<?xml version="1.0"?>
<!--
This CellML file was generated on 1/07/2008 at 4:39:09 at p.m. using:
COR (0.9.31.979)
Copyright 2002-2008 Dr Alan Garny
http://COR.physiol.ox.ac.uk/ - COR@physiol.ox.ac.uk
CellML 1.0 was used to generate this model
http://www.CellML.org/
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" cmeta:id="yamaguchi_takaki_matsubara_yasuhara_suga_1996" name="yamaguchi_takaki_matsubara_yasuhara_suga_1996">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Constancy and variability of contractile efficiency as a function of calcium and cross-bridge kinetics: simulation</title>
<author>
<firstname>Geoffrey</firstname>
<surname>Nunns</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This model is known to run in both OpenCell and COR. It recreates the published results for the simulation, except in the case of FTI_end, FLA_max and ATP, because CellML cannot compute finite integrals or maximums of functions. These values are instead estimated based on graphs, but must be re-estimated for different initial conditions. The parameters for this model are the control values.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Abstract: We simulated myocardial Ca2+ (Ca) and cross-bridge (CB) kinetics to get insight into the experimentally observed constancy and variability of cardiac contractile efficiency in generating total mechanical energy under various inotropic and pathological conditions. The simulation consisted of a Ca transient, Ca association and dissociation rate constants of troponin C, and CB on and off rate constants. We evaluated sarcomere isometric twitch contractions at a constant muscle length. We assumed that each CB cycle hydrolyzes one ATP and that the force-length area (FLA) quantifies the total mechanical energy generated by CB cycles in a twitch contraction. FLA is a linear version of pressure-volume area, which quantifies the total mechanical energy of cardiac twitch contraction and correlates linearly with cardiac oxygen consumption (H. Suga, Physiol. Rev. 70: 247-277, 1990). The simulation shows that the contractile efficiency varies with changes in the Ca transient and Ca and CB kinetics except when they simultaneously speed up or slow down proportionally. These results point to possible mechanisms underlying the constancy and variability of cardiac contractile efficiency.
</para>
<para>
The original paper reference is cited below:
</para>
<para>Constancy and variability of contractile efficiency as a function of calcium and cross-bridge kinetics: simulation, Hiroki Yamaguchi, Miyako Takaki, Hiromi Matsubara, Shingo Yasuhara, and Hiroyuki Suga, 1996, <emphasis>American Journal of Physiology</emphasis>, 270, H1501-1508. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=8967394 &dopt=Abstract">PubMed ID: 8967394 </ulink>
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
</objectinfo>
<imagedata fileref="yamaguchi_1996.png"/>
</imageobject>
</mediaobject>
<caption>Schematic diagram showing the calcium kinetics between transient calcium (Ca2+), and troponin C (Tn), and cross bridge kinetics (CB).</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<units name="force">
<unit prefix="kilo" units="gram"/>
<unit units="meter"/>
<unit exponent="-1" units="second"/>
</units>
<units name="energy">
<unit units="force"/>
<unit units="meter"/>
</units>
<units name="per_second">
<unit exponent="-1" units="second"/>
</units>
<units name="force_second">
<unit units="force"/>
<unit units="second"/>
</units>
<units name="second_per_meter">
<unit exponent="-1" units="meter"/>
<unit units="second"/>
</units>
<component name="environment">
<variable cmeta:id="environment_t" name="t" public_interface="out" units="second"/>
</component>
<component name="parameters">
<variable initial_value="0.1" name="D_Ca" public_interface="out" units="second"/>
<variable initial_value="40" name="k_1" public_interface="out" units="per_second"/>
<variable initial_value="20" name="k_2" public_interface="out" units="per_second"/>
<variable initial_value="10" name="f" public_interface="out" units="per_second"/>
