- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2007-11-29 00:17:24+13:00
- Desc:
- committing version04 of fitzhugh_1961
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/fitzhugh_1961/rawfile/b3521814b85f75b20b96cd598025503987b0e8af/fitzhugh_1961.cellml
<?xml version='1.0' encoding='utf-8'?>
<!--
This CellML file was generated on 30/10/2007 at 14:23:50 using:
COR (0.9.31.801)
Copyright 2002-2007 Dr Alan Garny
http://COR.physiol.ox.ac.uk/ - COR@physiol.ox.ac.uk
CellML 1.0 was used to generate this cellular model
http://www.CellML.org/
--><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#" xmlns:ns7="http://www.cellml.org/metadata/simulation/1.0#" name="fitzhugh_arimoto_yoshizawa_1961" cmeta:id="fitzhugh_arimoto_yoshizawa_1961">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>The FitzHugh-Nagumo Simplified Cardiac Myocyte Model</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 version of the model has been curated by Penny Noble using
COR and is also known to read in to JSim and PCEnv.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Often it is not necessary to model the ionic currents of a cell with the accuracy and complexity inherent in the biophysically based models. With a view to investigating phenomena on a larger spatial and temporal scale, several ionic current models have been developed that do not seek to model subcellular processes but only to provide an action potential at a minimal computational cost.
</para>
<para>
The FitzHugh-Nagumo model (1961) is based on the cubic excitation model (see <ulink url="${HTML_EXMPL_HMN_SIMPLE}">The Polynomial Model, 1975</ulink>), but it also includes a recovery variable so both depolarisation and repolarisation can be modelled. In 1994, Rogers and McCulloch modified the original model to generate a more realistic action potential. The velocity of the upstroke was increased and the large hyperpolarisation at the end of the recovery phase was removed. The model parameters were also updated. In 1996, this form of the already modified FitzHugh_Nagumo model was further updated by Aliev and Panfilov. They altered the equation which modelled the change of the recovery variable to provide a more realistic restitution period and to allow for reentrant phenomena.
</para>
<para>
The complete original paper references are cited below:
</para>
<para>
Impulses and physiological states in theoretical models of nerve membrane, FitzHugh, R.A., 1961, <ulink url="http://www.biophysj.org/">
<emphasis>Biophys. J.</emphasis>
</ulink>, 1, 445-466.
</para>
<para>
An active pulse transmission line simulating nerve axon, Nagumo, J., Animoto, S., Yoshizawa, S., 1962, <emphasis>Proc. Inst. Radio Engineers</emphasis>, 50, 2061-2070.
</para>
<para>
A collocation-Galerkin finite element model of cardiac action potential propagation, Rogers, J.M., McCulloch, A.D., 1994a, <ulink url="http://www.ieee.org/organizations/pubs/pub_preview/bme_toc.html">
<emphasis>IEEE Trans. Biomed. Eng.</emphasis>
</ulink>, 41, 743-757.
</para>
<para>
A simple two-variable model of cardiac excitation, Aliev, R.R. and Panfilov, A.V., 1996, <ulink url="http://www.theo-physik.uni-kiel.de/theo-physik/schuster/contents/csf95.html#7_2">
<emphasis>Chaos, Solitons and Fractals</emphasis>
</ulink>, 7, 293-301. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=8796189&dopt=Abstract">PubMed ID: 8796189</ulink>
</para>
<para>
The raw CellML description of the simplified cardiac myocyte models can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>. For an example of a more complete documentation for an electrophysiological model, see <ulink url="${HTML_EXMPL_HHSA_INTRO}">The Hodgkin-Huxley Squid Axon Model, 1952</ulink>.
