<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : drouhard_roberge_model_1987.xml
CREATED : 17th December 2001
LAST MODIFIED : 9th 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 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.
--><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_version02" name="drouhard_roberge_1987_version02">
<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="ms">
<unit units="second" prefix="milli"/>
</units>
<units name="per_ms">
<unit units="second" prefix="milli" exponent="-1"/>
</units>
<units name="mV">
<unit units="volt" prefix="milli"/>
</units>
<units name="per_mV">
<unit units="volt" prefix="milli" exponent="-1"/>
</units>
<units name="per_mV_ms">
<unit units="mV" exponent="-1"/>
<unit units="ms" exponent="-1"/>
</units>
<units name="mS_per_mm2">
<unit units="siemens" prefix="milli"/>
<unit units="metre" prefix="milli" exponent="-2"/>
</units>
<units name="uF_per_mm2">
<unit units="farad" prefix="micro"/>
<unit units="metre" prefix="milli" exponent="-2"/>
</units>
<units name="uA_per_mm2">
<unit units="ampere" prefix="micro"/>
<unit units="metre" prefix="milli" exponent="-2"/>
</units>
<units name="concentration_units">
<unit units="mole" prefix="nano"/>
<unit units="metre" prefix="milli" exponent="-3"/>
</units>
<units name="per_concentration_units">
<unit units="concentration_units" 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" cmeta:id="environment">
<variable units="ms" public_interface="out" name="time"/>
</component>
<component name="membrane" cmeta:id="membrane">
<variable units="mV" public_interface="out" name="V"/>
<variable units="uF_per_mm2" name="C" initial_value="0.013"/>
<variable units="ms" public_interface="in" name="time"/>
<variable units="uA_per_mm2" public_interface="in" name="i_Na"/>
<variable units="uA_per_mm2" public_interface="in" name="i_s"/>
<variable units="uA_per_mm2" public_interface="in" name="i_x1"/>
<variable units="uA_per_mm2" public_interface="in" name="i_K1"/>
<variable units="uA_per_mm2" name="Istim"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="membrane_voltage_diff_eq">
<apply id="membrane_voltage_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> V </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>Istim</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>
<variable units="uA_per_mm2" 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>
<component name="fast_sodium_current" cmeta:id="fast_sodium_current">
<variable units="uA_per_mm2" public_interface="out" name="i_Na"/>
<variable units="mS_per_mm2" name="g_Na" initial_value="0.15"/>
<variable units="mV" 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="ms" public_interface="in" private_interface="out" name="time"/>
<variable units="mV" public_interface="in" private_interface="out" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="i_Na_calculation_eq">
<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" cmeta:id="fast_sodium_current_m_gate">
<variable units="dimensionless" public_interface="out" name="m" initial_value="0.0"/>
<variable units="per_ms" name="alpha_m"/>
<variable units="per_ms" name="beta_m"/>
<variable units="mV" public_interface="in" name="V"/>
<variable units="ms" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="alpha_m_calculation_eq">
<apply id="alpha_m_calculation">
<eq/>
<ci> alpha_m </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_mV_ms"> 0.9 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 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="mV"> 42.65 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="beta_m_calculation_eq">
<apply id="beta_m_calculation">
<eq/>
<ci> beta_m </ci>
<apply>
<times/>
<cn cellml:units="per_ms"> 1.437 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.085 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 39.75 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="dm_dt_eq">
<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_mV"> 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" cmeta:id="fast_sodium_current_h_gate">
<variable units="dimensionless" public_interface="out" name="h" initial_value="0.99"/>
<variable units="per_ms" name="alpha_h"/>
<variable units="per_ms" name="beta_h"/>
<variable units="mV" public_interface="in" name="V"/>
<variable units="ms" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="alpha_h_calculation_eq">
<apply id="alpha_h_calculation">
<eq/>
