Location: Cardiovascular systems model @ d67c241f2dd0 / cvs-model.cellml
- Author:
- David Nickerson <david.nickerson@gmail.com>
- Date:
- 2024-11-27 15:27:29+13:00
- Desc:
- adding latest CVS BG models from Peter Hunter.
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/c3d/rawfile/d67c241f2dd0e4e667bcc390b21ccd3191a7279d/cvs-model.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 liver, stomach, spleen, pancreas, intestines, colon, brain, limbs and muscle in torso-->
<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>
<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_B_LV" units="kPa_per_L"/>
<variable initial_value="3" name="E_B_LVmax" units="kPa_per_L"/>
<variable initial_value="2" name="q_B_LV" units="litre"/>
<variable name="u_B_LV" units="kPa"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>E_B_LV</ci>
<piecewise>
<piece>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>E_B_LVmax</ci>
<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>
<apply>
<lt/>
<ci>mt</ci>
<cn cellml:units="dim">0.4</cn>
</apply>
</piece>
<piece>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>E_B_LVmax</ci>
<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>
<apply>
<lt/>
<ci>mt</ci>
<cn cellml:units="dim">0.6</cn>
</apply>
</piece>
<otherwise>
<cn cellml:units="kPa_per_L">0</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_B_LV</ci>
</apply>
<apply>
<minus/>
<ci>v_B_MV</ci>
<ci>v_B_AV</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_LV</ci>
<apply>
<times/>
<ci>E_B_LV</ci>
<ci>q_B_LV</ci>
</apply>
</apply>
</math>
<!--Right ventricle-->
<variable name="E_B_RV" units="kPa_per_L"/>
<variable initial_value="2" name="E_B_RVmax" units="kPa_per_L"/>
<variable initial_value="2" name="q_B_RV" units="litre"/>
<variable name="u_B_RV" units="kPa"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>E_B_RV</ci>
<piecewise>
<piece>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>E_B_RVmax</ci>
<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>
<apply>
<lt/>
<ci>mt</ci>
<cn cellml:units="dim">0.4</cn>
</apply>
</piece>
<piece>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>E_B_RVmax</ci>
<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>
<apply>
<lt/>
<ci>mt</ci>
<cn cellml:units="dim">0.6</cn>
</apply>
</piece>
<otherwise>
<cn cellml:units="kPa_per_L">0</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_B_RV</ci>
</apply>
<apply>
<minus/>
<ci>v_B_TV</ci>
<ci>v_B_PV</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_RV</ci>
<apply>
<times/>
<ci>E_B_RV</ci>
<ci>q_B_RV</ci>
</apply>
</apply>
</math>
<!-- Left atrium-->
<variable initial_value="10" name="E_B_LA" units="kPa_per_L"/>
<variable initial_value="0.02" name="q_B_LA" units="litre"/>
<variable name="u_B_LA" units="kPa"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_B_LA</ci>
</apply>
<apply>
<minus/>
<ci>v_B_pulmVein</ci>
<ci>v_B_MV</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_LA</ci>
<apply>
<times/>
<ci>E_B_LA</ci>
<ci>q_B_LA</ci>
</apply>
</apply>
</math>
<!-- Right atrium-->
<variable initial_value="10" name="E_B_RA" units="kPa_per_L"/>
<variable initial_value="0.02" name="q_B_RA" units="litre"/>
<variable name="u_B_RA" units="kPa"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_B_RA</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>v_B_brain3</ci>
<ci>v_B_liver2</ci>
<ci>v_B_lRenal3</ci>
<ci>v_B_rRenal3</ci>
<ci>v_B_musTorso3</ci>
<ci>v_B_lArm3</ci>
<ci>v_B_rArm3</ci>
<ci>v_B_lLeg3</ci>
<ci>v_B_rLeg3</ci>
</apply>
<ci>v_B_TV</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_RA</ci>
<apply>
<times/>
<ci>E_B_RA</ci>
<ci>q_B_RA</ci>
</apply>
</apply>
</math>
<!-- Aortic valve-->
<variable initial_value="1" name="R_B_AV" units="kPa_s_per_L"/>
<variable name="v_B_AV" units="L_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_B_AV</ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_LV</ci>
<ci>u_B_AA</ci>
</apply>
<ci>R_B_AV</ci>
</apply>
<apply>
<gt/>
<ci>u_B_LV</ci>
<ci>u_B_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_B_PV" units="kPa_s_per_L"/>
