- Author:
- James Lawson <j.lawson@auckland.ac.nz>
- Date:
- 2009-07-20 15:51:26+12:00
- Desc:
- for a, b, c: fixed e-notation, updated curation status, fixed ten Tusscher > Ten Tusscher in citation metadata
- Permanent Source URI:
- http://models.cellml.org/workspace/605/rawfile/5005395a3f3c6d075a7332a2eb7ade87fdbe2bdb/tentusscher_noble_noble_panfilov_2004_b.cellml
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<!--
This CellML file was generated on 05/11/2007 at 17:02:56 using:
COR (0.9.31.801)
Copyright 2002-2007 Dr Alan Garny
http://COR.physiol.ox.ac.uk/ - COR@physiol.ox.ac.uk
CellML 1.0 was used to generate this cellular model
http://www.CellML.org/
-->
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<article>
<articleinfo>
<title>A Model For Human Ventricular Tissue - epicardial cell variant</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This variant of the model was created by Penny Noble of Oxford University, and represents the parameters given for the epicardial cell variant in Ten Tusscher et al. 2004. This file is known to run in OpenCell and COR.
</para>
<para> This file is valid CellML and has full unit consistency.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Cardiac arrhythmias and sudden cardiac death are amongst the most common causes of premature death in the devloped world. However despite their prevalance, they remain relatively poorly understood. Mathematical models, which capture the function of the beating human heart, play an important role in cardiac research. In part this is because practical experiments on human hearts are limited, and animal hearts may differ significantly in their anatomy and physiology relative to the human heart. In addition, cardiac arrhythmias are three dimensional phenomena, while experimental observations are mainly limited to surface recordings.
</para>
<para>
Existing mathematical models of human ventricular cells include:
</para>
<itemizedlist>
<listitem>
<para>
>Priebe and Beuckelmann, Electrophysiological Model of the Human Ventricular Myocyte, 1998; and</para>
</listitem>
<listitem>
<para>
Bernus <emphasis>et al.</emphasis> A Computationally Efficient Electrophysiological Model of Human Ventricular Cells, 2002.</para>
</listitem>
<listitem>
<para/>
</listitem>
</itemizedlist>
<para>
However, these models have their limitations, such as the fact that several of the equations are based on animal data. The aim of the 2004 study by ten Tusscher <emphasis>et al.</emphasis>, is to develop a new model for human ventricular cells that is based on recent experimetnal data and that is computationally efficient for large-scale spatial simulations. A schematic diagrma of the modl can be seen in <xref linkend="fig_cell_diagram"/> below.
</para>
<para>
The model has been described here in CellML (the raw CellML description of the ten Tusscher <emphasis>et al.</emphasis> 2004 model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>).
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
A model for human ventricular tissue, K.H.W.J. ten Tusscher, D. Noble, P.J. Noble, and A.V. Panfilov, 2004,
<emphasis>American Journal of Physiology</emphasis>
, 286, H1573-H1589. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=14656705&dopt=Abstract">PubMed ID: 14656705</ulink>
</para>
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<caption>A schematic diagram describing the ion movement across the cell surface membrane and the sarcoplasmic reticulum, which are described by the Ten Tusscher <emphasis>et al.</emphasis> 2004 mathematical model of the human ventricular myocyte.</caption>
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</sect1>
</article>
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<apply>
<power/>
<ci>Xs</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Ks</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="slow_time_dependent_potassium_current_Xs_gate">
<variable units="dimensionless" public_interface="out" name="Xs" initial_value="0"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="dimensionless" name="xs_inf"/>
<variable units="dimensionless" name="alpha_xs"/>
<variable units="dimensionless" name="beta_xs"/>
<variable units="millisecond" name="tau_xs"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>xs_inf</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="millivolt">5</cn>
</apply>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">14</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_xs</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1100</cn>
<apply>
<root/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="millivolt">10</cn>
</apply>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">6</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_xs</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">60</cn>
</apply>
<cn cellml:units="millivolt">20</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_xs</ci>
<apply>
<times/>
<cn cellml:units="millisecond">1</cn>
<ci>alpha_xs</ci>
<ci>beta_xs</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Xs</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>xs_inf</ci>
<ci>Xs</ci>
</apply>
<ci>tau_xs</ci>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current">
<variable units="picoA_per_picoF" public_interface="out" name="i_Na"/>
<variable units="nanoS_per_picoF" name="g_Na" initial_value="14.838"/>