<ci> alpha_h </ci>
<apply>
<times/>
<cn cellml:units="per_ms"> 0.1 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.193 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 79.65 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="beta_h_calculation_eq">
<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/>
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<apply>
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<cn cellml:units="mV"> 20.5 </cn>
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</apply>
</apply>
</apply>
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<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="dh_dt_eq">
<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>
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<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" cmeta:id="slow_inward_current">
<variable units="uA_per_mm2" public_interface="out" name="i_s"/>
<variable units="mS_per_mm2" name="g_s" initial_value="9.0e-4"/>
<variable units="mV" name="E_s"/>
<variable units="concentration_units" name="Cai" initial_value="0.000000177"/>
<variable units="ms" public_interface="in" private_interface="out" name="time"/>
<variable units="mV" 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="mV"> -82.3 </cn>
<apply>
<times/>
<cn cellml:units="mV"> 13.0287 </cn>
<apply>
<ln/>
<apply>
<times/>
<cn cellml:units="per_concentration_units"> 0.001 </cn>
<ci> Cai </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="i_s_calculation">
<eq/>
<ci> i_s </ci>
<apply>
<times/>
<ci> g_s </ci>
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<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/>
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<ci> i_s </ci>
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<apply>
<times/>
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<apply>
<minus/>
<cn cellml:units="dimensionless"> -0.0001 </cn>
<ci> Cai </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="slow_inward_current_d_gate" cmeta:id="slow_inward_current_d_gate">
<variable units="dimensionless" public_interface="out" name="d" initial_value="0.003"/>
<variable units="per_ms" name="alpha_d"/>
<variable units="per_ms" name="beta_d"/>
<variable units="mV" public_interface="in" name="V"/>
<variable units="ms" 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/>
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<apply>
<exp/>
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<minus/>
<apply>
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<apply>
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<cn cellml:units="mV"> 100.0 </cn>
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<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
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<apply id="beta_d_calculation">
<eq/>
<ci> beta_d </ci>
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<apply>
<times/>
<cn cellml:units="per_ms"> 0.07 </cn>
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<plus/>
<ci> V </ci>
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<cn cellml:units="dimensionless"> 1.0 </cn>
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<ci> V </ci>
<cn cellml:units="mV"> 44.0 </cn>
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<cn cellml:units="mV"> 20.0 </cn>
</apply>
</apply>
</apply>
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</apply>
<apply id="dd_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> d </ci>
</apply>
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<times/>
<ci> alpha_d </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
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</apply>
<apply>
<times/>
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<ci> d </ci>
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</component>
<component name="slow_inward_current_f_gate" cmeta:id="slow_inward_current_f_gate">
<variable units="dimensionless" public_interface="out" name="f" initial_value="0.994"/>
<variable units="per_ms" name="alpha_f"/>
<variable units="per_ms" name="beta_f"/>
<variable units="mV" public_interface="in" name="V"/>
<variable units="ms" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<eq/>
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<apply>
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<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 28.0 </cn>
