- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2007-04-02 23:44:32+12:00
- Desc:
- committing version04 of nygren_fiset_firek_clark_lindblad_clark_giles_1998
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/nygren_fiset_firek_clark_lindblad_clark_giles_1998/rawfile/4386f8c0b20f9afc5f7471972d2c94cbd2e189c7/nygren_fiset_firek_clark_lindblad_clark_giles_1998.cellml
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<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Mathematical Model Of An Adult Human Atrial Cell, 1998</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
Version 01 is the original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
</para>
<para>
Update: Version 02 of this model was fixed from Version 01 to run in PCEnv on 20/03/07 by James Lawson
</para>
<para>
Update: Version 03 of this model was updated by James Lawson (to create Version 04) such that the model now produces a train of action potentials instead of just one - 26/03/07. Note, to alter the time that the model runs for change the value of the variable "IstimEnd."
</para>
<para>
Note for this model to work properly, the maximum step size must be reduced to 0.001 or less and the point density increased to 10,000 or more.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Over the past decade, extensive voltage-clamp and action potential data from human atrial myocytes have been published from a number of laboratories. Based on these experimental data, A. Nygren, C. Fiset, L. Firek, J.W. Clark, D.S. Lindblad, R.B. Clark and W.R. Giles have published a mathematical model of the electrophysiological responses of a representative human atrial cell. Their model is sufficiently accurate to have predictive capabilities for selected aspects of the electrophysiological responses in the human atrium. Emphasis has been placed on the functional roles of the K<superscript>+</superscript> currents during repolarisation.
</para>
<para>
The mathematical model is based on the classical formulation of Hodgkin and Huxley (see <ulink url="${HTML_EXMPL_HHSA_INTRO}">The Hodgkin-Huxley Squid Axon Model, 1952</ulink>). Ionic currents through the sarcolemma are coupled with a fluid compartment model (see <xref linkend="fig_fluid_compartment_model"/> below), which accounts for changes in ionic concentrations in the cytoplasm and sarcoplasmic reticulum.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://circres.ahajournals.org/cgi/content/abstract/82/1/63">Mathematical Model of an Adult Human Atrial Cell: The Role of K<superscript>+</superscript> Currents in Repolarization,</ulink> A Nygren, C. Fiset, L. Firek, J.W. Clark, D.S. Lindblad, R.B. Clark and W.R. Giles, 1998, <ulink url="http://circres.ahajournals.org/">
<emphasis>Circulation Research</emphasis>
</ulink>, 82, 63-81. (<ulink url="http://circres.ahajournals.org/cgi/content/full/82/1/63">Full text</ulink> and <ulink url="http://circres.ahajournals.org/cgi/reprint/82/1/63.pdf">PDF</ulink> versions of the article are available for Journal Members on the Circulation Research website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=9440706&dopt=Abstract">PubMed ID: 9440706</ulink>
</para>
<para>
The raw CellML description of the Nygren <emphasis>et al</emphasis> 1998 mathematical model of an adult human atrial cell can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>.
</para>
<informalfigure float="0" id="fig_fluid_compartment_model">
<mediaobject>
<imageobject>
<objectinfo>
<title>fluid compartment model of a human atrial cell</title>
</objectinfo>
<imagedata fileref="nygren_1998.png"/>
</imageobject>
</mediaobject>
<caption>A fluid compartment model of the human atrial cell, including intracellular, cleft and extracellular spaces.</caption>
</informalfigure>
</sect1>
</article>
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<apply>
<divide/>
<apply>
<minus/>
<ci>f_L_infinity</ci>
<ci>f_L_1</ci>
</apply>
<ci>tau_f_L1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>f_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>V</ci>
<cn cellml:units="millivolt">27.4</cn>
</apply>
<cn cellml:units="millivolt">7.1</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_f_L1</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="second">0.161</cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">40</cn>
</apply>
<cn cellml:units="millivolt">14.4</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="second">0.01</cn>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_channel_f_L2_gate">
<variable units="dimensionless" public_interface="out" name="f_L_2" initial_value="0.9986"/>
<variable units="second" name="tau_f_L2"/>
<variable units="dimensionless" public_interface="in" name="f_L_infinity"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>f_L_2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>f_L_infinity</ci>
<ci>f_L_2</ci>
</apply>
<ci>tau_f_L2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_f_L2</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="second">1.3323</cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">40</cn>
</apply>
<cn cellml:units="millivolt">14.2</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="second">0.0626</cn>