<variable initial_value="10" name="g" public_interface="out" units="per_second"/>
<variable initial_value="1" name="Ca_max" public_interface="out" units="dimensionless"/>
<variable initial_value="1" name="Total_Tn" public_interface="out" units="dimensionless"/>
<variable initial_value="1" name="Total_CB" public_interface="out" units="dimensionless"/>
</component>
<component name="Ca_t">
<variable cmeta:id="Ca_t_Ca_t" name="Ca_t" public_interface="out" units="dimensionless"/>
<variable name="t" public_interface="in" units="second"/>
<variable name="D_Ca" public_interface="in" units="second"/>
<variable name="Ca_max" public_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Ca_t</ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<times/>
<ci>Ca_max</ci>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<sin/>
<apply>
<divide/>
<apply>
<times/>
<pi/>
<apply>
<minus/>
<apply>
<divide/>
<ci>t</ci>
<ci>D_Ca</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.15</cn>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.3</cn>
</apply>
</apply>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<apply>
<and/>
<apply>
<geq/>
<ci>t</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">0</cn>
</apply>
<apply>
<lt/>
<ci>t</ci>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.3</cn>
<ci>D_Ca</ci>
</apply>
</apply>
</apply>
</piece>
<piece>
<apply>
<divide/>
<apply>
<times/>
<ci>Ca_max</ci>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<sin/>
<apply>
<divide/>
<apply>
<times/>
<pi/>
<apply>
<minus/>
<apply>
<divide/>
<ci>t</ci>
<ci>D_Ca</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.65</cn>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.7</cn>
</apply>
</apply>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<apply>
<and/>
<apply>
<geq/>
<ci>t</ci>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.3</cn>
<ci>D_Ca</ci>
</apply>
</apply>
<apply>
<lt/>
<ci>t</ci>
<ci>D_Ca</ci>
</apply>
</apply>
</piece>
<otherwise>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0</cn>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component name="TnCa">
<variable cmeta:id="TnCa_TnCa" initial_value="0" name="TnCa" public_interface="out" units="dimensionless"/>
<variable name="t" public_interface="in" units="second"/>
<variable name="Ca_t" public_interface="in" units="dimensionless"/>
<variable name="Total_Tn" public_interface="in" units="dimensionless"/>
<variable name="k_1" public_interface="in" units="per_second"/>
<variable name="k_2" public_interface="in" units="per_second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>TnCa</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k_1</ci>
<ci>Ca_t</ci>
<apply>
<minus/>
<ci>Total_Tn</ci>
<ci>TnCa</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k_2</ci>
<ci>TnCa</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="CB_on">
<variable cmeta:id="CB_on_CB_on" initial_value="0" name="CB_on" public_interface="out" units="dimensionless"/>
<variable name="t" public_interface="in" units="second"/>
<variable name="f" public_interface="in" units="per_second"/>
<variable name="g" public_interface="in" units="per_second"/>
<variable name="TnCa" public_interface="in" units="dimensionless"/>
<variable name="Total_CB" public_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>CB_on</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>f</ci>
<ci>TnCa</ci>
<apply>
<minus/>
<ci>Total_CB</ci>
<ci>CB_on</ci>
</apply>
</apply>
<apply>
<times/>
<ci>g</ci>
<ci>CB_on</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="CumCB">
<variable cmeta:id="CumCB_CumCB_on" initial_value="0" name="CumCB_on" public_interface="out" units="dimensionless"/>
<variable cmeta:id="CumCB_CumCB_off" initial_value="0" name="CumCB_off" public_interface="out" units="dimensionless"/>
<variable name="t" public_interface="in" units="second"/>
<variable name="f" public_interface="in" units="per_second"/>
<variable name="g" public_interface="in" units="per_second"/>
<variable name="CB_on" public_interface="in" units="dimensionless"/>