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<cn cellml:units="mV"> 125.0 </cn>
</apply>
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<cn cellml:units="mV"> 50.0 </cn>
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<variable units="uA_per_mm2" public_interface="out" name="i_x1"/>
<variable units="per_ms" name="alpha_x1"/>
<variable units="per_ms" name="beta_x1"/>
<variable units="ms" public_interface="in" private_interface="out" name="time"/>
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<math xmlns="http://www.w3.org/1998/Math/MathML">
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<eq/>
<ci> i_x1 </ci>
<apply>
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<ci> x1 </ci>
<cn cellml:units="dimensionless"> 8.0e-3 </cn>
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<apply>
<times/>
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<apply>
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</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
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<apply>
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<apply>
<times/>
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<variable units="per_ms" name="alpha_x1"/>
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<variable units="mV" public_interface="in" name="V"/>
<variable units="ms" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<apply>
<times/>
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<apply>
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<cn cellml:units="mV"> 50.0 </cn>
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<cn cellml:units="mV"> 12.1 </cn>
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<cn cellml:units="mV"> 25.0 </cn>
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<eq/>
<apply>
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<bvar>
<ci> time </ci>
</bvar>
<ci> x1 </ci>
</apply>
<apply>
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<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" cmeta:id="time_independent_outward_current">
<variable units="uA_per_mm2" public_interface="out" name="i_K1"/>
<variable units="ms" public_interface="in" name="time"/>
<variable units="mV" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<ci> i_K1 </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.35e-2 </cn>
<apply>
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<apply>
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<cn cellml:units="per_mV"> 0.04 </cn>
<apply>
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<ci> V </ci>
<cn cellml:units="mV"> 85.0 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
<apply>
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<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_mV"> 0.08 </cn>
<apply>
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<cn cellml:units="mV"> 53 </cn>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_mV"> 0.04 </cn>
<apply>
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<cn cellml:units="mV"> 53.0 </cn>
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</apply>
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<apply>
<times/>
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<apply>
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<cn cellml:units="mV"> 23.0 </cn>
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<apply>
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<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_mV"> -0.04 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 23.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</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:Seq rdf:about="rdf:#citationAuthorsSeq">
<rdf:li rdf:resource="rdf:#author1Vcard"/>
<rdf:li rdf:resource="rdf:#author2Vcard"/>
</rdf:Seq>
<rdf:Description rdf:about="rdf:#dac45851-70d2-450c-a1b5-a45cc8aa14f4">
<rdf:value>
The modified voltage-dependent activation gate for the fast sodium
channel - the m gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#dm_dt_eq">
<cmeta:comment rdf:resource="rdf:#87cb7c76-1fe5-4754-be83-f7f80e0bf604"/>
</rdf:Description>
<rdf:Description rdf:about="#alpha_h_calculation_eq">
<cmeta:comment rdf:resource="rdf:#a4cdf37c-395b-4f04-8275-77b0f13c3e8e"/>
</rdf:Description>
<rdf:Description rdf:about="#drouhard_roberge_1987_version02">
<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>
<cmeta:comment rdf:resource="rdf:#8c869415-ad92-4d3a-b29f-7a24102b94d0"/>
