Location: FTU Heart @ 107a37334b1e / Cardiac FTU v8.cellml
- Author:
- Soroush <ssaf006@aucklanduni.ac.nz>
- Date:
- 2021-09-22 10:34:52+12:00
- Desc:
- Added the initial model.
- Permanent Source URI:
- https://models.cellml.org/workspace/70b/rawfile/107a37334b1e2c51bb76edc1d3dba07527a9f497/Cardiac FTU v8.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 m^3 so radii are m.
Pressure is J.m^-3;
2nd P-K stresses: T11 & T33 are J.m^-3; T22 is J.m^-5; T23 is J.m^-4 -->
<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="dm">
<unit prefix="deci" units="metre"/>
</units>
<units name="dm2">
<unit exponent="2" prefix="deci" units="metre"/>
</units>
<units name="per_m">
<unit exponent="-1" units="metre"/>
</units>
<units name="per_m2">
<unit exponent="-2" units="metre"/>
</units>
<units name="radian_per_dm">
<unit units="radian"/>
<unit exponent="-1" units="dm"/>
</units>
<units name="J_per_L">
<unit units="joule"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="J_per_dm">
<unit units="joule"/>
<unit exponent="-1" units="dm"/>
</units>
<units name="J_per_m2">
<unit units="joule"/>
<unit exponent="-2" units="metre"/>
</units>
<units name="J_per_m3">
<unit units="joule"/>
<unit exponent="-3" units="metre"/>
</units>
<units name="J_per_m4">
<unit units="joule"/>
<unit exponent="-4" units="metre"/>
</units>
<units name="J_per_m5">
<unit units="joule"/>
<unit exponent="-5" units="metre"/>
</units>
<component name="main">
<!-- Integration variable-->
<variable initial_value="0" name="s" units="dimensionless"/>
<!-- Input Variables-->
<variable initial_value="0.0" name="T_0" units="J_per_L"/>
<variable initial_value="0.1" name="r_endo" units="dm"/>
<!-- Constants-->
<variable initial_value="0.1" name="R_endo" units="dm"/>
<variable initial_value="0.2" name="R_epi" units="dm"/>
<variable initial_value="0.0" name="phi_a" units="radian_per_dm"/>
<variable initial_value="1.0" name="lambda_a" units="dimensionless"/>
<variable initial_value="1" name="k_11" units="J_per_L"/>
<variable initial_value="0.01" name="k_22" units="J_per_dm"/>
<variable initial_value="1.2" name="c_11" units="dimensionless"/>
<variable initial_value="0.012" name="c_22" units="dm2"/>
<!-- State Variables-->
<variable name="alpha_f" units="radian"/>
<variable name="r_epi" units="dm"/>
<variable name="r" units="dm"/>
<variable name="R" units="dm"/>
<variable name="E_rr_epi" units="dimensionless"/>
<variable name="E_11" units="dimensionless"/>
<variable name="E_22" units="dm2"/>
<variable name="a11" units="dimensionless"/>
<variable name="Q_1" units="dimensionless"/>
<variable name="Q_2" units="J_per_L"/>
<variable name="Q_3" units="J_per_L"/>
<variable initial_value="0" name="p_0" units="J_per_L"/>
<variable name="p_epi" units="J_per_L"/>
<variable name="p" units="J_per_L"/>
<variable name="p_LV" units="J_per_L"/>
<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>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<power/>
<ci>R_epi</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>R_endo</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<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>
</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>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>E_rr_epi</ci>
<apply>
<times/>
<cn cellml:units="dim">0.5</cn>
<apply>
<minus/>
<apply>
<power/>
<apply>
<divide/>
<ci>R_epi</ci>
<apply>
<times/>
<ci>lambda_a</ci>
<ci>r_epi</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<cn cellml:units="dim">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>p_epi</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<divide/>
<ci>R_epi</ci>
<apply>
<times/>
<ci>lambda_a</ci>
<ci>r_epi</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<ci>k_11</ci>
<ci>E_rr_epi</ci>
</apply>
<apply>
<power/>
<apply>
<minus/>
<ci>c_11</ci>
<apply>
<abs/>
<ci>E_rr_epi</ci>
</apply>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>E_11</ci>
<apply>
<times/>
<cn cellml:units="dim">0.5</cn>
<apply>
<minus/>
<apply>
<power/>
<apply>
<divide/>
<ci>R</ci>
<apply>
<times/>
<ci>lambda_a</ci>
<ci>r</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<cn cellml:units="dim">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>E_22</ci>
<apply>
<times/>
<cn cellml:units="dim">0.5</cn>
<apply>
<minus/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>R</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_1</ci>
<apply>
<minus/>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>r</ci>
<ci>phi_a</ci>
</apply>
<ci>lambda_a</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>lambda_a</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dim">3</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>r</ci>
<ci>R</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dim">2</cn>
<ci>lambda_a</ci>
<apply>
<power/>
<apply>
<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>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>k_11</ci>
<ci>E_11</ci>
</apply>
<apply>
<power/>
<apply>
<minus/>
<ci>c_11</ci>
<apply>
<abs/>
<ci>E_11</ci>
</apply>
</apply>
<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>
</apply>
<apply>
<plus/>
<ci>c_11</ci>
<apply>
<times/>
<cn cellml:units="dim">2</cn>
<ci>E_11</ci>
</apply>
</apply>
</apply>
<apply>
<power/>
<apply>
<minus/>
<ci>c_11</ci>
<apply>
<abs/>
<ci>E_11</ci>
</apply>
</apply>
<cn cellml:units="dim">4</cn>
</apply>
</apply>
<apply>
<minus/>
<ci>lambda_a</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>R</ci>
<ci>r</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>s</ci>
</bvar>
<ci>p_0</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dim">0.001</cn>
<apply>
<minus/>
<ci>r_endo</ci>
<ci>r_epi</ci>
</apply>
</apply>
<ci>r</ci>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci>R</ci>
<apply>
<times/>
<ci>r</ci>
<ci>lambda_a</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>p</ci>
<ci>Q_1</ci>
</apply>
<ci>Q_2</ci>
</apply>
<ci>Q_3</ci>
</apply>
<apply>
<times/>
<ci>T_0</ci>
<apply>
<power/>
<apply>
<cos/>
<ci>alpha_f</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>p</ci>
<apply>
<plus/>
<ci>p_epi</ci>
<ci>p_0</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_f</ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<minus/>
<pi/>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>s</ci>
<cn cellml:units="dim">0.001</cn>
<cn cellml:units="dim">5</cn>
</apply>
<cn cellml:units="dim">6</cn>
</apply>
<pi/>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>a11</ci>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>lambda_a</ci>
<ci>r</ci>
</apply>
<ci>R</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>p_LV</ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<ci>k_11</ci>
<ci>E_11</ci>
</apply>
<apply>
<power/>
<apply>
<minus/>
<ci>c_11</ci>
<apply>
<abs/>
<ci>E_11</ci>
</apply>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
</apply>
<apply>
<times/>
<ci>p</ci>
<ci>a11</ci>
</apply>
</apply>
</apply>
</math>
</component>
</model>