Location: Anion Exchanger @ 449f8d5632de / BG / AE1_BG.cellml
- Author:
- Soroush Safaei <ssaf006@aucklanduni.ac.nz>
- Date:
- 2016-11-26 15:27:38+13:00
- Desc:
- Adding the bond graph version of AE1
- Permanent Source URI:
- https://models.cellml.org/workspace/290/rawfile/449f8d5632de6c5745dd74d7b1fe8b703f5773f0/BG/AE1_BG.cellml
<?xml version='1.0'?>
<model name="AE1_BG" 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="per_mol" units_ref="per_mol"/>
<units name="J_per_mol" units_ref="J_per_mol"/>
<units name="mol_per_s" units_ref="mol_per_s"/>
</import>
<import xlink:href="Parameters-AE1.cellml">
<component component_ref="param" name="param"/>
</import>
<component name="environment">
<variable name="time" public_interface="out" units="second"/>
</component>
<component name="main">
<variable name="t" public_interface="in" units="second"/>
<!-- Constants-->
<variable name="RT" public_interface="in" units="J_per_mol"/>
<!-- State variables-->
<variable initial_value="0.01" name="q_Cl_o" units="mole"/>
<variable initial_value="0.0" name="q_Cl_i" units="mole"/>
<variable initial_value="0.0" name="q_HCO3_i" units="mole"/>
<variable initial_value="0.01" name="q_HCO3_o" units="mole"/>
<variable initial_value="0.01" name="q_E_o" units="mole"/>
<variable initial_value="0.0" name="q_ECl_o" units="mole"/>
<variable initial_value="0.0" name="q_ECl_i" units="mole"/>
<variable initial_value="0.0" name="q_E_i" units="mole"/>
<variable initial_value="0.0" name="q_EHCO3_i" units="mole"/>
<variable initial_value="0.0" name="q_EHCO3_o" units="mole"/>
<variable name="nu_Re1" units="mol_per_s"/>
<variable name="nu_Re2" units="mol_per_s"/>
<variable name="nu_Re3" units="mol_per_s"/>
<variable name="nu_Re4" units="mol_per_s"/>
<variable name="nu_Re5" units="mol_per_s"/>
<variable name="nu_Re6" units="mol_per_s"/>
<variable name="mu_E_o" units="J_per_mol"/>
<variable name="mu_Cl_o" units="J_per_mol"/>
<variable name="mu_ExCl_o" units="J_per_mol"/>
<variable name="mu_ECl_o" units="J_per_mol"/>
<variable name="mu_ECl_i" units="J_per_mol"/>
<variable name="mu_ExCl_i" units="J_per_mol"/>
<variable name="mu_Cl_i" units="J_per_mol"/>
<variable name="mu_E_i" units="J_per_mol"/>
<variable name="mu_HCO3_i" units="J_per_mol"/>
<variable name="mu_ExHCO3_i" units="J_per_mol"/>
<variable name="mu_EHCO3_i" units="J_per_mol"/>
<variable name="mu_EHCO3_o" units="J_per_mol"/>
<variable name="mu_ExHCO3_o" units="J_per_mol"/>
<variable name="mu_HCO3_o" units="J_per_mol"/>
<!-- Constitutive parameters-->
<variable name="K_Cl_o" public_interface="in" units="per_mol"/>
<variable name="K_Cl_i" public_interface="in" units="per_mol"/>
<variable name="K_HCO3_i" public_interface="in" units="per_mol"/>
<variable name="K_HCO3_o" public_interface="in" units="per_mol"/>
<variable name="K_E_o" public_interface="in" units="per_mol"/>
<variable name="K_ECl_o" public_interface="in" units="per_mol"/>
<variable name="K_ECl_i" public_interface="in" units="per_mol"/>
<variable name="K_E_i" public_interface="in" units="per_mol"/>
<variable name="K_EHCO3_i" public_interface="in" units="per_mol"/>
<variable name="K_EHCO3_o" public_interface="in" units="per_mol"/>
<variable name="k_Re1" public_interface="in" units="mol_per_s"/>
<variable name="k_Re2" public_interface="in" units="mol_per_s"/>
<variable name="k_Re3" public_interface="in" units="mol_per_s"/>
<variable name="k_Re4" public_interface="in" units="mol_per_s"/>
<variable name="k_Re5" public_interface="in" units="mol_per_s"/>
<variable name="k_Re6" public_interface="in" units="mol_per_s"/>
<!-- Conservation laws-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>mu_ExCl_o</ci>
<apply>
<plus/>
<ci>mu_E_o</ci>
<ci>mu_Cl_o</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_ExCl_i</ci>
<apply>
<plus/>
<ci>mu_Cl_i</ci>
<ci>mu_E_i</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_ExHCO3_i</ci>
<apply>
<plus/>
<ci>mu_E_i</ci>
<ci>mu_HCO3_i</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_ExHCO3_o</ci>
<apply>
<plus/>
<ci>mu_HCO3_o</ci>
<ci>mu_E_o</ci>
</apply>
</apply>
<!-- Definitions-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_Cl_o</ci>
</apply>
<apply>
<minus/>
<ci>nu_Re1</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_Cl_i</ci>
</apply>
<ci>nu_Re3</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_HCO3_i</ci>
</apply>
<apply>
<minus/>
<ci>nu_Re4</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_HCO3_o</ci>
</apply>
<ci>nu_Re6</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_E_o</ci>
</apply>
<apply>
<minus/>
