- Author:
- aram148 <a.rampadarath@auckland.ac.nz>
- Date:
- 2021-06-24 21:32:07+12:00
- Desc:
- Added wang2010 paper
- Permanent Source URI:
- https://models.cellml.org/workspace/6b0/rawfile/14da2ec145288c1daa022dddf44460bf00cdbbe4/Airway_FTU/airway1_radius1.cellml
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<!--Vel of SMC contraction-->
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</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>
<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>
<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>
<times/>
<ci>fl_r22</ci>
<ci>kappa</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>
<times/>
<ci>noo</ci>
<apply>
<power/>
<ci>D_Rm_r22</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</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" public_interface="out" units="mm2"/>
<variable name="Ri_sq_r22" public_interface="out" units="mm2"/>
<variable initial_value="0.0876" name="rmax_sq_r21" public_interface="out" units="mm"/>
<variable name="rmax_sq_r22" public_interface="out" units="mm"/>
<variable initial_value="1" name="N1_r21" public_interface="out" units="dimensionless"/>
<variable name="N1_r22" public_interface="out" units="dimensionless"/>
<variable initial_value="7" name="N2_r21" public_interface="out" units="dimensionless"/>
<variable name="N2_r22" public_interface="out" units="dimensionless"/>
<variable initial_value="15.728" name="P1_r21" public_interface="out" units="pascal"/>
<variable name="P1_r22" public_interface="out" units="pascal"/>
<variable initial_value="-2757.374611" name="P2_r21" public_interface="out" units="pascal"/>
<variable name="P2_r22" public_interface="out" units="pascal"/>
<variable initial_value="1" name="rho" public_interface="out" units="dimensionless"/>
<variable initial_value="1333.2239" name="P0" public_interface="out" units="pascal"/>
<!-- var kappa: dimensionless {pub:in};-->
<variable initial_value="0.296" name="rmax_r21" public_interface="out" units="mm"/>
<variable name="rmax_r22" public_interface="out" units="mm"/>
<variable initial_value="25" name="gamma" public_interface="out" units="dimensionless"/>
<variable initial_value="0.109" name="Rw_r21" public_interface="out" units="mm"/>
<variable name="Rw_r22" public_interface="out" units="mm"/>
<variable initial_value="0.058" name="Ri_r21" public_interface="out" units="mm"/>
<variable name="Ri_r22" public_interface="out" units="mm"/>
<variable initial_value="0.121" name="Rm_r21" public_interface="out" units="mm"/>
<variable name="Rm_r22" public_interface="out" units="mm"/>
<variable initial_value="0.312" name="rsmax_r21" public_interface="out" units="mm"/>
<variable name="rsmax_r22" public_interface="out" units="mm"/>
<variable initial_value="5.8" name="moo" public_interface="out" units="dimensionless"/>
<variable initial_value="1.5" name="noo" public_interface="out" units="dimensionless"/>
<variable initial_value="0.25" name="f" public_interface="out" units="per_second"/>
<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>
<map_components 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>
<map_components 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>
<map_components 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>
<map_components component_1="Environment" component_2="airway2_vals"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="airway2_vals" component_2="stress"/>
<map_variables variable_1="stress" variable_2="stress"/>
</connection>
<connection>
<map_components component_1="Environment" component_2="lambert_r21"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="stress" component_2="lambert_r21"/>
<map_variables variable_1="stress" variable_2="stress"/>
</connection>
<connection>
<map_components 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>
<map_components 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>
<map_components 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>
<map_components component_1="Environment" component_2="airway22_vals"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="airway22_vals" component_2="stress"/>
<map_variables variable_1="stress" variable_2="stress"/>
</connection>
<connection>
<map_components component_1="Environment" component_2="lambert_r22"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="stress" component_2="lambert_r22"/>
<map_variables variable_1="stress" variable_2="stress"/>
</connection>
<connection>
<map_components component_1="Environment" component_2="AMp"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Environment" component_2="AM"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Environment" component_2="Mp"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Environment" component_2="M"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Environment" component_2="model_parameters"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
</model>
