- Author:
- David Nickerson <david.nickerson@gmail.com>
- Date:
- 2021-09-17 15:50:49+12:00
- Desc:
- tweak html formatting
- Permanent Source URI:
- https://models.cellml.org/workspace/a1/rawfile/1b3862589abf79ae9119ee0b5e99a8b785d762e1/models/1977_beeler/experiments/1987_drouhard_roberge.xml
<?xml version='1.0' encoding='UTF-8'?>
<model cmeta:id="drouhard_roberge_model_1987" name="drouhard_roberge_model_1987" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:xlink="http://www.w3.org/1999/xlink">
<import xlink:href="../model.xml">
<component component_ref="interface" name="math_model"/>
</import>
<import xlink:href="../../protocols/periodic-IStim.xml">
<component component_ref="stimulus_protocol" name="stimulus_protocol"/>
</import>
<component cmeta:id="stimulus_parameters" name="stimulus_parameters">
<variable initial_value="500.0" name="stimPeriod" private_interface="out" public_interface="out" units="ms"/>
<variable initial_value="2.0" name="stimDuration" private_interface="out" public_interface="out" units="ms"/>
<variable initial_value="72" name="stimCurrent" private_interface="out" public_interface="out" units="uA_per_mmcu"/>
<variable initial_value="200" name="Am" private_interface="out" public_interface="out" units="per_mm"/>
</component>
<connection>
<map_components component_1="stimulus_protocol" component_2="stimulus_parameters"/>
<map_variables variable_1="stimPeriod" variable_2="stimPeriod"/>
<map_variables variable_1="stimDuration" variable_2="stimDuration"/>
<map_variables variable_1="stimCurrent" variable_2="stimCurrent"/>
<map_variables variable_1="Am" variable_2="Am"/>
</connection>
<connection>
<map_components component_1="stimulus_protocol" component_2="time"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="math_model" component_2="stimulus_protocol"/>
<map_variables variable_1="Istim" variable_2="IStim"/>
</connection>
<component cmeta:id="time_component" name="time">
<variable cmeta:id="time" initial_value="0.0" name="time" public_interface="out" units="ms"/>
</component>
<connection>
<map_components component_1="math_model" component_2="time"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<import xlink:href="../model.xml">
<units name="ms" units_ref="ms"/>
<units name="per_ms" units_ref="per_ms"/>
<units name="mV" units_ref="mV"/>
<units name="per_mV" units_ref="per_mV"/>
<units name="per_mV_ms" units_ref="per_mV_ms"/>
<units name="mS_per_mm2" units_ref="mS_per_mm2"/>
<units name="uF_per_mm2" units_ref="uF_per_mm2"/>
<units name="uA_per_mm2" units_ref="uA_per_mm2"/>
<units name="concentration_units" units_ref="concentration_units"/>
</import>
<import xlink:href="../../common/units.xml">
<units name="per_mm" units_ref="per_mm"/>
<units name="uA_per_mmcu" units_ref="uA_per_mmcu"/>
</import>
<component cmeta:id="fast_sodium_current" name="fast_sodium_current">
<variable name="i_Na" public_interface="out" units="uA_per_mm2"/>
<variable initial_value="0.15" name="g_Na" units="mS_per_mm2"/>
<variable initial_value="40.0" name="E_Na" units="mV"/>
<variable name="m" private_interface="in" units="dimensionless"/>
<variable name="h" private_interface="in" units="dimensionless"/>
<variable name="time" private_interface="out" public_interface="in" units="ms"/>
<variable name="V" private_interface="out" public_interface="in" units="mV"/>
<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 cmeta:id="fast_sodium_current_m_gate" name="fast_sodium_current_m_gate">
<variable initial_value="0.0" name="m" public_interface="out" units="dimensionless"/>
<variable name="alpha_m" units="per_ms"/>
<variable name="beta_m" units="per_ms"/>
<variable name="V" public_interface="in" units="mV"/>
<variable name="time" public_interface="in" units="ms"/>
<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_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/>
<apply>
<minus/>
<cn cellml:units="dimensionless">0.22</cn>
</apply>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="mV">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_ms">1.437</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">0.085</cn>
</apply>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="mV">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_mV">1.0</cn>
<ci>m</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_m</ci>
<ci>m</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="fast_sodium_current_h_gate" name="fast_sodium_current_h_gate">
<variable initial_value="0.99" name="h" public_interface="out" units="dimensionless"/>
<variable name="alpha_h" units="per_ms"/>
<variable name="beta_h" units="per_ms"/>
<variable name="V" public_interface="in" units="mV"/>
<variable name="time" public_interface="in" units="ms"/>
<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_ms">0.1</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">0.193</cn>
</apply>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="mV">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/>
<apply>
<minus/>
<cn cellml:units="dimensionless">0.095</cn>
</apply>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="mV">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>
<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>
</group>
<connection>
<map_components component_1="fast_sodium_current" component_2="time"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="math_model" component_2="fast_sodium_current"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection>
<map_components component_1="fast_sodium_current" component_2="fast_sodium_current_m_gate"/>
<map_variables variable_1="m" variable_2="m"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection>
<map_components component_1="fast_sodium_current" component_2="fast_sodium_current_h_gate"/>
<map_variables variable_1="h" variable_2="h"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<component name="Iadd">
