Location: Blood volume control model @ f30e4c0a6879 / BloodVolumeControl.cellml
- Author:
- David Brooks <d.brooks@auckland.ac.nz>
- Date:
- 2025-08-15 10:17:54+12:00
- Desc:
- Update labels of elements to match variable names in the CellML model.
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/c99/rawfile/f30e4c0a68790589c6ff9fb6387bb2d012658fe9/BloodVolumeControl.cellml
<?xml version='1.0' encoding='UTF-8'?>
<model name="my_model" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<!-- Simple model of blood volume-->
<units name="dim">
<unit units="dimensionless"/>
</units>
<units name="per_s">
<unit exponent="-1" units="second"/>
</units>
<units name="L_per_s">
<unit units="litre"/>
<unit exponent="-1" units="second"/>
</units>
<units name="kPa">
<unit units="joule"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="kPa_s_per_L">
<unit units="kPa"/>
<unit units="second"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="kPa_per_L">
<unit units="kPa"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="L_per_s_per_kPa">
<unit units="L_per_s"/>
<unit exponent="-1" units="kPa"/>
</units>
<units name="per_mol">
<unit exponent="-1" units="mole"/>
</units>
<units name="mol_per_s">
<unit units="mole"/>
<unit exponent="-1" units="second"/>
</units>
<units name="mol_per_L">
<unit units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="L_per_mol">
<unit units="litre"/>
<unit exponent="-1" units="mole"/>
</units>
<units name="mM">
<unit prefix="milli" units="mol_per_L"/>
</units>
<units name="J_per_mol">
<unit units="joule"/>
<unit exponent="-1" units="mole"/>
</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>
<component name="main">
<variable name="t" units="second"/>
<variable initial_value="2.5e3" name="RT" units="J_per_mol"/>
<variable initial_value="0.965e5" name="F" units="C_per_mol"/>
<variable cmeta:id="q-ac-W" initial_value="1" name="q_ac_W" units="litre"/>
<variable initial_value="2" name="q_vc_W" units="litre"/>
<variable initial_value="1" name="q_gi_W" units="litre"/>
<variable initial_value="0.1" name="q_pt_W" units="litre"/>
<variable initial_value="0.5" name="q_giEpi_W" units="litre"/>
<variable initial_value="0.5" name="q_ptEpi_W" units="litre"/>
<variable name="q_tot_W" units="litre"/>
<variable initial_value="0.84" name="q_vc_Na" units="mole"/>
<variable initial_value="0.1" name="q_gi_Na" units="mole"/>
<variable initial_value="0.01" name="q_pt_Na" units="mole"/>
<variable initial_value="0.012" name="q_giEpi_Na" units="mole"/>
<variable initial_value="0.012" name="q_ptEpi_Na" units="mole"/>
<variable initial_value="0.03" name="q_vc_K" units="mole"/>
<variable initial_value="0.012" name="q_giEpi_K" units="mole"/>
<variable initial_value="0.012" name="q_ptEpi_K" units="mole"/>
<variable name="q_tot_Na" units="mole"/>
<variable name="c_vc_Na" units="mol_per_L"/>
<variable name="c_gi_Na" units="mol_per_L"/>
<variable name="c_pt_Na" units="mol_per_L"/>
<variable name="c_giEpi_Na" units="mol_per_L"/>
<variable name="c_ptEpi_Na" units="mol_per_L"/>
<variable name="C_vc_Na" units="mM"/>
<variable name="C_gi_Na" units="mM"/>
<variable name="C_pt_Na" units="mM"/>
<variable name="C_giEpi_Na" units="mM"/>
<variable name="C_ptEpi_Na" units="mM"/>
<variable initial_value="0.1" name="v_lv_W" units="L_per_s"/>
<variable initial_value="0" name="v_in_W_base" units="L_per_s"/>
<variable name="v_in_W" units="L_per_s"/>
<variable name="v_out1_W" units="L_per_s"/>
<variable name="v_out2_W" units="L_per_s"/>
<variable name="v_gl_W" units="L_per_s"/>
<variable name="v_gi_W" units="L_per_s"/>
<variable name="v_pt_W" units="L_per_s"/>
<variable name="v_cc_W" units="L_per_s"/>
<variable initial_value="1.16e-06" name="v_in_Na_base" units="mol_per_s"/>
