Location: Pulmonary Acinus pFTU @ ee4cf115a7c1 / AthanasiadesPHSinSIwithGasET.cellml
- Author:
- Jagirhussan <r.jagir@auckland.ac.nz>
- Date:
- 2025-06-10 12:56:52+12:00
- Desc:
- Consistent SI units
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/d35/rawfile/ee4cf115a7c1cbe2a64ac1e68d1313f66b2b1af0/AthanasiadesPHSinSIwithGasET.cellml
<?xml version='1.0' encoding='UTF-8'?>
<model name="PulmonaryAcinusFTUBasedOnAthanasiadesModel" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
<units name="per_second">
<unit exponent="-1" units="second"/>
</units>
<units name="minute">
<unit multiplier="60" units="second"/>
</units>
<units name="per_min">
<unit exponent="-1" units="minute"/>
</units>
<units name="Pa">
<unit units="pascal"/>
</units>
<units name="L">
<unit units="litre"/>
</units>
<units name="L_per_second">
<unit units="litre"/>
<unit exponent="-1" units="second"/>
</units>
<units name="L_per_Pa">
<unit units="L"/>
<unit exponent="-1" units="Pa"/>
</units>
<units name="per_L">
<unit exponent="-1" units="L"/>
</units>
<units name="Pa_sec_per_L">
<unit units="Pa"/>
<unit units="second"/>
<unit exponent="-1" units="liter"/>
</units>
<units name="Pa_sec2_per_L2">
<unit units="Pa"/>
<unit units="second"/>
<unit exponent="-2" units="liter"/>
</units>
<units name="J_per_mole_per_kelvin">
<unit units="joule"/>
<unit exponent="-1" units="mole"/>
<unit exponent="-1" units="kelvin"/>
</units>
<units name="grams_per_mole">
<unit units="gram"/>
<unit exponent="-1" units="mole"/>
</units>
<units name="L_per_mole">
<unit units="litre"/>
<unit exponent="-1" units="mole"/>
</units>
<units name="mole_per_second_Pa">
<unit units="mole"/>
<unit exponent="-1" units="second"/>
<unit exponent="-1" units="pascal"/>
</units>
<units name="Joule_per_mole_per_kelvin">
<unit units="joule"/>
<unit exponent="-1" units="mole"/>
<unit exponent="-1" units="kelvin"/>
</units>
<units name="mole_per_L">
<unit units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="mole_per_L_Pa">
<unit units="mole"/>
<unit exponent="-1" units="litre"/>
<unit exponent="-1" units="pascal"/>
</units>
<units name="L_per_second_mole">
<unit units="litre"/>
<unit exponent="-1" units="second"/>
<unit exponent="-1" units="mole"/>
</units>
<units name="Pa_second_per_meter3">
<unit units="Pa"/>
<unit units="second"/>
<unit exponent="-3" units="metre"/>
</units>
<component name="Environment">
<variable name="time" public_interface="out" units="second"/>
<variable initial_value="24064" name="numAlveoli" public_interface="out" units="dimensionless"/>
</component>
<component name="gasExchange">
<variable name="time" public_interface="in" units="second"/>
<variable name="numAlveoli" public_interface="in" units="dimensionless"/>
<variable name="breathsPerMin" public_interface="in" units="per_min"/>
<variable name="P_A" public_interface="in" units="Pa"/>
<variable name="V_A" public_interface="in" units="litre"/>
<variable initial_value="1.17e-07" name="D_o_" public_interface="out" units="mole_per_second_Pa"/>
<variable initial_value="0.21000" name="f_o" public_interface="out" units="dimensionless"/>
<variable name="f_oi" units="dimensionless"/>
<variable initial_value="2.37e-07" name="D_c" public_interface="out" units="mole_per_second_Pa"/>
<variable initial_value="2.7732e-06" name="f_c" units="dimensionless"/>
<variable name="f_ci" units="dimensionless"/>
<variable initial_value="6266.15" name="P_w" public_interface="out" units="Pa"/>
<variable initial_value="101325" name="P_m" units="Pa"/>
<variable name="p_ao" units="Pa"/>
<variable name="p_o" public_interface="in" units="Pa"/>
<variable name="p_ac" public_interface="out" units="Pa"/>
<variable initial_value="0.21" name="f_om" units="dimensionless"/>