<variable units="millivolt" public_interface="in" name="E_Na"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="m"/>
<variable units="dimensionless" private_interface="in" name="h"/>
<variable units="dimensionless" private_interface="in" name="j"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Na</ci>
<apply>
<times/>
<ci>g_Na</ci>
<apply>
<power/>
<ci>m</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>h</ci>
<ci>j</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Na</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current_m_gate">
<variable units="dimensionless" public_interface="out" name="m" initial_value="0"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="dimensionless" name="m_inf"/>
<variable units="dimensionless" name="alpha_m"/>
<variable units="dimensionless" name="beta_m"/>
<variable units="millisecond" name="tau_m"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>m_inf</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="millivolt">56.86</cn>
</apply>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">9.03</cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_m</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="millivolt">60</cn>
</apply>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_m</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="dimensionless">0.1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">35</cn>
</apply>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="dimensionless">0.1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">50</cn>
</apply>
<cn cellml:units="millivolt">200</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_m</ci>
<apply>
<times/>
<cn cellml:units="millisecond">1</cn>
<ci>alpha_m</ci>
<ci>beta_m</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>m</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>m_inf</ci>
<ci>m</ci>
</apply>
<ci>tau_m</ci>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current_h_gate">
<variable units="dimensionless" public_interface="out" name="h" initial_value="0.75"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="dimensionless" name="h_inf"/>
<variable units="per_millisecond" name="alpha_h"/>
<variable units="per_millisecond" name="beta_h"/>
<variable units="millisecond" name="tau_h"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>h_inf</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">71.55</cn>
</apply>
<cn cellml:units="millivolt">7.43</cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_h</ci>
<piecewise>
<piece>
<apply>
<times/>
<cn cellml:units="per_millisecond">0.057</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">80</cn>
</apply>
</apply>
<cn cellml:units="millivolt">6.8</cn>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci>V</ci>
<apply>
<minus/>
<cn cellml:units="millivolt">40</cn>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="per_millisecond">0</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>beta_h</ci>
<piecewise>
<piece>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_millisecond">2.7</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.079</cn>
<ci>V</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_millisecond">310000</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.3485</cn>
<ci>V</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci>V</ci>
<apply>
<minus/>
<cn cellml:units="millivolt">40</cn>
</apply>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<cn cellml:units="per_millisecond">0.77</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">0.13</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">10.66</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">11.1</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>tau_h</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>alpha_h</ci>
<ci>beta_h</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>h</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>h_inf</ci>
<ci>h</ci>
</apply>
<ci>tau_h</ci>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current_j_gate">
<variable units="dimensionless" public_interface="out" name="j" initial_value="0.75"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="dimensionless" name="j_inf"/>
<variable units="per_millisecond" name="alpha_j"/>
<variable units="per_millisecond" name="beta_j"/>
<variable units="millisecond" name="tau_j"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>j_inf</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">71.55</cn>
</apply>
<cn cellml:units="millivolt">7.43</cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_j</ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millisecond">25428</cn>
</apply>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.2444</cn>
<ci>V</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_millisecond" type="e-notation">6.948<sep/>-6</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt">0.04391</cn>
</apply>
<ci>V</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">37.78</cn>
</apply>
</apply>
<cn cellml:units="millivolt">1</cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.311</cn>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">79.23</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci>V</ci>
<apply>
<minus/>