<variable name="v_in_Na" units="mol_per_s"/>
<variable name="v_out1_Na" units="mol_per_s"/>
<variable name="v_out2_Na" units="mol_per_s"/>
<variable name="v_gl_Na" units="mol_per_s"/>
<variable name="v_gi_Na" units="mol_per_s"/>
<variable name="v_pt_Na" units="mol_per_s"/>
<variable name="v_giEpi_NKE" units="mol_per_s"/>
<variable name="v_ptEpi_NKE" units="mol_per_s"/>
<variable name="u_vc_W" units="kPa"/>
<variable name="u_ac_W" units="kPa"/>
<variable name="u_pt_W" units="kPa"/>
<variable name="u_vc_osmotic" units="kPa"/>
<variable name="u_gi_osmotic" units="kPa"/>
<variable name="u_pt_osmotic" units="kPa"/>
<variable initial_value="-0.040" name="u_giEpi_e" units="J_per_C"/>
<variable initial_value="-0.040" name="u_ptEpi_e" units="J_per_C"/>
<variable initial_value="1" name="k_gi_W" units="L_per_s_per_kPa"/>
<variable initial_value="0" name="k_pt_W" units="L_per_s_per_kPa"/>
<variable initial_value="1" name="k_gl_W" units="L_per_s_per_kPa"/>
<variable initial_value="1" name="k_cc_W" units="L_per_s_per_kPa"/>
<variable initial_value="1" name="kK_gi_Na" units="per_s"/>
<variable initial_value="1" name="kK_pt_Na" units="per_s"/>
<variable initial_value="1" name="kK_gl_Na" units="per_s"/>
<variable initial_value="1e4" name="k_giEpi_NKE" units="mol_per_s"/>
<variable initial_value="1e5" name="k_ptEpi_NKE" units="mol_per_s"/>
<variable initial_value="1" name="K_Na" units="L_per_mol"/>
<variable initial_value="1" name="K_K" units="L_per_mol"/>
<variable initial_value="6e1" name="E_vc" units="joule"/>
<variable initial_value="6e1" name="E_ac" units="joule"/>
<variable initial_value="1" name="E_pt" units="joule"/>
<variable initial_value="0.5" name="U_ac_W" units="litre"/>
<variable initial_value="1.5" name="U_vc_W" units="litre"/>
<variable initial_value="0.1" name="U_pt_W" units="litre"/>
<variable initial_value="1.5" name="L_ac_W" units="litre"/>
<variable initial_value="2.5" name="L_vc_W" units="litre"/>
<variable initial_value="1" name="L_pt_W" units="litre"/>
<!-- Water input and output BCs-->
<variable initial_value="0.01" name="water_intake" units="L_per_s"/>
<variable initial_value="10" name="water_intake_start" units="second"/>
<variable initial_value="5" name="water_intake_duration" units="second"/>
<!-- kidney excretion = 94% of intake-->
<variable initial_value="0.94" name="water_kidney_excretion" units="dimensionless"/>
<!-- GI excretion = 6% of intake-->
<variable initial_value="0.06" name="water_gi_excretion" units="dimensionless"/>
<!-- Sodium input and output BCs-->
<variable initial_value="0.001" name="Na_intake" units="mol_per_s"/>
<variable initial_value="10" name="Na_intake_start" units="second"/>
<variable initial_value="10" name="Na_intake_duration" units="second"/>
<!-- gi excretion = 7% of intake-->
<variable initial_value="0.07" name="Na_gi_excretion" units="dimensionless"/>
<!-- kidney excretion = 93% of intake-->
<variable initial_value="0.93" name="Na_kidney_excretion" units="dimensionless"/>
<!-- Drink of water-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_in_W</ci>
<piecewise>
<piece>
<ci>water_intake</ci>
<apply>
<and/>
<apply>
<gt/>
<ci>t</ci>
<ci>water_intake_start</ci>
</apply>
<apply>
<lt/>
<ci>t</ci>
<apply>
<plus/>
<ci>water_intake_start</ci>
<ci>water_intake_duration</ci>
</apply>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="L_per_s">0</cn>
</otherwise>
</piecewise>
</apply>
<!-- Water flow excreted in faeces-->
<apply>
<eq/>
<ci>v_out1_W</ci>
<apply>
<times/>
<ci>water_gi_excretion</ci>
<ci>v_in_W_base</ci>
</apply>
</apply>
<!-- Water flow excreted in urine-->
<apply>
<eq/>
<ci>v_out2_W</ci>
<apply>
<times/>
<ci>water_kidney_excretion</ci>
<ci>v_in_W_base</ci>
</apply>
</apply>
