Location: Respiratory System @ ef2111347414 / lung_gas_exchange.cellml
- Author:
- Soroush Safaei <ssaf006@aucklanduni.ac.nz>
- Date:
- 2018-07-26 17:41:12+12:00
- Desc:
- adding new model
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/3a4/rawfile/ef211134741455b4bb947067d786989076afe41e/lung_gas_exchange.cellml
<?xml version='1.0'?>
<model name="lung_gas_exchange" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#" xmlns:xlink="http://www.w3.org/1999/xlink">
<import xlink:href="Units.cellml">
<units name="m3" units_ref="m3"/>
<units name="mM" units_ref="mM"/>
<units name="m3_per_s" units_ref="m3_per_s"/>
<units name="m6_per_J" units_ref="m6_per_J"/>
<units name="m3_per_J" units_ref="m3_per_J"/>
<units name="per_m" units_ref="per_m"/>
<units name="J_per_m3" units_ref="J_per_m3"/>
<units name="J_s_per_m6" units_ref="J_s_per_m6"/>
<units name="J_s2_per_m6" units_ref="J_s2_per_m6"/>
<units name="J_s2_per_m5" units_ref="J_s2_per_m5"/>
<units name="J_per_s" units_ref="J_per_s"/>
<units name="J_per_m6" units_ref="J_per_m6"/>
<units name="J_s_per_m3" units_ref="J_s_per_m3"/>
<units name="mol_per_s_mmHg" units_ref="mol_per_s_mmHg"/>
<units name="mmHg" units_ref="mmHg"/>
<units name="per_s" units_ref="per_s"/>
</import>
<component name="environment">
<variable name="time" public_interface="out" units="second"/>
</component>
<component name="lung_gas_exchange">
<variable name="t" public_interface="in" units="second"/>
<!-- air flow from lung-->
<variable name="v_I" units="m3_per_s"/>
<variable initial_value="1.0" name="v_A" units="m3_per_s"/>
<!-- blood flow from pulmonary arteries, at the exit of pulmonary capillaries, and at the exit of pulmonary shunt-->
<variable initial_value="1.0" name="Q_pa" units="m3_per_s"/>
<variable initial_value="1.0" name="Q_pp" units="m3_per_s"/>
<variable initial_value="1.0" name="Q_ps" units="m3_per_s"/>
<variable initial_value="1.2103" name="K" units="dimensionless"/>
<variable initial_value="1.7" name="sh" units="dimensionless"/>
<!-- Gas fraction-->
<variable name="C_In_O2" units="dimensionless"/>
<variable name="C_In_CO2" units="dimensionless"/>
<variable initial_value="0.0" name="C_Al_O2" units="dimensionless"/>
<variable initial_value="0.0" name="C_Al_CO2" units="dimensionless"/>
<variable initial_value="0.210379" name="C_D_O2" units="dimensionless"/>
<variable initial_value="86.11" name="C_D_CO2" units="dimensionless"/>
<variable initial_value="760" name="P_atm" units="J_per_m3"/>
<variable initial_value="47" name="P_w" units="J_per_m3"/>
<variable initial_value="97.5" name="P_Al_O2" units="mmHg"/>
<variable initial_value="37.5" name="P_Al_CO2" units="mmHg"/>
<variable initial_value="40" name="P_pp_O2" units="J_per_m3"/>
<variable initial_value="46" name="P_pp_CO2" units="J_per_m3"/>
<variable initial_value="1.56e-5" name="D_O2" units="mol_per_s_mmHg"/>
<variable initial_value="3.16e-5" name="D_CO2" units="mol_per_s_mmHg"/>
<variable initial_value="0.151" name="V_D" units="m3"/>
<variable initial_value="0.41" name="V_T" units="m3"/>
<variable initial_value="0.071" name="V_pp" units="m3"/>
<variable initial_value="1.0" name="V_A" units="m3"/>
<variable initial_value="1.257" name="omega" units="per_s"/>
<!-- inspired air-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_I</ci>
<piecewise>
<piece>
<apply>
<times/>
<apply>
<divide/>
<ci>V_T</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>omega</ci>