<variable name="Iadd" public_interface="out" units="uA_per_mm2"/>
<variable name="INa_EJ" public_interface="in" units="uA_per_mm2"/>
<variable name="INa_original" public_interface="in" units="uA_per_mm2"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Iadd_calculate">
<eq/>
<ci>Iadd</ci>
<apply>
<minus/>
<ci>INa_EJ</ci>
<ci>INa_original</ci>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="fast_sodium_current" component_2="Iadd"/>
<map_variables variable_1="i_Na" variable_2="INa_EJ"/>
</connection>
<connection>
<map_components component_1="math_model" component_2="Iadd"/>
<map_variables variable_1="INa" variable_2="INa_original"/>
<map_variables variable_1="Iadd" variable_2="Iadd"/>
</connection>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="">
<dc:creator xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Nickerson</vCard:Family>
<vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">David</vCard:Given>
</vCard:N>
<vCard:ORG xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<vCard:Orgname xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">The University of Auckland</vCard:Orgname>
<vCard:Orgunit xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Auckland BioengineeringInstitute</vCard:Orgunit>
</vCard:ORG>
</dc:creator>
<dcterms:created xmlns:dcterms="http://purl.org/dc/terms/" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<dcterms:W3CDTF xmlns:dcterms="http://purl.org/dc/terms/">2009-06-23</dcterms:W3CDTF>
</dcterms:created>
</rdf:Description>
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#drouhard_roberge_model_1987">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">
The Drouhard-Roberge Model of the Fast Sodium Current in Cardiac Muscle,
1980
</dc:title>
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
This is the CellML description of Drouhard and Roberge's mathematical
model of the fast sodium current in cardiac muscle (1980) in the Beeler Reuter cellular model.
</rdf:value>
</cmeta:comment>
<cmeta:species xmlns:cmeta="http://www.cellml.org/metadata/1.0#">Mammalia</cmeta:species>
<cmeta:bio_entity xmlns:cmeta="http://www.cellml.org/metadata/1.0#">Cardiac Myocyte</cmeta:bio_entity>
<bqs:reference xmlns:bqs="http://www.cellml.org/bqs/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<bqs:Pubmed_id xmlns:bqs="http://www.cellml.org/bqs/1.0#">3621918</bqs:Pubmed_id>
</bqs:reference>
<cs:simulation xmlns:cs="http://www.cellml.org/metadata/simulation/1.0#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:ID="simulation">
<cs:multistepMethod xmlns:cs="http://www.cellml.org/metadata/simulation/1.0#">bdf</cs:multistepMethod>
<cs:iterationMethod xmlns:cs="http://www.cellml.org/metadata/simulation/1.0#">functional</cs:iterationMethod>
<cs:boundIntervals xmlns:cs="http://www.cellml.org/metadata/simulation/1.0#" rdf:parseType="Collection" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<cs:boundVariable xmlns:cs="http://www.cellml.org/metadata/simulation/1.0#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#time"/>
</cs:boundVariable>
<cs:maximumStepSize xmlns:cs="http://www.cellml.org/metadata/simulation/1.0#" rdf:datatype="http://www.w3.org/2001/XMLSchema#double" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
0.1
</cs:maximumStepSize>
<cs:tabulationStepSize xmlns:cs="http://www.cellml.org/metadata/simulation/1.0#" rdf:datatype="http://www.w3.org/2001/XMLSchema#double" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
0.5
</cs:tabulationStepSize>
<cs:startingValue xmlns:cs="http://www.cellml.org/metadata/simulation/1.0#" rdf:datatype="http://www.w3.org/2001/XMLSchema#double" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
0
</cs:startingValue>
<cs:endingValue xmlns:cs="http://www.cellml.org/metadata/simulation/1.0#" rdf:datatype="http://www.w3.org/2001/XMLSchema#double" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
1500
</cs:endingValue>
</rdf:Description>
</cs:boundIntervals>
</rdf:Description>
</cs:simulation>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#time_component">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
The actual definition of the time variable.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#fast_sodium_current">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
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>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#i_Na_calculation_eq">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
Calculation of the modified sodium current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#fast_sodium_current_m_gate">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
The modified voltage-dependent activation gate for the fast sodium
channel - the m gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#alpha_m_calculation_eq">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
The opening rate of the m gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#beta_m_calculation_eq">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
The closing rate of the m gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#dm_dt_eq">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
The m gate kinetics.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#fast_sodium_current_h_gate">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
The modified inactivation gate for the fast sodium channel - the h
gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#alpha_h_calculation_eq">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
The opening rate of the h gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#beta_h_calculation_eq">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
The closing rate of the h gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#dh_dt_eq">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
The h gate kinetics.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
</model>