<cn cellml:units="millivolt">40</cn>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="per_millisecond">0</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>beta_j</ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millisecond">0.02424</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt">0.01052</cn>
</apply>
<ci>V</ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt">0.1378</cn>
</apply>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">40.14</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci>V</ci>
<apply>
<minus/>
<cn cellml:units="millivolt">40</cn>
</apply>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millisecond">0.6</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.057</cn>
<ci>V</ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt">0.1</cn>
</apply>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">32</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>tau_j</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>alpha_j</ci>
<ci>beta_j</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>j</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>j_inf</ci>
<ci>j</ci>
</apply>
<ci>tau_j</ci>
</apply>
</apply>
</math>
</component>
<component name="sodium_background_current">
<variable units="picoA_per_picoF" public_interface="out" name="i_b_Na"/>
<variable units="nanoS_per_picoF" name="g_bna" initial_value="0.00029"/>
<variable units="millivolt" public_interface="in" name="E_Na"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_b_Na</ci>
<apply>
<times/>
<ci>g_bna</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Na</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_current">
<variable units="picoA_per_picoF" public_interface="out" name="i_CaL"/>
<variable units="litre_per_farad_second" name="g_CaL" initial_value="0.000175"/>
<variable units="millimolar" public_interface="in" name="Ca_o"/>
<variable units="millimolar" public_interface="in" private_interface="out" name="Ca_i"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" public_interface="out" private_interface="in" name="d"/>
<variable units="dimensionless" private_interface="in" name="f"/>
<variable units="dimensionless" private_interface="in" name="fCa"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_CaL</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>g_CaL</ci>
<ci>d</ci>
<ci>f</ci>
<ci>fCa</ci>
<cn cellml:units="dimensionless">4</cn>
<ci>V</ci>
<apply>
<power/>
<ci>F</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>Ca_i</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.341</cn>
<ci>Ca_o</ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_current_d_gate">
<variable units="dimensionless" public_interface="out" name="d" initial_value="0"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="dimensionless" name="d_inf"/>
<variable units="dimensionless" name="alpha_d"/>
<variable units="dimensionless" name="beta_d"/>
<variable units="millisecond" name="gamma_d"/>
<variable units="millisecond" name="tau_d"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>d_inf</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="millivolt">5</cn>
</apply>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">7.5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_d</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="dimensionless">1.4</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="millivolt">35</cn>
</apply>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">13</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">0.25</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_d</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1.4</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">5</cn>
</apply>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>gamma_d</ci>
<apply>
<divide/>
<cn cellml:units="millisecond">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="millivolt">50</cn>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">20</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_d</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="millisecond">1</cn>
<ci>alpha_d</ci>
<ci>beta_d</ci>
</apply>
<ci>gamma_d</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>d</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>d_inf</ci>
<ci>d</ci>
</apply>
<ci>tau_d</ci>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_current_f_gate">
<variable units="dimensionless" public_interface="out" name="f" initial_value="1"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="dimensionless" name="f_inf"/>
<variable units="millisecond" name="tau_f"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>f_inf</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">20</cn>
</apply>
<cn cellml:units="millivolt">7</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_f</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="millisecond">1125</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">27</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<cn cellml:units="millivolt_square">240</cn>
</apply>
</apply>
</apply>
<cn cellml:units="millisecond">80</cn>
<apply>
<divide/>
<cn cellml:units="millisecond">165</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="millivolt">25</cn>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>f</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>f_inf</ci>
<ci>f</ci>
</apply>
<ci>tau_f</ci>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_current_fCa_gate">
