Location: 12 L Platform 1 model codes @ a8a92308e217 / peripheral_airway / Updated_O3 / peripherl_airways.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/Updated_O3/peripherl_airways.cellml
<?xml version='1.0'?>
<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="meter_sq">
<unit exponent="2" units="meter"/>
</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>
<!-- def import using "uv_type.cellml" for
comp uv_type using comp uv_type;
enddef;-->
<!-- def comp main as
var stress: dimensionless {pub: in};
var kappa: Pa_mm {init: 100};
var f_a_r1: Pa_mm {pub: out};
var r_parent: mm {pub: in};
var v: m3_per_s {pub: in};-->
<!-- // var tau: pascal {pub: in};-->
<!-- f_a_r1 = kappa*stress;
enddef;-->
<component name="airway">
<variable name="u" public_interface="out" units="pascal"/>
<variable name="u_in" public_interface="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="0.0017" name="l" units="meter"/>
<variable name="time" public_interface="in" units="second"/>
<variable initial_value="0.000208" name="r1" public_interface="out" units="meter"/>
<variable initial_value="3.364E-09" name="Ri_sq_r1" public_interface="out" units="meter_sq"/>
<variable initial_value="8.7616E-08" name="rmax_sq_r1" public_interface="out" units="meter_sq"/>
<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="15.728" name="P1_r1" public_interface="out" units="pascal"/>
<variable initial_value="-2757.374611" 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="meter"/>
<variable initial_value="0.000296" name="rmax_r1" units="meter"/>
<variable initial_value="25" name="gamma" units="dimensionless"/>
<variable name="f_a_r1" public_interface="in" units="pascal"/>
<variable name="Ptm_r1" public_interface="out" units="pascal"/>
<variable initial_value="0.0010873" name="h1" units="meter"/>
<variable initial_value="0.0002792" name="R_ref" units="meter"/>
<variable name="tau_r1" units="pascal"/>
<variable initial_value="0" name="v_d" public_interface="out" units="m3_per_s"/>
<variable name="u_out" public_interface="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="0.25" 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="0.0001" name="V_tlc" units="litre"/>
<variable name="v1" public_interface="out" units="dimensionless"/>
<variable name="x" units="dimensionless"/>
<!-- var qr: mole {pub: out};-->
<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>
<!-- u_in = P_bar+Paw_bar*sin(omega*time);-->
<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>
<!-- tau_r1 = 1.4{dimensionless}*Ptm_r1*((R_ref-r1)/R_ref + 1.5{dimensionless}*sqr((R_ref-r1)/R_ref));
tau_r1 = u_out+u_out*(1.4{dimensionless}*(R_ref-r1)/R_ref+2.1{dimensionless}*sqr((R_ref-r1)/R_ref));-->
<apply>
<eq/>
<ci>Ptm_r1</ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci>u_in</ci>
<ci>u_out</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>u_out</ci>
</apply>
<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">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>
<!-- 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>
<!-- qr = 1{dimensionless}*u/R-u_out;-->
</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" 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="0.0017" name="l" units="meter"/>
<variable name="time" public_interface="in" units="second"/>
<variable initial_value="0.000208" name="r1" public_interface="out" units="meter"/>
<variable initial_value="3.364e-9" name="Ri_sq_r1" public_interface="out" units="meter_sq"/>
<variable initial_value="8.7616e-8" name="rmax_sq_r1" public_interface="out" units="meter_sq"/>
<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="15.728" name="P1_r1" public_interface="out" units="pascal"/>
<variable initial_value="-2757.374611" 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="meter"/>
<variable initial_value="0.000296" name="rmax_r1" units="meter"/>
<variable initial_value="25" name="gamma" units="dimensionless"/>
<variable name="f_a_r1" public_interface="in" units="pascal"/>
<variable name="Ptm_r1" public_interface="out" units="pascal"/>
<variable initial_value="0.0010873" name="h1" units="meter"/>
<variable initial_value="0.0002792" name="R_ref" units="meter"/>
<variable name="tau_r1" public_interface="out" units="pascal"/>
<variable initial_value="0" name="v_d" public_interface="out" units="m3_per_s"/>
<variable name="u_out" public_interface="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="0.25" 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="0.0001" name="V_tlc" units="litre"/>
<variable name="v1" public_interface="out" units="dimensionless"/>
<variable name="x" units="dimensionless"/>
<!-- var qr: mole {pub: in};-->
<!-- var qr1: mole;
var qp: mole {pub: in};-->
<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>
<!-- u_in = P_bar+Paw_bar*sin(omega*time);-->
<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>
<!-- tau_r1 = 1.4{dimensionless}*Ptm_r1*((R_ref-r1)/R_ref + 1.5{dimensionless}*sqr((R_ref-r1)/R_ref));
tau_r1 = u_out+u_out*(1.4{dimensionless}*(R_ref-r1)/R_ref+2.1{dimensionless}*sqr((R_ref-r1)/R_ref));-->
<apply>
<eq/>
<ci>Ptm_r1</ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci>u_in</ci>
<ci>u_out</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>u_out</ci>
</apply>
<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">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>
<!-- 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>
<!-- qr1 = qp-qr;-->
</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" 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="0.0017" name="l" units="meter"/>
