- Author:
- aram148 <a.rampadarath@auckland.ac.nz>
- Date:
- 2021-11-08 11:40:18+13:00
- Desc:
- Added updated order3
- Permanent Source URI:
- https://models.cellml.org/workspace/6b0/rawfile/2585da81062ff07f754993f4bbb065c930b09754/Airway_FTU/Airway_FTU/airwayradius1.cellml
<?xml version='1.0'?>
<!-- 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 name="airwayradius" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:xlink="http://www.w3.org/1999/xlink">
<units name="mm2">
<unit exponent="2" prefix="milli" units="metre"/>
</units>
<units name="mm">
<unit prefix="milli" units="metre"/>
</units>
<units name="per_sec">
<unit exponent="-1" units="second"/>
</units>
<component name="Environment">
<variable cmeta:id="Environment_time" name="time" public_interface="out" units="second"/>
</component>
<import xlink:href="hai_1.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_parameters1" name="model_parameters1"/>
</import>
<component name="lambert_r1">
<variable name="time" public_interface="in" units="second"/>
<variable name="Ri_sq_r1" public_interface="in" units="mm2"/>
<variable name="rmax_sq_r1" public_interface="in" units="mm"/>
<variable name="N1_r1" public_interface="in" units="dimensionless"/>
<variable name="N2_r1" public_interface="in" units="dimensionless"/>
<variable name="P1_r1" public_interface="in" units="pascal"/>
<variable name="P2_r1" public_interface="in" units="pascal"/>
<variable name="rho" public_interface="in" units="dimensionless"/>
<variable initial_value="0.318" name="r1" public_interface="out" units="mm"/>
<variable name="Ptm_r1" public_interface="out" units="pascal"/>
<variable name="P0" public_interface="in" units="pascal"/>
<variable name="rad_r1" public_interface="out" units="mm"/>
<variable name="rmax_r1" public_interface="in" units="mm"/>
<variable name="V_r1" units="dimensionless"/>
<variable name="gamma" public_interface="in" units="dimensionless"/>
<variable name="stress" public_interface="in" units="dimensionless"/>
<variable name="v_smc_r1" public_interface="in" units="dimensionless"/>
<variable name="f_a_r1" public_interface="in" units="pascal"/>
<variable name="Pmin_r1" public_interface="out" units="pascal"/>
<variable name="P_t_r1" public_interface="in" units="pascal"/>
<variable name="tau_r1" public_interface="in" units="dimensionless"/>
<variable name="pmidr1" public_interface="in" units="pascal"/>
<variable initial_value="0.445" name="R_ref" units="mm"/>
<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>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/>
<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" public_interface="out" units="mm"/>
<variable name="r_m_r1" public_interface="out" units="mm"/>
<variable name="r_s_r1" units="mm"/>
<variable name="Rw_r1" public_interface="in" units="mm"/>
<variable name="Ri_r1" public_interface="in" units="mm"/>
<variable name="Rm_r1" public_interface="in" units="mm"/>
<variable name="fl_r1" units="dimensionless"/>
<variable name="rsmax_r1" public_interface="in" units="mm"/>
<variable name="f_a_r1" public_interface="out" units="pascal"/>
<variable name="stress" public_interface="in" units="dimensionless"/>
<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" public_interface="in" units="dimensionless"/>
<variable name="noo" public_interface="in" units="dimensionless"/>
<variable name="P_t_r1" public_interface="out" units="pascal"/>
<variable name="f" public_interface="in" units="per_sec"/>
<variable name="time" public_interface="in" units="second"/>
<variable name="rad_r1" public_interface="in" units="mm"/>
<variable name="r1" public_interface="in" units="mm"/>
<variable name="v_smc_r1" public_interface="out" units="dimensionless"/>
<variable name="rho" public_interface="in" units="dimensionless"/>
<variable name="kappa" public_interface="in" units="pascal"/>
<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>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>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-->
<!-- fl_r1 = sel
case r_s_r1 <= 2{dimensionless}*rsmax_r1:
pow(sin(pi*r_s_r1/(2{dimensionless}*rsmax_r1)), 3{dimensionless});
otherwise:
0{dimensionless};
endsel;-->
<apply>
<eq/>
<ci>fl_r1</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<!-- Total active force-->
<apply>
<eq/>
<ci>f_a_r1</ci>
<apply>
<times/>
<ci>fl_r1</ci>
<ci>kappa</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>
<times/>
<ci>noo</ci>
<apply>
<power/>
<ci>D_Rm_r1</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</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" public_interface="out" units="mm2"/>
<variable initial_value="0.1011" name="rmax_sq_r1" public_interface="out" units="mm"/>
<variable initial_value="1" name="N1_r1" public_interface="out" units="dimensionless"/>
<variable initial_value="7" name="N2_r1" public_interface="out" units="dimensionless"/>
<variable initial_value="17.342" name="P1_r1" public_interface="out" units="pascal"/>
<variable initial_value="-2784.131883" name="P2_r1" public_interface="out" units="pascal"/>
<variable initial_value="1" name="rho" public_interface="out" units="dimensionless"/>
<variable initial_value="799.93434" name="P0" public_interface="out" units="pascal"/>
<!-- var kappa: dimensionless {pub:in};-->
<variable initial_value="0.318" name="rmax_r1" public_interface="out" units="mm"/>
<variable initial_value="25" name="gamma" public_interface="out" units="dimensionless"/>
<variable initial_value="0.116" name="Rw_r1" public_interface="out" units="mm"/>
<variable initial_value="0.065" name="Ri_r1" public_interface="out" units="mm"/>
<variable initial_value="0.128" name="Rm_r1" public_interface="out" units="mm"/>
<variable initial_value="0.334" name="rsmax_r1" 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_sec"/>
</component>
</model>
