Location: Nash, Panfilov, 2004 @ 466b6dac112d / nash_panfilov_2004.cellml

Author:
David Nickerson <nickerso@users.sourceforge.net>
Date:
2015-11-24 12:48:57+13:00
Desc:
adding a copy of the Nash Panfilov model from my PhD thesis
Permanent Source URI:
https://models.physiomeproject.org/workspace/nash_panfilov_2004/rawfile/466b6dac112daee9e9181f9d12612a9561c41725/nash_panfilov_2004.cellml

<?xml version='1.0'?>
<!--  FILE :  nash_model_2004.xml

CREATED : 22nd July 2004 

LAST MODIFIED : 22nd July 2004

AUTHOR :  Martyn Nash
          Bioengineering Institute
          The University of Auckland
          
MODEL STATUS :  This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/1/02 CellML Metadata 1.0 Specification.

DESCRIPTION :  This file contains a CellML description of the Nash and Panfilov 2004 electromechanical model of excitable tissue to study reentrant cardiac arrhythmias.

  
-->
<model cmeta:id="nash_panfilov_2004_version01" name="nash_panfilov_2004_version01" 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#">
    <!--    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 prefix="milli" units="volt"/>
    </units>
    <units name="uApmmsq">
        <unit prefix="micro" units="ampere"/>
        <unit exponent="-2" prefix="milli" units="metre"/>
    </units>
    <units name="uFpmmsq">
        <unit prefix="micro" units="farad"/>
        <unit exponent="-2" prefix="milli" units="metre"/>
    </units>
    <units name="ms">
        <unit prefix="milli" units="second"/>
    </units>
    <units name="pms">
        <unit exponent="-1" prefix="milli" units="second"/>
    </units>
    <units name="kPa">
        <unit prefix="kilo" units="pascal"/>
    </units>
    <component cmeta:id="interface" name="interface">
        <!-- Variables we expect to be set/controlled externally -->
        <variable name="t" private_interface="out" public_interface="out" units="ms"/>
        <variable initial_value="0.01" name="Cm" private_interface="out" units="uFpmmsq"/>
        <variable initial_value="-85.0" name="Vr" private_interface="out" units="mV"/>
        <variable initial_value="-75.0" name="Vth" private_interface="out" units="mV"/>
        <variable initial_value="15.0" name="Vp" private_interface="out" units="mV"/>
        <variable initial_value="8.0" name="k" private_interface="out" units="uApmmsq"/>
        <variable initial_value="0.000155" name="epsilon" private_interface="out" units="pms"/>
        <variable initial_value="0.0155" name="mu1" private_interface="out" units="pms"/>
        <variable initial_value="0.3" name="mu2" private_interface="out" units="dimensionless"/>
        <variable initial_value="1.0" name="e0" private_interface="out" units="dimensionless"/>
        <variable initial_value="47.9" name="kTa" private_interface="out" units="kPa"/>
        <variable name="Istim" private_interface="out" public_interface="in" units="uApmmsq"/>
        <!-- Variables we want to make available externally -->
        <variable name="Vm" private_interface="in" public_interface="out" units="mV"/>
        <variable name="Iion" private_interface="in" public_interface="out" units="uApmmsq"/>
        <variable name="r" private_interface="in" public_interface="out" units="dimensionless"/>
        <variable name="u" private_interface="in" public_interface="out" units="dimensionless"/>
        <variable name="Ta" private_interface="in" public_interface="out" units="kPa"/>
    </component>
    <!--interface-->
    <component cmeta:id="membrane_potential" name="membrane_potential">
        <!-- Inputs -->
        <variable name="t" public_interface="in" units="ms"/>
        <variable name="Cm" public_interface="in" units="uFpmmsq"/>
        <variable name="Vr" public_interface="in" units="mV"/>
        <variable name="Vth" public_interface="in" units="mV"/>
        <variable name="Vp" public_interface="in" units="mV"/>
        <variable name="Istim" public_interface="in" units="uApmmsq"/>
        <variable name="Iion" public_interface="in" units="uApmmsq"/>
        <!-- Outputs computed here -->
        <variable initial_value="-85" name="Vm" private_interface="out" public_interface="out" units="mV"/>
        <variable name="u" public_interface="out" units="dimensionless"/>
        <variable name="a" public_interface="out" units="dimensionless"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply id="Vm_deriv">
                <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>
            <apply id="u_calc">
                <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>
            <apply id="a_calc">
                <eq/>
                <ci>a</ci>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>Vth</ci>
                        <ci>Vr</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>Vp</ci>
                        <ci>Vr</ci>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <!--membrane_potential-->
    <component cmeta:id="ionic_current" name="ionic_current">
        <!-- Inputs -->
        <variable name="Vr" public_interface="in" units="mV"/>
        <variable name="Vth" public_interface="in" units="mV"/>