<variable name="time" public_interface="in" units="second"/>
<variable initial_value="0.000208" name="r1" public_interface="out" units="meter"/>
<variable initial_value="3.364e-9" name="Ri_sq_r1" public_interface="out" units="meter_sq"/>
<variable initial_value="8.7616e-8" name="rmax_sq_r1" public_interface="out" units="meter_sq"/>
<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="15.728" name="P1_r1" public_interface="out" units="pascal"/>
<variable initial_value="-2757.374611" 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="meter"/>
<variable initial_value="0.00028" name="rmax_r1" units="meter"/>
<variable initial_value="25" name="gamma" units="dimensionless"/>
<variable name="f_a_r1" public_interface="in" units="pascal"/>
<variable name="Ptm_r1" public_interface="out" units="pascal"/>
<variable initial_value="0.0010873" name="h1" units="meter"/>
<variable initial_value="0.0002792" name="R_ref" units="meter"/>
<variable name="tau_r1" public_interface="out" units="pascal"/>
<variable initial_value="0" name="v_d" public_interface="out" units="m3_per_s"/>
<variable name="u_out" public_interface="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="0.25" 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="0.0001" name="V_tlc" units="litre"/>
<variable name="v1" public_interface="out" units="dimensionless"/>
<variable name="x" units="dimensionless"/>
<!-- var qr: mole {pub: out};-->
<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>
<!-- u_in = P_bar+Paw_bar*sin(omega*time);-->
<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>
<!-- tau_r1 = u_out+u_out*(1.4{dimensionless}*(R_ref-r1)/R_ref+2.1{dimensionless}*sqr((R_ref-r1)/R_ref));-->
<apply>
<eq/>
<ci>Ptm_r1</ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci>u_in</ci>
<ci>u_out</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>u_out</ci>
</apply>
<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>
<!-- tau_r1 = 1.4{dimensionless}*Ptm_r1*((R_ref-r1)/R_ref + 1.5{dimensionless}*sqr((R_ref-r1)/R_ref));-->
<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">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>
<!-- 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>
<!-- qr = 1{dimensionless}*u/R-u_out;-->
</component>
<component name="airway21">
<variable name="u" public_interface="out" units="pascal"/>
<variable name="u_in" public_interface="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="0.0017" name="l" units="meter"/>
<variable name="time" public_interface="in" units="second"/>
<variable initial_value="0.0002080" name="r1" public_interface="out" units="meter"/>
<variable initial_value="3.364e-9" name="Ri_sq_r1" public_interface="out" units="meter_sq"/>
<variable initial_value="8.7616e-8" name="rmax_sq_r1" public_interface="out" units="meter_sq"/>
<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="15.728" name="P1_r1" public_interface="out" units="pascal"/>
<variable initial_value="-2757.374611" 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="meter"/>
<variable initial_value="0.00028" name="rmax_r1" units="meter"/>
<variable initial_value="25" name="gamma" units="dimensionless"/>
<variable name="f_a_r1" public_interface="in" units="pascal"/>
<variable name="Ptm_r1" public_interface="out" units="pascal"/>
<variable initial_value="0.0010873" name="h1" units="meter"/>
<variable initial_value="0.0002792" name="R_ref" units="meter"/>
<variable name="tau_r1" public_interface="out" units="pascal"/>
<variable initial_value="0" name="v_d" public_interface="out" units="m3_per_s"/>
<variable name="u_out" public_interface="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="0.25" 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="0.0001" name="V_tlc" units="litre"/>
<variable name="v1" public_interface="out" units="dimensionless"/>
<variable name="x" units="dimensionless"/>
<!-- var qr: mole {pub: in};-->
<!-- var qr1: mole;
var qp: mole {pub: in};-->
<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>
<!-- u_in = P_bar+Paw_bar*sin(omega*time);-->
<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>
<!-- tau_r1 = 1.4{dimensionless}*Ptm_r1*((R_ref-r1)/R_ref + 1.5{dimensionless}*sqr((R_ref-r1)/R_ref));-->
<apply>
<eq/>
<ci>Ptm_r1</ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci>u_in</ci>
<ci>u_out</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>u_out</ci>
</apply>
<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">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>
<!-- 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>
<!-- qr1 = qp-qr;-->
</component>
<!-- def map between airway and airway1 for
vars qr and qr;
enddef;-->
<!-- def map between uv_type and airway1 for
vars qp and qp;
enddef;-->
<!-- def map between main and airway for
vars f_a_r1 and f_a_r1;
enddef;-->
<!-- def map between main and airway1 for
vars f_a_r1 and f_a_r1;
enddef;-->
<connection>
<map_components component_1="airway" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="airway1" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<!-- def map between uv_type and environment for
vars time and time;
enddef;-->
<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>
<!-- def map between main and stress for
vars stress and stress;
enddef;-->
<!-- def map between uv_type and airway for
vars u and u_in;
vars v_out_1 and v;
enddef;-->
<!-- def map between uv_type and airway1 for
vars u and u_in;
vars v_out_2 and v;
vars tau_r1 and tau_r1;
enddef;-->
<!-- def map between main and uv_type for
vars f_a_r1 and f_a_r1;
vars r_parent and r1;
vars v and v;-->
<!-- // vars tau and tau_r1;
enddef;-->
</model>