Location: FTU Heart @ e1a23a38b70b / Cardiac FTU v7.cellml
- Author:
- Soroush <ssaf006@aucklanduni.ac.nz>
- Date:
- 2021-11-23 12:47:07+13:00
- Desc:
- minor change
- Permanent Source URI:
- https://models.fieldml.org/workspace/70b/rawfile/e1a23a38b70b72e2080e990995ba85f8c120e848/Cardiac FTU v7.cellml
<?xml version='1.0' encoding='UTF-8'?>
<!--
Implements pressure calculation based on stress equilibrium but integrating from outside radius
Displays radial distributions of fibre angle and stresses and strains for radial expansion of an orthotropic thick-walled cylinder
Volume has units of L (cm^3) so radii are cm.
Pressure is J/L (=kPa);
2nd P-K stresses: T11 is J/L; T22 is J/L.cm^-2; T33 is J/L; T23 is J/L.cm^-1 -->
<model name="Cardiac_FTU" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
<units name="dim">
<unit units="dimensionless"/>
</units>
<units name="cm">
<unit exponent="-2" units="meter"/>
</units>
<units name="cm2">
<unit exponent="2" units="cm"/>
</units>
<units name="per_cm">
<unit exponent="-1" units="cm"/>
</units>
<units name="per_cm2">
<unit exponent="-2" units="cm"/>
</units>
<units name="radian_per_cm">
<unit units="radian"/>
<unit exponent="-1" units="cm"/>
</units>
<units name="J_per_L">
<unit units="joule"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="Jcm_per_L">
<unit units="joule"/>
<unit units="cm"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="Jcm2_per_L">
<unit units="joule"/>
<unit exponent="2" units="cm"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="J_per_L_per_cm">
<unit units="J_per_L"/>
<unit exponent="-1" units="cm"/>
</units>
<units name="J_per_L_per_cm2">
<unit units="J_per_L"/>
<unit exponent="-2" units="cm"/>
</units>
<component name="main">
<variable initial_value="0" name="s" units="dim"/>
<variable initial_value="1.0" name="R_endo" units="cm"/>
<variable initial_value="2.0" name="R_epi" units="cm"/>
<variable initial_value="1.0" name="r_endo" units="cm"/>
<variable name="r_epi" units="cm"/>
<variable name="R" units="cm"/>
<variable name="r" units="cm"/>
<variable name="alpha_f" units="radian"/>
<variable initial_value="1.0" name="lambda_a" units="dim"/>
<variable name="lambda_f" units="dim"/>
<variable name="E_rr_endo" units="dim"/>
<variable name="E_rr_epi" units="dim"/>
<variable initial_value="0.0" name="phi_a" units="radian_per_cm"/>
<variable name="E_11" units="dim"/>
<variable name="E_22" units="cm2"/>
<variable name="E_33" units="dim"/>
<variable name="E_23" units="cm"/>
<variable name="a11" units="dim"/>
<variable name="a22" units="per_cm2"/>
<variable name="a33" units="dim"/>
<variable name="a23" units="per_cm"/>
<variable initial_value="1.0" name="k_11" units="J_per_L"/>
<variable initial_value="1.0" name="k_22" units="Jcm2_per_L"/>
<variable initial_value="1.0" name="k_33" units="J_per_L"/>
<variable initial_value="1.0" name="k_23" units="Jcm_per_L"/>
<variable initial_value="1.2" name="c_11" units="dim"/>
<variable initial_value="1.2" name="c_22" units="cm2"/>
<variable initial_value="1.2" name="c_33" units="dim"/>
<variable initial_value="1.2" name="c_23" units="cm"/>
<variable name="T11" units="J_per_L"/>
<variable name="T22" units="J_per_L_per_cm2"/>
<variable name="T33" units="J_per_L"/>
<variable name="T23" units="J_per_L_per_cm"/>
<variable initial_value="0.0" name="T_0" units="J_per_L"/>
<variable name="Q_1" units="dim"/>
<variable name="Q_2" units="J_per_L"/>
<variable name="Q_3" units="J_per_L"/>
<variable name="p_epi" units="J_per_L"/>
<variable name="p_LV" units="J_per_L"/>
<variable name="p" units="J_per_L"/>
<variable initial_value="0" name="p_0" units="J_per_L"/>
<variable initial_value="0" name="f_23" units="dim"/>
<variable initial_value="0" name="f_33" units="dim"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>r_epi</ci>
<apply>
<root/>
<apply>
<plus/>
<apply>
<power/>
<ci>r_endo</ci>
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</apply>
<apply>
<divide/>
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<power/>
<ci>R_epi</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>R_endo</ci>
<cn cellml:units="dimensionless">2</cn>
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<ci>lambda_a</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R</ci>
<apply>
<plus/>
<ci>R_epi</ci>
<apply>
<times/>
<ci>s</ci>
<cn cellml:units="dim">0.001</cn>
<apply>
<minus/>
<ci>R_endo</ci>
<ci>R_epi</ci>
</apply>
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</apply>
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<apply>
<eq/>
<ci>r</ci>
<apply>
<plus/>
<ci>r_epi</ci>
<apply>
<times/>
<ci>s</ci>
<cn cellml:units="dim">0.001</cn>
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<minus/>
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</apply>
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<apply>
<eq/>
<ci>E_rr_endo</ci>
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<times/>
<cn cellml:units="dim">0.5</cn>
<apply>
<minus/>
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<power/>
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<divide/>
<ci>R_endo</ci>
<apply>
<times/>
<ci>lambda_a</ci>
<ci>r_endo</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<cn cellml:units="dim">1</cn>
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<ci>R_epi</ci>
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<divide/>
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<times/>
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<minus/>
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<power/>
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<divide/>
<ci>R_epi</ci>
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<times/>
<ci>lambda_a</ci>
<ci>r_epi</ci>
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<cn cellml:units="dimensionless">2</cn>
