- Author:
- David Nickerson <nickerso@users.sourceforge.net>
- Date:
- 2009-07-16 03:08:50+12:00
- Desc:
- typos
- Permanent Source URI:
- https://models.fieldml.org/workspace/a1/rawfile/2d55d1ae86cfd6144a02402b9a6131de00b20601/models/1994_rogers/model.xml
<?xml version="1.0" encoding="iso-8859-1"?>
<model
name="Rogers_McCulloch_1994"
xmlns="http://www.cellml.org/cellml/1.0#"
xmlns:cellml="http://www.cellml.org/cellml/1.0#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#"
cmeta:id="1994_rogers_mcculloch">
<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/1.0#"
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#">
<!-- metadata about the CellML document itself -->
<rdf:Description rdf:about="">
<dc:creator rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Nickerson</vCard:Family>
<vCard:Given>David</vCard:Given>
</vCard:N>
<vCard:EMAIL rdf:parseType="Resource">
<rdf:value>d.nickerson@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>
<dcterms:created rdf:parseType="Resource">
<dcterms:W3CDTF>2003-06-10</dcterms:W3CDTF>
</dcterms:created>
</rdf:Description>
<rdf:Description rdf:about="#1994_rogers_mcculloch">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
This is a CellML version of the modified FitzHugh-Nagumo model,
published by Rogers and McCulloch in 1994. While the
original two-variable model described a non-dimensional activation
variable (u) and a non-dimensional recovery variable (v),
here we formulate the model in terms of the `real' action potential
given by the time course of the transmembrane potential (Vm). In so
doing, the time rate of change of the activation variable describes
the total `ionic current' through the membrane with the original
model parameters adjusted to give the correct dimensionality.
</rdf:value>
</cmeta:comment>
<bqs:reference>
<bqs:Pubmed_id>7927397</bqs:Pubmed_id>
<bqs:JournalArticle rdf:parseType="Resource">
<dc:creator rdf:parseType="Resource">
<rdf:Seq>
<rdf:li rdf:parseType="Resource">
<bqs:Person rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Rogers</vCard:Family>
<vCard:Given>J</vCard:Given>
<vCard:Other>M</vCard:Other>
</vCard:N>
</bqs:Person>
</rdf:li>
<rdf:li rdf:parseType="Resource">
<bqs:Person rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>McCulloch</vCard:Family>
<vCard:Given>A</vCard:Given>
<vCard:Other>D</vCard:Other>
</vCard:N>
</bqs:Person>
</rdf:li>
</rdf:Seq>
</dc:creator>
<dc:title>
A collocation--Galerkin finite element model of cardiac
action potential propagation
</dc:title>
<dcterms:issued rdf:parseType="Resource">
<dcterms:W3CDTF>1994</dcterms:W3CDTF>
</dcterms:issued>
<bqs:Journal rdf:parseType="Resource">
<dc:title>IEEE Transactions on Biomedical Engineering
</dc:title>
</bqs:Journal>
<bqs:volume>41</bqs:volume>
<bqs:first_page>743</bqs:first_page>
<bqs:last_page>757</bqs:last_page>
</bqs:JournalArticle>
</bqs:reference>
</rdf:Description>
</rdf:RDF>
<!--
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>
<component name="interface" cmeta:id="interface">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#interface">
<cmeta:comment rdf:parseType="Resource">
<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>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- Variables we expect to be set/controlled externally -->
<variable name="t" units="ms" public_interface="in" private_interface="out"/>
<variable name="Cm" units="uFpmmsq" private_interface="out" initial_value="0.01"/>
<variable name="Vr" units="mV" private_interface="out" initial_value="-85.0"/>
<variable name="Vth" units="mV" private_interface="out" initial_value="-75.0"/>
<variable name="Vp" units="mV" private_interface="out" initial_value="15.0"/>
<variable name="c1" units="uApmmsq" private_interface="out" initial_value="0.26"/>
<variable name="c2" units="uApmmsq" private_interface="out" initial_value="0.1"/>
<variable name="b" units="pms" private_interface="out" initial_value="0.013"/>
<variable name="d" units="dimensionless" private_interface="out" initial_value="0.8"/>
<variable name="Istim" units="uApmmsq" public_interface="in" private_interface="out"/>
<!-- Variables we want to make available externally -->
<variable name="Vm" cmeta:id="Vm" units="mV" public_interface="out" private_interface="in"/>
<variable name="v" units="dimensionless" public_interface="out" private_interface="in"/>
<variable name="Iion" units="uApmmsq" public_interface="out" private_interface="in"/>
</component> <!--interface-->
<component name="membrane_potential" cmeta:id="membrane_potential">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#membrane_potential">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The component which defines the kinetics of the transmembrane potential.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- Inputs -->
<variable name="t" units="ms" public_interface="in"/>
<variable name="Cm" units="uFpmmsq" public_interface="in"/>
<variable name="Vr" units="mV" public_interface="in"/>
<variable name="Vth" units="mV" public_interface="in"/>
<variable name="Vp" units="mV" public_interface="in"/>
<variable name="Istim" units="uApmmsq" public_interface="in"/>
<variable name="Iion" units="uApmmsq" public_interface="in"/>
<!-- Outputs computed here -->
<variable name="Vm" units="mV" public_interface="out" private_interface="out" initial_value="-85"/>
<variable name="u" units="dimensionless" public_interface="out"/>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#Vm_diff_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
