<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : viswanathan_model_1999.xml
CREATED : 1st April 2002
LAST MODIFIED : 31st July 2003
AUTHOR : Catherine Lloyd
The Bioengineering Institute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the CellML Metadata 1.0 Specification released on 16th
January, 2002.
DESCRIPTION : This file contains a CellML description of Viswanathan et al's 1999 mathematical model of the effects if Ikr and IKs heterogeneity on action potential duration and its rate dependence. This model builds on the Luo-Rudy II model, 1994.
CHANGES:
17/06/2002 - AAC - Changed equation 'i_leak_calcualtion' to
'i_leak_calculation'.
19/07/2002 - CML - Added more metadata.
09/04/2003 - AAC - Added publication date information.
31/07/2003 - CML - Corrected equations.
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="viswanathan_shaw_rudy_1999_version01" name="viswanathan_shaw_rudy_1999_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Updated Luo-Rudy Mammalian Ventricular Model II</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>
This is the original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>A subsequent pair of papers by Ching-hsing Luo and Yoram Rudy (1994a; 1994b) further developed the Luo-Rudy I model by addressing some of the issues which were not investigated in their original model. In particular, the LR-II model incorporates a more thorough description of the processes which regulate intracellular calcium ion concentration and the movement of calcium ions through the cell and to and from the sarcoplasmic reticulum (see figure 1 below).
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://circres.ahajournals.org/cgi/content/abstract/74/6/1071">A Dynamic Model of the Cardiac Ventricular Action Potential - Simulations of Ionic Currents and Concentration Changes</ulink>, Ching-hsing Luo and Yoram Rudy, 1994, <ulink url="http://circres.ahajournals.org/">
<emphasis>Circulation Research</emphasis>
</ulink>, 74, 1071-1097.
</para>
<para>
Since the model was published in 1994, it has been updated several times, incorporating new experimental data taken from papers written by other authors. These modifications have been considered in the model presented here. To illustrate how the Luo-Rudy II dynamic model has been developed, see the sequence of diagrams below. The 1997 Shaw and Rudy model diagram is identical to the 1999 Viswanathan model diagram since the only difference between the two models is that the Viswanathan model introduces a second activation gate (X<subscript>s2</subscript>) into the formulation of I<subscript>Ks</subscript>. In addition, the development of the Luo-Rudy II model has been documented by Case Western Reserve University (To view this website, follow this link: <ulink url="http://www.cwru.edu/med/CBRTC/LRdOnline/development.htm"> http://www.cwru.edu/med/CBRTC/LRdOnline/development.htm</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram_LR_II">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram of the LR-II model showing ionic currents, pumps and exchangers within the sarcolemma and the sarcoplasmic reticulum</title>
</objectinfo>
<imagedata fileref="luo_1994.png"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram describing the current flows across the cell membrane that are captured in the original, 1994 Luo-Rudy II, dynamic model.</caption>
</informalfigure>
<informalfigure float="0" id="fig_cell_diagram_zeng">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram of the zeng model showing ionic currents, pumps and exchangers within the sarcolemma and the sarcoplasmic reticulum</title>
</objectinfo>
<imagedata fileref="zeng_1995.png"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram showing the updated Luo-Rudy II, dynamic model. In their 1995 ventricular model Zeng <emphasis>et al</emphasis> have included the slow and fast components of the delayed rectifier K<superscript>+</superscript> current, I<subscript>Kr</subscript> and I<subscript>Ks</subscript>. A T-type Calcium channel (I<subscript>Ca(T)</subscript>) is also added.</caption>
</informalfigure>
<informalfigure float="0" id="fig_cell_diagram_shaw">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram of the shaw and viswanathan models showing ionic currents, pumps and exchangers within the sarcolemma and the sarcoplasmic reticulum</title>
</objectinfo>
<imagedata fileref="shaw_1997.png"/>
</imageobject>
</mediaobject>
<caption>
In their 1997 model Shaw and Rudy have built upon the 1995 Zeng <emphasis>et al</emphasis> version of the 1994 Luo-Rudy Dynamic Ventricular Model. In addition to the slow and fast components of the delayed rectifier K<superscript>+</superscript> current, (I<subscript>Kr</subscript> and I<subscript>Ks</subscript>) and the T-type Calcium channel (I<subscript>Ca(T)</subscript>), Shaw and Rudy have included an ATP-dependent potassium current (I<subscript>K(ATP)</subscript>) in their model. In turn, Viswanathan <emphasis>et al</emphasis> develop this model to include two activation gates (X<subscript>s1</subscript> and X<subscript>s2</subscript>) into the formulation of I<subscript>Ks</subscript>.</caption>
</informalfigure>
<para>
All the original paper references are cited below:
</para>
<para>
<ulink url="http://circres.ahajournals.org/cgi/content/abstract/77/1/140">Two Components of the Delayed Rectifier K<superscript>+</superscript> Current in Ventricular Myocytes of the Guinea Pig Type</ulink>, Jinglin Zeng, Kenneth R. Laurita, David S. Rosenbaum and Yoram Rudy, 1995, <ulink url="http://circres.ahajournals.org/">
<emphasis>Circulation Research</emphasis>
</ulink>, 77, 140-152. (The <ulink url="http://circres.ahajournals.org/cgi/content/full/77/1/140">full text</ulink> version of the article is 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=7788872&dopt=Abstract">PubMed ID: 7788872</ulink>
</para>
<para>
<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T14-3R37WSS-17&_user=140507&_coverDate=08%2F31%2F1997&_alid=185463716&_rdoc=1&_fmt=summary&_orig=search&_qd=1&_cdi=4880&_sort=d&_docanchor=&view=c&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=ad03ef8fddd6cc6d11f8484e421991f2">Electrophysiological effects of acute myocardial ischemia: a theoretical study of altered cell excitability and action potential duration</ulink>, Robin M. Shaw and Yoram Rudy, 1997, <ulink url="http://www.sciencedirect.com/science?_ob=JournalURL&_cdi=4880&_auth=y&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=845774525765eaf31dec5d2fc2a614f6">
<emphasis>Cardiovascular Research</emphasis>
</ulink>, 35, 256-272. <ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T14-3R37WSS-17&_coverDate=08%2F31%2F1997&_alid=185463716&_rdoc=1&_fmt=&_orig=search&_qd=1&_cdi=4880&_sort=d&view=c&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=2b061b7dec7050a8c72e2eba382d5e97">Full text</ulink> and PDF versions of the article are available to subscribers on the Science Direct website. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=9349389&dopt=Abstract">PubMed ID: 9349389</ulink>
</para>
<para>
<ulink url="http://circ.ahajournals.org/cgi/content/abstract/99/18/2466">Effects of I<subscript>Kr</subscript> and I<subscript>Ks</subscript> Heterogeneity on Action Potential Duration and Its Rate Dependence: A Simulation Study</ulink>, Prakash C. Viswanathan, BE; Robin M. Shaw, PhD; and Yoram Rudy, PhD, 1999, <ulink url="http://circ.ahajournals.org/">
<emphasis>Circulation</emphasis>
</ulink>, 99, 2466-2474. (<ulink url="http://www.circ.ahajournals.org/cgi/content/full/99/18/2466">Full text</ulink> and <ulink url="http://www.circ.ahajournals.org/cgi/reprint/99/18/2466.pdf">PDF</ulink> versions of the article are available for Journal Members on the Circulation website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=10318671&dopt=Abstract">PubMed ID: 10318671</ulink>
</para>
<para>
<ulink url="http://www.biophysj.org/cgi/content/abstract/78/5/2392">Action Potential and Contractility in [Na<superscript>+</superscript>]<subscript>i</subscript> Overloaded Cardiac Myocytes</ulink>, Gregory M. Faber and Yoram Rudy, 2000, <ulink url="http://www.biophysj.org/">
<emphasis>Biophysical Journal</emphasis>
</ulink>, 78, 2392-2404. (<ulink url="http://www.biophysj.org/cgi/content/full/78/5/2392">Full text</ulink> and <ulink url="http://www.biophysj.org/cgi/reprint/78/5/2392.pdf">PDF</ulink> versions of the article are available for Journal Members on the Biophysical Journal website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=10777735&dopt=Abstract">PubMed ID: 10777735</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram_faber">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram of the shaw and viswanathan models showing ionic currents, pumps and exchangers within the sarcolemma and the sarcoplasmic reticulum</title>
</objectinfo>
<imagedata fileref="faber_2000.png"/>
</imageobject>
</mediaobject>
<caption>In this most recent version of the 1994 Luo-Rudy Dynamic Ventricular Model, Faber and Rudy have built upon the 1999 Viswanathan model and they have added a sodium-dependent potassium current (I<subscript>K(Na)</subscript>).</caption>
</informalfigure>
<informalfigure float="0" id="fig_cellml_rendering">
<mediaobject>
<imageobject>
<objectinfo>
<title>the cellml rendering of the Luo-Rudy II model</title>
</objectinfo>
<imagedata fileref="cellml_rendering.gif"/>
</imageobject>
</mediaobject>
<caption>The network defined in the CellML description of the most recent version of the Luo-Rudy II model. A key describing the significance of the shapes of the components and the colours of the connections between them is in the <ulink url="${HTML_EXMPL_GRAPHICAL_NOTATION}">notation guide</ulink>. For simplicity, not all the variables are shown.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<!--
Below, we define some additional units for association with variables and
constants within the model. The identifiers are fairly self-explanatory.
