless" initial_value="0.00046" public_interface="out"/>
<variable name="E0_d_T" units="millivolt"/>
<variable name="alpha_d_T" units="per_second"/>
<variable name="beta_d_T" units="per_second"/>
<variable name="d_T_infinity" units="dimensionless"/>
<variable name="tau_d_T" units="second"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>E0_d_T</ci>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">23.3</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_d_T</ci>
<apply>
<times/>
<cn cellml:units="per_second">674.173</cn>
<apply>
<exp/>
<apply>
<divide/>
<ci>E0_d_T</ci>
<cn cellml:units="millivolt">30</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_d_T</ci>
<apply>
<times/>
<cn cellml:units="per_second">674.173</cn>
<apply>
<exp/>
<apply>
<divide/>
<ci>E0_d_T</ci>
<apply>
<minus/>
<cn cellml:units="millivolt">30</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>d_T_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>E0_d_T</ci>
<cn cellml:units="millivolt">0.3</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">6.1</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_d_T</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>alpha_d_T</ci>
<ci>beta_d_T</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>d_T</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>d_T_infinity</ci>
<ci>d_T</ci>
</apply>
<ci>tau_d_T</ci>
</apply>
</apply>
</math>
</component>
<component name="T_type_Ca_channel_f_T_gate">
<variable name="f_T" units="dimensionless" initial_value="0.30752" public_interface="out"/>
<variable name="E0_f_T" units="millivolt"/>
<variable name="alpha_f_T" units="per_second"/>
<variable name="beta_f_T" units="per_second"/>
<variable name="f_T_infinity" units="dimensionless" public_interface="out"/>
<variable name="tau_f_T" units="second"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>E0_f_T</ci>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">75</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_f_T</ci>
<apply>
<times/>
<cn cellml:units="per_second">9.637</cn>
<apply>
<exp/>
<apply>
<divide/>
<ci>E0_f_T</ci>
<apply>
<minus/>
<cn cellml:units="millivolt">83.3</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_f_T</ci>
<apply>
<times/>
<cn cellml:units="per_second">9.637</cn>
<apply>
<exp/>
<apply>
<divide/>
<ci>E0_f_T</ci>
<cn cellml:units="millivolt">15.38</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>f_T_infinity</ci>
<apply>
<divide/>
<ci>alpha_f_T</ci>
<apply>
<plus/>
<ci>alpha_f_T</ci>
<ci>beta_f_T</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_f_T</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>alpha_f_T</ci>
<ci>beta_f_T</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>f_T</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>f_T_infinity</ci>
<ci>f_T</ci>
</apply>
<ci>tau_f_T</ci>
</apply>
</apply>
</math>
</component>
<component name="Ca_independent_transient_outward_K_current">
<variable name="i_to" units="picoA" public_interface="out"/>
<variable name="i_sus" units="picoA" public_interface="out"/>
<variable name="E_K" units="millivolt" public_interface="out"/>
<variable name="g_to" units="nanoS" initial_value="0.050002"/>
<variable name="time" units="second" public_interface="in" private_interface="out"/>
<variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
<variable name="R" units="millijoule_per_mole_kelvin" public_interface="in"/>
<variable name="F" units="coulomb_per_mole" public_interface="in"/>
<variable name="T" units="kelvin" public_interface="in"/>
<variable name="K_c" units="millimolar" public_interface="in"/>
<variable name="K_i" units="millimolar" public_interface="in"/>
<variable name="r" units="dimensionless" private_interface="in"/>
<variable name="s1" units="dimensionless" private_interface="in"/>
<variable name="s2" units="dimensionless" private_interface="in"/>
<variable name="s3" units="dimensionless" private_interface="in"/>
<variable name="CT" units="dimensionless" public_interface="in"/>
<variable name="PM" units="dimensionless" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>E_K</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
<ci>F</ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci>K_c</ci>
<ci>K_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_to</ci>
<piecewise>
<piece>
<apply>
<times/>
<cn cellml:units="dimensionless">0.2</cn>
<ci>g_to</ci>
<ci>r</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.59</cn>
<apply>
<power/>
<ci>s1</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.41</cn>
<apply>
<power/>
<ci>s2</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.6</cn>