<!-- Eat some sodium-->
<apply>
<eq/>
<ci>v_in_Na</ci>
<piecewise>
<piece>
<apply>
<plus/>
<ci>v_in_Na_base</ci>
<ci>Na_intake</ci>
</apply>
<apply>
<and/>
<apply>
<gt/>
<ci>t</ci>
<ci>Na_intake_start</ci>
</apply>
<apply>
<lt/>
<ci>t</ci>
<apply>
<plus/>
<ci>Na_intake_start</ci>
<ci>Na_intake_duration</ci>
</apply>
</apply>
</apply>
</piece>
<otherwise>
<ci>v_in_Na_base</ci>
</otherwise>
</piecewise>
</apply>
<!-- Na excreted in faeces-->
<apply>
<eq/>
<ci>v_out1_Na</ci>
<apply>
<times/>
<ci>Na_gi_excretion</ci>
<ci>v_in_Na_base</ci>
</apply>
</apply>
<!-- Water flow excreted in urine-->
<apply>
<eq/>
<ci>v_out2_Na</ci>
<apply>
<times/>
<ci>Na_kidney_excretion</ci>
<ci>v_in_Na_base</ci>
</apply>
</apply>
<!-- ODEs for qtys of water & sodium in the 4 compartments-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_gi_W</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>v_in_W</ci>
<apply>
<times/>
<ci>RT</ci>
<ci>k_gi_W</ci>
<apply>
<minus/>
<apply>
<divide/>
<ci>q_vc_Na</ci>
<ci>q_vc_W</ci>
</apply>
<apply>
<divide/>
<ci>q_gi_Na</ci>
<ci>q_gi_W</ci>
</apply>
</apply>
</apply>
</apply>
<ci>v_out1_W</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_pt_W</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<ci>k_gl_W</ci>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>E_ac</ci>
<apply>
<minus/>
<ci>q_ac_W</ci>
<ci>U_ac_W</ci>
</apply>
</apply>
<apply>
<power/>
<apply>
<minus/>
<ci>L_ac_W</ci>
<ci>q_ac_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>E_pt</ci>
<apply>
<minus/>
<ci>q_pt_W</ci>
<ci>U_pt_W</ci>
</apply>
</apply>
<apply>
<power/>
<apply>
<minus/>
<ci>L_pt_W</ci>
<ci>q_pt_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>RT</ci>
<ci>k_pt_W</ci>
<apply>
<minus/>
<apply>
<divide/>
<ci>q_vc_Na</ci>
<ci>q_vc_W</ci>
</apply>
<apply>
<divide/>
<ci>q_pt_Na</ci>
<ci>q_pt_W</ci>
</apply>
</apply>
</apply>
</apply>
<ci>v_out2_W</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_vc_W</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>k_cc_W</ci>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>E_ac</ci>
<apply>
<minus/>
<ci>q_ac_W</ci>
<ci>U_ac_W</ci>
</apply>
</apply>
<apply>
<power/>
<apply>
<minus/>
<ci>L_ac_W</ci>
<ci>q_ac_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>E_vc</ci>
<apply>
<minus/>
<ci>q_vc_W</ci>
<ci>U_vc_W</ci>
</apply>
</apply>
<apply>
<power/>
<apply>
<minus/>
<ci>L_vc_W</ci>
<ci>q_vc_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>RT</ci>
<ci>k_gi_W</ci>
<apply>
<minus/>
<apply>
<divide/>
<ci>q_vc_Na</ci>
<ci>q_vc_W</ci>
</apply>
<apply>
<divide/>
<ci>q_gi_Na</ci>
<ci>q_gi_W</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>RT</ci>
<ci>k_pt_W</ci>
<apply>
<minus/>
<apply>
<divide/>
<ci>q_vc_Na</ci>
<ci>q_vc_W</ci>
</apply>
<apply>
<divide/>
<ci>q_pt_Na</ci>
<ci>q_pt_W</ci>
</apply>
</apply>
</apply>
</apply>
<ci>v_lv_W</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_ac_W</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>v_lv_W</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k_cc_W</ci>
<ci>E_vc</ci>
<apply>
<minus/>
<ci>q_vc_W</ci>
<ci>U_vc_W</ci>
</apply>
</apply>
<apply>
<power/>
<apply>
<minus/>
<ci>L_vc_W</ci>
<ci>q_vc_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<ci>k_gl_W</ci>
<ci>k_cc_W</ci>
</apply>
<ci>E_ac</ci>
<apply>
<minus/>
<ci>q_ac_W</ci>
<ci>U_ac_W</ci>
</apply>
</apply>
<apply>
<power/>
<apply>
<minus/>
<ci>L_ac_W</ci>
<ci>q_ac_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>k_gl_W</ci>
<ci>E_pt</ci>
<apply>
<minus/>
<ci>q_pt_W</ci>
<ci>U_pt_W</ci>
</apply>
</apply>
<apply>
<power/>
<apply>
<minus/>
<ci>L_pt_W</ci>
<ci>q_pt_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_gi_Na</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>v_in_Na</ci>
