- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-07-09 08:00:10+12:00
- Desc:
- committing version01 of luo_rudy_1994
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/luo_rudy_1994/rawfile/6befa47b60f5f6b4bdf5b6fc2fda80e33c5e1d41/luo_rudy_1994.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : LR_II_model_1994.xml
CREATED : 28th March 2002
LAST MODIFIED : 30th 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 the mammalian
ventricular action potential based on the Luo-Rudy II model, 1994. This model
is a development of the LR-I model. In particular, the LR-II model describes
the processes which regulate [Ca]i (intracellular Calcium concentration), and
the movement of calcium ions through the cell and to and from the sarcoplasmic
reticulum.
CHANGES:
18/07/2002 - CML - Added more metadata.
09/04/2003 - AAC - Added publication date information.
05/06/2003 - CML - Fixed MathML in a few components.
30/07/2003 - CML - Fixed MathML in a few components.
--><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="luo_rudy_1994_version01" name="luo_rudy_1994_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Luo-Rudy Mammalian Ventricular Model II (dynamic), 1994</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 <ulink url="${HTML_EXMPL_LR_I_MODEL}">Luo-Rudy I model</ulink> by addressing some of the issues which were not investigated in their original study. In particular, the LR-II model incorporates a more thorough description of the processes which regulate intracellular calcium ion concentration and the movement of calcium ions through the cell and to and from the sarcoplasmic reticulum (see <xref linkend="fig_cell_diagram"/> below).
</para>
<para>
Their mathematical model of the cardiac ventricular action potential is based upon experimental data from guinea pig ventricular cells, however it provides a framework for modelling other types of ventricular cells with appropriate modifications to account for interspecific heterogeneity.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://circres.ahajournals.org/cgi/content/abstract/74/6/1071">A Dynamic Model of the Cardiac Ventricular Action Potential - Simulations of Ionic Currents and Concentration Changes</ulink>, Ching-hsing Luo and Yoram Rudy, 1994, <ulink url="http://circres.ahajournals.org/">
<emphasis>Circulation Research</emphasis>
</ulink>, 74, 1071-1097. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=7514509&dopt=Abstract">PubMed ID: 7514509</ulink>
</para>
<para>
The Luo-Rudy II ventricular model has become a classical study. Several more recent ventricular and atrial cell models have been published using the Luo-Rudy dynamic model as their foundation and building upon those equations. Since the model was published in 1994, it has been updated several times, incorporating new experimental data taken from papers written by other authors. These modifications have been taken into consideration in another CellML model (see the <ulink url="${HTML_EXMPL_UPDATED_LR_II_MODEL}">Updated Luo-Rudy Mammalian Ventricular Model II</ulink>).
</para>
<para>
The raw CellML description of the Luo-Rudy II model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>.
</para>
<informalfigure float="0" id="fig_cell_diagram">
<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="cell_diagram.gif"/>
</imageobject>
<caption>
<para>A schematic diagram describing the ionic currents, pumps and exchangers that are captured in the LR-II model. The intracellular compartment is the sarcoplasmic reticulum (SR), which is divided into the two subcompartments, the network SR (NSR) and the junctional SR (JSR). Ca<superscript>2+</superscript> buffers are present in both the cytoplasm and the JSR.</para>
</caption>
</mediaobject>
</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="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"/>
<!-- These variables are defined here and only used internally. -->
<variable units="microF" name="Cm" initial_value="1.0"/>
<variable units="microA_per_microF" name="I_st" initial_value="-100.0"/>
<!-- These variables are imported from other components. -->
<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_K"/>
<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"/>
<!--
The membrane voltage (V) is calculated as an ordinary
differential equation in terms of the currents.