<apply>
<power/>
<ci>s3</ci>
<cn cellml:units="dimensionless">6</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">0.4</cn>
</apply>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
<apply>
<and/>
<apply>
<eq/>
<ci>CT</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<eq/>
<ci>PM</ci>
<cn cellml:units="dimensionless">0</cn>
</apply>
</apply>
</piece>
<piece>
<apply>
<times/>
<cn cellml:units="dimensionless">0.35</cn>
<ci>g_to</ci>
<ci>r</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.59</cn>
<apply>
<power/>
<ci>s1</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.41</cn>
<apply>
<power/>
<ci>s2</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.6</cn>
<apply>
<power/>
<ci>s3</ci>
<cn cellml:units="dimensionless">6</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">0.4</cn>
</apply>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
<apply>
<and/>
<apply>
<eq/>
<ci>CT</ci>
<cn cellml:units="dimensionless">0</cn>
</apply>
<apply>
<eq/>
<ci>PM</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<ci>g_to</ci>
<ci>r</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.59</cn>
<apply>
<power/>
<ci>s1</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.41</cn>
<apply>
<power/>
<ci>s2</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.6</cn>
<apply>
<power/>
<ci>s3</ci>
<cn cellml:units="dimensionless">6</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">0.4</cn>
</apply>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>i_sus</ci>
<piecewise>
<piece>
<apply>
<times/>
<cn cellml:units="nanoS">0.0014</cn>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">70</cn>
</apply>
</apply>
<apply>
<and/>
<apply>
<eq/>
<ci>CT</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<eq/>
<ci>PM</ci>
<cn cellml:units="dimensionless">0</cn>
</apply>
</apply>
</piece>
<piece>
<apply>
<times/>
<cn cellml:units="nanoS">0.0024</cn>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">70</cn>
</apply>
</apply>
<apply>
<and/>
<apply>
<eq/>
<ci>CT</ci>
<cn cellml:units="dimensionless">0</cn>
</apply>
<apply>
<eq/>
<ci>PM</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<cn cellml:units="nanoS">0.001</cn>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">70</cn>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component name="Ca_independent_transient_outward_K_current_r_gate">
<variable name="r" units="dimensionless" initial_value="0.00006" public_interface="out"/>
<variable name="alpha_r" units="per_second"/>
<variable name="beta_r" units="per_second"/>
<variable name="tau_r" units="second"/>
<variable name="r_infinity" units="dimensionless"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_r</ci>
<apply>
<times/>
<cn cellml:units="per_second">386.6</cn>
<apply>
<exp/>
<apply>
<divide/>
<ci>V</ci>
<cn cellml:units="millivolt">12</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_r</ci>
<apply>
<times/>
<cn cellml:units="per_second">8.011</cn>
<apply>
<exp/>
<apply>
<divide/>
<ci>V</ci>
<apply>
<minus/>
<cn cellml:units="millivolt">7.2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>r_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">15</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">5.633</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_r</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>alpha_r</ci>
<ci>beta_r</ci>
</apply>
</apply>
<cn type="e-notation" cellml:units="second">4<sep/>-4</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>r</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>r_infinity</ci>
<ci>r</ci>
</apply>
<ci>tau_r</ci>
</apply>
</apply>
</math>
</component>
<component name="Ca_independent_transient_outward_K_current_s1_gate">
<variable name="s1" units="dimensionless" initial_value="0.5753" public_interface="out"/>
<variable name="tau_s1" units="second"/>
<variable name="s1_infinity" units="dimensionless"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>s1_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">28.29</cn>
</apply>
<cn cellml:units="millivolt">7.06</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_s1</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="second">0.5466</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">32.8</cn>
</apply>
<cn cellml:units="millivolt">0.1</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="second">0.0204</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>s1</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>s1_infinity</ci>
<ci>s1</ci>
</apply>
<ci>tau_s1</ci>
</apply>
</apply>
</math>
</component>
<component name="Ca_independent_transient_outward_K_current_s2_gate">