</apply>
</apply>
</math>
</component>
<component name="Ca_independent_transient_outward_K_current">
<variable units="picoamp" public_interface="out" name="i_t"/>
<variable units="millivolt" public_interface="out" name="E_K"/>
<variable units="nanosiemens" name="g_t" initial_value="7.5"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millijoule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="millimolar" public_interface="in" name="K_c"/>
<variable units="millimolar" public_interface="in" name="K_i"/>
<variable units="dimensionless" private_interface="in" name="r"/>
<variable units="dimensionless" private_interface="in" name="s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_t</ci>
<apply>
<times/>
<ci>g_t</ci>
<ci>r</ci>
<ci>s</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
<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>
</math>
</component>
<component name="Ca_independent_transient_outward_K_current_r_gate">
<variable units="dimensionless" public_interface="out" name="r" initial_value="0.0010678"/>
<variable units="second" name="tau_r"/>
<variable units="dimensionless" name="r_infinity"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<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>
<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>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">1</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">11</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_r</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="second">0.0035</cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<divide/>
<ci>V</ci>
<cn cellml:units="millivolt">30</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="second">0.0015</cn>
</apply>
</apply>
</math>
</component>
<component name="Ca_independent_transient_outward_K_current_s_gate">
<variable units="dimensionless" public_interface="out" name="s" initial_value="0.949"/>
<variable units="second" name="tau_s"/>
<variable units="dimensionless" name="s_infinity"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>s</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>s_infinity</ci>
<ci>s</ci>
</apply>
<ci>tau_s</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>s_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">40.5</cn>
</apply>
<cn cellml:units="millivolt">11.5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_s</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="second">0.4812</cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">52.45</cn>
</apply>
<cn cellml:units="millivolt">14.97</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="second">0.01414</cn>
</apply>
</apply>
</math>
</component>
<component name="sustained_outward_K_current">
<variable units="picoamp" public_interface="out" name="i_sus"/>
<variable units="nanosiemens" name="g_sus" initial_value="2.75"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="dimensionless" private_interface="in" name="r_sus"/>
<variable units="dimensionless" private_interface="in" name="s_sus"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_sus</ci>
<apply>
<times/>
<ci>g_sus</ci>
<ci>r_sus</ci>
<ci>s_sus</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sustained_outward_K_current_r_sus_gate">
<variable units="dimensionless" public_interface="out" name="r_sus" initial_value="0.00015949"/>
<variable units="second" name="tau_r_sus"/>
<variable units="dimensionless" name="r_sus_infinity"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>r_sus</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>r_sus_infinity</ci>
<ci>r_sus</ci>
</apply>
<ci>tau_r_sus</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>r_sus_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">4.3</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">8</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_r_sus</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="second">0.009</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">12</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="second">0.0005</cn>
</apply>
</apply>
</math>
</component>
<component name="sustained_outward_K_current_s_sus_gate">
<variable units="dimensionless" public_interface="out" name="s_sus" initial_value="0.9912"/>
<variable units="second" name="tau_s_sus"/>
<variable units="dimensionless" name="s_sus_infinity"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>s_sus</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>s_sus_infinity</ci>
<ci>s_sus</ci>
</apply>
<ci>tau_s_sus</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>s_sus_infinity</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="dimensionless">0.4</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">10</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">0.6</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_s_sus</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="second">0.047</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">60</cn>
</apply>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="second">0.3</cn>
</apply>
</apply>
</math>
</component>
