Location: 12 L Platform 1 model codes @ a8a92308e217 / peripheral_airway / airway_order3.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/airway_order3.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="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>
<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>
<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="Params">
<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="1.8778" name="l" units="mm"/>
<variable initial_value="0.0017424" name="Ri_sq_r1" public_interface="out" units="mm2"/>
<variable initial_value="0.0012769" name="Ri_sq_r1_airway1" public_interface="out" units="mm2"/>
<variable initial_value="0.171396" name="rmax_sq_r1_airway1" public_interface="out" units="mm"/>
<variable initial_value="0.198025" name="rmax_sq_r1" public_interface="out" units="mm"/>
<variable initial_value="1" name="N1_r1" public_interface="out" units="dimensionless"/>
<variable initial_value="8" name="N2_r1" public_interface="out" units="dimensionless"/>
<variable initial_value="39.429" name="P1_r1" public_interface="out" units="pascal"/>
<variable initial_value="-3269.475128" name="P2_r1" public_interface="out" units="pascal"/>
<variable initial_value="32.205" name="P1_r1_airway1" public_interface="out" units="pascal"/>
<variable initial_value="-3200.615575" name="P2_r1_airway1" public_interface="out" units="pascal"/>
<variable initial_value="1" name="rho1" public_interface="out" units="dimensionless"/>
<variable initial_value="0.9732" name="h1_airway" units="mm"/>
<variable initial_value="0.445" name="R_ref_airway" units="mm"/>
<variable initial_value="1.0873" name="h1_airway1" units="mm"/>
<variable initial_value="0.414" name="R_ref_airway1" units="mm"/>
</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 name="mu" public_interface="in" units="Pas"/>
<variable name="rho" public_interface="in" units="kg_per_m3"/>
<variable name="E" public_interface="in" units="J_per_m3"/>
<variable name="v_out_1" public_interface="in" units="m3_per_s"/>
<variable name="v_out_2" public_interface="in" units="m3_per_s"/>
<variable initial_value="1.0e-6" 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 name="l" public_interface="in" units="mm"/>
<variable name="time" public_interface="in" units="second"/>
<variable initial_value="0.445" name="r1" public_interface="out" units="mm"/>
<variable name="Ri_sq_r1" public_interface="in" units="mm2"/>
<variable name="rmax_sq_r1" public_interface="in" units="mm"/>
<variable name="N1_r1" public_interface="in" units="dimensionless"/>
<variable name="N2_r1" public_interface="in" units="dimensionless"/>
<variable name="P1_r1" public_interface="in" units="pascal"/>
<variable name="P2_r1" public_interface="in" units="pascal"/>
<variable name="rho1" public_interface="in" units="dimensionless"/>
<variable name="rad_r1" public_interface="out" units="mm"/>
<variable initial_value="0.445" 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 name="h1" public_interface="in" units="mm"/>
<variable name="R_ref" public_interface="in" units="mm"/>
<variable name="v_conc" public_interface="out" units="mol_per_s"/>
<variable name="v_conc_out_1" public_interface="in" units="mol_per_s"/>
<variable name="v_conc_out_2" public_interface="in" units="mol_per_s"/>
<variable initial_value="1" name="q_in" units="mole"/>
<variable initial_value="0" name="q" public_interface="out" units="mole"/>
<variable name="tau_r1" units="pascal"/>
<variable initial_value="5e2" name="mu_r1" units="pascal"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>u_in</ci>
<apply>
<plus/>
<cn cellml:units="pascal">1000</cn>
<apply>
<times/>
<cn cellml:units="pascal">1000</cn>
<apply>
<sin/>
<apply>
<times/>
<cn cellml:units="per_s">1.5</cn>
<ci>time</ci>
</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>tau_r1</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>mu_r1</ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<minus/>
<ci>R_ref</ci>
<ci>r1</ci>
</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>
<!-- V_r1 = -gamma/(2{dimensionless}*pi*rmax_r1)*rho*(rad_r1-r1)*v_smc_r1;-->
<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">8</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>
<apply>
<eq/>
<ci>u</ci>
<apply>
<plus/>
<ci>u_v</ci>
<apply>
<times/>
<ci>R_v</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>v</ci>
<ci>v_out_1</ci>
</apply>
<ci>v_out_2</ci>
</apply>
</apply>
</apply>
</apply>
<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/>
<ci>R</ci>
<ci>v</ci>
</apply>
</apply>
<ci>I</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>u_v</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>v</ci>
<ci>v_out_1</ci>
</apply>
<ci>v_out_2</ci>
</apply>
<ci>C</ci>
</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>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>v_conc</ci>
<ci>v_conc_out_1</ci>
</apply>
<ci>v_conc_out_2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_conc</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>v</ci>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r1</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>l</ci>