<variable name="s2" units="dimensionless" initial_value="0.39871" public_interface="out"/>
<variable name="tau_s2" units="second"/>
<variable name="s2_infinity" units="dimensionless"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>s2_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">28.29</cn>
</apply>
<cn cellml:units="millivolt">7.06</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_s2</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="second">5.75</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">32.8</cn>
</apply>
<cn cellml:units="millivolt">0.1</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="second">0.45</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">13.54</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">13.97</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>s2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>s2_infinity</ci>
<ci>s2</ci>
</apply>
<ci>tau_s2</ci>
</apply>
</apply>
</math>
</component>
<component name="Ca_independent_transient_outward_K_current_s3_gate">
<variable name="s3" units="dimensionless" initial_value="0.57363" public_interface="out"/>
<variable name="tau_s3" units="second"/>
<variable name="s3_infinity" units="dimensionless"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>s3_infinity</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">50.67</cn>
</apply>
<cn cellml:units="millivolt">27.38</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">0.666</cn>
</apply>
<cn cellml:units="dimensionless">1.666</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_s3</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="second">7.5</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">23</cn>
</apply>
<cn cellml:units="millivolt">0.5</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="second">0.5</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>s3</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>s3_infinity</ci>
<ci>s3</ci>
</apply>
<ci>tau_s3</ci>
</apply>
</apply>
</math>
</component>
<component name="delayed_rectifier_K_current">
<variable name="i_Ks" units="picoA" public_interface="out"/>
<variable name="i_Kr" units="picoA" public_interface="out"/>
<variable name="g_Ks" units="nanoS" initial_value="0.0025"/>
<variable name="g_Kr" units="nanoS" initial_value="0.0035"/>
<variable name="time" units="second" public_interface="in" private_interface="out"/>
<variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
<variable name="E_K" units="millivolt" public_interface="in"/>
<variable name="z" units="dimensionless" private_interface="in"/>
<variable name="p_a" units="dimensionless" private_interface="in"/>
<variable name="p_i" units="dimensionless" private_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Ks</ci>
<apply>
<times/>
<ci>g_Ks</ci>
<ci>z</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_Kr</ci>
<apply>
<times/>
<ci>g_Kr</ci>
<ci>p_a</ci>
<ci>p_i</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="delayed_rectifier_K_current_z_gate">
<variable name="z" units="dimensionless" initial_value="0.02032" public_interface="out"/>
<variable name="alpha_z" units="per_second"/>
<variable name="beta_z" units="per_second"/>
<variable name="tau_z" units="second"/>
<variable name="z_infinity" units="dimensionless"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_z</ci>
<apply>
<times/>
<cn cellml:units="per_second">1.66</cn>
<apply>
<exp/>
<apply>
<divide/>
<ci>V</ci>
<cn cellml:units="millivolt">69.452</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_z</ci>
<apply>
<times/>
<cn cellml:units="per_second">0.3</cn>
<apply>
<exp/>
<apply>
<divide/>
<ci>V</ci>
<apply>
<minus/>
<cn cellml:units="millivolt">21.826</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>z_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">0.9</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">13.8</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_z</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>alpha_z</ci>
<ci>beta_z</ci>
</apply>
</apply>
<cn cellml:units="second">0.06</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>z</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>z_infinity</ci>
<ci>z</ci>
</apply>
<ci>tau_z</ci>
</apply>
</apply>
</math>
</component>
<component name="delayed_rectifier_K_current_pa_gate">
<variable name="p_a" units="dimensionless" initial_value="0.00016" public_interface="out"/>
<variable name="alpha_p_a" units="per_second"/>
<variable name="beta_p_a" units="per_second"/>
<variable name="tau_p_a" units="second"/>