<variable initial_value="0" name="f_cm" units="dimensionless"/>
<variable name="Q_A" public_interface="out" units="L_per_second"/>
<variable name="p_c" public_interface="in" units="Pa"/>
<variable initial_value="0.185" name="V_D" units="litre"/>
<variable initial_value="0.41" name="V_T" units="litre"/>
<variable initial_value="0.65" name="AlveolarResistance" units="Pa_second_per_meter3"/>
<variable name="D_o" units="mole_per_second_Pa"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>D_o</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>D_o_</ci>
<cn cellml:units="dimensionless">15</cn>
</apply>
<ci>breathsPerMin</ci>
</apply>
</apply>
</math>
<!--Diffusion capacity physiologically decreases at high frequencies (shorter alveolar contact time),-->
<!--var q: L_per_second {pub: in};-->
<variable name="q" units="L_per_second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>q</ci>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<minus/>
<ci>P_m</ci>
<ci>P_A</ci>
</apply>
<ci>numAlveoli</ci>
</apply>
<ci>AlveolarResistance</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>p_ao</ci>
<apply>
<times/>
<ci>f_o</ci>
<apply>
<minus/>
<ci>P_A</ci>
<ci>P_w</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>p_ac</ci>
<apply>
<times/>
<ci>f_c</ci>
<apply>
<minus/>
<ci>P_A</ci>
<ci>P_w</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_A</ci>
<apply>
<plus/>
<ci>q</ci>
<apply>
<times/>
<cn cellml:units="L_per_mole">1</cn>
<ci>D_c</ci>
<apply>
<minus/>
<ci>p_c</ci>
<ci>p_ac</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="L_per_mole">1</cn>
<ci>D_o</ci>
<apply>
<minus/>
<ci>p_o</ci>
<ci>p_ao</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>f_oi</ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci>f_o</ci>
<ci>V_D</ci>
</apply>
<apply>
<times/>
<ci>f_om</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>
<otherwise>
<ci>f_o</ci>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>f_ci</ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci>f_c</ci>
<ci>V_D</ci>
</apply>
<apply>
<times/>
<ci>f_cm</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>
<otherwise>
<ci>f_c</ci>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>f_o</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>V_A</ci>
<ci>numAlveoli</ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="L_per_mole">1</cn>
<ci>D_o</ci>
<apply>
<minus/>
<ci>p_o</ci>
<ci>p_ao</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<minus/>
<ci>f_oi</ci>
<ci>f_o</ci>
</apply>
<ci>q</ci>
</apply>
</apply>
<apply>
<times/>
<ci>f_o</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="L_per_mole">1</cn>
<ci>D_c</ci>
<apply>
<minus/>
<ci>p_c</ci>
<ci>p_ac</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="L_per_mole">1</cn>
<ci>D_o</ci>
<apply>
<minus/>
<ci>p_o</ci>
<ci>p_ao</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>f_c</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>V_A</ci>
<ci>numAlveoli</ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="L_per_mole">1</cn>
<ci>D_c</ci>
<apply>
<minus/>
<ci>p_c</ci>
<ci>p_ac</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<minus/>
<ci>f_ci</ci>
<ci>f_c</ci>
</apply>
<ci>q</ci>
</apply>
</apply>
<apply>
<times/>
<ci>f_c</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="L_per_mole">1</cn>
<ci>D_o</ci>
<apply>
<minus/>
<ci>p_o</ci>
<ci>p_ao</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="L_per_mole">1</cn>
<ci>D_c</ci>
<apply>
<minus/>
<ci>p_c</ci>
<ci>p_ac</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="gasTransport">
<variable name="time" public_interface="in" units="second"/>
<variable name="f_o" public_interface="in" units="dimensionless"/>
<variable name="df_satdp" units="dimensionless"/>
