- Author:
- Weiwei Ai <wai484@aucklanduni.ac.nz>
- Date:
- 2024-02-27 17:21:53+13:00
- Desc:
- Add H buffering in the acid BG model
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/b61/rawfile/920a714dbe070a8ab1215d82e465d4aaa7216a0a/models/CellMLV2/Boron_acid_EA.cellml
<?xml version="1.0" encoding="UTF-8"?>
<model xmlns="http://www.cellml.org/cellml/2.0#" name="Boron_CO2">
<units name="per_s">
<unit exponent="-1" units="second"/>
</units>
<units name="per_m">
<unit exponent="-1" units="metre"/>
</units>
<units name="m_per_s">
<unit units="metre"/>
<unit exponent="-1" units="second"/>
</units>
<units name="per_mol">
<unit exponent="-1" units="mole"/>
</units>
<units name="mol_per_m3">
<unit units="mole"/>
<unit exponent="-3" units="metre"/>
</units>
<units name="mol_per_m2_s">
<unit units="mole"/>
<unit exponent="-2" units="metre"/>
<unit exponent="-1" units="second"/>
</units>
<units name="mol_per_m3_s">
<unit units="mole"/>
<unit exponent="-3" units="metre"/>
<unit exponent="-1" units="second"/>
</units>
<units name="J_per_C">
<unit units="joule"/>
<unit exponent="-1" units="coulomb"/>
</units>
<units name="C_per_mol">
<unit units="coulomb"/>
<unit exponent="-1" units="mole"/>
</units>
<units name="J_per_mol_K">
<unit units="joule"/>
<unit exponent="-1" units="mole"/>
<unit exponent="-1" units="kelvin"/>
</units>
<units name="m3_per_mol">
<unit exponent="3" units="metre"/>
<unit exponent="-1" units="mole"/>
</units>
<units name="m3">
<unit exponent="3" units="metre"/>
</units>
<units name="dim">
<unit units="dimensionless"/>
</units>
<units name="mol_per_s">
<unit units="mole"/>
<unit exponent="-1" units="second"/>
</units>
<units name="J_per_s">
<unit units="joule"/>
<unit exponent="-1" units="second"/>
</units>
<component name="main">
<variable name="t" units="second"/>
<variable name="CO2_o" units="mol_per_m3"/>
<variable name="CO2_i" units="mol_per_m3"/>
<variable name="HCO3_i" units="mol_per_m3"/>
<variable name="HCO3_o" units="mol_per_m3"/>
<variable name="TA_i" units="mol_per_m3" initial_value="0.2"/>
<variable name="H_i" units="mol_per_m3" initial_value="3.981071705534970e-05"/>
<variable name="H_o" units="mol_per_m3" initial_value="1.995262314968879e-05"/>
<variable name="H_Lim" units="mol_per_m3" initial_value="5.011872336272725e-05"/>
<variable name="J_CO2" units="mol_per_m2_s"/>
<variable name="J_HCO3" units="mol_per_m2_s"/>
<variable name="J_H" units="mol_per_m2_s"/>
<variable name="pH_i" units="dimensionless"/>
<variable name="pH_o" units="dimensionless"/>
<variable name="pH_Lim" units="dimensionless"/>
<variable name="alpha" units="dimensionless"/>
<variable name="epsilon" units="dimensionless"/>
<variable name="T" units="kelvin" initial_value="296.15"/>
<variable name="R" units="J_per_mol_K" initial_value="8.314"/>
<variable name="F" units="C_per_mol" initial_value="96485"/>
<variable name="r" units="metre" initial_value="0.00025"/>
<variable name="rho" units="per_m"/>
<variable name="beta" units="mol_per_m3" initial_value="26"/>
<variable name="P_CO2" units="m_per_s" initial_value="6e-5"/>
<variable name="P_HCO3" units="m_per_s" initial_value="5e-9"/>
<variable name="K_HA" units="mol_per_m3" initial_value="1e-3"/>
<variable name="V_m" units="J_per_C" initial_value="-0.057" interface="public"/>
<variable name="k" units="per_s" initial_value="300"/>
<variable name="K_CO2_o" units="per_mol" initial_value="1e-8"/>
<variable name="K_CO2_i" units="per_mol" initial_value="1e-8"/>
<variable name="K_HCO3_o" units="per_mol" initial_value="1e-5"/>
<variable name="K_HCO3_i" units="per_mol" initial_value="1e-5"/>
<variable name="K_H_o" units="per_mol" initial_value="1"/>
<variable name="K_H_i" units="per_mol" initial_value="1"/>
<variable name="Q_CO2_o" units="dim"/>
<variable name="Q_CO2_i" units="dim"/>
<variable name="Q_HCO3_o" units="dim"/>
<variable name="Q_HCO3_i" units="dim"/>
<variable name="Q_H_o" units="dim"/>
<variable name="Q_H_i" units="dim"/>
<variable name="V_cell" units="m3" initial_value="1"/>
<variable name="v_CO2_m" units="mol_per_s"/>
<variable name="v_HCO3_m" units="mol_per_s"/>
<variable name="v_H_m" units="mol_per_s"/>
<variable name="v_H2CO3_i" units="mol_per_s"/>
<variable name="PC_CO2_i" units="J_per_s"/>
<variable name="PC_HCO3_i" units="J_per_s"/>
<variable name="PC_H_i" units="J_per_s"/>
<variable name="PC_CO2_o" units="J_per_s"/>
<variable name="PC_HCO3_o" units="J_per_s"/>
<variable name="PC_H_o" units="J_per_s"/>
<variable name="PRe_CO2_m" units="J_per_s"/>
<variable name="PRe_HCO3_m" units="J_per_s"/>
<variable name="PRe_H_m" units="J_per_s"/>
<variable name="PRe_HCO3_i" units="J_per_s"/>
<variable name="P_um" units="J_per_s"/>
<variable name="P_supply" units="J_per_s"/>
<variable name="P_absorb" units="J_per_s"/>
<variable name="AC_CO2_i" units="joule" initial_value="0"/>
<variable name="AC_HCO3_i" units="joule" initial_value="0"/>
<variable name="AC_H_i" units="joule" initial_value="0"/>
<variable name="AC_CO2_o" units="joule" initial_value="0"/>
<variable name="AC_HCO3_o" units="joule" initial_value="0"/>
<variable name="AC_H_o" units="joule" initial_value="0"/>
<variable name="ARe_CO2_m" units="joule" initial_value="0"/>
<variable name="ARe_HCO3_m" units="joule" initial_value="0"/>
<variable name="ARe_H_m" units="joule" initial_value="0"/>