<component name="delayed_rectifier_K_currents">
<variable units="picoamp" public_interface="out" name="i_Ks"/>
<variable units="picoamp" public_interface="out" name="i_Kr"/>
<variable units="nanosiemens" name="g_Ks" initial_value="1"/>
<variable units="nanosiemens" name="g_Kr" initial_value="0.5"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="dimensionless" private_interface="in" name="n"/>
<variable units="dimensionless" private_interface="in" name="p_a"/>
<variable units="dimensionless" private_interface="in" name="p_i"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Ks</ci>
<apply>
<times/>
<ci>g_Ks</ci>
<ci>n</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_currents_n_gate">
<variable units="dimensionless" public_interface="out" name="n" initial_value="0.0048357"/>
<variable units="second" name="tau_n"/>
<variable units="dimensionless" name="n_infinity"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>n</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>n_infinity</ci>
<ci>n</ci>
</apply>
<ci>tau_n</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>n_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">19.9</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">12.7</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_n</ci>
<apply>
<plus/>
<cn cellml:units="second">0.7</cn>
<apply>
<times/>
<cn cellml:units="second">0.4</cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">20</cn>
</apply>
<cn cellml:units="millivolt">20</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="delayed_rectifier_K_currents_pa_gate">
<variable units="dimensionless" public_interface="out" name="p_a" initial_value="0.0001"/>
<variable units="second" name="tau_p_a"/>
<variable units="dimensionless" name="p_a_infinity"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<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>
<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">15</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">6</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_p_a</ci>
<apply>
<plus/>
<cn cellml:units="second">0.03118</cn>
<apply>
<times/>
<cn cellml:units="second">0.21718</cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">20.1376</cn>
</apply>
<cn cellml:units="millivolt">22.1996</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="delayed_rectifier_K_currents_pi_gate">
<variable units="dimensionless" public_interface="out" name="p_i"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>p_i</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">55</cn>
</apply>
<cn cellml:units="millivolt">24</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="inward_rectifier">
<variable units="picoamp" public_interface="out" name="i_K1"/>
<variable units="nanosiemens" name="g_K1" initial_value="3"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millijoule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="millimolar" public_interface="in" name="K_c"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_K1</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>g_K1</ci>
<apply>
<power/>
<ci>K_c</ci>
<cn cellml:units="dimensionless">0.4457</cn>
</apply>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">1.5</cn>
<apply>
<plus/>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
<cn cellml:units="millivolt">3.6</cn>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="background_currents">
<variable units="picoamp" public_interface="out" name="i_B_Na"/>
<variable units="picoamp" public_interface="out" name="i_B_Ca"/>
<variable units="nanosiemens" name="g_B_Na" initial_value="0.060599"/>
<variable units="nanosiemens" name="g_B_Ca" initial_value="0.078681"/>
<variable units="millivolt" name="E_Ca"/>
<variable units="millivolt" public_interface="in" name="E_Na"/>
<variable units="millijoule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="millimolar" public_interface="in" name="Ca_c"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="second" 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_B_Na</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Na</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_B_Ca</ci>
<apply>
<times/>
<ci>g_B_Ca</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Ca</ci>
</apply>
</apply>
</apply>
<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>
</math>
</component>
<component name="sodium_potassium_pump">
<variable units="picoamp" public_interface="out" name="i_NaK"/>
<variable units="millimolar" name="k_NaK_K" initial_value="1"/>
<variable units="millimolar" name="k_NaK_Na" initial_value="11"/>
<variable units="picoamp" name="i_NaK_max" initial_value="70.8253"/>
<variable units="millimolar" public_interface="in" name="K_c"/>
<variable units="millimolar" public_interface="in" name="Na_i"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_NaK</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>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">150</cn>
</apply>
</apply>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">200</cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sarcolemmal_calcium_pump_current">
