Location: 12 L Platform 1 model codes @ 4c1ab73f48d7 / Airway_FTU / cellml2_version / experiment2 / uv_type_bran_order3.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/Airway_FTU/cellml2_version/experiment2/uv_type_bran_order3.cellml
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<divide/>
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<eq/>
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<plus/>
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<times/>
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<minus/>
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<minus/>
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<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
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<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
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<ci>u</ci>
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<apply>
<times/>
<ci>R</ci>
<ci>v</ci>
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<ci>I</ci>
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<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
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<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>v</ci>
<ci>v_out_1</ci>
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<ci>v_out_2</ci>
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<ci>C</ci>
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<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>
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<apply>
<minus/>
<ci>v_conc</ci>
<ci>v_conc_out_1</ci>
</apply>
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<apply>
<eq/>
<ci>v_conc</ci>
<apply>
<times/>
<apply>
<divide/>
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<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r1</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>l</ci>
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</apply>
<apply>
<minus/>
<ci>q_in</ci>
<ci>q</ci>
</apply>
</apply>
</apply>
</math>
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<variable name="u_in" units="pascal" interface="public"/>
<variable initial_value="0" name="u_v" units="pascal" interface="public"/>
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<variable name="R" units="Js_per_m6"/>
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<variable name="rad_r1" units="mm" interface="public"/>
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<variable name="Ptm_r1" units="pascal"/>
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<variable name="tau_r1" units="pascal" interface="public"/>
<variable initial_value="25000" name="E1" units="J_per_m3"/>
<variable initial_value="0.1" name="V_tlc" units="mL"/>
<variable name="v1" units="dimensionless"/>
<variable name="x" units="dimensionless"/>
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<eq/>
<ci>v1</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.2</cn>
<ci>V_tlc</ci>
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<apply>
<divide/>
<ci>u</ci>
<ci>E1</ci>
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<ci>V_tlc</ci>
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<apply>
<eq/>
<ci>x</ci>
<apply>
<minus/>
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<apply>
<divide/>
<ci>r1</ci>
<apply>
<power/>
<ci>v1</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<cn cellml:units="dimensionless">3</cn>
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</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>
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<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>
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<apply>
<minus/>
<ci>N1_r1</ci>
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<apply>
<leq/>
<ci>Ptm_r1</ci>
<cn cellml:units="dimensionless">0</cn>
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<piece>
<apply>
<root/>
<apply>
<minus/>
<ci>rmax_sq_r1</ci>
<apply>
<times/>
<apply>
<minus/>
<ci>rmax_sq_r1</ci>
<ci>Ri_sq_r1</ci>
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<apply>
<power/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Ptm_r1</ci>
<ci>P2_r1</ci>
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<apply>
<minus/>
<ci>N2_r1</ci>
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<apply>
<geq/>
<ci>Ptm_r1</ci>
<cn cellml:units="dimensionless">0</cn>
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<eq/>
<ci>I</ci>
<apply>
<divide/>
<apply>
<times/>
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<ci>l</ci>
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<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r1</ci>
<cn cellml:units="dimensionless">2</cn>
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<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>
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<times/>
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<eq/>
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<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">12</cn>
<ci>mu</ci>
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<times/>
<pi/>
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<power/>
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<cn cellml:units="dimensionless">4</cn>
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<eq/>
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<divide/>
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<ci>C</ci>
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<eq/>
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<plus/>
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<times/>
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<apply>
<minus/>
<apply>
<minus/>
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<eq/>
<apply>
<diff/>
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<divide/>
<apply>
<minus/>
<apply>
<minus/>
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<ci>u</ci>
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<times/>
