- 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/experiments/airwayradius.cellml
<!-- This is a Cellml implementation of lambert_r1's model of
airway radius coupled with ASM contraction force.
ASM contractile force is modelled as a P_Arameter kappa.
Time dependent radii is modeled via a 1st order ODE.
Airway P_Arameters are taken from Politi et al 2010.
Airway order 7 P_Arameter values are used in this model.
May include Hai-Murphy ODE for ASM contraction
--><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="airwayradius">
<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_r1">
<variable name="time" units="second" interface="public"/>
<variable name="Ri_sq_r1" units="mm2" interface="public"/>
<variable name="rmax_sq_r1" units="mm" interface="public"/>
<variable name="N1_r1" units="dimensionless" interface="public"/>
<variable name="N2_r1" units="dimensionless" interface="public"/>
<variable name="P1_r1" units="mmHg" interface="public"/>
<variable name="P2_r1" units="mmHg" interface="public"/>
<variable name="rho" units="dimensionless" interface="public"/>
<variable initial_value="0.318" name="r1" units="mm" interface="public"/>
<variable name="Ptm_r1" units="mmHg"/>
<variable name="P0" units="mmHg" interface="public"/>
<variable name="kappa" units="dimensionless" interface="public"/>
<variable name="rad_r1" units="mm" interface="public"/>
<variable name="rmax_r1" units="mm" interface="public"/>
<variable name="V_r1" units="dimensionless"/>
<variable name="gamma" units="dimensionless" interface="public"/>
<variable name="stress" units="dimensionless" interface="public"/>
<variable name="v_smc_r1" units="dimensionless" interface="public"/>
<variable name="f_a_r1" units="dimensionless" interface="public"/>
<variable name="Pmin_r1" units="mmHg" interface="public"/>
<variable name="P_t_r1" units="mmHg" interface="public"/>
<variable name="tau_r1" units="dimensionless" interface="public"/>
<variable name="pmidr1" units="mmHg" interface="public"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Pmin_r1</ci>
<apply>
<plus/>
<ci>P0</ci>
<ci>P_t_r1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Ptm_r1</ci>
<apply>
<plus/>
<apply>
<minus/>
<ci>pmidr1</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>kappa</ci>
<ci>f_a_r1</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/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>r1</ci>
</apply>
<apply>
<times/>
<ci>rho</ci>
<apply>
<minus/>
<ci>rad_r1</ci>
<ci>r1</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>V_r1</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<minus/>
<ci>gamma</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<pi/>
<ci>rmax_r1</ci>
</apply>
</apply>
<ci>rho</ci>
<apply>
<minus/>
<ci>rad_r1</ci>
<ci>r1</ci>
</apply>
<ci>v_smc_r1</ci>
</apply>
</apply>
</math>
</component>
<component name="airway1_vals">
<variable name="e_w_r1" units="dimensionless"/>
<variable name="e_m_r1" units="dimensionless"/>
<variable name="r_w_r1" units="dimensionless" interface="public"/>
<variable name="r_m_r1" units="dimensionless" interface="public"/>
<variable name="r_s_r1" units="dimensionless"/>
<variable name="Rw_r1" units="mm" interface="public"/>
<variable name="Ri_r1" units="mm" interface="public"/>
<variable name="Rm_r1" units="mm" interface="public"/>
<variable name="fl_r1" units="dimensionless"/>
<variable name="rsmax_r1" units="mm" interface="public"/>
<variable name="f_a_r1" units="dimensionless" interface="public"/>
<variable name="stress" units="dimensionless" interface="public"/>
<variable name="D_Rm_r1" units="dimensionless"/>
<variable name="sigma_rrm_r1" units="dimensionless"/>
