Location: 12 L Platform 1 model codes @ a8a92308e217 / peripheral_airway / Isolated_airway / anafi.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/peripheral_airway/Isolated_airway/anafi.cellml
<?xml version='1.0' encoding='UTF-8'?>
<model name="anafi_wilsom" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
<units name="mm">
<unit prefix="milli" units="meter"/>
</units>
<units name="Pas">
<unit units="pascal"/>
<unit units="second"/>
</units>
<units name="Js_per_m6">
<unit units="joule"/>
<unit units="second"/>
<unit exponent="-6" units="metre"/>
</units>
<units name="per_s">
<unit exponent="-1" units="second"/>
</units>
<units name="J_per_m3">
<unit units="joule"/>
<unit exponent="-3" units="metre"/>
</units>
<units name="mL">
<unit prefix="milli" units="litre"/>
</units>
<component name="environment">
<variable initial_value="0" name="time" public_interface="out" units="second"/>
</component>
<component name="anafi">
<variable name="time" public_interface="in" units="second"/>
<variable initial_value="0.27" name="r0" units="mm"/>
<variable initial_value="0.5" name="p_m" units="dimensionless"/>
<variable name="p_i" units="dimensionless"/>
<variable name="ri" units="mm"/>
<variable name="rm" units="mm"/>
<variable initial_value="0.16" name="f" units="dimensionless"/>
<variable initial_value="1.81e-5" name="mu" units="Pas"/>
<variable initial_value="3" name="l" units="mm"/>
<variable name="Raw" units="Js_per_m6"/>
<variable name="Paw" units="pascal"/>
<variable initial_value="490.3" name="P_bar" units="pascal"/>
<variable initial_value="490" name="Paw_bar" units="pascal"/>
<variable initial_value="0.33" name="freq" units="per_s"/>
<variable name="omega" units="dimensionless"/>
<variable initial_value="25000" name="E" units="J_per_m3"/>
<variable name="PA" units="pascal"/>
<variable name="PA_bar" units="pascal"/>
<variable name="alpha" units="second"/>
<variable name="Ptm" units="pascal"/>
<variable name="tau" units="pascal"/>
<variable name="P_lumen" units="pascal"/>
<variable initial_value="0.1" name="V_tlc" units="mL"/>
<variable name="v" units="dimensionless"/>
<variable name="x" units="dimensionless"/>
<variable initial_value="1" name="w" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>p_i</ci>
<apply>
<root/>
<apply>
<minus/>
<apply>
<power/>
<ci>p_m</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>f</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Raw</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">12</cn>
<ci>l</ci>
<ci>mu</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<apply>
<times/>
<ci>r0</ci>
<ci>p_i</ci>
</apply>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>omega</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<pi/>
<ci>freq</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Paw</ci>
<apply>
<plus/>
<ci>P_bar</ci>
<apply>
<times/>
<ci>Paw_bar</ci>
<apply>
<sin/>
<apply>
<times/>
<ci>omega</ci>
<ci>time</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>PA_bar</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>Paw_bar</ci>
<ci>E</ci>
</apply>
<apply>
<root/>
<apply>
<plus/>
<apply>
<power/>
<ci>E</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<apply>
<times/>
<ci>omega</ci>
<ci>Raw</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha</ci>
<apply>
<arctan/>
<apply>
<divide/>
<apply>
<times/>
<ci>omega</ci>
<ci>Raw</ci>
</apply>
<ci>E</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>PA</ci>
<apply>
<plus/>
<ci>P_bar</ci>
<apply>
<times/>
<ci>PA_bar</ci>
<apply>
<sin/>
<apply>
<minus/>
<apply>
<times/>
<ci>omega</ci>
<ci>time</ci>
</apply>
<ci>alpha</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>P_lumen</ci>
<apply>
<divide/>
<apply>
<plus/>
<ci>Paw</ci>
<ci>PA</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>v</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.2</cn>
<ci>V_tlc</ci>
</apply>
<apply>
<divide/>
<ci>PA</ci>
<ci>E</ci>
</apply>
</apply>
<ci>V_tlc</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>x</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>p_m</ci>
<apply>
<power/>
<ci>v</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau</ci>
<apply>
<plus/>
<ci>PA</ci>
<apply>
<times/>
<ci>PA</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1.4</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">2.1</cn>
<apply>
<power/>
<ci>x</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ptm</ci>
<apply>
<plus/>
<apply>
<minus/>
<ci>P_lumen</ci>
<ci>PA</ci>
</apply>
<ci>tau</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>ri</ci>
<apply>
<times/>
<ci>p_i</ci>
<ci>r0</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>rm</ci>
<apply>
<times/>
<ci>p_m</ci>
<ci>r0</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>w</ci>
</apply>
<cn cellml:units="dimensionless">0</cn>
</apply>
</math>
</component>
<connection>
<map_components component_1="environment" component_2="anafi"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
</model>