Location: 12 L Platform 1 model codes @ a8a92308e217 / Airway_FTU / cellml2_version / experiments / branched_algeb.cellml
- Author:
- aram148 <42922407+aram148@users.noreply.github.com>
- Date:
- 2022-07-22 15:47:05+12:00
- Desc:
- Added documentation for VSM model
- Permanent Source URI:
- http://models.cellml.org/workspace/6b0/rawfile/a8a92308e217ac5626809237dd90a31240b22834/Airway_FTU/cellml2_version/experiments/branched_algeb.cellml
<model xmlns="http://www.cellml.org/cellml/2.0#" xmlns:cellml="http://www.cellml.org/cellml/2.0#" xmlns:xlink="http://www.w3.org/1999/xlink" name="branched_algeb">
<units name="mm">
<unit prefix="milli" units="meter"/>
</units>
<units name="mm3">
<unit exponent="3" units="mm"/>
</units>
<units name="mmHg">
<unit multiplier="133.32" units="pascal"/>
</units>
<component name="algeb">
<variable name="Da1" units="mm3" interface="public"/>
<variable name="Da21" units="mm3" interface="public"/>
<variable name="Da22" units="mm3" interface="public"/>
<variable initial_value="10.19716213" name="aa" units="dimensionless"/>
<variable initial_value="1.9008e-8" name="moo1" units="dimensionless"/>
<variable name="r1" units="mm" interface="public"/>
<variable name="r21" units="mm" interface="public"/>
<variable name="r22" units="mm" interface="public"/>
<variable initial_value="1.8778" name="Lr1" units="mm"/>
<variable initial_value="1.7" name="Lr21" units="mm"/>
<variable initial_value="1.7" name="Lr22" units="mm"/>
<variable initial_value="-50" name="qhat" units="dimensionless"/>
<variable name="p" units="mmHg" interface="public"/>
<variable name="pbot" units="mmHg" interface="public"/>
<variable name="Pmin_r1" units="mmHg" interface="public"/>
<variable name="lambda" units="mm3" interface="public"/>
<variable name="temp" units="mm3" interface="public"/>
<variable name="ar1" units="mm"/>
<variable name="ar21" units="mm"/>
<variable name="ar22" units="mm"/>
<variable name="W" units="mm3" interface="public"/>
<variable name="Lambda" units="mm3" interface="public"/>
<variable name="q1p" units="dimensionless" interface="public"/>
<variable name="q21" units="dimensionless" interface="public"/>
<variable name="q22" units="dimensionless" interface="public"/>
<variable name="del_pr1" units="mmHg"/>
<variable name="del_pr21" units="mmHg"/>
<variable name="del_pr22" units="mmHg"/>
<variable name="mu_r21" units="dimensionless"/>
<variable name="mu_r22" units="dimensionless"/>
<variable name="mu_r1" units="dimensionless"/>
<variable initial_value="5E1" name="A" units="dimensionless"/>
<variable name="ptop" units="mmHg"/>
<variable name="tau_r1" units="dimensionless" interface="public"/>
<variable name="tau_r21" units="dimensionless" interface="public"/>
<variable name="tau_r22" units="dimensionless" interface="public"/>
<variable initial_value="0.445" name="R_ref" units="mm"/>
<variable name="pmidr1" units="mmHg" interface="public"/>
<variable name="pmidr21" units="mmHg" interface="public"/>
<variable name="pmidr22" units="mmHg" interface="public"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>ptop</ci>
<ci>Pmin_r1</ci>
</apply>
<apply>
<eq/>
<ci>ar1</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">8</cn>
<ci>aa</ci>
<ci>moo1</ci>
<ci>Lr1</ci>
</apply>
<pi/>
</apply>
</apply>
<apply>
<eq/>
<ci>ar21</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">8</cn>
<ci>aa</ci>
<ci>moo1</ci>
<ci>Lr21</ci>
</apply>
<pi/>
</apply>
</apply>
<apply>
<eq/>
<ci>ar22</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">8</cn>
<ci>aa</ci>
<ci>moo1</ci>
<ci>Lr22</ci>
</apply>
<pi/>
</apply>
</apply>
<apply>
<eq/>
<ci>lambda</ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<power/>
<ci>r21</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>ar21</ci>
</apply>
<apply>
<divide/>
<apply>
<power/>
<ci>r22</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>ar22</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Da1</ci>
<apply>
<divide/>
<apply>
<power/>
<ci>r1</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>ar1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Da21</ci>
<apply>
<divide/>
<apply>
<power/>
<ci>r21</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>ar21</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Da22</ci>
<apply>
<divide/>
<apply>
<power/>
<ci>r22</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>ar22</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>W</ci>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>Da1</ci>
</apply>
<ci>Da21</ci>
</apply>
<ci>Da22</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>temp</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<apply>
