- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-08-21 04:50:54+12:00
- Desc:
- committing version02 of fitzhugh_1961
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/fitzhugh_1961/rawfile/f0458eb8f1c87dd3eb819509df08cbe91073715a/fitzhugh_1961.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="1961_fitzhugh_nagumo" name="fitzhugh_1961_version02">
<!--
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">
<!-- 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="mV" private_interface="out" name="Vr" initial_value="-85.0"/>
<variable units="mV" private_interface="out" name="Vth" initial_value="-75.0"/>
<variable units="mV" private_interface="out" name="Vp" initial_value="15.0"/>
<variable units="uApmmsq" private_interface="out" name="c1" initial_value="0.175"/>
<variable units="uApmmsq" private_interface="out" name="c2" initial_value="0.03"/>
<variable units="pms" private_interface="out" name="b" initial_value="0.011"/>
<variable units="dimensionless" private_interface="out" name="d" initial_value="0.55"/>
<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="v"/>
<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 name="membrane_potential" cmeta:id="membrane_potential">
<!-- Inputs -->
<variable units="ms" public_interface="in" name="t"/>
<variable units="uFpmmsq" public_interface="in" name="Cm"/>
<variable units="mV" public_interface="in" name="Vr"/>
<variable units="mV" public_interface="in" name="Vth"/>
<variable units="mV" public_interface="in" name="Vp"/>
<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="-85"/>
<variable units="dimensionless" public_interface="out" name="u"/>
<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>
<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">
<!-- Inputs -->
<variable units="mV" public_interface="in" name="Vr"/>
<variable units="mV" public_interface="in" name="Vth"/>
<variable units="mV" public_interface="in" name="Vp"/>
<variable units="uApmmsq" public_interface="in" name="c1"/>
<variable units="uApmmsq" public_interface="in" name="c2"/>
<variable units="dimensionless" public_interface="in" name="v"/>
<variable units="dimensionless" public_interface="in" name="u"/>
<!-- Outputs computed here -->
<variable units="uApmmsq" public_interface="out" private_interface="out" name="Iion" initial_value="0.0"/>
<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>v</ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--ionic_current-->
<component name="recovery_variable" cmeta:id="recovery_variable">
<!-- Inputs -->
<variable units="ms" public_interface="in" name="t"/>
<variable units="pms" public_interface="in" name="b"/>
<variable units="dimensionless" public_interface="in" name="d"/>
<variable units="dimensionless" public_interface="in" name="u"/>
<!-- Outputs computed here -->
<variable units="dimensionless" public_interface="out" private_interface="out" name="v" initial_value="0.0"/>
<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_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="Vr" variable_1="Vr"/>
<map_variables variable_2="Vth" variable_1="Vth"/>
<map_variables variable_2="Vp" variable_1="Vp"/>
<map_variables variable_2="Vm" variable_1="Vm"/>
<map_variables variable_2="Istim" variable_1="Istim"/>
</connection>
<connection>
<map_components component_2="ionic_current" component_1="interface"/>
<map_variables variable_2="Vr" variable_1="Vr"/>
<map_variables variable_2="Vth" variable_1="Vth"/>
<map_variables variable_2="Vp" variable_1="Vp"/>
<map_variables variable_2="c1" variable_1="c1"/>
<map_variables variable_2="c2" variable_1="c2"/>
<map_variables variable_2="Iion" variable_1="Iion"/>
</connection>
<connection>
<map_components component_2="recovery_variable" component_1="interface"/>
<map_variables variable_2="t" variable_1="t"/>
<map_variables variable_2="b" variable_1="b"/>
<map_variables variable_2="d" variable_1="d"/>
<map_variables variable_2="v" variable_1="v"/>
</connection>
<connection>
<map_components component_2="ionic_current" component_1="membrane_potential"/>
<map_variables variable_2="u" variable_1="u"/>
<map_variables variable_2="Iion" variable_1="Iion"/>
</connection>
<connection>
<map_components component_2="recovery_variable" component_1="membrane_potential"/>
<map_variables variable_2="u" variable_1="u"/>
</connection>
<connection>
<map_components component_2="recovery_variable" component_1="ionic_current"/>
