- Author:
- Sander Land <sander.land@kcl.ac.uk>
- Date:
- 2015-12-09 11:13:55+00:00
- Desc:
- Bug fix for filament overlap function
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/1b9/rawfile/43f172b9541e1ab7af8d85839de26e5ba297088b/Takotsubo_Tref.cellml
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Copyright 2002-2015 Dr Alan Garny
http://cor.physiol.ox.ac.uk/ - cor@physiol.ox.ac.uk
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http://www.cellml.org/
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<apply>
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<apply>
<leq/>
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<apply>
<plus/>
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<apply>
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<leq/>
<ci>mtime</ci>
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<apply>
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<apply>
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<apply>
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<apply>
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<apply>
<minus/>
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<apply>
<leq/>
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<apply>
<plus/>
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<apply>
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<apply>
<minus/>
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<apply>
<leq/>
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<piece>
<apply>
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<apply>
<minus/>
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<apply>
<leq/>
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</apply>
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<piece>
<apply>
<plus/>
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<apply>
<times/>
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<apply>
<minus/>
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<apply>
<leq/>
<ci>mtime</ci>
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<piece>
<apply>
<plus/>
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<times/>
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<apply>
<minus/>
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</apply>
<apply>
<leq/>
<ci>mtime</ci>
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</apply>
</piece>
<piece>
<apply>
<plus/>
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<apply>
<times/>
<apply>
<minus/>
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<apply>
<minus/>
<ci>mtime</ci>
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<apply>
<leq/>
<ci>mtime</ci>
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</apply>
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<piece>
<apply>
<plus/>
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<apply>
<times/>
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<apply>
<minus/>
<ci>mtime</ci>
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</apply>
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</apply>
<apply>
<leq/>
<ci>mtime</ci>
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</apply>
</piece>
<piece>
<apply>
<plus/>
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<apply>
<times/>
<apply>
<minus/>
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<apply>
<minus/>
<ci>mtime</ci>
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</apply>
</apply>
</apply>
<apply>
<leq/>
<ci>mtime</ci>
<cn cellml:units="dimensionless">65</cn>
</apply>
</piece>
<piece>
<apply>
<plus/>
<cn cellml:units="uM">0.849</cn>
<apply>
<times/>
<cn cellml:units="uM">0</cn>
<apply>
<minus/>
<ci>mtime</ci>
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</apply>
</apply>
</apply>
<apply>
<leq/>
<ci>mtime</ci>
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</apply>
</piece>
<piece>
<apply>
<plus/>
<cn cellml:units="uM">0.851</cn>
<apply>
<times/>
<apply>
<minus/>
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</apply>
<apply>
<minus/>
<ci>mtime</ci>
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</apply>
</apply>
</apply>
<apply>
<leq/>
<ci>mtime</ci>
<cn cellml:units="dimensionless">75</cn>
</apply>
</piece>
<piece>
<apply>
<plus/>
<cn cellml:units="uM">0.783</cn>
<apply>
<times/>
<cn cellml:units="uM">0.008</cn>
<apply>
<minus/>
<ci>mtime</ci>
<cn cellml:units="dimensionless">75</cn>
</apply>
</apply>
</apply>
<apply>
<leq/>
<ci>mtime</ci>
<cn cellml:units="dimensionless">80</cn>
</apply>
</piece>
<piece>
<apply>
<plus/>
<cn cellml:units="uM">0.821</cn>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="uM">0.012</cn>
</apply>
<apply>
<minus/>
<ci>mtime</ci>
<cn cellml:units="dimensionless">80</cn>
</apply>
</apply>
</apply>
<apply>
<leq/>
<ci>mtime</ci>
<cn cellml:units="dimensionless">85</cn>
</apply>
</piece>
<piece>
<apply>
<plus/>
<cn cellml:units="uM">0.763</cn>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="uM">0.009</cn>
</apply>
<apply>
<minus/>
<ci>mtime</ci>
<cn cellml:units="dimensionless">85</cn>
</apply>
</apply>
</apply>
<apply>
<leq/>
<ci>mtime</ci>
<cn cellml:units="dimensionless">90</cn>
</apply>
</piece>
<piece>
<apply>
<plus/>
<cn cellml:units="uM">0.718</cn>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="uM">0.004</cn>
</apply>
<apply>
<minus/>
<ci>mtime</ci>
<cn cellml:units="dimensionless">90</cn>
</apply>
</apply>
</apply>
<apply>
<leq/>
<ci>mtime</ci>
<cn cellml:units="dimensionless">95</cn>
</apply>
</piece>
<piece>
<apply>
<plus/>
<cn cellml:units="uM">0.696</cn>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="uM">0.016</cn>
</apply>
<apply>
<minus/>
<ci>mtime</ci>
<cn cellml:units="dimensionless">95</cn>
</apply>
</apply>
</apply>
<apply>
<leq/>
<ci>mtime</ci>
<cn cellml:units="dimensionless">100</cn>
</apply>
</piece>
<piece>
<apply>
<plus/>
<cn cellml:units="uM">0.618</cn>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="uM">0.008</cn>
</apply>
<apply>
<minus/>
<ci>mtime</ci>
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</apply>
</apply>
</apply>
<apply>
<leq/>
<ci>mtime</ci>
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</apply>
</piece>
<piece>
<apply>
<plus/>
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<apply>
<times/>
<apply>
<minus/>
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</apply>
<apply>
<minus/>
<ci>mtime</ci>
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</apply>