-->
<units name="millisecond">
<unit units="second" prefix="milli"/>
</units>
<units name="per_millisecond">
<unit units="second" prefix="milli" exponent="-1"/>
</units>
<units name="millivolt">
<unit units="volt" prefix="milli"/>
</units>
<units name="per_millivolt">
<unit units="volt" prefix="milli" exponent="-1"/>
</units>
<units name="per_millivolt_millisecond">
<unit units="millivolt" exponent="-1"/>
<unit units="millisecond" exponent="-1"/>
</units>
<units name="milliS_per_microF">
<unit units="siemens" prefix="milli"/>
<unit units="farad" prefix="milli" exponent="-1"/>
</units>
<units name="milliS_per_cm2">
<unit units="siemens" prefix="milli"/>
<unit units="metre" prefix="centi" exponent="-2"/>
</units>
<units name="nanoS_per_cm2">
<unit units="siemens" prefix="nano"/>
<unit units="metre" prefix="centi" exponent="-2"/>
</units>
<units name="microF">
<unit units="farad" prefix="micro"/>
</units>
<units name="microA_per_microF">
<unit units="ampere" prefix="micro"/>
<unit units="farad" prefix="micro" exponent="-1"/>
</units>
<units name="millimolar_per_millisecond">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
<unit units="millisecond" exponent="-1"/>
</units>
<units name="millimolar">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="micromolar">
<unit units="mole" prefix="micro"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="joule_per_kilomole_kelvin">
<unit units="joule"/>
<unit units="mole" prefix="kilo" exponent="-1"/>
<unit units="kelvin" exponent="-1"/>
</units>
<units name="coulomb_per_mole">
<unit units="coulomb"/>
<unit units="mole" exponent="-1"/>
</units>
<units name="cm_per_second">
<unit units="metre" prefix="centi"/>
<unit units="second" exponent="-1"/>
</units>
<units name="cm2">
<unit units="metre" prefix="centi" exponent="2"/>
</units>
<units name="mm2">
<unit units="metre" prefix="milli" exponent="2"/>
</units>
<units name="micro_litre">
<unit units="litre" prefix="micro"/>
</units>
<!--
The "environment" component is used to declare variables that are used by
all or most of the other components, in this case just "time".
-->
<component name="environment">
<variable units="millisecond" public_interface="out" name="time"/>
</component>
<component name="membrane">
<variable units="millivolt" public_interface="out" name="V" initial_value="-84.624"/>
<variable units="joule_per_kilomole_kelvin" public_interface="out" name="R" initial_value="8314.0"/>
<variable units="kelvin" public_interface="out" name="T" initial_value="310.0"/>
<variable units="coulomb_per_mole" public_interface="out" name="F" initial_value="96500.0"/>
<variable units="microF" name="Cm" initial_value="1.0"/>
<variable units="microA_per_microF" name="I_st" initial_value="-100.0"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="microA_per_microF" public_interface="in" name="i_Na"/>
<variable units="microA_per_microF" public_interface="in" name="i_Ca_L"/>
<variable units="microA_per_microF" public_interface="in" name="i_Ca_T"/>
<variable units="microA_per_microF" public_interface="in" name="i_Kr"/>
<variable units="microA_per_microF" public_interface="in" name="i_Ks"/>
<variable units="microA_per_microF" public_interface="in" name="i_NaCa"/>
<variable units="microA_per_microF" public_interface="in" name="i_K1"/>
<variable units="microA_per_microF" public_interface="in" name="i_Kp"/>
<variable units="microA_per_microF" public_interface="in" name="i_p_Ca"/>
<variable units="microA_per_microF" public_interface="in" name="i_Na_b"/>
<variable units="microA_per_microF" public_interface="in" name="i_Ca_b"/>
<variable units="microA_per_microF" public_interface="in" name="i_NaK"/>
<variable units="microA_per_microF" public_interface="in" name="i_ns_Ca"/>
<variable units="microA_per_microF" public_interface="in" name="i_K_ATP"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="membrane_voltage_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> V </ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> Cm </ci>
</apply>
</apply>
<apply>
<plus/>
<ci> i_Na </ci>
<ci> i_Ca_L </ci>
<ci> i_Ca_T </ci>
<ci> i_Kr </ci>
<ci> i_Ks </ci>
<ci> i_K1 </ci>
<ci> i_K_ATP </ci>
<ci> i_Kp </ci>
<ci> i_NaCa </ci>
<ci> i_p_Ca </ci>
<ci> i_Na_b </ci>
<ci> i_Ca_b </ci>
<ci> i_NaK </ci>
<ci> i_ns_Ca </ci>
<ci> I_st </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current">
<variable units="microA_per_microF" public_interface="out" name="i_Na"/>
<variable units="millivolt" public_interface="out" name="E_Na"/>
<variable units="milliS_per_microF" name="g_Na" initial_value="16.0"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="joule_per_kilomole_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="Nai"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<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 id="i_Na_calculation">
<eq/>
<ci> i_Na </ci>
<apply>
<times/>
<ci> g_Na </ci>
<apply>
<power/>
<ci> m </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> h </ci>
<ci> j </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Na </ci>
</apply>
</apply>
</apply>
<apply id="E_Na_calculation">
<eq/>
<ci> E_Na </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Nao </ci>
<ci> Nai </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current_m_gate">
<variable units="dimensionless" public_interface="out" name="m"/>
<variable units="per_millisecond" name="alpha_m"/>
<variable units="per_millisecond" name="beta_m"/>
<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 id="alpha_m_calculation">
<eq/>
<ci> alpha_m </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> 0.32 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 47.13 </cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> -0.1 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 47.13 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_m_calculation">
<eq/>
<ci> beta_m </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.08 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 11.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="dm_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> m </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_m </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> m </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_m </ci>
<ci> m </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current_h_gate">
<variable units="dimensionless" public_interface="out" name="h"/>
<variable units="per_millisecond" name="alpha_h"/>
<variable units="per_millisecond" name="beta_h"/>
<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 id="alpha_h_calculation">
<eq/>
<ci> alpha_h </ci>
<piecewise>
<piece>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.135 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<cn cellml:units="millivolt"> 80.0 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> -6.8 </cn>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci> V </ci>
<cn cellml:units="millivolt"> -40.0 </cn>
</apply>
</piece>
<otherwise>
<cn cellml:units="per_millisecond"> 0.0 </cn>
</otherwise>
</piecewise>
</apply>
<apply id="beta_h_calculation">
<eq/>
<ci> beta_h </ci>
<piecewise>
<piece>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 3.56 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="millivolt"> 0.079 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 310000.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.35 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci> V </ci>
<cn cellml:units="millivolt"> -40.0 </cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<cn cellml:units="millisecond"> 0.13 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 10.66 </cn>
</apply>
<cn cellml:units="millivolt"> -11.1 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply id="dh_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> h </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_h </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> h </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_h </ci>
<ci> h </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current_j_gate">
<variable units="dimensionless" public_interface="out" name="j"/>
<variable units="per_millisecond" name="alpha_j"/>
<variable units="per_millisecond" name="beta_j"/>
<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 id="alpha_j_calculation">
<eq/>