<variable name="ARe_HCO3_i" units="joule" initial_value="0"/>
<variable name="A_um" units="joule" initial_value="0"/>
<variable name="E_supply" units="joule" initial_value="0"/>
<variable name="E_absorb" units="joule" initial_value="0"/>
<variable name="A_supply" units="joule" initial_value="0"/>
<variable name="A_absorb" units="joule" initial_value="0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:cellml="http://www.cellml.org/cellml/2.0#">
<apply>
<eq/>
<ci>CO2_o</ci>
<piecewise>
<piece>
<cn cellml:units="mol_per_m3">0.00765730077645094</cn>
<apply>
<lt/>
<ci>t</ci>
<cn cellml:units="second">100</cn>
</apply>
</piece>
<piece>
<cn cellml:units="mol_per_m3">1.1877</cn>
<apply>
<lt/>
<ci>t</ci>
<cn cellml:units="second">2800</cn>
</apply>
</piece>
<otherwise>
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<divide/>
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<ci>r</ci>
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<ci>HCO3_o</ci>
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<times/>
<ci>K_HA</ci>
<ci>CO2_o</ci>
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<ci>H_o</ci>
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<apply>
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<ci>epsilon</ci>
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<times/>
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<minus/>
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<ci>F</ci>
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<times/>
<ci>R</ci>
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</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>pH_Lim</ci>
<apply>
<minus/>
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<log/>
<apply>
<times/>
<cn type="e-notation" cellml:units="m3_per_mol">1<sep/>-3</cn>
<ci>H_Lim</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>pH_i</ci>
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<minus/>
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<log/>
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<times/>
<cn type="e-notation" cellml:units="m3_per_mol">1<sep/>-3</cn>
<ci>H_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>pH_o</ci>
<apply>
<minus/>
<apply>
<log/>
<apply>
<times/>
<cn type="e-notation" cellml:units="m3_per_mol">1<sep/>-3</cn>
<ci>H_o</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_CO2</ci>
<apply>
<times/>
<ci>P_CO2</ci>
<apply>
<minus/>
<ci>CO2_o</ci>
<ci>CO2_i</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_HCO3</ci>
<apply>
<divide/>
<apply>
<times/>
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<divide/>
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<times/>
<ci>P_HCO3</ci>
<ci>V_m</ci>
<ci>F</ci>
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<times/>
<ci>R</ci>
<ci>T</ci>
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<apply>
<minus/>
<ci>HCO3_o</ci>
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<times/>
<ci>HCO3_i</ci>
<ci>epsilon</ci>
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</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>epsilon</ci>
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<apply>
<eq/>
<ci>J_H</ci>
<piecewise>
<piece>
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<times/>
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<divide/>
<ci>k</ci>
<ci>rho</ci>
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<apply>
<minus/>
<ci>H_i</ci>
<ci>H_Lim</ci>
</apply>
</apply>
<apply>
<lt/>
<ci>pH_i</ci>
<ci>pH_Lim</ci>
</apply>
</piece>
<otherwise>
<cn cellml:units="mol_per_m2_s">0.0</cn>
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</piecewise>
</apply>
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<eq/>
<ci>alpha</ci>
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<divide/>
<ci>H_i</ci>
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<plus/>
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<apply>
<eq/>
<ci>CO2_i</ci>
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<times/>
<ci>alpha</ci>
<ci>TA_i</ci>
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<apply>
<eq/>
<ci>HCO3_i</ci>
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<times/>
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<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>alpha</ci>
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<ci>TA_i</ci>
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<apply>
<eq/>
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<diff/>
<bvar>
<ci>t</ci>
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<times/>
<ci>rho</ci>
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<plus/>
<ci>J_CO2</ci>
<ci>J_HCO3</ci>
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<apply>
<eq/>
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<diff/>
<bvar>
<ci>t</ci>
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<ci>H_i</ci>
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<times/>
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<divide/>
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<times/>
<cn cellml:units="dimensionless">2.303</cn>
<ci>H_i</ci>
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<ci>beta</ci>
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<ci>rho</ci>