<apply>
<times/>
<ci>kK_gi_Na</ci>
<apply>
<minus/>
<ci>q_gi_Na</ci>
<ci>q_giEpi_Na</ci>
</apply>
</apply>
</apply>
<ci>v_out1_Na</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_giEpi_Na</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>kK_gi_Na</ci>
<apply>
<minus/>
<ci>q_gi_Na</ci>
<ci>q_giEpi_Na</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dim">3</cn>
<ci>k_giEpi_NKE</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_Na</ci>
<ci>q_giEpi_Na</ci>
</apply>
<ci>q_giEpi_W</ci>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_K</ci>
<ci>q_vc_K</ci>
</apply>
<ci>q_vc_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_Na</ci>
<ci>q_vc_Na</ci>
</apply>
<ci>q_vc_W</ci>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_K</ci>
<ci>q_giEpi_K</ci>
</apply>
<ci>q_giEpi_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dim">2</cn>
<ci>F</ci>
<ci>u_giEpi_e</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_Na</ci>
<ci>q_giEpi_Na</ci>
</apply>
<ci>q_giEpi_W</ci>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_Na</ci>
<ci>q_vc_Na</ci>
</apply>
<ci>q_vc_W</ci>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_K</ci>
<ci>q_vc_K</ci>
</apply>
<ci>q_vc_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_K</ci>
<ci>q_giEpi_K</ci>
</apply>
<ci>q_giEpi_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_pt_Na</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<ci>kK_gl_Na</ci>
<apply>
<minus/>
<ci>q_vc_Na</ci>
<ci>q_pt_Na</ci>
</apply>
</apply>
<apply>
<times/>
<ci>kK_pt_Na</ci>
<apply>
<minus/>
<ci>q_pt_Na</ci>
<ci>q_ptEpi_Na</ci>
</apply>
</apply>
</apply>
<ci>v_out2_Na</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_ptEpi_Na</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>kK_pt_Na</ci>
<apply>
<minus/>
<ci>q_pt_Na</ci>
<ci>q_ptEpi_Na</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dim">3</cn>
<ci>k_ptEpi_NKE</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_Na</ci>
<ci>q_ptEpi_Na</ci>
</apply>
<ci>q_ptEpi_W</ci>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_K</ci>
<ci>q_vc_K</ci>
</apply>
<ci>q_vc_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_Na</ci>
<ci>q_vc_Na</ci>
</apply>
<ci>q_vc_W</ci>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_K</ci>
<ci>q_ptEpi_K</ci>
</apply>
<ci>q_ptEpi_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dim">2</cn>
<ci>F</ci>
<ci>u_ptEpi_e</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_Na</ci>
<ci>q_ptEpi_Na</ci>
</apply>
<ci>q_ptEpi_W</ci>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_Na</ci>
<ci>q_vc_Na</ci>
</apply>
<ci>q_vc_W</ci>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_K</ci>
<ci>q_vc_K</ci>
</apply>
<ci>q_vc_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_K</ci>
<ci>q_ptEpi_K</ci>
</apply>
<ci>q_ptEpi_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_vc_Na</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dim">3</cn>
<ci>k_giEpi_NKE</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_Na</ci>
<ci>q_giEpi_Na</ci>
</apply>
<ci>q_giEpi_W</ci>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_K</ci>
<ci>q_vc_K</ci>
</apply>
<ci>q_vc_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_Na</ci>
<ci>q_vc_Na</ci>
</apply>
<ci>q_vc_W</ci>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_K</ci>
<ci>q_giEpi_K</ci>
</apply>
<ci>q_giEpi_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dim">2</cn>
<ci>F</ci>
<ci>u_giEpi_e</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_Na</ci>
<ci>q_giEpi_Na</ci>
</apply>
<ci>q_giEpi_W</ci>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_Na</ci>
<ci>q_vc_Na</ci>
</apply>
<ci>q_vc_W</ci>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_K</ci>
