<?xml version="1.0"?>
<!-- FILE : LR_II_model_1994.xml
CREATED : 19th September 2003
LAST MODIFIED : 19th September 2003
AUTHOR : Catherine Lloyd
The Bioengineering Institute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.1 Specification 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, and where appropriate, the import and reuse features of CellML 1.1 have been used to import components and units from the LR I model intoth eLR II model.
CHANGES:
-->
<model
name="LR_II_model_1994"
cmeta:id="LR_II_model_1994"
xmlns="http://www.cellml.org/cellml/1.1#"
xmlns:cellml="http://www.cellml.org/cellml/1.1#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#"
xmlns:xlink="http://www.w3.org/1999/xlink">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#"
xmlns:bqs="http://www.cellml.org/bqs/1.1#"
xmlns:dc="http://purl.org/dc/elements/1.1/"
xmlns:dcterms="http://purl.org/dc/terms/"
xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">
<!--
The following RDF block contains metadata that applies to this document
as a whole, as indicated by the empty about attribute on the
<rdf:Description> element.
-->
<rdf:Description rdf:about="">
<!--
The Model Builder Metadata. The Dublin Core "creator" element is used
to indicate the person who translated the model into CellML.
-->
<dc:creator rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Lloyd</vCard:Family>
<vCard:Given>Catherine</vCard:Given>
<vCard:Other>May</vCard:Other>
</vCard:N>
<vCard:EMAIL rdf:parseType="Resource">
<rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet" />
</vCard:EMAIL>
<vCard:ORG rdf:parseType="Resource">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
</vCard:ORG>
</dc:creator>
<!--
The Creation Date metadata. This is the date on which the model
was translated into CellML.
-->
<dcterms:created rdf:parseType="Resource">
<dcterms:W3CDTF>2003-09-19</dcterms:W3CDTF>
</dcterms:created>
<!--
The Modification History metadata. This lists the changes that have been
made to the document, who made the changes, and when they were made.
-->
<!-- The Publisher metadata. -->
<dc:publisher>
The University of Auckland, The Bioengineering Institute
</dc:publisher>
</rdf:Description>
<!--
The following metadata refers to the model itself, as indicated by the
reference to the ID "LR_II_model_1994", which is declared on the
<model> element.
-->
<rdf:Description rdf:about="#LR_II_model_1994">
<!-- A human readable name for the model. -->
<dc:title>
The Luo-Rudy II Model of Mammalian Ventricular Cardiac Action
Potentials, 1994
</dc:title>
<!-- A comment regarding the model. -->
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
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, and where
appropriate, the import and reuse features of CellML 1.1 have been
used to import components and units from the LR I model intoth eLR II
model.
</rdf:value>
<!-- The creator of the comment. -->
<dc:creator rdf:parseType="Resource">
<vCard:FN>Catherine Lloyd</vCard:FN>
</dc:creator>
</cmeta:comment>
<!-- The model is relevant to all mammals. -->
<cmeta:species>Mammalia</cmeta:species>
<cmeta:bio_entity>Ventricular Myocyte</cmeta:bio_entity>
<!--
The CellML Metadata Specification recommends that bibliographic metadata
is used to provide information about the original model reference. The
"identifier" attribute on the "BibliographicReference" class provides an
elegant way to identify a cited reference using a database identifier such as Pubmed. All associated data such as author, journal title,
date, etc can be looked up on the database.
-->
<bqs:reference rdf:parseType="Resource">
<bqs:Pubmed_id>7514509</bqs:Pubmed_id>
<bqs:JournalArticle rdf:parseType="Resource">
<dc:creator>
<rdf:Seq>
<rdf:li rdf:parseType="Resource">
<bqs:Person rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Luo</vCard:Family>
<vCard:Given>Ching-hsing</vCard:Given>
</vCard:N>
</bqs:Person>
</rdf:li>
<rdf:li rdf:parseType="Resource">
<bqs:Person rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Rudy</vCard:Family>
<vCard:Given>Yoram</vCard:Given>
</vCard:N>
</bqs:Person>
</rdf:li>
</rdf:Seq>
</dc:creator>
<dc:title>
A Dynamic Model of the Cardiac Ventricular Action Potential I. Simulations of Ionic Currents and Concentration Changes
</dc:title>
<dcterms:issued rdf:parseType="Resource">
<dcterms:W3CDTF>1994-06</dcterms:W3CDTF>
</dcterms:issued>
<bqs:Journal rdf:parseType="Resource">
<dc:title>Circulation Research</dc:title>
</bqs:Journal>
<bqs:volume>74</bqs:volume>
<bqs:first_page>1071</bqs:first_page>
<bqs:last_page>1096</bqs:last_page>
</bqs:JournalArticle>
</bqs:reference>
</rdf:Description>
</rdf:RDF>
<import xlink:href="http://www.cellml.org/examples/models/luo_rudy_I_model_1991.xml">
<units name="millisecond" units_ref="millisecond" />
<units name="per_millisecond" units_ref="per_millisecond" />
<units name="millivolt" units_ref="millivolt" />
<units name="per_millivolt" units_ref="per_millivolt" />
<units name="per_millivolt_millisecond" units_ref="per_millivolt_millisecond" />
<units name="microF_per_cm2" units_ref="microF_per_cm2" />
<units name="joule_per_kilomole_kelvin" units_ref="joule_per_kilomole_kelvin" />
<units name="coulomb_per_mole" units_ref="coulomb_per_mole" />
<component name="environment" component_ref="environment" />
<component name="fast_sodium_current" component_ref="fast_sodium_current" />
<component name="time_dependent_potassium_current" component_ref="time_dependent_potassium_current" />
<component name="time_independent_potassium_current" component_ref="time_independent_potassium_current" />
<component name="plateau_potassium_current" component_ref="plateau_potassium_current" />
</import>
<!--
Below, we define some additional units for association with variables and
constants within the model.
