- 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/Airway_FTU/cellml2_version/experiments/airway1_radius.cellml
<model xmlns="http://www.cellml.org/cellml/2.0#" xmlns:cellml="http://www.cellml.org/cellml/2.0#" xmlns:xlink="http://www.w3.org/1999/xlink" name="airway2_radius">
<units name="mmHg">
<unit multiplier="133.32" units="pascal"/>
</units>
<units name="cmH2O">
<unit multiplier="98.0665" units="pascal"/>
</units>
<units name="mm2">
<unit exponent="2" prefix="milli" units="meter"/>
</units>
<units name="mm">
<unit prefix="milli" units="meter"/>
</units>
<units name="per_sec">
<unit exponent="-1" units="second"/>
</units>
<units name="mmHg_second_per_litre">
<unit units="mmHg"/>
<unit units="second"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="radian_per_second">
<unit units="radian"/>
<unit exponent="-1" units="second"/>
</units>
<units name="mmHg_per_second">
<unit units="mmHg"/>
<unit exponent="-1" units="second"/>
</units>
<units name="litre_per_second_mmHg">
<unit units="litre"/>
<unit exponent="-1" units="second"/>
<unit exponent="-1" units="mmHg"/>
</units>
<units name="litre_per_second">
<unit units="litre"/>
<unit exponent="-1" units="second"/>
</units>
<units name="mmHg">
<unit multiplier="133.32" units="pascal"/>
</units>
<units name="per_mmHg">
<unit exponent="-1" units="mmHg"/>
</units>
<units name="mmHg_second_per_litre">
<unit units="mmHg"/>
<unit units="second"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="mmHg_per_litre">
<unit units="mmHg"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="mmHg_litre_second2">
<unit units="mmHg"/>
<unit units="litre"/>
<unit exponent="2" units="second"/>
</units>
<units name="mole_per_litre">
<unit units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="litre_per_mole">
<unit units="litre"/>
<unit exponent="-1" units="mole"/>
</units>
<units name="per_second">
<unit exponent="-1" units="second"/>
</units>
<units name="litre_per_second_mole">
<unit units="litre"/>
<unit exponent="-1" units="second"/>
<unit exponent="-1" units="mole"/>
</units>
<units name="m2_kg_per_K_second2">
<unit exponent="2" units="metre"/>
<unit units="kilogram"/>
<unit exponent="-1" units="kelvin"/>
<unit exponent="2" units="second"/>
</units>
<units name="mm3">
<unit exponent="3" prefix="milli" units="metre"/>
</units>
<units name="mole_per_second_mmHg">
<unit units="mole"/>
<unit exponent="-1" units="second"/>
<unit exponent="-1" units="mmHg"/>
</units>
<units name="mole_per_litre_mmHg">
<unit units="mole"/>
<unit exponent="-1" units="litre"/>
<unit exponent="-1" units="mmHg"/>
</units>
<units name="ms">
<unit prefix="milli" units="second"/>
</units>
<component name="Environment">
<variable id="Environment_time" name="time" units="second" interface="public"/>
</component>
<units name="ml">
<unit prefix="milli" units="litre"/>
</units>
<import xlink:href="hai.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="lambert_r21">
<variable name="time" units="second" interface="public"/>
<variable name="Ri_sq_r21" units="mm2" interface="public"/>
<variable name="rmax_sq_r21" units="mm" interface="public"/>
<variable name="N1_r21" units="dimensionless" interface="public"/>
<variable name="N2_r21" units="dimensionless" interface="public"/>
<variable name="P1_r21" units="mmHg" interface="public"/>
<variable name="P2_r21" units="mmHg" interface="public"/>
<variable name="rho" units="dimensionless" interface="public"/>
<variable initial_value="0.2960" name="r21" units="mm" interface="public"/>
<variable name="Ptm_r21" units="mmHg"/>
<variable name="P0" units="mmHg" interface="public"/>
<variable name="kappa" units="dimensionless" interface="public"/>
<variable name="rad21" units="mm" interface="public"/>
<variable name="rmax_r21" units="mm" interface="public"/>
<variable name="V_r21" units="dimensionless"/>