<ci>q_vc_K</ci>
</apply>
<ci>q_vc_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_K</ci>
<ci>q_giEpi_K</ci>
</apply>
<ci>q_giEpi_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dim">3</cn>
<ci>k_ptEpi_NKE</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_Na</ci>
<ci>q_ptEpi_Na</ci>
</apply>
<ci>q_ptEpi_W</ci>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_K</ci>
<ci>q_vc_K</ci>
</apply>
<ci>q_vc_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_Na</ci>
<ci>q_vc_Na</ci>
</apply>
<ci>q_vc_W</ci>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_K</ci>
<ci>q_ptEpi_K</ci>
</apply>
<ci>q_ptEpi_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dim">2</cn>
<ci>F</ci>
<ci>u_ptEpi_e</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_Na</ci>
<ci>q_ptEpi_Na</ci>
</apply>
<ci>q_ptEpi_W</ci>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_Na</ci>
<ci>q_vc_Na</ci>
</apply>
<ci>q_vc_W</ci>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_K</ci>
<ci>q_vc_K</ci>
</apply>
<ci>q_vc_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_K</ci>
<ci>q_ptEpi_K</ci>
</apply>
<ci>q_ptEpi_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>kK_gl_Na</ci>
<apply>
<minus/>
<ci>q_vc_Na</ci>
<ci>q_pt_Na</ci>
</apply>
</apply>
</apply>
</apply>
<!-- Water pressures -->
<apply>
<eq/>
<ci>u_vc_W</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>E_vc</ci>
<apply>
<minus/>
<ci>q_vc_W</ci>
<ci>U_vc_W</ci>
</apply>
</apply>
<apply>
<power/>
<apply>
<minus/>
<ci>L_vc_W</ci>
<ci>q_vc_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_ac_W</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>E_ac</ci>
<apply>
<minus/>
<ci>q_ac_W</ci>
<ci>U_ac_W</ci>
</apply>
</apply>
<apply>
<power/>
<apply>
<minus/>
<ci>L_ac_W</ci>
<ci>q_ac_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_pt_W</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>E_pt</ci>
<apply>
<minus/>
<ci>q_pt_W</ci>
<ci>U_pt_W</ci>
</apply>
</apply>
<apply>
<power/>
<apply>
<minus/>
<ci>L_pt_W</ci>
<ci>q_pt_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<!-- Concentrations & Osmotic pressures-->
<apply>
<eq/>
<ci>c_vc_Na</ci>
<apply>
<divide/>
<ci>q_vc_Na</ci>
<ci>q_vc_W</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_gi_Na</ci>
<apply>
<divide/>
<ci>q_gi_Na</ci>
<ci>q_gi_W</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_pt_Na</ci>
<apply>
<divide/>
<ci>q_pt_Na</ci>
<ci>q_pt_W</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_giEpi_Na</ci>
<apply>
<divide/>
<ci>q_giEpi_Na</ci>
<ci>q_giEpi_W</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_ptEpi_Na</ci>
<apply>
<divide/>
<ci>q_ptEpi_Na</ci>
<ci>q_ptEpi_W</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>C_vc_Na</ci>
<apply>
<times/>
<cn cellml:units="dim" type="e-notation">1<sep/>3</cn>
<ci>c_vc_Na</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>C_gi_Na</ci>
<apply>
<times/>
<cn cellml:units="dim" type="e-notation">1<sep/>3</cn>
<ci>c_gi_Na</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>C_pt_Na</ci>
<apply>
<times/>
<cn cellml:units="dim" type="e-notation">1<sep/>3</cn>
<ci>c_pt_Na</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>C_giEpi_Na</ci>
<apply>
<times/>
<cn cellml:units="dim" type="e-notation">1<sep/>3</cn>
<ci>c_giEpi_Na</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>C_ptEpi_Na</ci>
<apply>
<times/>
<cn cellml:units="dim" type="e-notation">1<sep/>3</cn>
<ci>c_ptEpi_Na</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_gi_osmotic</ci>
<apply>
<times/>
<ci>RT</ci>
<ci>c_gi_Na</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_vc_osmotic</ci>
<apply>
<times/>
<ci>RT</ci>
<ci>c_vc_Na</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_pt_osmotic</ci>
