- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-08-21 04:54:33+12:00
- Desc:
- committing version01 of vancapelle_durrer_1980
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/vancapelle_durrer_1980/rawfile/5a2a21deb9f86d3b76d025a0d87bf378497b03e4/vancapelle_durrer_1980.cellml
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<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="1980_vanCapelle_Durrer" name="vancapelle_durrer_1980_version01">
<!--
Generally, we want to move away from initial/default values being
stored in the model directly. But until we are using CellML 1.1
it is probably quite useful to include the values in the model.
-->
<!-- Global units -->
<units name="mV">
<unit units="volt" prefix="milli"/>
</units>
<units name="uApmmsq">
<unit units="ampere" prefix="micro"/>
<unit units="metre" prefix="milli" exponent="-2"/>
</units>
<units name="uFpmmsq">
<unit units="farad" prefix="micro"/>
<unit units="metre" prefix="milli" exponent="-2"/>
</units>
<units name="ms">
<unit units="second" prefix="milli"/>
</units>
<units name="pms">
<unit units="second" prefix="milli" exponent="-1"/>
</units>
<units name="uApmmsqpmVcu">
<unit units="uApmmsq"/>
<unit units="mV" exponent="-1"/>
</units>
<units name="uApmmsqpmVsq">
<unit units="uApmmsq"/>
<unit units="mV" exponent="-1"/>
</units>
<units name="uApmmsqpmV">
<unit units="uApmmsq"/>
<unit units="mV" exponent="-1"/>
</units>
<component cmeta:id="interface" name="interface">
<!-- Variables we expect to be set/controlled externally -->
<variable units="ms" private_interface="out" name="t"/>
<variable units="uFpmmsq" private_interface="out" name="Cm" initial_value="0.01"/>
<variable units="pms" private_interface="out" name="T" initial_value="50.0"/>
<variable units="uApmmsqpmVcu" private_interface="out" name="af" initial_value="3.837854e-5"/>
<variable units="uApmmsqpmVsq" private_interface="out" name="bf" initial_value="5.84649e-3"/>
<variable units="uApmmsqpmV" private_interface="out" name="cf" initial_value="0.2531834"/>
<variable units="uApmmsq" private_interface="out" name="df" initial_value="2.356256"/>
<variable units="uApmmsq" private_interface="out" name="Istim"/>
<!-- Variables we want to make available externally -->
<variable units="mV" public_interface="out" private_interface="in" name="Vm"/>
<variable units="dimensionless" public_interface="out" private_interface="in" name="Y"/>
<variable units="uApmmsq" public_interface="out" private_interface="in" name="Iion"/>
<variable units="uApmmsq" public_interface="out" name="IStimC"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="IStim_for_cmiss_eq">
<apply id="IStim_for_cmiss">
<eq/>
<ci>IStimC</ci>
<ci>Istim</ci>
</apply>
</math>
</component> <!--interface-->
<component cmeta:id="membrane_potential" name="membrane_potential">
<!-- Inputs -->
<variable units="ms" public_interface="in" name="t"/>
<variable units="uFpmmsq" public_interface="in" name="Cm"/>
<variable units="uApmmsq" public_interface="in" name="Istim"/>
<variable units="uApmmsq" public_interface="in" name="Iion"/>
<!-- Outputs computed here -->
<variable units="mV" public_interface="out" private_interface="out" name="Vm" initial_value="-78.6"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Vm_diff_calculation_eq">
<apply id="Vm_diff_calculation">
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Vm</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>Istim</ci>
<ci>Iion</ci>
</apply>
<ci>Cm</ci>
</apply>
</apply>
</math>
</component>
<!--membrane_potential-->
<component cmeta:id="ionic_current" name="ionic_current">
<!-- Inputs -->
<variable units="dimensionless" public_interface="in" name="Y"/>
<variable units="mV" public_interface="in" name="Vm"/>
<variable units="uApmmsqpmVcu" public_interface="in" name="af"/>
<variable units="uApmmsqpmVsq" public_interface="in" name="bf"/>
<variable units="uApmmsqpmV" public_interface="in" name="cf"/>
<variable units="uApmmsq" public_interface="in" name="df"/>
<!-- Outputs computed here -->
<variable units="uApmmsq" public_interface="out" private_interface="out" name="Iion"/>
<!-- local variables -->
<variable units="uApmmsq" name="i0"/>
<variable units="uApmmsq" name="i1"/>
<variable units="uApmmsq" name="f"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Iion_calculation_eq">
<apply id="Iion_calculation">
<eq/>
<ci>Iion</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>Y</ci>