<variable units="picoamp" public_interface="out" name="i_CaP"/>
<variable units="picoamp" name="i_CaP_max" initial_value="4"/>
<variable units="millimolar" name="k_CaP" initial_value="0.0002"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="second" public_interface="in" name="time"/>
<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 units="picoamp" public_interface="out" name="i_NaCa"/>
<variable units="picoamp_per_millimolar_4" name="k_NaCa" initial_value="0.0374842"/>
<variable units="per_millimolar_4" name="d_NaCa" initial_value="0.0003"/>
<variable units="dimensionless" name="gamma" initial_value="0.45"/>
<variable units="millimolar" public_interface="in" name="Na_i"/>
<variable units="millimolar" public_interface="in" name="Na_c"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="millimolar" public_interface="in" name="Ca_c"/>
<variable units="millijoule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" 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>
<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 units="millimolar" public_interface="out" name="Na_i" initial_value="8.5547"/>
<variable units="millimolar" public_interface="out" name="Ca_i" initial_value="6.729e-5"/>
<variable units="millimolar" public_interface="out" name="K_i" initial_value="129.435"/>
<variable units="millimolar" public_interface="out" name="Ca_d" initial_value="7.2495e-5"/>
<variable units="picoamp" public_interface="out" name="phi_Na_en" initial_value="-1.68"/>
<variable units="nanolitre" public_interface="out" name="Vol_i" initial_value="0.005884"/>
<variable units="nanolitre" name="Vol_d"/>
<variable units="picoamp" name="i_di"/>
<variable units="second" name="tau_di" initial_value="0.01"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="picoamp" public_interface="in" name="i_Na"/>
<variable units="picoamp" public_interface="in" name="i_Ca_L"/>
<variable units="picoamp" public_interface="in" name="i_B_Na"/>
<variable units="picoamp" public_interface="in" name="i_NaCa"/>
<variable units="picoamp" public_interface="in" name="i_NaK"/>
<variable units="picoamp" public_interface="in" name="i_Ks"/>
<variable units="picoamp" public_interface="in" name="i_Kr"/>
<variable units="picoamp" public_interface="in" name="i_K1"/>
<variable units="picoamp" public_interface="in" name="i_t"/>
<variable units="picoamp" public_interface="in" name="i_sus"/>
<variable units="picoamp" public_interface="in" name="i_CaP"/>
<variable units="picoamp" public_interface="in" name="i_B_Ca"/>
<variable units="picoamp" public_interface="in" name="i_up"/>
<variable units="picoamp" public_interface="in" name="i_rel"/>
<variable units="dimensionless" public_interface="in" name="O_C"/>
<variable units="dimensionless" public_interface="in" name="O_TC"/>
<variable units="dimensionless" public_interface="in" name="O_TMgC"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Vol_d</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.02</cn>
<ci>Vol_i</ci>
</apply>
</apply>
<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_NaK</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>i_NaCa</ci>
</apply>
<ci>phi_Na_en</ci>
</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_t</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_NaK</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>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<ci>i_di</ci>
</apply>
<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>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>Vol_i</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.08</cn>
<ci>dO_TC_dtime</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.16</cn>
<ci>dO_TMgC_dtime</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.045</cn>
<ci>dO_C_dtime</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_d</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_Ca_L</ci>
<ci>i_di</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>Vol_d</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_di</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>Ca_d</ci>
<ci>Ca_i</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
<ci>F</ci>
<ci>Vol_d</ci>
</apply>
<ci>tau_di</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>dO_C_dtime</ci>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>O_C</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>dO_TMgC_dtime</ci>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>O_TMgC</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>dO_TC_dtime</ci>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>O_TC</ci>
</apply>
</apply>
</math>
<variable units="dimensionless" public_interface="in" name="dO_C_dtime"/>
<variable units="dimensionless" public_interface="in" name="dO_TMgC_dtime"/>
<variable units="dimensionless" public_interface="in" name="dO_TC_dtime"/>
</component>
<component name="intracellular_Ca_buffering">
<variable units="dimensionless" public_interface="out" name="O_C" initial_value="0.0275"/>
<variable units="dimensionless" public_interface="out" name="O_TC" initial_value="0.0133"/>
<variable units="dimensionless" public_interface="out" name="O_TMgC" initial_value="0.1961"/>