<variable name="v_B_PV" units="L_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_B_PV</ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_RV</ci>
<ci>u_B_PA</ci>
</apply>
<ci>R_B_PV</ci>
</apply>
<apply>
<gt/>
<ci>u_B_RV</ci>
<ci>u_B_PA</ci>
</apply>
</piece>
<otherwise>
<cn cellml:units="L_per_s">0</cn>
</otherwise>
</piecewise>
</apply>
</math>
<!-- Tricuspid Valve-->
<variable initial_value="1" name="R_B_TV" units="kPa_s_per_L"/>
<variable name="v_B_TV" units="L_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_B_TV</ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_RA</ci>
<ci>u_B_RV</ci>
</apply>
<ci>R_B_TV</ci>
</apply>
<apply>
<gt/>
<ci>u_B_RA</ci>
<ci>u_B_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_B_MV" units="kPa_s_per_L"/>
<variable name="v_B_MV" units="L_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_B_MV</ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_LA</ci>
<ci>u_B_LV</ci>
</apply>
<ci>R_B_MV</ci>
</apply>
<apply>
<gt/>
<ci>u_B_LA</ci>
<ci>u_B_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_B_PA" units="litre"/>
<variable name="u_B_PA" units="kPa"/>
<variable initial_value="10" name="E_B_PA" units="kPa_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_B_PA</ci>
</apply>
<apply>
<minus/>
<ci>v_B_PV</ci>
<ci>v_B_lung1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_PA</ci>
<apply>
<times/>
<ci>E_B_PA</ci>
<ci>q_B_PA</ci>
</apply>
</apply>
</math>
<!-- Lungs -->
<variable initial_value="0.2" name="q_B_lung" units="litre"/>
<variable name="u_B_lung" units="kPa"/>
<variable initial_value="20" name="E_B_lung" units="kPa_per_L"/>
<variable initial_value="0.20" name="z_lung" units="meter"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_B_lung</ci>
</apply>
<apply>
<minus/>
<ci>v_B_lung1</ci>
<ci>v_B_lung2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_lung</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>E_B_lung</ci>
<ci>q_B_lung</ci>
</apply>
<apply>
<times/>
<ci>rho</ci>
<ci>g</ci>
<ci>z_lung</ci>
<apply>
<cos/>
<ci>theta_rad</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<variable name="v_B_lung1" units="L_per_s"/>
<variable name="v_B_lung2" units="L_per_s"/>
<variable initial_value="50" name="R_B_lung1" units="kPa_s_per_L"/>
<variable initial_value="10" name="R_B_lung2" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_B_lung1</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_PA</ci>
<ci>u_B_lung</ci>
</apply>
<ci>R_B_lung1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_B_lung2</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_lung</ci>
<ci>u_B_pulmVein</ci>
</apply>
<ci>R_B_lung2</ci>
</apply>
</apply>
</math>
<!-- Pulmonary vein-->
<variable initial_value="10" name="E_B_pulmVein" units="kPa_per_L"/>
<variable initial_value="0.02" name="q_B_pulmVein" units="litre"/>
<variable name="u_B_pulmVein" units="kPa"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_B_pulmVein</ci>
</apply>
<apply>
<minus/>
<ci>v_B_lung2</ci>
<ci>v_B_pulmVein</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_pulmVein</ci>
<apply>
<times/>
<ci>E_B_pulmVein</ci>
<ci>q_B_pulmVein</ci>
</apply>
</apply>
</math>
<variable name="v_B_pulmVein" units="L_per_s"/>
<variable initial_value="1" name="R_B_pulmVein" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_B_pulmVein</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_pulmVein</ci>
<ci>u_B_LA</ci>
</apply>
<ci>R_B_pulmVein</ci>
</apply>
</apply>
</math>
<!-- Brain-->
<variable initial_value="0.5" name="q_B_brain" units="litre"/>
<variable initial_value="0.5" name="q_B_brainVein" units="litre"/>
<variable name="u_B_brain" units="kPa"/>
<variable name="u_B_brainVein" units="kPa"/>
<variable initial_value="20" name="E_B_brain" units="kPa_per_L"/>
<variable initial_value="20" name="E_B_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_B_brain</ci>
</apply>
<apply>
<minus/>
<ci>v_B_brain1</ci>
<ci>v_B_brain2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_brain</ci>
<apply>
<times/>
<ci>E_B_brain</ci>
