Location: Pulmonary Acinus pFTU @ 506c61e2bac6 / AthanasiadesPHSinSIwithGasET.cellml
- Author:
- Jagirhussan <r.jagir@auckland.ac.nz>
- Date:
- 2025-06-05 14:31:16+12:00
- Desc:
- Initial Commit
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/d35/rawfile/506c61e2bac6dad9a15ec298cee38237070ba0ef/AthanasiadesPHSinSIwithGasET.cellml
<?xml version='1.0' encoding='UTF-8'?>
<model name="Athanasiades" 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="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>
<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="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="0.210002633761558" 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="2.77326013681902e-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="dimensionless"/>
<!--var q: L_per_second {pub: in};-->
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<ci>AlveolarResistance</ci>
</apply>
</apply>
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<ci>Q_A</ci>
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<ci>D_c</ci>
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<minus/>
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<times/>
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<ci>D_o</ci>
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<minus/>
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<apply>
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<cn cellml:units="dimensionless">1</cn>
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<ci>V_A</ci>
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<apply>
<minus/>
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<plus/>
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<times/>
<cn cellml:units="L_per_mole">1</cn>
<ci>D_o</ci>
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<plus/>
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<minus/>
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<plus/>
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<times/>
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<times/>
<cn cellml:units="L_per_mole">1</cn>
<ci>D_o</ci>
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<minus/>
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<times/>
<cn cellml:units="L_per_mole">1</cn>
<ci>D_c</ci>
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<minus/>
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</apply>
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</apply>
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</math>
</component>
<component name="gasTransport">
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<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="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"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
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<power/>
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<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/>
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<apply>
<minus/>
<cn cellml:units="dimensionless">7.4</cn>
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<apply>
<eq/>
<ci>df_satdp</ci>
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<divide/>
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<times/>
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<plus/>
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<times/>
<ci>L</ci>
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<power/>
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<plus/>
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<times/>
<ci>K_T</ci>
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<power/>
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<apply>
<power/>
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<apply>
<power/>
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<plus/>
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<times/>
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<apply>
<times/>
<ci>L</ci>
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<apply>
<power/>
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<plus/>
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<times/>
<ci>K_T</ci>
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<times/>
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<apply>
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<times/>
<ci>K_R</ci>
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<ci>L</ci>
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<power/>
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<plus/>
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<plus/>
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<times/>
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<divide/>
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<times/>
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<minus/>
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<minus/>
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<minus/>
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<plus/>
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<times/>
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<minus/>
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<times/>
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<times/>
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<minus/>
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<cn cellml:units="mole_per_L">1</cn>
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<component name="Acinus">
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<variable name="numAlveoli" public_interface="in" units="dimensionless"/>
<variable initial_value="0.181843755366182" name="Vc" units="L"/>
<variable initial_value="0.000147903469601923" name="VA" units="L"/>
<variable initial_value="1.50821105715851e-05" name="Vve" units="L"/>
<variable name="QA" public_interface="out" units="L_per_second"/>
<variable initial_value="1.9" name="RV" units="L"/>
<variable initial_value="7.3" name="TLC" units="L"/>
<variable initial_value="0.185" name="VD" units="L"/>
<variable initial_value="15" name="f" units="per_min"/>
<variable initial_value="695.29" name="Ac" units="Pa"/>
<variable initial_value="137.29" name="Acw" units="Pa"/>
<variable initial_value="19.61" name="Al" units="Pa"/>
<variable initial_value="215.75" name="As" units="Pa_sec_per_L"/>
<variable initial_value="3657.88" name="Bc" units="Pa"/>
<variable initial_value="365.788" name="Bcp" units="Pa"/>
<variable initial_value="-343.23" name="Bcw" units="Pa"/>
<variable initial_value="-49.03" name="Bl" units="Pa"/>
<variable initial_value="1.961" name="Bs" units="Pa"/>
<variable initial_value="0.0051" name="Cve" units="L_per_Pa"/>
<variable initial_value="0.0102" name="Rve" units="L_per_Pa"/>
<variable initial_value="1" name="Kl" units="per_L"/>
<variable initial_value="-10.9" name="Ks" units="dimensionless"/>
<variable initial_value="5.3" name="Vstar" units="L"/>
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<variable initial_value="0.1" name="tau" units="second"/>
<variable initial_value="196.133" name="Amus" units="Pa"/>
<!-- 4.5 L (at max) / 187e-6-->
<variable name="Vcw" units="L"/>
<variable name="Pcw" units="Pa"/>
<variable name="Pl" units="Pa"/>
<variable name="PA" units="Pa"/>
<variable name="Pc" units="Pa"/>
<variable name="Pve" units="Pa"/>
<variable name="Ppl" units="Pa"/>
<variable name="Pmus" units="Pa"/>
<variable name="Rs" units="Pa_sec_per_L"/>
<!--y = 2.500514 + (0.03826521 - 2.500514)/(1 + (x/0.6482999)^9.558973)-->
<variable name="recruitmentFactor" units="dimensionless"/>
<!--recruitmentFactoruction in pressure - [1 (4 breaths per min),3.3 (50 breath per min)]-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>recruitmentFactor</ci>
<apply>
<divide/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1.0</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<divide/>
<ci>f</ci>
<cn cellml:units="dimensionless">60.0</cn>
</apply>
<cn cellml:units="dimensionless">0.64</cn>
</apply>
<cn cellml:units="dimensionless">10</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">3.462</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<divide/>
<ci>f</ci>
<cn cellml:units="dimensionless">60.0</cn>
</apply>
<cn cellml:units="dimensionless">0.64</cn>
</apply>
<cn cellml:units="dimensionless">10</cn>
</apply>
</apply>
</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/>
<apply>
<times/>
<ci>numAlveoli</ci>
<ci>VA</ci>
</apply>
<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>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci>Al</ci>
<apply>
<exp/>
<apply>
<times/>
<ci>Kl</ci>
<ci>numAlveoli</ci>
<ci>VA</ci>
</apply>
</apply>
</apply>
<ci>Bl</ci>
</apply>
<ci>recruitmentFactor</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Pmus</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>Amus</ci>
<apply>
<sin/>
<apply>
<times/>
<cn cellml:units="dimensionless">6.283185307179586</cn>
<ci>f</ci>
<ci>time</ci>
<cn cellml:units="dimensionless" type="e-notation">1.6666666666666667<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>
<!--PA = Ppl+Pl+Pve;-->
<apply>
<eq/>
<ci>PA</ci>
<apply>
<times/>
<apply>
<plus/>
<ci>Pl</ci>
<ci>Pve</ci>
</apply>
<cn cellml:units="dimensionless">133.33</cn>
</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>
<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="Acinus" component_2="gasTransport"/>
<map_variables variable_1="PA" variable_2="P_A"/>
</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>
</model>