- Author:
- Catherine Lloyd <c.lloyd@auckland.ac.nz>
- Date:
- 2010-08-06 05:27:29+12:00
- Desc:
- updated curation comment.
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/landesberg_sideman_1994/rawfile/614313fee8acc661fcb52865e809cceff5616afb/landesberg_sideman_1994.cellml
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This CellML file was generated on 25/07/2008 at 3:40:37 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
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<title>Mechanical regulation of cardiac muscle by coupling calcium kinetics with cross-bridge cycling: a dynamic model</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 does not run in OpenCell or COR because all variables are not initialized and some variables are undefined. This is only the case for the component force equations but it seems that all the variables in that component cannot be calculated because some of the equations in the original paper look like partial differential equations which are beyond the scope of CellML.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Abstract: This study describes the regulation of mechanical activity in the intact cardiac muscle, the effects of the free calcium transients and the mechanical constraints, and emphasizes the central role of the troponin complex in regulating muscle activity. A "loose coupling" between calcium binding to troponin and cross-bridge cycling is stipulated, allowing the existence of cross bridges in the strong conformation without having bound calcium on the neighboring troponin. The model includes two feedback mechanisms: 1) a positive feedback, or cooperativity, in which the cycling cross bridges affect the affinity of troponin for calcium, and 2) a negative mechanical feedback, where the filament-sliding velocity affects cross-bridge cycling. The model simulates the reported experimental force-length and force-velocity relationships at different levels of activation. The dependence of the shortening velocity on calcium concentration, sarcomere length, internal load, and rate of cross-bridge cycling is described analytically in agreement with reported data. Furthermore, the model provides an analytic solution for Hill's equation of the force-velocity relationship and for the phenomena of unloaded shortening velocity and force deficit. The model-calculated changes in free calcium in various mechanical conditions are in good agreement with the available experimental results.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
Mechanical regulation of cardiac muscle by coupling calcium kinetics with cross-bridge cycling: a dynamic model, A. Landesberg, S. Sideman, 1994, <emphasis>Am. J. Physiol- Heart Circ. Physiol</emphasis>, 267, H779-795. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=8067434&dopt=Abstract">PubMed ID: 8067434 </ulink>
</para>
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<apply>
<times/>
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<minus/>
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<times/>
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<apply>
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<times/>
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</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
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<apply>
<plus/>
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<times/>
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<apply>
<times/>
<apply>
<minus/>
<apply>
<minus/>
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<minus/>
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<apply>
<times/>
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</apply>
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<apply>
<times/>
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</apply>
</apply>
<apply>
<eq/>
<ci>T_d</ci>
<apply>
<times/>
<ci>Tbar_d</ci>
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</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
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<apply>
<plus/>
<apply>
<times/>
<ci>k_minus_m</ci>
<ci>T_d</ci>
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<apply>
<times/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
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</apply>
<ci>g_prime_0</ci>
</apply>
<apply>
<times/>
<ci>g_prime_1</ci>
<ci>V</ci>
</apply>
</apply>
<ci>U_d</ci>
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</apply>
</apply>
<apply>
<eq/>
<ci>U_d</ci>
<apply>
<times/>
<ci>Ubar_d</ci>
<ci>alpha</ci>
<ci>L_m</ci>
</apply>
</apply>
</math>
</component>
<component name="calcium_flux">
<variable units="uM" public_interface="out" name="Ca" initial_value="0"/>
<variable units="uM" name="Ca_0" initial_value="2000"/>
<variable units="uM_per_second" name="I_o"/>
<variable units="uM_per_second" name="I_s"/>