        <variable name="Vp" public_interface="in" units="mV"/>
        <variable name="k" public_interface="in" units="uApmmsq"/>
        <variable name="r" public_interface="in" units="dimensionless"/>
        <variable name="u" public_interface="in" units="dimensionless"/>
        <variable name="a" public_interface="in" units="dimensionless"/>
        <!-- Outputs computed here -->
        <variable name="Iion" private_interface="out" public_interface="out" units="uApmmsq"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply id="Iion_calc">
                <eq/>
                <ci>Iion</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <ci>k</ci>
                        <ci>u</ci>
                        <apply>
                            <minus/>
                            <ci>u</ci>
                            <ci>a</ci>
                        </apply>
                        <apply>
                            <minus/>
                            <ci>u</ci>
                            <cn cellml:units="dimensionless">1.0</cn>
                        </apply>
                    </apply>
                    <apply>
                        <times/>
                        <ci>r</ci>
                        <ci>u</ci>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <!--ionic_current-->
    <component cmeta:id="recovery_variable" name="recovery_variable">
        <!-- Inputs -->
        <variable name="t" public_interface="in" units="ms"/>
        <variable name="k" public_interface="in" units="uApmmsq"/>
        <variable name="epsilon" public_interface="in" units="pms"/>
        <variable name="mu1" public_interface="in" units="pms"/>
        <variable name="mu2" public_interface="in" units="dimensionless"/>
        <variable name="u" public_interface="in" units="dimensionless"/>
        <variable name="a" public_interface="in" units="dimensionless"/>
        <!-- Outputs computed here -->
        <variable initial_value="0.0" name="r" private_interface="out" public_interface="out" units="dimensionless"/>
        <!-- Local variables -->
        <variable name="eps" units="pms"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply id="r_deriv">
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>r</ci>
                </apply>
                <apply>
                    <times/>
                    <ci>eps</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>r</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>k</ci>
                            <ci>u</ci>
                            <apply>
                                <minus/>
                                <ci>u</ci>
                                <apply>
                                    <plus/>
                                    <ci>a</ci>
                                    <cn cellml:units="dimensionless">1.0</cn>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply id="eps_calc">
                <eq/>
                <ci>eps</ci>
                <apply>
                    <plus/>
                    <ci>epsilon</ci>
                    <apply>
                        <divide/>
                        <apply>
                            <times/>
                            <ci>mu1</ci>
                            <ci>r</ci>
                        </apply>
                        <apply>
                            <plus/>
                            <ci>mu2</ci>
                            <ci>u</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <!--recovery_variable-->
    <component cmeta:id="active_tension" name="active_tension">
        <!-- Inputs -->
        <variable name="t" public_interface="in" units="ms"/>
        <variable name="u" public_interface="in" units="dimensionless"/>
        <variable name="e0" public_interface="in" units="dimensionless"/>
        <variable name="kTa" public_interface="in" units="kPa"/>
        <!-- Outputs computed here -->
        <variable initial_value="0.0" name="Ta" private_interface="out" public_interface="out" units="kPa"/>
        <!-- Local variables -->
        <variable name="e_" units="dimensionless"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply id="Ta_deriv">
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>Ta</ci>
                </apply>
                <apply>
                    <times/>
                    <ci>e_</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <times/>
                            <ci>kTa</ci>
                            <ci>u</ci>
                        </apply>
                        <ci>Ta</ci>
                    </apply>
                </apply>
            </apply>
            <apply id="e_calc">
                <eq/>
                <ci>e_</ci>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <cn cellml:units="dimensionless">100.0</cn>
                            <ci>e0</ci>
                        </apply>
                        <apply>
                            <lt/>
                            <ci>u</ci>
                            <cn cellml:units="dimensionless">0.05</cn>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <times/>