<ci>R</ci>
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<eq/>
<apply>
<diff/>
<bvar>
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<divide/>
<apply>
<minus/>
<apply>
<minus/>
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<ci>v_out_2</ci>
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<ci>C</ci>
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<eq/>
<apply>
<diff/>
<bvar>
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<ci>r1</ci>
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<apply>
<times/>
<ci>rho1</ci>
<apply>
<minus/>
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<ci>r1</ci>
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<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
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<minus/>
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<ci>v_conc_out_1</ci>
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<eq/>
<ci>v_conc</ci>
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<times/>
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<divide/>
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<times/>
<pi/>
<apply>
<power/>
<ci>r1</ci>
<cn cellml:units="dimensionless">2</cn>
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<ci>l</ci>
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<apply>
<minus/>
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<ci>q</ci>
</apply>
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<variable name="AMp" units="dimensionless" interface="public"/>
<variable name="AM" units="dimensionless" interface="public"/>
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<eq/>
<ci>stress</ci>
<apply>
<plus/>
<ci>AMp</ci>
<ci>AM</ci>
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<component name="AMp">
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<variable name="Mp" units="dimensionless" interface="public"/>
<variable name="AM" units="dimensionless" interface="public"/>
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<variable name="k4" units="first_order_rate_constant" interface="public"/>
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<eq/>
<apply>
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<minus/>
<apply>
<plus/>
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<times/>
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<times/>
<ci>k6</ci>
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<times/>
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<plus/>
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<ci>AMp</ci>
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</math>
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<component name="AM">
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<variable name="AMp" units="dimensionless" interface="public"/>
<variable name="k5" units="first_order_rate_constant" interface="public"/>
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<variable name="k7" units="first_order_rate_constant" interface="public"/>
<variable name="time" units="second" interface="public"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" a6:xmlns="http://www.w3.org/1998/Math/MathML" xmlns:a6="http://www.cellml.org/cellml/1.0#">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
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<ci>AM</ci>
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<apply>
<minus/>
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<times/>
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<apply>
<times/>
<apply>
<plus/>
<ci>k6</ci>
<ci>k7</ci>
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<ci>AM</ci>
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</apply>
</apply>
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<component name="Mp">
<variable initial_value="0.0" name="Mp" units="dimensionless" interface="public"/>
<variable name="AMp" units="dimensionless" interface="public"/>
<variable name="M" units="dimensionless" interface="public"/>
<variable name="k1" units="first_order_rate_constant" interface="public"/>
<variable name="k2" units="first_order_rate_constant" interface="public"/>
<variable name="k3" units="first_order_rate_constant" interface="public"/>
<variable name="k4" units="first_order_rate_constant" interface="public"/>
<variable name="time" units="second" interface="public"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" a7:xmlns="http://www.w3.org/1998/Math/MathML" xmlns:a7="http://www.cellml.org/cellml/1.0#">
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<eq/>
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<diff/>
<bvar>
<ci>time</ci>
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<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>k4</ci>
<ci>AMp</ci>
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<apply>
<times/>
<ci>k1</ci>
<ci>M</ci>
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<apply>
<times/>
<apply>
<plus/>
<ci>k2</ci>
<ci>k3</ci>
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<ci>Mp</ci>
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</apply>
</apply>
</math>
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<component name="M">
<variable initial_value="1.0" name="M" units="dimensionless" interface="public"/>
<variable name="AM" units="dimensionless" interface="public"/>
<variable name="Mp" units="dimensionless" interface="public"/>
<variable name="k1" units="first_order_rate_constant" interface="public"/>
<variable name="k2" units="first_order_rate_constant" interface="public"/>
<variable name="k7" units="first_order_rate_constant" interface="public"/>
<variable name="time" units="second" interface="public"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" a8:xmlns="http://www.w3.org/1998/Math/MathML" xmlns:a8="http://www.cellml.org/cellml/1.0#">
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<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
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<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