<variable name="gamma" units="dimensionless" interface="public"/>
<variable name="stress" units="dimensionless" interface="public"/>
<variable name="v_smc_r21" units="dimensionless" interface="public"/>
<variable name="f_a_r21" units="dimensionless" interface="public"/>
<variable name="Pmin_r21" units="mmHg" interface="public"/>
<variable name="P_t_r21" units="mmHg" interface="public"/>
<variable name="tau_r21" units="dimensionless" interface="public"/>
<variable name="pmidr21" units="mmHg" interface="public"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Pmin_r21</ci>
<apply>
<plus/>
<ci>P0</ci>
<ci>P_t_r21</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Ptm_r21</ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>pmidr21</ci>
<cn cellml:units="mmHg">0.735</cn>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>kappa</ci>
<ci>f_a_r21</ci>
</apply>
<ci>r21</ci>
</apply>
</apply>
<ci>tau_r21</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>rad21</ci>
<piecewise>
<piece>
<apply>
<root/>
<apply>
<times/>
<ci>Ri_sq_r21</ci>
<apply>
<power/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Ptm_r21</ci>
<ci>P1_r21</ci>
</apply>
</apply>
<apply>
<minus/>
<ci>N1_r21</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<leq/>
<ci>Ptm_r21</ci>
<cn cellml:units="dimensionless">0</cn>
</apply>
</piece>
<piece>
<apply>
<root/>
<apply>
<minus/>
<ci>rmax_sq_r21</ci>
<apply>
<times/>
<apply>
<minus/>
<ci>rmax_sq_r21</ci>
<ci>Ri_sq_r21</ci>
</apply>
<apply>
<power/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Ptm_r21</ci>
<ci>P2_r21</ci>
</apply>
</apply>
<apply>
<minus/>
<ci>N2_r21</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<geq/>
<ci>Ptm_r21</ci>
<cn cellml:units="dimensionless">0</cn>
</apply>
</piece>
</piecewise>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>r21</ci>
</apply>
<apply>
<times/>
<ci>rho</ci>
<apply>
<minus/>
<ci>rad21</ci>
<ci>r21</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>V_r21</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<minus/>
<ci>gamma</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<pi/>
<ci>rmax_r21</ci>
</apply>
</apply>
<ci>rho</ci>
<apply>
<minus/>
<ci>rad21</ci>
<ci>r21</ci>
</apply>
<ci>v_smc_r21</ci>
</apply>
</apply>
</math>
</component>
<component name="lambert_r22">
<variable name="time" units="second" interface="public"/>
<variable name="Ri_sq_r22" units="mm2" interface="public"/>
<variable name="rmax_sq_r22" units="mm" interface="public"/>
<variable name="N1_r22" units="dimensionless" interface="public"/>
<variable name="N2_r22" units="dimensionless" interface="public"/>
<variable name="P1_r22" units="mmHg" interface="public"/>
<variable name="P2_r22" units="mmHg" interface="public"/>
<variable name="rho" units="dimensionless" interface="public"/>
<variable initial_value="0.2960" name="r22" units="mm" interface="public"/>
<variable name="Ptm_r22" units="mmHg"/>
<variable name="P0" units="mmHg" interface="public"/>
<variable name="kappa" units="dimensionless" interface="public"/>
<variable name="rad22" units="mm" interface="public"/>
<variable name="rmax_r22" units="mm" interface="public"/>
<variable name="V_r22" units="dimensionless"/>
<variable name="gamma" units="dimensionless" interface="public"/>
<variable name="stress" units="dimensionless" interface="public"/>
<variable name="v_smc_r22" units="dimensionless" interface="public"/>
<variable name="f_a_r22" units="dimensionless" interface="public"/>
<variable name="Pmin_r22" units="mmHg" interface="public"/>
<variable name="P_t_r22" units="mmHg" interface="public"/>
<variable name="tau_r22" units="dimensionless" interface="public"/>
<variable name="pmidr22" units="mmHg" interface="public"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Pmin_r22</ci>
<apply>
<plus/>
<ci>P0</ci>