<ci> alpha_j </ci>
<piecewise>
<piece>
<apply>
<times/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> -127140.0
</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.2444 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> 0.00003474 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> -0.04391 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 37.78 </cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </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>
<apply>
<lt/>
<ci> V </ci>
<cn cellml:units="millivolt"> -40.0 </cn>
</apply>
</piece>
<otherwise>
<cn cellml:units="per_millisecond"> 0.0 </cn>
</otherwise>
</piecewise>
</apply>
<apply id="beta_j_calculation">
<eq/>
<ci> beta_j </ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.1212 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> -0.01052 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> -0.1378 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 40.14 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci> V </ci>
<cn cellml:units="millivolt"> -40.0 </cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.3 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> -0.0000002535 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> -0.1 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 32.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply id="dj_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> j </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_j </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> j </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_j </ci>
<ci> j </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_channel">
<variable units="microA_per_microF" public_interface="out" name="i_Ca_L"/>
<variable units="microA_per_microF" public_interface="out" name="i_CaCa"/>
<variable units="microA_per_microF" public_interface="out" name="i_CaK"/>
<variable units="microA_per_microF" public_interface="out" name="i_CaNa"/>
<variable units="dimensionless" public_interface="out" name="gamma_Nai" initial_value="0.75"/>
<variable units="dimensionless" public_interface="out" name="gamma_Nao" initial_value="0.75"/>
<variable units="dimensionless" public_interface="out" name="gamma_Ki" initial_value="0.75"/>
<variable units="dimensionless" public_interface="out" name="gamma_Ko" initial_value="0.75"/>
<variable units="microA_per_microF" name="I_CaCa"/>
<variable units="microA_per_microF" name="I_CaK"/>
<variable units="microA_per_microF" name="I_CaNa"/>
<variable units="cm_per_second" name="P_Ca" initial_value="0.00054"/>
<variable units="cm_per_second" name="P_Na" initial_value="0.000000675"/>
<variable units="cm_per_second" name="P_K" initial_value="0.000000193"/>
<variable units="dimensionless" name="gamma_Cai" initial_value="1.0"/>
<variable units="dimensionless" name="gamma_Cao" initial_value="0.34"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="micromolar" public_interface="in" private_interface="out" name="Cai"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="Cao"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<variable units="dimensionless" private_interface="in" name="d"/>
<variable units="dimensionless" private_interface="in" name="f"/>
<variable units="dimensionless" private_interface="in" name="f_Ca"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_CaCa_calculation">
<eq/>
<ci> i_CaCa </ci>
<apply>
<times/>
<ci> d </ci>
<ci> f </ci>
<ci> f_Ca </ci>
<ci> I_CaCa </ci>
</apply>
</apply>
<apply id="i_CaNa_calculation">
<eq/>
<ci> i_CaNa </ci>
<apply>
<times/>
<ci> d </ci>
<ci> f </ci>
<ci> f_Ca </ci>
<ci> I_CaNa </ci>
</apply>
</apply>
<apply id="i_CaK_calculation">
<eq/>
<ci> i_CaK </ci>
<apply>
<times/>
<ci> d </ci>
<ci> f </ci>
<ci> f_Ca </ci>
<ci> I_CaK </ci>
</apply>
</apply>
<apply id="I_CaCa_calculation">
<eq/>
<ci> I_CaCa </ci>
<apply>
<times/>
<ci> P_Ca </ci>
<apply>
<power/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> V </ci>
<apply>
<power/>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> gamma_Cai </ci>
<ci> Cai </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> gamma_Cao </ci>
<ci> Cao </ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="I_CaNa_calculation">
<eq/>
<ci> I_CaNa </ci>
<apply>
<times/>
<ci> P_Na </ci>
<apply>
<power/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> V </ci>
<apply>
<power/>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> gamma_Nai </ci>
<ci> Nai </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> gamma_Nao </ci>
<ci> Nao </ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="I_CaK_calculation">
<eq/>
<ci> I_CaK </ci>
<apply>
<times/>
<ci> P_K </ci>
<apply>
<power/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> V </ci>
<apply>
<power/>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> gamma_Ki </ci>
<ci> Ki </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> gamma_Ko </ci>
<ci> Ko </ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="i_Ca_L_calculation">
<eq/>
<ci> i_Ca_L </ci>
<apply> <plus/>
<ci> i_CaCa </ci>
<ci> i_CaK </ci>
<ci> i_CaNa </ci>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_channel_d_gate">
<variable units="dimensionless" public_interface="out" name="d"/>
<variable units="per_millisecond" name="alpha_d"/>
<variable units="per_millisecond" name="beta_d"/>
<variable units="dimensionless" name="d_infinity"/>
<variable units="millisecond" name="tau_d"/>
<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 id="alpha_d_calculation">
<eq/>
<ci> alpha_d </ci>
<apply>
<divide/>
<ci> d_infinity </ci>
<ci> tau_d </ci>
</apply>
</apply>
<apply id="d_infinity_calculation">
<eq/>
<ci> d_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
<cn cellml:units="millivolt"> 6.24 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_d_calculation">
<eq/>
<ci> tau_d </ci>
<apply>
<times/>
<ci> d_infinity </ci>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
<cn cellml:units="millivolt"> 6.24 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> 0.035 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_d_calculation">
<eq/>
<ci> beta_d </ci>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> d_infinity </ci>
</apply>
<ci> tau_d </ci>
</apply>
</apply>
<apply id="dd_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> d </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_d </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> d </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_d </ci>
<ci> d </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_channel_f_gate">
<variable units="dimensionless" public_interface="out" name="f"/>
<variable units="per_millisecond" name="alpha_f"/>
<variable units="per_millisecond" name="beta_f"/>
<variable units="dimensionless" name="f_infinity"/>
<variable units="millisecond" name="tau_f"/>
<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 id="alpha_f_calculation">
<eq/>
<ci> alpha_f </ci>
<apply>
<divide/>
<ci> f_infinity </ci>
<ci> tau_f </ci>
</apply>
</apply>
<apply id="f_infinity_calculation">
<eq/>
<ci> f_infinity </ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 35.06 </cn>
</apply>
<cn cellml:units="millivolt"> 8.6 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 0.6 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="millivolt"> 50.0 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 20.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_f_calculation">
<eq/>
<ci> tau_f </ci>
<apply>
<divide/>
<cn cellml:units="millisecond"> 1.0 </cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.0197 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.0337 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 0.02 </cn>
</apply>
</apply>
</apply>
<apply id="beta_f_calculation">
<eq/>
<ci> beta_f </ci>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> f_infinity </ci>
</apply>
<ci> tau_f </ci>
</apply>
</apply>
<apply id="df_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> f </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_f </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> f </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_f </ci>
<ci> f </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_channel_f_Ca_gate">
<variable units="dimensionless" public_interface="out" name="f_Ca"/>