<variable units="dimensionless" public_interface="out" name="O_TMgMg" initial_value="0.7094"/>
<variable units="millimolar" name="Mg_i" initial_value="2.5"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>O_C</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless">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="dimensionless">476</cn>
<ci>O_C</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>O_TC</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless">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="dimensionless">392</cn>
<ci>O_TC</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>O_TMgC</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless">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="dimensionless">6.6</cn>
<ci>O_TMgC</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>O_TMgMg</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless">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="dimensionless">666</cn>
<ci>O_TMgMg</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>dO_C_dtime</ci>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless">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="dimensionless">476</cn>
<ci>O_C</ci>
</apply>
</apply>
</apply>
<error xmlns="http://www.cellml.org/tools/mathml-input/error#" column="13" problem="syntax error"/>
<apply>
<eq/>
<ci>dO_TC_dtime</ci>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless">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="dimensionless">392</cn>
<ci>O_TC</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>dO_TMgC_dtime</ci>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless">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="dimensionless">6.6</cn>
<ci>O_TMgC</ci>
</apply>
</apply>
</apply>
</math>
<variable units="dimensionless" public_interface="out" name="dO_C_dtime"/>
<variable units="dimensionless" public_interface="out" name="dO_TC_dtime"/>
<variable units="dimensionless" public_interface="out" name="dO_TMgC_dtime"/>
</component>
<component name="cleft_space_ion_concentrations">
<variable units="millimolar" public_interface="out" name="Na_c" initial_value="130.011"/>
<variable units="millimolar" public_interface="out" name="Ca_c" initial_value="1.8147"/>
<variable units="millimolar" public_interface="out" name="K_c" initial_value="5.3581"/>
<variable units="nanolitre" public_interface="in" name="Vol_i"/>
<variable units="nanolitre" name="Vol_c"/>
<variable units="second" name="tau_Na" initial_value="14.3"/>
<variable units="second" name="tau_K" initial_value="10"/>
<variable units="second" name="tau_Ca" initial_value="24.7"/>
<variable units="millimolar" name="Na_b" initial_value="130"/>
<variable units="millimolar" name="Ca_b" initial_value="1.8"/>
<variable units="millimolar" name="K_b" initial_value="5.4"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="picoamp" public_interface="in" name="i_Na"/>
<variable units="picoamp" public_interface="in" name="i_Ca_L"/>
<variable units="picoamp" public_interface="in" name="i_B_Na"/>
<variable units="picoamp" public_interface="in" name="i_NaCa"/>
<variable units="picoamp" public_interface="in" name="i_NaK"/>
<variable units="picoamp" public_interface="in" name="i_Ks"/>
<variable units="picoamp" public_interface="in" name="i_Kr"/>
<variable units="picoamp" public_interface="in" name="i_K1"/>
<variable units="picoamp" public_interface="in" name="i_t"/>
<variable units="picoamp" public_interface="in" name="i_sus"/>
<variable units="picoamp" public_interface="in" name="i_CaP"/>
<variable units="picoamp" public_interface="in" name="i_B_Ca"/>
<variable units="picoamp" public_interface="in" name="phi_Na_en"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Vol_c</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.136</cn>
<ci>Vol_i</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Na_c</ci>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<minus/>
<ci>Na_b</ci>
<ci>Na_c</ci>
</apply>
<ci>tau_Na</ci>
</apply>
<apply>
<divide/>
<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>
<ci>phi_Na_en</ci>
</apply>
<apply>
<times/>
<ci>Vol_c</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>K_c</ci>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<minus/>
<ci>K_b</ci>
<ci>K_c</ci>
</apply>
<ci>tau_K</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_t</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_NaK</ci>
</apply>
</apply>
<apply>
<times/>
<ci>Vol_c</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_c</ci>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<minus/>
<ci>Ca_b</ci>
<ci>Ca_c</ci>
</apply>
<ci>tau_Ca</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_Ca_L</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>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>Vol_c</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Ca_handling_by_the_SR">
<variable units="picoamp" public_interface="out" name="i_rel"/>
<variable units="picoamp" public_interface="out" name="i_up"/>
<variable units="picoamp" name="i_tr"/>
<variable units="picoamp" name="I_up_max" initial_value="2800"/>
<variable units="millimolar" name="k_cyca" initial_value="0.0003"/>