<variable name="sigma_rrw_r1" units="dimensionless"/>
<variable name="sigma_ttm_r1" units="dimensionless"/>
<variable name="sigma_ttw_r1" units="dimensionless"/>
<variable name="moo" units="dimensionless" interface="public"/>
<variable name="noo" units="dimensionless" interface="public"/>
<variable name="P_t_r1" units="mmHg" interface="public"/>
<variable name="f" units="per_second" interface="public"/>
<variable name="time" units="second" interface="public"/>
<variable name="rad_r1" units="mm" interface="public"/>
<variable name="r1" units="mm" interface="public"/>
<variable name="v_smc_r1" 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_r1</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_r1</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>Rw_r1</ci>
<ci>Ri_r1</ci>
</apply>
<ci>Ri_r1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>e_m_r1</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>Rm_r1</ci>
<ci>Rw_r1</ci>
</apply>
<ci>Ri_r1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>r_w_r1</ci>
<apply>
<times/>
<ci>Ri_r1</ci>
<apply>
<root/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<ci>e_w_r1</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci>rad_r1</ci>
<ci>Ri_r1</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_r1</ci>
<apply>
<times/>
<ci>Ri_r1</ci>
<apply>
<root/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<power/>
<apply>
<plus/>
<ci>e_m_r1</ci>
<ci>e_w_r1</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci>rad_r1</ci>
<ci>Ri_r1</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_r1</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.5</cn>
<apply>
<plus/>
<ci>r_w_r1</ci>
<ci>r_m_r1</ci>
</apply>
</apply>
</apply>
<!-- Expt data fit for AM force at latch state-->
<apply>
<eq/>
<ci>fl_r1</ci>
<piecewise>
<piece>
<apply>
<power/>
<apply>
<times/>
<cn cellml:units="dimensionless">0</cn>
<apply>
<sin/>
<apply>
<divide/>
<apply>
<times/>
<pi/>
<ci>r_s_r1</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>rsmax_r1</ci>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
<apply>
<leq/>
<ci>r_s_r1</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>rsmax_r1</ci>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="dimensionless">0</cn>
</otherwise>
</piecewise>
</apply>
<!-- Total active force-->
<apply>
<eq/>
<ci>f_a_r1</ci>
<apply>
<plus/>
<ci>fl_r1</ci>
<ci>stress</ci>
</apply>
</apply>
<!-- Radial stress-->
<apply>
<eq/>
<ci>D_Rm_r1</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>Rm_r1</ci>
<ci>r_m_r1</ci>
</apply>
<ci>Rm_r1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>sigma_rrm_r1</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>moo</ci>
<apply>
<plus/>
<ci>D_Rm_r1</ci>
<apply>
<power/>
<apply>
<times/>
<ci>noo</ci>
<ci>D_Rm_r1</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<ci>P_t_r1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>sigma_rrw_r1</ci>
<apply>
<minus/>
<ci>sigma_rrm_r1</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>f_a_r1</ci>
<apply>
<minus/>
<ci>Rm_r1</ci>
<ci>Rw_r1</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.5</cn>
<apply>
<plus/>
<ci>r_m_r1</ci>
<ci>r_w_r1</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<!-- Hoop stress-->
<apply>
<eq/>
<ci>sigma_ttm_r1</ci>
<apply>
<plus/>
<ci>sigma_rrm_r1</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>f_a_r1</ci>
<apply>
<minus/>
<ci>Rm_r1</ci>
<ci>Rw_r1</ci>
</apply>
</apply>
<apply>
<plus/>
<ci>r_m_r1</ci>
<ci>r_w_r1</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>sigma_ttw_r1</ci>
<apply>
<plus/>
<ci>sigma_rrw_r1</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>f_a_r1</ci>