<variable units="uM_per_second" name="I_i"/>
<variable units="uM_per_second" name="I_u"/>
<variable units="per_second" name="Q_o" initial_value="30"/>
<variable units="per_second" name="Q_s" initial_value="0.3"/>
<variable units="second" name="tau_SR" initial_value="0.002"/>
<variable units="second" name="tau_SF" initial_value="0.02"/>
<variable units="per_second" name="Q_i" initial_value="0.6"/>
<variable units="second" name="tau_iR" initial_value="0.002"/>
<variable units="second" name="tau_iF" initial_value="0.1"/>
<variable units="uM_per_second" name="Q_u" initial_value="1000"/>
<variable units="uM" name="K_mu" initial_value="1"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="uM_per_second" name="I_l" initial_value="0"/>
<variable units="uM" name="Ca_r" initial_value="0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
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<apply>
<times/>
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</apply>
</apply>
<apply>
<eq/>
<ci>I_s</ci>
<apply>
<times/>
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<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>time</ci>
</apply>
<ci>tau_SR</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>time</ci>
</apply>
<ci>tau_SF</ci>
</apply>
</apply>
</apply>
<ci>I_l</ci>
</apply>
<ci>Ca_0</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>I_i</ci>
<apply>
<times/>
<ci>Q_i</ci>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>time</ci>
</apply>
<ci>tau_iR</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>time</ci>
</apply>
<ci>tau_iF</ci>
</apply>
</apply>
</apply>
<ci>I_l</ci>
</apply>
<ci>Ca_r</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>I_u</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>Q_u</ci>
<ci>Ca</ci>
</apply>
<apply>
<plus/>
<ci>K_mu</ci>
<ci>Ca</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>I_s</ci>
<ci>I_i</ci>
</apply>
<apply>
<plus/>
<ci>I_o</ci>
<ci>I_u</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="bound_calcium">
<variable units="uM" public_interface="out" name="BCa_L"/>
<variable units="uM" public_interface="out" name="BCa_h" initial_value="0"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="uM" public_interface="in" name="TRo"/>
<variable units="uM" public_interface="in" name="Ca"/>
<variable units="uM" public_interface="in" name="A_s"/>
<variable units="uM" public_interface="in" name="T_s"/>
<variable units="uM" public_interface="in" name="A_d"/>
<variable units="uM" public_interface="in" name="T_d"/>
<variable units="uM" public_interface="in" name="A_n"/>
<variable units="per_uM_per_second" public_interface="in" name="k_h"/>
<variable units="per_second" public_interface="in" name="k_minus_h"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>BCa_L</ci>
<apply>
<plus/>
<ci>A_s</ci>
<ci>T_s</ci>
<ci>A_d</ci>
<ci>T_d</ci>
<ci>A_n</ci>
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</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
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<apply>
<minus/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>TRo</ci>
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<ci>BCa_h</ci>
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<ci>Ca</ci>
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<apply>
<times/>
<ci>BCa_h</ci>
<ci>k_minus_h</ci>
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</apply>
</apply>
</math>
</component>
<component name="force_equations">
<variable units="mN" name="F"/>
<variable units="mN" name="F_CB"/>
<variable units="mN" name="F_CE"/>
<variable units="mN" name="F_PE"/>
<variable units="mN" name="F_bar"/>
<variable units="mN_second_per_umeter" name="eta"/>
<variable units="mN_second_per_umeter" name="eta_PE"/>
<variable units="dimensionless" name="T_s"/>
<variable units="dimensionless" name="U_s"/>
<variable units="mN" name="E"/>
<variable units="dimensionless" name="D"/>
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<variable units="umeter" name="SL"/>
<variable units="umeter" name="Sp_0"/>
<variable units="per_second" public_interface="in" name="V"/>
<variable units="per_second" public_interface="in" name="V_SL"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
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<apply>
<minus/>
<ci>F_bar</ci>
<apply>
<times/>
<ci>eta</ci>
<ci>V</ci>
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</apply>
</apply>
<apply>
<eq/>
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<apply>
<times/>
<apply>
<plus/>
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<ci>F_CB</ci>
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</apply>
<apply>
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<ci>F_PE</ci>
<piecewise>
<piece>
<apply>
<plus/>
<apply>
<times/>
<ci>E</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<times/>
<ci>D</ci>
