Location: 12 L Platform 1 model codes @ 4c1ab73f48d7 / peripheral_airway / Isolated_airway / iso_airway.cellml
- Author:
- aram148 <a.rampadarath@auckland.ac.nz>
- Date:
- 2021-11-04 16:02:42+13:00
- Desc:
- Updated USMC-Bursztyn model
- Permanent Source URI:
- http://models.cellml.org/workspace/6b0/rawfile/4c1ab73f48d7150c2094cf8017425482a1594ccf/peripheral_airway/Isolated_airway/iso_airway.cellml
<?xml version='1.0' encoding='UTF-8'?>
<model name="iso_airway" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#" xmlns:xlink="http://www.w3.org/1999/xlink">
<component name="environment">
<variable name="time" public_interface="out" units="second"/>
</component>
<units name="Pas">
<unit units="pascal"/>
<unit units="second"/>
</units>
<units name="per_s">
<unit exponent="-1" units="second"/>
</units>
<units name="Js_per_m6">
<unit units="joule"/>
<unit units="second"/>
<unit exponent="-6" units="metre"/>
</units>
<units name="m6_per_J">
<unit exponent="6" units="metre"/>
<unit exponent="-1" units="joule"/>
</units>
<units name="kg_per_m3">
<unit prefix="kilo" units="gram"/>
<unit exponent="-3" units="meter"/>
</units>
<units name="J_per_m3">
<unit units="joule"/>
<unit exponent="-3" units="metre"/>
</units>
<units name="mol_per_s">
<unit units="mole"/>
<unit exponent="-1" units="second"/>
</units>
<units name="Js2_per_m6">
<unit units="joule"/>
<unit exponent="2" units="second"/>
<unit exponent="-6" units="metre"/>
</units>
<units name="Pa_mm">
<unit units="pascal"/>
<unit prefix="milli" units="metre"/>
</units>
<units name="mm">
<unit prefix="milli" units="meter"/>
</units>
<units name="mm2">
<unit exponent="2" units="mm"/>
</units>
<units name="per_m">
<unit exponent="-1" units="metre"/>
</units>
<units name="m3_per_s">
<unit exponent="3" units="metre"/>
<unit exponent="-1" units="second"/>
</units>
<units name="mL">
<unit prefix="milli" units="litre"/>
</units>
<import xlink:href="hai1.cellml">
<component component_ref="stress" name="stress"/>
<component component_ref="AMp" name="AMp"/>
<component component_ref="AM" name="AM"/>
<component component_ref="Mp" name="Mp"/>
<component component_ref="M" name="M"/>
<component component_ref="model_parameters" name="model_parameters"/>
</import>
<component name="main">
<variable name="stress" public_interface="in" units="dimensionless"/>
<variable initial_value="100" name="kappa" units="Pa_mm"/>
<variable name="f_a_r1" public_interface="out" units="Pa_mm"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>f_a_r1</ci>
<apply>
<times/>
<ci>kappa</ci>
<ci>stress</ci>
</apply>
</apply>
</math>
</component>
<component name="airway">
<variable name="u" public_interface="out" units="pascal"/>
<variable name="u_in" units="pascal"/>
<variable initial_value="0" name="u_v" public_interface="out" units="pascal"/>
<variable initial_value="1.81e-5" name="mu" units="Pas"/>
<variable initial_value="1.225" name="rho" units="kg_per_m3"/>
<variable initial_value="0.35e6" name="E" units="J_per_m3"/>
<variable initial_value="0" name="v" public_interface="out" units="m3_per_s"/>
<variable name="R" units="Js_per_m6"/>
<variable name="R_v" units="Js_per_m6"/>
<variable name="C" units="m6_per_J"/>
<variable name="I" units="Js2_per_m6"/>
<variable initial_value="1.8778" name="l" units="mm"/>
<variable name="time" public_interface="in" units="second"/>
<variable initial_value="0.318" name="r1" public_interface="out" units="mm"/>
<variable initial_value="0.004225" name="Ri_sq_r1" public_interface="out" units="mm2"/>
<variable initial_value="0.1011" name="rmax_sq_r1" public_interface="out" units="mm"/>
<variable initial_value="1" name="N1_r1" public_interface="out" units="dimensionless"/>
<variable initial_value="7" name="N2_r1" public_interface="out" units="dimensionless"/>
<variable initial_value="17.342" name="P1_r1" public_interface="out" units="pascal"/>
<variable initial_value="-2784.131883" name="P2_r1" public_interface="out" units="pascal"/>
<variable initial_value="1" name="rho1" public_interface="out" units="dimensionless"/>
<variable name="rad_r1" public_interface="out" units="mm"/>
<variable initial_value="0.318" name="rmax_r1" units="mm"/>
<variable initial_value="25" name="gamma" units="dimensionless"/>
<variable name="f_a_r1" public_interface="in" units="Pa_mm"/>
<variable name="Ptm_r1" units="pascal"/>
<variable initial_value="0.9732" name="h1" units="mm"/>
<variable initial_value="0.318" name="R_ref" units="mm"/>
<variable name="tau_r1" units="pascal"/>
<variable initial_value="5e2" name="mu_r1" units="pascal"/>
<variable initial_value="0.0" name="v_d" public_interface="out" units="m3_per_s"/>
<variable name="u_out" units="J_per_m3"/>
<variable initial_value="0.33" name="freq" units="per_s"/>
<variable initial_value="490.3" name="P_bar" units="pascal"/>
<variable initial_value="490" name="Paw_bar" units="pascal"/>