<variable name="Total_CB" public_interface="in" units="dimensionless"/>
<variable name="TnCa" public_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>CumCB_on</ci>
</apply>
<apply>
<times/>
<ci>f</ci>
<ci>TnCa</ci>
<apply>
<minus/>
<ci>Total_CB</ci>
<ci>CB_on</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>CumCB_off</ci>
</apply>
<apply>
<times/>
<ci>g</ci>
<ci>CB_on</ci>
</apply>
</apply>
</math>
</component>
<component name="force_development">
<variable name="F" units="force"/>
<variable cmeta:id="force_development_FTI" initial_value="0" name="FTI" units="force_second"/>
<variable name="FLA" public_interface="out" units="energy"/>
<variable name="t" public_interface="in" units="second"/>
<variable initial_value="1" name="phi" public_interface="out" units="force"/>
<variable initial_value="1" name="s" units="dimensionless"/>
<variable initial_value="1" name="L" units="meter"/>
<variable initial_value="0" name="L_0" units="meter"/>
<variable initial_value="0.228" name="F_max" units="force"/>
<variable name="CB_on" public_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>F</ci>
<apply>
<times/>
<ci>CB_on</ci>
<ci>phi</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>FTI</ci>
</apply>
<ci>F</ci>
</apply>
<apply>
<eq/>
<ci>FLA</ci>
<apply>
<times/>
<ci>F_max</ci>
<ci>s</ci>
<apply>
<minus/>
<ci>L</ci>
<ci>L_0</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="ATP">
<variable name="ATP" units="dimensionless"/>
<variable name="ATP_energy" public_interface="out" units="energy"/>
<variable initial_value="1" name="epsilon" public_interface="out" units="energy"/>
<variable initial_value="1" name="CumCB_on_end" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>ATP</ci>
<ci>CumCB_on_end</ci>
</apply>
<apply>
<eq/>
<ci>ATP_energy</ci>
<apply>
<times/>
<ci>ATP</ci>
<ci>epsilon</ci>
</apply>
</apply>
</math>
</component>
<component name="equations_main">
<variable name="Efficiency" units="dimensionless"/>
<variable name="Economy" units="second_per_meter"/>
<variable name="FLA" public_interface="in" units="energy"/>
<variable name="ATP_energy" public_interface="in" units="energy"/>
<variable name="g" public_interface="in" units="per_second"/>
<variable name="phi" public_interface="in" units="force"/>
<variable name="epsilon" public_interface="in" units="energy"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Efficiency</ci>
<apply>
<divide/>
<ci>FLA</ci>
<ci>ATP_energy</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Economy</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>phi</ci>
<ci>epsilon</ci>
</apply>
<apply>
<divide/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>g</ci>
</apply>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="environment" component_2="Ca_t"/>
<map_variables variable_1="t" variable_2="t"/>
</connection>
<connection>
<map_components component_1="environment" component_2="TnCa"/>
<map_variables variable_1="t" variable_2="t"/>
</connection>
<connection>
<map_components component_1="environment" component_2="CB_on"/>
<map_variables variable_1="t" variable_2="t"/>
</connection>
<connection>
<map_components component_1="environment" component_2="CumCB"/>
<map_variables variable_1="t" variable_2="t"/>
</connection>
<connection>
<map_components component_1="environment" component_2="force_development"/>
<map_variables variable_1="t" variable_2="t"/>
</connection>
<connection>
<map_components component_1="TnCa" component_2="Ca_t"/>
<map_variables variable_1="Ca_t" variable_2="Ca_t"/>
</connection>
<connection>
<map_components component_1="CB_on" component_2="TnCa"/>
<map_variables variable_1="TnCa" variable_2="TnCa"/>
</connection>
<connection>
<map_components component_1="parameters" component_2="Ca_t"/>
<map_variables variable_1="D_Ca" variable_2="D_Ca"/>
<map_variables variable_1="Ca_max" variable_2="Ca_max"/>
</connection>
<connection>
<map_components component_1="parameters" component_2="TnCa"/>
<map_variables variable_1="Total_Tn" variable_2="Total_Tn"/>
<map_variables variable_1="k_1" variable_2="k_1"/>
<map_variables variable_1="k_2" variable_2="k_2"/>