<apply>
<sin/>
<apply>
<times/>
<ci>omega</ci>
<ci>t</ci>
</apply>
</apply>
</apply>
<apply>
<leq/>
<apply>
<lt/>
<cn cellml:units="dimensionless">0</cn>
<ci>t</ci>
</apply>
<apply>
<divide/>
<pi/>
<ci>omega</ci>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="dimensionless">0</cn>
<apply>
<leq/>
<apply>
<lt/>
<apply>
<divide/>
<pi/>
<ci>omega</ci>
</apply>
<ci>t</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<pi/>
</apply>
<ci>omega</ci>
</apply>
</apply>
</piece>
</piecewise>
</apply>
<!-- inspired O2 & CO2 concentration-->
<apply>
<eq/>
<ci>C_In_O2</ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci>C_Al_O2</ci>
<ci>V_D</ci>
</apply>
<apply>
<times/>
<ci>C_D_O2</ci>
<apply>
<minus/>
<ci>V_T</ci>
<ci>V_D</ci>
</apply>
</apply>
</apply>
<ci>V_T</ci>
</apply>
<apply>
<geq/>
<ci>V_T</ci>
<ci>V_D</ci>
</apply>
</piece>
<piece>
<ci>C_Al_O2</ci>
<apply>
<lt/>
<ci>V_T</ci>
<ci>V_D</ci>
</apply>
</piece>
</piecewise>
</apply>
<apply>
<eq/>
<ci>C_In_CO2</ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci>C_Al_CO2</ci>
<ci>V_D</ci>
</apply>
<apply>
<times/>
<ci>C_D_CO2</ci>
<apply>
<minus/>
<ci>V_T</ci>
<ci>V_D</ci>
</apply>
</apply>
</apply>
<ci>V_T</ci>
</apply>
<apply>
<geq/>
<ci>V_T</ci>
<ci>V_D</ci>
</apply>
</piece>
<piece>
<ci>C_Al_CO2</ci>
<apply>
<lt/>
<ci>V_T</ci>
<ci>V_D</ci>
</apply>
</piece>
</piecewise>
</apply>
<!-- alveoli O2 & CO2 concentration-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>C_Al_O2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>D_O2</ci>
<apply>
<minus/>
<ci>P_pp_O2</ci>
<ci>P_Al_O2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>v_I</ci>
<apply>
<minus/>
<ci>C_In_O2</ci>
<ci>C_Al_O2</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>C_Al_O2</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>D_CO2</ci>
<apply>
<minus/>
<ci>P_pp_CO2</ci>
<ci>P_Al_CO2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>D_O2</ci>
<apply>
<minus/>
<ci>P_pp_O2</ci>
<ci>P_Al_O2</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<ci>V_A</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>C_Al_CO2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>D_CO2</ci>
<apply>
<minus/>
<ci>P_pp_CO2</ci>
<ci>P_Al_CO2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>v_I</ci>
<apply>
<minus/>
<ci>C_In_CO2</ci>
<ci>C_Al_CO2</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>C_Al_CO2</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>D_CO2</ci>
<apply>
<minus/>
<ci>P_pp_CO2</ci>
<ci>P_Al_CO2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>D_O2</ci>
<apply>
<minus/>
<ci>P_pp_O2</ci>
<ci>P_Al_O2</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<ci>V_A</ci>
</apply>
</apply>
</math>
<!-- // Gas concentration in pulmonary capillaries-->
<variable name="C_pp_O2" units="mM"/>
<variable name="C_pp_CO2" units="mM"/>
<variable name="X_pp_O2" units="dimensionless"/>
<variable name="X_pp_CO2" units="dimensionless"/>
<variable initial_value="9" name="C_sat_O2" units="mM"/>
<variable initial_value="86.11" name="C_sat_CO2" units="mM"/>
<variable initial_value="0.3836" name="h_1" units="dimensionless"/>
<variable initial_value="1.819" name="h_2" units="dimensionless"/>
<variable initial_value="0.03198" name="alpha_1" units="m3_per_J"/>
<variable initial_value="0.05591" name="alpha_2" units="m3_per_J"/>
<variable initial_value="0.008275" name="beta_1" units="m3_per_J"/>
