Location: Blood volume control model @ 44e8475655b0 / BG_CVS.cellml
- Author:
- Shelley Fong <sfon036@UoA.auckland.ac.nz>
- Date:
- 2025-03-04 12:10:17+13:00
- Desc:
- New pic in frontpage
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/c99/rawfile/44e8475655b050de3a462cfc36b8e05c8dee4928/BG_CVS.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#">
<!-- BG CVS model extended to include a more detailed lung circulation-->
<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="L_per_s_per_kPa">
<unit units="L_per_s"/>
<unit exponent="-1" units="kPa"/>
</units>
<units name="kPa_per_L">
<unit units="kPa"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="kPa_s_per_L">
<unit units="kPa"/>
<unit exponent="-1" units="L_per_s"/>
</units>
<units name="Js2_per_m5">
<unit units="joule"/>
<unit exponent="2" units="second"/>
<unit exponent="-5" units="meter"/>
</units>
<units name="m_per_s2">
<unit units="meter"/>
<unit exponent="-2" units="second"/>
</units>
<units name="fmol">
<unit prefix="femto" units="mole"/>
</units>
<units name="per_fmol">
<unit exponent="-1" units="fmol"/>
</units>
<units name="fmol_per_s">
<unit units="fmol"/>
<unit exponent="-1" units="second"/>
</units>
<component name="main">
<variable name="t" units="second"/>
<variable initial_value="1e3" name="rho" units="Js2_per_m5"/>
<variable initial_value="9.81" name="g" units="m_per_s2"/>
<variable initial_value="90" name="theta_deg" units="dim"/>
<variable name="theta_rad" units="radian"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>theta_rad</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>theta_deg</ci>
<pi/>
</apply>
<cn cellml:units="dim">180</cn>
</apply>
</apply>
</math>
<variable name="z" units="dim"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>z</ci>
<piecewise>
<piece>
<cn cellml:units="dim">1</cn>
<apply>
<and/>
<apply>
<gt/>
<ci>t</ci>
<cn cellml:units="second">100</cn>
</apply>
<apply>
<lt/>
<ci>t</ci>
<cn cellml:units="second">101</cn>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="dim">0</cn>
</otherwise>
</piecewise>
</apply>
</math>
<!--Triangular waveform mt with period T. Triangular waveform delayed by a constant is mta-->
<variable initial_value="1" name="T" units="second"/>
<variable name="mt" units="dim"/>
<variable name="mta" units="dim"/>
<variable initial_value="0.1" name="delay" units="dim"/>
<variable initial_value="0.1" name="To_pk" units="dim"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>mt</ci>
<apply>
<minus/>
<apply>
<divide/>
<ci>t</ci>
<ci>T</ci>
</apply>
<apply>
<floor/>
<apply>
<divide/>
<ci>t</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mta</ci>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<divide/>
<ci>t</ci>
<ci>T</ci>
</apply>
<ci>delay</ci>
</apply>
<apply>
<floor/>
<apply>
<divide/>
<apply>
<minus/>
<ci>t</ci>
<apply>
<times/>
<ci>delay</ci>
<ci>T</ci>
</apply>
</apply>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<!--Left ventricle-->
<variable name="E_LV" units="kPa_per_L"/>
<variable initial_value="320" name="E_LVmax" units="kPa_per_L"/>
<variable initial_value="6.667" name="E_LVmin" units="kPa_per_L"/>
<variable initial_value="1" name="q_LV" units="litre"/>
<variable initial_value="0.005" name="q_LV_us" units="litre"/>
<variable name="u_LV" units="kPa"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>E_LV</ci>
<piecewise>
<piece>
<apply>
<plus/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>E_LVmax</ci>
<ci>E_LVmin</ci>
</apply>
<ci>mt</ci>
</apply>
<ci>To_pk</ci>
</apply>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dim">0.5</cn>
<apply>
<minus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>mt</ci>
<ci>To_pk</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<ci>E_LVmin</ci>
</apply>
<apply>
<lt/>
<ci>mt</ci>
<cn cellml:units="dim">0.4</cn>
</apply>
</piece>
<piece>
<apply>
<plus/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>E_LVmax</ci>
<ci>E_LVmin</ci>
</apply>
<cn cellml:units="dim">0.4</cn>
</apply>
<ci>To_pk</ci>
</apply>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dim">0.5</cn>
<apply>
<minus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<cn cellml:units="dim">0.4</cn>
<ci>To_pk</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<ci>E_LVmin</ci>
</apply>
<apply>
<lt/>
<ci>mt</ci>
<cn cellml:units="dim">0.6</cn>
</apply>
</piece>
<otherwise>
<ci>E_LVmin</ci>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_LV</ci>
</apply>
<apply>
<minus/>
<ci>v_MV</ci>
<ci>v_AV</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_LV</ci>
<apply>
<times/>
<ci>E_LV</ci>
<apply>
<minus/>
<ci>q_LV</ci>
<ci>q_LV_us</ci>
</apply>
</apply>
</apply>
</math>
<!--Right ventricle-->
<variable name="E_RV" units="kPa_per_L"/>
<variable initial_value="70" name="E_RVmax" units="kPa_per_L"/>
<variable initial_value="2" name="E_RVmin" units="kPa_per_L"/>
<variable initial_value="0.2" name="q_RV" units="litre"/>
<variable initial_value="0.01" name="q_RV_us" units="litre"/>
<variable name="u_RV" units="kPa"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>E_RV</ci>
<piecewise>
<piece>
<apply>
<plus/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>E_RVmax</ci>
<ci>E_RVmin</ci>
</apply>
<ci>mt</ci>
</apply>
<ci>To_pk</ci>
</apply>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dim">0.5</cn>
<apply>
<minus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>mt</ci>
<ci>To_pk</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<ci>E_RVmin</ci>
</apply>
<apply>
<lt/>
<ci>mt</ci>
<cn cellml:units="dim">0.4</cn>
</apply>
</piece>
<piece>
<apply>
<plus/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>E_RVmax</ci>
<ci>E_RVmin</ci>
</apply>
<cn cellml:units="dim">0.4</cn>
</apply>
<ci>To_pk</ci>
</apply>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dim">0.5</cn>
<apply>
<minus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<cn cellml:units="dim">0.4</cn>
<ci>To_pk</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<ci>E_RVmin</ci>
</apply>
<apply>
<lt/>
<ci>mt</ci>
<cn cellml:units="dim">0.6</cn>
</apply>
</piece>
<otherwise>
<ci>E_RVmin</ci>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_RV</ci>
</apply>
<apply>
<minus/>
<ci>v_TV</ci>
<ci>v_PV</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_RV</ci>
<apply>
<times/>
<ci>E_RV</ci>
<apply>
<minus/>
<ci>q_RV</ci>
<ci>q_RV_us</ci>
</apply>
</apply>
</apply>
</math>
<!-- Left atrium-->
<variable initial_value="10" name="E_LA" units="kPa_per_L"/>
<variable initial_value="0.02" name="q_LA" units="litre"/>
<variable initial_value="0.004" name="q_LA_us" units="litre"/>
<variable name="u_LA" units="kPa"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_LA</ci>
</apply>
<apply>
<minus/>
<ci>v_PulmV</ci>
<ci>v_MV</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_LA</ci>
<apply>
<times/>
<ci>E_LA</ci>
<apply>
<minus/>
<ci>q_LA</ci>
<ci>q_LA_us</ci>
</apply>
</apply>
</apply>
</math>
<!-- Right atrium-->
<variable initial_value="10" name="E_RA" units="kPa_per_L"/>
<variable initial_value="0.02" name="q_RA" units="litre"/>
<variable initial_value="0.004" name="q_RA_us" units="litre"/>
<variable name="u_RA" units="kPa"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_RA</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>v_brain3</ci>
<ci>v_liver2</ci>
<ci>v_lRenalV</ci>
<ci>v_rRenalV</ci>
<ci>v_musTorso3</ci>
<ci>v_lArm3</ci>
