Location: Respiratory System @ ef2111347414 / full.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/full.cellml
<?xml version='1.0'?>
<model name="lung_mechanics" 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"/>
</import>
<component name="environment">
<variable name="time" public_interface="out" units="second"/>
</component>
<component name="lung_mechanics">
<variable name="t" public_interface="in" units="second"/>
<variable name="time" public_interface="out" units="second"/>
<!-- air pressure-->
<variable initial_value="0.0" name="u_ao" units="J_per_m3"/>
<variable initial_value="0.0" name="u_l" units="J_per_m3"/>
<variable name="u_tr" units="J_per_m3"/>
<variable name="u_b" units="J_per_m3"/>
<variable name="u_bA" units="J_per_m3"/>
<variable name="u_pl" units="J_per_m3"/>
<variable name="u_mus" units="J_per_m3"/>
<variable initial_value="0.0" name="u_trpl" units="J_per_m3"/>
<variable initial_value="0.0" name="u_bpl" units="J_per_m3"/>
<variable initial_value="0.0" name="u_A" units="J_per_m3"/>
<variable initial_value="0.0" name="u_cw" units="J_per_m3"/>
<!-- air flow-->
<variable name="v_lt" public_interface="out" units="m3_per_s"/>
<variable name="v_tb" public_interface="out" units="m3_per_s"/>
<variable name="v_A" public_interface="out" units="m3_per_s"/>
<variable name="v_tr" public_interface="out" units="m3_per_s"/>
<variable name="v_b" public_interface="out" units="m3_per_s"/>
<variable name="v_cw" public_interface="out" units="m3_per_s"/>
<variable name="v_l" public_interface="out" units="m3_per_s"/>
<!-- unstressed volume-->
<variable initial_value="34.4e-6" name="q_l" public_interface="out" units="m3"/>
<variable initial_value="6.63e-6" name="q_tr" public_interface="out" units="m3"/>
<variable initial_value="18.7e-6" name="q_b" public_interface="out" units="m3"/>
<variable initial_value="1.263e-6" name="q_A" public_interface="out" units="m3"/>
<variable initial_value="0.0" name="q_cw" public_interface="out" units="m3"/>
<!-- resistance-->
<variable initial_value="100125.9" name="R_ml" units="J_s_per_m6"/>
<variable initial_value="33038.604" name="R_lt" units="J_s_per_m6"/>
<variable initial_value="30037.769" name="R_tb" units="J_s_per_m6"/>
<variable initial_value="8012.033" name="R_bA" units="J_s_per_m6"/>
<!-- compliance-->
<variable initial_value="0.00000001295" name="C_l" units="m6_per_J"/>
<variable initial_value="0.000000024269246" name="C_tr" units="m6_per_J"/>
<variable initial_value="0.000000133582824" name="C_b" units="m6_per_J"/>
<variable initial_value="0.0000020239432426" name="C_A" units="m6_per_J"/>
<variable initial_value="0.000002493206141" name="C_cw" units="m6_per_J"/>
<!-- parameters-->
<variable initial_value="0.6" name="IE_ratio" units="dimensionless"/>
<variable initial_value="12" name="RR" units="dimensionless"/>
<variable initial_value="-490.333" name="u_mus_min" units="J_per_m3"/>
<variable name="tau" units="second"/>
<variable name="T" units="second"/>
<variable name="T_E" units="second"/>
<variable name="T_l" units="second"/>
<!-- respiratory muscle-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>time</ci>
<apply>
<minus/>
<ci>t</ci>
<apply>
<times/>
<apply>
<floor/>
<apply>
<divide/>
<ci>t</ci>
<ci>T</ci>
</apply>
</apply>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>T</ci>
<apply>
<divide/>
<cn cellml:units="second">60</cn>
<ci>RR</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>T_l</ci>
<apply>
<times/>
<ci>T_E</ci>
<ci>IE_ratio</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>T</ci>
<apply>
<plus/>
<ci>T_E</ci>
<ci>T_l</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>tau</ci>
<apply>
<divide/>
<ci>T_E</ci>
<cn cellml:units="dimensionless">5</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>u_mus</ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci>u_mus_min</ci>
</apply>
<ci>time</ci>
<ci>time</ci>
</apply>
<apply>
<times/>
<ci>u_mus_min</ci>
<ci>T</ci>
<ci>time</ci>
</apply>
</apply>
<apply>
<times/>
<ci>T_l</ci>
<ci>T_E</ci>
</apply>
</apply>
<apply>
<and/>
<apply>
<geq/>
<ci>time</ci>
<cn cellml:units="second">0</cn>
</apply>
<apply>
<leq/>
<ci>time</ci>
<ci>T_l</ci>
</apply>
</apply>
</piece>
<piece>
<apply>
<times/>
<apply>
<divide/>