</apply>
</apply>
<apply>
<minus/>
<ci>q_in</ci>
<ci>q</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="airway1">
<variable name="u" public_interface="out" units="pascal"/>
<variable name="u_in" public_interface="in" units="pascal"/>
<variable initial_value="0" name="u_v" units="pascal"/>
<variable name="mu" public_interface="in" units="Pas"/>
<variable name="rho" public_interface="in" units="kg_per_m3"/>
<variable name="E" public_interface="in" units="J_per_m3"/>
<variable initial_value="1.0e-6" name="v_out" units="m3_per_s"/>
<variable initial_value="1.0e-6" 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 name="l" public_interface="in" units="mm"/>
<variable name="time" public_interface="in" units="second"/>
<variable initial_value="0.414" name="r1" public_interface="out" units="mm"/>
<variable name="Ri_sq_r1" public_interface="in" units="mm2"/>
<variable name="rmax_sq_r1" public_interface="in" units="mm"/>
<variable name="N1_r1" public_interface="in" units="dimensionless"/>
<variable name="N2_r1" public_interface="in" units="dimensionless"/>
<variable name="P1_r1" public_interface="in" units="pascal"/>
<variable name="P2_r1" public_interface="in" units="pascal"/>
<variable name="rho1" public_interface="in" units="dimensionless"/>
<variable name="rad_r1" public_interface="out" units="mm"/>
<variable initial_value="0.414" 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 name="h1" public_interface="in" units="mm"/>
<variable name="R_ref" public_interface="in" units="mm"/>
<variable name="q_in" public_interface="in" units="mole"/>
<variable initial_value="0" name="q" public_interface="out" units="mole"/>
<variable initial_value="0.0" name="v_conc_out" units="mol_per_s"/>
<variable name="v_conc" public_interface="out" units="mol_per_s"/>
<variable initial_value="5e2" name="mu_r1" units="pascal"/>
<variable name="tau_r1" units="pascal"/>
<!-- u_in = 1000{pascal}+1000{pascal}*sin(5{per_s}*time);-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<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>tau_r1</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>mu_r1</ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<minus/>
<ci>R_ref</ci>
<ci>r1</ci>
</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>
<!-- V_r1 = -gamma/(2{dimensionless}*pi*rmax_r1)*rho*(rad_r1-r1)*v_smc_r1;-->
<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">8</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>
<apply>
<eq/>
<ci>u</ci>
<apply>
<plus/>
<ci>u_v</ci>
<apply>
<times/>
<ci>R_v</ci>
<apply>
<minus/>
<ci>v</ci>
<ci>v_out</ci>
</apply>
</apply>
</apply>
</apply>
<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/>
<ci>R</ci>
<ci>v</ci>
</apply>
</apply>
<ci>I</ci>
</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_out</ci>
</apply>
<ci>C</ci>
</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>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q</ci>
</apply>
<apply>
<minus/>
<ci>v_conc</ci>
<ci>v_conc_out</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_conc</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>v</ci>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r1</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>l</ci>
</apply>
</apply>
<apply>
<minus/>
<ci>q_in</ci>
<ci>q</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="airway2">
<variable name="u" public_interface="out" units="pascal"/>
<variable name="u_in" public_interface="in" units="pascal"/>
<variable initial_value="0" name="u_v" units="pascal"/>
<variable name="mu" public_interface="in" units="Pas"/>
<variable name="rho" public_interface="in" units="kg_per_m3"/>
<variable name="E" public_interface="in" units="J_per_m3"/>
<variable initial_value="1.0e-6" name="v_out" units="m3_per_s"/>
<variable initial_value="1.0e-6" 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 name="l" public_interface="in" units="mm"/>
<variable name="time" public_interface="in" units="second"/>
<variable initial_value="0.40" name="r1" public_interface="out" units="mm"/>
<variable name="Ri_sq_r1" public_interface="in" units="mm2"/>
<variable name="rmax_sq_r1" public_interface="in" units="mm"/>
<variable name="N1_r1" public_interface="in" units="dimensionless"/>
<variable name="N2_r1" public_interface="in" units="dimensionless"/>
<variable name="P1_r1" public_interface="in" units="pascal"/>
<variable name="P2_r1" public_interface="in" units="pascal"/>
<variable name="rho1" public_interface="in" units="dimensionless"/>
<variable name="rad_r1" public_interface="out" units="mm"/>
<variable initial_value="0.414" 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 name="h1" public_interface="in" units="mm"/>
<variable name="R_ref" public_interface="in" units="mm"/>
<variable name="q_in" public_interface="in" units="mole"/>
<variable initial_value="0" name="q" public_interface="out" units="mole"/>
<variable initial_value="0.0" name="v_conc_out" units="mol_per_s"/>
<variable name="v_conc" public_interface="out" units="mol_per_s"/>
<variable initial_value="5e2" name="mu_r1" units="pascal"/>
<variable name="tau_r1" units="pascal"/>