<ci>i1</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1.0</cn>
<ci>Y</ci>
</apply>
<ci>i0</ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="i1_calculation_eq">
<apply id="i1_calculation">
<eq/>
<ci>i1</ci>
<piecewise>
<piece>
<apply>
<plus/>
<cn cellml:units="uApmmsq">0.05</cn>
<apply>
<times/>
<cn cellml:units="uApmmsqpmV">0.005</cn>
<apply>
<plus/>
<ci>Vm</ci>
<cn cellml:units="mV">70.0</cn>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci>Vm</ci>
<cn cellml:units="mV">-70.0</cn>
</apply>
</piece>
<piece>
<apply>
<plus/>
<cn cellml:units="uApmmsq">0.06</cn>
<apply>
<times/>
<cn cellml:units="uApmmsqpmV">0.00425</cn>
<ci>Vm</ci>
</apply>
</apply>
<apply>
<gt/>
<ci>Vm</ci>
<cn cellml:units="mV">0.0</cn>
</apply>
</piece>
<otherwise>
<apply>
<plus/>
<cn cellml:units="uApmmsq">0.05</cn>
<apply>
<times/>
<cn cellml:units="uApmmsq">0.01</cn>
<apply>
<divide/>
<apply>
<plus/>
<ci>Vm</ci>
<cn cellml:units="mV">70.0</cn>
</apply>
<cn cellml:units="mV">70.0</cn>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="i0_calculation_eq">
<apply id="i0_calculation">
<eq/>
<ci>i0</ci>
<apply>
<plus/>
<ci>i1</ci>
<ci>f</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="f_calculation_eq">
<apply id="f_calculation">
<eq/>
<ci>f</ci>
<piecewise>
<piece>
<apply>
<plus/>
<cn cellml:units="uApmmsq">0.0784</cn>
<apply>
<times/>
<cn cellml:units="uApmmsqpmV">0.02</cn>
<apply>
<plus/>
<ci>Vm</ci>
<cn cellml:units="mV">74.3</cn>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci>Vm</ci>
<cn cellml:units="mV">-74.3</cn>
</apply>
</piece>
<piece>
<apply>
<plus/>
<cn cellml:units="uApmmsq">-0.9884</cn>
<apply>
<times/>
<cn cellml:units="uApmmsqpmV">0.0171</cn>
<apply>
<plus/>
<ci>Vm</ci>
<cn cellml:units="mV">27.8</cn>
</apply>
</apply>
</apply>
<apply>
<gt/>
<ci>Vm</ci>
<cn cellml:units="mV">-27.8</cn>
</apply>
</piece>
<otherwise>
<apply>
<plus/>
<apply>
<times/>
<ci>af</ci>
<apply>
<power/>
<ci>Vm</ci>
<cn cellml:units="dimensionless">3.0</cn>
</apply>
</apply>
<apply>
<times/>
<ci>bf</ci>
<apply>
<power/>
<ci>Vm</ci>
<cn cellml:units="dimensionless">2.0</cn>
</apply>
</apply>
<apply>
<times/>
<ci>cf</ci>
<ci>Vm</ci>
</apply>
<ci>df</ci>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<!--ionic_current-->
<component cmeta:id="excitability_variable" name="excitability_variable">
<!-- Inputs -->
<variable units="ms" public_interface="in" name="t"/>
<variable units="pms" public_interface="in" name="T"/>
<variable units="mV" public_interface="in" name="Vm"/>
<!-- Outputs computed here -->
<variable units="dimensionless" public_interface="out" private_interface="out" name="Y" initial_value="0.07"/>
<!-- Local variables -->
<variable units="dimensionless" name="Yinf"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Y_diff_eq">
<apply id="Y_diff">
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Y</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="dimensionless">1.0</cn>
<ci>T</ci>
</apply>
<apply>
<minus/>
<ci>Yinf</ci>
<ci>Y</ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Yinf_calculation_eq">
<apply id="Yinf_calculation">
<eq/>
<ci>Yinf</ci>
<piecewise>
<piece>
<cn cellml:units="dimensionless">0.0</cn>
<apply>
<lt/>
<ci>Vm</ci>
<cn cellml:units="mV">-80.0</cn>
</apply>
</piece>
<piece>
<cn cellml:units="dimensionless">1.0</cn>
<apply>
<gt/>
<ci>Vm</ci>
<cn cellml:units="mV">-60.0</cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<apply>
<plus/>
<ci>Vm</ci>
<cn cellml:units="mV">80.0</cn>
</apply>
<cn cellml:units="mV">20.0</cn>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<!--ionic_current-->
<connection>
<map_components component_2="membrane_potential" component_1="interface"/>
<map_variables variable_2="t" variable_1="t"/>
<map_variables variable_2="Cm" variable_1="Cm"/>
<map_variables variable_2="Istim" variable_1="Istim"/>
<map_variables variable_2="Vm" variable_1="Vm"/>
</connection>
<connection>
<map_components component_2="ionic_current" component_1="interface"/>
<map_variables variable_2="af" variable_1="af"/>
<map_variables variable_2="bf" variable_1="bf"/>
<map_variables variable_2="cf" variable_1="cf"/>
<map_variables variable_2="df" variable_1="df"/>
<map_variables variable_2="Iion" variable_1="Iion"/>
</connection>
<connection>
<map_components component_2="excitability_variable" component_1="interface"/>
<map_variables variable_2="t" variable_1="t"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="Y" variable_1="Y"/>