<bqs:reference rdf:resource="rdf:#5feda280-ea34-44ed-a0cd-542aec916823"/>
<bqs:reference rdf:parseType="Resource">
<dc:subject rdf:parseType="Resource">
<bqs:subject_type>keyword</bqs:subject_type>
<rdf:value>
<rdf:Bag>
<rdf:li>Ventricular Myocyte</rdf:li>
<rdf:li>cardiac</rdf:li>
<rdf:li>electrophysiology</rdf:li>
<rdf:li>hodgkin huxley</rdf:li>
</rdf:Bag>
</rdf:value>
</dc:subject>
</bqs:reference>
<cmeta:species>Mammalia</cmeta:species>
</rdf:Description>
<rdf:Description rdf:about="#time_dependent_outward_current">
<cmeta:comment rdf:resource="rdf:#cb6e369c-23d3-4970-b711-614b888178df"/>
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<rdf:Description rdf:about="rdf:#fd408b34-ce2d-40b8-ba57-47b1e79b412a">
<vCard:N rdf:resource="rdf:#6e296b5e-e627-44f6-a5f9-5e2f6aa8e35b"/>
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<rdf:Description rdf:about="rdf:#bda50fa6-a72d-46ea-bc30-db9a74f2c68b">
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
<rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#53c65136-2a51-4df7-a300-e7dbacc23e1d">
<vCard:N rdf:resource="rdf:#cfad46b3-0ef7-4256-802a-0405d9162c2e"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#72efefcf-f6be-4739-a6f6-75ac97762cf2">
<rdf:value>
The standard Beeler Reuter (1977) time-dependent outward (potassium)
current gating variable.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#3e2b1ef6-ba72-4403-9c1c-e94b67c15bff">
<dcterms:modified rdf:resource="rdf:#4f4b9daa-4b18-4d12-841b-ccb4fd2c548e"/>
<rdf:value>
Changed some units and added a stimulus current.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#53c65136-2a51-4df7-a300-e7dbacc23e1d"/>
</rdf:Description>
<rdf:Description rdf:about="#alpha_m_calculation_eq">
<cmeta:comment rdf:resource="rdf:#f1951c77-917f-4bf1-9538-d4ad236aef9c"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#7d201cf6-18f8-4ba1-bb22-a74501e155db">
<dcterms:modified rdf:resource="rdf:#86964ac8-5b96-41aa-a474-5673f1c559d4"/>
<rdf:value>
Corrected the membrane voltage differential equation.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#515889ca-3c29-4fa3-8efc-7b7bd085a2be"/>
</rdf:Description>
<rdf:Description rdf:about="#dh_dt_eq">
<cmeta:comment rdf:resource="rdf:#dc1022af-aa9d-4045-8453-d35d008f0c8f"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#cb6e369c-23d3-4970-b711-614b888178df">
<rdf:value>
The standard Beeler Reuter (1977) time-dependent outward (potassium)
current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#03520b86-af8d-4bb9-9032-e74b36daa1f4">
<dc:title>Computers and Biomedical Research</dc:title>
</rdf:Description>
<rdf:Description rdf:about="rdf:#38ec0b68-976c-4c85-abe9-7d238fe738b5">
<rdf:type rdf:resource="http://www.w3.org/2001/vcard-rdf/3.0#N"/>
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#94861915-891a-4d3f-b2be-87881bc10e8f">
<rdf:value>
The standard Beeler Reuter (1977) slow inward (calcium) current
activation gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f75ff9b3-a580-4e54-9551-ec68c1a8b54c">
<vCard:ORG rdf:resource="rdf:#5329b7cc-e9f4-4312-af3d-927aa2941b95"/>
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</rdf:Description>
<rdf:Description rdf:about="rdf:#fcd2b568-ac30-4709-b0fc-91a8749ca994">
<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>
</rdf:Description>
<rdf:Description rdf:about="rdf:#30991c89-0f03-4466-905f-a45cb85d0aae">
<dcterms:W3CDTF>2003-04-09</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#51869bc0-2200-41bf-bbbb-38861b568b65">
<dcterms:modified rdf:resource="rdf:#e74bbf39-fdf6-425b-88fa-c5a5ca8b8e45"/>
<rdf:value>
Added the components of the Beeler-Reuter Model.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#38ec0b68-976c-4c85-abe9-7d238fe738b5"/>
</rdf:Description>
<rdf:Description rdf:about="#slow_inward_current_d_gate">
<cmeta:comment rdf:resource="rdf:#94861915-891a-4d3f-b2be-87881bc10e8f"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#49a7cd31-87ab-4bdb-aa47-0dd41d92c7d5">
<dcterms:modified rdf:resource="rdf:#53f05d1d-6013-4ab8-be98-c096dbc46cba"/>
<rdf:value>
Added more metadata.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#4392e510-9923-4c01-8e12-76496bf7bfd0"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#5329b7cc-e9f4-4312-af3d-927aa2941b95">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Research Group</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a4cdf37c-395b-4f04-8275-77b0f13c3e8e">