<ci>u_mus_min</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>T_E</ci>
</apply>
<ci>tau</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>time</ci>
<ci>T_l</ci>
</apply>
</apply>
<ci>tau</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>T_E</ci>
</apply>
<ci>tau</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<and/>
<apply>
<gt/>
<ci>time</ci>
<ci>T_l</ci>
</apply>
<apply>
<leq/>
<ci>time</ci>
<ci>T</ci>
</apply>
</apply>
</piece>
</piecewise>
</apply>
<apply>
<eq/>
<ci>v_cw</ci>
<apply>
<plus/>
<ci>v_tr</ci>
<ci>v_b</ci>
<ci>v_A</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_b</ci>
<apply>
<minus/>
<ci>v_tb</ci>
<ci>v_A</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_tr</ci>
<apply>
<minus/>
<ci>v_lt</ci>
<ci>v_tb</ci>
</apply>
</apply>
<!-- chest wall-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>u_cw</ci>
</apply>
<apply>
<divide/>
<ci>v_cw</ci>
<ci>C_cw</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_cw</ci>
<apply>
<minus/>
<ci>u_pl</ci>
<ci>u_mus</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_cw</ci>
</apply>
<ci>v_cw</ci>
</apply>
<!-- alveolar-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>u_A</ci>
</apply>
<apply>
<divide/>
<ci>v_A</ci>
<ci>C_A</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_A</ci>
<apply>
<divide/>
<ci>u_bA</ci>
<ci>R_bA</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_bA</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>u_b</ci>
<ci>u_A</ci>
</apply>
<ci>u_pl</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_A</ci>
</apply>
<ci>v_A</ci>
</apply>
<!-- bronchea-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>u_bpl</ci>
</apply>
<apply>
<divide/>
<ci>v_b</ci>
<ci>C_b</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_b</ci>
<apply>
<plus/>
<ci>u_bpl</ci>
<ci>u_pl</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_b</ci>
</apply>
<ci>v_b</ci>
</apply>
<!-- trachea-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>u_trpl</ci>
</apply>
<apply>
<divide/>
<ci>v_tr</ci>
<ci>C_tr</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_tr</ci>
<apply>
<plus/>
<ci>u_trpl</ci>
<ci>u_pl</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_tr</ci>
</apply>
<ci>v_tr</ci>
</apply>
<!-- larynx-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>u_l</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_ao</ci>
<ci>u_l</ci>
</apply>
<ci>R_ml</ci>
</apply>
<ci>v_lt</ci>
</apply>
<ci>C_l</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_l</ci>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_l</ci>
</apply>
<ci>R_ml</ci>
</apply>
<ci>v_lt</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_l</ci>
</apply>
<ci>v_l</ci>
</apply>
<!-- -->
<apply>
<eq/>
<ci>v_lt</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_l</ci>
<ci>u_tr</ci>
</apply>
<ci>R_lt</ci>
</apply>
</apply>
<!-- -->
<apply>
<eq/>
<ci>v_tb</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_tr</ci>
<ci>u_b</ci>
</apply>
<ci>R_tb</ci>
</apply>
</apply>
<!-- -->
<apply>
<eq/>
<ci>V_D</ci>
<apply>
<plus/>
<ci>q_l</ci>
<ci>q_tr</ci>
<ci>q_b</ci>
</apply>
</apply>
</math>
<!-- air flow from lung-->
<variable initial_value="1.0" name="v_I" units="m3_per_s"/>
<variable initial_value="1.0" name="vv_A" units="m3_per_s"/>
<!-- air volume from dead space, alveolar, and pulmonary capillaries-->
<variable name="V_D" units="m3"/>
<variable initial_value="1.0" name="V_A" units="m3"/>
<variable initial_value="1.0" name="V_PP" units="m3"/>
<!-- 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"/>
<!-- Inhale and Exhale-->
<variable name="H" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>H</ci>
<piecewise>
<piece>
<cn cellml:units="dimensionless">1</cn>
<apply>
<gt/>
<ci>v_I</ci>
<cn cellml:units="m3_per_s">0</cn>
</apply>
</piece>
<piece>
<cn cellml:units="dimensionless">0</cn>
<apply>
<leq/>
<ci>v_I</ci>
<cn cellml:units="m3_per_s">0</cn>
</apply>
</piece>
</piecewise>
</apply>
</math>
<!-- Gas fraction-->
<variable initial_value="0.210379" name="F_I_O2" units="dimensionless"/>
<variable initial_value="86.11" name="F_I_CO2" units="dimensionless"/>
<variable initial_value="0.0" name="F_A_O2" units="dimensionless"/>
<variable initial_value="0.0" name="F_A_CO2" units="dimensionless"/>