</connection>
<connection>
<map_components component_1="parameters" component_2="CB_on"/>
<map_variables variable_1="f" variable_2="f"/>
<map_variables variable_1="g" variable_2="g"/>
<map_variables variable_1="Total_CB" variable_2="Total_CB"/>
</connection>
<connection>
<map_components component_1="parameters" component_2="CumCB"/>
<map_variables variable_1="f" variable_2="f"/>
<map_variables variable_1="g" variable_2="g"/>
<map_variables variable_1="Total_CB" variable_2="Total_CB"/>
</connection>
<connection>
<map_components component_1="CB_on" component_2="CumCB"/>
<map_variables variable_1="CB_on" variable_2="CB_on"/>
</connection>
<connection>
<map_components component_1="TnCa" component_2="CumCB"/>
<map_variables variable_1="TnCa" variable_2="TnCa"/>
</connection>
<connection>
<map_components component_1="force_development" component_2="CB_on"/>
<map_variables variable_1="CB_on" variable_2="CB_on"/>
</connection>
<connection>
<map_components component_1="equations_main" component_2="force_development"/>
<map_variables variable_1="FLA" variable_2="FLA"/>
<map_variables variable_1="phi" variable_2="phi"/>
</connection>
<connection>
<map_components component_1="equations_main" component_2="ATP"/>
<map_variables variable_1="ATP_energy" variable_2="ATP_energy"/>
<map_variables variable_1="epsilon" variable_2="epsilon"/>
</connection>
<connection>
<map_components component_1="parameters" component_2="equations_main"/>
<map_variables variable_1="g" variable_2="g"/>
</connection>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Seq rdf:about="rdf:#6476bfe2-66f5-42bd-84cf-0bfca5c6adff">
<rdf:li rdf:resource="rdf:#37aa8e11-be12-4686-847c-9475fcc358cb"/>
<rdf:li rdf:resource="rdf:#39359680-5dee-479f-b95b-0d53cb1eaad0"/>
<rdf:li rdf:resource="rdf:#2e26b6af-cada-481e-bb93-a6c31d3b8ae7"/>
<rdf:li rdf:resource="rdf:#72ed4a01-5cb2-4076-8482-cdb328a519ad"/>
<rdf:li rdf:resource="rdf:#c8e8f9b5-5f98-44f0-b324-a8a28d4086c8"/>
</rdf:Seq>
<rdf:Description rdf:about="rdf:#1d5a07c5-b955-4f49-ae17-7257cb343060">
<dc:creator xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:resource="rdf:#91d95849-eb80-419e-bd3e-8525a3bb9c25"/>
<rdf:value>This model is known to run in both PCEnv and COR. It recreates the published results for the simulation, except in the case of FTI_end, FLA_max and ATP, because CellML cannot compute finite integrals or maximums of functions. These values are instead estimated based on graphs, but must be re-estimated for different initial conditions. The parameters for this model are the control values.</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#fbf64143-b011-4342-9195-039132d98fc4">
<vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Shingo</vCard:Given>
<vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Yasuhara</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#37aa8e11-be12-4686-847c-9475fcc358cb">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#0d0a8bd0-212f-4ce5-b59f-582541d121e6"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#39359680-5dee-479f-b95b-0d53cb1eaad0">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#d9dad641-b390-4593-a02a-afec1bc21662"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#91d95849-eb80-419e-bd3e-8525a3bb9c25">
<vCard:FN xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Geoff Nunns</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e7c7c0c7-ee41-414d-bd9b-5bb1bdf443b2">
<dcterms:W3CDTF xmlns:dcterms="http://purl.org/dc/terms/">1996-00-00 00:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0d0a8bd0-212f-4ce5-b59f-582541d121e6">
<vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Hiroki</vCard:Given>
<vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Yamaguchi</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4bfd1f49-2ecb-4aae-82f7-53a185c51660">
<dc:creator xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:resource="rdf:#fe9a9cb4-46c4-463b-8dbe-6fdf8ec30f71"/>