</para>
</sect1>
</article>
</documentation>
<units name="millisecond">
<unit units="second" prefix="milli"/>
</units>
<units name="per_millisecond">
<unit units="second" prefix="milli" exponent="-1"/>
</units>
<component name="Main">
<variable units="millisecond" name="t"/>
<variable units="dimensionless" name="v" initial_value="0"/>
<variable units="dimensionless" name="w" initial_value="0"/>
<variable units="dimensionless" name="alpha" initial_value="-0.08"/>
<variable units="dimensionless" name="gamma" initial_value="3"/>
<variable units="dimensionless" name="epsilon" initial_value="0.005"/>
<variable units="dimensionless" name="I"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>I</ci>
<piecewise>
<piece>
<apply>
<minus/>
<cn cellml:units="dimensionless">80</cn>
</apply>
<apply>
<and/>
<apply>
<geq/>
<ci>t</ci>
<cn cellml:units="millisecond">0</cn>
</apply>
<apply>
<leq/>
<ci>t</ci>
<cn cellml:units="millisecond">0.5</cn>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="dimensionless">0</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v</ci>
</apply>
<apply>
<times/>
<cn cellml:units="per_millisecond">1</cn>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci>v</ci>
<apply>
<minus/>
<ci>v</ci>
<ci>alpha</ci>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>v</ci>
</apply>
</apply>
<ci>w</ci>
</apply>
<ci>I</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>w</ci>
</apply>
<apply>
<times/>
<cn cellml:units="per_millisecond">1</cn>
<ci>epsilon</ci>
<apply>
<minus/>
<ci>v</ci>
<apply>
<times/>
<ci>gamma</ci>
<ci>w</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<rdf:RDF>
<rdf:Seq rdf:about="rdf:#6a7621f2-aa42-4d88-84fa-0a00aa5fd739">
<rdf:li rdf:resource="rdf:#58aa73c6-59b7-4c1c-8cd9-638dedab3659"/>
</rdf:Seq>
<rdf:Seq rdf:about="rdf:#f5de9499-997d-487f-a4a7-f4c7a4b0fa43">
<rdf:li rdf:resource="rdf:#8c2f750a-9b7e-4d3d-b343-e84a5e626a82"/>
<rdf:li rdf:resource="rdf:#9a3ccc38-3a74-4765-a78e-e899ceaa4982"/>
<rdf:li rdf:resource="rdf:#7a9138bf-89a5-486b-9063-a5e18d3cf9ae"/>
</rdf:Seq>
<rdf:Description rdf:about="rdf:#e4e1be29-a030-49d4-9c49-f5fae0ec70d8">
<vCard:N rdf:resource="rdf:#fc6bde02-d31b-4f7a-9aff-3e797f805248"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#544c4afa-8650-4519-a391-e323a5708d47">
<vCard:N rdf:resource="rdf:#a1a24936-0b6a-480a-b261-b4f770ed2c59"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9a3ccc38-3a74-4765-a78e-e899ceaa4982">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#7796abec-9f1b-40de-b263-341b47fe6bcd"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#33127423-0355-4f89-9f21-89d95176029e">
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
<rdf:value>penny.noble@physiol.ox.ac.uk</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#49504fbf-8ab8-4e2e-8c1c-0487ebf89e18">
<dc:creator rdf:resource="rdf:#f5de9499-997d-487f-a4a7-f4c7a4b0fa43"/>
<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:#f68c1cdf-f0a1-4a48-bca4-88e0c60ec538"/>
<dcterms:issued rdf:resource="rdf:#d295c416-9e3e-41c1-be16-24019930d4e3"/>
<bqs:last_page>2070</bqs:last_page>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ecc1e7ab-3016-4793-a4e8-ed5816ba5126">
<vCard:ORG rdf:resource="rdf:#0b675e2d-f723-4847-a66f-e70f53f39b21"/>
<vCard:EMAIL rdf:resource="rdf:#33127423-0355-4f89-9f21-89d95176029e"/>
<vCard:N rdf:resource="rdf:#9dd328df-7da3-49d4-9ca2-71c89fba009e"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#58b3cdc4-d1fa-4a08-9fe8-4dbec84764ba">
<dc:creator rdf:resource="rdf:#b38c75f3-41dd-4c32-a56f-ae82f59bf2b9"/>
<rdf:value/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#b871b529-397d-42ac-8dcb-147d8751281d">
<dc:title>Biophysical Journal</dc:title>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f68c1cdf-f0a1-4a48-bca4-88e0c60ec538">
<dc:title>Biophysical Journal</dc:title>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a1a24936-0b6a-480a-b261-b4f770ed2c59">
<vCard:Given>Peter</vCard:Given>
<vCard:Family>Villiger</vCard:Family>
<vCard:Other>J</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#7796abec-9f1b-40de-b263-341b47fe6bcd">
<vCard:Given>S</vCard:Given>
<vCard:Family>Arimoto</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="#fitzhugh_arimoto_yoshizawa_1961">
<ns7:simulation rdf:resource="rdf:#$5oZPu1"/>
<bqs:reference rdf:resource="rdf:#18e84fae-3970-484d-b4bd-3ebf7efae287"/>
<bqs:reference rdf:resource="rdf:#6e0124ee-76c6-413d-b47c-d14b3e358a18"/>
<cmeta:comment rdf:resource="rdf:#58b3cdc4-d1fa-4a08-9fe8-4dbec84764ba"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a6262423-2533-4e2d-8016-abe657b87b6b">
<vCard:Given>J</vCard:Given>
<vCard:Family>Nagumo</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#fc6bde02-d31b-4f7a-9aff-3e797f805248">
<vCard:Given>Penny</vCard:Given>
<vCard:Family>Noble</vCard:Family>
<vCard:Other>J</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d295c416-9e3e-41c1-be16-24019930d4e3">