<variable units="millimolar" name="k_srca" initial_value="0.5"/>
<variable units="dimensionless" name="k_xcs" initial_value="0.4"/>
<variable units="picoamp_per_millimolar" name="alpha_rel" initial_value="200000"/>
<variable units="millimolar" name="Ca_rel" initial_value="0.6465"/>
<variable units="millimolar" name="Ca_up" initial_value="0.6646"/>
<variable units="nanolitre" name="Vol_up" initial_value="0.0003969"/>
<variable units="nanolitre" name="Vol_rel" initial_value="4.41e-5"/>
<variable units="per_second" name="r_act"/>
<variable units="per_second" name="r_inact"/>
<variable units="per_second" name="r_recov" initial_value="0.815"/>
<variable units="dimensionless" name="O_Calse" initial_value="0.4369"/>
<variable units="dimensionless" name="F1" initial_value="0.4284"/>
<variable units="dimensionless" name="F2" initial_value="0.0028"/>
<variable units="second" name="tau_tr" initial_value="0.01"/>
<variable units="millimolar" name="k_rel_i" initial_value="0.0003"/>
<variable units="millimolar" name="k_rel_d" initial_value="0.003"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="millimolar" public_interface="in" name="Ca_d"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<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>
<ci>tau_tr</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>i_rel</ci>
<apply>
<times/>
<ci>alpha_rel</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>F2</ci>
<apply>
<plus/>
<ci>F2</ci>
<cn cellml:units="dimensionless">0.25</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<minus/>
<ci>Ca_rel</ci>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>O_Calse</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless">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="dimensionless">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>
<times/>
<apply>
<divide/>
<apply>
<minus/>
<ci>i_tr</ci>
<ci>i_rel</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>Vol_rel</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">31</cn>
<ci>dO_Calse_dtime</ci>
</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>r_recov</ci>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>F1</ci>
</apply>
<ci>F2</ci>
</apply>
</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/>
<ci>r_act</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">203.8</cn>
<apply>
<plus/>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_i</ci>
<apply>
<plus/>
<ci>Ca_i</ci>
<ci>k_rel_i</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">4</cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_d</ci>
<apply>
<plus/>
<ci>Ca_d</ci>
<ci>k_rel_d</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>r_inact</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">33.96</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">339.6</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_i</ci>
<apply>
<plus/>
<ci>Ca_i</ci>
<ci>k_rel_i</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>dO_Calse_dtime</ci>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless">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="dimensionless">400</cn>
<ci>O_Calse</ci>
</apply>
</apply>
</apply>
</math>
<variable units="dimensionless" name="dO_Calse_dtime"/>
</component>
<group>
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="sodium_current">
<component_ref component="sodium_current_m_gate"/>
<component_ref component="sodium_current_h1_gate"/>
<component_ref component="sodium_current_h2_gate"/>
</component_ref>
<component_ref component="L_type_Ca_channel">
<component_ref component="L_type_Ca_channel_d_L_gate"/>
<component_ref component="L_type_Ca_channel_f_L1_gate"/>
<component_ref component="L_type_Ca_channel_f_L2_gate"/>
</component_ref>
<component_ref component="Ca_independent_transient_outward_K_current">
<component_ref component="Ca_independent_transient_outward_K_current_r_gate"/>
<component_ref component="Ca_independent_transient_outward_K_current_s_gate"/>
</component_ref>
<component_ref component="sustained_outward_K_current">
<component_ref component="sustained_outward_K_current_r_sus_gate"/>
<component_ref component="sustained_outward_K_current_s_sus_gate"/>
</component_ref>
<component_ref component="delayed_rectifier_K_currents">
<component_ref component="delayed_rectifier_K_currents_n_gate"/>
<component_ref component="delayed_rectifier_K_currents_pa_gate"/>
<component_ref component="delayed_rectifier_K_currents_pi_gate"/>
</component_ref>
<component_ref component="inward_rectifier"/>
<component_ref component="background_currents"/>
<component_ref component="sodium_potassium_pump"/>
<component_ref component="sarcolemmal_calcium_pump_current"/>
<component_ref component="Na_Ca_ion_exchanger_current"/>
<component_ref component="Ca_handling_by_the_SR"/>
<component_ref component="intracellular_ion_concentrations"/>
<component_ref component="intracellular_Ca_buffering"/>
<component_ref component="cleft_space_ion_concentrations"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="sodium_current">
<component_ref component="sodium_current_m_gate"/>
<component_ref component="sodium_current_h1_gate"/>