<variable initial_value="0.0" name="F_D_O2" units="dimensionless"/>
<variable initial_value="0.0" name="F_D_CO2" units="dimensionless"/>
<variable initial_value="1.2103" name="K" units="dimensionless"/>
<variable initial_value="1.7" name="sh" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>F_D_O2</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci>H</ci>
<ci>v_I</ci>
<apply>
<minus/>
<ci>F_I_O2</ci>
<ci>F_D_O2</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<abs/>
<apply>
<minus/>
<ci>H</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
<ci>vv_A</ci>
<apply>
<minus/>
<ci>F_D_O2</ci>
<ci>F_A_O2</ci>
</apply>
</apply>
</apply>
<ci>V_D</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>F_D_CO2</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci>H</ci>
<ci>v_I</ci>
<apply>
<minus/>
<ci>F_I_CO2</ci>
<ci>F_D_CO2</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<abs/>
<apply>
<minus/>
<ci>H</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
<ci>vv_A</ci>
<apply>
<minus/>
<ci>F_D_CO2</ci>
<ci>F_A_CO2</ci>
</apply>
</apply>
</apply>
<ci>V_D</ci>
</apply>
</apply>
<!-- ode(F_A_O2, t) = (H*v_A*(F_D_O2-F_A_O2)-K*(Q_pa*(1{dimensionless}-sh)*(C_pp_O2-C_v_O2)+V_PP*ode(C_pp_O2, t)))/V_A;
ode(F_A_CO2, t) = (H*v_A*(F_D_CO2-F_A_CO2)-K*(Q_pa*(1{dimensionless}-sh)*(C_pp_CO2-C_v_CO2)+V_PP*ode(C_pp_CO2, t)))/V_A;-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>F_A_O2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>H</ci>
<ci>v_A</ci>
<apply>
<minus/>
<ci>F_D_O2</ci>
<ci>F_A_O2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>K</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>Q_pa</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>sh</ci>
</apply>
<apply>
<minus/>
<ci>C_pp_O2</ci>
<ci>C_v_O2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>V_PP</ci>
<ci>C_pp_O2</ci>
</apply>
</apply>
</apply>
</apply>
<ci>V_A</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>F_A_CO2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>H</ci>
<ci>v_A</ci>
<apply>
<minus/>
<ci>F_D_CO2</ci>
<ci>F_A_CO2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>K</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>Q_pa</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>sh</ci>
</apply>
<apply>
<minus/>
<ci>C_pp_CO2</ci>
<ci>C_v_CO2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>V_PP</ci>
<ci>C_pp_CO2</ci>
</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>
</math>
<!-- Gas pressure in alveoli and pulmonary capillaries-->
<variable name="P_A_O2" public_interface="out" units="J_per_m3"/>
<variable name="P_A_CO2" public_interface="out" units="J_per_m3"/>
<variable name="P_pp_O2" units="J_per_m3"/>
<variable name="P_pp_CO2" units="J_per_m3"/>
<variable initial_value="760" name="P_atm" units="J_per_m3"/>
<variable initial_value="47" name="P_WS" units="J_per_m3"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>P_A_O2</ci>
<apply>
<times/>
<ci>F_A_O2</ci>
<apply>
<minus/>
<ci>P_atm</ci>
<ci>P_WS</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>P_A_CO2</ci>
<apply>
<times/>
<ci>F_A_CO2</ci>
<apply>
<minus/>
<ci>P_atm</ci>
<ci>P_WS</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>P_pp_O2</ci>
<ci>P_A_O2</ci>
</apply>
<apply>
<eq/>
<ci>P_pp_CO2</ci>
<ci>P_A_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" units="mM"/>
<variable initial_value="0.0" name="C_v_CO2" 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-->
<variable name="S_a_O2" units="mM"/>
<variable initial_value="0.0" name="P_a_O2" units="J_per_m3"/>
<variable initial_value="15" name="Hgb" public_interface="out" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>S_a_O2</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<minus/>
<ci>C_a_O2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>P_a_O2</ci>
<cn cellml:units="dimensionless">0.003</cn>
</apply>
<cn cellml:units="dimensionless">100</cn>
</apply>
</apply>
<apply>
<times/>
<ci>Hgb</ci>
<cn cellml:units="dimensionless">1.34</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">100</cn>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="environment" component_2="lung_mechanics"/>
<map_variables variable_1="time" variable_2="t"/>
</connection>
</model>