</connection>
<connection>
<map_components component_2="ionic_current" component_1="membrane_potential"/>
<map_variables variable_2="Iion" variable_1="Iion"/>
<map_variables variable_2="Vm" variable_1="Vm"/>
</connection>
<connection>
<map_components component_2="excitability_variable" component_1="membrane_potential"/>
<map_variables variable_2="Vm" variable_1="Vm"/>
</connection>
<connection>
<map_components component_2="excitability_variable" component_1="ionic_current"/>
<map_variables variable_2="Y" variable_1="Y"/>
</connection>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="interface">
<component_ref component="membrane_potential"/>
<component_ref component="ionic_current"/>
<component_ref component="excitability_variable"/>
</component_ref>
</group>
<rdf:RDF>
<rdf:Seq rdf:about="rdf:#citationAuthorsSeq">
<rdf:li rdf:resource="rdf:#author1Vcard"/>
<rdf:li rdf:resource="rdf:#author2Vcard"/>
</rdf:Seq>
<rdf:Description rdf:about="rdf:#ee8cbbbd-3243-4e97-8cf3-6d8a1f8bc182">
<rdf:value>
This equation describes the kinetics of the transmembrane
potential - the action potential.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8b23a0cb-706e-4cc1-a41c-2f338adf67b4">
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
<rdf:value>d.nickerson@auckland.ac.nz</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#7f6340ae-0356-4f5c-aeb4-ec9cb79f0617">
<rdf:value>
Here we define the ionic current through the cellular
membrane, defined as the summation of the two component
currents weighted by the excitability variable.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#i1_calculation_eq">
<cmeta:comment rdf:resource="rdf:#6f4e7cac-d2f6-4e7d-85f0-11badcf0aa0f"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#2eada367-8168-4c71-97b4-7005dcd50a68">
<rdf:value>This is a CellML version of the 1980 van Capelle & Durrer activation model. This model was designed to be used in simulations of arrhythmias in a network of coupled excitable elements. They developed a membrane kinetics model with two variables of state: the transmembrane potential, V; and a generalised excitability parameter, Y.</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#98cce08d-1dc8-4c25-abb4-312318c22c64">
<bqs:Pubmed_id>7408126</bqs:Pubmed_id>
<bqs:JournalArticle rdf:resource="rdf:#e244335f-f410-420d-addf-9efa4c40a93c"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author1Vcard">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#author1VcardN"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9540691e-fab2-4270-83a3-cc72b08a524a">
<rdf:value>
The component which defines the kinetics of the transmembrane potential.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#Y_diff_eq">
<cmeta:comment rdf:resource="rdf:#e227aa60-d6cf-4a48-a3df-dd8111752f6c"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#41247165-5ec2-4450-a77d-09101325a7d4">
<rdf:value>
The function f, used to define the i0 component current, consists
of three sections: two linear components joined by a cubic
component. The function was fitted such that both the function
value and its derivative df/dVm were continuous.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#Iion_calculation_eq">
<cmeta:comment rdf:resource="rdf:#bb067d65-bb3e-44e6-a43b-de58b46c696c"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#6f4e7cac-d2f6-4e7d-85f0-11badcf0aa0f">
<rdf:value>
The current-voltage relation for when the membrane is
completely inexcitable. van Capelle & Durrer used a
simple three segment piecewise linear function to
represent this component of the total current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author2VcardN">
<vCard:Given>D</vCard:Given>
<vCard:Family>Durrer</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#80405cd0-1a66-4a7e-ae8d-a0e4d902a45f">
<rdf:value>
We'll use this component as the "interface" to the model, all
other components are hidden via encapsulation in this component.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d965df68-d01c-4903-981b-a0dddd2e1d80">
<vCard:ORG rdf:resource="rdf:#f7501d54-c7a2-4cb9-b7ee-692df9382260"/>
<vCard:EMAIL rdf:resource="rdf:#8b23a0cb-706e-4cc1-a41c-2f338adf67b4"/>
<vCard:N rdf:resource="rdf:#29274929-d9c1-4ef8-b725-8ee6f1488279"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author2Vcard">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#author2VcardN"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#bb067d65-bb3e-44e6-a43b-de58b46c696c">