<component_ref component="sodium_current_h2_gate"/>
</component_ref>
<component_ref component="L_type_Ca_channel">
<component_ref component="L_type_Ca_channel_d_L_gate"/>
<component_ref component="L_type_Ca_channel_f_L1_gate"/>
<component_ref component="L_type_Ca_channel_f_L2_gate"/>
</component_ref>
<component_ref component="Ca_independent_transient_outward_K_current">
<component_ref component="Ca_independent_transient_outward_K_current_r_gate"/>
<component_ref component="Ca_independent_transient_outward_K_current_s_gate"/>
</component_ref>
<component_ref component="sustained_outward_K_current">
<component_ref component="sustained_outward_K_current_r_sus_gate"/>
<component_ref component="sustained_outward_K_current_s_sus_gate"/>
</component_ref>
<component_ref component="delayed_rectifier_K_currents">
<component_ref component="delayed_rectifier_K_currents_n_gate"/>
<component_ref component="delayed_rectifier_K_currents_pa_gate"/>
<component_ref component="delayed_rectifier_K_currents_pi_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="sodium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="L_type_Ca_channel"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Ca_independent_transient_outward_K_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sustained_outward_K_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="delayed_rectifier_K_currents"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="inward_rectifier"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="background_currents"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sodium_potassium_pump"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sarcolemmal_calcium_pump_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Na_Ca_ion_exchanger_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Ca_handling_by_the_SR"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="intracellular_Ca_buffering"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="intracellular_ion_concentrations"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="cleft_space_ion_concentrations"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="sodium_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="i_Na" variable_1="i_Na"/>
</connection>
<connection>
<map_components component_2="L_type_Ca_channel" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Ca_L" variable_1="i_Ca_L"/>
</connection>
<connection>
<map_components component_2="Ca_independent_transient_outward_K_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_t" variable_1="i_t"/>
<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="sustained_outward_K_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_sus" variable_1="i_sus"/>
</connection>
<connection>
<map_components component_2="inward_rectifier" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_K1" variable_1="i_K1"/>
<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="delayed_rectifier_K_currents" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Kr" variable_1="i_Kr"/>
<map_variables variable_2="i_Ks" variable_1="i_Ks"/>
</connection>
<connection>
<map_components component_2="background_currents" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_B_Na" variable_1="i_B_Na"/>
<map_variables variable_2="i_B_Ca" variable_1="i_B_Ca"/>
<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_potassium_pump" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_NaK" variable_1="i_NaK"/>
</connection>
<connection>
<map_components component_2="sarcolemmal_calcium_pump_current" component_1="membrane"/>
<map_variables variable_2="i_CaP" variable_1="i_CaP"/>
</connection>
<connection>
<map_components component_2="Na_Ca_ion_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="intracellular_ion_concentrations" component_1="membrane"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="cleft_space_ion_concentrations" component_1="membrane"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="Ca_handling_by_the_SR" component_1="membrane"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="intracellular_ion_concentrations" component_1="sodium_current"/>
<map_variables variable_2="i_Na" variable_1="i_Na"/>
<map_variables variable_2="Na_i" variable_1="Na_i"/>
</connection>
<connection>
<map_components component_2="background_currents" component_1="sodium_current"/>
<map_variables variable_2="E_Na" variable_1="E_Na"/>
</connection>
<connection>
<map_components component_2="cleft_space_ion_concentrations" component_1="sodium_current"/>
<map_variables variable_2="i_Na" variable_1="i_Na"/>
<map_variables variable_2="Na_c" variable_1="Na_c"/>
</connection>
<connection>
<map_components component_2="intracellular_ion_concentrations" component_1="L_type_Ca_channel"/>
<map_variables variable_2="i_Ca_L" variable_1="i_Ca_L"/>
<map_variables variable_2="Ca_d" variable_1="Ca_d"/>
</connection>
<connection>
<map_components component_2="cleft_space_ion_concentrations" component_1="L_type_Ca_channel"/>
<map_variables variable_2="i_Ca_L" variable_1="i_Ca_L"/>
</connection>
<connection>
<map_components component_2="intracellular_ion_concentrations" component_1="Ca_independent_transient_outward_K_current"/>