<apply>
<times/>
<ci>RT</ci>
<ci>c_pt_Na</ci>
</apply>
</apply>
<!-- Water fluxes -->
<apply>
<eq/>
<ci>v_gi_W</ci>
<apply>
<times/>
<ci>k_gi_W</ci>
<apply>
<minus/>
<ci>u_vc_osmotic</ci>
<ci>u_gi_osmotic</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_pt_W</ci>
<apply>
<times/>
<ci>k_pt_W</ci>
<apply>
<minus/>
<ci>u_vc_osmotic</ci>
<ci>u_pt_osmotic</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_gl_W</ci>
<apply>
<times/>
<ci>k_gl_W</ci>
<apply>
<minus/>
<ci>u_ac_W</ci>
<ci>u_pt_W</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_cc_W</ci>
<apply>
<times/>
<ci>k_cc_W</ci>
<apply>
<minus/>
<ci>u_ac_W</ci>
<ci>u_vc_W</ci>
</apply>
</apply>
</apply>
<!-- Sodium fluxes-->
<apply>
<eq/>
<ci>v_gl_Na</ci>
<apply>
<times/>
<ci>kK_gl_Na</ci>
<apply>
<minus/>
<ci>q_vc_Na</ci>
<ci>q_pt_Na</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_gi_Na</ci>
<apply>
<times/>
<ci>kK_gi_Na</ci>
<apply>
<minus/>
<ci>q_gi_Na</ci>
<ci>q_giEpi_Na</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_pt_Na</ci>
<apply>
<times/>
<ci>kK_pt_Na</ci>
<apply>
<minus/>
<ci>q_pt_Na</ci>
<ci>q_ptEpi_Na</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_giEpi_NKE</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dim">3</cn>
<ci>k_giEpi_NKE</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_Na</ci>
<ci>q_giEpi_Na</ci>
</apply>
<ci>q_giEpi_W</ci>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_K</ci>
<ci>q_vc_K</ci>
</apply>
<ci>q_vc_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_Na</ci>
<ci>q_vc_Na</ci>
</apply>
<ci>q_vc_W</ci>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_K</ci>
<ci>q_giEpi_K</ci>
</apply>
<ci>q_giEpi_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dim">2</cn>
<ci>F</ci>
<ci>u_giEpi_e</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_Na</ci>
<ci>q_giEpi_Na</ci>
</apply>
<ci>q_giEpi_W</ci>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_Na</ci>
<ci>q_vc_Na</ci>
</apply>
<ci>q_vc_W</ci>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_K</ci>
<ci>q_vc_K</ci>
</apply>
<ci>q_vc_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_K</ci>
<ci>q_giEpi_K</ci>
</apply>
<ci>q_giEpi_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_ptEpi_NKE</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dim">3</cn>
<ci>k_ptEpi_NKE</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_Na</ci>
<ci>q_ptEpi_Na</ci>
</apply>
<ci>q_ptEpi_W</ci>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_K</ci>
<ci>q_vc_K</ci>
</apply>
<ci>q_vc_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_Na</ci>
<ci>q_vc_Na</ci>
</apply>
<ci>q_vc_W</ci>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_K</ci>
<ci>q_ptEpi_K</ci>
</apply>
<ci>q_ptEpi_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dim">2</cn>
<ci>F</ci>
<ci>u_ptEpi_e</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_Na</ci>
<ci>q_ptEpi_Na</ci>
</apply>
<ci>q_ptEpi_W</ci>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_Na</ci>
<ci>q_vc_Na</ci>
</apply>
<ci>q_vc_W</ci>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_K</ci>
<ci>q_vc_K</ci>
</apply>
<ci>q_vc_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_K</ci>
<ci>q_ptEpi_K</ci>
</apply>
<ci>q_ptEpi_W</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<!--Total water & total sodium-->
<apply>
<eq/>
<ci>q_tot_W</ci>
<apply>
<plus/>
<ci>q_ac_W</ci>
<ci>q_vc_W</ci>
<ci>q_gi_W</ci>
<ci>q_pt_W</ci>
<ci>q_giEpi_W</ci>
<ci>q_ptEpi_W</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_tot_Na</ci>
<apply>
<plus/>
<ci>q_vc_Na</ci>
<ci>q_gi_Na</ci>
<ci>q_pt_Na</ci>
<ci>q_giEpi_Na</ci>
<ci>q_ptEpi_Na</ci>
</apply>
</apply>
</math>
</component>
</model>