<ci>v_rArm3</ci>
<ci>v_lLeg3</ci>
<ci>v_rLeg3</ci>
</apply>
<ci>v_TV</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_RA</ci>
<apply>
<times/>
<ci>E_RA</ci>
<apply>
<minus/>
<ci>q_RA</ci>
<ci>q_RA_us</ci>
</apply>
</apply>
</apply>
</math>
<!-- Aortic valve-->
<variable initial_value="1" name="R_AV" units="kPa_s_per_L"/>
<variable name="v_AV" units="L_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_AV</ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_LV</ci>
<ci>u_AA</ci>
</apply>
<ci>R_AV</ci>
</apply>
<apply>
<gt/>
<ci>u_LV</ci>
<ci>u_AA</ci>
</apply>
</piece>
<otherwise>
<cn cellml:units="L_per_s">0</cn>
</otherwise>
</piecewise>
</apply>
</math>
<!-- Pulmonary Valve-->
<variable initial_value="1" name="R_PV" units="kPa_s_per_L"/>
<variable name="v_PV" units="L_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_PV</ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_RV</ci>
<ci>u_PulmA</ci>
</apply>
<ci>R_PV</ci>
</apply>
<apply>
<gt/>
<ci>u_RV</ci>
<ci>u_PulmA</ci>
</apply>
</piece>
<otherwise>
<cn cellml:units="L_per_s">0</cn>
</otherwise>
</piecewise>
</apply>
</math>
<!-- Tricuspid Valve-->
<variable initial_value="1" name="R_TV" units="kPa_s_per_L"/>
<variable name="v_TV" units="L_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_TV</ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_RA</ci>
<ci>u_RV</ci>
</apply>
<ci>R_TV</ci>
</apply>
<apply>
<gt/>
<ci>u_RA</ci>
<ci>u_RV</ci>
</apply>
</piece>
<otherwise>
<cn cellml:units="L_per_s">0</cn>
</otherwise>
</piecewise>
</apply>
</math>
<!-- Mitral Valve-->
<variable initial_value="1" name="R_MV" units="kPa_s_per_L"/>
<variable name="v_MV" units="L_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_MV</ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_LA</ci>
<ci>u_LV</ci>
</apply>
<ci>R_MV</ci>
</apply>
<apply>
<gt/>
<ci>u_LA</ci>
<ci>u_LV</ci>
</apply>
</piece>
<otherwise>
<cn cellml:units="L_per_s">0</cn>
</otherwise>
</piecewise>
</apply>
</math>
<!-- Pulmonary artery-->
<variable initial_value="0.3" name="q_PulmA" units="litre"/>
<variable initial_value="0.2" name="q_PulmA_us" units="litre"/>
<variable name="u_PulmA" units="kPa"/>
<variable initial_value="200" name="E_PulmA" units="kPa_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_PulmA</ci>
</apply>
<apply>
<minus/>
<ci>v_PV</ci>
<ci>v_lPulmA</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_PulmA</ci>
<apply>
<times/>
<ci>E_PulmA</ci>
<apply>
<minus/>
<ci>q_PulmA</ci>
<ci>q_PulmA_us</ci>
</apply>
</apply>
</apply>
</math>
<!-- Left lung -->
<variable name="v_lPulmA" units="L_per_s"/>
<variable initial_value="1" name="R_lPulmA" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_lPulmA</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_PulmA</ci>
<ci>u_lPulmA</ci>
</apply>
<ci>R_lPulmA</ci>
</apply>
</apply>
</math>
<variable initial_value="0.3" name="q_lPulmA" units="litre"/>
<variable initial_value="0.2" name="q_lPulmA_us" units="litre"/>
<variable name="u_lPulmA" units="kPa"/>
<variable initial_value="200" name="E_lPulmA" units="kPa_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_lPulmA</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>v_lPulmA</ci>
<ci>v_lULobeA</ci>
</apply>
<ci>v_lInterlobarA</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_lPulmA</ci>
<apply>
<times/>
<ci>E_lPulmA</ci>
<apply>
<minus/>
<ci>q_lPulmA</ci>
<ci>q_lPulmA_us</ci>
</apply>
</apply>
</apply>
</math>
<variable name="v_lULobeA" units="L_per_s"/>
<variable initial_value="1" name="R_lULobeA" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_lULobeA</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_lPulmA</ci>
<ci>u_lULobeC</ci>
</apply>
<ci>R_lULobeA</ci>
</apply>
</apply>
</math>
<variable initial_value="0.3" name="q_lULobeC" units="litre"/>
<variable initial_value="0.2" name="q_lULobeC_us" units="litre"/>
<variable name="u_lULobeC" units="kPa"/>
<variable initial_value="200" name="E_lULobeC" units="kPa_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_lULobeC</ci>
</apply>
<apply>
<minus/>
<ci>v_lULobeA</ci>
<ci>v_lULobeV</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_lULobeC</ci>
<apply>
<times/>
<ci>E_lULobeC</ci>
<apply>
<minus/>
<ci>q_lULobeC</ci>
<ci>q_lULobeC_us</ci>
</apply>
</apply>
</apply>
</math>
<variable name="v_lULobeV" units="L_per_s"/>
<variable initial_value="1" name="R_lULobeV" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_lULobeV</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_lULobeC</ci>
<ci>u_PulmV</ci>
</apply>
<ci>R_lULobeV</ci>
</apply>
</apply>
</math>
<variable name="v_lLungInterlobarA" units="L_per_s"/>
<variable initial_value="1" name="R_lLungInterlobarA" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_lLungInterlobarA</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_lPulmA</ci>
<ci>u_lLungInterlobarA</ci>
</apply>
<ci>R_lLungInterlobarA</ci>
</apply>
</apply>
</math>
<variable initial_value="0.3" name="q_lLungInterlobarA" units="litre"/>
<variable initial_value="0.2" name="q_lLungInterlobarA_us" units="litre"/>
<variable name="u_lLungInterlobarA" units="kPa"/>
<variable initial_value="200" name="E_lLungInterlobarA" units="kPa_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_lLungInterlobarA</ci>
</apply>
<apply>
<minus/>
<ci>v_lLungInterlobarA</ci>
<ci>v_lLLobeA</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_lLungInterlobarA</ci>
<apply>
<times/>
<ci>E_lLungInterlobarA</ci>
<apply>
<minus/>
<ci>q_lLungInterlobarA</ci>
<ci>q_lLungInterlobarA_us</ci>
</apply>
</apply>
</apply>
</math>
<variable name="v_lLLobeA" units="L_per_s"/>
<variable initial_value="1" name="R_lLLobeA" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_lLLobeA</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_lLungInterlobarA</ci>
<ci>u_lLLobeA</ci>
</apply>
<ci>R_lLLobeA</ci>
</apply>
</apply>
</math>
<variable initial_value="0.3" name="q_lLLobeA" units="litre"/>
<variable initial_value="0.2" name="q_lLLobeA_us" units="litre"/>
<variable name="u_lLLobeA" units="kPa"/>
<variable initial_value="200" name="E_lLLobeA" units="kPa_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_lLLobeA</ci>
</apply>
<apply>
<minus/>
<ci>v_lLLobeA</ci>
<ci>v_lLLobeV</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_lLLobeA</ci>
<apply>
<times/>
<ci>E_lLLobeA</ci>
<apply>
<minus/>
<ci>q_lLLobeA</ci>
<ci>q_lLLobeA_us</ci>
</apply>
</apply>
</apply>
</math>
<variable name="v_lLLobeV" units="L_per_s"/>
<variable initial_value="1" name="R_lLLobeV" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_lLLobeV</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_lLLobeA</ci>
<ci>u_PulmV</ci>
</apply>
<ci>R_lLLobeV</ci>
</apply>
</apply>
</math>
<!-- Right lung -->
<variable name="v_rPulmA" units="L_per_s"/>
<variable initial_value="1" name="R_rPulmA" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_rPulmA</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_PulmA</ci>
<ci>u_rPulmA</ci>
</apply>
<ci>R_rPulmA</ci>
</apply>
</apply>
</math>
<variable initial_value="0.3" name="q_rPulmA" units="litre"/>
<variable initial_value="0.2" name="q_rPulmA_us" units="litre"/>
<variable name="u_rPulmA" units="kPa"/>
<variable initial_value="200" name="E_rPulmA" units="kPa_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_rPulmA</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>v_rPulmA</ci>
