- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-09-04 03:04:06+12:00
- Desc:
- committing version01 of drouhard_roberge_1987
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/drouhard_roberge_1987/rawfile/89d94d93a0ccb31c0cdcffb45de83e9083dc9e6a/drouhard_roberge_1987.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : drouhard_roberge_model_1987.xml
CREATED : 17th December 2001
LAST MODIFIED : 30th July 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 fast sodium current
in ventricular myocardial cells, based on the Drouhard-Roberge model, 1987.
CHANGES:
04/01/2002 - CML - Added the components of the Beeler-Reuter Model.
21/01/2002 - AAC - Updated metadata to conform to the 16/1/02 CellML Metadata
1.0 Specification.
28/02/2002 - CML - Corrected the membrane voltage differential equation.
19/07/2002 - CML - Added more metadata.
09/04/2003 - AAC - Added publication date information.
30/07/2003 - CML - Changed equations.
--><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="drouhard_roberge_1987_version01" name="drouhard_roberge_1987_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>The Drouhard-Roberge Sodium Current Model (1987)</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>
In 1987, Jean-Pierre Drouhard and Fernand A. Roberge published a revised formulation of the <ulink url="${HTML_EXMPL_HHSA_INTRO}">Hodgkin-Huxley representation</ulink> of the sodium current in ventricular myocardial cells. Their improvements have ensured that the action potential upstroke is much faster, and in agreement with experimental observations the peak depolarisation is close to the sodium potential. Like the <ulink url="${HTML_EXMPL_EJ_MODEL}">Ebihara-Johnson model (1980)</ulink>, the Drouhard-Roberge model can be used to replace the sodium kinetics of the <ulink url="${HTML_EXMPL_BR_MODEL}">Beeler-Reuter model (1977)</ulink>.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
Revised Formulation of the Hodgkin-Huxley Representation of the Sodium Current in Cardiac Cells, Jean-Pierre Drouhard and Fernand A. Roberge, 1987, <ulink url="http://www.academicpress.com/jbi">
<emphasis>Computers and Biomedical Research</emphasis>
</ulink>, 20, 333-350. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=3621918&dopt=Abstract">PubMed ID: 3621918</ulink>
</para>
<para>
The raw CellML description of the Drouhard-Roberge model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>. For an example of a more complete documentation for an electrophysiological model, see <ulink url="${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_mm2">
<unit units="siemens" prefix="milli"/>
<unit units="metre" prefix="centi" exponent="-2"/>
</units>
<units name="microF_per_mm2">
<unit units="farad" prefix="micro"/>
<unit units="metre" prefix="centi" exponent="-2"/>
</units>
<units name="microA_per_mm2">
<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>
<!--
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 cmeta:id="membrane" name="membrane">
<variable units="millivolt" public_interface="out" name="V"/>
<variable units="microF_per_mm2" name="C" initial_value="1.3e-2"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="microA_per_mm2" public_interface="in" name="i_Na"/>
<variable units="microA_per_mm2" public_interface="in" name="i_s"/>
<variable units="microA_per_mm2" public_interface="in" name="i_x1"/>
<variable units="microA_per_mm2" 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/>
<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 cmeta:id="fast_sodium_current" name="fast_sodium_current">
<variable units="microA_per_mm2" public_interface="out" name="i_Na"/>
<variable units="milliS_per_mm2" name="g_Na" initial_value="15.0e-2"/>
<variable units="millivolt" name="E_Na" initial_value="40.0"/>
<variable units="dimensionless" private_interface="in" name="m"/>
<variable units="dimensionless" private_interface="in" name="h"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<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>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> 0.9 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 42.65 </cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.22 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 42.65 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_m_calculation">
<eq/>
<ci> beta_m </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 1.437 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.085 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 39.75 </cn>
</apply>
</apply>
</apply>
</apply>
</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>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.1 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.193 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 79.65 </cn>
</apply>
</apply>
</apply>
</apply>
</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>
<times/>
<cn cellml:units="dimensionless"> -0.095 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 20.5 </cn>
</apply>
</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 name="slow_inward_current">
<variable units="microA_per_mm2" public_interface="out" name="i_s"/>
<variable units="milliS_per_mm2" name="g_s" initial_value="9.0e-4"/>
<variable units="millivolt" name="E_s"/>
<variable units="concentration_units" name="Cai" initial_value="0.000000177"/>
<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>
</apply>
</apply>
</apply>
<apply id="dCai_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Cai </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.001 </cn>
<ci> i_s </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.07 </cn>
<apply>
<minus/>
<cn cellml:units="dimensionless"> -0.001 </cn>
<ci> Cai </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="slow_inward_current_d_gate">
<variable units="dimensionless" public_interface="out" name="d" initial_value="0.003"/>
<variable units="per_millisecond" name="alpha_d"/>
<variable units="per_millisecond" name="beta_d"/>
<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_d_calculation">
<eq/>
<ci> alpha_d </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.095 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> -5.0 </cn>
</apply>
<cn cellml:units="millivolt"> 100.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> -5.0 </cn>
</apply>
<cn cellml:units="millivolt"> 13.89 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_d_calculation">
<eq/>
<ci> beta_d </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.07 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 44.0 </cn>
</apply>
<cn cellml:units="millivolt"> 59.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 44.0 </cn>
</apply>
<cn cellml:units="millivolt"> 20.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="dd_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> d </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_d </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> d </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_d </ci>
<ci> d </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="slow_inward_current_f_gate">
<variable units="dimensionless" public_interface="out" name="f" initial_value="0.994"/>
<variable units="per_millisecond" name="alpha_f"/>
<variable units="per_millisecond" name="beta_f"/>
<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_f_calculation">
<eq/>
<ci> alpha_f </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.012 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 28.0 </cn>
</apply>
<cn cellml:units="millivolt"> 125.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 28.0 </cn>
</apply>
<cn cellml:units="millivolt"> 6.67 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_f_calculation">
<eq/>
<ci> beta_f </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.0065 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 30.0 </cn>
</apply>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<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/>
<ci> alpha_f </ci>
<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>
<component name="time_dependent_outward_current">
<variable units="microA_per_mm2" public_interface="out" name="i_x1"/>
<variable units="per_millisecond" name="alpha_x1"/>