<ci>q_B_brain</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_B_brainVein</ci>
</apply>
<apply>
<minus/>
<ci>v_B_brain2</ci>
<ci>v_B_brain3</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_brainVein</ci>
<apply>
<times/>
<ci>E_B_brainVein</ci>
<ci>q_B_brainVein</ci>
</apply>
</apply>
</math>
<variable name="v_B_brain1" units="L_per_s"/>
<variable name="v_B_brain2" units="L_per_s"/>
<variable name="v_B_brain3" units="L_per_s"/>
<variable initial_value="6000" name="R_B_brain1" units="kPa_s_per_L"/>
<variable initial_value="2000" name="R_B_brain2" units="kPa_s_per_L"/>
<variable initial_value="2000" name="R_B_brain3" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_B_brain1</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_AA</ci>
<ci>u_B_brain</ci>
</apply>
<ci>R_B_brain1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_B_brain2</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_brain</ci>
<ci>u_B_brainVein</ci>
</apply>
<ci>R_B_brain2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_B_brain3</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_brainVein</ci>
<ci>u_B_RA</ci>
</apply>
<ci>R_B_brain3</ci>
</apply>
</apply>
</math>
<!-- Ascending aorta-->
<variable initial_value="0.5" name="q_B_AA" units="litre"/>
<variable name="u_B_AA" units="kPa"/>
<variable initial_value="20" name="E_B_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_B_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_B_AV</ci>
<ci>v_B_brain1</ci>
</apply>
<ci>v_B_celiac</ci>
</apply>
<ci>v_B_supMes</ci>
</apply>
<ci>v_B_infMes</ci>
</apply>
<ci>v_B_lRenal1</ci>
</apply>
<ci>v_B_rRenal1</ci>
</apply>
<ci>v_B_musTorso1</ci>
</apply>
<ci>v_B_lArm1</ci>
</apply>
<ci>v_B_rArm1</ci>
</apply>
<ci>v_B_lLeg1</ci>
</apply>
<ci>v_B_rLeg1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_AA</ci>
<apply>
<times/>
<ci>E_B_AA</ci>
<ci>q_B_AA</ci>
</apply>
</apply>
</math>
<!-- Celiac branch of the aorta -->
<variable initial_value="0.2" name="q_B_celiac" units="litre"/>
<variable name="u_B_celiac" units="kPa"/>
<variable initial_value="20" name="E_B_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_B_celiac</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>v_B_celiac</ci>
<ci>v_B_liver1</ci>
</apply>
<ci>v_B_stomach1</ci>
</apply>
<ci>v_B_spleen1</ci>
</apply>
<ci>v_B_pancreas1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_celiac</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>E_B_celiac</ci>
<ci>q_B_celiac</ci>
</apply>
<apply>
<times/>
<ci>rho</ci>
<ci>g</ci>
<ci>z_celiac</ci>
<apply>
<cos/>
<ci>theta_rad</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<variable name="v_B_celiac" units="L_per_s"/>
<variable initial_value="6000" name="R_B_celiac" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_B_celiac</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_AA</ci>
<ci>u_B_celiac</ci>
</apply>
<ci>R_B_celiac</ci>
</apply>
</apply>
</math>
<!-- Superior mesentery branch of the aorta -->
<variable initial_value="0.2" name="q_B_supMes" units="litre"/>
<variable name="u_B_supMes" units="kPa"/>
<variable initial_value="20" name="E_B_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_B_supMes</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>v_B_supMes</ci>
<ci>v_B_pancreas2</ci>
</apply>
<ci>v_B_intestine1</ci>
</apply>
<ci>v_B_colon1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_supMes</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>E_B_supMes</ci>
<ci>q_B_supMes</ci>
</apply>
<apply>
<times/>
<ci>rho</ci>
<ci>g</ci>
<ci>z_supMes</ci>
<apply>
<cos/>
<ci>theta_rad</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<variable name="v_B_supMes" units="L_per_s"/>
<variable initial_value="6000" name="R_B_supMes" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_B_supMes</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_AA</ci>
<ci>u_B_supMes</ci>
</apply>
<ci>R_B_supMes</ci>
</apply>
</apply>
</math>
<!-- Inferior mesentery branch of the aorta -->
<variable name="v_B_infMes" units="L_per_s"/>