<ci>P_t_r22</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Ptm_r22</ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>pmidr22</ci>
<cn cellml:units="mmHg">0.735</cn>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>kappa</ci>
<ci>f_a_r22</ci>
</apply>
<ci>r22</ci>
</apply>
</apply>
<ci>tau_r22</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>rad22</ci>
<piecewise>
<piece>
<apply>
<root/>
<apply>
<times/>
<ci>Ri_sq_r22</ci>
<apply>
<power/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Ptm_r22</ci>
<ci>P1_r22</ci>
</apply>
</apply>
<apply>
<minus/>
<ci>N1_r22</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<leq/>
<ci>Ptm_r22</ci>
<cn cellml:units="dimensionless">0</cn>
</apply>
</piece>
<piece>
<apply>
<root/>
<apply>
<minus/>
<ci>rmax_sq_r22</ci>
<apply>
<times/>
<apply>
<minus/>
<ci>rmax_sq_r22</ci>
<ci>Ri_sq_r22</ci>
</apply>
<apply>
<power/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Ptm_r22</ci>
<ci>P2_r22</ci>
</apply>
</apply>
<apply>
<minus/>
<ci>N2_r22</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<geq/>
<ci>Ptm_r22</ci>
<cn cellml:units="dimensionless">0</cn>
</apply>
</piece>
</piecewise>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>r22</ci>
</apply>
<apply>
<times/>
<ci>rho</ci>
<apply>
<minus/>
<ci>rad22</ci>
<ci>r22</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>V_r22</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<minus/>
<ci>gamma</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<pi/>
<ci>rmax_r22</ci>
</apply>
</apply>
<ci>rho</ci>
<apply>
<minus/>
<ci>rad22</ci>
<ci>r22</ci>
</apply>
<ci>v_smc_r22</ci>
</apply>
</apply>
</math>
</component>
<component name="airway2_vals">
<variable name="e_w_r21" units="dimensionless"/>
<variable name="e_m_r21" units="dimensionless"/>
<variable name="r_w_r21" units="dimensionless"/>
<variable name="r_m_r21" units="dimensionless"/>
<variable name="r_s_r21" units="dimensionless"/>
<variable name="Rw_r21" units="mm" interface="public"/>
<variable name="Ri_r21" units="mm" interface="public"/>
<variable name="Rm_r21" units="mm" interface="public"/>
<variable name="fl_r21" units="dimensionless"/>
<variable name="rsmax_r21" units="mm" interface="public"/>
<variable name="f_a_r21" units="dimensionless" interface="public"/>
<variable name="stress" units="dimensionless" interface="public"/>
<variable name="D_Rm_r21" units="dimensionless"/>
<variable name="sigma_rrm_r21" units="dimensionless"/>
<variable name="sigma_rrw_r21" units="dimensionless"/>
<variable name="sigma_ttm_r21" units="dimensionless"/>
<variable name="sigma_ttw_r21" units="dimensionless"/>
<variable name="moo" units="dimensionless" interface="public"/>
<variable name="noo" units="dimensionless" interface="public"/>
<variable name="P_t_r21" units="mmHg" interface="public"/>
<variable name="f" units="per_second" interface="public"/>
<variable name="time" units="second" interface="public"/>
<variable name="rad21" units="mm" interface="public"/>
<variable name="r21" units="mm" interface="public"/>
<variable name="v_smc_r21" units="dimensionless" interface="public"/>
<variable name="rho" units="dimensionless" interface="public"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>P_t_r21</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0</cn>
<apply>
<sin/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<pi/>
<ci>f</ci>
<ci>time</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>e_w_r21</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>Rw_r21</ci>
<ci>Ri_r21</ci>
</apply>
<ci>Ri_r21</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>e_m_r21</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>Rm_r21</ci>
<ci>Rw_r21</ci>
</apply>
<ci>Ri_r21</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>r_w_r21</ci>
<apply>
<times/>
<ci>Ri_r21</ci>
<apply>