<ci>v_rULobeA</ci>
</apply>
<ci>v_rInterlobarA</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_rPulmA</ci>
<apply>
<times/>
<ci>E_rPulmA</ci>
<apply>
<minus/>
<ci>q_rPulmA</ci>
<ci>q_rPulmA_us</ci>
</apply>
</apply>
</apply>
</math>
<variable name="v_rULobeA" units="L_per_s"/>
<variable initial_value="1" name="R_rULobeA" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_rULobeA</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_rPulmA</ci>
<ci>u_rULobeC</ci>
</apply>
<ci>R_rULobeA</ci>
</apply>
</apply>
</math>
<variable initial_value="0.3" name="q_rULobeC" units="litre"/>
<variable initial_value="0.2" name="q_rULobeC_us" units="litre"/>
<variable name="u_rULobeC" units="kPa"/>
<variable initial_value="200" name="E_rULobeC" units="kPa_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_rULobeC</ci>
</apply>
<apply>
<minus/>
<ci>v_rULobeA</ci>
<ci>v_rULobeV</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_rULobeC</ci>
<apply>
<times/>
<ci>E_rULobeC</ci>
<apply>
<minus/>
<ci>q_rULobeC</ci>
<ci>q_rULobeC_us</ci>
</apply>
</apply>
</apply>
</math>
<variable name="v_rULobeV" units="L_per_s"/>
<variable initial_value="1" name="R_rULobeV" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_rULobeV</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_rULobeC</ci>
<ci>u_PulmV</ci>
</apply>
<ci>R_rULobeV</ci>
</apply>
</apply>
</math>
<variable name="v_rInterlobarA" units="L_per_s"/>
<variable initial_value="1" name="R_rInterlobarA" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_rInterlobarA</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_rPulmA</ci>
<ci>u_rInterlobarA</ci>
</apply>
<ci>R_rInterlobarA</ci>
</apply>
</apply>
</math>
<variable initial_value="0.3" name="q_rInterlobarA" units="litre"/>
<variable initial_value="0.2" name="q_rInterlobarA_us" units="litre"/>
<variable name="u_rInterlobarA" units="kPa"/>
<variable initial_value="200" name="E_rInterlobarA" units="kPa_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_rInterlobarA</ci>
</apply>
<apply>
<minus/>
<ci>v_rInterlobarA</ci>
<ci>v_rLLobeA</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_rInterlobarA</ci>
<apply>
<times/>
<ci>E_rInterlobarA</ci>
<apply>
<minus/>
<ci>q_rInterlobarA</ci>
<ci>q_rInterlobarA_us</ci>
</apply>
</apply>
</apply>
</math>
<variable name="v_rLLobeA" units="L_per_s"/>
<variable initial_value="1" name="R_rLLobeA" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_rLLobeA</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_rInterlobarA</ci>
<ci>u_rLLobeA</ci>
</apply>
<ci>R_rLLobeA</ci>
</apply>
</apply>
</math>
<variable initial_value="0.3" name="q_rLLobeA" units="litre"/>
<variable initial_value="0.2" name="q_rLLobeA_us" units="litre"/>
<variable name="u_rLLobeA" units="kPa"/>
<variable initial_value="200" name="E_rLLobeA" units="kPa_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_rLLobeA</ci>
</apply>
<apply>
<minus/>
<ci>v_rLLobeA</ci>
<ci>v_rLLobeV</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_rLLobeA</ci>
<apply>
<times/>
<ci>E_rLLobeA</ci>
<apply>
<minus/>
<ci>q_rLLobeA</ci>
<ci>q_rLLobeA_us</ci>
</apply>
</apply>
</apply>
</math>
<variable name="v_rLLobeV" units="L_per_s"/>
<variable initial_value="1" name="R_rLLobeV" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_rLLobeV</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_rLLobeA</ci>
<ci>u_PulmV</ci>
</apply>
<ci>R_rLLobeV</ci>
</apply>
</apply>
</math>
<!-- Pulmonary vein-->
<variable initial_value="20" name="E_PulmV" units="kPa_per_L"/>
<variable initial_value="0.02" name="q_PulmV" units="litre"/>
<variable initial_value="0.012" name="q_PulmV_us" units="litre"/>
<variable name="u_PulmV" units="kPa"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_PulmV</ci>
</apply>
<apply>
<minus/>
<ci>v_lULobeV</ci>
<ci>v_PulmV</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_PulmV</ci>
<apply>
<times/>
<ci>E_PulmV</ci>
<apply>
<minus/>
<ci>q_PulmV</ci>
<ci>q_PulmV_us</ci>
</apply>
</apply>
</apply>
</math>
<variable name="v_PulmV" units="L_per_s"/>
<variable initial_value="1" name="R_PulmV" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_PulmV</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_PulmV</ci>
<ci>u_LA</ci>
</apply>
<ci>R_PulmV</ci>
</apply>
</apply>
</math>
<!-- Brain-->
<variable initial_value="0.1" name="q_brain" units="litre"/>
<variable initial_value="0.06" name="q_brain_us" units="litre"/>
<variable initial_value="0.1" name="q_brainVein" units="litre"/>
<variable initial_value="0.06" name="q_brainVein_us" units="litre"/>
<variable name="u_brain" units="kPa"/>
<variable name="u_brainVein" units="kPa"/>
<variable initial_value="20" name="E_brain" units="kPa_per_L"/>
<variable initial_value="20" name="E_brainVein" units="kPa_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_brain</ci>
</apply>
<apply>
<minus/>
<ci>v_brain1</ci>
<ci>v_brain2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_brain</ci>
<apply>
<times/>
<ci>E_brain</ci>
<apply>
<minus/>
<ci>q_brain</ci>
<ci>q_brain_us</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_brainVein</ci>
</apply>
<apply>
<minus/>
<ci>v_brain2</ci>
<ci>v_brain3</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_brainVein</ci>
<apply>
<times/>
<ci>E_brainVein</ci>
<apply>
<minus/>
<ci>q_brainVein</ci>
<ci>q_brainVein_us</ci>
</apply>
</apply>
</apply>
</math>
<variable name="v_brain1" units="L_per_s"/>
<variable name="v_brain2" units="L_per_s"/>
<variable name="v_brain3" units="L_per_s"/>
<variable initial_value="100" name="R_brain1" units="kPa_s_per_L"/>
<variable initial_value="600" name="R_brain2" units="kPa_s_per_L"/>
<variable initial_value="1" name="R_brain3" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_brain1</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_AA</ci>
<ci>u_brain</ci>
</apply>
<ci>R_brain1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_brain2</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_brain</ci>
<ci>u_brainVein</ci>
</apply>
<ci>R_brain2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_brain3</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_brainVein</ci>
<ci>u_RA</ci>
</apply>
<ci>R_brain3</ci>
</apply>
</apply>
</math>
<!-- Ascending aorta-->
<variable initial_value="0.2" name="q_AA" units="litre"/>
<variable initial_value="0.12" name="q_AA_us" units="litre"/>
<variable name="u_AA" units="kPa"/>
<variable initial_value="80" name="E_AA" units="kPa_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_AA</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>v_AV</ci>
<ci>v_brain1</ci>
</apply>
<ci>v_celiac</ci>
</apply>
<ci>v_supMes</ci>
</apply>
<ci>v_infMes</ci>
</apply>
<ci>v_lRenalA</ci>
</apply>
<ci>v_rRenalA</ci>
</apply>
<ci>v_musTorso1</ci>
</apply>
<ci>v_lArm1</ci>
</apply>
<ci>v_rArm1</ci>
</apply>
<ci>v_lLeg1</ci>
</apply>
<ci>v_rLeg1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_AA</ci>
<apply>
<times/>
<ci>E_AA</ci>
<apply>
<minus/>
<ci>q_AA</ci>
<ci>q_AA_us</ci>
</apply>
</apply>
</apply>
</math>
<!-- Celiac branch of the aorta -->
<variable initial_value="0.1" name="q_celiac" units="litre"/>
<variable initial_value="0.06" name="q_celiac_us" units="litre"/>
<variable name="u_celiac" units="kPa"/>
<variable initial_value="400" name="E_celiac" units="kPa_per_L"/>