<variable initial_value="6000" name="R_B_infMes" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_B_infMes</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_AA</ci>
<ci>u_B_colon</ci>
</apply>
<ci>R_B_infMes</ci>
</apply>
</apply>
</math>
<!-- Stomach-->
<variable initial_value="0.2" name="q_B_stomach" units="litre"/>
<variable name="u_B_stomach" units="kPa"/>
<variable initial_value="20" name="E_B_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_B_stomach</ci>
</apply>
<apply>
<minus/>
<ci>v_B_stomach1</ci>
<ci>v_B_stomach2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_stomach</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>E_B_stomach</ci>
<ci>q_B_stomach</ci>
</apply>
<apply>
<times/>
<ci>rho</ci>
<ci>g</ci>
<ci>z_stomach</ci>
<apply>
<cos/>
<ci>theta_rad</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<variable name="v_B_stomach1" units="L_per_s"/>
<variable name="v_B_stomach2" units="L_per_s"/>
<variable initial_value="6000" name="R_B_stomach1" units="kPa_s_per_L"/>
<variable initial_value="2000" name="R_B_stomach2" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_B_stomach1</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_celiac</ci>
<ci>u_B_stomach</ci>
</apply>
<ci>R_B_stomach1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_B_stomach2</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_stomach</ci>
<ci>u_B_portalVein</ci>
</apply>
<ci>R_B_stomach2</ci>
</apply>
</apply>
</math>
<!-- Spleen-->
<variable initial_value="0.2" name="q_B_spleen" units="litre"/>
<variable name="u_B_spleen" units="kPa"/>
<variable initial_value="20" name="E_B_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_B_spleen</ci>
</apply>
<apply>
<minus/>
<ci>v_B_spleen1</ci>
<ci>v_B_spleen2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_spleen</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>E_B_colon</ci>
<ci>q_B_spleen</ci>
</apply>
<apply>
<times/>
<ci>rho</ci>
<ci>g</ci>
<ci>z_spleen</ci>
<apply>
<cos/>
<ci>theta_rad</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<variable name="v_B_spleen1" units="L_per_s"/>
<variable name="v_B_spleen2" units="L_per_s"/>
<variable initial_value="6000" name="R_B_spleen1" units="kPa_s_per_L"/>
<variable initial_value="2000" name="R_B_spleen2" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_B_spleen1</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_celiac</ci>
<ci>u_B_spleen</ci>
</apply>
<ci>R_B_spleen1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_B_spleen2</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_spleen</ci>
<ci>u_B_portalVein</ci>
</apply>
<ci>R_B_spleen2</ci>
</apply>
</apply>
</math>
<!-- Pancreas-->
<variable initial_value="0.2" name="q_B_pancreas" units="litre"/>
<variable name="u_B_pancreas" units="kPa"/>
<variable initial_value="20" name="E_B_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_B_pancreas</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>v_B_pancreas1</ci>
<ci>v_B_pancreas2</ci>
</apply>
<ci>v_B_pancreas3</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_pancreas</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>E_B_pancreas</ci>
<ci>q_B_pancreas</ci>
</apply>
<apply>
<times/>
<ci>rho</ci>
<ci>g</ci>
<ci>z_pancreas</ci>
<apply>
<cos/>
<ci>theta_rad</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<variable name="v_B_pancreas1" units="L_per_s"/>
<variable name="v_B_pancreas2" units="L_per_s"/>
<variable name="v_B_pancreas3" units="L_per_s"/>
<variable initial_value="6000" name="R_B_pancreas1" units="kPa_s_per_L"/>
<variable initial_value="6000" name="R_B_pancreas2" units="kPa_s_per_L"/>
<variable initial_value="2000" name="R_B_pancreas3" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_B_pancreas1</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_celiac</ci>
<ci>u_B_pancreas</ci>
</apply>
<ci>R_B_pancreas1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_B_pancreas2</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_supMes</ci>
<ci>u_B_pancreas</ci>
</apply>