<root/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<ci>e_w_r21</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci>rad21</ci>
<ci>Ri_r21</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>r_m_r21</ci>
<apply>
<times/>
<ci>Ri_r21</ci>
<apply>
<root/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<power/>
<apply>
<plus/>
<ci>e_m_r21</ci>
<ci>e_w_r21</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci>rad21</ci>
<ci>Ri_r21</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>r_s_r21</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.5</cn>
<apply>
<plus/>
<ci>r_w_r21</ci>
<ci>r_m_r21</ci>
</apply>
</apply>
</apply>
<!-- Expt data fit for AM force at latch state-->
<apply>
<eq/>
<ci>fl_r21</ci>
<piecewise>
<piece>
<apply>
<power/>
<apply>
<times/>
<cn cellml:units="dimensionless">0</cn>
<apply>
<sin/>
<apply>
<divide/>
<apply>
<times/>
<pi/>
<ci>r_s_r21</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>rsmax_r21</ci>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
<apply>
<leq/>
<ci>r_s_r21</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>rsmax_r21</ci>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="dimensionless">0</cn>
</otherwise>
</piecewise>
</apply>
<!-- Total active force-->
<apply>
<eq/>
<ci>f_a_r21</ci>
<apply>
<plus/>
<ci>fl_r21</ci>
<ci>stress</ci>
</apply>
</apply>
<!-- Radial stress-->
<apply>
<eq/>
<ci>D_Rm_r21</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>Rm_r21</ci>
<ci>r_m_r21</ci>
</apply>
<ci>Rm_r21</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>sigma_rrm_r21</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>moo</ci>
<apply>
<plus/>
<ci>D_Rm_r21</ci>
<apply>
<power/>
<apply>
<times/>
<ci>noo</ci>
<ci>D_Rm_r21</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<ci>P_t_r21</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>sigma_rrw_r21</ci>
<apply>
<minus/>
<ci>sigma_rrm_r21</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>f_a_r21</ci>
<apply>
<minus/>
<ci>Rm_r21</ci>
<ci>Rw_r21</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.5</cn>
<apply>
<plus/>
<ci>r_m_r21</ci>
<ci>r_w_r21</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<!-- Hoop stress-->
<apply>
<eq/>
<ci>sigma_ttm_r21</ci>
<apply>
<plus/>
<ci>sigma_rrm_r21</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>f_a_r21</ci>
<apply>
<minus/>
<ci>Rm_r21</ci>
<ci>Rw_r21</ci>
</apply>
</apply>
<apply>
<plus/>
<ci>r_m_r21</ci>
<ci>r_w_r21</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>sigma_ttw_r21</ci>
<apply>
<plus/>
<ci>sigma_rrw_r21</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>f_a_r21</ci>
<apply>
<minus/>
<ci>Rm_r21</ci>
<ci>Rw_r21</ci>
</apply>
</apply>
<apply>
<plus/>
<ci>r_m_r21</ci>
<ci>r_w_r21</ci>
</apply>
</apply>
</apply>
</apply>
<!--Vel of SMC contraction-->
<apply>
<eq/>
<ci>v_smc_r21</ci>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<minus/>
<ci>r_w_r21</ci>
<ci>r_m_r21</ci>
</apply>
</apply>
<ci>rho</ci>
<apply>
<minus/>
<ci>rad21</ci>
<ci>r21</ci>
</apply>
<ci>rad21</ci>
<apply>
<ln/>
<apply>
<divide/>
<ci>r_w_r21</ci>
<ci>r_m_r21</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="airway22_vals">
<variable name="e_w_r22" units="dimensionless"/>
<variable name="e_m_r22" units="dimensionless"/>
<variable name="r_w_r22" units="dimensionless"/>
<variable name="r_m_r22" units="dimensionless"/>
<variable name="r_s_r22" units="dimensionless"/>
<variable name="Rw_r22" units="mm" interface="public"/>
<variable name="Ri_r22" units="mm" interface="public"/>
<variable name="Rm_r22" units="mm" interface="public"/>
<variable name="fl_r22" units="dimensionless"/>
<variable name="rsmax_r22" units="mm" interface="public"/>
<variable name="f_a_r22" units="dimensionless" interface="public"/>
<variable name="stress" units="dimensionless" interface="public"/>
<variable name="D_Rm_r22" units="dimensionless"/>
<variable name="sigma_rrm_r22" units="dimensionless"/>