<variable initial_value="0.20" name="z_celiac" units="meter"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_celiac</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>v_celiac</ci>
<ci>v_liver1</ci>
</apply>
<ci>v_stomach1</ci>
</apply>
<ci>v_spleen1</ci>
</apply>
<ci>v_pancreas1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_celiac</ci>
<apply>
<times/>
<ci>E_celiac</ci>
<apply>
<minus/>
<ci>q_celiac</ci>
<ci>q_celiac_us</ci>
</apply>
</apply>
</apply>
</math>
<variable name="v_celiac" units="L_per_s"/>
<variable initial_value="100" name="R_celiac" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_celiac</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_AA</ci>
<ci>u_celiac</ci>
</apply>
<ci>R_celiac</ci>
</apply>
</apply>
</math>
<!-- Superior mesentery branch of the aorta -->
<variable initial_value="0.1" name="q_supMes" units="litre"/>
<variable initial_value="0.06" name="q_supMes_us" units="litre"/>
<variable name="u_supMes" units="kPa"/>
<variable initial_value="400" name="E_supMes" units="kPa_per_L"/>
<variable initial_value="0.20" name="z_supMes" units="meter"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_supMes</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>v_supMes</ci>
<ci>v_pancreas2</ci>
</apply>
<ci>v_intestine1</ci>
</apply>
<ci>v_colon1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_supMes</ci>
<apply>
<times/>
<ci>E_supMes</ci>
<apply>
<minus/>
<ci>q_supMes</ci>
<ci>q_supMes_us</ci>
</apply>
</apply>
</apply>
</math>
<variable name="v_supMes" units="L_per_s"/>
<variable initial_value="100" name="R_supMes" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_supMes</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_AA</ci>
<ci>u_supMes</ci>
</apply>
<ci>R_supMes</ci>
</apply>
</apply>
</math>
<!-- Inferior mesentery branch of the aorta -->
<variable name="v_infMes" units="L_per_s"/>
<variable initial_value="100" name="R_infMes" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_infMes</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_AA</ci>
<ci>u_colon</ci>
</apply>
<ci>R_infMes</ci>
</apply>
</apply>
</math>
<!-- Stomach-->
<variable initial_value="0.1" name="q_stomach" units="litre"/>
<variable initial_value="0.06" name="q_stomach_us" units="litre"/>
<variable name="u_stomach" units="kPa"/>
<variable initial_value="100" name="E_stomach" units="kPa_per_L"/>
<variable initial_value="0.20" name="z_stomach" units="meter"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_stomach</ci>
</apply>
<apply>
<minus/>
<ci>v_stomach1</ci>
<ci>v_stomach2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_stomach</ci>
<apply>
<times/>
<ci>E_stomach</ci>
<apply>
<minus/>
<ci>q_stomach</ci>
<ci>q_stomach_us</ci>
</apply>
</apply>
</apply>
</math>
<variable name="v_stomach1" units="L_per_s"/>
<variable name="v_stomach2" units="L_per_s"/>
<variable initial_value="100" name="R_stomach1" units="kPa_s_per_L"/>
<variable initial_value="2400" name="R_stomach2" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_stomach1</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_celiac</ci>
<ci>u_stomach</ci>
</apply>
<ci>R_stomach1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_stomach2</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_stomach</ci>
<ci>u_portalVein</ci>
</apply>
<ci>R_stomach2</ci>
</apply>
</apply>
</math>
<!-- Spleen-->
<variable initial_value="0.1" name="q_spleen" units="litre"/>
<variable initial_value="0.06" name="q_spleen_us" units="litre"/>
<variable name="u_spleen" units="kPa"/>
<variable initial_value="100" name="E_spleen" units="kPa_per_L"/>
<variable initial_value="0.20" name="z_spleen" units="meter"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_spleen</ci>
</apply>
<apply>
<minus/>
<ci>v_spleen1</ci>
<ci>v_spleen2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_spleen</ci>
<apply>
<times/>
<ci>E_colon</ci>
<apply>
<minus/>
<ci>q_spleen</ci>
<ci>q_spleen_us</ci>
</apply>
</apply>
</apply>
</math>
<variable name="v_spleen1" units="L_per_s"/>
<variable name="v_spleen2" units="L_per_s"/>
<variable initial_value="100" name="R_spleen1" units="kPa_s_per_L"/>
<variable initial_value="3000" name="R_spleen2" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_spleen1</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_celiac</ci>
<ci>u_spleen</ci>
</apply>
<ci>R_spleen1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_spleen2</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_spleen</ci>
<ci>u_portalVein</ci>
</apply>
<ci>R_spleen2</ci>
</apply>
</apply>
</math>
<!-- Pancreas-->
<variable initial_value="0.1" name="q_pancreas" units="litre"/>
<variable initial_value="0.06" name="q_pancreas_us" units="litre"/>
<variable name="u_pancreas" units="kPa"/>
<variable initial_value="100" name="E_pancreas" units="kPa_per_L"/>
<variable initial_value="0.20" name="z_pancreas" units="meter"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_pancreas</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>v_pancreas1</ci>
<ci>v_pancreas2</ci>
</apply>
<ci>v_pancreas3</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_pancreas</ci>
<apply>
<times/>
<ci>E_pancreas</ci>
<apply>
<minus/>
<ci>q_pancreas</ci>
<ci>q_pancreas_us</ci>
</apply>
</apply>
</apply>
</math>
<variable name="v_pancreas1" units="L_per_s"/>
<variable name="v_pancreas2" units="L_per_s"/>
<variable name="v_pancreas3" units="L_per_s"/>
<variable initial_value="100" name="R_pancreas1" units="kPa_s_per_L"/>
<variable initial_value="100" name="R_pancreas2" units="kPa_s_per_L"/>
<variable initial_value="4000" name="R_pancreas3" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_pancreas1</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_celiac</ci>
<ci>u_pancreas</ci>
</apply>
<ci>R_pancreas1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_pancreas2</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_supMes</ci>
<ci>u_pancreas</ci>
</apply>
<ci>R_pancreas2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_pancreas3</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_pancreas</ci>
<ci>u_portalVein</ci>
</apply>
<ci>R_pancreas3</ci>
</apply>
</apply>
</math>
<!-- Intestine-->
<variable initial_value="0.1" name="q_intestine" units="litre"/>
<variable initial_value="0.06" name="q_intestine_us" units="litre"/>
<variable name="u_intestine" units="kPa"/>
<variable initial_value="100" name="E_intestine" units="kPa_per_L"/>
<variable initial_value="0.20" name="z_" units="meter"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_intestine</ci>
</apply>
<apply>
<minus/>
<ci>v_intestine1</ci>
<ci>v_intestine2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_intestine</ci>
<apply>
<times/>
<ci>E_intestine</ci>
<apply>
<minus/>
<ci>q_intestine</ci>
<ci>q_intestine_us</ci>
</apply>
</apply>
</apply>
</math>
<variable name="v_intestine1" units="L_per_s"/>
<variable name="v_intestine2" units="L_per_s"/>
<variable initial_value="100" name="R_intestine1" units="kPa_s_per_L"/>
<variable initial_value="1200" name="R_intestine2" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_intestine1</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_supMes</ci>
<ci>u_intestine</ci>
</apply>
<ci>R_intestine1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_intestine2</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_intestine</ci>
<ci>u_portalVein</ci>
</apply>
<ci>R_intestine2</ci>
</apply>
</apply>
</math>
<!-- Colon-->