                            <cn cellml:units="dimensionless">10.0</cn>
                            <ci>e0</ci>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
        </math>
    </component>
    <!--active_tension-->
    <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="Istim" variable_2="Istim"/>
        <map_variables variable_1="Vm" variable_2="Vm"/>
        <map_variables variable_1="u" variable_2="u"/>
    </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="k" variable_2="k"/>
        <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="k" variable_2="k"/>
        <map_variables variable_1="epsilon" variable_2="epsilon"/>
        <map_variables variable_1="mu1" variable_2="mu1"/>
        <map_variables variable_1="mu2" variable_2="mu2"/>
        <map_variables variable_1="r" variable_2="r"/>
    </connection>
    <connection>
        <map_components component_1="interface" component_2="active_tension"/>
        <map_variables variable_1="t" variable_2="t"/>
        <map_variables variable_1="e0" variable_2="e0"/>
        <map_variables variable_1="kTa" variable_2="kTa"/>
        <map_variables variable_1="Ta" variable_2="Ta"/>
    </connection>
    <connection>
        <map_components component_1="membrane_potential" component_2="ionic_current"/>
        <map_variables variable_1="u" variable_2="u"/>
        <map_variables variable_1="a" variable_2="a"/>
        <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"/>
        <map_variables variable_1="a" variable_2="a"/>
    </connection>
    <connection>
        <map_components component_1="recovery_variable" component_2="ionic_current"/>
        <map_variables variable_1="r" variable_2="r"/>
    </connection>
    <connection>
        <map_components component_1="membrane_potential" component_2="active_tension"/>
        <map_variables variable_1="u" variable_2="u"/>
    </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 component="active_tension"/>
        </component_ref>
    </group>
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
        <rdf:Seq xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#d2217bf5-29ca-434a-a174-7dd35011a958">
            <rdf:li xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:resource="rdf:#d8a1f290-9512-423b-abcb-d6507e542104"/>
            <rdf:li xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:resource="rdf:#219b0293-9d1f-411b-9e00-ddde2e973de6"/>
        </rdf:Seq>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#membrane_potential">
            <cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:resource="rdf:#9ca973a1-0cf4-4cbf-8fdd-75aa4cb51f55" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#d1a2af11-008e-4823-ae5d-0ba90f03560e">
            <rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
            Here we define the non-dimensional recovery variable, r. The kinetics
            of the recovery variable have been reworked by Aliev and Panfilov to
            provide more realistic restitution properties.
          </rdf:value>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#56301c52-ecc1-412f-9196-e0e0bf8ffca2">
            <rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
            The kinetics of the active tension.
          </rdf:value>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#u_calc_eqn">
            <cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:resource="rdf:#a8dff835-17e3-4be9-93fa-a73254c3e333" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#ionic_current">
            <cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:resource="rdf:#af85210b-52d5-4a52-9d1a-8744bd77501f" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#d166b344-78fc-4bcb-a54e-a5a3932a2ca4">
            <rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
            The non-dimensional and scaled threshold potential value.
          </rdf:value>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#33d38b0b-a53b-43d4-91f1-9e1accc960ed">
            <vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Martyn</vCard:Given>
            <vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Nash</vCard:Family>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#c5e65c50-1dcd-4131-a448-efc2aaca12f8">
            <rdf:type xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:resource="http://imc.org/vCard/3.0#internet"/>
            <rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">martyn.nash@auckland.ac.nz</rdf:value>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#0f855a1e-1a8b-4abf-beaa-18910135341d">
            <rdf:type xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:resource="http://imc.org/vCard/3.0#internet"/>
            <rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">d.nickerson@auckland.ac.nz</rdf:value>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#c87ee15f-edf8-4517-a35d-15165e30eb1b">
            <rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
            This is a dummy equation that we simply use to make grabbing the
            value in CMISS much easier.
