<?xml version='1.0'?>
<model cmeta:id="nash_1998" name="nash_1998" xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<!--
Generally, we want to move away from initial/default values being
stored in the model directly. But until we are using CellML 1.1
it is probably quite useful to include the values in the model.
-->
<!-- Global units -->
<units name="ms">
<unit prefix="milli" units="second"/>
</units>
<units name="pms">
<unit exponent="-1" prefix="milli" units="second"/>
</units>
<units name="nmol">
<unit prefix="nano" units="mole"/>
</units>
<units name="mM">
<unit units="nmol"/>
<unit exponent="-3" prefix="milli" units="metre"/>
</units>
<units name="pmspmM">
<unit units="pms"/>
<unit exponent="-1" units="mM"/>
</units>
<units name="kPa">
<unit prefix="kilo" units="pascal"/>
</units>
<component cmeta:id="interface" name="interface">
<!-- Variables we expect to be set/controlled externally -->
<variable name="time" private_interface="out" units="ms"/>
<variable initial_value="1" name="lambda" private_interface="out" units="dimensionless"/>
<variable initial_value="1" name="Ca_max" private_interface="out" units="mM"/>
<variable initial_value="1.45" name="beta" private_interface="out" units="dimensionless"/>
<variable initial_value="0.5" name="c50" private_interface="out" units="mM"/>
<variable initial_value="3" name="h" private_interface="out" units="dimensionless"/>
<variable initial_value="100" name="T_ref" private_interface="out" units="kPa"/>
<!-- Variables we want to make available externally -->
<variable name="T" private_interface="in" public_interface="out" units="kPa"/>
<variable initial_value="0" name="Ca_actn" private_interface="out" public_interface="out" units="mM"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="dummy_ode_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_actn</ci>
</apply>
<apply>
<times/>
<ci>time</ci>
<ci>Ca_max</ci>
</apply>
</apply>
</math>
<!-- Ca_actn ={Ca_actn_calculation} sel
case time <= 5.0{ms}:
time*Ca_max;
case time >= 2.0{ms}:
(2.0{ms}-time)*Ca_max;
otherwise:
0.0{mM};
endsel;-->
</component>
<!--interface-->
<component name="active_contraction">
<!-- Inputs -->
<variable name="time" public_interface="in" units="ms"/>
<variable name="lambda" public_interface="in" units="dimensionless"/>
<variable name="Ca_max" public_interface="in" units="mM"/>
<variable name="beta" public_interface="in" units="dimensionless"/>
<variable name="c50" public_interface="in" units="mM"/>
<variable name="h" public_interface="in" units="dimensionless"/>
<variable name="T_ref" public_interface="in" units="kPa"/>
<variable name="Ca_actn" public_interface="in" units="mM"/>
<!-- Outputs computed here -->
<variable name="T" public_interface="out" units="kPa"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="T_calculation">
<eq/>
<ci>T</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>Ca_max</ci>
<apply>
<power/>
<ci>Ca_actn</ci>
<ci>h</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>Ca_actn</ci>
<ci>h</ci>
</apply>
<apply>
<power/>
<ci>c50</ci>
<ci>h</ci>
</apply>
</apply>
</apply>
<ci>T_ref</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1.0</cn>
<apply>
<times/>
<ci>beta</ci>
<apply>
<minus/>
<ci>lambda</ci>
<cn cellml:units="dimensionless">1.0</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--active_contraction-->
<connection>
<map_components component_1="interface" component_2="active_contraction"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="Ca_actn" variable_2="Ca_actn"/>
<map_variables variable_1="lambda" variable_2="lambda"/>
<map_variables variable_1="Ca_max" variable_2="Ca_max"/>
<map_variables variable_1="beta" variable_2="beta"/>
<map_variables variable_1="c50" variable_2="c50"/>
<map_variables variable_1="h" variable_2="h"/>
<map_variables variable_1="T_ref" variable_2="T_ref"/>
<map_variables variable_1="T" variable_2="T"/>
</connection>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="interface">
<component_ref component="active_contraction"/>
</component_ref>
</group>
<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="">
<creator xmlns="http://purl.org/dc/elements/1.1/">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:nodeID="n1"/>
</creator>
<created xmlns="http://purl.org/dc/terms/">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:nodeID="n2"/>
</created>
</rdf:Description>
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:nodeID="n1">
<N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:nodeID="n3"/>
</N>
<EMAIL xmlns="http://www.w3.org/2001/vcard-rdf/3.0#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:nodeID="n4"/>
</EMAIL>
<ORG xmlns="http://www.w3.org/2001/vcard-rdf/3.0#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:nodeID="n5"/>
</ORG>
</rdf:Description>
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:nodeID="n2">