<!-- u_in = 1000{pascal}+1000{pascal}*sin(5{per_s}*time);-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<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>tau_r1</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>mu_r1</ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<minus/>
<ci>R_ref</ci>
<ci>r1</ci>
</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>
<!-- V_r1 = -gamma/(2{dimensionless}*pi*rmax_r1)*rho*(rad_r1-r1)*v_smc_r1;-->
<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">8</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>
<apply>
<eq/>
<ci>u</ci>
<apply>
<plus/>
<ci>u_v</ci>
<apply>
<times/>
<ci>R_v</ci>
<apply>
<minus/>
<ci>v</ci>
<ci>v_out</ci>
</apply>
</apply>
</apply>
</apply>
<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/>
<ci>R</ci>
<ci>v</ci>
</apply>
</apply>
<ci>I</ci>
</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_out</ci>
</apply>
<ci>C</ci>
</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>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q</ci>
</apply>
<apply>
<minus/>
<ci>v_conc</ci>
<ci>v_conc_out</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_conc</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>v</ci>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r1</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>l</ci>
</apply>
</apply>
<apply>
<minus/>
<ci>q_in</ci>
<ci>q</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="main" component_2="airway1"/>
<map_variables variable_1="f_a_r1" variable_2="f_a_r1"/>
</connection>
<connection>
<map_components component_1="main" component_2="airway2"/>
<map_variables variable_1="f_a_r1" variable_2="f_a_r1"/>
</connection>
<connection>
<map_components component_1="airway1" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="airway" component_2="airway1"/>
<map_variables variable_1="v_out_1" variable_2="v"/>
<map_variables variable_1="u" variable_2="u_in"/>
<map_variables variable_1="q" variable_2="q_in"/>
<map_variables variable_1="v_conc_out_1" variable_2="v_conc"/>
</connection>
<connection>
<map_components component_1="airway" component_2="airway2"/>
<map_variables variable_1="v_out_2" variable_2="v"/>
<map_variables variable_1="u" variable_2="u_in"/>
<map_variables variable_1="q" variable_2="q_in"/>
<map_variables variable_1="v_conc_out_2" variable_2="v_conc"/>
</connection>
<connection>
<map_components component_1="airway" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="airway2" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Params" component_2="airway"/>
<map_variables variable_1="mu" variable_2="mu"/>
<map_variables variable_1="rho" variable_2="rho"/>
<map_variables variable_1="E" variable_2="E"/>
<map_variables variable_1="l" variable_2="l"/>
<map_variables variable_1="Ri_sq_r1" variable_2="Ri_sq_r1"/>
<map_variables variable_1="rmax_sq_r1" variable_2="rmax_sq_r1"/>
<map_variables variable_1="N1_r1" variable_2="N1_r1"/>
<map_variables variable_1="N2_r1" variable_2="N2_r1"/>
<map_variables variable_1="P1_r1" variable_2="P1_r1"/>
<map_variables variable_1="P2_r1" variable_2="P2_r1"/>
<map_variables variable_1="rho1" variable_2="rho1"/>
<map_variables variable_1="h1_airway" variable_2="h1"/>
<map_variables variable_1="R_ref_airway" variable_2="R_ref"/>
</connection>
<connection>
<map_components component_1="Params" component_2="airway1"/>
<map_variables variable_1="mu" variable_2="mu"/>
<map_variables variable_1="rho" variable_2="rho"/>
<map_variables variable_1="E" variable_2="E"/>
<map_variables variable_1="l" variable_2="l"/>
<map_variables variable_1="Ri_sq_r1_airway1" variable_2="Ri_sq_r1"/>
<map_variables variable_1="rmax_sq_r1_airway1" variable_2="rmax_sq_r1"/>
<map_variables variable_1="N1_r1" variable_2="N1_r1"/>
<map_variables variable_1="N2_r1" variable_2="N2_r1"/>
<map_variables variable_1="P1_r1_airway1" variable_2="P1_r1"/>
<map_variables variable_1="P2_r1_airway1" variable_2="P2_r1"/>
<map_variables variable_1="rho1" variable_2="rho1"/>
<map_variables variable_1="h1_airway" variable_2="h1"/>
<map_variables variable_1="R_ref_airway1" variable_2="R_ref"/>
</connection>
<connection>
<map_components component_1="Params" component_2="airway2"/>
<map_variables variable_1="mu" variable_2="mu"/>
<map_variables variable_1="rho" variable_2="rho"/>
<map_variables variable_1="E" variable_2="E"/>
<map_variables variable_1="l" variable_2="l"/>
<map_variables variable_1="Ri_sq_r1_airway1" variable_2="Ri_sq_r1"/>
<map_variables variable_1="rmax_sq_r1_airway1" variable_2="rmax_sq_r1"/>
<map_variables variable_1="N1_r1" variable_2="N1_r1"/>
<map_variables variable_1="N2_r1" variable_2="N2_r1"/>
<map_variables variable_1="P1_r1_airway1" variable_2="P1_r1"/>
<map_variables variable_1="P2_r1_airway1" variable_2="P2_r1"/>
<map_variables variable_1="rho1" variable_2="rho1"/>
<map_variables variable_1="h1_airway" variable_2="h1"/>
<map_variables variable_1="R_ref_airway1" variable_2="R_ref"/>
</connection>
<connection>
<map_components component_1="main" component_2="stress"/>
<map_variables variable_1="stress" variable_2="stress"/>
</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>
</model>