<variable units="dimensionless" public_interface="out" name="fCa" initial_value="1"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="dimensionless" name="alpha_fCa"/>
<variable units="dimensionless" name="beta_fCa"/>
<variable units="dimensionless" name="gama_fCa"/>
<variable units="dimensionless" name="fCa_inf"/>
<variable units="millisecond" name="tau_fCa"/>
<variable units="per_millisecond" name="d_fCa"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_fCa</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_i</ci>
<cn cellml:units="millimolar">0.000325</cn>
</apply>
<cn cellml:units="dimensionless">8</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_fCa</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">0.1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>Ca_i</ci>
<cn cellml:units="millimolar">0.0005</cn>
</apply>
<cn cellml:units="millimolar">0.0001</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>gama_fCa</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">0.2</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>Ca_i</ci>
<cn cellml:units="millimolar">0.00075</cn>
</apply>
<cn cellml:units="millimolar">0.0008</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>fCa_inf</ci>
<apply>
<divide/>
<apply>
<plus/>
<ci>alpha_fCa</ci>
<ci>beta_fCa</ci>
<ci>gama_fCa</ci>
<cn cellml:units="dimensionless">0.23</cn>
</apply>
<cn cellml:units="dimensionless">1.46</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_fCa</ci>
<cn cellml:units="millisecond">2</cn>
</apply>
<apply>
<eq/>
<ci>d_fCa</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>fCa_inf</ci>
<ci>fCa</ci>
</apply>
<ci>tau_fCa</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>fCa</ci>
</apply>
<piecewise>
<piece>
<cn cellml:units="per_millisecond">0</cn>
<apply>
<and/>
<apply>
<gt/>
<apply>
<times/>
<cn cellml:units="millisecond">0.01</cn>
<ci>d_fCa</ci>
</apply>
<cn cellml:units="dimensionless">0</cn>
</apply>
<apply>
<gt/>
<ci>V</ci>
<apply>
<minus/>
<cn cellml:units="millivolt">60</cn>
</apply>
</apply>
</apply>
</piece>
<otherwise>
<ci>d_fCa</ci>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component name="calcium_background_current">
<variable units="picoA_per_picoF" public_interface="out" name="i_b_Ca"/>
<variable units="nanoS_per_picoF" name="g_bca" initial_value="0.000592"/>
<variable units="millivolt" public_interface="in" name="E_Ca"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_b_Ca</ci>
<apply>
<times/>
<ci>g_bca</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Ca</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="transient_outward_current">
<variable units="picoA_per_picoF" public_interface="out" name="i_to"/>
<variable units="nanoS_per_picoF" name="g_to" initial_value="0.294"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="dimensionless" private_interface="in" name="s"/>
<variable units="dimensionless" private_interface="in" name="r"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_to</ci>
<apply>
<times/>
<ci>g_to</ci>
<ci>r</ci>
<ci>s</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="transient_outward_current_s_gate">
<variable units="dimensionless" public_interface="out" name="s" initial_value="1"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="dimensionless" name="s_inf"/>
<variable units="millisecond" name="tau_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>s_inf</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">20</cn>
</apply>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_s</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="millisecond">85</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">45</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<cn cellml:units="millivolt_square">320</cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="millisecond">5</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">20</cn>
</apply>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="millisecond">3</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>s</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>s_inf</ci>
<ci>s</ci>
</apply>
<ci>tau_s</ci>
</apply>
</apply>
</math>
</component>
<component name="transient_outward_current_r_gate">
<variable units="dimensionless" public_interface="out" name="r" initial_value="0"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="dimensionless" name="r_inf"/>
<variable units="millisecond" name="tau_r"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>r_inf</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="millivolt">20</cn>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">6</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_r</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="millisecond">9.5</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">40</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<cn cellml:units="millivolt_square">1800</cn>
</apply>
</apply>
</apply>
<cn cellml:units="millisecond">0.8</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>r</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>r_inf</ci>
<ci>r</ci>
</apply>
<ci>tau_r</ci>
</apply>
</apply>
</math>
</component>
<component name="sodium_potassium_pump_current">
<variable units="picoA_per_picoF" public_interface="out" name="i_NaK"/>
<variable units="picoA_per_picoF" name="P_NaK" initial_value="1.362"/>