<rdf:value>
The calcuation of the total ionic current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#Vm_diff_calculation_eq">
<cmeta:comment rdf:resource="rdf:#ee8cbbbd-3243-4e97-8cf3-6d8a1f8bc182"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e227aa60-d6cf-4a48-a3df-dd8111752f6c">
<rdf:value>
The kinetics of the excitability variable. The time constant, T,
can be used to scale the duration of the action potential.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ca4294bb-5593-4ebf-8932-06717d4ee531">
<dc:title>Circulation Research</dc:title>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e244335f-f410-420d-addf-9efa4c40a93c">
<dc:creator rdf:resource="rdf:#citationAuthorsSeq"/>
<dc:title>Computer Simulation of Arrhythmias in a Network of Coupled Excitable Elements</dc:title>
<bqs:volume>47</bqs:volume>
<bqs:first_page>454</bqs:first_page>
<bqs:Journal rdf:resource="rdf:#ca4294bb-5593-4ebf-8932-06717d4ee531"/>
<dcterms:issued rdf:resource="rdf:#318ab0c3-d19b-41d6-8281-a18dcee33ed5"/>
<bqs:last_page>466</bqs:last_page>
</rdf:Description>
<rdf:Description rdf:about="rdf:#097c5731-d5c1-433b-ad72-5526c609edc1">
<rdf:value>
This is a dummy equation that we simply use to make grabbing the
value in CMISS much easier.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#16ed4377-7ff3-4fb4-b6ab-c81721f166d7">
<rdf:value>
Here we define the kinetics of the non-dimensional excitability
variable.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#Yinf_calculation_eq">
<cmeta:comment rdf:resource="rdf:#c675425d-a4e9-4461-a589-3a72db850c5b"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ac5856fb-d9c7-44ba-8bad-fe7c9d3e8b2b">
<rdf:value>
The current-voltage relation for when the membrane
is maximally excitable. This is defined as the addition
of a piecewise function, f, to the i1 component current.
van Capelle & Durrer defined i0 as this to improve
the efficiency of their algorithm.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#i0_calculation_eq">
<cmeta:comment rdf:resource="rdf:#ac5856fb-d9c7-44ba-8bad-fe7c9d3e8b2b"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#29274929-d9c1-4ef8-b725-8ee6f1488279">
<vCard:Given>David</vCard:Given>
<vCard:Family>Nickerson</vCard:Family>
<vCard:Other>N</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author1VcardN">
<vCard:Given>F</vCard:Given>
<vCard:Family>van Capelle</vCard:Family>
<vCard:Other>J. L</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="#IStim_for_cmiss_eq">
<cmeta:comment rdf:resource="rdf:#097c5731-d5c1-433b-ad72-5526c609edc1"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#318ab0c3-d19b-41d6-8281-a18dcee33ed5">
<dcterms:W3CDTF>1980-01-01</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="#f_calculation_eq">
<cmeta:comment rdf:resource="rdf:#41247165-5ec2-4450-a77d-09101325a7d4"/>
</rdf:Description>
<rdf:Description rdf:about="#1980_vanCapelle_Durrer">
<bqs:reference rdf:resource="rdf:#98cce08d-1dc8-4c25-abb4-312318c22c64"/>
<cmeta:comment rdf:resource="rdf:#2eada367-8168-4c71-97b4-7005dcd50a68"/>
</rdf:Description>
<rdf:Description rdf:about="#ionic_current">
<cmeta:comment rdf:resource="rdf:#7f6340ae-0356-4f5c-aeb4-ec9cb79f0617"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0a9fa179-3077-493d-b41c-89c00729a369">
<dcterms:W3CDTF>2003-06-10</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c675425d-a4e9-4461-a589-3a72db850c5b">
<rdf:value>
The voltage dependent steady-state value for the excitability
variable. Must be an S-shaped function, increasing from zero
when Vm is more negative than the resting potential to 1 at more
positive values of Vm.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#membrane_potential">
<cmeta:comment rdf:resource="rdf:#9540691e-fab2-4270-83a3-cc72b08a524a"/>
</rdf:Description>
<rdf:Description rdf:about="">
<dcterms:created rdf:resource="rdf:#0a9fa179-3077-493d-b41c-89c00729a369"/>
<dc:creator rdf:resource="rdf:#d965df68-d01c-4903-981b-a0dddd2e1d80"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f7501d54-c7a2-4cb9-b7ee-692df9382260">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="#interface">
<cmeta:comment rdf:resource="rdf:#80405cd0-1a66-4a7e-ae8d-a0e4d902a45f"/>
</rdf:Description>
<rdf:Description rdf:about="#excitability_variable">
<cmeta:comment rdf:resource="rdf:#16ed4377-7ff3-4fb4-b6ab-c81721f166d7"/>
</rdf:Description>
</rdf:RDF>
</model>