<rdf:value>
The opening rate of the h gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#5feda280-ea34-44ed-a0cd-542aec916823">
<bqs:Pubmed_id>3621918</bqs:Pubmed_id>
<bqs:JournalArticle rdf:resource="rdf:#55d3ddb9-764c-458c-b754-29364351f906"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8c869415-ad92-4d3a-b29f-7a24102b94d0">
<dc:creator rdf:resource="rdf:#301cd1dc-7c8d-4e95-9d7d-4268f8dc9569"/>
<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>
</rdf:Description>
<rdf:Description rdf:about="rdf:#451bd5b7-66b9-4d09-b4a1-c937f1effa38">
<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:#26076ad8-9df1-4c3a-8859-647932fc3528">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author2Vcard">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#author2VcardN"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4f4b9daa-4b18-4d12-841b-ccb4fd2c548e">
<dcterms:W3CDTF>2003-07-28</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author2VcardN">
<vCard:Given>F</vCard:Given>
<vCard:Family>Roberge</vCard:Family>
<vCard:Other>A</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4392e510-9923-4c01-8e12-76496bf7bfd0">
<vCard:N rdf:resource="rdf:#8f152b03-048e-4db8-afea-337106d176f3"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8f17503e-11af-4fa8-853c-7f87a6822c42">
<dcterms:W3CDTF>1987-01-01</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#cfad46b3-0ef7-4256-802a-0405d9162c2e">
<vCard:Given>David</vCard:Given>
<vCard:Family>Nickerson</vCard:Family>
<vCard:Other>P</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e74bbf39-fdf6-425b-88fa-c5a5ca8b8e45">
<rdf:type rdf:resource="http://purl.org/dc/terms/W3CDTF"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#dc1022af-aa9d-4045-8453-d35d008f0c8f">
<rdf:value>
The h gate kinetics.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#32b549bd-ee55-4fc3-8ec4-af44ba5d6ff8">
<rdf:value>
The closing rate of the h gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#fast_sodium_current_h_gate">
<cmeta:comment rdf:resource="rdf:#48d57ec0-69ae-429f-8977-06ff24a87eba"/>
</rdf:Description>
<rdf:Description rdf:about="#membrane_voltage_diff_eq">
<cmeta:comment rdf:resource="rdf:#c8789fc9-fa52-442c-af21-95fb4a4f526a"/>
</rdf:Description>
<rdf:Description rdf:about="#beta_m_calculation_eq">
<cmeta:comment rdf:resource="rdf:#94d72380-90aa-4285-9c3e-e593e91465e7"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0124a9dd-eac1-4d42-8b59-d8560002c334">
<rdf:value>
The standard Beeler Reuter (1977) slow inward (calcium) current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#time_independent_outward_current">
<cmeta:comment rdf:resource="rdf:#05f4ce13-8faa-4763-bd79-bd20b8392d08"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#95d97342-fa36-4d40-b813-cdad33d95d14">
<rdf:type rdf:resource="http://purl.org/dc/terms/W3CDTF"/>
</rdf:Description>
<rdf:Description rdf:about="#time_dependent_outward_current_x1_gate">
<cmeta:comment rdf:resource="rdf:#72efefcf-f6be-4739-a6f6-75ac97762cf2"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c62bfa16-bde5-470b-95de-fdae434b075e">
<dcterms:modified rdf:resource="rdf:#30991c89-0f03-4466-905f-a45cb85d0aae"/>
<rdf:value>
Added publication date information.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#fd408b34-ce2d-40b8-ba57-47b1e79b412a"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#142bbc39-24c0-41b9-ac82-716828ffd79a">
<rdf:value>
The standard Beeler Reuter (1977) slow inward (calcium) current
inactivation gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#membrane">
<cmeta:comment rdf:resource="rdf:#89357937-9494-4745-b50c-2b271dd930b6"/>
</rdf:Description>
<rdf:Description rdf:about="#slow_inward_current">
<cmeta:comment rdf:resource="rdf:#0124a9dd-eac1-4d42-8b59-d8560002c334"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author1VcardN">
<vCard:Given>J</vCard:Given>
<vCard:Family>Drouhard</vCard:Family>
<vCard:Other>P</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#301cd1dc-7c8d-4e95-9d7d-4268f8dc9569">
<vCard:FN>Catherine Lloyd</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a9c9dac6-96f0-4513-8c84-0e6b2a1fdb42">
<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>
<rdf:Description rdf:about="rdf:#9ad87fe5-5d27-44db-a428-44c8aa317a06">
<dcterms:W3CDTF>2001-12-17</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#515889ca-3c29-4fa3-8efc-7b7bd085a2be">
<rdf:type rdf:resource="http://www.w3.org/2001/vcard-rdf/3.0#N"/>
