<?xml version='1.0' encoding='utf-8'?>
<!-- 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 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="nash_panfilov_2004_version01" name="nash_panfilov_2004_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>An Electromechanical Model of Excitable Tissue to Study Reentrant Cardiac Arrhythmias</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This is the original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Sudden cardiac death is the leading cause of premature death in the developed world. Underlying these potentially lethal cardiac arrhythmias are reentrant electrical sources, or rotating spiral waves of excitation, and it has been shown that each class of cardiac arrhythmia is associated with a particular type of spiral wave. Sudden cardiac death during ventricular fibrillation results in a compromised mechanical pump function of the heart. Disrupted patterns of electrical excitation during ventricular fibrillation results in desynchronised cardiac contractions.
</para>
<para>
Mathematical modelling is a useful technique for investigating the electrical activity of the heart. Over the past 40 years models have also been used to study the spatio-temporal dynamics of reentrant arrhythmias in 2D, 3D, and in anatomically accurate geometric models of the heart. The mathematical models are based on physiological data, and in parallel with the increasing sophistication of experimental techniques, the mathematical models has also evolved in their complexity and biological accuracy. Previously, mathematical models have tended to focus on either the electrical properties of the heart, or on cardiac mechanics. In the study described here, Nash and Panfilov establish a mathematical model which combines the effects of cardiac mechanics and electrical activity during arrhythmia.
</para>
<para>
The model described here in CellML is based on the Nash and Panfilov 2004 paper, which describes an electromechanical model of excitable tissue, which is used to study reentrant cardiac arrhythmias. This mathematical model is a version of the modified FitzHugh-Nagumo model, published by Aliev and Panfilov in 1996 (for details on the original model please see <ulink url="${HTML_EXMPL_FN_SIMPLE}">The FitzHugh-Nagumo Model, 1961</ulink>). While the original two-variable model described a non-dimensional activation variable (u) and a non-dimensional recovery variable (v), here Nash and Panfilov formulate the model in terms of the <emphasis>real</emphasis> 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 1996 version of the FitzHugh-Nagumo model has been further modified by Nash and Panfilov in this 2004 study to include the simplest model of active tension development.
</para>
<para>
The main equations in the paper are Eqn 22abc and Eqn 23. When the first author of this paper converted the model into CellML, he noticed two main errors in the original paper:
</para>
<itemizedlist>
<listitem>
<para>Eqn 22b: <emphasis>b</emphasis> should be <emphasis>a</emphasis>, and</para>
</listitem>
<listitem>
<para>Eqn 23: the factor 10 should be on first case line (V is less than 0.05). The second case should have the factor 1.</para>
</listitem>
</itemizedlist>
<para>A new set of model parameters is also used.</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TBN-4C2NHX5-1&_user=140507&_coverDate=07%2F31%2F2004&_alid=193357751&_rdoc=1&_fmt=summary&_orig=search&_qd=1&_cdi=5147&_sort=d&_docanchor=&view=c&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=6cecd2fed3472348a3964b5c44a20cd0">Electromechanical model of excitable tissue to study reentrant cardiac arrhythmias</ulink>, M. P. Nash and A. V. Panfilov, 2004, <ulink url="http://www.sciencedirect.com/science/journal/00796107">
<emphasis>Progress in Biophysics and Molecular Biology</emphasis>
</ulink>, 85, 501-522. (<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TBN-4C2NHX5-1&_coverDate=07%2F31%2F2004&_alid=193357751&_rdoc=1&_fmt=&_orig=search&_qd=1&_cdi=5147&_sort=d&view=c&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=2d12625c6eacd2fe840333aa37bd53a9">Full text (HTML)</ulink> and PDF versions of the article are available to subscribers on the <emphasis>Progress in Biophysics and Molecular Biology</emphasis> website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=15142759&dopt=Abstract">PubMed ID: 15142759</ulink>
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>reaction diagram</title>
</objectinfo>