<variable name="sigma_rrw_r22" units="dimensionless"/>
<variable name="sigma_ttm_r22" units="dimensionless"/>
<variable name="sigma_ttw_r22" units="dimensionless"/>
<variable name="moo" units="dimensionless" interface="public"/>
<variable name="noo" units="dimensionless" interface="public"/>
<variable name="P_t_r22" units="mmHg" interface="public"/>
<variable name="f" units="per_second" interface="public"/>
<variable name="time" units="second" interface="public"/>
<variable name="rad22" units="mm" interface="public"/>
<variable name="r22" units="mm" interface="public"/>
<variable name="v_smc_r22" units="dimensionless" interface="public"/>
<variable name="rho" units="dimensionless" interface="public"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>P_t_r22</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0</cn>
<apply>
<sin/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<pi/>
<ci>f</ci>
<ci>time</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>e_w_r22</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>Rw_r22</ci>
<ci>Ri_r22</ci>
</apply>
<ci>Ri_r22</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>e_m_r22</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>Rm_r22</ci>
<ci>Rw_r22</ci>
</apply>
<ci>Ri_r22</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>r_w_r22</ci>
<apply>
<times/>
<ci>Ri_r22</ci>
<apply>
<root/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<ci>e_w_r22</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci>rad22</ci>
<ci>Ri_r22</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>r_m_r22</ci>
<apply>
<times/>
<ci>Ri_r22</ci>
<apply>
<root/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<power/>
<apply>
<plus/>
<ci>e_m_r22</ci>
<ci>e_w_r22</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci>rad22</ci>
<ci>Ri_r22</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>r_s_r22</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.5</cn>
<apply>
<plus/>
<ci>r_w_r22</ci>
<ci>r_m_r22</ci>
</apply>
</apply>
</apply>
<!-- Expt data fit for AM force at latch state-->
<apply>
<eq/>
<ci>fl_r22</ci>
<piecewise>
<piece>
<apply>
<power/>
<apply>
<times/>
<cn cellml:units="dimensionless">0</cn>
<apply>
<sin/>
<apply>
<divide/>
<apply>
<times/>
<pi/>
<ci>r_s_r22</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>rsmax_r22</ci>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
<apply>
<leq/>
<ci>r_s_r22</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>rsmax_r22</ci>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="dimensionless">0</cn>
</otherwise>
</piecewise>
</apply>
<!-- Total active force-->
<apply>
<eq/>
<ci>f_a_r22</ci>
<apply>
<plus/>
<ci>fl_r22</ci>
<ci>stress</ci>
</apply>
</apply>
<!-- Radial stress-->
<apply>
<eq/>
<ci>D_Rm_r22</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>Rm_r22</ci>
<ci>r_m_r22</ci>
</apply>
<ci>Rm_r22</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>sigma_rrm_r22</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>moo</ci>
<apply>
<plus/>
<ci>D_Rm_r22</ci>
<apply>
<power/>
<apply>
<times/>
<ci>noo</ci>
<ci>D_Rm_r22</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<ci>P_t_r22</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>sigma_rrw_r22</ci>
<apply>
<minus/>
<ci>sigma_rrm_r22</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>f_a_r22</ci>
<apply>
<minus/>
<ci>Rm_r22</ci>
<ci>Rw_r22</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.5</cn>
<apply>
<plus/>
<ci>r_m_r22</ci>
<ci>r_w_r22</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<!-- Hoop stress-->
<apply>
<eq/>
<ci>sigma_ttm_r22</ci>
<apply>
<plus/>
<ci>sigma_rrm_r22</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>f_a_r22</ci>
<apply>
<minus/>
<ci>Rm_r22</ci>
<ci>Rw_r22</ci>
</apply>
</apply>
<apply>
<plus/>
<ci>r_m_r22</ci>