<variable units="millimolar" name="K_mk" initial_value="1"/>
<variable units="millimolar" name="K_mNa" initial_value="40"/>
<variable units="millimolar" public_interface="in" name="K_o"/>
<variable units="millimolar" public_interface="in" name="Na_i"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_NaK</ci>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>P_NaK</ci>
<ci>K_o</ci>
</apply>
<apply>
<plus/>
<ci>K_o</ci>
<ci>K_mk</ci>
</apply>
</apply>
<ci>Na_i</ci>
</apply>
<apply>
<plus/>
<ci>Na_i</ci>
<ci>K_mNa</ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">0.1245</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">0.1</cn>
</apply>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.0353</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>V</ci>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_calcium_exchanger_current">
<variable units="picoA_per_picoF" public_interface="out" name="i_NaCa"/>
<variable units="picoA_per_picoF" name="K_NaCa" initial_value="1000"/>
<variable units="dimensionless" name="K_sat" initial_value="0.1"/>
<variable units="dimensionless" name="alpha" initial_value="2.5"/>
<variable units="dimensionless" name="gamma" initial_value="0.35"/>
<variable units="millimolar" name="Km_Ca" initial_value="1.38"/>
<variable units="millimolar" name="Km_Nai" initial_value="87.5"/>
<variable units="millimolar" public_interface="in" name="Na_i"/>
<variable units="millimolar" public_interface="in" name="Na_o"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="millimolar" public_interface="in" name="Ca_o"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<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>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>gamma</ci>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci>Na_i</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>Ca_o</ci>
</apply>
<apply>
<times/>
<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>
<power/>
<ci>Na_o</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>Ca_i</ci>
<ci>alpha</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<power/>
<ci>Km_Nai</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<apply>
<power/>
<ci>Na_o</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
<apply>
<plus/>
<ci>Km_Ca</ci>
<ci>Ca_o</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>K_sat</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>
</apply>
</math>
</component>
<component name="calcium_pump_current">
<variable units="picoA_per_picoF" public_interface="out" name="i_p_Ca"/>
<variable units="picoA_per_picoF" name="g_pCa" initial_value="0.825"/>
<variable units="millimolar" name="K_pCa" initial_value="0.0005"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_p_Ca</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>g_pCa</ci>
<ci>Ca_i</ci>
</apply>
<apply>
<plus/>
<ci>Ca_i</ci>
<ci>K_pCa</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="potassium_pump_current">
<variable units="picoA_per_picoF" public_interface="out" name="i_p_K"/>
<variable units="nanoS_per_picoF" name="g_pK" initial_value="0.0146"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_p_K</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>g_pK</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="millivolt">25</cn>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">5.98</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_dynamics">
<variable units="millimolar" public_interface="out" name="Ca_i" initial_value="0.0002"/>
<variable units="millimolar" public_interface="out" name="Ca_o" initial_value="2"/>
<variable units="millimolar" name="Ca_SR" initial_value="0.2"/>
<variable units="millimolar_per_millisecond" name="i_rel"/>
<variable units="millimolar_per_millisecond" name="i_up"/>
<variable units="millimolar_per_millisecond" name="i_leak"/>
<variable units="dimensionless" name="g" initial_value="1"/>
<variable units="millisecond" name="tau_g" initial_value="2"/>
<variable units="dimensionless" name="g_inf"/>
<variable units="millimolar_per_millisecond" name="a_rel" initial_value="0.016464"/>
<variable units="millimolar" name="b_rel" initial_value="0.25"/>
<variable units="millimolar_per_millisecond" name="c_rel" initial_value="0.008232"/>
<variable units="millimolar" name="K_up" initial_value="0.00025"/>
<variable units="per_millisecond" name="V_leak" initial_value="8e-5"/>
<variable units="millimolar_per_millisecond" name="Vmax_up" initial_value="0.000425"/>
<variable units="dimensionless" name="Ca_i_bufc"/>
<variable units="dimensionless" name="Ca_sr_bufsr"/>
<variable units="millimolar" name="Buf_c" initial_value="0.15"/>
<variable units="millimolar" name="K_buf_c" initial_value="0.001"/>
<variable units="millimolar" name="Buf_sr" initial_value="10"/>
<variable units="millimolar" name="K_buf_sr" initial_value="0.3"/>
<variable units="micrometre3" name="V_sr" initial_value="0.001094"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="micrometre3" public_interface="in" name="V_c"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="dimensionless" public_interface="in" name="d"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="microF" public_interface="in" name="Cm"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_CaL"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_NaCa"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_p_Ca"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_b_Ca"/>