<variable initial_value="0.1" name="q_colon" units="litre"/>
<variable initial_value="0.06" name="q_colon_us" units="litre"/>
<variable name="u_colon" units="kPa"/>
<variable initial_value="100" name="E_colon" units="kPa_per_L"/>
<variable initial_value="0.20" name="z_colon" units="meter"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_colon</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>v_colon1</ci>
<ci>v_infMes</ci>
</apply>
<ci>v_colon2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_colon</ci>
<apply>
<times/>
<ci>E_colon</ci>
<apply>
<minus/>
<ci>q_colon</ci>
<ci>q_colon_us</ci>
</apply>
</apply>
</apply>
</math>
<variable name="v_colon1" units="L_per_s"/>
<variable name="v_colon2" units="L_per_s"/>
<variable initial_value="100" name="R_colon1" units="kPa_s_per_L"/>
<variable initial_value="2000" name="R_colon2" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_colon1</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_supMes</ci>
<ci>u_colon</ci>
</apply>
<ci>R_colon1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_colon2</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_colon</ci>
<ci>u_portalVein</ci>
</apply>
<ci>R_colon2</ci>
</apply>
</apply>
</math>
<!-- Portal vein-->
<variable initial_value="0.1" name="q_portalVein" units="litre"/>
<variable initial_value="0.06" name="q_portalVein_us" units="litre"/>
<variable name="u_portalVein" units="kPa"/>
<variable initial_value="50" name="E_portalVein" units="kPa_per_L"/>
<variable initial_value="0.20" name="z_portalVein" units="meter"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_portalVein</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>v_stomach2</ci>
<ci>v_spleen2</ci>
<ci>v_pancreas3</ci>
<ci>v_intestine2</ci>
<ci>v_colon2</ci>
</apply>
<ci>v_portalVein</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_portalVein</ci>
<apply>
<times/>
<ci>E_portalVein</ci>
<apply>
<minus/>
<ci>q_portalVein</ci>
<ci>q_portalVein_us</ci>
</apply>
</apply>
</apply>
</math>
<variable name="v_portalVein" units="L_per_s"/>
<variable initial_value="100" name="R_portalVein" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_portalVein</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_portalVein</ci>
<ci>u_liver</ci>
</apply>
<ci>R_portalVein</ci>
</apply>
</apply>
</math>
<!-- Liver-->
<variable initial_value="0.2" name="q_liver" units="litre"/>
<variable initial_value="0.06" name="q_liver_us" units="litre"/>
<variable name="u_liver" units="kPa"/>
<variable initial_value="10" name="E_liver" units="kPa_per_L"/>
<variable initial_value="-0.50" name="z_liver" units="meter"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_liver</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>v_liver1</ci>
<ci>v_portalVein</ci>
</apply>
<ci>v_liver2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_liver</ci>
<apply>
<times/>
<ci>E_liver</ci>
<apply>
<minus/>
<ci>q_liver</ci>
<ci>q_liver_us</ci>
</apply>
</apply>
</apply>
</math>
<variable name="v_liver1" units="L_per_s"/>
<variable name="v_liver2" units="L_per_s"/>
<variable initial_value="800" name="R_liver1" units="kPa_s_per_L"/>
<variable initial_value="1" name="R_liver2" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_liver1</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_celiac</ci>
<ci>u_liver</ci>
</apply>
<ci>R_liver1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_liver2</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_liver</ci>
<ci>u_RA</ci>
</apply>
<ci>R_liver2</ci>
</apply>
</apply>
</math>
<!-- Kidneys (left kidney in detail and right is assumed to be identical)-->
<!-- Left Renal artery-->
<variable name="v_lRenalA" units="L_per_s"/>
<variable name="v_rRenalA" units="L_per_s"/>
<variable initial_value="100" name="R_lRenalA" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_lRenalA</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_AA</ci>
<ci>u_lRenalA</ci>
</apply>
<ci>R_lRenalA</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_rRenalA</ci>
<ci>v_lRenalA</ci>
</apply>
</math>
<variable initial_value="0.3" name="q_lRenalA" units="litre"/>
<variable initial_value="0.2" name="q_lRenalA_us" units="litre"/>
<variable name="u_lRenalA" units="kPa"/>
<variable name="u_rRenalA" units="kPa"/>
<variable initial_value="200" name="E_lRenalA" units="kPa_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_lRenalA</ci>
</apply>
<apply>
<minus/>
<ci>v_lRenalA</ci>
<ci>v_lSegmentalA</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_lRenalA</ci>
<apply>
<times/>
<ci>E_lRenalA</ci>
<apply>
<minus/>
<ci>q_lRenalA</ci>
<ci>q_lRenalA_us</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_rRenalA</ci>
<ci>u_lRenalA</ci>
</apply>
</math>
<!-- Left Segmental artery-->
<variable name="v_lSegmentalA" units="L_per_s"/>
<variable initial_value="100" name="R_lSegmentalA" units="kPa_s_per_L"/>
<variable initial_value="7" name="n_lSegmentalA" units="dim"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_lSegmentalA</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_lRenalA</ci>
<ci>u_lSegmentalA</ci>
</apply>
<ci>R_lSegmentalA</ci>
</apply>
</apply>
</math>
<variable initial_value="0.3" name="q_lSegmentalA" units="litre"/>
<variable initial_value="0.2" name="q_lSegmentalA_us" units="litre"/>
<variable name="u_lSegmentalA" units="kPa"/>
<variable initial_value="200" name="E_lSegmentalA" units="kPa_per_L"/>
<variable initial_value="2" name="n_lInterlobarA" units="dim"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_lSegmentalA</ci>
</apply>
<apply>
<minus/>
<ci>v_lSegmentalA</ci>
<apply>
<times/>
<ci>n_lInterlobarA</ci>
<ci>v_lInterlobarA</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_lSegmentalA</ci>
<apply>
<times/>
<ci>E_lSegmentalA</ci>
<apply>
<minus/>
<ci>q_lSegmentalA</ci>
<ci>q_lSegmentalA_us</ci>
</apply>
</apply>
</apply>
</math>
<!-- Left Interlobar & Arcuate arteries-->
<variable name="v_lInterlobarA" units="L_per_s"/>
<variable initial_value="10" name="R_lInterlobarA" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_lInterlobarA</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_lSegmentalA</ci>
<ci>u_lArcuateA</ci>
</apply>
<ci>R_lInterlobarA</ci>
</apply>
</apply>
</math>
<variable initial_value="0.3" name="q_lArcuateA" units="litre"/>
<variable initial_value="0.2" name="q_lArcuateA_us" units="litre"/>
<variable name="u_lArcuateA" units="kPa"/>
<variable initial_value="200" name="E_lArcuateA" units="kPa_per_L"/>
<variable initial_value="2" name="n_lArcuateA" units="dim"/>
<variable initial_value="2" name="n_lInterlobularA" units="dim"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_lArcuateA</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>n_lArcuateA</ci>
<ci>v_lInterlobarA</ci>
</apply>
<apply>
<times/>
<ci>n_lInterlobularA</ci>
<ci>v_lInterlobularA</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_lArcuateA</ci>
<apply>
<times/>
<ci>E_lArcuateA</ci>
<apply>
<minus/>
<ci>q_lArcuateA</ci>
<ci>q_lArcuateA_us</ci>
</apply>
</apply>
</apply>
</math>
<!-- Left Interlobular artery-->
<variable name="v_lInterlobularA" units="L_per_s"/>
<variable initial_value="10" name="R_lInterlobularA" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_lInterlobularA</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_lArcuateA</ci>
<ci>u_lInterlobularA</ci>
</apply>
<ci>R_lInterlobularA</ci>
</apply>
</apply>