</apply>
</apply>
<apply>
<leq/>
<ci>mtime</ci>
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</apply>
</piece>
<piece>
<apply>
<plus/>
<cn cellml:units="uM">0.522</cn>
<apply>
<times/>
<apply>
<minus/>
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</apply>
<apply>
<minus/>
<ci>mtime</ci>
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</apply>
</apply>
</apply>
<apply>
<leq/>
<ci>mtime</ci>
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</apply>
</piece>
<piece>
<apply>
<plus/>
<cn cellml:units="uM">0.463</cn>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="uM">0.005</cn>
</apply>
<apply>
<minus/>
<ci>mtime</ci>
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</apply>
</apply>
</apply>
<apply>
<leq/>
<ci>mtime</ci>
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</apply>
</piece>
<piece>
<apply>
<plus/>
<cn cellml:units="uM">0.44</cn>
<apply>
<times/>
<apply>
<minus/>
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<apply>
<minus/>
<ci>mtime</ci>
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</apply>
</apply>
</apply>
<apply>
<leq/>
<ci>mtime</ci>
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</apply>
</piece>
<piece>
<apply>
<plus/>
<cn cellml:units="uM">0.37</cn>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="uM">0.006</cn>
</apply>
<apply>
<minus/>
<ci>mtime</ci>
<cn cellml:units="dimensionless">125</cn>
</apply>
</apply>
</apply>
<apply>
<leq/>
<ci>mtime</ci>
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</apply>
</piece>
<piece>
<apply>
<plus/>
<cn cellml:units="uM">0.34</cn>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="uM">0.01</cn>
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<apply>
<minus/>
<ci>mtime</ci>
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</apply>
</apply>
</apply>
<apply>
<leq/>
<ci>mtime</ci>
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</apply>
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<piece>
<apply>
<plus/>
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<apply>
<times/>
<apply>
<minus/>
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<apply>
<minus/>
<ci>mtime</ci>
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</apply>
<apply>
<leq/>
<ci>mtime</ci>
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<piece>
<apply>
<plus/>
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<apply>
<times/>
<apply>
<minus/>
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<apply>
<minus/>
<ci>mtime</ci>
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<apply>
<leq/>
<ci>mtime</ci>
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<piece>
<apply>
<plus/>
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<apply>
<times/>
<apply>
<minus/>
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<apply>
<minus/>
<ci>mtime</ci>
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<leq/>
<ci>mtime</ci>
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<apply>
<plus/>
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<times/>
<apply>
<minus/>
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<apply>
<minus/>
<ci>mtime</ci>
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<leq/>
<ci>mtime</ci>
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<piece>
<apply>
<plus/>
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<apply>
<times/>
<apply>
<minus/>
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<minus/>
<ci>mtime</ci>
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</apply>
</apply>
</apply>
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<leq/>
<ci>mtime</ci>
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</piece>
<piece>
<apply>
<plus/>
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<apply>
<times/>
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<apply>
<minus/>
<ci>mtime</ci>
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</apply>
</apply>
</apply>
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<leq/>
<ci>mtime</ci>
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</apply>
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</otherwise>
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<component xmlns="http://www.cellml.org/cellml/1.0#" name="crossbridges">
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<variable name="time" units="ms" public_interface="in"/>
<variable name="TRPN" units="dimensionless" public_interface="in"/>
<variable name="k_xb" units="per_ms" initial_value="0.02"/>
<variable name="nperm" units="dimensionless" initial_value="5"/>
<variable name="perm50" units="dimensionless" initial_value="0.35"/>
<variable name="permtot" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>permtot</ci>
<apply>
<root/>
<apply>
<power/>
<apply>
<divide/>
<ci>TRPN</ci>
<ci>perm50</ci>
</apply>
<ci>nperm</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>xb</ci>
</apply>
<apply>
<times/>
<ci>k_xb</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>permtot</ci>
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<minus/>
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<ci>xb</ci>
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</apply>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<ci>permtot</ci>
</apply>
<ci>xb</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="troponin">
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<variable name="time" units="ms" public_interface="in"/>
<variable name="Ca" units="uM" public_interface="in"/>
<variable name="Ca_beta" units="uM" public_interface="in"/>
<variable name="Ca_i" units="uM"/>
<variable name="Ca_50ref" units="uM" initial_value="1.1"/>
<variable name="beta_1" units="dimensionless" initial_value="-1.5"/>
<variable name="k_off" units="per_ms" initial_value="0.1"/>
<variable name="n_TRPN" units="dimensionless" initial_value="2"/>
<variable name="lambda_m" units="dimensionless" public_interface="in"/>
<variable name="Ca_50" units="uM"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Ca_i</ci>
<ci>Ca_beta</ci>
</apply>
<apply>
<eq/>
<ci>Ca_50</ci>
<apply>
<times/>
<ci>Ca_50ref</ci>
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<plus/>
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<times/>
<ci>beta_1</ci>
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<minus/>
<ci>lambda_m</ci>
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</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>TRPN</ci>