          </rdf:value>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#3d0f7dcd-d98d-4560-945d-6cdf4e01540b">
            <vCard:ORG xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#8e5ffc80-42ca-4b9d-b32a-1260dfda9c2e" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
            <vCard:EMAIL xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#c5e65c50-1dcd-4131-a448-efc2aaca12f8" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
            <vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#33d38b0b-a53b-43d4-91f1-9e1accc960ed" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#2f0b14b0-a766-4111-bc46-81ee50020de2">
            <rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
            This equation describes the kinetics of the transmembrane,
            potential - the action potential.
          </rdf:value>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#03dff719-bff5-46b7-903e-84f2e10e6cd3">
            <dcterms:W3CDTF xmlns:dcterms="http://purl.org/dc/terms/">2004</dcterms:W3CDTF>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#active_tension">
            <cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:resource="rdf:#397fbdc3-2882-4426-aa8a-5efa7292e07c" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#c7f7f07a-4058-4275-b20d-7667183954f3">
            <dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Prog. Biophys. Molec. Biol.
            </dc:title>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#r_deriv_eqn">
            <cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:resource="rdf:#c18f63f2-f928-4b14-90ec-b031813daebf" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#Iion_calc_eqn">
            <cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:resource="rdf:#96e163b2-3dbb-41c0-a13b-66ec64aecf7a" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#interface">
            <cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:resource="rdf:#c888d02d-3927-46e8-bfe1-a408016dc44a" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#81aa6d82-f8a9-4485-bf1f-0a78381dd343">
            <vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">M</vCard:Given>
            <vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Nash</vCard:Family>
            <vCard:Other xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">P</vCard:Other>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#IStim_for_cmiss_eq">
            <cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:resource="rdf:#c87ee15f-edf8-4517-a35d-15165e30eb1b" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#nash_panfilov_2004_version01">
            <dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">
        Modified FitzHugh-Nagumo model
      </dc:title>
            <cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:resource="rdf:#3084bc4e-304b-4ecb-a847-57f18b8c0ef8" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
            <bqs:reference xmlns:bqs="http://www.cellml.org/bqs/1.0#" rdf:resource="rdf:#4f283f2b-2cf3-4683-b1ac-97b4099ee4c1" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
            <bqs:reference xmlns:bqs="http://www.cellml.org/bqs/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
                <dc:subject xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
                    <bqs:subject_type xmlns:bqs="http://www.cellml.org/bqs/1.0#">keyword</bqs:subject_type>
                    <rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
                        <rdf:Bag xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
                            <rdf:li xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">electromechanical</rdf:li>
                            <rdf:li xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">electrophysiology</rdf:li>
                            <rdf:li xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">myofilament mechanics</rdf:li>
                            <rdf:li xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">excitable tissue</rdf:li>
                        </rdf:Bag>
                    </rdf:value>
                </dc:subject>
            </bqs:reference>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="">
            <dcterms:created xmlns:dcterms="http://purl.org/dc/terms/" rdf:resource="rdf:#59d320a1-84d2-4c2a-b0b1-d97373ed351f" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
            <dc:creator xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:resource="rdf:#3d0f7dcd-d98d-4560-945d-6cdf4e01540b" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
            <dc:creator xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:resource="rdf:#645ee413-b7df-40fc-be2e-9c8e3dabd3a0" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#61db89ed-909f-432b-9df3-47d7b8a6041b">
            <vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">David</vCard:Given>
            <vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Nickerson</vCard:Family>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#fbef0f98-ca6d-4419-86ca-2f9fe72ea6f8">
            <dc:creator xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:resource="rdf:#d2217bf5-29ca-434a-a174-7dd35011a958" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
            <dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">
            Electromechanical model of excitable tissue to study reentrant
            cardiac arrhythmias
          </dc:title>
            <bqs:volume xmlns:bqs="http://www.cellml.org/bqs/1.0#">85</bqs:volume>
            <bqs:first_page xmlns:bqs="http://www.cellml.org/bqs/1.0#">501</bqs:first_page>
            <bqs:Journal xmlns:bqs="http://www.cellml.org/bqs/1.0#" rdf:resource="rdf:#c7f7f07a-4058-4275-b20d-7667183954f3" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
            <dcterms:issued xmlns:dcterms="http://purl.org/dc/terms/" rdf:resource="rdf:#03dff719-bff5-46b7-903e-84f2e10e6cd3" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
            <bqs:last_page xmlns:bqs="http://www.cellml.org/bqs/1.0#">522</bqs:last_page>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#Vm_deriv_eqn">
            <cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:resource="rdf:#2f0b14b0-a766-4111-bc46-81ee50020de2" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#5dc219c0-f39f-4bf0-821a-baa31b8586ee">
            <vCard:Orgname xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">The University of Auckland</vCard:Orgname>
            <vCard:Orgunit xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">The Bioengineering Institute</vCard:Orgunit>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#4f283f2b-2cf3-4683-b1ac-97b4099ee4c1">
            <bqs:JournalArticle xmlns:bqs="http://www.cellml.org/bqs/1.0#" rdf:resource="rdf:#fbef0f98-ca6d-4419-86ca-2f9fe72ea6f8" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#3084bc4e-304b-4ecb-a847-57f18b8c0ef8">
            <rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
          This is a CellML version of the modified FitzHugh-Nagumo model, 
          published by Aliev and Panfilov in 1996. 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.