<ci>r_w_r22</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>sigma_ttw_r22</ci>
<apply>
<plus/>
<ci>sigma_rrw_r22</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>f_a_r22</ci>
<apply>
<minus/>
<ci>Rm_r22</ci>
<ci>Rw_r22</ci>
</apply>
</apply>
<apply>
<plus/>
<ci>r_m_r22</ci>
<ci>r_w_r22</ci>
</apply>
</apply>
</apply>
</apply>
<!--Vel of SMC contraction-->
<apply>
<eq/>
<ci>v_smc_r22</ci>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<minus/>
<ci>r_w_r22</ci>
<ci>r_m_r22</ci>
</apply>
</apply>
<ci>rho</ci>
<apply>
<minus/>
<ci>rad22</ci>
<ci>r22</ci>
</apply>
<ci>rad22</ci>
<apply>
<ln/>
<apply>
<divide/>
<ci>r_w_r22</ci>
<ci>r_m_r22</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="parameters_r2">
<variable initial_value="0.003364" name="Ri_sq_r21" units="mm2" interface="public"/>
<variable name="Ri_sq_r22" units="mm2" interface="public"/>
<variable initial_value="0.0876" name="rmax_sq_r21" units="mm" interface="public"/>
<variable name="rmax_sq_r22" units="mm" interface="public"/>
<variable initial_value="1" name="N1_r21" units="dimensionless" interface="public"/>
<variable name="N1_r22" units="dimensionless" interface="public"/>
<variable initial_value="8" name="N2_r21" units="dimensionless" interface="public"/>
<variable name="N2_r22" units="dimensionless" interface="public"/>
<variable initial_value="0.117969751" name="P1_r21" units="mmHg" interface="public"/>
<variable name="P1_r22" units="mmHg" interface="public"/>
<variable initial_value="-20.68201916" name="P2_r21" units="mmHg" interface="public"/>
<variable name="P2_r22" units="mmHg" interface="public"/>
<variable initial_value="1" name="rho" units="dimensionless" interface="public"/>
<variable initial_value="10" name="P0" units="mmHg" interface="public"/>
<!-- var kappa: dimensionless {pub:in};-->
<variable initial_value="0.296" name="rmax_r21" units="mm" interface="public"/>
<variable name="rmax_r22" units="mm" interface="public"/>
<variable initial_value="25" name="gamma" units="dimensionless" interface="public"/>
<variable initial_value="0.109" name="Rw_r21" units="mm" interface="public"/>
<variable name="Rw_r22" units="mm" interface="public"/>
<variable initial_value="0.058" name="Ri_r21" units="mm" interface="public"/>
<variable name="Ri_r22" units="mm" interface="public"/>
<variable initial_value="0.121" name="Rm_r21" units="mm" interface="public"/>
<variable name="Rm_r22" units="mm" interface="public"/>
<variable initial_value="0.312" name="rsmax_r21" units="mm" interface="public"/>
<variable name="rsmax_r22" units="mm" interface="public"/>
<variable initial_value="15.09" name="moo" units="dimensionless" interface="public"/>
<variable initial_value="1.5" name="noo" units="dimensionless" interface="public"/>
<variable initial_value="0.25" name="f" units="per_second" interface="public"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Ri_sq_r22</ci>
<ci>Ri_sq_r21</ci>
</apply>
<apply>
<eq/>
<ci>rmax_sq_r22</ci>
<ci>rmax_sq_r21</ci>
</apply>
<apply>
<eq/>
<ci>N1_r22</ci>
<ci>N1_r21</ci>
</apply>
<apply>
<eq/>
<ci>N2_r22</ci>
<ci>N2_r21</ci>
</apply>
<apply>
<eq/>
<ci>P1_r22</ci>
<ci>P1_r21</ci>
</apply>
<apply>
<eq/>
<ci>P2_r22</ci>
<ci>P2_r21</ci>
</apply>
<apply>
<eq/>
<ci>rmax_r22</ci>
<ci>rmax_r21</ci>
</apply>
<apply>
<eq/>
<ci>Rw_r22</ci>
<ci>Rw_r21</ci>
</apply>
<apply>
<eq/>
<ci>Ri_r22</ci>
<ci>Ri_r21</ci>
</apply>
<apply>
<eq/>
<ci>Rm_r22</ci>
<ci>Rm_r21</ci>
</apply>
<apply>
<eq/>
<ci>rsmax_r22</ci>
<ci>rsmax_r21</ci>
</apply>
</math>
</component>
<connection component_1="parameters_r2" component_2="airway2_vals">
<map_variables variable_1="Rw_r21" variable_2="Rw_r21"/>
<map_variables variable_1="Rm_r21" variable_2="Rm_r21"/>
<map_variables variable_1="Ri_r21" variable_2="Ri_r21"/>
<map_variables variable_1="rsmax_r21" variable_2="rsmax_r21"/>
<map_variables variable_1="moo" variable_2="moo"/>