<map_variables variable_2="v" variable_1="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>
<rdf:RDF>
<rdf:Seq rdf:about="rdf:#a59052fd-0ad6-4bff-90af-9f26f96bc2fe">
<rdf:li rdf:resource="rdf:#8fc48516-d9f9-422b-bd6e-e9bd4cfced19"/>
<rdf:li rdf:resource="rdf:#affe7d0c-b033-4114-8ca2-ecbe044ed8f8"/>
<rdf:li rdf:resource="rdf:#89ca6775-e1b4-45e4-8af5-ab7328a83e02"/>
</rdf:Seq>
<rdf:Seq rdf:about="rdf:#4cd7c7f1-e82e-4517-a878-a505bd9b570c">
<rdf:li rdf:resource="rdf:#5fca49d2-2cc5-41dd-bddc-4058e2ac75b7"/>
</rdf:Seq>
<rdf:Description rdf:about="rdf:#2e2b6e6e-a95b-44ed-a44c-2abb8eebfa56">
<vCard:ORG rdf:resource="rdf:#ba886891-f21a-4cb1-a20e-760ca4046e07"/>
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<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#b420c161-9784-4837-9bfd-042274578e82"/>
</rdf:Description>
<rdf:Description rdf:about="">
<dcterms:created rdf:resource="rdf:#cd8bc58b-c500-4c94-ad56-cb3a1bc20db8"/>
<dc:creator rdf:resource="rdf:#2e2b6e6e-a95b-44ed-a44c-2abb8eebfa56"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4d233d6b-863d-428b-902d-36729b8b5005">
<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:#277553e2-ca0e-4ba2-b474-f0e6d526687f">
<rdf:value>
The non-dimensional and scaled potential value.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#200ccc93-222d-4e2f-b7ce-8728a64ed654">
<vCard:Given>David</vCard:Given>
<vCard:Family>Nickerson</vCard:Family>
<vCard:Other>P</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#cab0c9de-34c4-4eb7-a9fe-604778efda4a">
<rdf:value>
The kinetics of the recovery variable.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d2db9d87-e1e8-4e53-9c5a-e06cc97c99ef">
<dc:creator rdf:resource="rdf:#4cd7c7f1-e82e-4517-a878-a505bd9b570c"/>
<dc:title>Impulses and physiological states in theoretical models of nerve membrane</dc:title>
<bqs:volume>1</bqs:volume>
<bqs:first_page>445</bqs:first_page>
<bqs:Journal rdf:resource="rdf:#325ae8c6-20dd-4d4c-9cad-69edf2a534a4"/>
<dcterms:issued rdf:resource="rdf:#efbb3842-29ab-41f1-a5c6-f938565af5f2"/>
<bqs:last_page>466</bqs:last_page>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4f4dbae8-86fa-4b2e-9e5f-10db9ea33126">
<vCard:Given>J</vCard:Given>
<vCard:Family>Nagumo</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e0daee78-85d5-48f6-888c-145429b02ddb">
<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:#6719a18a-de29-4d6d-90e5-934a1703d2b5">
<vCard:Given>S</vCard:Given>
<vCard:Family>Yoshizawa</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="#u_calculation_eq">
<cmeta:comment rdf:resource="rdf:#277553e2-ca0e-4ba2-b474-f0e6d526687f"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8f0def9c-f18b-4b1a-940c-67c0555957bd">
<rdf:value>
Here we define the non-dimensional recovery variable, v.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#interface">
<cmeta:comment rdf:resource="rdf:#4d233d6b-863d-428b-902d-36729b8b5005"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#475255e4-0872-4e46-9812-08e229ea86da">
<bqs:JournalArticle rdf:resource="rdf:#d2db9d87-e1e8-4e53-9c5a-e06cc97c99ef"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#423968e6-a2ee-44a6-8498-1794b85327cf">
<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:#41080da5-3a69-44a9-b9bd-4ca62d4dbaa7">
<vCard:Given>R</vCard:Given>
<vCard:Family>Fitzhugh</vCard:Family>
<vCard:Other>A</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#5fca49d2-2cc5-41dd-bddc-4058e2ac75b7">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#41080da5-3a69-44a9-b9bd-4ca62d4dbaa7"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#b0a2a00a-c653-450d-9412-38e223d59af4">
<vCard:ORG rdf:resource="rdf:#b2445ebe-7bf4-4e3a-8ac9-997c9996d714"/>
<vCard:EMAIL rdf:resource="rdf:#e0daee78-85d5-48f6-888c-145429b02ddb"/>
<vCard:N rdf:resource="rdf:#200ccc93-222d-4e2f-b7ce-8728a64ed654"/>
</rdf:Description>
<rdf:Description rdf:about="#1961_fitzhugh_nagumo">
<bqs:reference rdf:resource="rdf:#0f9c6e13-4d7b-4c96-b8d9-836c41c34125"/>
<bqs:reference rdf:resource="rdf:#475255e4-0872-4e46-9812-08e229ea86da"/>
<cmeta:comment rdf:resource="rdf:#67e529c1-70fa-49f6-a9a1-c0209fa4b559"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#b2445ebe-7bf4-4e3a-8ac9-997c9996d714">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="rdf:#89ca6775-e1b4-45e4-8af5-ab7328a83e02">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#6719a18a-de29-4d6d-90e5-934a1703d2b5"/>
</rdf:Description>
<rdf:Description rdf:about="#membrane_potential">