<variable name="p_a_infinity" units="dimensionless"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_p_a</ci>
<apply>
<times/>
<cn cellml:units="per_second">9</cn>
<apply>
<exp/>
<apply>
<divide/>
<ci>V</ci>
<cn cellml:units="millivolt">25.371</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_p_a</ci>
<apply>
<times/>
<cn cellml:units="per_second">1.3</cn>
<apply>
<exp/>
<apply>
<divide/>
<ci>V</ci>
<apply>
<minus/>
<cn cellml:units="millivolt">13.026</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>p_a_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">5.1</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">7.4</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_p_a</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>alpha_p_a</ci>
<ci>beta_p_a</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>p_a</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>p_a_infinity</ci>
<ci>p_a</ci>
</apply>
<ci>tau_p_a</ci>
</apply>
</apply>
</math>
</component>
<component name="delayed_rectifier_K_current_pi_gate">
<variable name="p_i" units="dimensionless" initial_value="0.76898" public_interface="out"/>
<variable name="alpha_p_i" units="per_second"/>
<variable name="beta_p_i" units="per_second"/>
<variable name="tau_p_i" units="second"/>
<variable name="p_i_infinity" units="dimensionless"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_p_i</ci>
<apply>
<times/>
<cn cellml:units="per_second">100</cn>
<apply>
<exp/>
<apply>
<divide/>
<ci>V</ci>
<apply>
<minus/>
<cn cellml:units="millivolt">54.645</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_p_i</ci>
<apply>
<times/>
<cn cellml:units="per_second">656</cn>
<apply>
<exp/>
<apply>
<divide/>
<ci>V</ci>
<cn cellml:units="millivolt">106.157</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>p_i_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">47.3921</cn>
</apply>
<cn cellml:units="millivolt">18.6603</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_p_i</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>alpha_p_i</ci>
<ci>beta_p_i</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>p_i</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>p_i_infinity</ci>
<ci>p_i</ci>
</apply>
<ci>tau_p_i</ci>
</apply>
</apply>
</math>
</component>
<component name="inward_rectifier">
<variable name="i_K1" units="picoA" public_interface="out"/>
<variable name="g_K1" units="nanoS" initial_value="0.00508"/>
<variable name="KmK1" units="millimolar" initial_value="0.59"/>
<variable name="steepK1" units="dimensionless" initial_value="1.393"/>
<variable name="shiftK1" units="millivolt" initial_value="-3.6"/>
<variable name="time" units="second" public_interface="in"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="R" units="millijoule_per_mole_kelvin" public_interface="in"/>
<variable name="F" units="coulomb_per_mole" public_interface="in"/>
<variable name="T" units="kelvin" public_interface="in"/>
<variable name="K_c" units="millimolar" public_interface="in"/>
<variable name="E_K" units="millivolt" public_interface="in"/>
<variable name="CT" units="dimensionless" public_interface="in"/>
<variable name="PM" units="dimensionless" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_K1</ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>g_K1</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci>K_c</ci>
<apply>
<plus/>
<ci>K_c</ci>
<ci>KmK1</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>steepK1</ci>
<ci>F</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
<ci>shiftK1</ci>
</apply>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<and/>
<apply>
<eq/>
<ci>CT</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<eq/>
<ci>PM</ci>
<cn cellml:units="dimensionless">0</cn>
</apply>
</apply>
</piece>
<piece>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2.5</cn>
<ci>g_K1</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci>K_c</ci>
<apply>
<plus/>
<ci>K_c</ci>
<ci>KmK1</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>steepK1</ci>
<ci>F</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
<ci>shiftK1</ci>
</apply>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<and/>
<apply>
<eq/>
<ci>CT</ci>
<cn cellml:units="dimensionless">0</cn>
</apply>
<apply>
<eq/>
<ci>PM</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<apply>
<times/>
<ci>g_K1</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci>K_c</ci>
<apply>
<plus/>
<ci>K_c</ci>
<ci>KmK1</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>steepK1</ci>
<ci>F</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
<ci>shiftK1</ci>