</apply>
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<ci>k_11</ci>
<ci>E_rr_epi</ci>
</apply>
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<power/>
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<minus/>
<ci>c_11</ci>
<apply>
<abs/>
<ci>E_rr_epi</ci>
</apply>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
</apply>
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<apply>
<eq/>
<ci>E_11</ci>
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<times/>
<cn cellml:units="dim">0.5</cn>
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<minus/>
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<power/>
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<ci>r</ci>
</apply>
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<cn cellml:units="dimensionless">2</cn>
</apply>
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<eq/>
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<times/>
<cn cellml:units="dim">0.5</cn>
<apply>
<minus/>
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<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>R</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
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</apply>
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<apply>
<eq/>
<ci>Q_1</ci>
<apply>
<minus/>
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<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
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<times/>
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<apply>
<times/>
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<power/>
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<cn cellml:units="dimensionless">2</cn>
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<minus/>
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<times/>
<cn cellml:units="dim">3</cn>
<apply>
<power/>
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<divide/>
<ci>r</ci>
<ci>R</ci>
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<cn cellml:units="dimensionless">2</cn>
</apply>
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<apply>
<times/>
<cn cellml:units="dim">2</cn>
<ci>lambda_a</ci>
<apply>
<power/>
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<divide/>
<ci>r</ci>
<ci>R</ci>
</apply>
<cn cellml:units="dim">4</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_2</ci>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>k_22</ci>
<ci>E_22</ci>
</apply>
<apply>
<power/>
<apply>
<minus/>
<ci>c_22</ci>
<apply>
<abs/>
<ci>E_22</ci>
</apply>
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<cn cellml:units="dim">3</cn>
</apply>
</apply>
<apply>
<divide/>
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<times/>
<ci>k_11</ci>
<ci>E_11</ci>
</apply>
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<power/>
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<minus/>
<ci>c_11</ci>
<apply>
<abs/>
<ci>E_11</ci>
</apply>
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<cn cellml:units="dim">3</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_3</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>k_11</ci>
<apply>
<power/>
<ci>lambda_a</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
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<apply>
<plus/>
<ci>c_11</ci>
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<times/>
<cn cellml:units="dim">2</cn>
<ci>E_11</ci>
</apply>
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<apply>
<power/>
<apply>
<minus/>
<ci>c_11</ci>
<apply>
<abs/>
<ci>E_11</ci>
</apply>
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<cn cellml:units="dim">4</cn>
</apply>
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<apply>
<minus/>
<ci>lambda_a</ci>
<apply>
<power/>
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<divide/>
<ci>R</ci>
<ci>r</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
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<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>s</ci>
</bvar>
<ci>p_0</ci>
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<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dim">0.001</cn>
<apply>
<minus/>
<ci>r_endo</ci>
<ci>r_epi</ci>
</apply>
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<ci>r</ci>
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<apply>
<power/>
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<divide/>
<ci>R</ci>
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<times/>
<ci>r</ci>
<ci>lambda_a</ci>
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<cn cellml:units="dimensionless">2</cn>
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<plus/>
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<minus/>
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<plus/>
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<times/>
<ci>p</ci>
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<ci>Q_2</ci>
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<ci>Q_3</ci>
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<apply>
<times/>
<ci>T_0</ci>
<apply>
<power/>
<apply>
<cos/>
<ci>alpha_f</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
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<eq/>
<ci>p</ci>
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<plus/>
<ci>p_epi</ci>
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<eq/>
<ci>alpha_f</ci>
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<plus/>
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<minus/>
<pi/>
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<cn cellml:units="dim">3</cn>
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<times/>
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<divide/>
