- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-09-03 23:47:06+12:00
- Desc:
- committing version01 of skouibine_trayanova_moore_1999
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/skouibine_trayanova_moore_1999/rawfile/8898685c0e01f95a4ca80a4b7f3d65faaacdbc5d/skouibine_trayanova_moore_1999.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : defibrillation_beeler_reuter_model_1999.xml
CREATED : 28th December 2001
LAST MODIFIED : 5th April 2003
AUTHOR : Catherine Lloyd
Department of Engineering Science
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/01/2002 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of the defibrillation Beeler-Reuter model.
CHANGES:
21/01/2002 - AAC - Updated metadata to conform to the 16/1/02 CellML Metadata
1.0 Specification.
01/04/2003 - AAC - Added citation metadata.
05/04/2003 - AAC - Changed the model name so the model loads in the database
easier.
--><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="defibrillation_beeler_reuter_model_1999" name="skouibine_trayanova_moore_1999_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>The Defibrillation Beeler-Reuter 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 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>
The original Beeler-Reuter mammalian ventricular model (1977) (see <ulink url="${HTML_EXMPL_BR_MODEL}">The Beeler-Reuter Model, 1977</ulink>) was modified by Drouhard and Roberge (1987) (see <ulink url="${HTML_EXMPL_DR_MODEL}">The Drouhard-Roberge Model, 1987</ulink>) to improve the fast sodium current kinetics. This model was then further modified by Skouibine <emphasis>et al</emphasis>. (1999) to handle potentials outside the range of normal physiological activity, allowing the model to be used in defibrillation studies.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
Anode/cathode make and break phenomena during defibrillation: Does electroporation make a difference?, Skouibine, K., Trayanova, N., Moore, P. 1999 <ulink url="http://www.ieee.org/organizations/pubs/pub_preview/bme_toc.html">
<emphasis>IEEE Trans. Biomed. Eng</emphasis>
</ulink>, 46, 769-777. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=10396895&dopt=Abstract">PubMed ID: 10396895</ulink>
</para>
<para>
The raw CellML description of the defibrillation Beeler-Reuter model 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>
<!--
Below, we define some additional units for association with variables and
constants within the model. The identifiers are fairly self-explanatory.
-->
<units name="millisecond">
<unit units="second" prefix="milli"/>
</units>
<units name="per_millisecond">
<unit units="second" prefix="milli" exponent="-1"/>
</units>
<units name="millivolt">
<unit units="volt" prefix="milli"/>
</units>
<units name="per_millivolt">
<unit units="volt" prefix="milli" exponent="-1"/>
</units>
<units name="per_millivolt_millisecond">
<unit units="millivolt" exponent="-1"/>
<unit units="millisecond" exponent="-1"/>
</units>
<units name="milliS_per_cm2">
<unit units="siemens" prefix="milli"/>
<unit units="metre" prefix="centi" exponent="-2"/>
</units>
<units name="milliS_per_mm2">
<unit units="siemens" prefix="milli"/>
<unit units="metre" prefix="milli" exponent="-2"/>
</units>
<units name="microF_per_cm2">
<unit units="farad" prefix="micro"/>
<unit units="metre" prefix="centi" exponent="-2"/>
</units>
<units name="microA_per_cm2">
<unit units="ampere" prefix="micro"/>
<unit units="metre" prefix="centi" exponent="-2"/>
</units>
<units name="concentration_units">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="flux">
<unit units="concentration_units"/>
<unit units="millisecond" exponent="-1"/>
</units>
<!--
The "environment" component is used to declare variables that are used by
all or most of the other components, in this case just "time".