<variable initial_value="171200000" name="L" units="dimensionless"/>
<variable initial_value="10000" name="K_T" units="L_per_mole"/>
<variable initial_value="3600000" name="K_R" units="L_per_mole"/>
<variable initial_value="5332.9" name="p_o" public_interface="out" units="Pa"/>
<variable initial_value="133.332" name="mmHg2Pa" units="dimensionless"/>
<variable initial_value="1.05e-08" name="sigma" units="mole_per_L_Pa"/>
<variable name="D_o" public_interface="in" units="mole_per_second_Pa"/>
<variable initial_value="0.071" name="V_c" units="litre"/>
<variable name="P_A" public_interface="in" units="Pa"/>
<variable name="P_w" public_interface="in" units="Pa"/>
<variable initial_value="0.002" name="T_h" units="mole_per_L"/>
<variable name="D_c" public_interface="in" units="mole_per_second_Pa"/>
<variable name="delta" units="dimensionless"/>
<variable name="h" units="mole_per_L"/>
<variable initial_value="164000" name="l_2" units="L_per_second_mole"/>
<variable initial_value="6132.83" name="p_c" public_interface="out" units="Pa"/>
<variable name="p_ac" public_interface="in" units="Pa"/>
<variable initial_value="0.12" name="r_2" units="per_second"/>
<variable initial_value="2.475e-07" name="sigma_c" units="mole_per_L_Pa"/>
<variable initial_value="0.00000044219" name="z" units="dimensionless"/>
<variable initial_value="8.3145" name="R" units="Joule_per_mole_per_kelvin"/>
<variable initial_value="312.0" name="T" units="kelvin"/>
<!--Calculate oxygen saturation-->
<variable initial_value="2.78e-3" name="Q" units="L_per_second"/>
<!--Blood flow rate per second per acinus cardiac output 5L per min/30000 acini-->
<variable initial_value="0.0" name="C_O2" public_interface="out" units="L"/>
<!--Total transported Oxygen -->
<variable initial_value="15.0" name="Hb" units="mole_per_L"/>
<!-- hemoglobin concentration (usually ~15 g/dL in healthy adults)-->
<!-- Haemoglobin saturation function (4-ligand binding model with T and R states)-->
<variable initial_value="3.6e6" name="K_R" units="L_per_mole"/>
<!--Relaxed state affinity-->
<variable initial_value="1.0e4" name="K_T" units="L_per_mole"/>
<!--Tense state affinity-->
<variable initial_value="1.712e8" name="L" units="dimensionless"/>
<!--Allosteric equilibrium constant-->
<variable initial_value="1.05e-8" name="sigma" units="mol_per_L_per_Pa"/>
<!-- O2 solubility in plasma-->
<variable name="satpo" units="dimensionless"/>
<variable name="satt1" units="dimensionless"/>
<variable name="satt2" units="dimensionless"/>
<variable name="saturation" public_interface="out" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>satt1</ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1.0</cn>
<apply>
<times/>
<ci>K_R</ci>
<ci>sigma</ci>
<ci>p_o</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>satt2</ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1.0</cn>
<apply>
<times/>
<ci>K_T</ci>
<ci>sigma</ci>
<ci>p_o</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>satpo</ci>
<apply>
<divide/>
<ci>satt1</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>L</ci>
<ci>satt2</ci>
</apply>
<ci>satt1</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>saturation</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless" type="e-notation">2.25<sep/>-5</cn>
<ci>p_o</ci>
</apply>
<apply>
<times/>
<ci>Hb</ci>
<cn cellml:units="dimensionless">1.34</cn>
<ci>satpo</ci>
</apply>
</apply>
</apply>
<!--dissolved + bound-->
<apply>
<eq/>
<ci>delta</ci>
<apply>
<power/>
<cn cellml:units="dimensionless">10</cn>
<cn cellml:units="dimensionless">1.9</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>h</ci>
<apply>
<times/>
<cn cellml:units="mole_per_L">1</cn>
<apply>
<power/>
<cn cellml:units="dimensionless">10</cn>
<apply>
<minus/>
<cn cellml:units="dimensionless">7.4</cn>
</apply>