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<times/>
<ci>s</ci>
<cn cellml:units="dim">0.001</cn>
<cn cellml:units="dim">5</cn>
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<cn cellml:units="dim">6</cn>
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<pi/>
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<apply>
<eq/>
<ci>lambda_f</ci>
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<root/>
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<plus/>
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<power/>
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<times/>
<ci>lambda_a</ci>
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<sin/>
<ci>alpha_f</ci>
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<cn cellml:units="dimensionless">2</cn>
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<ci>r</ci>
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<plus/>
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<divide/>
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<cos/>
<ci>alpha_f</ci>
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<ci>R</ci>
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<ci>phi_a</ci>
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<sin/>
<ci>alpha_f</ci>
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<cn cellml:units="dimensionless">2</cn>
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<eq/>
<ci>E_33</ci>
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<minus/>
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<plus/>
<apply>
<power/>
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<power/>
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<cn cellml:units="dim">1</cn>
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<eq/>
<ci>E_23</ci>
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<times/>
<cn cellml:units="dim">0.5</cn>
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<power/>
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<ci>a11</ci>
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<power/>
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<divide/>
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<times/>
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<ci>R</ci>
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<eq/>
<ci>a22</ci>
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<plus/>
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<divide/>
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<ci>a33</ci>
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<apply>
<eq/>
<ci>a23</ci>
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<divide/>
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<eq/>
<ci>T11</ci>
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<plus/>
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<divide/>
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<times/>
<ci>k_11</ci>
<ci>E_11</ci>
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<minus/>
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<eq/>
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<plus/>
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<divide/>
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<times/>
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<ci>E_22</ci>
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<minus/>
<ci>c_22</ci>
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<ci>p</ci>
<ci>a22</ci>
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<times/>
<ci>T_0</ci>
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<power/>
<apply>
<cos/>
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<apply>
<eq/>
<ci>T33</ci>
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<plus/>
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<divide/>
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<times/>
<ci>k_33</ci>
<ci>E_33</ci>
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<minus/>
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<abs/>
<ci>E_33</ci>
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<cn cellml:units="dim">3</cn>
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<times/>
<ci>p</ci>
<ci>a33</ci>
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<times/>
<ci>T_0</ci>
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<power/>
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<sin/>
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<eq/>
<ci>T23</ci>
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<divide/>
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<times/>
<ci>k_23</ci>
<ci>E_23</ci>
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<minus/>
<ci>c_23</ci>
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<abs/>
<ci>E_23</ci>
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<ci>T_0</ci>
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<cos/>
<ci>alpha_f</ci>
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<sin/>
<ci>alpha_f</ci>
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<eq/>
<apply>
<diff/>
<bvar>
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<ci>f_33</ci>
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<apply>
<times/>
<cn cellml:units="dim">0.002</cn>
<pi/>
<ci>r</ci>
<ci>T33</ci>
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<eq/>
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<diff/>
<bvar>
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<times/>
<cn cellml:units="dim">0.002</cn>
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<ci>T23</ci>
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<apply>
<eq/>
<ci>p_LV</ci>
<ci>T11</ci>
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</math>
</component>
</model>