<variable units="micromolar" name="Km_Ca" initial_value="0.6"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="micromolar" public_interface="in" name="Cai"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="f_Ca_calculation">
<eq/>
<ci> f_Ca </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> Cai </ci>
<ci> Km_Ca </ci>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="T_type_Ca_channel">
<variable units="microA_per_microF" public_interface="out" name="i_Ca_T"/>
<variable units="milliS_per_microF" name="g_Ca_T" initial_value="0.05"/>
<variable units="millivolt" name="E_Ca"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="micromolar" public_interface="in" name="Cai"/>
<variable units="millimolar" public_interface="in" name="Cao"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="dimensionless" private_interface="in" name="b"/>
<variable units="dimensionless" private_interface="in" name="g"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Ca_T_calculation">
<eq/>
<ci> i_Ca_T </ci>
<apply>
<times/>
<ci> g_Ca_T </ci>
<apply>
<power/>
<ci> b </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<ci> g </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Ca </ci>
</apply>
</apply>
</apply>
<apply id="E_Ca_calculation">
<eq/>
<ci> E_Ca </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> F </ci>
</apply>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Cao </ci>
<ci> Cai </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="T_type_Ca_channel_b_gate">
<variable units="dimensionless" public_interface="out" name="b"/>
<variable units="dimensionless" name="b_infinity"/>
<variable units="millisecond" name="tau_b"/>
<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 id="b_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> b </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> b_infinity </ci>
<ci> b </ci>
</apply>
<ci> tau_b </ci>
</apply>
</apply>
<apply id="b_infinity_calculation">
<eq/>
<ci> b_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 14.0 </cn>
</apply>
<cn cellml:units="millivolt"> 10.8 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_b_calculation">
<eq/>
<ci> tau_b </ci>
<apply>
<divide/>
<apply>
<plus/>
<cn cellml:units="per_millivolt_millisecond"> 3.7 </cn>
<cn cellml:units="per_millivolt_millisecond"> 6.1 </cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<cn cellml:units="millivolt"> 25.0 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 4.5 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="T_type_Ca_channel_g_gate">
<variable units="dimensionless" public_interface="out" name="g"/>
<variable units="dimensionless" name="g_infinity"/>
<variable units="millisecond" name="tau_g"/>
<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 id="g_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> g </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> g_infinity </ci>
<ci> g </ci>
</apply>
<ci> tau_g </ci>
</apply>
</apply>
<apply id="g_infinity_calculation">
<eq/>
<ci> g_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 60.0 </cn>
</apply>
<cn cellml:units="millivolt"> 5.6 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_g_calculation">
<eq/>
<ci> tau_g </ci>
<piecewise>
<piece>
<cn cellml:units="millisecond"> 12.0 </cn>
<apply>
<gt/>
<ci> V </ci>
<cn cellml:units="millivolt"> 0.0 </cn>
</apply>
</piece>
<otherwise>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> -0.875 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="millisecond"> 12.0 </cn>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component name="rapid_time_dependent_potassium_current">
<variable units="microA_per_microF" public_interface="out" name="i_Kr"/>
<variable units="milliS_per_microF" name="g_Kr"/>
<variable units="millivolt" name="E_Kr"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<variable units="dimensionless" private_interface="in" name="Xr"/>
<variable units="dimensionless" private_interface="in" name="Rr"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="g_Kr_calculation">
<eq/>
<ci> g_Kr </ci>
<apply>
<times/>
<cn cellml:units="milliS_per_microF"> 0.02614 </cn>
<apply>
<root/>
<apply>
<divide/>
<ci> Ko </ci>
<cn cellml:units="millimolar"> 5.4 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="E_Kr_calculation">
<eq/>
<ci> E_Kr </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Ko </ci>
<ci> Ki </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="i_Kr_calculation">
<eq/>
<ci> i_Kr </ci>
<apply>
<times/>
<ci> g_Kr </ci>
<ci> Xr </ci>
<ci> Rr </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Kr </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="rapid_time_dependent_potassium_current_Xr_gate">
<variable units="dimensionless" public_interface="out" name="Xr"/>
<variable units="dimensionless" name="Xr_infinity"/>
<variable units="millisecond" name="tau_Xr"/>
<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 id="Xr_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Xr </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> Xr_infinity </ci>
<ci> Xr </ci>
</apply>
<ci> tau_Xr </ci>
</apply>
</apply>
<apply id="Xr_infinity_calculation">
<eq/>
<ci> Xr_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 21.5 </cn>
</apply>
<cn cellml:units="millivolt"> 7.5 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_Xr_calculation">
<eq/>
<ci> tau_Xr </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.00138 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 14.2 </cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.123 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 14.2 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.00061 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 38.9 </cn>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.145 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 38.9 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="rapid_time_dependent_potassium_current_Rr_gate">
<variable units="dimensionless" public_interface="out" name="Rr"/>
<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 id="Rr_calculation">
<eq/>
<ci> Rr </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 9.0 </cn>
</apply>
<cn cellml:units="millivolt"> 22.4 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="slow_time_dependent_potassium_current">
<variable units="microA_per_microF" public_interface="out" name="i_Ks"/>
<variable units="milliS_per_microF" name="g_Ks"/>
<variable units="millivolt" name="E_Ks"/>
<variable units="dimensionless" name="P_NaK" initial_value="0.01833"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="micromolar" public_interface="in" name="Cai"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="dimensionless" private_interface="in" name="Xs1"/>
<variable units="dimensionless" private_interface="in" name="Xs2"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="g_Ks_calculation">
<eq/>
<ci> g_Ks </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.433 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 0.6 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<cn cellml:units="micromolar"> 0.000038 </cn>
<ci> Cai </ci>
</apply>
<cn cellml:units="dimensionless"> 1.4 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="E_Ks_calculation">
<eq/>
<ci> E_Ks </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<apply>
<plus/>
<ci> Ko </ci>
<apply>
<times/>
<ci> P_NaK </ci>
<ci> Nao </ci>
</apply>
</apply>
<apply>
<plus/>
<ci> Ki </ci>
<apply>
<times/>
<ci> P_NaK </ci>
<ci> Nai </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="i_Ks_calculation">
<eq/>
<ci> i_Ks </ci>
<apply>
<times/>
<ci> g_Ks </ci>
<ci> Xs1 </ci>
<ci> Xs2 </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Ks </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="slow_time_dependent_potassium_current_Xs1_gate">
<variable units="dimensionless" public_interface="out" name="Xs1"/>
<variable units="millisecond" public_interface="out" name="tau_Xs1"/>
<variable units="dimensionless" public_interface="out" name="Xs_infinity"/>
<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 id="Xs1_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Xs1 </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> Xs_infinity </ci>
<ci> Xs1 </ci>
</apply>
<ci> tau_Xs1 </ci>
</apply>
</apply>
<apply id="Xs_infinity_calculation">
<eq/>
<ci> Xs_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 1.5 </cn>