<variable units="per_millisecond" name="d_g"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_rel</ci>
<apply>
<times/>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<ci>a_rel</ci>
<apply>
<power/>
<ci>Ca_SR</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>b_rel</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>Ca_SR</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<ci>c_rel</ci>
</apply>
<ci>d</ci>
<ci>g</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>i_up</ci>
<apply>
<divide/>
<ci>Vmax_up</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<power/>
<ci>K_up</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>Ca_i</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_leak</ci>
<apply>
<times/>
<ci>V_leak</ci>
<apply>
<minus/>
<ci>Ca_SR</ci>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>g_inf</ci>
<piecewise>
<piece>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_i</ci>
<cn cellml:units="millimolar">0.00035</cn>
</apply>
<cn cellml:units="dimensionless">6</cn>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci>Ca_i</ci>
<cn cellml:units="millimolar">0.00035</cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_i</ci>
<cn cellml:units="millimolar">0.00035</cn>
</apply>
<cn cellml:units="dimensionless">16</cn>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>d_g</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>g_inf</ci>
<ci>g</ci>
</apply>
<ci>tau_g</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>g</ci>
</apply>
<piecewise>
<piece>
<cn cellml:units="per_millisecond">0</cn>
<apply>
<and/>
<apply>
<gt/>
<apply>
<times/>
<cn cellml:units="millisecond">0.01</cn>
<ci>d_g</ci>
</apply>
<cn cellml:units="dimensionless">0</cn>
</apply>
<apply>
<gt/>
<ci>V</ci>
<apply>
<minus/>
<cn cellml:units="millivolt">60</cn>
</apply>
</apply>
</apply>
</piece>
<otherwise>
<ci>d_g</ci>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>Ca_i_bufc</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<times/>
<ci>Buf_c</ci>
<ci>K_buf_c</ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci>Ca_i</ci>
<ci>K_buf_c</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ca_sr_bufsr</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<times/>
<ci>Buf_sr</ci>
<ci>K_buf_sr</ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci>Ca_SR</ci>
<ci>K_buf_sr</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_i</ci>
</apply>
<apply>
<times/>
<ci>Ca_i_bufc</ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<ci>i_leak</ci>
<ci>i_up</ci>
</apply>
<ci>i_rel</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="mA_pA">1</cn>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_CaL</ci>
<ci>i_b_Ca</ci>
<ci>i_p_Ca</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>i_NaCa</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<cn cellml:units="litre_micrometre3">1</cn>
<ci>V_c</ci>
<ci>F</ci>
</apply>
</apply>
<ci>Cm</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_SR</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>Ca_sr_bufsr</ci>
<ci>V_c</ci>
</apply>
<ci>V_sr</ci>
</apply>
<apply>
<minus/>
<ci>i_up</ci>
<apply>
<plus/>
<ci>i_rel</ci>
<ci>i_leak</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_dynamics">
<variable units="millimolar" public_interface="out" name="Na_i" initial_value="11.6"/>
<variable units="millimolar" public_interface="out" name="Na_o" initial_value="140"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="microF" public_interface="in" name="Cm"/>
<variable units="micrometre3" public_interface="in" name="V_c"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_Na"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_NaCa"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_NaK"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_b_Na"/>
<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>
<times/>
<apply>
<minus/>
<cn cellml:units="mA_pA">1</cn>
</apply>
<apply>
<plus/>
<ci>i_Na</ci>
<ci>i_b_Na</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>i_NaK</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>i_NaCa</ci>
</apply>
</apply>
<ci>Cm</ci>
</apply>
<apply>
<times/>
<cn cellml:units="litre_micrometre3">1</cn>
<ci>V_c</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="potassium_dynamics">
<variable units="millimolar" public_interface="out" name="K_i" initial_value="138.3"/>
<variable units="millimolar" public_interface="out" name="K_o" initial_value="5.4"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="microF" public_interface="in" name="Cm"/>
<variable units="micrometre3" public_interface="in" name="V_c"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_K1"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_to"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_NaK"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_Kr"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_Ks"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_p_K"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_Stim"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>K_i</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="mA_pA">1</cn>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_K1</ci>
<ci>i_to</ci>
<ci>i_Kr</ci>
<ci>i_Ks</ci>
<ci>i_p_K</ci>
<ci>i_Stim</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>i_NaK</ci>