</apply>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component name="background_currents">
<variable name="i_B_Na" units="picoA" public_interface="out"/>
<variable name="i_B_Ca" units="picoA" public_interface="out"/>
<variable name="g_B_Na" units="nanoS" initial_value="6.4e-5"/>
<variable name="g_B_Ca" units="nanoS" initial_value="3.1e-5"/>
<variable name="E_Ca" units="millivolt"/>
<variable name="E_Na" units="millivolt" public_interface="in"/>
<variable name="R" units="millijoule_per_mole_kelvin" public_interface="in"/>
<variable name="F" units="coulomb_per_mole" public_interface="in"/>
<variable name="T" units="kelvin" public_interface="in"/>
<variable name="Ca_c" units="millimolar" public_interface="in"/>
<variable name="Ca_i" units="millimolar" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="CT" units="dimensionless" public_interface="in"/>
<variable name="PM" units="dimensionless" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>E_Ca</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>F</ci>
</apply>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci>Ca_c</ci>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_B_Na</ci>
<piecewise>
<piece>
<apply>
<times/>
<cn cellml:units="nanoS">0.00002</cn>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Na</ci>
</apply>
</apply>
<apply>
<and/>
<apply>
<eq/>
<ci>CT</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<eq/>
<ci>PM</ci>
<cn cellml:units="dimensionless">0</cn>
</apply>
</apply>
</piece>
<piece>
<apply>
<times/>
<cn cellml:units="nanoS">0.00003</cn>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Na</ci>
</apply>
</apply>
<apply>
<and/>
<apply>
<eq/>
<ci>CT</ci>
<cn cellml:units="dimensionless">0</cn>
</apply>
<apply>
<eq/>
<ci>PM</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<ci>g_B_Na</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Na</ci>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>i_B_Ca</ci>
<piecewise>
<piece>
<apply>
<times/>
<cn cellml:units="nanoS">0.00002</cn>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Ca</ci>
</apply>
</apply>
<apply>
<and/>
<apply>
<eq/>
<ci>CT</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<eq/>
<ci>PM</ci>
<cn cellml:units="dimensionless">0</cn>
</apply>
</apply>
</piece>
<piece>
<apply>
<times/>
<cn cellml:units="nanoS">0.00003</cn>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Ca</ci>
</apply>
</apply>
<apply>
<and/>
<apply>
<eq/>
<ci>CT</ci>
<cn cellml:units="dimensionless">0</cn>
</apply>
<apply>
<eq/>
<ci>PM</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<ci>g_B_Ca</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Ca</ci>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component name="sodium_potassium_pump">
<variable name="i_p" units="picoA" public_interface="out"/>
<variable name="k_NaK_K" units="millimolar" initial_value="1"/>
<variable name="k_NaK_Na" units="millimolar" initial_value="11"/>
<variable name="i_NaK_max" units="picoA" initial_value="0.06441"/>
<variable name="K_c" units="millimolar" public_interface="in"/>
<variable name="Na_i" units="millimolar" public_interface="in"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_p</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>i_NaK_max</ci>
<ci>K_c</ci>
</apply>
<apply>
<plus/>
<ci>K_c</ci>
<ci>k_NaK_K</ci>
</apply>
</apply>
<apply>
<power/>
<ci>Na_i</ci>
<cn cellml:units="dimensionless">1.5</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>Na_i</ci>
<cn cellml:units="dimensionless">1.5</cn>
</apply>
<apply>
<power/>
<ci>k_NaK_Na</ci>
<cn cellml:units="dimensionless">1.5</cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">1.6</cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1.5</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">60</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">40</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sarcolemmal_calcium_pump_current">
<variable name="i_CaP" units="picoA" public_interface="out"/>
<variable name="i_CaP_max" units="picoA" initial_value="0.009509"/>
<variable name="k_CaP" units="millimolar" initial_value="2e-4"/>
<variable name="Ca_i" units="millimolar" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_CaP</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>i_CaP_max</ci>
<ci>Ca_i</ci>
</apply>
<apply>
<plus/>
<ci>Ca_i</ci>
<ci>k_CaP</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Na_Ca_ion_exchanger_current">
<variable name="i_NaCa" units="picoA" public_interface="out"/>
<variable name="k_NaCa" units="picoA_per_millimolar_4" initial_value="2e-5"/>
<variable name="d_NaCa" units="per_millimolar_4" initial_value="3e-4"/>