<ci>R_B_pancreas1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_B_pancreas3</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_pancreas</ci>
<ci>u_B_portalVein</ci>
</apply>
<ci>R_B_pancreas2</ci>
</apply>
</apply>
</math>
<!-- Intestine-->
<variable initial_value="0.2" name="q_B_intestine" units="litre"/>
<variable name="u_B_intestine" units="kPa"/>
<variable initial_value="20" name="E_B_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_B_intestine</ci>
</apply>
<apply>
<minus/>
<ci>v_B_intestine1</ci>
<ci>v_B_intestine2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_intestine</ci>
<apply>
<times/>
<ci>E_B_intestine</ci>
<ci>q_B_intestine</ci>
</apply>
</apply>
</math>
<variable name="v_B_intestine1" units="L_per_s"/>
<variable name="v_B_intestine2" units="L_per_s"/>
<variable initial_value="6000" name="R_B_intestine1" units="kPa_s_per_L"/>
<variable initial_value="2000" name="R_B_intestine2" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_B_intestine1</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_supMes</ci>
<ci>u_B_intestine</ci>
</apply>
<ci>R_B_intestine1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_B_intestine2</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_intestine</ci>
<ci>u_B_portalVein</ci>
</apply>
<ci>R_B_intestine2</ci>
</apply>
</apply>
</math>
<!-- Colon-->
<variable initial_value="0.2" name="q_B_colon" units="litre"/>
<variable name="u_B_colon" units="kPa"/>
<variable initial_value="20" name="E_B_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_B_colon</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>v_B_colon1</ci>
<ci>v_B_infMes</ci>
</apply>
<ci>v_B_colon2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_colon</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>E_B_colon</ci>
<ci>q_B_colon</ci>
</apply>
<apply>
<times/>
<ci>rho</ci>
<ci>g</ci>
<ci>z_colon</ci>
<apply>
<cos/>
<ci>theta_rad</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<variable name="v_B_colon1" units="L_per_s"/>
<variable name="v_B_colon2" units="L_per_s"/>
<variable initial_value="6000" name="R_B_colon1" units="kPa_s_per_L"/>
<variable initial_value="2000" name="R_B_colon2" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_B_colon1</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_supMes</ci>
<ci>u_B_colon</ci>
</apply>
<ci>R_B_colon1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_B_colon2</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_colon</ci>
<ci>u_B_portalVein</ci>
</apply>
<ci>R_B_colon2</ci>
</apply>
</apply>
</math>
<!-- Portal vein-->
<variable initial_value="0.2" name="q_B_portalVein" units="litre"/>
<variable name="u_B_portalVein" units="kPa"/>
<variable initial_value="20" name="E_B_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_B_portalVein</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>v_B_stomach2</ci>
<ci>v_B_spleen2</ci>
<ci>v_B_pancreas3</ci>
<ci>v_B_intestine2</ci>
<ci>v_B_colon2</ci>
</apply>
<ci>v_B_portalVein</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_portalVein</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>E_B_portalVein</ci>
<ci>q_B_portalVein</ci>
</apply>
<apply>
<times/>
<ci>rho</ci>
<ci>g</ci>
<ci>z_portalVein</ci>
<apply>
<cos/>
<ci>theta_rad</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<variable name="v_B_portalVein" units="L_per_s"/>
<variable initial_value="6000" name="R_B_portalVein" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_B_portalVein</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_portalVein</ci>
<ci>u_B_liver</ci>
</apply>
<ci>R_B_portalVein</ci>
</apply>
</apply>
</math>
<!-- Liver-->
<variable initial_value="0.3" name="q_B_liver" units="litre"/>
<variable name="u_B_liver" units="kPa"/>
<variable initial_value="10" name="E_B_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_B_liver</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>v_B_liver1</ci>
<ci>v_B_portalVein</ci>
</apply>
<ci>v_B_liver2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_liver</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>E_B_liver</ci>