</apply>
<cn cellml:units="millivolt"> 16.7 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_Xs1_calculation">
<eq/>
<ci> tau_Xs1 </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.0000719 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 30.0 </cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.148 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 30.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.000131 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 30.0 </cn>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.0687 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 30.0 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="slow_time_dependent_potassium_current_Xs2_gate">
<variable units="dimensionless" public_interface="out" name="Xs2"/>
<variable units="millisecond" name="tau_Xs2"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millisecond" public_interface="in" name="tau_Xs1"/>
<variable units="dimensionless" public_interface="in" name="Xs_infinity"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Xs2_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Xs2 </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> Xs_infinity </ci>
<ci> Xs2 </ci>
</apply>
<ci> tau_Xs2 </ci>
</apply>
</apply>
<apply id="tau_Xs2_calculation">
<eq/>
<ci> tau_Xs2 </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> tau_Xs1 </ci>
</apply>
</apply>
</math>
</component>
<component name="time_independent_potassium_current">
<variable units="microA_per_microF" public_interface="out" name="i_K1"/>
<variable units="millivolt" public_interface="out" private_interface="out" name="E_K1"/>
<variable units="milliS_per_cm2" name="g_K1"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="dimensionless" private_interface="in" name="K1_infinity"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="g_K1_calculation">
<eq/>
<ci> g_K1 </ci>
<apply>
<times/>
<cn cellml:units="milliS_per_microF"> 0.75 </cn>
<apply>
<root/>
<apply>
<divide/>
<ci> Ko </ci>
<cn cellml:units="millimolar"> 5.4 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="E_K1_calculation">
<eq/>
<ci> E_K1 </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Ko </ci>
<ci> Ki </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="i_K1_calculation">
<eq/>
<ci> i_K1 </ci>
<apply>
<times/>
<ci> g_K1 </ci>
<ci> K1_infinity </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K1 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="time_independent_potassium_current_K1_gate">
<variable units="dimensionless" public_interface="out" name="K1_infinity"/>
<variable units="per_millisecond" name="alpha_K1"/>
<variable units="per_millisecond" name="beta_K1"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="E_K1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_K1_calculation">
<eq/>
<ci> alpha_K1 </ci>
<apply>
<divide/>
<cn cellml:units="per_millisecond"> 1.02 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.2385 </cn>
<apply>
<minus/>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K1 </ci>
</apply>
<cn cellml:units="millivolt"> 59.215 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_K1_calculation">
<eq/>
<ci> beta_K1 </ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.49124 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.08032 </cn>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 5.476 </cn>
</apply>
<ci> E_K1 </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.06175 </cn>
<apply>
<minus/>
<ci> V </ci>
<apply>
<plus/>
<ci> E_K1 </ci>
<cn cellml:units="millivolt"> 594.31 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> -0.5143 </cn>
<apply>
<minus/>
<ci> V </ci>
<apply>
<plus/>
<ci> E_K1 </ci>
<cn cellml:units="millivolt"> 4.753 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="K1_infinity_calculation">
<eq/>
<ci> K1_infinity </ci>
<apply>
<divide/>
<ci> alpha_K1 </ci>
<apply>
<plus/>
<ci> alpha_K1 </ci>
<ci> beta_K1 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="plateau_potassium_current">
<variable units="microA_per_microF" public_interface="out" name="i_Kp"/>
<variable units="millivolt" name="E_Kp"/>
<variable units="milliS_per_microF" name="g_Kp" initial_value="0.0183"/>
<variable units="dimensionless" name="Kp"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millivolt" public_interface="in" name="E_K1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="E_Kp_calculation">
<eq/>
<ci> E_Kp </ci>
<ci> E_K1 </ci>
</apply>
<apply id="Kp_calculation">
<eq/>
<ci> Kp </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="millivolt"> 7.488 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 5.98 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="i_Kp_calculation">
<eq/>
<ci> i_Kp </ci>
<apply>
<times/>
<ci> g_Kp </ci>
<ci> Kp </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Kp </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sarcolemmal_calcium_pump">
<variable units="microA_per_microF" public_interface="out" name="i_p_Ca"/>
<variable units="micromolar" name="K_mpCa" initial_value="0.5"/>
<variable units="microA_per_microF" name="I_pCa" initial_value="1.15"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="micromolar" public_interface="in" name="Cai"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_p_Ca_calculation">
<eq/>
<ci> i_p_Ca </ci>
<apply>
<times/>
<ci> I_pCa </ci>
<apply>
<divide/>
<ci> Cai </ci>
<apply>
<plus/>
<ci> K_mpCa </ci>
<ci> Cai </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_background_current">
<variable units="microA_per_microF" public_interface="out" name="i_Na_b"/>
<variable units="milliS_per_microF" name="g_Nab" initial_value="0.00141"/>
<variable units="millivolt" name="E_NaN"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millivolt" public_interface="in" name="E_Na"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="E_NaN_calculation">
<eq/>
<ci> E_NaN </ci>
<ci> E_Na </ci>
</apply>
<apply id="i_Na_b_calculation">
<eq/>
<ci> i_Na_b </ci>
<apply>
<times/>
<ci> g_Nab </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_NaN </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_background_current">
<variable units="microA_per_microF" public_interface="out" name="i_Ca_b"/>
<variable units="milliS_per_microF" name="g_Cab" initial_value="0.003016"/>
<variable units="millivolt" name="E_CaN"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="micromolar" public_interface="in" name="Cai"/>
<variable units="millimolar" public_interface="in" name="Cao"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="E_CaN_calculation">
<eq/>
<ci> E_CaN </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> F </ci>
</apply>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Cao </ci>
<ci> Cai </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="i_Ca_b_calculation">
<eq/>
<ci> i_Ca_b </ci>
<apply>
<times/>
<ci> g_Cab </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_CaN </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_potassium_pump">
<variable units="microA_per_microF" public_interface="out" name="i_NaK"/>
<variable units="microA_per_microF" name="I_NaK"/>
<variable units="dimensionless" name="f_NaK"/>
<variable units="millimolar" name="K_mNai" initial_value="10.0"/>
<variable units="millimolar" name="K_mKo" initial_value="1.5"/>
<variable units="dimensionless" name="sigma"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="f_NaK_calculation">
<eq/>
<ci> f_NaK </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.1245 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.1 </cn>
<apply>
<divide/>
<apply>
<times/>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.0365 </cn>
<ci> sigma </ci>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="sigma_calculation">
<eq/>
<ci> sigma </ci>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<cn cellml:units="dimensionless"> 7.0 </cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci> Nao </ci>
<cn cellml:units="dimensionless"> 67.3 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
<apply id="i_NaK_calculation">
<eq/>
<ci> i_NaK </ci>
<apply>
<times/>
<ci> I_NaK </ci>
<ci> f_NaK </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> K_mNai </ci>
<ci> Nai </ci>
</apply>
<cn cellml:units="dimensionless"> 1.5 </cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> Ko </ci>