</math>
<variable initial_value="0.3" name="q_lInterlobularA" units="litre"/>
<variable initial_value="0.2" name="q_lInterlobularA_us" units="litre"/>
<variable name="u_lInterlobularA" units="kPa"/>
<variable initial_value="200" name="E_lInterlobularA" units="kPa_per_L"/>
<variable initial_value="2000" name="n_lAfferentA" units="dim"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_lInterlobularA</ci>
</apply>
<apply>
<minus/>
<ci>v_lInterlobularA</ci>
<apply>
<times/>
<ci>n_lAfferentA</ci>
<ci>v_lAfferentA</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_lInterlobularA</ci>
<apply>
<times/>
<ci>E_lInterlobularA</ci>
<apply>
<minus/>
<ci>q_lInterlobularA</ci>
<ci>q_lInterlobularA_us</ci>
</apply>
</apply>
</apply>
</math>
<!-- Left Afferent, Glomerulus -->
<variable name="v_lAfferentA" units="L_per_s"/>
<variable initial_value="10" name="R_lAfferentA" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_lAfferentA</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_lInterlobularA</ci>
<ci>u_lGlomerulus</ci>
</apply>
<ci>R_lAfferentA</ci>
</apply>
</apply>
</math>
<variable initial_value="0.1" name="q_lGlomerulus" units="litre"/>
<variable initial_value="0.1" name="q_lGlomerulus_us" units="litre"/>
<variable name="u_lGlomerulus" units="kPa"/>
<variable initial_value="200" name="E_lGlomerulus" units="kPa_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_lGlomerulus</ci>
</apply>
<apply>
<minus/>
<ci>v_lAfferentA</ci>
<ci>v_lPeritubularA</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_lGlomerulus</ci>
<apply>
<times/>
<ci>E_lGlomerulus</ci>
<apply>
<minus/>
<ci>q_lGlomerulus</ci>
<ci>q_lGlomerulus_us</ci>
</apply>
</apply>
</apply>
</math>
<!-- Left Peritubular artery-->
<variable name="v_lPeritubularA" units="L_per_s"/>
<variable initial_value="10" name="R_lPeritubularA" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_lPeritubularA</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_lGlomerulus</ci>
<ci>u_lPeritubularA</ci>
</apply>
<ci>R_lPeritubularA</ci>
</apply>
</apply>
</math>
<variable initial_value="0.1" name="q_lPeritubularA" units="litre"/>
<variable initial_value="0.1" name="q_lPeritubularA_us" units="litre"/>
<variable name="u_lPeritubularA" units="kPa"/>
<variable initial_value="200" name="E_lPeritubularA" units="kPa_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_lPeritubularA</ci>
</apply>
<apply>
<minus/>
<ci>v_lPeritubularA</ci>
<ci>v_lInterlobularA</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_lPeritubularA</ci>
<apply>
<times/>
<ci>E_lPeritubularA</ci>
<apply>
<minus/>
<ci>q_lPeritubularA</ci>
<ci>q_lPeritubularA_us</ci>
</apply>
</apply>
</apply>
</math>
<!-- Left Interlobular vein-->
<variable name="v_lInterlobularV" units="L_per_s"/>
<variable initial_value="10" name="R_lInterlobularV" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_lInterlobularV</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_lPeritubularA</ci>
<ci>u_lArcuateV</ci>
</apply>
<ci>R_lInterlobularV</ci>
</apply>
</apply>
</math>
<!-- Left Arcuate vein-->
<variable name="v_lArcuateV" units="L_per_s"/>
<variable initial_value="10" name="R_lArcuateV" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_lArcuateV</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_lArcuateV</ci>
<ci>u_lInterlobarV</ci>
</apply>
<ci>R_lArcuateV</ci>
</apply>
</apply>
</math>
<variable initial_value="0.1" name="q_lArcuateV" units="litre"/>
<variable initial_value="0.1" name="q_lArcuateV_us" units="litre"/>
<variable name="u_lArcuateV" units="kPa"/>
<variable initial_value="200" name="E_lArcuateV" units="kPa_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_lArcuateV</ci>
</apply>
<apply>
<minus/>
<ci>v_lInterlobularV</ci>
<ci>v_lArcuateV</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_lArcuateV</ci>
<apply>
<times/>
<ci>E_lArcuateV</ci>
<apply>
<minus/>
<ci>q_lArcuateV</ci>
<ci>q_lArcuateV_us</ci>
</apply>
</apply>
</apply>
</math>
<!-- Left Interlobar vein-->
<variable name="v_lInterlobarV" units="L_per_s"/>
<variable initial_value="10" name="R_lInterlobarV" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_lInterlobarV</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_lInterlobarV</ci>
<ci>u_lInfTrunkV</ci>
</apply>
<ci>R_lInterlobarV</ci>
</apply>
</apply>
</math>
<variable initial_value="0.1" name="q_lInterlobarV" units="litre"/>
<variable initial_value="0.1" name="q_lInterlobarV_us" units="litre"/>
<variable name="u_lInterlobarV" units="kPa"/>
<variable initial_value="200" name="E_lInterlobarV" units="kPa_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_lInterlobarV</ci>
</apply>
<apply>
<minus/>
<ci>v_lArcuateV</ci>
<ci>v_lInterlobularV</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_lInterlobarV</ci>
<apply>
<times/>
<ci>E_lInterlobarV</ci>
<apply>
<minus/>
<ci>q_lInterlobarV</ci>
<ci>q_lInterlobarV_us</ci>
</apply>
</apply>
</apply>
</math>
<!-- Left Inferior trunk vein-->
<variable name="v_lInfTrunkV" units="L_per_s"/>
<variable initial_value="10" name="R_lInfTrunkV" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_lInfTrunkV</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_lInfTrunkV</ci>
<ci>u_lRenalV</ci>
</apply>
<ci>R_lInfTrunkV</ci>
</apply>
</apply>
</math>
<variable initial_value="0.1" name="q_lInfTrunkV" units="litre"/>
<variable initial_value="0.1" name="q_lInfTrunkV_us" units="litre"/>
<variable name="u_lInfTrunkV" units="kPa"/>
<variable initial_value="200" name="E_lInfTrunkV" units="kPa_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_lInfTrunkV</ci>
</apply>
<apply>
<minus/>
<ci>v_lInterlobarV</ci>
<ci>v_lInfTrunkV</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_lInfTrunkV</ci>
<apply>
<times/>
<ci>E_lInfTrunkV</ci>
<apply>
<minus/>
<ci>q_lInfTrunkV</ci>
<ci>q_lInfTrunkV_us</ci>
</apply>
</apply>
</apply>
</math>
<!-- Left Renal vein -->
<variable name="v_lRenalV" units="L_per_s"/>
<variable name="v_rRenalV" units="L_per_s"/>
<variable initial_value="100" name="R_lRenalV" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_lRenalV</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_lRenalV</ci>
<ci>u_RA</ci>
</apply>
<ci>R_lRenalV</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_rRenalV</ci>
<ci>v_lRenalV</ci>
</apply>
</math>
<variable initial_value="0.3" name="q_lRenalV" units="litre"/>
<variable initial_value="0.2" name="q_lRenalV_us" units="litre"/>
<variable name="u_lRenalV" units="kPa"/>
<variable name="u_rRenalV" units="kPa"/>
<variable initial_value="200" name="E_lRenalV" units="kPa_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_lRenalV</ci>
</apply>
<apply>
<minus/>
<ci>v_lInfTrunkV</ci>
<ci>v_lRenalV</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_lRenalV</ci>
<apply>
<times/>
<ci>E_lRenalV</ci>
<apply>
<minus/>
<ci>q_lRenalV</ci>
<ci>q_lRenalV_us</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_rRenalV</ci>
<ci>u_lRenalV</ci>
</apply>
</math>
<!-- Muscle in torso-->
<variable initial_value="0.2" name="q_musTorso" units="litre"/>
<variable initial_value="0.2" name="q_musTorsoVein" units="litre"/>
<variable initial_value="0.12" name="q_musTorso_us" units="litre"/>
<variable initial_value="0.12" name="q_musTorsoVein_us" units="litre"/>
<variable name="u_musTorso" units="kPa"/>
<variable name="u_musTorsoVein" units="kPa"/>
<variable initial_value="60" name="E_musTorso" units="kPa_per_L"/>