<cmeta:comment rdf:resource="rdf:#e58fc20a-afc0-4965-adc8-cf35a30c1174"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#7f224114-a620-4ea6-a62a-c8d6c7277bc5">
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#5d09461f-9a9a-447e-bb67-66e354a72156">
<dcterms:W3CDTF>2003-06-10</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d8390437-18da-4659-8de4-763653eca71b">
<bqs:Person rdf:resource="rdf:#73c28a82-675e-4ee1-916b-23b7864f89bd"/>
</rdf:Description>
<rdf:Description rdf:about="">
<dcterms:created rdf:resource="rdf:#5d09461f-9a9a-447e-bb67-66e354a72156"/>
<dc:creator rdf:resource="rdf:#b0a2a00a-c653-450d-9412-38e223d59af4"/>
</rdf:Description>
<rdf:Description rdf:about="#recovery_variable">
<cmeta:comment rdf:resource="rdf:#8f0def9c-f18b-4b1a-940c-67c0555957bd"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#631acdce-a12d-4eb0-8c40-44c31e67dda1">
<rdf:value>
Here we define the total ionic current through the cellular
membrane - equivalent to the temporal derivative of the original
activation variable.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#cd8bc58b-c500-4c94-ad56-cb3a1bc20db8">
<dcterms:W3CDTF>2007-05-02</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="#ionic_current">
<cmeta:comment rdf:resource="rdf:#631acdce-a12d-4eb0-8c40-44c31e67dda1"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#73c28a82-675e-4ee1-916b-23b7864f89bd">
<vCard:N rdf:resource="rdf:#7a1cfea7-6321-4796-b02b-3dc5ad5b8fd5"/>
</rdf:Description>
<rdf:Description rdf:about="#Vm_diff_calculation_eq">
<cmeta:comment rdf:resource="rdf:#66fa7263-4812-4c96-a36f-c628e1b6b01e"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8fc48516-d9f9-422b-bd6e-e9bd4cfced19">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#4f4dbae8-86fa-4b2e-9e5f-10db9ea33126"/>
</rdf:Description>
<rdf:Description rdf:about="#Iion_calculation_eq">
<cmeta:comment rdf:resource="rdf:#460a45fc-6d04-474e-81c6-5b2e4e56fd1d"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#efbb3842-29ab-41f1-a5c6-f938565af5f2">
<dcterms:W3CDTF>1961-01-01</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0292aa0c-f5a4-46b6-91ec-d67c67ad6a1d">
<dcterms:W3CDTF>1962</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#67e529c1-70fa-49f6-a9a1-c0209fa4b559">
<dc:creator rdf:resource="rdf:#c3d3bc42-ea67-44d3-a986-1a4ef118949d"/>
<rdf:value>This is a CellML version of the FitzHugh-Nagumo model, published separately by FitzHugh in 1961 and Nagumo et. al. in 1962. While the original two-variable model described a non-dimensional activation variable (x or u) and a non-dimensional recovery variable (y or 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>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e58fc20a-afc0-4965-adc8-cf35a30c1174">
<rdf:value>
The component which defines the kinetics of the transmembrane potential.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#b420c161-9784-4837-9bfd-042274578e82">
<vCard:Given>S</vCard:Given>
<vCard:Family>Animoto</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#460a45fc-6d04-474e-81c6-5b2e4e56fd1d">
<rdf:value>
The calcuation of the total ionic current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#325ae8c6-20dd-4d4c-9cad-69edf2a534a4">
<dc:title>Biophysical Journal</dc:title>
</rdf:Description>
<rdf:Description rdf:about="rdf:#66fa7263-4812-4c96-a36f-c628e1b6b01e">
<rdf:value>
This equation describes the kinetics of the transmembrane,
potential - the action potential.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#v_diff_eq">
<cmeta:comment rdf:resource="rdf:#cab0c9de-34c4-4eb7-a9fe-604778efda4a"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0f9c6e13-4d7b-4c96-b8d9-836c41c34125">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#JournalArticle"/>
<dc:creator rdf:resource="rdf:#a59052fd-0ad6-4bff-90af-9f26f96bc2fe"/>
<dc:title>
An active pulse transmission line simulating nerve axon
</dc:title>
<bqs:volume>50</bqs:volume>
<bqs:first_page>2061</bqs:first_page>
<bqs:Journal rdf:resource="rdf:#a011eb84-5f30-49cf-9f51-2f0befd8f74f"/>
<dcterms:issued rdf:resource="rdf:#0292aa0c-f5a4-46b6-91ec-d67c67ad6a1d"/>
<bqs:last_page>2070</bqs:last_page>
</rdf:Description>
<rdf:Description rdf:about="rdf:#7a1cfea7-6321-4796-b02b-3dc5ad5b8fd5">
<vCard:Given>R</vCard:Given>
<vCard:Family>Fitzhugh</vCard:Family>
<vCard:Other>A</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="#IStim_for_cmiss_eq">
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