<variable name="gamma" units="dimensionless" initial_value="0.45"/>
<variable name="Na_i" units="millimolar" public_interface="in"/>
<variable name="Na_c" units="millimolar" public_interface="in"/>
<variable name="Ca_i" units="millimolar" public_interface="in"/>
<variable name="Ca_c" units="millimolar" public_interface="in"/>
<variable name="R" units="millijoule_per_mole_kelvin" public_interface="in"/>
<variable name="F" units="coulomb_per_mole" public_interface="in"/>
<variable name="T" units="kelvin" public_interface="in"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_NaCa</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k_NaCa</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<power/>
<ci>Na_i</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>Ca_c</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>gamma</ci>
<ci>F</ci>
<ci>V</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>Na_c</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>Ca_i</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>gamma</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>d_NaCa</ci>
<apply>
<plus/>
<apply>
<times/>
<apply>
<power/>
<ci>Na_c</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>Ca_i</ci>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>Na_i</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>Ca_c</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="intracellular_ion_concentrations">
<variable name="Na_i" units="millimolar" initial_value="8.4" public_interface="out"/>
<variable name="Ca_i" units="millimolar" initial_value="0.000071" public_interface="out"/>
<variable name="K_i" units="millimolar" initial_value="100" public_interface="out"/>
<variable name="Vol_i" units="nanolitre" initial_value="1.26e-5" public_interface="out"/>
<variable name="Vol_Ca" units="nanolitre" initial_value="5.884e-6"/>
<variable name="time" units="second" public_interface="in"/>
<variable name="F" units="coulomb_per_mole" public_interface="in"/>
<variable name="i_Na" units="picoA" public_interface="in"/>
<variable name="i_Ca_L" units="picoA" public_interface="in"/>
<variable name="i_Ca_T" units="picoA" public_interface="in"/>
<variable name="i_B_Na" units="picoA" public_interface="in"/>
<variable name="i_NaCa" units="picoA" public_interface="in"/>
<variable name="i_p" units="picoA" public_interface="in"/>
<variable name="i_Kr" units="picoA" public_interface="in"/>
<variable name="i_Ks" units="picoA" public_interface="in"/>
<variable name="i_K1" units="picoA" public_interface="in"/>
<variable name="i_to" units="picoA" public_interface="in"/>
<variable name="i_sus" units="picoA" public_interface="in"/>
<variable name="i_CaP" units="picoA" public_interface="in"/>
<variable name="i_B_Ca" units="picoA" public_interface="in"/>
<variable name="i_up" units="picoA" public_interface="in"/>
<variable name="i_rel" units="picoA" public_interface="in"/>
<variable name="dOCdt" units="per_second" public_interface="in"/>
<variable name="dOTCdt" units="per_second" public_interface="in"/>
<variable name="dOTMgCdt" units="per_second" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Na_i</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_Na</ci>
<ci>i_B_Na</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>i_p</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>i_NaCa</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>Vol_i</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>K_i</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_to</ci>
<ci>i_sus</ci>
<ci>i_K1</ci>
<ci>i_Kr</ci>
<ci>i_Ks</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>i_p</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>Vol_i</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_i</ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_Ca_L</ci>
<ci>i_Ca_T</ci>
<ci>i_B_Ca</ci>
<ci>i_CaP</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>i_NaCa</ci>
</apply>
</apply>
<ci>i_up</ci>
</apply>
<ci>i_rel</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>Vol_Ca</ci>
<ci>F</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="millimolar">0.08</cn>
<ci>dOTCdt</ci>
</apply>
<apply>
<times/>
<cn cellml:units="millimolar">0.16</cn>
<ci>dOTMgCdt</ci>
</apply>
<apply>
<times/>
<cn cellml:units="millimolar">0.045</cn>
<ci>dOCdt</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="intracellular_Ca_buffering">
<variable name="O_C" units="dimensionless" initial_value="0.029108"/>
<variable name="dOCdt" units="per_second" public_interface="out"/>
<variable name="O_TC" units="dimensionless" initial_value="0.014071"/>