<ci>q_B_liver</ci>
</apply>
<apply>
<times/>
<ci>rho</ci>
<ci>g</ci>
<ci>z_liver</ci>
<apply>
<cos/>
<ci>theta_rad</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<variable name="v_B_liver1" units="L_per_s"/>
<variable name="v_B_liver2" units="L_per_s"/>
<variable initial_value="6000" name="R_B_liver1" units="kPa_s_per_L"/>
<variable initial_value="2000" name="R_B_liver2" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_B_liver1</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_celiac</ci>
<ci>u_B_liver</ci>
</apply>
<ci>R_B_liver1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_B_liver2</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_liver</ci>
<ci>u_B_RA</ci>
</apply>
<ci>R_B_liver2</ci>
</apply>
</apply>
</math>
<!-- Kidneys. Renal 1 -> Glomerular bed (gCap) -> Renal 2 -> Peritubular bed (pCap) -> Renal 3-->
<variable initial_value="0.1" name="q_B_lGlomerulus" units="litre"/>
<variable initial_value="0.1" name="q_B_rGlomerulus" units="litre"/>
<variable initial_value="0.1" name="q_B_lPeritubular" units="litre"/>
<variable initial_value="0.1" name="q_B_rPeritubular" units="litre"/>
<variable name="u_B_lGlomerulus" units="kPa"/>
<variable name="u_B_rGlomerulus" units="kPa"/>
<variable name="u_B_lPeritubular" units="kPa"/>
<variable name="u_B_rPeritubular" units="kPa"/>
<variable initial_value="20" name="E_B_lGlomerulus" units="kPa_per_L"/>
<variable initial_value="20" name="E_B_rGlomerulus" units="kPa_per_L"/>
<variable initial_value="20" name="E_B_lPeritubular" units="kPa_per_L"/>
<variable initial_value="20" name="E_B_rPeritubular" units="kPa_per_L"/>
<variable initial_value="-0.25" name="z_kidney" units="meter"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_B_lGlomerulus</ci>
</apply>
<apply>
<minus/>
<ci>v_B_lRenal1</ci>
<ci>v_B_lRenal2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_B_rGlomerulus</ci>
</apply>
<apply>
<minus/>
<ci>v_B_lRenal1</ci>
<ci>v_B_lRenal2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_B_lPeritubular</ci>
</apply>
<apply>
<minus/>
<ci>v_B_lRenal2</ci>
<ci>v_B_lRenal3</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_B_rPeritubular</ci>
</apply>
<apply>
<minus/>
<ci>v_B_lRenal2</ci>
<ci>v_B_lRenal3</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_lGlomerulus</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>E_B_lGlomerulus</ci>
<ci>q_B_lGlomerulus</ci>
</apply>
<apply>
<times/>
<ci>rho</ci>
<ci>g</ci>
<ci>z_kidney</ci>
<apply>
<cos/>
<ci>theta_rad</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_rGlomerulus</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>E_B_rGlomerulus</ci>
<ci>q_B_rGlomerulus</ci>
</apply>
<apply>
<times/>
<ci>rho</ci>
<ci>g</ci>
<ci>z_kidney</ci>
<apply>
<cos/>
<ci>theta_rad</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_lPeritubular</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>E_B_lPeritubular</ci>
<ci>q_B_lPeritubular</ci>
</apply>
<apply>
<times/>
<ci>rho</ci>
<ci>g</ci>
<ci>z_kidney</ci>
<apply>
<cos/>
<ci>theta_rad</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_rPeritubular</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>E_B_rPeritubular</ci>
<ci>q_B_rPeritubular</ci>
</apply>
<apply>
<times/>
<ci>rho</ci>
<ci>g</ci>
<ci>z_kidney</ci>
<apply>
<cos/>
<ci>theta_rad</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<variable name="v_B_lRenal1" units="L_per_s"/>
<variable name="v_B_rRenal1" units="L_per_s"/>
<variable name="v_B_lRenal2" units="L_per_s"/>
<variable name="v_B_rRenal2" units="L_per_s"/>
<variable name="v_B_lRenal3" units="L_per_s"/>
<variable name="v_B_rRenal3" units="L_per_s"/>
<variable initial_value="6000" name="R_B_lRenal1" units="kPa_s_per_L"/>
<variable initial_value="6000" name="R_B_rRenal1" units="kPa_s_per_L"/>
<variable initial_value="1000" name="R_B_lRenal2" units="kPa_s_per_L"/>
<variable initial_value="1000" name="R_B_rRenal2" units="kPa_s_per_L"/>
<variable initial_value="1000" name="R_B_lRenal3" units="kPa_s_per_L"/>