<apply>
<plus/>
<ci> Ko </ci>
<ci> K_mKo </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="non_specific_calcium_activated_current">
<variable units="microA_per_microF" public_interface="out" name="i_ns_Ca"/>
<variable units="microA_per_microF" public_interface="out" name="i_ns_Na"/>
<variable units="microA_per_microF" public_interface="out" name="i_ns_K"/>
<variable units="cm_per_second" name="P_ns_Ca" initial_value="1.75E-7"/>
<variable units="dimensionless" public_interface="in" name="gamma_Nai"/>
<variable units="dimensionless" public_interface="in" name="gamma_Nao"/>
<variable units="dimensionless" public_interface="in" name="gamma_Ki"/>
<variable units="dimensionless" public_interface="in" name="gamma_Ko"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="Cao"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<variable units="microA_per_microF" name="I_ns_Na"/>
<variable units="microA_per_microF" name="I_ns_K"/>
<variable units="micromolar" name="K_m_ns_Ca" initial_value="1.2"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="micromolar" public_interface="in" name="Cai"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_ns_Na_calculation">
<eq/>
<ci> i_ns_Na </ci>
<apply>
<times/>
<ci> I_ns_Na </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> K_m_ns_Ca </ci>
<ci> Cai </ci>
</apply>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="i_ns_K_calculation">
<eq/>
<ci> i_ns_K </ci>
<apply>
<times/>
<ci> I_ns_K </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> K_m_ns_Ca </ci>
<ci> Cai </ci>
</apply>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="i_ns_Ca_calculation">
<eq/>
<ci> i_ns_Ca </ci>
<apply>
<plus/>
<ci> i_ns_Na </ci>
<ci> i_ns_K </ci>
</apply>
</apply>
<apply id="I_ns_Na_calculation">
<eq/>
<ci> I_ns_Na </ci>
<apply>
<times/>
<ci> P_ns_Ca </ci>
<apply>
<power/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> V </ci>
<apply>
<power/>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> gamma_Nai </ci>
<ci> Nai </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> gamma_Nao </ci>
<ci> Nao </ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="I_ns_K_calculation">
<eq/>
<ci> I_ns_K </ci>
<apply>
<times/>
<ci> P_ns_Ca </ci>
<apply>
<power/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> V </ci>
<apply>
<power/>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> gamma_Ki </ci>
<ci> Ki </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> gamma_Ko </ci>
<ci> Ko </ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="ATP_dependent_potassium_current">
<variable units="microA_per_microF" public_interface="out" name="i_K_ATP"/>
<variable units="milliS_per_microF" name="g_K_ATP"/>
<variable units="nanoS_per_cm2" name="G_K_ATP"/>
<variable units="dimensionless" name="P_ATP"/>
<variable units="millivolt" name="E_K"/>
<variable units="millimolar" name="Ko_normal" initial_value="4.0"/>
<variable units="micromolar" name="K_05" initial_value="0.250"/>
<variable units="millimolar" name="ATP_i" initial_value="3.0"/>
<variable units="dimensionless" name="n" initial_value="0.24"/>
<variable units="dimensionless" name="H" initial_value="2.0"/>
<variable units="cm2" name="Nichols_area" initial_value="0.005"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_K_ATP_calculation">
<eq/>
<ci> i_K_ATP </ci>
<apply>
<times/>
<ci> g_K_ATP </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
</apply>
</apply>
<apply id="g_K_ATP_calculation">
<eq/>
<ci> g_K_ATP </ci>
<apply>
<times/>
<ci> G_K_ATP </ci>
<ci> P_ATP </ci>
<apply>
<power/>
<apply>
<divide/>
<ci> Ko </ci>
<ci> Ko_normal </ci>
</apply>
<ci> n </ci>
</apply>
</apply>
</apply>
<apply id="E_K_calculation">
<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> Ko </ci>
<ci> Ki </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="G_K_ATP_calculation">
<eq/>
<ci> G_K_ATP </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 0.000195 </cn>
<ci> Nichols_area </ci>
</apply>
</apply>
<apply id="P_ATP_calculation">
<eq/>
<ci> P_ATP </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> ATP_i </ci>
<ci> K_05 </ci>
</apply>
<ci> H </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Na_Ca_exchanger">
<variable units="microA_per_microF" public_interface="out" name="i_NaCa"/>
<variable units="microA_per_microF" name="K_NaCa" initial_value="2000.0"/>
<variable units="millimolar" name="K_mNa" initial_value="87.5"/>
<variable units="millimolar" name="K_mCa" initial_value="1.38"/>
<variable units="dimensionless" name="K_sat" initial_value="0.1"/>
<variable units="dimensionless" name="eta" initial_value="0.35"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="micromolar" public_interface="in" name="Cai"/>
<variable units="millimolar" public_interface="in" name="Cao"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Na_Ca_exchanger">
<eq/>
<ci> i_NaCa </ci>
<apply>
<times/>
<ci> K_NaCa </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<apply>
<power/>
<ci> K_mNa </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply>
<power/>
<ci> Nao </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<ci> K_mCa </ci>
<ci> Cao </ci>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> K_sat </ci>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci> eta </ci>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
<ci> V </ci>
<apply>
<divide/>
<ci> F </ci>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<apply>
<exp/>
<apply>
<times/>
<ci> eta </ci>
<ci> V </ci>
<apply>
<divide/>
<ci> F </ci>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci> Nai </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> Cao </ci>
</apply>
<apply>
<times/>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci> eta </ci>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
<ci> V </ci>
<apply>
<divide/>
<ci> F </ci>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci> Nao </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> Cai </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_buffers_in_the_myoplasm">
<variable units="millimolar" public_interface="out" name="Ca_JSR_new"/>
<variable units="micromolar" public_interface="out" name="Cai" initial_value="0.12"/>
<variable units="micromolar" name="K_mTRPN" initial_value="0.5"/>
<variable units="micromolar" name="K_mCMDN" initial_value="2.38"/>
<variable units="micromolar" name="TRPN_max" initial_value="70.0"/>
<variable units="micromolar" name="CMDN_max" initial_value="50.0"/>
<variable units="micromolar" name="TRPN_buff"/>
<variable units="micromolar" name="CMDN_buff"/>
<variable units="micromolar" name="Ca_total"/>
<variable units="millimolar" name="Ca_JSR_old"/>
<variable units="millimolar" name="delta_Ca_JSR"/>
<variable units="millimolar" name="delta_Cai"/>
<variable units="millimolar" name="Cai_old"/>
<variable units="dimensionless" name="b1"/>
<variable units="dimensionless" name="c1"/>
<variable units="dimensionless" name="b"/>
<variable units="dimensionless" name="c"/>
<variable units="dimensionless" name="d"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="micromolar" public_interface="in" name="CSQN_max"/>
<variable units="micromolar" public_interface="in" name="K_mCSQN"/>
<variable units="micromolar" public_interface="in" name="CSQN_buff"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="TRPN_buff_calculation">
<eq/>
<ci> TRPN_buff </ci>
<apply>
<times/>
<ci> TRPN_max </ci>
<apply>
<divide/>
<ci> Cai </ci>
<apply>
<plus/>
<ci> Cai </ci>
<ci> K_mTRPN </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="CMDN_buff_calculation">
<eq/>
<ci> CMDN_buff </ci>
<apply>
<times/>
<ci> CMDN_max </ci>
<apply>
<divide/>
<ci> Cai </ci>
<apply>
<plus/>
<ci> Cai </ci>
<ci> K_mCMDN </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="Ca_JSR_new_calculation">
<eq/>
<ci> Ca_JSR_new </ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<root/>
<apply>
<plus/>
<apply>
<power/>
<ci> b1 </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> c1 </ci>
</apply>
</apply>
</apply>
<ci> b1 </ci>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply id="delta_Ca_JSR_calculation">
<eq/>
<ci> delta_Ca_JSR </ci>
<apply>
<minus/>
<ci> Ca_JSR_old </ci>
<ci> Ca_JSR_new </ci>
</apply>
</apply>
<apply id="delta_Cai_calculation">
<eq/>
<ci> delta_Cai </ci>
<apply>
<minus/>
<ci> Cai_old </ci>
<ci> Cai </ci>
</apply>