<dcterms:W3CDTF>1962-10-01 00:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1a1848ce-994c-4903-9852-ea1db92f271e">
<dcterms:W3CDTF>1961-01-01</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#673426a4-80b2-418a-a806-29ec6ec61170">
<vCard:FN/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#60ce8291-3624-4d15-8dc2-5333c45466fe">
<vCard:Given>S</vCard:Given>
<vCard:Family>Yoshizawa</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#5de2f5db-2bc1-4b7c-aed8-6b947aba0e80">
<vCard:Given>J</vCard:Given>
<vCard:Family>Nagumo</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#$7oZPu1">
<ns7:endingValue>1000</ns7:endingValue>
<ns7:nonstandard-pointDensity>10000</ns7:nonstandard-pointDensity>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0b675e2d-f723-4847-a66f-e70f53f39b21">
<vCard:Orgname>Oxford University</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a89860c7-20da-414b-b7e1-dcce00895c26">
<dc:creator rdf:resource="rdf:#6a7621f2-aa42-4d88-84fa-0a00aa5fd739"/>
<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:#b871b529-397d-42ac-8dcb-147d8751281d"/>
<dcterms:issued rdf:resource="rdf:#1a1848ce-994c-4903-9852-ea1db92f271e"/>
<bqs:last_page>466</bqs:last_page>
</rdf:Description>
<rdf:Description rdf:about="rdf:#7a9138bf-89a5-486b-9063-a5e18d3cf9ae">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#60ce8291-3624-4d15-8dc2-5333c45466fe"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#58aa73c6-59b7-4c1c-8cd9-638dedab3659">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#148f1515-3e3d-417a-890f-bd285f7c6e97"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9dd328df-7da3-49d4-9ca2-71c89fba009e">
<vCard:Given>Penny</vCard:Given>
<vCard:Family>Noble</vCard:Family>
<vCard:Other/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#$6oZPu1">
<rdf:rest rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#nil"/>
<rdf:first rdf:resource="rdf:#$7oZPu1"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#6b7bfb3b-0fdc-49c4-8a79-9e18b43f2030">
<dcterms:modified rdf:resource="rdf:#0313b367-644b-4f37-9b35-aa8fff838ccc"/>
<rdf:value>Units checked, curated.</rdf:value>
<cmeta:modifier rdf:resource="rdf:#e4e1be29-a030-49d4-9c49-f5fae0ec70d8"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#898ae253-514f-46c7-98df-8e362cb26e4b">
<dc:creator rdf:resource="rdf:#673426a4-80b2-418a-a806-29ec6ec61170"/>
<rdf:value/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#6043ea80-2628-41ba-8df8-f0cbe34d22a5">
<dcterms:modified rdf:resource="rdf:#ced487df-80a8-413f-bb1b-458659b1640b"/>
<rdf:value>added metadata</rdf:value>
<cmeta:modifier rdf:resource="rdf:#544c4afa-8650-4519-a391-e323a5708d47"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#6e0124ee-76c6-413d-b47c-d14b3e358a18">
<bqs:Pubmed_id/>
<bqs:JournalArticle rdf:resource="rdf:#a89860c7-20da-414b-b7e1-dcce00895c26"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9b3ee688-9f52-440b-91ea-68af2ff8db75">
<dcterms:W3CDTF>2005-06-14T00:00:00+00:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#6abb2ddf-62fe-4a10-b568-a12ea2e2ca85">
<dc:creator rdf:resource="rdf:#8cca07d6-a776-44cd-a7a1-5c31a31bae0b"/>
<rdf:value/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8cca07d6-a776-44cd-a7a1-5c31a31bae0b">
<vCard:FN/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0313b367-644b-4f37-9b35-aa8fff838ccc">
<dcterms:W3CDTF>2007-11-29T12:16:16+13:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#$5oZPu1">
<ns7:boundIntervals rdf:resource="rdf:#$6oZPu1"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8c2f750a-9b7e-4d3d-b343-e84a5e626a82">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#5de2f5db-2bc1-4b7c-aed8-6b947aba0e80"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#b38c75f3-41dd-4c32-a56f-ae82f59bf2b9">
<vCard:FN/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#3d6b0a64-3ee8-4e8b-b25f-6b0f010ed34f">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#a6262423-2533-4e2d-8016-abe657b87b6b"/>
</rdf:Description>
<rdf:Description rdf:about="">
<dc:publisher>Department of Physiology, Anatomy & Genetics, University of Oxford</dc:publisher>
<cmeta:comment rdf:resource="rdf:#898ae253-514f-46c7-98df-8e362cb26e4b"/>
<dcterms:created rdf:resource="rdf:#9b3ee688-9f52-440b-91ea-68af2ff8db75"/>
<dc:creator rdf:resource="rdf:#ecc1e7ab-3016-4793-a4e8-ed5816ba5126"/>
<cmeta:modification rdf:resource="rdf:#6b7bfb3b-0fdc-49c4-8a79-9e18b43f2030"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#148f1515-3e3d-417a-890f-bd285f7c6e97">
<vCard:Given>Richard</vCard:Given>
<vCard:Family>Fitzhugh</vCard:Family>
<vCard:Other>A</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#18e84fae-3970-484d-b4bd-3ebf7efae287">
<bqs:Pubmed_id/>
<bqs:JournalArticle rdf:resource="rdf:#49504fbf-8ab8-4e2e-8c1c-0487ebf89e18"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ced487df-80a8-413f-bb1b-458659b1640b">
<dcterms:W3CDTF>2006-03-31</dcterms:W3CDTF>
</rdf:Description>
</rdf:RDF>
</model>