-->
<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_K </ci>
<ci> i_K1 </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="time_dependent_potassium_current">
<variable units="microA_per_microF" public_interface="out" name="i_K"/>
<variable units="milliS_per_microF" name="g_K" initial_value="0.282"/>
<variable units="millivolt" name="E_K"/>
<variable units="dimensionless" name="PR_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="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="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="dimensionless" private_interface="in" name="X"/>
<variable units="dimensionless" private_interface="in" name="Xi"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="g_K_calculation">
<eq/>
<ci> g_K </ci>
<apply>
<times/>
<cn cellml:units="milliS_per_cm2"> 0.282 </cn>
<apply>
<root/>
<apply>
<divide/>
<ci> Ko </ci>
<cn cellml:units="millimolar"> 5.4 </cn>
</apply>
</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/>
<apply>
<plus/>
<ci> Ko </ci>
<apply>
<times/>
<ci> PR_NaK </ci>
<ci> Nao </ci>
</apply>
</apply>
<apply>
<plus/>
<ci> Ki </ci>
<apply>
<times/>
<ci> PR_NaK </ci>
<ci> Nai </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="i_K_calculation">
<eq/>
<ci> i_K </ci>
<apply>
<times/>
<ci> g_K </ci>
<apply>
<power/>
<ci> X </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<ci> Xi </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="time_dependent_potassium_current_X_gate">
<variable units="dimensionless" public_interface="out" name="X"/>
<variable units="per_millisecond" name="alpha_X"/>
<variable units="per_millisecond" name="beta_X"/>
<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_X_calculation">
<eq/>
<ci> alpha_X </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> 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>
<apply id="beta_X_calculation">
<eq/>
<ci> beta_X </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> 0.000131 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 30.0 </cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<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>
</apply>
</apply>
</apply>
<apply id="dX_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> X </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_X </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> X </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_X </ci>
<ci> X </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="time_dependent_potassium_current_Xi_gate">
<variable units="dimensionless" public_interface="out" name="Xi"/>
<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="Xi_calculation">
<eq/>
<ci> Xi </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/>
<ci> V </ci>
<cn cellml:units="millivolt"> 56.26 </cn>
</apply>
<cn cellml:units="millivolt"> 32.1 </cn>
</apply>
</apply>
</apply>
</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" initial_value="1.5"/>
<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="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="micromolar" name="K_mTn" initial_value="0.5"/>
<variable units="micromolar" name="K_mCMDN" initial_value="2.38"/>
<variable units="micromolar" name="Tn_max" initial_value="70.0"/>
<variable units="micromolar" name="CMDN_max" initial_value="50.0"/>
<variable units="micromolar" name="Tn_buff"/>
<variable units="micromolar" name="CMDN_buff"/>
<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="Tn_buff_calculation">
<eq/>
<ci> Tn_buff </ci>
<apply>
<times/>
<ci> Tn_max </ci>
<apply>
<divide/>
<ci> Cai </ci>
<apply>
<plus/>
<ci> Cai </ci>
<ci> K_mTn </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>
</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="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_buff"/>
<variable units="millimolar" name="CSQN_max" initial_value="10.0"/>
<variable units="millimolar" name="CSQN_th" initial_value="0.7"/>
<variable units="millimolar" name="K_mCSQN" initial_value="0.8"/>
<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"/>
<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 </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 </ci>
<apply>
<plus/>
<ci> Ca_JSR </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_calcualtion">
<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 </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="micromolar" public_interface="out" name="Cai" initial_value="0.12"/>
<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_JSR"/>
<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="micro_litre" name="V_JSR"/>
<variable units="micro_litre" name="V_NSR"/>
<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_p_Ca"/>
<variable units="microA_per_microF" public_interface="in" name="i_Ca_b"/>
<variable units="microA_per_microF" public_interface="in" name="i_K"/>
<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="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="calcium_internal_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Cai </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_CaCa </ci>
<ci> i_p_Ca </ci>
<ci> i_Ca_b </ci>
</apply>
<ci> i_NaCa </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>
</apply>
<apply>
<times/>
<ci> i_rel </ci>
<apply>
<divide/>
<ci> V_JSR </ci>
<ci> V_myo </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<minus/>
<ci> i_leak </ci>
<ci> i_up </ci>
</apply>
<apply>
<divide/>
<ci> V_NSR </ci>
<ci> V_myo </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_K </ci>
<ci> i_K1 </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_K </ci>
<ci> i_K1 </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_JSR_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_JSR </ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci> i_rel </ci>
<apply>
<times/>
<ci> i_tr </ci>
<apply>
<divide/>
<ci> V_NSR </ci>
<ci> V_JSR </ci>
</apply>
</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="time_dependent_potassium_current">
<component_ref component="time_dependent_potassium_current_X_gate"/>
<component_ref component="time_dependent_potassium_current_Xi_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="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="time_dependent_potassium_current">
<component_ref component="time_dependent_potassium_current_X_gate"/>
<component_ref component="time_dependent_potassium_current_Xi_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="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="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="time_dependent_potassium_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_K" variable_1="i_K"/>
