- Author:
- David Nickerson <david.nickerson@gmail.com>
- Date:
- 2021-09-16 01:20:40+12:00
- Desc:
- Upadte jupyter notebook with MNT and DFN comparison figure
- Permanent Source URI:
- https://models.fieldml.org/workspace/a1/rawfile/ae7a0b93f4ee5fda3d81ba97eb459f958b2819c9/models/1975_hunter/1975_cubic_polynomial.xml
<?xml version="1.0" encoding="iso-8859-1"?>
<model
name="cubic_polynomial_1975"
cmeta:id="cubic_polynomial_1975"
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/1.0#"
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>2005-01-06</dcterms:W3CDTF>
</dcterms:created>
</rdf:Description>
<rdf:Description rdf:about="#cubic_polynomial_1975">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
This is a CellML version of the cubic polynomial model of activation
from the 1975 paper by Hunter et. al.
</rdf:value>
</cmeta:comment>
<bqs:reference>
<bqs:Pubmed_id>792954</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>Hunter</vCard:Family>
<vCard:Given>P</vCard:Given>
<vCard:Other>J</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>McNaughton</vCard:Family>
<vCard:Given>P</vCard:Given>
<vCard:Other>A</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>Noble</vCard:Family>
<vCard:Given>D</vCard:Given>
</vCard:N>
</bqs:Person>
</rdf:li>
</rdf:Seq>
</dc:creator>
<dc:title>
Analytical models of propagation in excitable cells
</dc:title>
<dcterms:issued rdf:parseType="Resource">
<dcterms:W3CDTF>1975</dcterms:W3CDTF>
</dcterms:issued>
<bqs:Journal rdf:parseType="Resource">
<dc:title>Progress in Biophysics and Molecular Biology</dc:title>
</bqs:Journal>
<bqs:volume>30</bqs:volume>
<bqs:first_page>99</bqs:first_page>
<bqs:last_page>144</bqs:last_page>
</bqs:JournalArticle>
</bqs:reference>
</rdf:Description>
</rdf:RDF>
<import xlink:href="../common/units.xml">
<units name="mV" units_ref="mV"/>
<units name="uApmmsq" units_ref="uA_per_mmsq"/>
<units name="uFpmmsq" units_ref="uF_per_mmsq"/>
<units name="mSpmmsq" units_ref="mS_per_mmsq"/>
<units name="ms" units_ref="ms"/>
</import>
<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" public_interface="in" private_interface="out"/>
<variable name="Vm_rest" units="mV" public_interface="in" private_interface="out"/>
<variable name="Vm_plateau" units="mV" public_interface="in" private_interface="out"/>
<variable name="Vm_threshold" units="mV" public_interface="in" private_interface="out"/>
<variable name="Vm_initial" units="mV" public_interface="in" private_interface="out"/>
<variable name="membrane_conductance" units="mSpmmsq" public_interface="in" private_interface="out"/>
<variable name="Istim" units="uApmmsq" public_interface="in" private_interface="out"/>
<!-- Variables we want to make available externally -->
<variable name="Vm" units="mV" public_interface="out" private_interface="in"/>
<variable name="I" units="uApmmsq" public_interface="out" private_interface="in"/>
</component> <!--interface-->
<component name="membrane" cmeta:id="membrane">
<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">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Evaluation of the membrane potential ODE.
</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="Istim" units="uApmmsq" public_interface="in"/>
<variable name="I" units="uApmmsq" public_interface="in"/>
<variable name="Vm_initial" units="mV" public_interface="in"/>
<!-- Outputs computed here -->
<variable name="Vm" cmeta:id="Vm" units="mV" public_interface="out" initial_value="Vm_initial"/>
<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 is the main equation for the model, describing the dependency
of the time course of transmembrane potential on the single ionic
current plus any applied stimulus current.
</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>I</ci>
</apply>
<ci>Cm</ci>
</apply>
</apply>
</math>
</component><!--membrane-->
<component name="current" cmeta:id="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="#current">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The single current calculation.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<variable name="I" cmeta:id="I" units="uApmmsq" public_interface="out"/>
<variable name="Cm" units="uFpmmsq" public_interface="in"/>
<variable name="Vm_rest" units="mV" public_interface="in"/>
<variable name="Vm_plateau" units="mV" public_interface="in"/>
<variable name="Vm_threshold" units="mV" public_interface="in"/>
<variable name="membrane_conductance" units="mSpmmsq" public_interface="in"/>
<variable name="Vm" units="mV" public_interface="in"/>
<variable name="plateau" units="mV"/>
<variable name="threshold" units="mV"/>
<variable name="phi" units="mV"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="plateau_calculation_eq">
<apply id="plateau_calculation"><eq/>
<ci>plateau</ci>
<apply><minus/>
<ci>Vm_plateau</ci>
<ci>Vm_rest</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="threshold_calculation_eq">
<apply id="threshold_calculation"><eq/>
<ci>threshold</ci>
<apply><minus/>
<ci>Vm_threshold</ci>
<ci>Vm_rest</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="phi_calculation_eq">
<apply id="phi_calculation"><eq/>
<ci>phi</ci>
<apply><minus/>
<ci>Vm</ci>
<ci>Vm_rest</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="#current_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
This is the calculation of the single current in this model, and where
the model name comes from.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="current_calculation_eq">
<apply id="current_calculation"><eq/>
<ci>I</ci>
<apply><times/>
<ci>membrane_conductance</ci>
<ci>phi</ci>
<apply><minus/>
<cn cellml:units="dimensionless">1.0</cn>
<apply><divide/>
<ci>phi</ci>
<ci>threshold</ci>
</apply>
</apply>
<apply><minus/>
<cn cellml:units="dimensionless">1.0</cn>
<apply><divide/>
<ci>phi</ci>
<ci>plateau</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component><!--current-->
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="interface">
<component_ref component="membrane"/>
<component_ref component="current"/>
</component_ref>
</group>
<connection>
<map_components component_1="interface" component_2="membrane"/>
<map_variables variable_1="t" variable_2="t"/>
<map_variables variable_1="Cm" variable_2="Cm"/>
<map_variables variable_1="Istim" variable_2="Istim"/>
<map_variables variable_1="Vm" variable_2="Vm"/>
<map_variables variable_1="Vm_initial" variable_2="Vm_initial"/>
</connection>
<connection>
<map_components component_1="interface" component_2="current"/>
<map_variables variable_1="Cm" variable_2="Cm"/>
<map_variables variable_1="Vm_rest" variable_2="Vm_rest"/>
<map_variables variable_1="Vm_plateau" variable_2="Vm_plateau"/>
<map_variables variable_1="Vm_threshold" variable_2="Vm_threshold"/>
<map_variables variable_1="membrane_conductance" variable_2="membrane_conductance"/>
<map_variables variable_1="I" variable_2="I"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="current"/>
<map_variables variable_1="I" variable_2="I"/>
<map_variables variable_1="Vm" variable_2="Vm"/>
</connection>
</model>