<variable name="dOTCdt" units="per_second" public_interface="out"/>
<variable name="O_TMgC" units="dimensionless" initial_value="0.214036"/>
<variable name="dOTMgCdt" units="per_second" public_interface="out"/>
<variable name="O_TMgMg" units="dimensionless" initial_value="0.693565" public_interface="out"/>
<variable name="Mg_i" units="millimolar" initial_value="2.5"/>
<variable name="Ca_i" units="millimolar" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>dOCdt</ci>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="per_millimolar_second">200000</cn>
<ci>Ca_i</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>O_C</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_second">476</cn>
<ci>O_C</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>O_C</ci>
</apply>
<ci>dOCdt</ci>
</apply>
<apply>
<eq/>
<ci>dOTCdt</ci>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="per_millimolar_second">78400</cn>
<ci>Ca_i</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>O_TC</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_second">392</cn>
<ci>O_TC</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>O_TC</ci>
</apply>
<ci>dOTCdt</ci>
</apply>
<apply>
<eq/>
<ci>dOTMgCdt</ci>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="per_millimolar_second">200000</cn>
<ci>Ca_i</ci>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>O_TMgC</ci>
</apply>
<ci>O_TMgMg</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_second">6.6</cn>
<ci>O_TMgC</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>O_TMgC</ci>
</apply>
<ci>dOTMgCdt</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>O_TMgMg</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="per_millimolar_second">2000</cn>
<ci>Mg_i</ci>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>O_TMgC</ci>
</apply>
<ci>O_TMgMg</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_second">666</cn>
<ci>O_TMgMg</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="cleft_space_ion_concentrations">
<variable name="Na_c" units="millimolar" initial_value="140" public_interface="out"/>
<variable name="Ca_c" units="millimolar" initial_value="2.5" public_interface="out"/>
<variable name="K_c" units="millimolar" initial_value="5" public_interface="out"/>
<variable name="Vol_c" units="nanolitre" initial_value="0.0000025" public_interface="out"/>
<variable name="time" units="second" public_interface="in"/>
<variable name="F" units="coulomb_per_mole" public_interface="in"/>
<variable name="i_p" units="picoA" public_interface="in"/>
<variable name="i_Kr" units="picoA" public_interface="in"/>
<variable name="i_Ks" units="picoA" public_interface="in"/>
<variable name="i_K1" units="picoA" public_interface="in"/>
<variable name="i_to" units="picoA" public_interface="in"/>
<variable name="i_sus" units="picoA" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>K_c</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_to</ci>
<ci>i_sus</ci>
<ci>i_K1</ci>
<ci>i_Kr</ci>
<ci>i_Ks</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>i_p</ci>
</apply>
</apply>
<apply>
<times/>
<ci>Vol_c</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Ca_handling_by_the_SR">
<variable name="i_rel" units="picoA" public_interface="out"/>
<variable name="i_up" units="picoA" public_interface="out"/>
<variable name="i_tr" units="picoA"/>
<variable name="I_up_max" units="picoA" initial_value="2.8"/>
<variable name="k_cyca" units="millimolar" initial_value="0.0003"/>
<variable name="k_srca" units="millimolar" initial_value="0.5"/>
<variable name="k_xcs" units="dimensionless" initial_value="0.4"/>
<variable name="alpha_rel" units="picoA_per_millimolar" initial_value="200"/>
<variable name="Ca_rel" units="millimolar" initial_value="0.726776"/>
<variable name="Ca_up" units="millimolar" initial_value="0.730866"/>
<variable name="Vol_up" units="nanolitre" initial_value="3.969e-7"/>
<variable name="Vol_rel" units="nanolitre" initial_value="4.4e-8"/>
<variable name="r_act" units="per_second"/>
<variable name="r_inact" units="per_second"/>
<variable name="O_Calse" units="dimensionless" initial_value="0.465921"/>
<variable name="F1" units="dimensionless" initial_value="0.288039"/>
<variable name="F2" units="dimensionless" initial_value="0.002262"/>
<variable name="F3" units="dimensionless" initial_value="0.612697"/>
<variable name="tau_tr" units="second" initial_value="0.01"/>
<variable name="k_rel" units="millimolar" initial_value="0.0003"/>
<variable name="k_F3" units="per_second" initial_value="0.815"/>
<variable name="time" units="second" public_interface="in"/>