</apply>
<apply id="b1_calculation">
<eq/>
<ci> b1 </ci>
<apply>
<minus/>
<ci> K_mCSQN </ci>
<apply>
<plus/>
<ci> CSQN_max </ci>
<ci> CSQN_buff </ci>
<ci> delta_Ca_JSR </ci>
<ci> Ca_JSR_old </ci>
</apply>
</apply>
</apply>
<apply id="c1_calculation">
<eq/>
<ci> c1 </ci>
<apply>
<times/>
<ci> K_mCSQN </ci>
<apply>
<plus/>
<ci> CSQN_buff </ci>
<ci> delta_Ca_JSR </ci>
<ci> Ca_JSR_old </ci>
</apply>
</apply>
</apply>
<apply id="Cai_calculation">
<eq/>
<ci> Cai </ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply>
<root/>
<apply>
<minus/>
<apply>
<power/>
<ci> b </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> c </ci>
</apply>
</apply>
</apply>
<apply>
<cos/>
<apply>
<divide/>
<apply>
<arccos/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 9.0 </cn>
<ci> b </ci>
<ci> c </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<apply>
<power/>
<ci> b </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 27.0 </cn>
<ci> d </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<apply>
<power/>
<apply>
<minus/>
<apply>
<power/>
<ci> b </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> c </ci>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> b </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
<apply id="b_calculation">
<eq/>
<ci> b </ci>
<apply>
<minus/>
<apply>
<plus/>
<ci> CMDN_max </ci>
<ci> TRPN_max </ci>
<ci> K_mTRPN </ci>
<ci> K_mCMDN </ci>
</apply>
<ci> Ca_total </ci>
</apply>
</apply>
<apply id="c_calculation">
<eq/>
<ci> c </ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> K_mCMDN </ci>
<ci> K_mTRPN </ci>
</apply>
<apply>
<times/>
<ci> TRPN_max </ci>
<ci> K_mCMDN </ci>
</apply>
<apply>
<times/>
<ci> CMDN_max </ci>
<ci> K_mTRPN </ci>
</apply>
</apply>
<apply>
<times/>
<ci> Ca_total </ci>
<apply>
<plus/>
<ci> K_mTRPN </ci>
<ci> K_mCMDN </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="d_calculation">
<eq/>
<ci> d </ci>
<apply>
<times/>
<apply>
<minus/>
<apply>
<times/>
<ci> K_mTRPN </ci>
<ci> K_mCMDN </ci>
</apply>
</apply>
<ci> Ca_total </ci>
</apply>
</apply>
<apply id="Ca_total_calculation">
<eq/>
<ci> Ca_total </ci>
<apply>
<plus/>
<ci> TRPN_buff </ci>
<ci> CMDN_buff </ci>
<ci> delta_Cai </ci>
<ci> Cai_old </ci>
</apply>
</apply>
</math>
</component>
<component name="calcium_fluxes_in_the_SR">
<variable units="millimolar_per_millisecond" public_interface="out" name="i_rel"/>
<variable units="millimolar_per_millisecond" public_interface="out" name="i_up"/>
<variable units="millimolar_per_millisecond" public_interface="out" name="i_leak"/>
<variable units="millimolar_per_millisecond" public_interface="out" name="i_tr"/>
<variable units="millimolar" public_interface="out" name="CSQN_buff"/>
<variable units="millimolar" public_interface="out" name="CSQN_max" initial_value="10.0"/>
<variable units="millimolar" public_interface="out" name="K_mCSQN" initial_value="0.8"/>
<variable units="per_millisecond" name="G_rel"/>
<variable units="per_millisecond" name="G_rel_max"/>
<variable units="millisecond" name="tau_on" initial_value="2.0"/>
<variable units="millisecond" name="tau_off" initial_value="2.0"/>
<variable units="millisecond" name="tau_tr" initial_value="180.0"/>
<variable units="millisecond" name="t" initial_value="0.0"/>
<variable units="micromolar" name="K_mrel" initial_value="0.8"/>
<variable units="micromolar" name="delta_Ca_i2"/>
<variable units="micromolar" name="delta_Ca_ith" initial_value="0.18"/>
<variable units="millimolar" name="CSQN_th" initial_value="0.7"/>
<variable units="micromolar" name="K_mup" initial_value="0.92"/>
<variable units="per_millisecond" name="K_leak"/>
<variable units="millimolar_per_millisecond" name="I_up" initial_value="0.005"/>
<variable units="millimolar" name="Ca_NSR_max" initial_value="0.15"/>
<variable units="dimensionless" name="calcium_overload"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="micromolar" public_interface="in" name="Cai"/>
<variable units="millimolar" public_interface="in" name="Ca_JSR_new"/>
<variable units="millimolar" public_interface="in" name="Ca_NSR"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_rel_calculation">
<eq/>
<ci> i_rel </ci>
<apply>
<times/>
<ci> G_rel </ci>
<apply>
<minus/>
<ci> Ca_JSR_new </ci>
<ci> Cai </ci>
</apply>
</apply>
</apply>
<apply id="G_rel_calculation">
<eq/>
<ci> G_rel </ci>
<piecewise>
<piece>
<apply>
<times/>
<ci> G_rel_max </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> delta_Ca_i2 </ci>
<ci> delta_Ca_ith </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci> K_mrel </ci>
<ci> delta_Ca_i2 </ci>
</apply>
<ci> delta_Ca_ith </ci>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<ci> t </ci>
<ci> tau_on </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<ci> t </ci>
<ci> tau_off </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci> calcium_overload </ci>
<cn cellml:units="dimensionless"> 0.0 </cn>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<ci> G_rel_max </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<ci> t </ci>
<ci> tau_on </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<ci> t </ci>
<ci> tau_off </ci>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply id="G_rel_max_calculation">
<eq/>
<ci> G_rel_max </ci>
<piecewise>
<piece>
<piecewise>
<piece>
<cn cellml:units="per_millisecond"> 0.0 </cn>
<apply>
<lt/>
<ci> delta_Ca_i2 </ci>
<ci> delta_Ca_ith </ci>
</apply>
</piece>
<otherwise>
<cn cellml:units="per_millisecond"> 60.0 </cn>
</otherwise>
</piecewise>
<apply>
<eq/>
<ci> calcium_overload </ci>
<cn cellml:units="dimensionless"> 0.0 </cn>
</apply>
</piece>
<otherwise>
<piecewise>
<piece>
<cn cellml:units="per_millisecond"> 0.0 </cn>
<apply>
<lt/>
<ci> CSQN_buff </ci>
<ci> CSQN_th </ci>
</apply>
</piece>
<otherwise>
<cn cellml:units="per_millisecond"> 4.0 </cn>
</otherwise>
</piecewise>
</otherwise>
</piecewise>
</apply>
<apply id="CSQN_buff_calculation">
<eq/>
<ci> CSQN_buff </ci>
<apply>
<times/>
<ci> CSQN_max </ci>
<apply>
<divide/>
<ci> Ca_JSR_new </ci>
<apply>
<plus/>
<ci> Ca_JSR_new </ci>
<ci> K_mCSQN </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="i_up_calculation">
<eq/>
<ci> i_up </ci>
<apply>
<times/>
<ci> I_up </ci>
<apply>
<divide/>
<ci> Cai </ci>
<apply>
<plus/>
<ci> Cai </ci>
<ci> K_mup </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="i_leak_calculation">
<eq/>
<ci> i_leak </ci>
<apply>
<times/>
<ci> K_leak </ci>
<ci> Ca_NSR </ci>
</apply>
</apply>
<apply id="K_leak_calculation">
<eq/>
<ci> K_leak </ci>
<apply>
<divide/>
<ci> I_up </ci>
<ci> Ca_NSR_max </ci>
</apply>
</apply>
<apply id="i_tr_calculation">
<eq/>
<ci> i_tr </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> Ca_NSR </ci>
<ci> Ca_JSR_new </ci>
</apply>
<ci> tau_tr </ci>
</apply>
</apply>
</math>
</component>
<component name="ionic_concentrations">
<variable units="millimolar" public_interface="out" name="Nai" initial_value="10.0"/>
<variable units="millimolar" public_interface="out" name="Nao" initial_value="140.0"/>
<variable units="millimolar" public_interface="out" name="Cao" initial_value="1.8"/>
<variable units="millimolar" public_interface="out" name="Ki" initial_value="145.0"/>
<variable units="millimolar" public_interface="out" name="Ko" initial_value="5.4"/>
<variable units="millimolar" public_interface="out" name="Ca_NSR" initial_value="15.0"/>
<variable units="micromolar" name="Ca_foot"/>
<variable units="mm2" name="A_cap" initial_value="0.000153"/>
<variable units="dimensionless" name="R_A_V"/>
<variable units="micro_litre" name="V_myo"/>
<variable units="micro_litre" name="V_cleft"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="microA_per_microF" public_interface="in" name="i_Na"/> <variable units="microA_per_microF" public_interface="in" name="i_CaNa"/>
<variable units="microA_per_microF" public_interface="in" name="i_Na_b"/>
<variable units="microA_per_microF" public_interface="in" name="i_ns_Na"/> <variable units="microA_per_microF" public_interface="in" name="i_NaCa"/>
<variable units="microA_per_microF" public_interface="in" name="i_NaK"/>
<variable units="microA_per_microF" public_interface="in" name="i_CaCa"/>
<variable units="microA_per_microF" public_interface="in" name="i_CaK"/>
<variable units="microA_per_microF" public_interface="in" name="i_Kr"/>
<variable units="microA_per_microF" public_interface="in" name="i_Ks"/>