<apply>
<minus/>
<apply>
<divide/>
<ci>SL</ci>
<ci>Sp_0</ci>
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<cn cellml:units="dimensionless">1</cn>
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</apply>
<cn cellml:units="dimensionless">1</cn>
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<apply>
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<ci>V_SL</ci>
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</apply>
<apply>
<geq/>
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<ci>Sp_0</ci>
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</piece>
<otherwise>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci>B</ci>
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<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>SL</ci>
<ci>Sp_0</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>eta_PE</ci>
<ci>V_SL</ci>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>F</ci>
<apply>
<plus/>
<ci>F_CE</ci>
<ci>F_PE</ci>
</apply>
</apply>
</math>
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<component name="input">
<variable units="dimensionless" public_interface="out" name="alpha" initial_value="1"/>
<variable units="per_second" name="d_alpha_dt" initial_value="0"/>
<variable units="per_second" public_interface="out" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>V</ci>
<ci>d_alpha_dt</ci>
</apply>
</math>
</component>
<connection>
<map_components component_2="single_overlap" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="double_overlap" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="calcium_flux" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="bound_calcium" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="non_overlap" component_1="parameters"/>
<map_variables variable_2="K_1" variable_1="K_1"/>
<map_variables variable_2="k_minus_1" variable_1="k_minus_1"/>
<map_variables variable_2="L_m" variable_1="L_m"/>
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<connection>
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<map_variables variable_2="g_0" variable_1="g_0"/>
<map_variables variable_2="g_1" variable_1="g_1"/>
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<map_variables variable_2="g_prime_1" variable_1="g_prime_1"/>
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<map_variables variable_2="K_m" variable_1="K_m"/>
<map_variables variable_2="k_minus_1" variable_1="k_minus_1"/>
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<connection>
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<map_variables variable_2="g_1" variable_1="g_1"/>
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<map_variables variable_2="k_minus_m" variable_1="k_minus_m"/>
<map_variables variable_2="L_m" variable_1="L_m"/>
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<connection>
<map_components component_2="calcium_flux" component_1="parameters"/>
<map_variables variable_2="Ca" variable_1="Ca"/>
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<connection>
<map_components component_2="bound_calcium" component_1="parameters"/>
<map_variables variable_2="TRo" variable_1="Troponin"/>
<map_variables variable_2="k_h" variable_1="k_h"/>
<map_variables variable_2="k_minus_h" variable_1="k_minus_h"/>
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<connection>
<map_components component_2="double_overlap" component_1="single_overlap"/>
<map_variables variable_2="Rbar_d" variable_1="Rbar_d"/>
<map_variables variable_2="Abar_d" variable_1="Abar_d"/>
<map_variables variable_2="Tbar_d" variable_1="Tbar_d"/>
<map_variables variable_2="Ubar_d" variable_1="Ubar_d"/>
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<connection>
<map_components component_2="calcium_flux" component_1="bound_calcium"/>
<map_variables variable_2="Ca" variable_1="Ca"/>
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<connection>
<map_components component_2="non_overlap" component_1="bound_calcium"/>
<map_variables variable_2="A_n" variable_1="A_n"/>
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<connection>
<map_components component_2="single_overlap" component_1="bound_calcium"/>
<map_variables variable_2="A_s" variable_1="A_s"/>
<map_variables variable_2="T_s" variable_1="T_s"/>
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<connection>
<map_components component_2="double_overlap" component_1="bound_calcium"/>
<map_variables variable_2="A_d" variable_1="A_d"/>
<map_variables variable_2="T_d" variable_1="T_d"/>
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<connection>
<map_components component_2="input" component_1="non_overlap"/>
<map_variables variable_2="alpha" variable_1="alpha"/>
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<connection>
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<map_variables variable_2="alpha" variable_1="alpha"/>
<map_variables variable_2="V" variable_1="V"/>