<variable initial_value="25000" name="E1" units="J_per_m3"/>
<variable name="PA_bar" units="pascal"/>
<variable name="alpha" units="second"/>
<variable name="omega" units="dimensionless"/>
<variable initial_value="0.1" name="V_tlc" units="mL"/>
<variable name="v1" units="dimensionless"/>
<variable name="x" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>omega</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<pi/>
<ci>freq</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_in</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>E1</ci>
</apply>
<apply>
<root/>
<apply>
<plus/>
<apply>
<power/>
<ci>E1</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<apply>
<times/>
<ci>omega</ci>
<ci>R</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>R</ci>
</apply>
<ci>E1</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_out</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>v1</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.2</cn>
<ci>V_tlc</ci>
</apply>
<apply>
<divide/>
<ci>u_out</ci>
<ci>E1</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>r1</ci>
<apply>
<power/>
<ci>v1</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_r1</ci>
<apply>
<plus/>
<ci>u_out</ci>
<apply>
<times/>
<ci>u_out</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">1.4</cn>
<ci>x</ci>
</apply>
<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_r1</ci>
<apply>
<plus/>
<apply>
<minus/>
<ci>u_in</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>f_a_r1</ci>
<ci>R_ref</ci>
</apply>
<ci>r1</ci>
</apply>
</apply>
<ci>tau_r1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>rad_r1</ci>
<piecewise>
<piece>
<apply>
<root/>
<apply>
<times/>
<ci>Ri_sq_r1</ci>
<apply>
<power/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Ptm_r1</ci>
<ci>P1_r1</ci>
</apply>
</apply>
<apply>
<minus/>
<ci>N1_r1</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<leq/>
<ci>Ptm_r1</ci>
<cn cellml:units="dimensionless">0</cn>
</apply>
</piece>
<piece>
<apply>
<root/>
<apply>
<minus/>
<ci>rmax_sq_r1</ci>
<apply>
<times/>
<apply>
<minus/>
<ci>rmax_sq_r1</ci>
<ci>Ri_sq_r1</ci>
</apply>
<apply>
<power/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Ptm_r1</ci>
<ci>P2_r1</ci>
</apply>
</apply>
<apply>
<minus/>
<ci>N2_r1</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<geq/>
<ci>Ptm_r1</ci>
<cn cellml:units="dimensionless">0</cn>
</apply>
</piece>
</piecewise>
</apply>
<apply>
<eq/>
<ci>I</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>rho</ci>
<ci>l</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r1</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>C</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<pi/>
<apply>
<power/>
<ci>r1</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>l</ci>
</apply>
<apply>
<times/>
<ci>E</ci>
<ci>h1</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">12</cn>
<ci>mu</ci>
<ci>l</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r1</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R_v</ci>
<apply>
<divide/>
<cn cellml:units="second">0.01</cn>
<ci>C</ci>
</apply>
</apply>
<!-- pp type-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>v</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>u_in</ci>
<ci>u</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci>R</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>v</ci>
</apply>
</apply>
<apply>
<divide/>
<ci>I</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>u_v</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>v</ci>
<ci>v_d</ci>
</apply>
<ci>C</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u</ci>
<apply>
<plus/>
<ci>u_v</ci>
<apply>
<times/>
<ci>R_v</ci>
<apply>
<minus/>
<ci>v</ci>
<ci>v_d</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>v_d</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>u</ci>
<ci>u_out</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci>R</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>v_d</ci>
</apply>
</apply>
<apply>
<divide/>
<ci>I</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>r1</ci>
</apply>
<apply>
<times/>
<ci>rho1</ci>
<apply>
<minus/>
<ci>rad_r1</ci>
<ci>r1</ci>
</apply>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="main" component_2="airway"/>
<map_variables variable_1="f_a_r1" variable_2="f_a_r1"/>
</connection>
<connection>
<map_components component_1="airway" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="AMp"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="AM"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="Mp"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="M"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="model_parameters"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="main" component_2="stress"/>
<map_variables variable_1="stress" variable_2="stress"/>
</connection>
</model>