</apply>
</apply>
<ci>Cm</ci>
</apply>
<apply>
<times/>
<cn cellml:units="litre_micrometre3">1</cn>
<ci>V_c</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="stimulus_protocol">
<variable units="picoA_per_picoF" public_interface="out" name="Istim" cmeta:id="stimulus_protocol_Istim"/>
<variable units="millisecond" cmeta:id="stimulus_protocol_IstimStart" name="IstimStart" initial_value="100"/>
<variable units="millisecond" cmeta:id="stimulus_protocol_IstimEnd" name="IstimEnd" initial_value="50000"/>
<variable units="picoA_per_picoF" cmeta:id="stimulus_protocol_IstimAmplitude" name="IstimAmplitude" initial_value="-52"/>
<variable units="millisecond" cmeta:id="stimulus_protocol_IstimPeriod" name="IstimPeriod" initial_value="1000"/>
<variable units="millisecond" cmeta:id="stimulus_protocol_IstimPulseDuration" name="IstimPulseDuration" initial_value="1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="Stimulus_Current_Equation">
<apply>
<eq/>
<ci>Istim</ci>
<piecewise>
<piece>
<ci>IstimAmplitude</ci>
<apply>
<and/>
<apply>
<geq/>
<ci>time</ci>
<ci>IstimStart</ci>
</apply>
<apply>
<leq/>
<ci>time</ci>
<ci>IstimEnd</ci>
</apply>
<apply>
<leq/>
<apply>
<minus/>
<apply>
<minus/>
<ci>time</ci>
<ci>IstimStart</ci>
</apply>
<apply>
<times/>
<apply>
<floor/>
<apply>
<divide/>
<apply>
<minus/>
<ci>time</ci>
<ci>IstimStart</ci>
</apply>
<ci>IstimPeriod</ci>
</apply>
</apply>
<ci>IstimPeriod</ci>
</apply>
</apply>
<ci>IstimPulseDuration</ci>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="picoA_per_picoF">0</cn>
</otherwise>
</piecewise>
</apply>
</math>
<variable units="millisecond" public_interface="in" name="time"/>
</component>
<connection>
<map_components component_2="stimulus_protocol" component_1="membrane"/>
<map_variables variable_2="Istim" variable_1="i_Stim"/>
</connection>
<connection>
<map_components component_2="stimulus_protocol" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<group>
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="fast_sodium_current">
<component_ref component="fast_sodium_current_m_gate"/>
<component_ref component="fast_sodium_current_h_gate"/>
<component_ref component="fast_sodium_current_j_gate"/>
</component_ref>
<component_ref component="L_type_Ca_current">
<component_ref component="L_type_Ca_current_d_gate"/>
<component_ref component="L_type_Ca_current_f_gate"/>
<component_ref component="L_type_Ca_current_fCa_gate"/>
</component_ref>
<component_ref component="rapid_time_dependent_potassium_current">
<component_ref component="rapid_time_dependent_potassium_current_Xr1_gate"/>
<component_ref component="rapid_time_dependent_potassium_current_Xr2_gate"/>
</component_ref>
<component_ref component="slow_time_dependent_potassium_current">
<component_ref component="slow_time_dependent_potassium_current_Xs_gate"/>
</component_ref>
<component_ref component="sodium_background_current"/>
<component_ref component="calcium_background_current"/>
<component_ref component="transient_outward_current">
<component_ref component="transient_outward_current_s_gate"/>
<component_ref component="transient_outward_current_r_gate"/>
</component_ref>
<component_ref component="sodium_potassium_pump_current"/>
<component_ref component="sodium_calcium_exchanger_current"/>
<component_ref component="calcium_pump_current"/>
<component_ref component="potassium_pump_current"/>
<component_ref component="calcium_dynamics"/>
<component_ref component="sodium_dynamics"/>
<component_ref component="potassium_dynamics"/>
<component_ref component="reversal_potentials"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="fast_sodium_current">
<component_ref component="fast_sodium_current_m_gate"/>
<component_ref component="fast_sodium_current_h_gate"/>
<component_ref component="fast_sodium_current_j_gate"/>
</component_ref>
<component_ref component="L_type_Ca_current">
<component_ref component="L_type_Ca_current_d_gate"/>
<component_ref component="L_type_Ca_current_f_gate"/>
<component_ref component="L_type_Ca_current_fCa_gate"/>
</component_ref>
<component_ref component="rapid_time_dependent_potassium_current">
<component_ref component="rapid_time_dependent_potassium_current_Xr1_gate"/>
<component_ref component="rapid_time_dependent_potassium_current_Xr2_gate"/>
</component_ref>
<component_ref component="slow_time_dependent_potassium_current">
<component_ref component="slow_time_dependent_potassium_current_Xs_gate"/>
</component_ref>
<component_ref component="transient_outward_current">
<component_ref component="transient_outward_current_s_gate"/>
<component_ref component="transient_outward_current_r_gate"/>
</component_ref>
</group>
<connection>
<map_components component_2="environment" component_1="membrane"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="reversal_potentials"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="fast_sodium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="L_type_Ca_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="rapid_time_dependent_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="slow_time_dependent_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="inward_rectifier_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sodium_background_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="calcium_background_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="transient_outward_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sodium_potassium_pump_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sodium_calcium_exchanger_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="calcium_dynamics"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sodium_dynamics"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="potassium_dynamics"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="reversal_potentials" component_1="membrane"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="fast_sodium_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Na" variable_1="i_Na"/>