<power/>
<ci>Da21</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<apply>
<power/>
<ci>Da22</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci>W</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<ci>lambda</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Lambda</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>temp</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>p</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<ci>Da21</ci>
<ci>Da22</ci>
</apply>
<ci>qhat</ci>
</apply>
<ci>lambda</ci>
</apply>
<apply>
<times/>
<ci>ptop</ci>
<ci>Da1</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>W</ci>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>Lambda</ci>
</apply>
</apply>
<!--*pow(W, -1{dimensionless})*pow(Lambda, -1{dimensionless});-->
<apply>
<eq/>
<ci>pbot</ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>lambda</ci>
<ci>p</ci>
</apply>
<ci>qhat</ci>
</apply>
<ci>lambda</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q1p</ci>
<apply>
<minus/>
<ci>ptop</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<power/>
<ci>r1</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>ar1</ci>
</apply>
<ci>p</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>q21</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<power/>
<ci>r21</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>ar21</ci>
</apply>
<ci>p</ci>
</apply>
<ci>pbot</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q22</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<power/>
<ci>r22</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>ar22</ci>
</apply>
<ci>p</ci>
</apply>
<ci>pbot</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>del_pr1</ci>
<apply>
<minus/>
<ci>ptop</ci>
<ci>p</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>del_pr21</ci>
<apply>
<minus/>
<ci>p</ci>
<ci>pbot</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>del_pr22</ci>
<apply>
<minus/>
<ci>p</ci>
<ci>pbot</ci>
</apply>
</apply>
<!-- For parenchymal tethering-->
<apply>
<eq/>
<ci>mu_r21</ci>
<apply>
<divide/>
<apply>
<abs/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<divide/>
<ci>A</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>del_pr21</ci>
<apply>
<power/>
<ci>r21</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
<apply>
<times/>
<ci>del_pr22</ci>
<apply>
<power/>
<ci>r22</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_r22</ci>
<apply>
<divide/>
<apply>
<abs/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<divide/>
<ci>A</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>del_pr22</ci>
<apply>
<power/>
<ci>r22</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
<apply>
<times/>
<ci>del_pr21</ci>
<apply>
<power/>
<ci>r21</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_r1</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.5</cn>
<ci>mu_r21</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.5</cn>
<ci>mu_r22</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_r1</ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>mu_r1</ci>
<apply>
<minus/>
<ci>R_ref</ci>
<ci>r1</ci>
</apply>
</apply>
<ci>R_ref</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">1.5</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<minus/>
<ci>R_ref</ci>
<ci>r1</ci>
</apply>
<ci>R_ref</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_r21</ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>mu_r21</ci>
<apply>
<minus/>
<ci>R_ref</ci>
<ci>r21</ci>
</apply>
</apply>
<ci>R_ref</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">1.5</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<minus/>
<ci>R_ref</ci>
<ci>r21</ci>
</apply>
<ci>R_ref</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_r22</ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>mu_r22</ci>
<apply>
<minus/>
<ci>R_ref</ci>
<ci>r22</ci>
</apply>
</apply>
<ci>R_ref</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">1.5</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<minus/>
<ci>R_ref</ci>
<ci>r22</ci>
</apply>
<ci>R_ref</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>pmidr1</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.5</cn>
<apply>
<plus/>
<ci>ptop</ci>
<ci>p</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>pmidr21</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.5</cn>
<apply>
<plus/>
<ci>pbot</ci>
<ci>p</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>pmidr22</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.5</cn>
<apply>
<plus/>
<ci>pbot</ci>
<ci>p</ci>
</apply>
</apply>
</apply>
</math>
</component>
</model>