</apply>
</apply>
</apply>
<!--df_satdp = ((L*pow(1{dimensionless}+K_T*sigma*p_o, 4{dimensionless})+pow(1{dimensionless}+K_R*sigma*p_o, 4{dimensionless}))*(3{dimensionless}*L*sqr(K_T)*sqr(sigma)*p_o*133.332{mmHg}*sqr(1{dimensionless}+K_T*sigma*p_o)+L*K_T*sigma*133.332{mmHg}*pow(1{dimensionless}+K_T*sigma*p_o, 3{dimensionless})+3{dimensionless}*sqr(K_R)*sqr(sigma)*p_o*133.332{mmHg}*sqr(1{dimensionless}+K_R*sigma*p_o)+K_R*sigma*133.332{mmHg}*pow(1{dimensionless}+K_R*sigma*p_o, 3{dimensionless}))-(L*K_T*sigma*p_o*pow(1{dimensionless}+K_T*sigma*p_o, 3{dimensionless})+K_R*sigma*p_o*pow(1{dimensionless}+K_R*sigma*p_o, 3{dimensionless}))*(4{dimensionless}*L*K_T*sigma*133.332{mmHg}*pow(1{dimensionless}+K_T*sigma*p_o, 3{dimensionless})+4{dimensionless}*K_R*sigma*133.332{mmHg}*pow(1{dimensionless}+K_R*sigma*p_o, 3{dimensionless})))/sqr(L*pow(1{dimensionless}+K_T*sigma*p_o, 4{dimensionless})+pow(1{dimensionless}+K_R*sigma*p_o, 4{dimensionless}));
ode(p_o, time) = D_o/(sigma*V_c)*pow(1{dimensionless}+4{dimensionless}/133.332{mmHg}*T_h/sigma*df_satdp, -1{dimensionless})*(f_o*(P_A-P_w)-p_o);-->
<apply>
<eq/>
<ci>df_satdp</ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci>L</ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>K_T</ci>
<ci>sigma</ci>
<ci>p_o</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>K_R</ci>
<ci>sigma</ci>
<ci>p_o</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>L</ci>
<apply>
<power/>
<ci>K_T</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>sigma</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>p_o</ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>K_T</ci>
<ci>sigma</ci>
<ci>p_o</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>L</ci>
<ci>K_T</ci>
<ci>sigma</ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>K_T</ci>
<ci>sigma</ci>
<ci>p_o</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<apply>
<power/>
<ci>K_R</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>sigma</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>p_o</ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>K_R</ci>
<ci>sigma</ci>
<ci>p_o</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>K_R</ci>
<ci>sigma</ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>K_R</ci>
<ci>sigma</ci>
<ci>p_o</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci>L</ci>
<ci>K_T</ci>
<ci>sigma</ci>
<ci>p_o</ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>K_T</ci>
<ci>sigma</ci>
<ci>p_o</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
<apply>
<times/>
<ci>K_R</ci>
<ci>sigma</ci>
<ci>p_o</ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>K_R</ci>
<ci>sigma</ci>
<ci>p_o</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>L</ci>
<ci>K_T</ci>
<ci>sigma</ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>K_T</ci>
<ci>sigma</ci>
<ci>p_o</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>K_R</ci>
<ci>sigma</ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>K_R</ci>
<ci>sigma</ci>
<ci>p_o</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<power/>
<apply>
<plus/>
<apply>
<times/>
<ci>L</ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>K_T</ci>
<ci>sigma</ci>
<ci>p_o</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>K_R</ci>
<ci>sigma</ci>
<ci>p_o</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>p_o</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci>D_o</ci>
<apply>
<times/>
<ci>sigma</ci>
<ci>V_c</ci>
</apply>
</apply>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<times/>
<ci>T_h</ci>
<ci>df_satdp</ci>
</apply>
<apply>
<times/>
<ci>sigma</ci>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>f_o</ci>
<apply>
<minus/>
<ci>P_A</ci>
<ci>P_w</ci>
</apply>
</apply>