This equation describes the kinetics of the transmembrane,
potential - the action potential.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<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>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#u_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The non-dimensional and scaled potential value.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="u_calculation_eq">
<apply id="u_calculation"><eq/>
<ci>u</ci>
<apply><divide/>
<apply><minus/>
<ci>Vm</ci>
<ci>Vr</ci>
</apply>
<apply><minus/>
<ci>Vp</ci>
<ci>Vr</ci>
</apply>
</apply>
</apply>
</math>
</component><!--membrane_potential-->
<component name="ionic_current" cmeta:id="ionic_current">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#ionic_current">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Here we define the total ionic current through the cellular
membrane - equivalent to the temporal derivative of the original
activation variable. The modification of Rogers and McCulloch is
in this equation, with the additional multiplication of recovery
variable with the normalised potential.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- Inputs -->
<variable name="Vr" units="mV" public_interface="in"/>
<variable name="Vth" units="mV" public_interface="in"/>
<variable name="Vp" units="mV" public_interface="in"/>
<variable name="c1" units="uApmmsq" public_interface="in"/>
<variable name="c2" units="uApmmsq" public_interface="in"/>
<variable name="v" units="dimensionless" public_interface="in"/>
<variable name="u" units="dimensionless" public_interface="in"/>
<!-- Outputs computed here -->
<variable name="Iion" units="uApmmsq" public_interface="out" private_interface="out"/>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#Iion_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The calcuation of the total ionic current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<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>c1</ci>
<ci>u</ci>
<apply><minus/>
<ci>u</ci>
<apply><divide/>
<apply><minus/>
<ci>Vth</ci>
<ci>Vr</ci>
</apply>
<apply><minus/>
<ci>Vp</ci>
<ci>Vr</ci>
</apply>
</apply>
</apply>
<apply><minus/>
<ci>u</ci>
<cn cellml:units="dimensionless">1.0</cn>
</apply>
</apply>
<apply><times/>
<ci>c2</ci>
<ci>u</ci>
<ci>v</ci>
</apply>
</apply>
</apply>
</math>
</component><!--ionic_current-->
<component name="recovery_variable" cmeta:id="recovery_variable">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#recovery_variable">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Here we define the non-dimensional recovery variable, v.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- Inputs -->
<variable name="t" units="ms" public_interface="in"/>
<variable name="b" units="pms" public_interface="in"/>
<variable name="d" units="dimensionless" public_interface="in"/>
<variable name="u" units="dimensionless" public_interface="in"/>
<!-- Outputs computed here -->
<variable name="v" units="dimensionless" public_interface="out" private_interface="out" initial_value="0.0"/>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#v_diff_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The kinetics of the recovery variable.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="v_diff_eq">
<apply id="v_diff"><eq/>
<apply><diff/>
<bvar><ci>t</ci></bvar>
<ci>v</ci>
</apply>
<apply><times/>
<ci>b</ci>
<apply><minus/>
<ci>u</ci>
<apply><times/>
<ci>d</ci>
<ci>v</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component><!--ionic_current-->
<connection>
<map_components component_1="interface" component_2="membrane_potential"/>
<map_variables variable_1="t" variable_2="t"/>
<map_variables variable_1="Cm" variable_2="Cm"/>
<map_variables variable_1="Vr" variable_2="Vr"/>
<map_variables variable_1="Vth" variable_2="Vth"/>
<map_variables variable_1="Vp" variable_2="Vp"/>
<map_variables variable_1="Vm" variable_2="Vm"/>
<map_variables variable_1="Istim" variable_2="Istim"/>
</connection>
<connection>
<map_components component_1="interface" component_2="ionic_current"/>
<map_variables variable_1="Vr" variable_2="Vr"/>
<map_variables variable_1="Vth" variable_2="Vth"/>
<map_variables variable_1="Vp" variable_2="Vp"/>
<map_variables variable_1="c1" variable_2="c1"/>
<map_variables variable_1="c2" variable_2="c2"/>
<map_variables variable_1="Iion" variable_2="Iion"/>
</connection>
<connection>
<map_components component_1="interface" component_2="recovery_variable"/>
<map_variables variable_1="t" variable_2="t"/>
<map_variables variable_1="b" variable_2="b"/>
<map_variables variable_1="d" variable_2="d"/>
<map_variables variable_1="v" variable_2="v"/>
</connection>
<connection>
<map_components component_1="membrane_potential" component_2="ionic_current"/>
<map_variables variable_1="u" variable_2="u"/>
<map_variables variable_1="Iion" variable_2="Iion"/>
</connection>
<connection>
<map_components component_1="membrane_potential" component_2="recovery_variable"/>
<map_variables variable_1="u" variable_2="u"/>
</connection>
<connection>
<map_components component_1="ionic_current" component_2="recovery_variable"/>
<map_variables variable_1="v" variable_2="v"/>
</connection>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="interface">
<component_ref component="membrane_potential"/>
<component_ref component="ionic_current"/>
<component_ref component="recovery_variable"/>
</component_ref>
</group>
</model>