<map_variables variable_1="noo" variable_2="noo"/>
<map_variables variable_1="rho" variable_2="rho"/>
<map_variables variable_1="f" variable_2="f"/>
</connection>
<connection component_1="parameters_r2" component_2="lambert_r21">
<map_variables variable_1="Ri_sq_r21" variable_2="Ri_sq_r21"/>
<map_variables variable_1="rmax_sq_r21" variable_2="rmax_sq_r21"/>
<map_variables variable_1="N1_r21" variable_2="N1_r21"/>
<map_variables variable_1="N2_r21" variable_2="N2_r21"/>
<map_variables variable_1="P1_r21" variable_2="P1_r21"/>
<map_variables variable_1="P2_r21" variable_2="P2_r21"/>
<map_variables variable_1="rho" variable_2="rho"/>
<map_variables variable_1="rmax_r21" variable_2="rmax_r21"/>
<!-- vars kappa and kappa;-->
<map_variables variable_1="P0" variable_2="P0"/>
<map_variables variable_1="gamma" variable_2="gamma"/>
</connection>
<connection component_1="airway2_vals" component_2="lambert_r21">
<map_variables variable_1="v_smc_r21" variable_2="v_smc_r21"/>
<map_variables variable_1="rad21" variable_2="rad21"/>
<map_variables variable_1="r21" variable_2="r21"/>
<map_variables variable_1="f_a_r21" variable_2="f_a_r21"/>
<map_variables variable_1="P_t_r21" variable_2="P_t_r21"/>
</connection>
<connection component_1="Environment" component_2="airway2_vals">
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection component_1="airway2_vals" component_2="stress">
<map_variables variable_1="stress" variable_2="stress"/>
</connection>
<connection component_1="Environment" component_2="lambert_r21">
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection component_1="stress" component_2="lambert_r21">
<map_variables variable_1="stress" variable_2="stress"/>
</connection>
<connection component_1="parameters_r2" component_2="airway22_vals">
<map_variables variable_1="Rw_r22" variable_2="Rw_r22"/>
<map_variables variable_1="Rm_r22" variable_2="Rm_r22"/>
<map_variables variable_1="Ri_r22" variable_2="Ri_r22"/>
<map_variables variable_1="rsmax_r22" variable_2="rsmax_r22"/>
<map_variables variable_1="moo" variable_2="moo"/>
<map_variables variable_1="noo" variable_2="noo"/>
<map_variables variable_1="rho" variable_2="rho"/>
<map_variables variable_1="f" variable_2="f"/>
</connection>
<connection component_1="parameters_r2" component_2="lambert_r22">
<map_variables variable_1="Ri_sq_r22" variable_2="Ri_sq_r22"/>
<map_variables variable_1="rmax_sq_r22" variable_2="rmax_sq_r22"/>
<map_variables variable_1="N1_r22" variable_2="N1_r22"/>
<map_variables variable_1="N2_r22" variable_2="N2_r22"/>
<map_variables variable_1="P1_r22" variable_2="P1_r22"/>
<map_variables variable_1="P2_r22" variable_2="P2_r22"/>
<map_variables variable_1="rho" variable_2="rho"/>
<map_variables variable_1="rmax_r22" variable_2="rmax_r22"/>
<!-- vars kappa and kappa;-->
<map_variables variable_1="P0" variable_2="P0"/>
<map_variables variable_1="gamma" variable_2="gamma"/>
</connection>
<connection component_1="airway22_vals" component_2="lambert_r22">
<map_variables variable_1="v_smc_r22" variable_2="v_smc_r22"/>
<map_variables variable_1="rad22" variable_2="rad22"/>
<map_variables variable_1="r22" variable_2="r22"/>
<map_variables variable_1="f_a_r22" variable_2="f_a_r22"/>
<map_variables variable_1="P_t_r22" variable_2="P_t_r22"/>
</connection>
<connection component_1="Environment" component_2="airway22_vals">
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection component_1="airway22_vals" component_2="stress">
<map_variables variable_1="stress" variable_2="stress"/>
</connection>
<connection component_1="Environment" component_2="lambert_r22">
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection component_1="stress" component_2="lambert_r22">
<map_variables variable_1="stress" variable_2="stress"/>
</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>
</model>