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<apply>
<times/>
<ci>k_off</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_i</ci>
<ci>Ca_50</ci>
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<ci>n_TRPN</ci>
</apply>
<apply>
<minus/>
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<ci>TRPN</ci>
</apply>
</apply>
<ci>TRPN</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="Myofilaments">
<variable name="lambda" units="dimensionless" public_interface="out"/>
<variable name="dlambdadt" units="per_ms" public_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>lambda</ci>
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<apply>
<eq/>
<ci>dlambdadt</ci>
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<component xmlns="http://www.cellml.org/cellml/1.0#" name="filament_overlap">
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<variable name="overlap" units="dimensionless" public_interface="out"/>
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<variable name="lambda_m" units="dimensionless" public_interface="out"/>
<variable name="lambda_s" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<eq/>
<ci>lambda_m</ci>
<piecewise>
<piece>
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<apply>
<gt/>
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<geq/>
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<apply>
<eq/>
<ci>overlap</ci>
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<plus/>
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<times/>
<ci>beta_0</ci>
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<minus/>
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<plus/>
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<ci>lambda_s</ci>
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</apply>
</apply>
</apply>
</math>
</component>
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<variable name="T_refapex" units="kPa" initial_value="30"/>
<variable name="T_0" units="kPa" public_interface="out"/>
<variable name="xb" units="dimensionless" public_interface="in"/>
<variable name="overlap" units="dimensionless" public_interface="in"/>
<variable name="beta_z" units="dimensionless" initial_value="0.5"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>T_ref</ci>
<apply>
<plus/>
<ci>T_refapex</ci>
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<times/>
<apply>
<minus/>
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<ci>T_refapex</ci>
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<ci>beta_z</ci>
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</apply>
</apply>
<apply>
<eq/>
<ci>T_0</ci>
<apply>
<times/>
<ci>T_ref</ci>
<ci>xb</ci>
<ci>overlap</ci>
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<variable name="dlambdadt" units="per_ms" public_interface="in"/>
<variable name="Q" units="dimensionless"/>
<variable name="a" units="dimensionless" initial_value="0.35"/>
<variable name="Q_1" units="dimensionless" initial_value="0"/>
<variable name="Q_2" units="dimensionless" initial_value="0"/>
<variable name="A_1" units="dimensionless" initial_value="-29"/>
<variable name="A_2" units="dimensionless" initial_value="116"/>
<variable name="alpha_1" units="per_ms" initial_value="0.1"/>
<variable name="alpha_2" units="per_ms" initial_value="0.5"/>
<variable name="T_0" units="kPa" public_interface="in"/>
<variable name="Tension" units="kPa" public_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<eq/>
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<apply>
<plus/>
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<ci>Q_2</ci>
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<apply>
<eq/>
<ci>Tension</ci>
<piecewise>
<piece>
<apply>
<divide/>
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<times/>
<ci>T_0</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>a</ci>
<ci>Q</ci>
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<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>Q</ci>
</apply>
</apply>
<apply>
<lt/>
<ci>Q</ci>
<cn cellml:units="dimensionless">0</cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<apply>
<times/>
<ci>T_0</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<apply>
<plus/>
<ci>a</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>Q</ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<ci>Q</ci>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Q_1</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>A_1</ci>
<ci>dlambdadt</ci>
</apply>
<apply>
<times/>
<ci>alpha_1</ci>
<ci>Q_1</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Q_2</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>A_2</ci>
<ci>dlambdadt</ci>
</apply>
<apply>
<times/>
<ci>alpha_2</ci>
<ci>Q_2</ci>
</apply>
</apply>
</apply>
</math>
</component>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="intracellular_ion_concentrations" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="troponin" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="crossbridges" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="dynamic_stiffness" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="troponin" component_2="intracellular_ion_concentrations"/>
<map_variables variable_1="Ca" variable_2="Ca"/>
<map_variables variable_1="Ca_beta" variable_2="Ca_beta"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="crossbridges" component_2="troponin"/>
<map_variables variable_1="TRPN" variable_2="TRPN"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="isometric_tension" component_2="crossbridges"/>
<map_variables variable_1="xb" variable_2="xb"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="troponin" component_2="filament_overlap"/>
<map_variables variable_1="lambda_m" variable_2="lambda_m"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="filament_overlap" component_2="Myofilaments"/>
<map_variables variable_1="lambda" variable_2="lambda"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="isometric_tension" component_2="filament_overlap"/>
<map_variables variable_1="overlap" variable_2="overlap"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="dynamic_stiffness" component_2="Myofilaments"/>
<map_variables variable_1="dlambdadt" variable_2="dlambdadt"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="dynamic_stiffness" component_2="isometric_tension"/>
<map_variables variable_1="T_0" variable_2="T_0"/>
</connection>
</model>