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<ci>M</ci>
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<apply>
<times/>
<ci>k2</ci>
<ci>Mp</ci>
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<apply>
<times/>
<ci>k7</ci>
<ci>AM</ci>
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</apply>
</apply>
</math>
</component>
<component name="model_parameters">
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<variable initial_value="0.5" name="k2" units="first_order_rate_constant" interface="public"/>
<variable initial_value="0.5" name="k5" units="first_order_rate_constant" interface="public"/>
<variable name="k6" units="first_order_rate_constant" interface="public"/>
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<variable initial_value="0.01" name="k7" units="first_order_rate_constant" interface="public"/>
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<eq/>
<ci>k1</ci>
<piecewise>
<piece>
<cn cellml:units="first_order_rate_constant">0.55</cn>
<apply>
<and/>
<apply>
<geq/>
<ci>time</ci>
<cn cellml:units="second">0.0</cn>
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<apply>
<lt/>
<ci>time</ci>
<cn cellml:units="second">5.0</cn>
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</piece>
<otherwise>
<cn cellml:units="first_order_rate_constant">0.3</cn>
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<apply a9:id="k6_calculation">
<eq/>
<ci>k6</ci>
<ci>k1</ci>
</apply>
</math>
</component>
<component name="airwayr1">
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<variable name="u_in" units="pascal" interface="public"/>
<variable initial_value="0" name="u_v" units="pascal" interface="public"/>
<variable initial_value="1.81e-5" name="mu" units="Pas"/>
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<variable initial_value="0.0009" name="v" units="m3_per_s" interface="public"/>
<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"/>
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<variable name="time" units="second" interface="public"/>
<variable initial_value="0.28" name="r1" units="mm" interface="public"/>
<variable initial_value="0.003364" name="Ri_sq_r1" units="mm2" interface="public"/>
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<variable initial_value="7" name="N2_r1" units="dimensionless" interface="public"/>
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<variable initial_value="1" name="rho1" units="dimensionless" interface="public"/>
<variable name="rad_r1" units="mm" interface="public"/>
<variable initial_value="0.296" name="rmax_r1" units="mm"/>
<variable initial_value="25" name="gamma" units="dimensionless"/>
<variable name="f_a_r1" units="Pa_mm" interface="public"/>
<variable name="Ptm_r1" units="pascal"/>
<variable initial_value="1.0873" name="h1" units="mm"/>
<variable initial_value="0.318" name="R_ref" units="mm"/>
<variable name="tau_r1" units="pascal"/>
<variable initial_value="0.0009" name="v_d" units="m3_per_s" interface="public"/>
<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" a12:xmlns="http://www.w3.org/1998/Math/MathML" xmlns:a12="http://www.cellml.org/cellml/1.0#">
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<eq/>
<ci>omega</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<pi/>
<ci>freq</ci>
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<apply>
<eq/>
<ci>PA_bar</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>Paw_bar</ci>
<ci>E1</ci>
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<root/>
<apply>
<plus/>
<apply>
<power/>
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<cn cellml:units="dimensionless">2</cn>
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<apply>
<power/>
<apply>
<times/>
<ci>omega</ci>
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<cn cellml:units="dimensionless">2</cn>
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<apply>
<eq/>
<ci>alpha</ci>
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<arctan/>
<apply>
<divide/>
<apply>
<times/>
<ci>omega</ci>
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<ci>E1</ci>
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<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/>
<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_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">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>
<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>
<component name="airwayr2">
<variable name="u" units="pascal" interface="public"/>
<variable name="u_in" units="pascal" interface="public"/>
<variable initial_value="0" name="u_v" units="pascal" interface="public"/>
<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="0.0009" name="v" units="m3_per_s" interface="public"/>
<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="3" name="l" units="mm"/>
<variable name="time" units="second" interface="public"/>
<variable initial_value="0.296" name="r1" units="mm" interface="public"/>
<variable initial_value="0.003364" name="Ri_sq_r1" units="mm2" interface="public"/>
<variable initial_value="0.0876" name="rmax_sq_r1" units="mm" interface="public"/>
<variable initial_value="1" name="N1_r1" units="dimensionless" interface="public"/>
<variable initial_value="7" name="N2_r1" units="dimensionless" interface="public"/>
<variable initial_value="15.728" name="P1_r1" units="pascal" interface="public"/>
<variable initial_value="-2757.374611" name="P2_r1" units="pascal" interface="public"/>
<variable initial_value="1" name="rho1" units="dimensionless" interface="public"/>
<variable name="rad_r1" units="mm" interface="public"/>
<variable initial_value="0.296" name="rmax_r1" units="mm"/>
<variable initial_value="25" name="gamma" units="dimensionless"/>
<variable name="f_a_r1" units="Pa_mm" interface="public"/>
<variable name="Ptm_r1" units="pascal"/>
<variable initial_value="1.0873" name="h1" units="mm"/>
<variable initial_value="0.318" name="R_ref" units="mm"/>
<variable name="tau_r1" units="pascal" interface="public"/>
<variable initial_value="0.0009" name="v_d" units="m3_per_s" interface="public"/>