<imagedata fileref="nash_2004.png"/>
</imageobject>
</mediaobject>
<caption>Properties of the action potential described by the model.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<!--
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="kPa">
<unit units="pascal" prefix="kilo"/>
</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="1.0"/>
<variable units="mV" private_interface="out" name="Vr" initial_value="-80.0"/>
<variable units="mV" private_interface="out" name="Vth" initial_value="-70.0"/>
<variable units="mV" private_interface="out" name="Vp" initial_value="20.0"/>
<variable units="uApmmsq" private_interface="out" name="k" initial_value="8.0"/>
<variable units="pms" private_interface="out" name="epsilon" initial_value="0.01"/>
<variable units="pms" private_interface="out" name="mu1" initial_value="0.2"/>
<variable units="dimensionless" private_interface="out" name="mu2" initial_value="0.3"/>
<variable units="dimensionless" private_interface="out" name="e0" initial_value="1.0"/>
<variable units="kPa" private_interface="out" name="kTa" initial_value="47.9"/>
<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="uApmmsq" public_interface="out" private_interface="in" name="Iion"/>
<variable units="dimensionless" public_interface="out" private_interface="in" name="r"/>
<variable units="kPa" public_interface="out" private_interface="in" name="Ta"/>
<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="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"/>
<variable units="dimensionless" public_interface="out" name="a"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Vm_deriv_eqn">
<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>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="u_calc_eqn">
<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>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="a_calc_eqn">
<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 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="k"/>
<variable units="dimensionless" public_interface="in" name="r"/>
<variable units="dimensionless" public_interface="in" name="u"/>
<variable units="dimensionless" public_interface="in" name="a"/>
<!-- Outputs computed here -->
<variable units="uApmmsq" public_interface="out" private_interface="out" name="Iion"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Iion_calc_eqn">
<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 units="ms" public_interface="in" name="t"/>
<variable units="uApmmsq" public_interface="in" name="k"/>
<variable units="pms" public_interface="in" name="epsilon"/>
<variable units="pms" public_interface="in" name="mu1"/>
<variable units="dimensionless" public_interface="in" name="mu2"/>
<variable units="dimensionless" public_interface="in" name="u"/>
<variable units="dimensionless" public_interface="in" name="a"/>
<!-- Outputs computed here -->
<variable units="dimensionless" public_interface="out" private_interface="out" name="r" initial_value="0.0"/>
<!-- Local variables -->
<variable units="pms" name="eps"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="r_deriv_eqn">
<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>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="eps_calc_eqn">
<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 units="ms" public_interface="in" name="t"/>
<variable units="dimensionless" public_interface="in" name="u"/>
<variable units="dimensionless" public_interface="in" name="e0"/>
<variable units="kPa" public_interface="in" name="kTa"/>
<!-- Outputs computed here -->
<variable units="kPa" public_interface="out" private_interface="out" name="Ta" initial_value="0.0"/>
<!-- Local variables -->
<variable units="dimensionless" name="e"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Ta_deriv_eqn">
<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>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="e_calc_eqn">
<apply id="e_calc">
<eq/>
<ci>e</ci>
<piecewise>
<piece>
<apply>
<times/>
<cn cellml:units="dimensionless">10.0</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">1.0</cn>
<ci>e0</ci>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<!--active_tension-->
<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="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="Vr" variable_1="Vr"/>
<map_variables variable_2="Vth" variable_1="Vth"/>
<map_variables variable_2="Vp" variable_1="Vp"/>
<map_variables variable_2="k" variable_1="k"/>
<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="k" variable_1="k"/>