<variable initial_value="10" name="E_musTorsoVein" units="kPa_per_L"/>
<variable initial_value="-0.50" name="z_musTorso" units="meter"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_musTorso</ci>
</apply>
<apply>
<minus/>
<ci>v_musTorso1</ci>
<ci>v_musTorso2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_musTorso</ci>
<apply>
<times/>
<ci>E_musTorso</ci>
<apply>
<minus/>
<ci>q_musTorso</ci>
<ci>q_musTorso_us</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_musTorsoVein</ci>
</apply>
<apply>
<minus/>
<ci>v_musTorso2</ci>
<ci>v_musTorso3</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_musTorsoVein</ci>
<apply>
<times/>
<ci>E_musTorsoVein</ci>
<apply>
<minus/>
<ci>q_musTorsoVein</ci>
<ci>q_musTorsoVein_us</ci>
</apply>
</apply>
</apply>
</math>
<variable name="v_musTorso1" units="L_per_s"/>
<variable name="v_musTorso2" units="L_per_s"/>
<variable name="v_musTorso3" units="L_per_s"/>
<variable initial_value="100" name="R_musTorso1" units="kPa_s_per_L"/>
<variable initial_value="1000" name="R_musTorso2" units="kPa_s_per_L"/>
<variable initial_value="1" name="R_musTorso3" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_musTorso1</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_AA</ci>
<ci>u_musTorso</ci>
</apply>
<ci>R_musTorso1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_musTorso2</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_musTorso</ci>
<ci>u_musTorsoVein</ci>
</apply>
<ci>R_musTorso2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_musTorso3</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_musTorsoVein</ci>
<ci>u_RA</ci>
</apply>
<ci>R_musTorso3</ci>
</apply>
</apply>
</math>
<!-- Left arm-->
<variable initial_value="0.1" name="q_lArm" units="litre"/>
<variable initial_value="0.1" name="q_lArmVein" units="litre"/>
<variable initial_value="0.06" name="q_lArm_us" units="litre"/>
<variable initial_value="0.06" name="q_lArmVein_us" units="litre"/>
<variable name="u_lArm" units="kPa"/>
<variable name="u_lArmVein" units="kPa"/>
<variable initial_value="150" name="E_lArm" units="kPa_per_L"/>
<variable initial_value="60" name="E_lArmVein" units="kPa_per_L"/>
<variable initial_value="-0.50" name="z_lArm" units="meter"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_lArm</ci>
</apply>
<apply>
<minus/>
<ci>v_lArm1</ci>
<ci>v_lArm2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_lArm</ci>
<apply>
<times/>
<ci>E_lArm</ci>
<apply>
<minus/>
<ci>q_lArm</ci>
<ci>q_lArm_us</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_lArmVein</ci>
</apply>
<apply>
<minus/>
<ci>v_lArm2</ci>
<ci>v_lArm3</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_lArmVein</ci>
<apply>
<times/>
<ci>E_lArmVein</ci>
<apply>
<minus/>
<ci>q_lArmVein</ci>
<ci>q_lArmVein_us</ci>
</apply>
</apply>
</apply>
</math>
<variable name="v_lArm1" units="L_per_s"/>
<variable name="v_lArm2" units="L_per_s"/>
<variable name="v_lArm3" units="L_per_s"/>
<variable initial_value="100" name="R_lArm1" units="kPa_s_per_L"/>
<variable initial_value="6000" name="R_lArm2" units="kPa_s_per_L"/>
<variable initial_value="1" name="R_lArm3" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_lArm1</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_AA</ci>
<ci>u_lArm</ci>
</apply>
<ci>R_lArm1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_lArm2</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_lArm</ci>
<ci>u_lArmVein</ci>
</apply>
<ci>R_lArm2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_lArm3</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_lArmVein</ci>
<ci>u_RA</ci>
</apply>
<ci>R_lArm3</ci>
</apply>
</apply>
</math>
<!-- Right arm-->
<variable initial_value="0.1" name="q_rArm" units="litre"/>
<variable initial_value="0.1" name="q_rArmVein" units="litre"/>
<variable initial_value="0.06" name="q_rArm_us" units="litre"/>
<variable initial_value="0.06" name="q_rArmVein_us" units="litre"/>
<variable name="u_rArm" units="kPa"/>
<variable name="u_rArmVein" units="kPa"/>
<variable initial_value="150" name="E_rArm" units="kPa_per_L"/>
<variable initial_value="60" name="E_rArmVein" units="kPa_per_L"/>
<variable initial_value="-0.50" name="z_rArm" units="meter"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_rArm</ci>
</apply>
<apply>
<minus/>
<ci>v_rArm1</ci>
<ci>v_rArm2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_rArm</ci>
<apply>
<times/>
<ci>E_rArm</ci>
<apply>
<minus/>
<ci>q_rArm</ci>
<ci>q_rArm_us</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_rArmVein</ci>
</apply>
<apply>
<minus/>
<ci>v_rArm2</ci>
<ci>v_rArm3</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_rArmVein</ci>
<apply>
<times/>
<ci>E_rArmVein</ci>
<apply>
<minus/>
<ci>q_rArmVein</ci>
<ci>q_rArm_us</ci>
</apply>
</apply>
</apply>
</math>
<variable name="v_rArm1" units="L_per_s"/>
<variable name="v_rArm2" units="L_per_s"/>
<variable name="v_rArm3" units="L_per_s"/>
<variable initial_value="100" name="R_rArm1" units="kPa_s_per_L"/>
<variable initial_value="6000" name="R_rArm2" units="kPa_s_per_L"/>
<variable initial_value="1" name="R_rArm3" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_rArm1</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_AA</ci>
<ci>u_rArm</ci>
</apply>
<ci>R_rArm1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_rArm2</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_rArm</ci>
<ci>u_rArmVein</ci>
</apply>
<ci>R_rArm2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_rArm3</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_rArmVein</ci>
<ci>u_RA</ci>
</apply>
<ci>R_rArm3</ci>
</apply>
</apply>
</math>
<!-- Left leg-->
<variable initial_value="0.1" name="q_lLeg" units="litre"/>
<variable initial_value="0.1" name="q_lLegVein" units="litre"/>
<variable initial_value="0.06" name="q_lLeg_us" units="litre"/>
<variable initial_value="0.06" name="q_lLegVein_us" units="litre"/>
<variable name="u_lLeg" units="kPa"/>
<variable name="u_lLegVein" units="kPa"/>
<variable initial_value="150" name="E_lLeg" units="kPa_per_L"/>
<variable initial_value="60" name="E_lLegVein" units="kPa_per_L"/>
<variable initial_value="-0.50" name="z_lLeg" units="meter"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_lLeg</ci>
</apply>
<apply>
<minus/>
<ci>v_lLeg1</ci>
<ci>v_lLeg2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_lLeg</ci>
<apply>
<times/>
<ci>E_lLeg</ci>
<apply>
<minus/>
<ci>q_lLeg</ci>
<ci>q_lLeg_us</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_lLegVein</ci>
</apply>
<apply>
<minus/>
<ci>v_lLeg2</ci>
<ci>v_lLeg3</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_lLegVein</ci>
<apply>
<times/>
<ci>E_lLegVein</ci>
<apply>
<minus/>
<ci>q_lLegVein</ci>
<ci>q_lLeg_us</ci>
</apply>
</apply>
</apply>
</math>
<variable name="v_lLeg1" units="L_per_s"/>
<variable name="v_lLeg2" units="L_per_s"/>
<variable name="v_lLeg3" units="L_per_s"/>
<variable initial_value="100" name="R_lLeg1" units="kPa_s_per_L"/>
<variable initial_value="4000" name="R_lLeg2" units="kPa_s_per_L"/>
<variable initial_value="1" name="R_lLeg3" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_lLeg1</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_AA</ci>
<ci>u_lLeg</ci>
</apply>
<ci>R_lLeg1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_lLeg2</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_lLeg</ci>
<ci>u_lLegVein</ci>
</apply>