<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="time_independent_potassium_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_K1" variable_1="i_K1"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="plateau_potassium_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Kp" variable_1="i_Kp"/>
</connection>
<connection>
<map_components component_2="sarcolemmal_calcium_pump" component_1="membrane"/>
<map_variables variable_2="i_p_Ca" variable_1="i_p_Ca"/>
</connection>
<connection>
<map_components component_2="sodium_background_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Na_b" variable_1="i_Na_b"/>
</connection>
<connection>
<map_components component_2="calcium_background_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Ca_b" variable_1="i_Ca_b"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="sodium_potassium_pump" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_NaK" variable_1="i_NaK"/>
<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="non_specific_calcium_activated_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="i_ns_Ca" variable_1="i_ns_Ca"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="membrane"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="fast_sodium_current"/>
<map_variables variable_2="i_Na" variable_1="i_Na"/>
<map_variables variable_2="Nao" variable_1="Nao"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
</connection>
<connection>
<map_components component_2="sodium_background_current" component_1="fast_sodium_current"/>
<map_variables variable_2="E_Na" variable_1="E_Na"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="L_type_Ca_channel"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
<map_variables variable_2="Cao" variable_1="Cao"/>
<map_variables variable_2="Nao" variable_1="Nao"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
<map_variables variable_2="Ko" variable_1="Ko"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
<map_variables variable_2="i_CaCa" variable_1="i_CaCa"/>
<map_variables variable_2="i_CaNa" variable_1="i_CaNa"/>
<map_variables variable_2="i_CaK" variable_1="i_CaK"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="time_dependent_potassium_current"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
<map_variables variable_2="Ko" variable_1="Ko"/>
<map_variables variable_2="Nao" variable_1="Nao"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
<map_variables variable_2="i_K" variable_1="i_K"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="Na_Ca_exchanger"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
<map_variables variable_2="Cao" variable_1="Cao"/>
<map_variables variable_2="Nao" variable_1="Nao"/>
<map_variables variable_2="i_NaCa" variable_1="i_NaCa"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="time_independent_potassium_current"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
<map_variables variable_2="Ko" variable_1="Ko"/>
<map_variables variable_2="i_K1" variable_1="i_K1"/>
</connection>
<connection>
<map_components component_2="time_independent_potassium_current" component_1="plateau_potassium_current"/>
<map_variables variable_2="E_K1" variable_1="E_K1"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="plateau_potassium_current"/>
<map_variables variable_2="i_Kp" variable_1="i_Kp"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="sarcolemmal_calcium_pump"/>
<map_variables variable_2="i_p_Ca" variable_1="i_p_Ca"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="sodium_background_current"/>
<map_variables variable_2="i_Na_b" variable_1="i_Na_b"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="calcium_background_current"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
<map_variables variable_2="Cao" variable_1="Cao"/>
<map_variables variable_2="i_Ca_b" variable_1="i_Ca_b"/>
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<connection>
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<connection>
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<connection>
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<connection>
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<connection>
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<connection>
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<map_variables variable_2="time" variable_1="time"/>
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<connection>
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<map_variables variable_2="Xi" variable_1="Xi"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
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<connection>
<map_components component_2="time_independent_potassium_current_K1_gate" component_1="time_independent_potassium_current"/>
<map_variables variable_2="K1_infinity" variable_1="K1_infinity"/>
<map_variables variable_2="E_K1" variable_1="E_K1"/>
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<vCard:Given>Catherine</vCard:Given>
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<vCard:FN>Catherine Lloyd</vCard:FN>
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<dc:title>Circulation Research</dc:title>
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This is the CellML description of Luo and Rudy's mathematical model of
the mammalian cardiac ventricular action potential. It is a
significant development on their original 1991 model.
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Fixed maths.
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The Luo-Rudy II Model of Mammalian Ventricular Cardiac Action
Potentials, 1994
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<vCard:Given>Catherine</vCard:Given>
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The University of Auckland, The Bioengineering Institute
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Fixed maths: alpha_J_calculation in fast_sodium_current_j_gate,
beta_K1_calculation in time_independent_potassium_current_K1_gate, and i_NaK_calculation in sodium_potassium_pump.
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<dcterms:W3CDTF>2003-06-05</dcterms:W3CDTF>
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<dcterms:W3CDTF>2003-07-30</dcterms:W3CDTF>
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A Dynamic Model of the Cardiac Ventricular Action Potential I. Simulations of Ionic Currents and Concentration Changes
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<bqs:volume>74</bqs:volume>
<bqs:first_page>1071</bqs:first_page>
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