-->
<units name="milliS_per_microF">
<unit prefix="milli" units="siemens" />
<unit prefix="milli" units="farad" exponent="-1" />
</units>
<units name="microF">
<unit prefix="micro" units="farad" />
</units>
<units name="microA_per_microF">
<unit prefix="micro" units="ampere" />
<unit prefix="micro" units="farad" exponent="-1" />
</units>
<units name="millimolar_per_millisecond">
<unit prefix="milli" units="mole" />
<unit units="litre" exponent="-1" />
<unit units="millisecond" exponent="-1" />
</units>
<units name="millimolar">
<unit prefix="milli" units="mole" />
<unit units="litre" exponent="-1" />
</units>
<units name="micromolar">
<unit prefix="micro" units="mole" />
<unit units="litre" exponent="-1" />
</units>
<units name="cm_per_second">
<unit prefix="centi" units="metre" />
<unit units="second" exponent="-1" />
</units>
<units name="mm2">
<unit prefix="milli" units="metre" exponent="2" />
</units>
<units name="micro_litre">
<unit prefix="micro" units="litre" />
</units>
<component name="membrane">
<variable name="V" public_interface="out" initial_value="-84.624" units="millivolt" />
<variable name="R" public_interface="out" initial_value="8314.0" units="joule_per_kilomole_kelvin" />
<variable name="T" public_interface="out" initial_value="310.0" units="kelvin" />
<variable name="F" public_interface="out" initial_value="96500.0" units="coulomb_per_mole" />
<variable name="Cm" initial_value="1.0" units="microF" />
<variable name="I_st" initial_value="-100.0" units="microA_per_microF" />
<variable name="time" public_interface="in" units="millisecond" />
<variable name="i_Na" public_interface="in" units="microA_per_microF" />
<variable name="i_Ca_L" public_interface="in" units="microA_per_microF" />
<variable name="i_K" public_interface="in" units="microA_per_microF" />
<variable name="i_NaCa" public_interface="in" units="microA_per_microF" />
<variable name="i_K1" public_interface="in" units="microA_per_microF" />
<variable name="i_Kp" public_interface="in" units="microA_per_microF" />
<variable name="i_p_Ca" public_interface="in" units="microA_per_microF" />
<variable name="i_Na_b" public_interface="in" units="microA_per_microF" />
<variable name="i_Ca_b" public_interface="in" units="microA_per_microF" />
<variable name="i_NaK" public_interface="in" units="microA_per_microF" />
<variable name="i_ns_Ca" public_interface="in" units="microA_per_microF" />
<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="L_type_Ca_channel">
<variable name="i_Ca_L" public_interface="out" units="microA_per_microF" />
<variable name="i_CaCa" public_interface="out" units="microA_per_microF" />
<variable name="i_CaK" public_interface="out" units="microA_per_microF" />
<variable name="i_CaNa" public_interface="out" units="microA_per_microF" />
<variable name="gamma_Nai" public_interface="out" initial_value="0.75" units="dimensionless" />
<variable name="gamma_Nao" public_interface="out" initial_value="0.75" units="dimensionless" />
<variable name="gamma_Ki" public_interface="out" initial_value="0.75" units="dimensionless" />
<variable name="gamma_Ko" public_interface="out" initial_value="0.75" units="dimensionless" />
<variable name="I_CaCa" units="microA_per_microF" />
<variable name="I_CaK" units="microA_per_microF" />
<variable name="I_CaNa" units="microA_per_microF" />
<variable name="P_Ca" initial_value="0.00054" units="cm_per_second" />
<variable name="P_Na" initial_value="0.000000675" units="cm_per_second" />
<variable name="P_K" initial_value="0.000000193" units="cm_per_second" />
<variable name="gamma_Cai" initial_value="1.0" units="dimensionless" />
<variable name="gamma_Cao" initial_value="0.34" units="dimensionless" />
<variable name="time" public_interface="in" private_interface="out" units="millisecond" />
<variable name="V" public_interface="in" private_interface="out" units="millivolt" />
<variable name="Cai" public_interface="in" private_interface="out" units="micromolar" />
<variable name="R" public_interface="in" units="joule_per_kilomole_kelvin" />
<variable name="T" public_interface="in" units="kelvin" />
<variable name="F" public_interface="in" units="coulomb_per_mole" />
<variable name="Cao" public_interface="in" units="millimolar" />
<variable name="Nao" public_interface="in" units="millimolar" />
<variable name="Ko" public_interface="in" units="millimolar" />
<variable name="Nai" public_interface="in" units="millimolar" />
<variable name="Ki" public_interface="in" units="millimolar" />
<variable name="d" private_interface="in" units="dimensionless" />
<variable name="f" private_interface="in" units="dimensionless" />
<variable name="f_Ca" private_interface="in" units="dimensionless" />
<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 name="d" public_interface="out" units="dimensionless" />
<variable name="alpha_d" units="per_millisecond" />
<variable name="beta_d" units="per_millisecond" />
<variable name="d_infinity" units="dimensionless" />
<variable name="tau_d" units="millisecond" />
<variable name="V" public_interface="in" units="millivolt" />
<variable name="time" public_interface="in" units="millisecond" />
<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