<ci>p_o</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>p_c</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<divide/>
<ci>D_c</ci>
<apply>
<times/>
<ci>sigma_c</ci>
<ci>V_c</ci>
</apply>
</apply>
<apply>
<minus/>
<ci>p_ac</ci>
<ci>p_c</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="mole_per_L">1</cn>
<ci>delta</ci>
<ci>l_2</ci>
</apply>
<ci>sigma_c</ci>
</apply>
<ci>h</ci>
<ci>z</ci>
</apply>
</apply>
<apply>
<times/>
<ci>delta</ci>
<ci>r_2</ci>
<ci>p_c</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>z</ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>delta</ci>
<ci>r_2</ci>
<ci>sigma_c</ci>
<ci>p_c</ci>
</apply>
<cn cellml:units="mole_per_L">1</cn>
</apply>
<apply>
<times/>
<ci>delta</ci>
<ci>l_2</ci>
<ci>h</ci>
<ci>z</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>C_O2</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>saturation</ci>
<ci>Q</ci>
</apply>
<cn cellml:units="dimensionless">100</cn>
</apply>
</apply>
</math>
</component>
<component name="AlveolarRecruitment">
<variable name="time" public_interface="in" units="second"/>
<variable initial_value="3.462" name="k1" units="per_second"/>
<variable initial_value="1.0" name="k2" units="per_second"/>
<variable initial_value="15" name="breathsPerMin" public_interface="out" units="per_min"/>
<variable initial_value="10" name="alevolar_cooperativity" units="dimensionless"/>
<variable initial_value="0.5" name="Less_active_alveoli" units="dimensionless"/>
<!-- Assumed initial value-->
<variable initial_value="0.5" name="Fully_active_alveoli" units="dimensionless"/>
<!-- So total is 1
Define S as normalized breaths per min input, like in original recruitmentFactor-->
<variable name="S" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>S</ci>
<apply>
<divide/>
<apply>
<divide/>
<ci>breathsPerMin</ci>
<cn cellml:units="dimensionless">60.0</cn>
</apply>
<cn cellml:units="dimensionless">0.64</cn>
</apply>
</apply>
</math>
<variable name="Ra" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Ra</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1.0</cn>
<apply>
<divide/>
<ci>k2</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>k1</ci>
<apply>
<power/>
<ci>S</ci>
<ci>alevolar_cooperativity</ci>
</apply>
</apply>
<ci>k2</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<!-- recruitmentFactor with Less_active_alveoli-->
<variable name="recruitmentFactor" public_interface="out" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>recruitmentFactor</ci>
<apply>
<min/>
<apply>
<max/>
<ci>Fully_active_alveoli</ci>
<cn cellml:units="dimensionless">0.1</cn>
</apply>
<cn cellml:units="dimensionless">1.0</cn>
</apply>
</apply>
<!--ensure that resistance does not go below phyological limits as Less_active_alveoli can go close to zero-->
<!-- Define the ODEs for Less_active_alveoli and Fully_active_alveoli-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Less_active_alveoli</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci>k1</ci>
</apply>
<ci>Less_active_alveoli</ci>
<apply>
<power/>
<ci>S</ci>
<ci>alevolar_cooperativity</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k2</ci>
<ci>Fully_active_alveoli</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Fully_active_alveoli</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k1</ci>
<ci>Less_active_alveoli</ci>
<apply>
<power/>
<ci>S</ci>
<ci>alevolar_cooperativity</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k2</ci>
<ci>Fully_active_alveoli</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Acinus">
<variable name="time" public_interface="in" units="second"/>
<variable name="numAlveoli" public_interface="in" units="dimensionless"/>
<variable name="V_lung" public_interface="in" units="L"/>
<!--Total lung volume (input to the acinus)-->