<ci>nu_Re6</ci>
<ci>nu_Re1</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_ECl_o</ci>
</apply>
<apply>
<minus/>
<ci>nu_Re1</ci>
<ci>nu_Re2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_ECl_i</ci>
</apply>
<apply>
<minus/>
<ci>nu_Re2</ci>
<ci>nu_Re3</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_E_i</ci>
</apply>
<apply>
<minus/>
<ci>nu_Re3</ci>
<ci>nu_Re4</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_EHCO3_i</ci>
</apply>
<apply>
<minus/>
<ci>nu_Re4</ci>
<ci>nu_Re5</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_EHCO3_o</ci>
</apply>
<apply>
<minus/>
<ci>nu_Re5</ci>
<ci>nu_Re6</ci>
</apply>
</apply>
<!-- Constitutive relations-->
<apply>
<eq/>
<ci>mu_E_o</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_E_o</ci>
<ci>q_E_o</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_Cl_o</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_Cl_o</ci>
<ci>q_Cl_o</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_ECl_o</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_ECl_o</ci>
<ci>q_ECl_o</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_ECl_i</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_ECl_i</ci>
<ci>q_ECl_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_Cl_i</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_Cl_i</ci>
<ci>q_Cl_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_E_i</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_E_i</ci>
<ci>q_E_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_HCO3_i</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_HCO3_i</ci>
<ci>q_HCO3_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_EHCO3_i</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_EHCO3_i</ci>
<ci>q_EHCO3_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_EHCO3_o</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_EHCO3_o</ci>
<ci>q_EHCO3_o</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_HCO3_o</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_HCO3_o</ci>
<ci>q_HCO3_o</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>nu_Re1</ci>
<apply>
<times/>
<ci>k_Re1</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_ExCl_o</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_ECl_o</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>nu_Re2</ci>
<apply>
<times/>
<ci>k_Re2</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_ECl_o</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_ECl_i</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>nu_Re3</ci>
<apply>
<times/>
<ci>k_Re3</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_ECl_i</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_ExCl_i</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>nu_Re4</ci>
<apply>
<times/>
<ci>k_Re4</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_ExHCO3_i</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_EHCO3_i</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>nu_Re5</ci>
<apply>
<times/>
<ci>k_Re5</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_EHCO3_i</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_EHCO3_o</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>nu_Re6</ci>
<apply>
<times/>
<ci>k_Re6</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_EHCO3_o</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_ExHCO3_o</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="main" component_2="param"/>
<map_variables variable_1="RT" variable_2="RT"/>
<map_variables variable_1="K_Cl_o" variable_2="K_Cl_o"/>
<map_variables variable_1="K_Cl_i" variable_2="K_Cl_i"/>
<map_variables variable_1="K_HCO3_i" variable_2="K_HCO3_i"/>
<map_variables variable_1="K_HCO3_o" variable_2="K_HCO3_o"/>
<map_variables variable_1="K_E_o" variable_2="K_E_o"/>
<map_variables variable_1="K_ECl_o" variable_2="K_ECl_o"/>
<map_variables variable_1="K_ECl_i" variable_2="K_ECl_i"/>
<map_variables variable_1="K_E_i" variable_2="K_E_i"/>
<map_variables variable_1="K_EHCO3_i" variable_2="K_EHCO3_i"/>
<map_variables variable_1="K_EHCO3_o" variable_2="K_EHCO3_o"/>
<map_variables variable_1="k_Re1" variable_2="k_Re1"/>
<map_variables variable_1="k_Re2" variable_2="k_Re2"/>
<map_variables variable_1="k_Re3" variable_2="k_Re3"/>
<map_variables variable_1="k_Re4" variable_2="k_Re4"/>
<map_variables variable_1="k_Re5" variable_2="k_Re5"/>
<map_variables variable_1="k_Re6" variable_2="k_Re6"/>
</connection>
<connection>
<map_components component_1="main" component_2="environment"/>
<map_variables variable_1="t" variable_2="time"/>
</connection>
</model>