</connection>
<connection>
<map_components component_2="L_type_Ca_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_CaL" variable_1="i_CaL"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="rapid_time_dependent_potassium_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Kr" variable_1="i_Kr"/>
</connection>
<connection>
<map_components component_2="slow_time_dependent_potassium_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Ks" variable_1="i_Ks"/>
</connection>
<connection>
<map_components component_2="transient_outward_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_to" variable_1="i_to"/>
</connection>
<connection>
<map_components component_2="inward_rectifier_potassium_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_K1" variable_1="i_K1"/>
</connection>
<connection>
<map_components component_2="sodium_background_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_b_Na" variable_1="i_b_Na"/>
</connection>
<connection>
<map_components component_2="calcium_background_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_b_Ca" variable_1="i_b_Ca"/>
</connection>
<connection>
<map_components component_2="sodium_potassium_pump_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_NaK" variable_1="i_NaK"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="sodium_calcium_exchanger_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_NaCa" variable_1="i_NaCa"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="calcium_pump_current" component_1="membrane"/>
<map_variables variable_2="i_p_Ca" variable_1="i_p_Ca"/>
</connection>
<connection>
<map_components component_2="potassium_pump_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_p_K" variable_1="i_p_K"/>
</connection>
<connection>
<map_components component_2="calcium_dynamics" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="V_c" variable_1="V_c"/>
<map_variables variable_2="Cm" variable_1="Cm"/>
</connection>
<connection>
<map_components component_2="sodium_dynamics" component_1="membrane"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="V_c" variable_1="V_c"/>
<map_variables variable_2="Cm" variable_1="Cm"/>
</connection>
<connection>
<map_components component_2="potassium_dynamics" component_1="membrane"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="V_c" variable_1="V_c"/>
<map_variables variable_2="Cm" variable_1="Cm"/>
<map_variables variable_2="i_Stim" variable_1="i_Stim"/>
</connection>
<connection>
<map_components component_2="sodium_background_current" component_1="reversal_potentials"/>
<map_variables variable_2="E_Na" variable_1="E_Na"/>
</connection>
<connection>
<map_components component_2="inward_rectifier_potassium_current" component_1="reversal_potentials"/>
<map_variables variable_2="E_K" variable_1="E_K"/>
</connection>
<connection>
<map_components component_2="rapid_time_dependent_potassium_current" component_1="reversal_potentials"/>
<map_variables variable_2="E_K" variable_1="E_K"/>
</connection>
<connection>
<map_components component_2="transient_outward_current" component_1="reversal_potentials"/>
<map_variables variable_2="E_K" variable_1="E_K"/>
</connection>
<connection>
<map_components component_2="potassium_pump_current" component_1="reversal_potentials"/>
<map_variables variable_2="E_K" variable_1="E_K"/>
</connection>
<connection>
<map_components component_2="slow_time_dependent_potassium_current" component_1="reversal_potentials"/>
<map_variables variable_2="E_Ks" variable_1="E_Ks"/>
</connection>
<connection>
<map_components component_2="calcium_background_current" component_1="reversal_potentials"/>
<map_variables variable_2="E_Ca" variable_1="E_Ca"/>
</connection>
<connection>
<map_components component_2="fast_sodium_current" component_1="reversal_potentials"/>
<map_variables variable_2="E_Na" variable_1="E_Na"/>
</connection>
<connection>
<map_components component_2="calcium_dynamics" component_1="reversal_potentials"/>
<map_variables variable_2="Ca_o" variable_1="Ca_o"/>
<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
</connection>
<connection>
<map_components component_2="potassium_dynamics" component_1="reversal_potentials"/>
<map_variables variable_2="K_o" variable_1="K_o"/>
<map_variables variable_2="K_i" variable_1="K_i"/>
</connection>
<connection>
<map_components component_2="sodium_dynamics" component_1="reversal_potentials"/>
<map_variables variable_2="Na_o" variable_1="Na_o"/>
<map_variables variable_2="Na_i" variable_1="Na_i"/>
</connection>
<connection>
<map_components component_2="potassium_dynamics" component_1="inward_rectifier_potassium_current"/>
<map_variables variable_2="i_K1" variable_1="i_K1"/>
<map_variables variable_2="K_o" variable_1="K_o"/>
</connection>
<connection>
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