<variable initial_value="0.1818" name="Vc" units="L"/>
<!--Volume of the central compartment (conducting airways)-->
<variable initial_value="0.00014" name="VA" public_interface="out" units="L"/>
<!--Volume of the acinus (alveolar air space) - 4.5 L/ 30000 (acini)-->
<variable initial_value="1.5082e-05" name="Vve" units="L"/>
<!--Volume related to viscoelastic components (tissue compartments)-->
<variable initial_value="1.9" name="RV" units="L"/>
<!--Residual volume (minimum lung volume after full exhalation)-->
<variable initial_value="7.3" name="TLC" units="L"/>
<!--Total lung capacity-->
<variable initial_value="0.185" name="VD" units="L"/>
<!-- Dead space volume (non-gas-exchanging airways)-->
<variable name="breathsPerMin" public_interface="in" units="per_min"/>
<!-- Breaths per minute-->
<variable initial_value="92685.4" name="Ac" units="Pa"/>
<!--Central airway elastic coefficient-->
<variable initial_value="18307.3" name="Acw" units="Pa"/>
<!--Chest wall pressure coefficient-->
<variable initial_value="2614.0" name="Al" units="Pa"/>
<!--Lung pressure coefficient-->
<variable initial_value="28759.3" name="As" units="Pa_sec_per_L"/>
<variable initial_value="487741.5" name="Bc" units="Pa"/>
<!--Central airway recoil pressure constants-->
<variable initial_value="48768.4" name="Bcp" units="Pa"/>
<!--Central airway recoil pressure constants-->
<variable initial_value="-45751.4" name="Bcw" units="Pa"/>
<!--Chest wall pressure decay constant-->
<variable initial_value="-6539.6" name="Bl" units="Pa"/>
<!--Lung pressure offset-->
<variable initial_value="0.0" name="PEEP" units="Pa"/>
<!--Positive end expiratory pressure-->
<variable initial_value="-0.1" name="k_peep" units="dimensionless"/>
<!--gain factor-->
<variable initial_value="261.5" name="Bs" units="Pa"/>
<!--Serial resistance pressure offset-->
<variable initial_value="3.827e-5" name="Cve" units="L_per_Pa"/>
<!--Viscoelastic compliance-->
<variable initial_value="7.65e-5" name="Rve" units="L_per_Pa"/>
<!--Viscoelastic resistance-->
<variable initial_value="1" name="Kl" units="per_L"/>
<!--Lung elasticity factor-->
<variable initial_value="-2.5" name="Ks" units="dimensionless"/>
<!-- {init: -10.9}; //-3.1 (COPD) to -10.9 (ARDS)-->
<!--Coefficient for resistance change with volume-->
<variable initial_value="5.3" name="Vstar" units="L"/>
<!--A reference lung volume used in calculations-->
<variable initial_value="0.185" name="Vcmax" units="L"/>
<!--Maximum volume of the central (conducting) compartment
var tau: second {init: 0.1};-->
<variable initial_value="26150.4" name="Amus" units="Pa"/>
<!--Muscle pressure amplitude-->
<!-- 4.5 L (at max) / 187e-6-->
<variable name="Vcw" units="L"/>
<!--Chest wall volume-->
<variable name="Pcw" units="Pa"/>
<!--Chest wall pressure-->
<variable name="Pl" units="Pa"/>
<!--Lung elastic recoil pressure-->
<variable name="PA" public_interface="out" units="Pa"/>
<!--Alveolar pressure-->
<variable name="Pc" units="Pa"/>
<!--Pressure from central airways (elastic recoil of lung)-->
<variable name="Pve" units="Pa"/>
<!--Viscoelastic pressure (resistance from tissue deformation)-->
<variable name="Ppl" units="Pa"/>
<!--Pleural pressure-->
<variable name="Pmus" units="Pa"/>
<!--Muscle pressure (respiratory muscle effort)-->
<variable name="QA" public_interface="out" units="L_per_second"/>
<!--y = 2.500514 + (0.03826521 - 2.500514)/(1 + (x/0.6482999)^9.558973)-->
<variable name="Al_effective" units="Pa"/>
<variable name="Rs" units="Pa_sec_per_L"/>
<!--Lung pressure reduces with recruitment-->
<variable name="Bl_effective" units="Pa"/>
<!--Base line elastic pressure also reduces with recruitment-->
<variable name="recruitmentFactor" public_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Al_effective</ci>