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<minus/>
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<minus/>
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<ci>alpha</ci>
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<ci>alpha</ci>
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<ci>J_H</ci>
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<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Q_CO2_o</ci>
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<times/>
<ci>K_CO2_o</ci>
<ci>CO2_o</ci>
<ci>V_cell</ci>
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</apply>
<apply>
<eq/>
<ci>Q_CO2_i</ci>
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<times/>
<ci>K_CO2_i</ci>
<ci>CO2_i</ci>
<ci>V_cell</ci>
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<eq/>
<ci>Q_HCO3_o</ci>
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<times/>
<ci>K_HCO3_o</ci>
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<ci>V_cell</ci>
</apply>
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<apply>
<eq/>
<ci>Q_HCO3_i</ci>
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<times/>
<ci>K_HCO3_i</ci>
<ci>HCO3_i</ci>
<ci>V_cell</ci>
</apply>
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<apply>
<eq/>
<ci>Q_H_o</ci>
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<times/>
<ci>K_H_o</ci>
<ci>H_o</ci>
<ci>V_cell</ci>
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<apply>
<eq/>
<ci>Q_H_i</ci>
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<times/>
<ci>K_H_i</ci>
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<ci>V_cell</ci>
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<math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:cellml="http://www.cellml.org/cellml/2.0#">
<apply>
<eq/>
<ci>v_CO2_m</ci>
<apply>
<times/>
<ci>rho</ci>
<ci>J_CO2</ci>
<ci>V_cell</ci>
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<apply>
<eq/>
<ci>v_HCO3_m</ci>
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<times/>
<ci>rho</ci>
<ci>J_HCO3</ci>
<ci>V_cell</ci>
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<ci>v_H_m</ci>
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<times/>
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<minus/>
<ci>rho</ci>
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<ci>v_H2CO3_i</ci>
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<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>PC_CO2_o</ci>
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<times/>
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<minus/>
<ci>R</ci>
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<ln/>
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<eq/>
<ci>PC_CO2_i</ci>
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<times/>
<ci>R</ci>
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<eq/>
<ci>PC_HCO3_o</ci>
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<minus/>
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<ci>PC_HCO3_i</ci>
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<ci>PC_H_o</ci>
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<times/>
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<minus/>
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<ci>PC_H_i</ci>
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<plus/>
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<ci>PRe_CO2_m</ci>
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<ci>R</ci>
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<ci>PRe_H_m</ci>
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<minus/>
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<minus/>
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<ln/>
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<ln/>
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<ci>v_H2CO3_i</ci>
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<eq/>
<ci>P_supply</ci>
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<plus/>
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<ci>P_um</ci>
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<plus/>
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<diff/>
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<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>AC_H_i</ci>
</apply>
<apply>
<abs/>
<ci>PC_H_i</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>ARe_CO2_m</ci>
</apply>
<apply>
<abs/>
<ci>PRe_CO2_m</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>ARe_HCO3_m</ci>
</apply>
<apply>
<abs/>
<ci>PRe_HCO3_m</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>ARe_H_m</ci>
</apply>
<apply>
<abs/>
<ci>PRe_H_m</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>A_um</ci>
</apply>
<apply>
<abs/>
<ci>P_um</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>ARe_HCO3_i</ci>
</apply>
<apply>
<abs/>
<ci>PRe_HCO3_i</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>E_supply</ci>
</apply>
<ci>P_supply</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>E_absorb</ci>
</apply>
<ci>P_absorb</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>A_supply</ci>
</apply>
<apply>
<abs/>
<ci>P_supply</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>A_absorb</ci>
</apply>
<apply>
<abs/>
<ci>P_absorb</ci>
</apply>
</apply>
</math>
</component>
</model>