          This model has been further modified by Nash and Panfilov 2004 to
          include the simplest model of active tension development.
        </rdf:value>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#9ca973a1-0cf4-4cbf-8fdd-75aa4cb51f55">
            <rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
            The component which defines the kinetics of the transmembrane potential.
          </rdf:value>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#8cbf0378-f099-4b93-a475-3dad969b3eee">
            <vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">A</vCard:Given>
            <vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Panfilov</vCard:Family>
            <vCard:Other xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">V</vCard:Other>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#397fbdc3-2882-4426-aa8a-5efa7292e07c">
            <rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
            This is the active tension relation from the Nash and Panfilov
            article.
          </rdf:value>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#a8dff835-17e3-4be9-93fa-a73254c3e333">
            <rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
            The non-dimensional and scaled potential value.
          </rdf:value>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#c888d02d-3927-46e8-bfe1-a408016dc44a">
            <rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
            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 xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#219b0293-9d1f-411b-9e00-ddde2e973de6">
            <rdf:type xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
            <vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#8cbf0378-f099-4b93-a475-3dad969b3eee" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#59d320a1-84d2-4c2a-b0b1-d97373ed351f">
            <dcterms:W3CDTF xmlns:dcterms="http://purl.org/dc/terms/">2004-07-22</dcterms:W3CDTF>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#recovery_variable">
            <cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:resource="rdf:#d1a2af11-008e-4823-ae5d-0ba90f03560e" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#c18f63f2-f928-4b14-90ec-b031813daebf">
            <rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
            The kinetics of the recovery variable.
          </rdf:value>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#Ta_deriv_eqn">
            <cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:resource="rdf:#56301c52-ecc1-412f-9196-e0e0bf8ffca2" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#d8a1f290-9512-423b-abcb-d6507e542104">
            <rdf:type xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
            <vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#81aa6d82-f8a9-4485-bf1f-0a78381dd343" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#8e5ffc80-42ca-4b9d-b32a-1260dfda9c2e">
            <vCard:Orgname xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">The University of Auckland</vCard:Orgname>
            <vCard:Orgunit xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">The Bioengineering Institute</vCard:Orgunit>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#645ee413-b7df-40fc-be2e-9c8e3dabd3a0">
            <vCard:ORG xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#5dc219c0-f39f-4bf0-821a-baa31b8586ee" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
            <vCard:EMAIL xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#0f855a1e-1a8b-4abf-beaa-18910135341d" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
            <vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#61db89ed-909f-432b-9df3-47d7b8a6041b" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#af85210b-52d5-4a52-9d1a-8744bd77501f">
            <rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
            Here we define the total ionic current through the cellular
            membrane - equivalent to the temporal derivative of the original
            activation variable. One modification of Aliev and Panfilov is
            in this equation, with the additional multiplication of the recovery 
            variable with the normalised potential and removal of the scalar
            multiplier.
          </rdf:value>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#a_calc_eqn">
            <cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:resource="rdf:#d166b344-78fc-4bcb-a54e-a5a3932a2ca4" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
        </rdf:Description>
        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#96e163b2-3dbb-41c0-a13b-66ec64aecf7a">
            <rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
            The calcuation of the total ionic current.
          </rdf:value>
        </rdf:Description>
    </rdf:RDF>
</model>