<apply>
<times/>
<ci>Al</ci>
<ci>recruitmentFactor</ci>
</apply>
</apply>
<!--Linear approximation - recruitment affects both the number of open units and their individual mechanical properties in a non-linear way.-->
<apply>
<eq/>
<ci>Bl_effective</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>Bl</ci>
<ci>recruitmentFactor</ci>
</apply>
<apply>
<times/>
<ci>k_peep</ci>
<ci>PEEP</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Rs</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>As</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>Ks</ci>
<apply>
<minus/>
<ci>V_lung</ci>
<ci>RV</ci>
</apply>
</apply>
<apply>
<minus/>
<ci>Vstar</ci>
<ci>RV</ci>
</apply>
</apply>
</apply>
</apply>
<ci>Bs</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Pl</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>Al_effective</ci>
<apply>
<exp/>
<apply>
<times/>
<ci>Kl</ci>
<ci>V_lung</ci>
</apply>
</apply>
</apply>
<ci>Bl_effective</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Pmus</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>Amus</ci>
<apply>
<sin/>
<apply>
<times/>
<cn cellml:units="dimensionless">6.2831</cn>
<ci>breathsPerMin</ci>
<ci>time</ci>
<cn cellml:units="dimensionless" type="e-notation">1.6666<sep/>-2</cn>
</apply>
</apply>
</apply>
<ci>Amus</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Pc</ci>
<piecewise>
<piece>
<apply>
<minus/>
<ci>Ac</ci>
<apply>
<times/>
<ci>Bc</ci>
<apply>
<power/>
<apply>
<minus/>
<apply>
<divide/>
<ci>Vc</ci>
<ci>Vcmax</ci>
</apply>
<cn cellml:units="dimensionless">0.7</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<lt/>
<apply>
<divide/>
<ci>Vc</ci>
<ci>Vcmax</ci>
</apply>
<cn cellml:units="dimensionless">0.5</cn>
</apply>
</piece>
<otherwise>
<apply>
<minus/>
<cn cellml:units="dimensionless">5.6</cn>
<apply>
<times/>
<ci>Bcp</ci>
<apply>
<log/>
<apply>
<minus/>
<apply>
<divide/>
<ci>Vcmax</ci>
<ci>Vc</ci>
</apply>
<cn cellml:units="dimensionless">0.999</cn>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>Pve</ci>
<apply>
<divide/>
<ci>Vve</ci>
<ci>Cve</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Vcw</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>numAlveoli</ci>
<ci>VA</ci>
</apply>
<ci>VD</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Pcw</ci>
<apply>
<minus/>
<ci>Acw</ci>
<apply>
<times/>
<ci>Bcw</ci>
<apply>
<ln/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<ci>TLC</ci>
<ci>RV</ci>
</apply>
<apply>
<minus/>
<ci>Vcw</ci>
<ci>RV</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">0.999</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ppl</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>Pcw</ci>
</apply>
<ci>Pmus</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>PA</ci>
<apply>
<plus/>
<ci>Pl</ci>
<ci>Pve</ci>
</apply>
</apply>
</math>
<variable name="JR11" units="dimensionless"/>
<variable name="JR2" units="dimensionless"/>
<variable name="JR33" units="dimensionless"/>
<variable name="U1" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>JR11</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>JR2</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<ci>numAlveoli</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>JR33</ci>
<apply>
<divide/>
<apply>
<plus/>
<ci>Rs</ci>
<ci>Rve</ci>
</apply>
<ci>Rve</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>U1</ci>
<apply>
<plus/>
<ci>Pcw</ci>
<ci>Pmus</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>QA</ci>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<ci>numAlveoli</ci>
<ci>JR2</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>Pc</ci>
<ci>Pl</ci>
</apply>
<ci>Pve</ci>
</apply>
</apply>
<ci>Rs</ci>
</apply>