<variable initial_value="0.03255" name="beta_2" units="m3_per_J"/>
<variable initial_value="14.99" name="K_1" units="J_per_m3"/>
<variable initial_value="194.4" name="K_2" units="J_per_m3"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>C_pp_O2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>C_sat_O2</ci>
<apply>
<power/>
<ci>X_pp_O2</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<ci>h_1</ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<ci>X_pp_O2</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<ci>h_1</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>C_pp_CO2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>C_sat_CO2</ci>
<apply>
<power/>
<ci>X_pp_CO2</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<ci>h_2</ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<ci>X_pp_CO2</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<ci>h_2</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>X_pp_O2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>P_pp_O2</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>beta_1</ci>
<ci>P_pp_CO2</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>K_1</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>alpha_1</ci>
<ci>P_pp_CO2</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>X_pp_CO2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>P_pp_CO2</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>beta_2</ci>
<ci>P_pp_O2</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>K_2</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>alpha_2</ci>
<ci>P_pp_O2</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<!-- // Gas pressure in alveoli and pulmonary capillaries-->
<apply>
<eq/>
<ci>P_Al_O2</ci>
<apply>
<times/>
<ci>C_Al_O2</ci>
<apply>
<minus/>
<ci>P_atm</ci>
<ci>P_w</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>P_Al_CO2</ci>
<apply>
<times/>
<ci>C_Al_CO2</ci>
<apply>
<minus/>
<ci>P_atm</ci>
<ci>P_w</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>P_pp_O2</ci>
<ci>P_Al_O2</ci>
</apply>
<apply>
<eq/>
<ci>P_pp_CO2</ci>
<ci>P_Al_CO2</ci>
</apply>
</math>
<!-- // Gas concentration in arterial blood-->
<variable name="C_a_O2" public_interface="out" units="mM"/>
<variable name="C_a_CO2" public_interface="out" units="mM"/>
<variable initial_value="0.0" name="C_v_O2" public_interface="in" units="mM"/>
<variable initial_value="0.0" name="C_v_CO2" public_interface="in" units="mM"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>C_a_O2</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci>Q_pp</ci>
<ci>C_pp_O2</ci>
</apply>
<apply>
<times/>
<ci>Q_ps</ci>
<ci>C_v_O2</ci>
</apply>
</apply>
<apply>
<plus/>
<ci>Q_pp</ci>
<ci>Q_ps</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>C_a_CO2</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci>Q_pp</ci>
<ci>C_pp_CO2</ci>
</apply>
<apply>
<times/>
<ci>Q_ps</ci>
<ci>C_v_CO2</ci>
</apply>
</apply>
<apply>
<plus/>
<ci>Q_pp</ci>
<ci>Q_ps</ci>
</apply>
</apply>
</apply>
</math>
<!-- // O2 solubility-->
<!-- var S_a_O2: mM;
var P_a_O2: J_per_m3 {init: 0.0, pub: in};
var Hgb: dimensionless {init: 15, pub: out};-->
<!-- S_a_O2 = (C_a_O2-P_a_O2*0.003{dimensionless}/100{dimensionless})/(Hgb*1.34{dimensionless})*100{dimensionless};-->
</component>
<connection>
<map_components component_1="environment" component_2="lung_gas_exchange"/>
<map_variables variable_1="time" variable_2="t"/>
</connection>
</model>