<apply>
<minus/>
<ci>Rm_r1</ci>
<ci>Rw_r1</ci>
</apply>
</apply>
<apply>
<plus/>
<ci>r_m_r1</ci>
<ci>r_w_r1</ci>
</apply>
</apply>
</apply>
</apply>
<!--Vel of SMC contraction-->
<apply>
<eq/>
<ci>v_smc_r1</ci>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<minus/>
<ci>r_w_r1</ci>
<ci>r_m_r1</ci>
</apply>
</apply>
<ci>rho</ci>
<apply>
<minus/>
<ci>rad_r1</ci>
<ci>r1</ci>
</apply>
<ci>rad_r1</ci>
<apply>
<ln/>
<apply>
<divide/>
<ci>r_w_r1</ci>
<ci>r_m_r1</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="parameters">
<variable initial_value="0.004225" name="Ri_sq_r1" units="mm2" interface="public"/>
<variable initial_value="0.1011" name="rmax_sq_r1" units="mm" interface="public"/>
<variable initial_value="1" name="N1_r1" units="dimensionless" interface="public"/>
<variable initial_value="8" name="N2_r1" units="dimensionless" interface="public"/>
<variable initial_value="0.130075752" name="P1_r1" units="mmHg" interface="public"/>
<variable initial_value="-20.88271528" name="P2_r1" units="mmHg" interface="public"/>
<variable initial_value="1" name="rho" units="dimensionless" interface="public"/>
<variable initial_value="6" name="P0" units="mmHg" interface="public"/>
<!-- var kappa: dimensionless {pub:in};-->
<variable initial_value="0.318" name="rmax_r1" units="mm" interface="public"/>
<variable initial_value="25" name="gamma" units="dimensionless" interface="public"/>
<variable initial_value="0.116" name="Rw_r1" units="mm" interface="public"/>
<variable initial_value="0.065" name="Ri_r1" units="mm" interface="public"/>
<variable initial_value="0.128" name="Rm_r1" units="mm" interface="public"/>
<variable initial_value="0.334" name="rsmax_r1" 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"/>
</component>
<connection component_1="parameters" component_2="airway1_vals">
<map_variables variable_1="Rw_r1" variable_2="Rw_r1"/>
<map_variables variable_1="Rm_r1" variable_2="Rm_r1"/>
<map_variables variable_1="Ri_r1" variable_2="Ri_r1"/>
<map_variables variable_1="rsmax_r1" variable_2="rsmax_r1"/>
<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" component_2="lambert_r1">
<map_variables variable_1="Ri_sq_r1" variable_2="Ri_sq_r1"/>
<map_variables variable_1="rmax_sq_r1" variable_2="rmax_sq_r1"/>
<map_variables variable_1="N1_r1" variable_2="N1_r1"/>
<map_variables variable_1="N2_r1" variable_2="N2_r1"/>
<map_variables variable_1="P1_r1" variable_2="P1_r1"/>
<map_variables variable_1="P2_r1" variable_2="P2_r1"/>
<map_variables variable_1="rho" variable_2="rho"/>
<map_variables variable_1="rmax_r1" variable_2="rmax_r1"/>
<!-- vars kappa and kappa;-->
<map_variables variable_1="P0" variable_2="P0"/>
<map_variables variable_1="gamma" variable_2="gamma"/>
</connection>
<connection component_1="airway1_vals" component_2="lambert_r1">
<map_variables variable_1="v_smc_r1" variable_2="v_smc_r1"/>
<map_variables variable_1="rad_r1" variable_2="rad_r1"/>
<map_variables variable_1="r1" variable_2="r1"/>
<map_variables variable_1="f_a_r1" variable_2="f_a_r1"/>
<map_variables variable_1="P_t_r1" variable_2="P_t_r1"/>
</connection>
<connection component_1="airway1_vals" component_2="stress">
<map_variables variable_1="stress" variable_2="stress"/>
</connection>
<connection component_1="Environment" component_2="airway1_vals">
<map_variables variable_1="time" variable_2="time"/>
</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="Environment" component_2="lambert_r1">
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection component_1="stress" component_2="lambert_r1">
<map_variables variable_1="stress" variable_2="stress"/>
</connection>
</model>