<ci>R_lLeg2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_lLeg3</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_lLegVein</ci>
<ci>u_RA</ci>
</apply>
<ci>R_lLeg3</ci>
</apply>
</apply>
</math>
<!-- Right leg-->
<variable initial_value="0.1" name="q_rLeg" units="litre"/>
<variable initial_value="0.1" name="q_rLegVein" units="litre"/>
<variable initial_value="0.06" name="q_rLeg_us" units="litre"/>
<variable initial_value="0.06" name="q_rLegVein_us" units="litre"/>
<variable name="u_rLeg" units="kPa"/>
<variable name="u_rLegVein" units="kPa"/>
<variable initial_value="150" name="E_rLeg" units="kPa_per_L"/>
<variable initial_value="60" name="E_rLegVein" units="kPa_per_L"/>
<variable initial_value="-0.50" name="z_rLeg" units="meter"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_rLeg</ci>
</apply>
<apply>
<minus/>
<ci>v_rLeg1</ci>
<ci>v_rLeg2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_rLeg</ci>
<apply>
<times/>
<ci>E_rLeg</ci>
<apply>
<minus/>
<ci>q_rLeg</ci>
<ci>q_rLeg_us</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_rLegVein</ci>
</apply>
<apply>
<minus/>
<ci>v_rLeg2</ci>
<ci>v_rLeg3</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_rLegVein</ci>
<apply>
<times/>
<ci>E_rLegVein</ci>
<apply>
<minus/>
<ci>q_rLegVein</ci>
<ci>q_rLeg_us</ci>
</apply>
</apply>
</apply>
</math>
<variable name="v_rLeg1" units="L_per_s"/>
<variable name="v_rLeg2" units="L_per_s"/>
<variable name="v_rLeg3" units="L_per_s"/>
<variable initial_value="100" name="R_rLeg1" units="kPa_s_per_L"/>
<variable initial_value="4000" name="R_rLeg2" units="kPa_s_per_L"/>
<variable initial_value="1" name="R_rLeg3" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_rLeg1</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_AA</ci>
<ci>u_rLeg</ci>
</apply>
<ci>R_rLeg1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_rLeg2</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_rLeg</ci>
<ci>u_rLegVein</ci>
</apply>
<ci>R_rLeg2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_rLeg3</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_rLegVein</ci>
<ci>u_RA</ci>
</apply>
<ci>R_rLeg3</ci>
</apply>
</apply>
</math>
<!-- Total volumes of blood in torso, brain, limbs and combination-->
<variable name="q_heartTot" units="litre"/>
<variable name="q_lungTot" units="litre"/>
<variable name="q_renalTot" units="litre"/>
<variable name="q_gutTot" units="litre"/>
<variable name="q_brainTot" units="litre"/>
<variable name="q_limbTot" units="litre"/>
<variable name="q_Blood" units="litre"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>q_heartTot</ci>
<apply>
<plus/>
<ci>q_LV</ci>
<ci>q_RV</ci>
<ci>q_LA</ci>
<ci>q_RA</ci>
<ci>q_AA</ci>
<ci>q_PulmA</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_lungTot</ci>
<apply>
<plus/>
<ci>q_lULobeC</ci>
<ci>q_lLungInterlobarA</ci>
<ci>q_lLLobeA</ci>
<ci>q_rULobeC</ci>
<ci>q_rInterlobarA</ci>
<ci>q_rLLobeA</ci>
<ci>q_PulmV</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_renalTot</ci>
<apply>
<times/>
<cn cellml:units="dim">2</cn>
<apply>
<plus/>
<ci>q_lGlomerulus</ci>
<ci>q_lPeritubularA</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>q_gutTot</ci>
<apply>
<plus/>
<ci>q_celiac</ci>
<ci>q_supMes</ci>
<ci>q_stomach</ci>
<ci>q_spleen</ci>
<ci>q_pancreas</ci>
<ci>q_intestine</ci>
<ci>q_colon</ci>
<ci>q_portalVein</ci>
<ci>q_liver</ci>
<ci>q_musTorso</ci>
<ci>q_musTorsoVein</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_brainTot</ci>
<apply>
<plus/>
<ci>q_brain</ci>
<ci>q_brainVein</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_limbTot</ci>
<apply>
<plus/>
<ci>q_lArm</ci>
<ci>q_lArmVein</ci>
<ci>q_rArm</ci>
<ci>q_rArmVein</ci>
<ci>q_lLeg</ci>
<ci>q_lLegVein</ci>
<ci>q_rLeg</ci>
<ci>q_rLegVein</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_Blood</ci>
<apply>
<plus/>
<ci>q_heartTot</ci>
<ci>q_lungTot</ci>
<ci>q_renalTot</ci>
<ci>q_gutTot</ci>
<ci>q_brainTot</ci>
<ci>q_limbTot</ci>
</apply>
</apply>
</math>
<!-- Glucose transport (GLUT2 only) in the proximal convoluted tubule of the kidney nephron-->
<variable initial_value="10" name="q_Glc_o" units="fmol"/>
<variable initial_value="5" name="q_Glc_i" units="fmol"/>
<variable name="Q_Glc_o" units="dim"/>
<variable name="Q_Glc_i" units="dim"/>
<variable initial_value="3.2e-3" name="K_Glc" units="per_fmol"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Q_Glc_o</ci>
<apply>
<times/>
<ci>K_Glc</ci>
<ci>q_Glc_o</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_Glc_i</ci>
<apply>
<times/>
<ci>K_Glc</ci>
<ci>q_Glc_i</ci>
</apply>
</apply>
</math>
<variable name="a_1" units="fmol"/>
<variable name="a_2" units="fmol"/>
<variable name="a_3" units="fmol"/>
<variable name="a_4" units="fmol"/>
<variable initial_value="1" name="K_1" units="per_fmol"/>
<variable initial_value="1" name="K_2" units="per_fmol"/>
<variable initial_value="1" name="K_3" units="per_fmol"/>
<variable initial_value="1" name="K_4" units="per_fmol"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>a_1</ci>
<apply>
<divide/>
<cn cellml:units="dim">1</cn>
<ci>K_1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>a_2</ci>
<apply>
<divide/>
<cn cellml:units="dim">1</cn>
<ci>K_2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>a_3</ci>
<apply>
<divide/>
<cn cellml:units="dim">1</cn>
<ci>K_3</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>a_4</ci>
<apply>
<divide/>
<cn cellml:units="dim">1</cn>
<ci>K_4</ci>
</apply>
</apply>
</math>
<variable initial_value="1" name="kappa_2" units="fmol_per_s"/>
<variable initial_value="2" name="kappa_4" units="fmol_per_s"/>
<variable name="gamma" units="dim"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>gamma</ci>
<apply>
<divide/>
<ci>kappa_2</ci>
<ci>kappa_4</ci>
</apply>
</apply>
</math>
<variable name="km_1" units="dim"/>
<variable name="km_2" units="dim"/>
<variable name="km_3" units="dim"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>km_1</ci>
<apply>
<divide/>
<apply>
<plus/>
<ci>a_1</ci>
<ci>a_4</ci>
</apply>
<apply>
<plus/>
<ci>a_2</ci>
<apply>
<times/>
<ci>gamma</ci>
<ci>a_4</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>km_2</ci>
<apply>
<divide/>
<apply>
<plus/>
<ci>a_1</ci>
<ci>a_4</ci>
</apply>
<apply>
<plus/>
<ci>a_3</ci>
<apply>
<times/>
<ci>gamma</ci>
<ci>a_1</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>km_3</ci>
<apply>
<divide/>
<apply>
<plus/>
<ci>a_1</ci>
<ci>a_4</ci>
</apply>
<apply>
<times/>
<ci>gamma</ci>
<apply>
<plus/>
<ci>a_2</ci>
<ci>a_3</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<variable initial_value="1" name="q_tot" units="fmol"/>
<variable name="v_GLUT2_max" units="fmol_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_GLUT2_max</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>q_tot</ci>
<ci>kappa_2</ci>
</apply>
<apply>
<plus/>
<ci>a_1</ci>
<ci>a_4</ci>
</apply>
</apply>
</apply>
</math>
<variable name="v_GLUT2" units="fmol_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_GLUT2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>v_GLUT2_max</ci>
<apply>
<minus/>
<ci>Q_Glc_o</ci>
<ci>Q_Glc_i</ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<divide/>
<ci>Q_Glc_o</ci>
<ci>km_1</ci>
</apply>
<apply>
<divide/>
<ci>Q_Glc_i</ci>
<ci>km_2</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>Q_Glc_o</ci>
<ci>Q_Glc_i</ci>
</apply>
<ci>km_3</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
</model>