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#87cb7c76-1fe5-4754-be83-f7f80e0bf604">
<rdf:value>
The m gate kinetics.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#IStim_for_cmiss_eq">
<cmeta:comment rdf:resource="rdf:#451bd5b7-66b9-4d09-b4a1-c937f1effa38"/>
</rdf:Description>
<rdf:Description rdf:about="">
<dc:publisher>
Bioengineering Institute, The University of Auckland
</dc:publisher>
<cmeta:modification rdf:resource="rdf:#07886545-20fa-4af4-8ec3-cb1687504bfb"/>
<cmeta:modification rdf:resource="rdf:#3e2b1ef6-ba72-4403-9c1c-e94b67c15bff"/>
<cmeta:modification rdf:resource="rdf:#49a7cd31-87ab-4bdb-aa47-0dd41d92c7d5"/>
<cmeta:modification rdf:resource="rdf:#51869bc0-2200-41bf-bbbb-38861b568b65"/>
<cmeta:modification rdf:resource="rdf:#7d201cf6-18f8-4ba1-bb22-a74501e155db"/>
<cmeta:modification rdf:resource="rdf:#c62bfa16-bde5-470b-95de-fdae434b075e"/>
<dcterms:created rdf:resource="rdf:#9ad87fe5-5d27-44db-a428-44c8aa317a06"/>
<dc:creator rdf:resource="rdf:#f75ff9b3-a580-4e54-9551-ec68c1a8b54c"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#07886545-20fa-4af4-8ec3-cb1687504bfb">
<dcterms:modified rdf:resource="rdf:#95d97342-fa36-4d40-b813-cdad33d95d14"/>
<rdf:value>
Updated metadata to conform to the 16/1/02 CellML Metadata 1.0
Specification.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#fcd2b568-ac30-4709-b0fc-91a8749ca994"/>
</rdf:Description>
<rdf:Description rdf:about="#slow_inward_current_f_gate">
<cmeta:comment rdf:resource="rdf:#142bbc39-24c0-41b9-ac82-716828ffd79a"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#48d57ec0-69ae-429f-8977-06ff24a87eba">
<rdf:value>
The modified inactivation gate for the fast sodium channel - the h
gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#95734698-3b40-4689-aab5-259bbcfb41f6">
<rdf:value>
Calculation of the modified sodium current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#fast_sodium_current">
<cmeta:comment rdf:resource="rdf:#a9c9dac6-96f0-4513-8c84-0e6b2a1fdb42"/>
</rdf:Description>
<rdf:Description rdf:about="#fast_sodium_current_m_gate">
<cmeta:comment rdf:resource="rdf:#dac45851-70d2-450c-a1b5-a45cc8aa14f4"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8f152b03-048e-4db8-afea-337106d176f3">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#05f4ce13-8faa-4763-bd79-bd20b8392d08">
<rdf:value>
The standard Beeler Reuter (1977) time-independent outward
(potassium) current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#beta_h_calculation_eq">
<cmeta:comment rdf:resource="rdf:#32b549bd-ee55-4fc3-8ec4-af44ba5d6ff8"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#6e296b5e-e627-44f6-a5f9-5e2f6aa8e35b">
<vCard:Given>Autumn</vCard:Given>
<vCard:Family>Cuellar</vCard:Family>
<vCard:Other>A</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c8789fc9-fa52-442c-af21-95fb4a4f526a">
<rdf:value>
The main differential equation of the model which defines the change
of membrane potential as a function of the total ionic current
across the membrane plus an applied stimulus current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f1951c77-917f-4bf1-9538-d4ad236aef9c">
<rdf:value>
The opening rate of the m gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#53f05d1d-6013-4ab8-be98-c096dbc46cba">
<dcterms:W3CDTF>2002-07-19</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#94d72380-90aa-4285-9c3e-e593e91465e7">
<rdf:value>
The closing rate of the m gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#55d3ddb9-764c-458c-b754-29364351f906">
<dc:creator rdf:resource="rdf:#citationAuthorsSeq"/>
<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>
<bqs:Journal rdf:resource="rdf:#03520b86-af8d-4bb9-9032-e74b36daa1f4"/>
<dcterms:issued rdf:resource="rdf:#8f17503e-11af-4fa8-853c-7f87a6822c42"/>
<bqs:last_page>350</bqs:last_page>
</rdf:Description>
<rdf:Description rdf:about="rdf:#89357937-9494-4745-b50c-2b271dd930b6">
<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.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#86964ac8-5b96-41aa-a474-5673f1c559d4">
<rdf:type rdf:resource="http://purl.org/dc/terms/W3CDTF"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author1Vcard">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#author1VcardN"/>
</rdf:Description>
<rdf:Description rdf:about="#i_Na_calculation_eq">
<cmeta:comment rdf:resource="rdf:#95734698-3b40-4689-aab5-259bbcfb41f6"/>
</rdf:Description>
</rdf:RDF>
</model>