<rdf:value>This model is known to run in both PCEnv and COR. It recreates the published results for the simulation, except in the case of FTI_end, FLA_max and ATP, because CellML cannot compute finite integrals or maximums of functions. These values are instead estimated based on graphs, but must be re-estimated for different initial conditions. The parameters for this model are the control values.</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a4ad92bd-6383-41d3-9461-864fb8cd87d4">
<vCard:FN xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Geoff Nunns</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="rdf:#756bdc91-9b7e-4bf8-b6c8-a336a72a6205">
<vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#39adbeb4-8dae-47eb-ad1e-ff0032df4a0d"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9901bbc6-e45c-4e52-9d04-97a589212da7">
<vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Hiroyuki</vCard:Given>
<vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Suga</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#$Ie8fD2">
<rdf:rest rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#nil"/>
<rdf:first rdf:resource="rdf:#$Je8fD2"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#$He8fD2">
<ns7:boundIntervals xmlns:ns7="http://www.cellml.org/metadata/simulation/1.0#" rdf:resource="rdf:#$Ie8fD2"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ab00d4a2-3bef-4758-a6c1-e6b6b9c5f44b">
<vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Hiromi</vCard:Given>
<vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Matsubara</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#39adbeb4-8dae-47eb-ad1e-ff0032df4a0d">
<vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Geoffrey</vCard:Given>
<vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Nunns</vCard:Family>
<vCard:Other xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Rogan</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d9dad641-b390-4593-a02a-afec1bc21662">
<vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Miyako</vCard:Given>
<vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Takaki</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#7c01780a-c238-4602-af10-c9ce6a6d178d">
<vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Geoffrey</vCard:Given>
<vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Nunns</vCard:Family>
<vCard:Other xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Rogan</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#00dfdd87-1034-45ac-aab5-f26b52e8f704">
<dc:creator xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:resource="rdf:#a4ad92bd-6383-41d3-9461-864fb8cd87d4"/>
<rdf:value>This model is known to run in both PCEnv and COR. It recreates the published results for the simulation, except in the case of FTI_end, FLA_max and ATP, because CellML cannot compute finite integrals or maximums of functions. These values are instead estimated based on graphs, but must be re-estimated for different initial conditions. The parameters for this model are the control values.</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c7b4422b-c131-428a-a6b2-6d26a66ad9fc">
<vCard:ORG xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#b0be0caa-17d9-44a1-adbe-c5abe75de39c"/>
<vCard:EMAIL xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#34252856-ee22-47f2-921d-dcff4d00b6c5"/>
<vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#7c01780a-c238-4602-af10-c9ce6a6d178d"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#fe9a9cb4-46c4-463b-8dbe-6fdf8ec30f71">
<vCard:FN xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Geoff Nunns</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="rdf:#238b73ff-35c2-417b-80ac-d554b3b53bb4">
<dcterms:W3CDTF xmlns:dcterms="http://purl.org/dc/terms/">2008-06-26T00:00:00+00:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#$Je8fD2">
<ns7:endingValue xmlns:ns7="http://www.cellml.org/metadata/simulation/1.0#">0.5</ns7:endingValue>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c8e8f9b5-5f98-44f0-b324-a8a28d4086c8">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#9901bbc6-e45c-4e52-9d04-97a589212da7"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#05f25c83-6c64-499d-9d35-ecefe16d37a7">