<variable units="per_millisecond" name="beta_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/>
<ci> x1 </ci>
<cn cellml:units="dimensionless"> 0.8 </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"> 77.0 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.04 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 35.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="time_dependent_outward_current_x1_gate">
<variable units="dimensionless" public_interface="out" name="x1"/>
<variable units="per_millisecond" name="alpha_x1"/>
<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>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 5e-4 </cn>
<apply>
<divide/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
<cn cellml:units="millivolt"> 12.1 </cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
<cn cellml:units="millivolt"> 17.5 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_x1_calculation">
<eq/>
<ci> beta_x1 </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.0013 </cn>
<apply>
<divide/>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 20.0 </cn>
</apply>
<cn cellml:units="millivolt"> 16.67 </cn>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 20.0 </cn>
</apply>
<cn cellml:units="millivolt"> 25.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="dx1_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> x1 </ci>
</apply>
<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 name="time_independent_outward_current">
<variable units="microA_per_mm2" public_interface="out" name="i_K1"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
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<apply>
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<apply>
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<apply>
<divide/>
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<ci> V </ci>
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<apply>
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<apply>
<exp/>
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<times/>
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<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>
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<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="fast_sodium_current">
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<component_ref component="fast_sodium_current_h_gate"/>
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<component_ref component="slow_inward_current">
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<component_ref component="slow_inward_current_f_gate"/>
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<component_ref component="time_dependent_outward_current">
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<connection>
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<map_variables variable_2="time" variable_1="time"/>
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<connection>
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<map_variables variable_2="time" variable_1="time"/>
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<connection>
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<map_variables variable_2="time" variable_1="time"/>
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<connection>
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<map_variables variable_2="time" variable_1="time"/>
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<connection>
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<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Na" variable_1="i_Na"/>
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<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>
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<vCard:Given>Catherine</vCard:Given>
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Added more metadata.
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<dcterms:W3CDTF>2003-04-09</dcterms:W3CDTF>
</rdf:Description>
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<vCard:Given>F</vCard:Given>
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<vCard:Other>A</vCard:Other>
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<rdf:value>
Updated metadata to conform to the 16/1/02 CellML Metadata 1.0
Specification.
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<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#51b8bbc2-2d4d-4321-a1f0-8a29f8fe1e0d">
<vCard:Given>Autumn</vCard:Given>
<vCard:Family>Cuellar</vCard:Family>
<vCard:Other>A</vCard:Other>
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<rdf:value>
The Drouhard-Roberge model uses the Hodgkin-Huxley formulation for
the sodium membrane current with only one inactivation variable (h)
rather than the two (h and j) of the Beeler-Reuter model. At the
time of the study (1987) there was still much uncertainty regarding
the existence and function of the j gate.
</rdf:value>
</rdf:Description>
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Added publication date information.
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<dcterms:W3CDTF>2002-07-19</dcterms:W3CDTF>
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<dcterms:W3CDTF>1987-08-01</dcterms:W3CDTF>
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Added the components of the Beeler-Reuter Model.
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Changed equations.
</rdf:value>
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<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
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<bqs:Pubmed_id>3621918</bqs:Pubmed_id>
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<dc:title>Computers and Biomedical Research</dc:title>
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<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Research Group</vCard:Orgunit>
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<vCard:FN>Catherine Lloyd</vCard:FN>
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<dc:title>Revised formulation of the Hodgkin-Huxley representation of the sodium current in cardiac cells</dc:title>
<bqs:volume>20</bqs:volume>
<bqs:first_page>333</bqs:first_page>
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<vCard:Given>J</vCard:Given>
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<vCard:Other>P</vCard:Other>
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<rdf:value>This is the CellML description of Drouhard and Roberge's mathematical model of the fast sodium current in ventricular myocardial cells. It describes the ionic current with Hodgkin-Huxley formalism, but revises the original parameters of the equation.</rdf:value>
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<dc:publisher>
The University of Auckland, Bioengineering Research Group
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Corrected the membrane voltage differential equation.
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<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
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<bqs:subject_type>keyword</bqs:subject_type>
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<rdf:value>
Like the Ebihara-Johnson model (1980), the Drouhard-Roberge model
can be used as a direct replacement for the sodium kinetics of the
Beeler-Reuter model. The other ionic equations and membrane
potential are quoted from the original 1977 paper.
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<rdf:type rdf:resource="http://www.w3.org/2001/vcard-rdf/3.0#N"/>
<vCard:Given>Autumn</vCard:Given>
<vCard:Family>Cuellar</vCard:Family>
<vCard:Other>A.</vCard:Other>
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<dcterms:W3CDTF>2003-07-23</dcterms:W3CDTF>
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<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
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<rdf:Description rdf:about="#drouhard_roberge_1987_version01">
<dc:title>
The Drouhard-Roberge Model of the Fast Sodium Current in Ventricular
Myocardial Cells
</dc:title>
<cmeta:bio_entity>Ventricular Myocyte</cmeta:bio_entity>
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<cmeta:species>Mammalia</cmeta:species>
</rdf:Description>
</rdf:RDF>
</model>