<cn cellml:units="dimensionless">1000</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Vc</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci>JR11</ci>
<ci>Pc</ci>
</apply>
<ci>Pl</ci>
<ci>Pve</ci>
<ci>U1</ci>
</apply>
<ci>Rs</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>VA</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>JR2</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>Pc</ci>
<ci>Pl</ci>
</apply>
<ci>Pve</ci>
</apply>
</apply>
<ci>Rs</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Vve</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>Pc</ci>
<ci>Pl</ci>
</apply>
<apply>
<times/>
<ci>JR33</ci>
<ci>Pve</ci>
</apply>
</apply>
<ci>Rs</ci>
</apply>
</apply>
</math>
</component>
<component name="AcinusToLungScaleCoupling">
<variable name="PA_acinus" public_interface="in" units="Pa"/>
<variable name="P_A" public_interface="out" units="Pa"/>
<variable name="VA_acinus" public_interface="in" units="L"/>
<variable name="V_A" public_interface="out" units="L"/>
<variable name="Resistance" public_interface="out" units="dimensionless"/>
<variable initial_value="24064" name="LungToAcinusVolRatio" public_interface="out" units="dimensionless"/>
<!-- Ratio of Lung volume to acini volume at full inhalation - 4.5 L (at max) / 187e-6-->
<variable initial_value="0.65" name="AlveolarResistance" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>V_A</ci>
<apply>
<times/>
<ci>VA_acinus</ci>
<ci>LungToAcinusVolRatio</ci>
</apply>
</apply>
<!--P_A = PA_acinus*133.33{dimensionless}; // 1mmHg = 133.33 Pa-->
<apply>
<eq/>
<ci>P_A</ci>
<ci>PA_acinus</ci>
</apply>
<apply>
<eq/>
<ci>Resistance</ci>
<apply>
<times/>
<ci>LungToAcinusVolRatio</ci>
<ci>AlveolarResistance</ci>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="gasTransport" component_2="gasExchange"/>
<map_variables variable_1="p_o" variable_2="p_o"/>
<map_variables variable_1="D_o" variable_2="D_o"/>
<map_variables variable_1="f_o" variable_2="f_o"/>
<map_variables variable_1="P_w" variable_2="P_w"/>
<map_variables variable_1="p_c" variable_2="p_c"/>
<map_variables variable_1="D_c" variable_2="D_c"/>
<map_variables variable_1="p_ac" variable_2="p_ac"/>
</connection>
<connection>
<map_components component_1="Environment" component_2="gasTransport"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Environment" component_2="AlveolarRecruitment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Acinus" component_2="gasTransport"/>
<map_variables variable_1="PA" variable_2="P_A"/>
</connection>
<connection>
<map_components component_1="Acinus" component_2="AlveolarRecruitment"/>
<map_variables variable_1="recruitmentFactor" variable_2="recruitmentFactor"/>
<map_variables variable_1="breathsPerMin" variable_2="breathsPerMin"/>
</connection>
<connection>
<map_components component_1="gasExchange" component_2="AlveolarRecruitment"/>
<map_variables variable_1="breathsPerMin" variable_2="breathsPerMin"/>
</connection>
<connection>
<map_components component_1="Environment" component_2="gasExchange"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="numAlveoli" variable_2="numAlveoli"/>
</connection>
<connection>
<map_components component_1="Acinus" component_2="gasExchange"/>
<map_variables variable_1="PA" variable_2="P_A"/>
<map_variables variable_1="VA" variable_2="V_A"/>
</connection>
<connection>
<map_components component_1="Environment" component_2="Acinus"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="numAlveoli" variable_2="numAlveoli"/>
</connection>
<connection>
<map_components component_1="Acinus" component_2="AcinusToLungScaleCoupling"/>
<map_variables variable_1="PA" variable_2="PA_acinus"/>
<map_variables variable_1="VA" variable_2="VA_acinus"/>
<map_variables variable_1="V_lung" variable_2="V_A"/>
</connection>
</model>