<dcterms:W3CDTF xmlns:dcterms="http://purl.org/dc/terms/">2008-07-18T14:10:09+12:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4daa6e55-44d1-4e1c-85be-669e68e84e29">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">American Journal of Physiology</dc:title>
</rdf:Description>
<rdf:Description rdf:about="rdf:#34252856-ee22-47f2-921d-dcff4d00b6c5">
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
<rdf:value>gnunns1@jhem.jhu.edu</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#yamaguchi_takaki_matsubara_yasuhara_suga_1996">
<ns7:simulation xmlns:ns7="http://www.cellml.org/metadata/simulation/1.0#" rdf:resource="rdf:#$He8fD2"/>
<bqs:reference xmlns:bqs="http://www.cellml.org/bqs/1.0#" rdf:resource="rdf:#4d7cbeb3-e50f-4dc3-a7ea-2795ecc19401"/>
<bqs:reference xmlns:bqs="http://www.cellml.org/bqs/1.0#" rdf:parseType="Resource">
<dc:subject xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:parseType="Resource">
<bqs:subject_type>keyword</bqs:subject_type>
<rdf:value>
<rdf:Bag>
<rdf:li>calcium dynamics</rdf:li>
<rdf:li>myofilament mechanics</rdf:li>
<rdf:li>excitation-contraction coupling</rdf:li>
</rdf:Bag>
</rdf:value>
</dc:subject>
</bqs:reference>
<cmeta:comment rdf:resource="rdf:#1d5a07c5-b955-4f49-ae17-7257cb343060"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#2e26b6af-cada-481e-bb93-a6c31d3b8ae7">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#ab00d4a2-3bef-4758-a6c1-e6b6b9c5f44b"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#b0be0caa-17d9-44a1-adbe-c5abe75de39c">
<vCard:Orgname xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Auckland Bioengineering Institute</vCard:Orgname>
<vCard:Orgunit xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">CellML Team</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="">
<dc:publisher xmlns:dc="http://purl.org/dc/elements/1.1/"/>
<cmeta:comment rdf:resource="rdf:#00dfdd87-1034-45ac-aab5-f26b52e8f704"/>
<dcterms:created xmlns:dcterms="http://purl.org/dc/terms/" rdf:resource="rdf:#238b73ff-35c2-417b-80ac-d554b3b53bb4"/>
<dc:creator xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:resource="rdf:#c7b4422b-c131-428a-a6b2-6d26a66ad9fc"/>
<cmeta:modification rdf:resource="rdf:#22c39aeb-832f-48e2-8b17-61e2d1ba7fe6"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#72ed4a01-5cb2-4076-8482-cdb328a519ad">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#fbf64143-b011-4342-9195-039132d98fc4"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4d7cbeb3-e50f-4dc3-a7ea-2795ecc19401">
<bqs:Pubmed_id xmlns:bqs="http://www.cellml.org/bqs/1.0#">8967394</bqs:Pubmed_id>
<bqs:JournalArticle xmlns:bqs="http://www.cellml.org/bqs/1.0#" rdf:resource="rdf:#18e335aa-4ce7-4e60-bc84-b585152627a5"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#18e335aa-4ce7-4e60-bc84-b585152627a5">
<dc:creator xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:resource="rdf:#6476bfe2-66f5-42bd-84cf-0bfca5c6adff"/>
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Constancy and variability of contractile efficiency as a function of calcium and cross-bridge kinetics: simulation</dc:title>
<bqs:volume xmlns:bqs="http://www.cellml.org/bqs/1.0#">270</bqs:volume>
<bqs:first_page xmlns:bqs="http://www.cellml.org/bqs/1.0#">H1501</bqs:first_page>
<bqs:Journal xmlns:bqs="http://www.cellml.org/bqs/1.0#" rdf:resource="rdf:#4daa6e55-44d1-4e1c-85be-669e68e84e29"/>
<dcterms:issued xmlns:dcterms="http://purl.org/dc/terms/" rdf:resource="rdf:#e7c7c0c7-ee41-414d-bd9b-5bb1bdf443b2"/>
<bqs:last_page xmlns:bqs="http://www.cellml.org/bqs/1.0#">H1508</bqs:last_page>
</rdf:Description>
<rdf:Description rdf:about="rdf:#22c39aeb-832f-48e2-8b17-61e2d1ba7fe6">
<dcterms:modified xmlns:dcterms="http://purl.org/dc/terms/" rdf:resource="rdf:#05f25c83-6c64-499d-9d35-ecefe16d37a7"/>
<rdf:value>Added cmeta ids to variables so that the model works with session files</rdf:value>
<cmeta:modifier rdf:resource="rdf:#756bdc91-9b7e-4bf8-b6c8-a336a72a6205"/>
</rdf:Description>
</rdf:RDF>
</model>