<map_variables variable_2="epsilon" variable_1="epsilon"/>
<map_variables variable_2="mu1" variable_1="mu1"/>
<map_variables variable_2="mu2" variable_1="mu2"/>
<map_variables variable_2="r" variable_1="r"/>
</connection>
<connection>
<map_components component_2="active_tension" component_1="interface"/>
<map_variables variable_2="t" variable_1="t"/>
<map_variables variable_2="e0" variable_1="e0"/>
<map_variables variable_2="kTa" variable_1="kTa"/>
<map_variables variable_2="Ta" variable_1="Ta"/>
</connection>
<connection>
<map_components component_2="ionic_current" component_1="membrane_potential"/>
<map_variables variable_2="u" variable_1="u"/>
<map_variables variable_2="a" variable_1="a"/>
<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"/>
<map_variables variable_2="a" variable_1="a"/>
</connection>
<connection>
<map_components component_2="ionic_current" component_1="recovery_variable"/>
<map_variables variable_2="r" variable_1="r"/>
</connection>
<connection>
<map_components component_2="active_tension" component_1="membrane_potential"/>
<map_variables variable_2="u" variable_1="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>
<rdf:Seq rdf:about="rdf:#d2217bf5-29ca-434a-a174-7dd35011a958">
<rdf:li rdf:resource="rdf:#d8a1f290-9512-423b-abcb-d6507e542104"/>
<rdf:li rdf:resource="rdf:#219b0293-9d1f-411b-9e00-ddde2e973de6"/>
</rdf:Seq>
<rdf:Description rdf:about="#membrane_potential">
<cmeta:comment rdf:resource="rdf:#9ca973a1-0cf4-4cbf-8fdd-75aa4cb51f55"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d1a2af11-008e-4823-ae5d-0ba90f03560e">
<rdf:value>
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 rdf:about="rdf:#56301c52-ecc1-412f-9196-e0e0bf8ffca2">
<rdf:value>
The kinetics of the active tension.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#u_calc_eqn">
<cmeta:comment rdf:resource="rdf:#a8dff835-17e3-4be9-93fa-a73254c3e333"/>
</rdf:Description>
<rdf:Description rdf:about="#ionic_current">
<cmeta:comment rdf:resource="rdf:#af85210b-52d5-4a52-9d1a-8744bd77501f"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d166b344-78fc-4bcb-a54e-a5a3932a2ca4">
<rdf:value>
The non-dimensional and scaled threshold potential value.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#33d38b0b-a53b-43d4-91f1-9e1accc960ed">
<vCard:Given>Martyn</vCard:Given>
<vCard:Family>Nash</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c5e65c50-1dcd-4131-a448-efc2aaca12f8">
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
<rdf:value>martyn.nash@auckland.ac.nz</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0f855a1e-1a8b-4abf-beaa-18910135341d">
<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:#c87ee15f-edf8-4517-a35d-15165e30eb1b">
<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:#3d0f7dcd-d98d-4560-945d-6cdf4e01540b">
<vCard:ORG rdf:resource="rdf:#8e5ffc80-42ca-4b9d-b32a-1260dfda9c2e"/>
<vCard:EMAIL rdf:resource="rdf:#c5e65c50-1dcd-4131-a448-efc2aaca12f8"/>
<vCard:N rdf:resource="rdf:#33d38b0b-a53b-43d4-91f1-9e1accc960ed"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#2f0b14b0-a766-4111-bc46-81ee50020de2">
<rdf:value>
This equation describes the kinetics of the transmembrane,
potential - the action potential.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#03dff719-bff5-46b7-903e-84f2e10e6cd3">
<dcterms:W3CDTF>2004</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="#active_tension">
<cmeta:comment rdf:resource="rdf:#397fbdc3-2882-4426-aa8a-5efa7292e07c"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c7f7f07a-4058-4275-b20d-7667183954f3">
<dc:title>Prog. Biophys. Molec. Biol.
</dc:title>
</rdf:Description>
<rdf:Description rdf:about="#r_deriv_eqn">
<cmeta:comment rdf:resource="rdf:#c18f63f2-f928-4b14-90ec-b031813daebf"/>
</rdf:Description>
<rdf:Description rdf:about="#Iion_calc_eqn">
<cmeta:comment rdf:resource="rdf:#96e163b2-3dbb-41c0-a13b-66ec64aecf7a"/>
</rdf:Description>
<rdf:Description rdf:about="#interface">
<cmeta:comment rdf:resource="rdf:#c888d02d-3927-46e8-bfe1-a408016dc44a"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#81aa6d82-f8a9-4485-bf1f-0a78381dd343">
<vCard:Given>M</vCard:Given>
<vCard:Family>Nash</vCard:Family>
<vCard:Other>P</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="#IStim_for_cmiss_eq">
<cmeta:comment rdf:resource="rdf:#c87ee15f-edf8-4517-a35d-15165e30eb1b"/>
</rdf:Description>
<rdf:Description rdf:about="#nash_panfilov_2004_version01">
<dc:title>
Modified FitzHugh-Nagumo model