<variable units="microA_per_microF" public_interface="in" name="i_K1"/>
<variable units="microA_per_microF" public_interface="in" name="i_Kp"/> <variable units="microA_per_microF" public_interface="in" name="i_ns_K"/>
<variable units="microA_per_microF" public_interface="in" name="i_K_ATP"/>
<variable units="millimolar_per_millisecond" public_interface="in" name="i_tr"/>
<variable units="millimolar_per_millisecond" public_interface="in" name="i_rel"/>
<variable units="millimolar_per_millisecond" public_interface="in" name="i_leak"/>
<variable units="millimolar_per_millisecond" public_interface="in" name="i_up"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="sodium_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Nai </ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_Na </ci>
<ci> i_CaNa </ci>
<ci> i_Na_b </ci>
<ci> i_ns_Na </ci>
<apply>
<times/>
<ci> i_NaCa </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply>
<times/>
<ci> i_NaK </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> A_cap </ci>
<apply>
<times/>
<ci> V_myo </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="potassium_internal_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ki </ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_CaK </ci>
<ci> i_Kr </ci>
<ci> i_Ks </ci>
<ci> i_K1 </ci>
<ci> i_K_ATP </ci>
<ci> i_Kp </ci>
<ci> i_ns_K </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> i_NaK </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> A_cap </ci>
<apply>
<times/>
<ci> V_myo </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="potassium_external_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ko </ci>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci> i_CaK </ci>
<ci> i_Kr </ci>
<ci> i_Ks </ci>
<ci> i_K1 </ci>
<ci> i_K_ATP </ci>
<ci> i_Kp </ci>
<ci> i_ns_K </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> i_NaK </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> A_cap </ci>
<apply>
<times/>
<ci> V_cleft </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="calcium_NSR_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_NSR </ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_leak </ci>
<ci> i_tr </ci>
</apply>
<ci> i_up </ci>
</apply>
</apply>
</apply>
<apply id="calcium_foot_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_foot </ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<ci> i_CaCa </ci>
</apply>
<apply>
<divide/>
<ci> A_cap </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V_myo </ci>
<ci> F </ci>
</apply>
</apply>
<ci> R_A_V </ci>
</apply>
</apply>
</math>
</component>
<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_channel">
<component_ref component="L_type_Ca_channel_d_gate"/>
<component_ref component="L_type_Ca_channel_f_gate"/>
<component_ref component="L_type_Ca_channel_f_Ca_gate"/>
</component_ref>
<component_ref component="T_type_Ca_channel">
<component_ref component="T_type_Ca_channel_b_gate"/>
<component_ref component="T_type_Ca_channel_g_gate"/>
</component_ref>
<component_ref component="rapid_time_dependent_potassium_current">
<component_ref component="rapid_time_dependent_potassium_current_Xr_gate"/>
<component_ref component="rapid_time_dependent_potassium_current_Rr_gate"/>
</component_ref>
<component_ref component="slow_time_dependent_potassium_current">
<component_ref component="slow_time_dependent_potassium_current_Xs1_gate"/>
<component_ref component="slow_time_dependent_potassium_current_Xs2_gate"/>
</component_ref>
<component_ref component="time_independent_potassium_current">
<component_ref component="time_independent_potassium_current_K1_gate"/>
</component_ref>
<component_ref component="Na_Ca_exchanger"/>
<component_ref component="plateau_potassium_current"/>
<component_ref component="sarcolemmal_calcium_pump"/>
<component_ref component="ATP_dependent_potassium_current"/>
<component_ref component="sodium_background_current"/>
<component_ref component="calcium_background_current"/>
<component_ref component="sodium_potassium_pump"/>
<component_ref component="non_specific_calcium_activated_current"/>
<component_ref component="ionic_concentrations"/>
<component_ref component="calcium_buffers_in_the_myoplasm"/>
<component_ref component="calcium_fluxes_in_the_SR"/>
</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_channel">
<component_ref component="L_type_Ca_channel_d_gate"/>
<component_ref component="L_type_Ca_channel_f_gate"/>
<component_ref component="L_type_Ca_channel_f_Ca_gate"/>
</component_ref>
<component_ref component="T_type_Ca_channel">
<component_ref component="T_type_Ca_channel_b_gate"/>
<component_ref component="T_type_Ca_channel_g_gate"/>
</component_ref>
<component_ref component="rapid_time_dependent_potassium_current">
<component_ref component="rapid_time_dependent_potassium_current_Xr_gate"/>
<component_ref component="rapid_time_dependent_potassium_current_Rr_gate"/>
</component_ref>
<component_ref component="slow_time_dependent_potassium_current">
<component_ref component="slow_time_dependent_potassium_current_Xs1_gate"/>
<component_ref component="slow_time_dependent_potassium_current_Xs2_gate"/>
</component_ref>
<component_ref component="time_independent_potassium_current">
<component_ref component="time_independent_potassium_current_K1_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="fast_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="T_type_Ca_channel"/>
<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="time_independent_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="ATP_dependent_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Na_Ca_exchanger"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="plateau_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sarcolemmal_calcium_pump"/>
<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="sodium_potassium_pump"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="non_specific_calcium_activated_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="ionic_concentrations"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="calcium_buffers_in_the_myoplasm"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="calcium_fluxes_in_the_SR"/>
<map_variables variable_2="time" variable_1="time"/>
</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"/>
<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="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"/>
<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="T_type_Ca_channel" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Ca_T" variable_1="i_Ca_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="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"/>
<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="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"/>
<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="Na_Ca_exchanger" 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="ATP_dependent_potassium_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_K_ATP" variable_1="i_K_ATP"/>
<map_variables variable_2="R" variable_1="R"/>
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<dc:title>
The Viswanathan et al 1999 Model of Mammalian Ventricular Cardiac Action
Potentials.
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<cmeta:bio_entity>Ventricular Myocyte</cmeta:bio_entity>
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<cmeta:species>Mammalia</cmeta:species>
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<rdf:value>
Added publication date information.
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<rdf:Description rdf:about="rdf:#94f085dc-2bd1-43c3-9465-2d40f36875f6">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
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<rdf:value>
Added more metadata.
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<cmeta:modifier rdf:resource="rdf:#9d133f53-37e5-427f-a94b-f32f5c798b71"/>
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<rdf:Description rdf:about="rdf:#028f44d9-6ec0-4650-9838-933494164caa">
<dc:creator rdf:resource="rdf:#f0842062-bbdb-4a0f-80de-4ee82b0439ed"/>
<rdf:value>This is the CellML description of Viswanathan et al's 1999 mathematical model of the mammalian cardiac ventricular action potential. It is a development of the Luo-Rudy II dynamic model (1994).</rdf:value>
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