<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" a13:xmlns="http://www.w3.org/1998/Math/MathML" xmlns:a13="http://www.cellml.org/cellml/1.0#">
<apply>
<eq/>
<ci>omega</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<pi/>
<ci>freq</ci>
</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/>
<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_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">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>
<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 component_1="uv_type" component_2="environment">
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection component_1="uv_type1" component_2="environment">
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection component_1="uv_type2" component_2="environment">
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection component_1="uv_type" component_2="uv_type1">
<map_variables variable_1="u" variable_2="u_in"/>
<map_variables variable_1="v_out_1" variable_2="v"/>
</connection>
<connection component_1="uv_type" component_2="uv_type2">
<map_variables variable_1="u" variable_2="u_in"/>
<map_variables variable_1="v_out_2" variable_2="v"/>
</connection>
<connection component_1="main" component_2="uv_type">
<map_variables variable_1="f_a_r1" variable_2="f_a_r1"/>
</connection>
<connection component_1="main" component_2="uv_type1">
<map_variables variable_1="f_a_r1" variable_2="f_a_r1"/>
</connection>
<connection component_1="main" component_2="uv_type2">
<map_variables variable_1="f_a_r1" variable_2="f_a_r1"/>
</connection>
<connection component_1="environment" component_2="AMp">
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection component_1="environment" component_2="AM">
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection component_1="environment" component_2="Mp">
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection component_1="environment" component_2="M">
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection component_1="environment" component_2="model_parameters">
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection component_1="main" component_2="stress">
<map_variables variable_1="stress" variable_2="stress"/>
</connection>
<connection component_1="main" component_2="airwayr1">
<map_variables variable_1="f_a_r1" variable_2="f_a_r1"/>
<map_variables variable_1="r_lq" variable_2="r1"/>
</connection>
<connection component_1="main" component_2="airwayr2">
<map_variables variable_1="f_a_r1" variable_2="f_a_r1"/>
</connection>
<connection component_1="airwayr1" component_2="environment">
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection component_1="airwayr2" component_2="environment">
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection component_1="uv_type1" component_2="airwayr1">
<map_variables variable_1="u" variable_2="u_in"/>
<map_variables variable_1="v_out_1" variable_2="v"/>
</connection>
<connection component_1="uv_type1" component_2="airwayr2">
<map_variables variable_1="u" variable_2="u_in"/>
<map_variables variable_1="v_out_2" variable_2="v"/>
<map_variables variable_1="tau_r1" variable_2="tau_r1"/>
</connection>
<connection component_1="main" component_2="uv_type1">
<map_variables variable_1="f_a_r1" variable_2="f_a_r1"/>
</connection>
<connection component_1="main" component_2="airwayr1">
<map_variables variable_1="f_a_r1" variable_2="f_a_r1"/>
</connection>
<connection component_1="main" component_2="airwayr2">
<map_variables variable_1="f_a_r1" variable_2="f_a_r1"/>
</connection>
<connection component_1="airwayr1" component_2="environment">
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection component_1="airwayr2" component_2="environment">
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection component_1="uv_type2" component_2="airwayr1">
<map_variables variable_1="u" variable_2="u_in"/>
<map_variables variable_1="v_out_1" variable_2="v"/>
</connection>
<connection component_1="uv_type2" component_2="airwayr2">
<map_variables variable_1="u" variable_2="u_in"/>
<map_variables variable_1="v_out_2" variable_2="v"/>
<map_variables variable_1="tau_r1" variable_2="tau_r1"/>
</connection>
<connection component_1="main" component_2="uv_type2">
<map_variables variable_1="f_a_r1" variable_2="f_a_r1"/>
</connection>
<connection component_1="M" component_2="model_parameters">
<map_variables variable_1="k7" variable_2="k7"/>
<map_variables variable_1="k1" variable_2="k1"/>
<map_variables variable_1="k2" variable_2="k2"/>
</connection>
<connection component_1="Mp" component_2="model_parameters">
<map_variables variable_1="k4" variable_2="k4"/>
<map_variables variable_1="k3" variable_2="k3"/>
<map_variables variable_1="k2" variable_2="k2"/>
<map_variables variable_1="k1" variable_2="k1"/>
</connection>
<connection component_1="AMp" component_2="model_parameters">
<map_variables variable_1="k5" variable_2="k5"/>
<map_variables variable_1="k6" variable_2="k6"/>
<map_variables variable_1="k4" variable_2="k4"/>
<map_variables variable_1="k3" variable_2="k3"/>
</connection>
<connection component_1="AM" component_2="model_parameters">
<map_variables variable_1="k5" variable_2="k5"/>
<map_variables variable_1="k6" variable_2="k6"/>
<map_variables variable_1="k7" variable_2="k7"/>
</connection>
<connection component_1="AM" component_2="M">
<map_variables variable_1="AM" variable_2="AM"/>
</connection>
<connection component_1="AM" component_2="AMp">
<map_variables variable_1="AMp" variable_2="AMp"/>
<map_variables variable_1="AM" variable_2="AM"/>
</connection>
<connection component_1="M" component_2="Mp">
<map_variables variable_1="M" variable_2="M"/>
<map_variables variable_1="Mp" variable_2="Mp"/>
</connection>
<connection component_1="Mp" component_2="AMp">
<map_variables variable_1="Mp" variable_2="Mp"/>
<map_variables variable_1="AMp" variable_2="AMp"/>
</connection>
<connection component_1="stress" component_2="AMp">
<map_variables variable_1="AMp" variable_2="AMp"/>
</connection>
<connection component_1="stress" component_2="AM">
<map_variables variable_1="AM" variable_2="AM"/>
</connection>
</model>