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<connection>
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<map_variables variable_2="alpha" variable_1="alpha"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="input" component_1="force_equations"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="V" variable_1="V_SL"/>
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<rdf:RDF>
<rdf:Seq rdf:about="rdf:#5508b2ac-b8f5-4b8a-9e6e-6e5aea97a0b6">
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<rdf:Description rdf:about="rdf:#4ea64db3-9cae-4a4c-b19c-47a740d5474b">
<vCard:FN>Geoff Nunns</vCard:FN>
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<rdf:Description rdf:about="rdf:#425e19a4-549e-4fef-9627-8d79eb79d00b">
<dc:creator rdf:resource="rdf:#5508b2ac-b8f5-4b8a-9e6e-6e5aea97a0b6"/>
<dc:title>Mechanical regulation of cardiac muscle by coupling calcium kinetics with cross-bridge cycling: a dynamic model</dc:title>
<bqs:volume>267</bqs:volume>
<bqs:first_page>H779</bqs:first_page>
<bqs:Journal rdf:resource="rdf:#ef6c8ebc-4245-47af-a615-bf2497faf23e"/>
<dcterms:issued rdf:resource="rdf:#999ad860-a936-4f36-b99f-23c60321fec9"/>
<bqs:last_page>H795</bqs:last_page>
</rdf:Description>
<rdf:Description rdf:about="rdf:#316194d4-f78e-4353-a131-c11631555d06">
<vCard:Given>S</vCard:Given>
<vCard:Family>Sideman</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ef6c8ebc-4245-47af-a615-bf2497faf23e">
<dc:title>Am J Physiol Heart Circ Physiol</dc:title>
</rdf:Description>
<rdf:Description rdf:about="">
<dc:publisher/>
<cmeta:comment rdf:resource="rdf:#a2537844-d506-4782-bc1a-69cb4b76efad"/>
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<vCard:ORG rdf:resource="rdf:#76b5fc6d-bc6b-4be2-847a-7d48f9d01432"/>
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<vCard:N rdf:resource="rdf:#f43eb646-20c1-43f4-b35a-17e998c113ad"/>
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<rdf:Description rdf:about="rdf:#7005ab5c-148b-4257-9838-a07cf6a9b88b">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#316194d4-f78e-4353-a131-c11631555d06"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#999ad860-a936-4f36-b99f-23c60321fec9">
<dcterms:W3CDTF>1994-00-00 00:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#b2c17697-5614-4cec-a072-c7a3b9611241">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#7d61c5e8-ffb7-4e15-ad96-7893f2722c4e"/>
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<dc:creator rdf:resource="rdf:#ae8997b5-a0c4-4e0e-81b7-a7508bc78c82"/>
<rdf:value>This model does not run in PCEnv or COR because all variables are not initialized and some variables are undefined. This in only the case for the component force equations, but I don't think all the variables in that component can be calculated, as some of the paper equations look like PDEs. Further curation is needed.</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#2dc425af-7d22-4dd4-97c8-0e66f73bd3ae">
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
<rdf:value>gnunns1@jhem.jhu.edu</rdf:value>
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<rdf:Description rdf:about="rdf:#ae8997b5-a0c4-4e0e-81b7-a7508bc78c82">
<vCard:FN>Geoff Nunns</vCard:FN>
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<rdf:Description rdf:about="rdf:#7d61c5e8-ffb7-4e15-ad96-7893f2722c4e">
<vCard:Given>A</vCard:Given>
<vCard:Family>Landesberg</vCard:Family>
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<dcterms:W3CDTF>2008-07-18T00:00:00+12:00</dcterms:W3CDTF>
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<vCard:Given>Geoffrey</vCard:Given>
<vCard:Family>Nunns</vCard:Family>
<vCard:Other>Rogan</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#76b5fc6d-bc6b-4be2-847a-7d48f9d01432">
<vCard:Orgname>Auckland Bioengineering Institute</vCard:Orgname>
<vCard:Orgunit>CellML Team</vCard:Orgunit>
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<rdf:Description rdf:about="#landesberg_sideman_1994">
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<rdf:li>cardiac</rdf:li>
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</dc:subject>
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<bqs:Pubmed_id>8067434</bqs:Pubmed_id>
<bqs:JournalArticle rdf:resource="rdf:#425e19a4-549e-4fef-9627-8d79eb79d00b"/>
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<rdf:Description rdf:about="rdf:#76fff257-840d-41e5-96f5-a3841f11db64">
<dc:creator rdf:resource="rdf:#4ea64db3-9cae-4a4c-b19c-47a740d5474b"/>
<rdf:value>This model does not run in PCEnv or COR because all variables are not initialized and some variables are undefined. This in only the case for the component force equations, but I don't think all the variables in that component can be calculated, as some of the paper equations look like PDEs. Further curation is needed.</rdf:value>
</rdf:Description>
</rdf:RDF>
</model>