<variable name="Ca_i" units="millimolar" public_interface="in"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="F" units="coulomb_per_mole" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>O_Calse</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="per_millimolar_second">480</cn>
<ci>Ca_rel</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>O_Calse</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_second">400</cn>
<ci>O_Calse</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_rel</ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<ci>i_tr</ci>
<ci>i_rel</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>Vol_rel</ci>
<ci>F</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="millimolar">31</cn>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>O_Calse</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_up</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>i_up</ci>
<ci>i_tr</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>Vol_up</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>F1</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k_F3</ci>
<ci>F3</ci>
</apply>
<apply>
<times/>
<ci>r_act</ci>
<ci>F1</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>F2</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>r_act</ci>
<ci>F1</ci>
</apply>
<apply>
<times/>
<ci>r_inact</ci>
<ci>F2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>F3</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>F2</ci>
<ci>r_inact</ci>
</apply>
<apply>
<times/>
<ci>k_F3</ci>
<ci>F3</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>r_act</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_second">240</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.08</cn>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">20</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_second">203.8</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_i</ci>
<apply>
<plus/>
<ci>Ca_i</ci>
<ci>k_rel</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>r_inact</ci>
<apply>
<plus/>
<cn cellml:units="per_second">33.96</cn>
<apply>
<times/>
<cn cellml:units="per_second">339.6</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_i</ci>
<apply>
<plus/>
<ci>Ca_i</ci>
<ci>k_rel</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_up</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>I_up_max</ci>
<apply>
<minus/>
<apply>
<divide/>
<ci>Ca_i</ci>
<ci>k_cyca</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<power/>
<ci>k_xcs</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>Ca_up</ci>
</apply>
<ci>k_srca</ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<plus/>
<ci>Ca_i</ci>
<ci>k_cyca</ci>
</apply>
<ci>k_cyca</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>k_xcs</ci>
<apply>
<plus/>
<ci>Ca_up</ci>
<ci>k_srca</ci>
</apply>
</apply>
<ci>k_srca</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_tr</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>Ca_up</ci>
<ci>Ca_rel</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
<ci>F</ci>
<ci>Vol_rel</ci>
</apply>
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<times/>
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<apply>
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<ci>F2</ci>
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</math>
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<connection>
<map_components component_1="Na_Ca_ion_exchanger_current" component_2="environment"/>
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<connection>
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<connection>
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<connection>
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<connection>
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<connection>
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<connection>
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<connection>
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<connection>
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<connection>
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<connection>
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<connection>
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<dc:title>
Mechanisms of transition from normal to reentrant electrical activity in a model of rabbit atrial tissue: interaction of tissue heterogeneity and anisotropy
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<dcterms:W3CDTF>2009-02</dcterms:W3CDTF>
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<dc:title>Biophysical Journal</dc:title>
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