-->
<component name="environment">
<variable units="millisecond" public_interface="out" name="time"/>
</component>
<component name="membrane">
<variable units="millivolt" public_interface="out" name="V" initial_value="-84.624"/>
<variable units="microA_per_cm2" name="I_stim"/>
<variable units="microF_per_cm2" name="C" initial_value="1.0"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="microA_per_cm2" public_interface="in" name="i_Na"/>
<variable units="microA_per_cm2" public_interface="in" name="i_s"/>
<variable units="microA_per_cm2" public_interface="in" name="i_x1"/>
<variable units="microA_per_cm2" public_interface="in" name="i_K1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="membrane_voltage_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> V </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> I_stim </ci>
<apply>
<plus/>
<ci> i_Na </ci>
<ci> i_s </ci>
<ci> i_x1 </ci>
<ci> i_K1 </ci>
</apply>
</apply>
<ci> C </ci>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current">
<variable units="microA_per_cm2" public_interface="out" name="i_Na"/>
<variable units="milliS_per_mm2" name="g_Na" initial_value="0.15"/>
<variable units="millivolt" name="E_Na" initial_value="40.0"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="m"/>
<variable units="dimensionless" private_interface="in" name="h"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Na_calculation">
<eq/>
<ci> i_Na </ci>
<apply>
<times/>
<ci> g_Na </ci>
<apply>
<power/>
<ci> m </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> h </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Na </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current_m_gate">
<variable units="dimensionless" public_interface="out" name="m" initial_value="0.0"/>
<variable units="per_millisecond" name="alpha_m"/>
<variable units="per_millisecond" name="beta_m"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_m_calculation">
<eq/>
<ci> alpha_m </ci>
<piecewise>
<piece>
<apply>
<times/>
<cn cellml:units="dimensionless"> 890.9437890 </cn>
<apply>
<divide/>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="millivolt"> 0.0486479 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 4.8647916 </cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<cn cellml:units="dimensionless"> 5.93962526 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="millivolt"> 0.0486479 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 4.8647916 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<gt/>
<ci> V </ci>
<cn cellml:units="millivolt"> 100.0 </cn>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.9 </cn>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 42.65 </cn>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.22 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 9.3830 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply id="beta_m_calculation">
<eq/>
<ci> beta_m </ci>
<piecewise>
<piece>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.437 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.085 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 3.37875 </cn>
</apply>
</apply>
</apply>
<apply>
<gt/>
<ci> V </ci>
<cn cellml:units="millivolt"> -85.0 </cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 100.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.2597504 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 22.0787804 </cn>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply id="dm_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> m </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_m </ci>
<apply>
<minus/>
<cn cellml:units="per_millivolt"> 1.0 </cn>
<ci> m </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_m </ci>
<ci> m </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current_h_gate">
<variable units="dimensionless" public_interface="out" name="h" initial_value="0.18"/>
<variable units="per_millisecond" name="alpha_h"/>
<variable units="per_millisecond" name="beta_h"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_h_calculation">
<eq/>
<ci> alpha_h </ci>
<piecewise>
<piece>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.1 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.193 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 15.37245 </cn>
</apply>
</apply>
</apply>
<apply>
<gt/>
<ci> V </ci>
<cn cellml:units="millivolt"> -90.0 </cn>
</apply>
</piece>
<otherwise>
<apply>
<minus/>
<cn cellml:units="dimensionless"> -12.0662845 </cn>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.1422598 </cn>
<ci> V </ci>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply id="beta_h_calculation">
<eq/>
<ci> beta_h </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.7 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.095 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 1.9475 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="dh_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> h </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_h </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> h </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_h </ci>
<ci> h </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="time_independent_outward_current" name="time_independent_outward_current">
<variable units="microA_per_cm2" public_interface="out" name="i_K1"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_K1_calculation">
<eq/>
<ci> i_K1 </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.35 </cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 4.0 </cn>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.04 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 85.0 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.08 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 53 </cn>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.04 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 53.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.2 </cn>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 23.0 </cn>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> -0.04 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 23.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
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</apply>
</math>
</component>
<component cmeta:id="time_dependent_outward_current" name="time_dependent_outward_current">