<map_variables variable_2="i_t" variable_1="i_t"/>
<map_variables variable_2="K_i" variable_1="K_i"/>
</connection>
<connection>
<map_components component_2="cleft_space_ion_concentrations" component_1="Ca_independent_transient_outward_K_current"/>
<map_variables variable_2="i_t" variable_1="i_t"/>
<map_variables variable_2="K_c" variable_1="K_c"/>
</connection>
<connection>
<map_components component_2="sustained_outward_K_current" component_1="Ca_independent_transient_outward_K_current"/>
<map_variables variable_2="E_K" variable_1="E_K"/>
</connection>
<connection>
<map_components component_2="inward_rectifier" component_1="Ca_independent_transient_outward_K_current"/>
<map_variables variable_2="E_K" variable_1="E_K"/>
</connection>
<connection>
<map_components component_2="delayed_rectifier_K_currents" component_1="Ca_independent_transient_outward_K_current"/>
<map_variables variable_2="E_K" variable_1="E_K"/>
</connection>
<connection>
<map_components component_2="intracellular_ion_concentrations" component_1="sustained_outward_K_current"/>
<map_variables variable_2="i_sus" variable_1="i_sus"/>
</connection>
<connection>
<map_components component_2="cleft_space_ion_concentrations" component_1="sustained_outward_K_current"/>
<map_variables variable_2="i_sus" variable_1="i_sus"/>
</connection>
<connection>
<map_components component_2="intracellular_ion_concentrations" component_1="delayed_rectifier_K_currents"/>
<map_variables variable_2="i_Kr" variable_1="i_Kr"/>
<map_variables variable_2="i_Ks" variable_1="i_Ks"/>
</connection>
<connection>
<map_components component_2="cleft_space_ion_concentrations" component_1="delayed_rectifier_K_currents"/>
<map_variables variable_2="i_Kr" variable_1="i_Kr"/>
<map_variables variable_2="i_Ks" variable_1="i_Ks"/>
</connection>
<connection>
<map_components component_2="intracellular_ion_concentrations" component_1="inward_rectifier"/>
<map_variables variable_2="i_K1" variable_1="i_K1"/>
</connection>
<connection>
<map_components component_2="cleft_space_ion_concentrations" component_1="inward_rectifier"/>
<map_variables variable_2="i_K1" variable_1="i_K1"/>
<map_variables variable_2="K_c" variable_1="K_c"/>
</connection>
<connection>
<map_components component_2="intracellular_ion_concentrations" component_1="background_currents"/>
<map_variables variable_2="i_B_Na" variable_1="i_B_Na"/>
<map_variables variable_2="i_B_Ca" variable_1="i_B_Ca"/>
<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
</connection>
<connection>
<map_components component_2="cleft_space_ion_concentrations" component_1="background_currents"/>
<map_variables variable_2="i_B_Na" variable_1="i_B_Na"/>
<map_variables variable_2="i_B_Ca" variable_1="i_B_Ca"/>
<map_variables variable_2="Ca_c" variable_1="Ca_c"/>
</connection>
<connection>
<map_components component_2="intracellular_ion_concentrations" component_1="sodium_potassium_pump"/>
<map_variables variable_2="i_NaK" variable_1="i_NaK"/>
<map_variables variable_2="Na_i" variable_1="Na_i"/>
</connection>
<connection>
<map_components component_2="cleft_space_ion_concentrations" component_1="sodium_potassium_pump"/>
<map_variables variable_2="i_NaK" variable_1="i_NaK"/>
<map_variables variable_2="K_c" variable_1="K_c"/>
</connection>
<connection>
<map_components component_2="intracellular_ion_concentrations" component_1="sarcolemmal_calcium_pump_current"/>
<map_variables variable_2="i_CaP" variable_1="i_CaP"/>
<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
</connection>
<connection>
<map_components component_2="cleft_space_ion_concentrations" component_1="sarcolemmal_calcium_pump_current"/>
<map_variables variable_2="i_CaP" variable_1="i_CaP"/>
</connection>
<connection>
<map_components component_2="intracellular_ion_concentrations" component_1="Na_Ca_ion_exchanger_current"/>
<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
<map_variables variable_2="Na_i" variable_1="Na_i"/>
<map_variables variable_2="i_NaCa" variable_1="i_NaCa"/>
</connection>
<connection>
<map_components component_2="cleft_space_ion_concentrations" component_1="Na_Ca_ion_exchanger_current"/>
<map_variables variable_2="Ca_c" variable_1="Ca_c"/>
<map_variables variable_2="Na_c" variable_1="Na_c"/>
<map_variables variable_2="i_NaCa" variable_1="i_NaCa"/>
</connection>
<connection>
<map_components component_2="intracellular_ion_concentrations" component_1="Ca_handling_by_the_SR"/>
<map_variables variable_2="i_rel" variable_1="i_rel"/>
<map_variables variable_2="i_up" variable_1="i_up"/>
<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
<map_variables variable_2="Ca_d" variable_1="Ca_d"/>
</connection>
<connection>
<map_components component_2="intracellular_ion_concentrations" component_1="cleft_space_ion_concentrations"/>
<map_variables variable_2="phi_Na_en" variable_1="phi_Na_en"/>
<map_variables variable_2="Vol_i" variable_1="Vol_i"/>
</connection>
<connection>
<map_components component_2="intracellular_ion_concentrations" component_1="intracellular_Ca_buffering"/>
<map_variables variable_2="O_C" variable_1="O_C"/>
<map_variables variable_2="O_TC" variable_1="O_TC"/>
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