<W3CDTF xmlns="http://purl.org/dc/terms/" xml:lang="en" xmlns:xml="http://www.w3.org/XML/1998/namespace">2003-12-08</W3CDTF>
</rdf:Description>
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:nodeID="n3">
<Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en" xmlns:xml="http://www.w3.org/XML/1998/namespace">Nickerson</Family>
<Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en" xmlns:xml="http://www.w3.org/XML/1998/namespace">David</Given>
</rdf:Description>
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:nodeID="n4">
<rdf:type 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="http://imc.org/vCard/3.0#internet"/>
</rdf:type>
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xml:lang="en" xmlns:xml="http://www.w3.org/XML/1998/namespace">d.nickerson@auckland.ac.nz</rdf:value>
</rdf:Description>
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:nodeID="n5">
<Orgname xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en" xmlns:xml="http://www.w3.org/XML/1998/namespace">The University of Auckland</Orgname>
<Orgunit xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en" xmlns:xml="http://www.w3.org/XML/1998/namespace">The Bioengineering Institute</Orgunit>
</rdf:Description>
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#nash_1998">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:nodeID="n6"/>
</cmeta:comment>
</rdf:Description>
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:nodeID="n6">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xml:lang="en" xmlns:xml="http://www.w3.org/XML/1998/namespace">
This is a CellML version of the steady-state length-tension-calcium
relationship described by Martyn Nash in his thesis.
</rdf:value>
</rdf:Description>
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#interface">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:nodeID="n7"/>
</cmeta:comment>
</rdf:Description>
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:nodeID="n7">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xml:lang="en" xmlns:xml="http://www.w3.org/XML/1998/namespace">
We'll use this component as the "interface" to the model, all
other components are hidden via encapsulation in this component.
With this model, we expect the extension ratio to be
controlled externally for non-isometric simulations.
</rdf:value>
</rdf:Description>
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#lambda_for_cmiss_eq">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:nodeID="n8"/>
</cmeta:comment>
</rdf:Description>
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:nodeID="n8">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xml:lang="en" xmlns:xml="http://www.w3.org/XML/1998/namespace">
A dummy equation that we simply use to make grabbing the
value in CMISS much easier.
</rdf:value>
</rdf:Description>
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#dummy_ode_eq">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:nodeID="n9"/>
</cmeta:comment>
</rdf:Description>
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:nodeID="n9">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xml:lang="en" xmlns:xml="http://www.w3.org/XML/1998/namespace">
We need a dummy ODE to establish time as the bound variable to
get things to work properly with CMISS.
</rdf:value>
</rdf:Description>
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#active_contraction_eq">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:nodeID="n10"/>
</cmeta:comment>
</rdf:Description>
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:nodeID="n10">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xml:lang="en" xmlns:xml="http://www.w3.org/XML/1998/namespace">
The component which defines the kinetics of the active
tension development.
</rdf:value>
</rdf:Description>
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#T_calculation_eq">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:nodeID="n11"/>
</cmeta:comment>
</rdf:Description>
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:nodeID="n11">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xml:lang="en" xmlns:xml="http://www.w3.org/XML/1998/namespace">
The kinetics of the active tension development using the
steady-state description from the Nash model.
</rdf:value>
</rdf:Description>
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#Ca_actn_calculation_eq">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:nodeID="n12"/>
</cmeta:comment>
</rdf:Description>
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:nodeID="n12">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xml:lang="en" xmlns:xml="http://www.w3.org/XML/1998/namespace">
Here we define the calcium activation transient which simply
goes from 0 to 1 and back to 0 over a period of 2ms.
</rdf:value>
</rdf:Description>
</rdf:RDF>
</model>