</dc:title>
<cmeta:comment rdf:resource="rdf:#3084bc4e-304b-4ecb-a847-57f18b8c0ef8"/>
<bqs:reference rdf:resource="rdf:#4f283f2b-2cf3-4683-b1ac-97b4099ee4c1"/>
<bqs:reference rdf:parseType="Resource">
<dc:subject rdf:parseType="Resource">
<bqs:subject_type>keyword</bqs:subject_type>
<rdf:value>
<rdf:Bag>
<rdf:li>electromechanical</rdf:li>
<rdf:li>electrophysiology</rdf:li>
<rdf:li>myofilament mechanics</rdf:li>
<rdf:li>excitable tissue</rdf:li>
</rdf:Bag>
</rdf:value>
</dc:subject>
</bqs:reference>
</rdf:Description>
<rdf:Description rdf:about="">
<dcterms:created rdf:resource="rdf:#59d320a1-84d2-4c2a-b0b1-d97373ed351f"/>
<dc:creator rdf:resource="rdf:#3d0f7dcd-d98d-4560-945d-6cdf4e01540b"/>
<dc:creator rdf:resource="rdf:#645ee413-b7df-40fc-be2e-9c8e3dabd3a0"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#61db89ed-909f-432b-9df3-47d7b8a6041b">
<vCard:Given>David</vCard:Given>
<vCard:Family>Nickerson</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#fbef0f98-ca6d-4419-86ca-2f9fe72ea6f8">
<dc:creator rdf:resource="rdf:#d2217bf5-29ca-434a-a174-7dd35011a958"/>
<dc:title>
Electromechanical model of excitable tissue to study reentrant
cardiac arrhythmias
</dc:title>
<bqs:volume>85</bqs:volume>
<bqs:first_page>501</bqs:first_page>
<bqs:Journal rdf:resource="rdf:#c7f7f07a-4058-4275-b20d-7667183954f3"/>
<dcterms:issued rdf:resource="rdf:#03dff719-bff5-46b7-903e-84f2e10e6cd3"/>
<bqs:last_page>522</bqs:last_page>
</rdf:Description>
<rdf:Description rdf:about="#Vm_deriv_eqn">
<cmeta:comment rdf:resource="rdf:#2f0b14b0-a766-4111-bc46-81ee50020de2"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#5dc219c0-f39f-4bf0-821a-baa31b8586ee">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4f283f2b-2cf3-4683-b1ac-97b4099ee4c1">
<bqs:JournalArticle rdf:resource="rdf:#fbef0f98-ca6d-4419-86ca-2f9fe72ea6f8"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#3084bc4e-304b-4ecb-a847-57f18b8c0ef8">
<rdf:value>
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 rdf:about="rdf:#9ca973a1-0cf4-4cbf-8fdd-75aa4cb51f55">
<rdf:value>
The component which defines the kinetics of the transmembrane potential.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8cbf0378-f099-4b93-a475-3dad969b3eee">
<vCard:Given>A</vCard:Given>
<vCard:Family>Panfilov</vCard:Family>
<vCard:Other>V</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#397fbdc3-2882-4426-aa8a-5efa7292e07c">
<rdf:value>
This is the active tension relation from the Nash and Panfilov
article.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a8dff835-17e3-4be9-93fa-a73254c3e333">
<rdf:value>
The non-dimensional and scaled potential value.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c888d02d-3927-46e8-bfe1-a408016dc44a">
<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:#219b0293-9d1f-411b-9e00-ddde2e973de6">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#8cbf0378-f099-4b93-a475-3dad969b3eee"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#59d320a1-84d2-4c2a-b0b1-d97373ed351f">
<dcterms:W3CDTF>2004-07-22</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="#recovery_variable">
<cmeta:comment rdf:resource="rdf:#d1a2af11-008e-4823-ae5d-0ba90f03560e"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c18f63f2-f928-4b14-90ec-b031813daebf">
<rdf:value>
The kinetics of the recovery variable.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#Ta_deriv_eqn">
<cmeta:comment rdf:resource="rdf:#56301c52-ecc1-412f-9196-e0e0bf8ffca2"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d8a1f290-9512-423b-abcb-d6507e542104">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#81aa6d82-f8a9-4485-bf1f-0a78381dd343"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8e5ffc80-42ca-4b9d-b32a-1260dfda9c2e">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="rdf:#645ee413-b7df-40fc-be2e-9c8e3dabd3a0">
<vCard:ORG rdf:resource="rdf:#5dc219c0-f39f-4bf0-821a-baa31b8586ee"/>
<vCard:EMAIL rdf:resource="rdf:#0f855a1e-1a8b-4abf-beaa-18910135341d"/>
<vCard:N rdf:resource="rdf:#61db89ed-909f-432b-9df3-47d7b8a6041b"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#af85210b-52d5-4a52-9d1a-8744bd77501f">
<rdf:value>
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 rdf:about="#a_calc_eqn">
<cmeta:comment rdf:resource="rdf:#d166b344-78fc-4bcb-a54e-a5a3932a2ca4"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#96e163b2-3dbb-41c0-a13b-66ec64aecf7a">
<rdf:value>
The calcuation of the total ionic current.
</rdf:value>
</rdf:Description>
</rdf:RDF>
</model>