<variable units="microA_per_cm2" public_interface="out" name="i_x1"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="x1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_x1_calculation">
<eq/>
<ci> i_x1 </ci>
<apply>
<times/>
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<apply>
<divide/>
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<minus/>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.04 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 77.0 </cn>
</apply>
</apply>
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<cn cellml:units="dimensionless"> 1.0 </cn>
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<apply>
<exp/>
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<times/>
<cn cellml:units="per_millivolt"> 0.04 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 35.0 </cn>
</apply>
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</apply>
</apply>
</apply>
</math>
</component>
<component name="time_dependent_outward_current_x1_gate">
<variable units="dimensionless" public_interface="out" name="x1"/>
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<variable units="per_millisecond" name="beta_x1"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_x1_calculation">
<eq/>
<ci> alpha_x1 </ci>
<piecewise>
<piece>
<apply>
<times/>
<cn cellml:units="dimensionless"> 151.7994692 </cn>
<apply>
<divide/>
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<exp/>
<apply>
<minus/>
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<times/>
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<ci> V </ci>
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<times/>
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<cn cellml:units="millivolt"> 0.0654679 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 26.1871448 </cn>
</apply>
</apply>
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</apply>
<apply>
<gt/>
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<times/>
<cn cellml:units="dimensionless"> 0.0005 </cn>
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<divide/>
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<plus/>
<apply>
<times/>
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<plus/>
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<apply>
<plus/>
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<cn cellml:units="dimensionless"> 0.057 </cn>
<ci> V </ci>
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<apply id="beta_x1_calculation">
<eq/>
<ci> beta_x1 </ci>
<apply>
<times/>
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<apply>
<divide/>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<times/>
<ci> V </ci>
<cn cellml:units="dimensionless"> -0.06 </cn>
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<plus/>
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<exp/>
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<cn cellml:units="dimensionless"> -0.04 </cn>
<ci> V </ci>
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<cn cellml:units="millivolt"> 0.8 </cn>
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</apply>
</apply>
</apply>
</apply>
<apply id="dx1_dt">
<eq/>
<apply>
<diff/>
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<ci> time </ci>
</bvar>
<ci> x1 </ci>
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<apply>
<minus/>
<apply>
<times/>
<ci> alpha_x1 </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> x1 </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_x1 </ci>
<ci> x1 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="slow_inward_current" name="slow_inward_current">
<variable units="microA_per_cm2" public_interface="out" name="i_s"/>
<variable units="milliS_per_cm2" name="g_s"/>
<variable units="millivolt" name="E_s"/>
<variable units="concentration_units" name="Cai"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="d"/>
<variable units="dimensionless" private_interface="in" name="f"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="E_s_calculation">
<eq/>
<ci> E_s </ci>
<apply>
<minus/>
<cn cellml:units="millivolt"> -82.3 </cn>
<apply>
<times/>
<cn cellml:units="millivolt"> 13.0287 </cn>
<apply>
<ln/>
<ci> Cai </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="i_s_calculation">
<eq/>
<ci> i_s </ci>
<apply>
<times/>
<ci> g_s </ci>
<ci> d </ci>
<ci> f </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_s </ci>
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</apply>
<apply id="dCai_dt">
<eq/>
<apply>
<diff/>
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<ci> time </ci>
</bvar>
<ci> Cai </ci>
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<apply>
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<plus/>
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<cn cellml:units="dimensionless"> -0.01 </cn>
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<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.07 </cn>
<apply>
<minus/>
<cn cellml:units="concentration_units"> 0.0001 </cn>
<ci> Cai </ci>
</apply>
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</apply>
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<variable units="per_millisecond" name="alpha_d"/>
<variable units="per_millisecond" name="beta_d"/>
<variable units="dimensionless" name="R"/>
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<eq/>
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<ci> time </ci>
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<ci> d </ci>
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<apply>
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<ci> d </ci>
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<apply>
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<ci> beta_d </ci>
<ci> d </ci>
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</apply>
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<variable units="per_millisecond" name="alpha_f"/>
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<variable units="millisecond" public_interface="in" name="time"/>
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<eq/>
<ci> alpha_f </ci>
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<eq/>
<ci> beta_f </ci>
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<divide/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.0065 </cn>
<apply>
<exp/>
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<minus/>
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<ci> V </ci>
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<cn cellml:units="millivolt"> 50.0 </cn>
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<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
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<ci> V </ci>
<cn cellml:units="millivolt"> 30.0 </cn>
</apply>
<cn cellml:units="millivolt"> 5.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="df_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> f </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<apply>
<divide/>
<ci> alpha_f </ci>
<ci> R </ci>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> f </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_f </ci>
<ci> f </ci>
</apply>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="fast_sodium_current">
<component_ref component="fast_sodium_current_m_gate"/>
<component_ref component="fast_sodium_current_h_gate"/>
</component_ref>
<component_ref component="slow_inward_current">
<component_ref component="slow_inward_current_d_gate"/>
<component_ref component="slow_inward_current_f_gate"/>
</component_ref>
<component_ref component="time_dependent_outward_current">
<component_ref component="time_dependent_outward_current_x1_gate"/>
</component_ref>
<component_ref component="time_independent_outward_current"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="fast_sodium_current">
<component_ref component="fast_sodium_current_m_gate"/>
<component_ref component="fast_sodium_current_h_gate"/>
</component_ref>
<component_ref component="slow_inward_current">
<component_ref component="slow_inward_current_d_gate"/>
<component_ref component="slow_inward_current_f_gate"/>
</component_ref>
<component_ref component="time_dependent_outward_current">
<component_ref component="time_dependent_outward_current_x1_gate"/>
</component_ref>
</group>
<connection>
<map_components component_2="environment" component_1="membrane"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="fast_sodium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="slow_inward_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="time_dependent_outward_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="time_independent_outward_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="fast_sodium_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Na" variable_1="i_Na"/>
</connection>
<connection>
<map_components component_2="slow_inward_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_s" variable_1="i_s"/>
</connection>
<connection>
<map_components component_2="time_dependent_outward_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_x1" variable_1="i_x1"/>
</connection>
<connection>
<map_components component_2="time_independent_outward_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_K1" variable_1="i_K1"/>
</connection>
<connection>
<map_components component_2="fast_sodium_current_m_gate" component_1="fast_sodium_current"/>
<map_variables variable_2="m" variable_1="m"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="fast_sodium_current_h_gate" component_1="fast_sodium_current"/>
<map_variables variable_2="h" variable_1="h"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="time_dependent_outward_current_x1_gate" component_1="time_dependent_outward_current"/>
<map_variables variable_2="x1" variable_1="x1"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="slow_inward_current_d_gate" component_1="slow_inward_current"/>
<map_variables variable_2="d" variable_1="d"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="slow_inward_current_f_gate" component_1="slow_inward_current"/>
<map_variables variable_2="f" variable_1="f"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<rdf:RDF>
<rdf:Bag rdf:about="rdf:#a0a5d14a-965a-4ee6-9592-8925b8399ec9">
<rdf:li>cardiac</rdf:li>
<rdf:li>defibrillation</rdf:li>
<rdf:li>ventricular myocyte</rdf:li>
<rdf:li>electrophysiology</rdf:li>
</rdf:Bag>
<rdf:Seq rdf:about="rdf:#citationAuthorsSeq">
<rdf:li rdf:resource="rdf:#author1Vcard"/>
<rdf:li rdf:resource="rdf:#author2Vcard"/>
<rdf:li rdf:resource="rdf:#author3Vcard"/>
</rdf:Seq>
<rdf:Description rdf:about="rdf:#c006ec61-381d-4519-9762-cbcf20cc9371">
<rdf:value>
The formula for the time independent outward potassium current of
the defibrillation Beeler-Reuter model is the same as for the
original Beeler-Reuter model.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="">
<dc:publisher>
The University of Auckland, Bioengineering Research Group
</dc:publisher>
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<rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
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</rdf:Description>
<rdf:Description rdf:about="rdf:#32a73418-bc72-480b-a429-e18205780abf">
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<rdf:value>This is the CellML description of the defibrillation Beeler-Reuter model. The original Beeler-Reuter model was modified by Drouhard and Roberge (1987) to improve the fast sodium kinetics. This model was then further modified by Skouibine et al (1999) to handle potentials outside the range of normal physiological activity, allowing the model to be used in defibrillation studies.</rdf:value>
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<vCard:Given>P</vCard:Given>
<vCard:Family>Moore</vCard:Family>
<vCard:Other>K</vCard:Other>
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<rdf:Description rdf:about="rdf:#86356cad-a088-4458-a880-931e1c757aef">
<dcterms:W3CDTF>1999-07-01</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a0b41a3a-fcf3-404d-8325-5141e219d8ab">
<bqs:Pubmed_id>10396895</bqs:Pubmed_id>
<bqs:JournalArticle rdf:resource="rdf:#5788056d-688a-47b3-a466-58a383bbe506"/>
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<vCard:Given>N</vCard:Given>
<vCard:Family>Trayanova</vCard:Family>
<vCard:Other>A</vCard:Other>
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<rdf:Description rdf:about="rdf:#351b094e-65c0-44c3-8f3b-e5380f390585">
<vCard:FN>Catherine Lloyd</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="rdf:#b14113bf-307f-4b80-8c12-689f857497ad">
<rdf:value>
A minor change is made to the intracellular calcium ion tracking to
limit the movement of calcium ions at large potentials. In addition to these changes, a scale factor can be added to the time dependent
d and f gates to allow the scaling of the action potential duration. This enables a better representation of an action potential from
ischemic tissue.
</rdf:value>
</rdf:Description>
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<vCard:Given>Autumn</vCard:Given>
<vCard:Family>Cuellar</vCard:Family>
<vCard:Other>A</vCard:Other>
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<dcterms:W3CDTF>2003-04-05</dcterms:W3CDTF>
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<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Research Group</vCard:Orgunit>
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<bqs:subject_type>keyword</bqs:subject_type>
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<dcterms:modified rdf:resource="rdf:#2ad59465-76c5-4d4c-a642-1670ec32ca9e"/>
<rdf:value>
Added more metadata.
</rdf:value>
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<vCard:Given>Autumn</vCard:Given>
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Changed the model name so the model loads in the database easier.
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<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
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<dcterms:W3CDTF>2001-12-28</dcterms:W3CDTF>
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<vCard:Given>K</vCard:Given>
<vCard:Family>Skouibine</vCard:Family>
<vCard:Other>B</vCard:Other>
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<vCard:Given>Autumn</vCard:Given>
<vCard:Family>Cuellar</vCard:Family>
<vCard:Other>A.</vCard:Other>
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<dc:creator rdf:resource="rdf:#citationAuthorsSeq"/>
<dc:title>Anode/cathode make and break phenomena in a model of defibrillation</dc:title>
<bqs:volume>46</bqs:volume>
<bqs:first_page>769</bqs:first_page>
<bqs:Journal rdf:resource="rdf:#e2d6a460-c4f4-4881-942f-9cdcdb6b4c48"/>
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</rdf:Description>
<rdf:Description rdf:about="rdf:#2ad59465-76c5-4d4c-a642-1670ec32ca9e">
<dcterms:W3CDTF>2003-04-01</dcterms:W3CDTF>
</rdf:Description>
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<dcterms:modified rdf:resource="rdf:#274c69a2-ff31-490a-ac37-3c09d83391a9"/>
<rdf:value>
Updated metadata to conform to the 16/1/02 CellML Metadata 1.0
Specification.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#ca2c528f-a60b-4332-b2fa-b0a560c8534a"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e2d6a460-c4f4-4881-942f-9cdcdb6b4c48">
<dc:title>IEEE Trans Biomed Eng.</dc:title>
</rdf:Description>
<rdf:Description rdf:about="#defibrillation_beeler_reuter_model_1999">
<dc:title>The defibrillation Beeler-Reuter model</dc:title>
<cmeta:comment rdf:resource="rdf:#32a73418-bc72-480b-a429-e18205780abf"/>
<bqs:reference rdf:resource="rdf:#9cac74dc-d857-4ff5-8e53-27fe475325e5"/>
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<vCard:N rdf:resource="rdf:#0fd8b43a-3dbb-41fd-856b-dd38a859b949"/>
</rdf:Description>
<rdf:Description rdf:about="#slow_inward_current">
<cmeta:comment rdf:resource="rdf:#b14113bf-307f-4b80-8c12-689f857497ad"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ca2c528f-a60b-4332-b2fa-b0a560c8534a">
<vCard:N rdf:resource="rdf:#ab3f865b-0059-4fc5-8600-c32674f8bcb5"/>
</rdf:Description>
<rdf:Description rdf:about="#time_dependent_outward_current">
<cmeta:comment rdf:resource="rdf:#9fae1327-cc1f-4366-9f86-f3f8caec4c05"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#274c69a2-ff31-490a-ac37-3c09d83391a9">
<dcterms:W3CDTF>2002-01-21</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9fae1327-cc1f-4366-9f86-f3f8caec4c05">
<rdf:value>
While the governing equations for the time dependent outward
potassium current are unchanged, the gating variables (alpha_x1 and
beta_x1) are modified.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9cac74dc-d857-4ff5-8e53-27fe475325e5">
<dc:subject rdf:resource="rdf:#39b6e166-d543-451d-818e-1a0eb091c648"/>
</rdf:Description>
</rdf:RDF>
</model>