<variable initial_value="1000" name="R_B_rRenal3" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_B_lRenal1</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_AA</ci>
<ci>u_B_lGlomerulus</ci>
</apply>
<ci>R_B_lRenal1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_B_rRenal1</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_AA</ci>
<ci>u_B_rGlomerulus</ci>
</apply>
<ci>R_B_rRenal1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_B_lRenal2</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_lGlomerulus</ci>
<ci>u_B_lPeritubular</ci>
</apply>
<ci>R_B_lRenal2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_B_rRenal2</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_rGlomerulus</ci>
<ci>u_B_rPeritubular</ci>
</apply>
<ci>R_B_rRenal2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_B_lRenal3</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_lPeritubular</ci>
<ci>u_B_RA</ci>
</apply>
<ci>R_B_lRenal3</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_B_rRenal3</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_rPeritubular</ci>
<ci>u_B_RA</ci>
</apply>
<ci>R_B_rRenal3</ci>
</apply>
</apply>
</math>
<!-- Muscle in torso-->
<variable initial_value="0.5" name="q_B_musTorso" units="litre"/>
<variable initial_value="0.5" name="q_B_musTorsoVein" units="litre"/>
<variable name="u_B_musTorso" units="kPa"/>
<variable name="u_B_musTorsoVein" units="kPa"/>
<variable initial_value="20" name="E_B_musTorso" units="kPa_per_L"/>
<variable initial_value="20" name="E_B_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_B_musTorso</ci>
</apply>
<apply>
<minus/>
<ci>v_B_musTorso1</ci>
<ci>v_B_musTorso2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_musTorso</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>E_B_musTorso</ci>
<ci>q_B_musTorso</ci>
</apply>
<apply>
<times/>
<ci>rho</ci>
<ci>g</ci>
<ci>z_musTorso</ci>
<apply>
<cos/>
<ci>theta_rad</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_B_musTorsoVein</ci>
</apply>
<apply>
<minus/>
<ci>v_B_musTorso2</ci>
<ci>v_B_musTorso3</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_musTorsoVein</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>E_B_musTorsoVein</ci>
<ci>q_B_musTorsoVein</ci>
</apply>
<apply>
<times/>
<ci>rho</ci>
<ci>g</ci>
<ci>z_musTorso</ci>
<apply>
<cos/>
<ci>theta_rad</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<variable name="v_B_musTorso1" units="L_per_s"/>
<variable name="v_B_musTorso2" units="L_per_s"/>
<variable name="v_B_musTorso3" units="L_per_s"/>
<variable initial_value="6000" name="R_B_musTorso1" units="kPa_s_per_L"/>
<variable initial_value="1000" name="R_B_musTorso2" units="kPa_s_per_L"/>
<variable initial_value="1000" name="R_B_musTorso3" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_B_musTorso1</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_AA</ci>
<ci>u_B_musTorso</ci>
</apply>
<ci>R_B_musTorso1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_B_musTorso2</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_musTorso</ci>
<ci>u_B_musTorsoVein</ci>
</apply>
<ci>R_B_musTorso2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_B_musTorso3</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_musTorsoVein</ci>
<ci>u_B_RA</ci>
</apply>
<ci>R_B_musTorso3</ci>
</apply>
</apply>
</math>
<!-- Left arm-->
<variable initial_value="0.5" name="q_B_lArm" units="litre"/>
<variable initial_value="0.5" name="q_B_lArmVein" units="litre"/>
<variable name="u_B_lArm" units="kPa"/>
<variable name="u_B_lArmVein" units="kPa"/>
<variable initial_value="20" name="E_B_lArm" units="kPa_per_L"/>
<variable initial_value="20" name="E_B_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_B_lArm</ci>
</apply>
<apply>
<minus/>
<ci>v_B_lArm1</ci>
<ci>v_B_lArm2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_lArm</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>E_B_lArm</ci>
<ci>q_B_lArm</ci>
</apply>
<apply>
<times/>
<ci>rho</ci>
<ci>g</ci>
<ci>z_lArm</ci>
<apply>
<cos/>
<ci>theta_rad</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_B_lArmVein</ci>
</apply>
<apply>
<minus/>
<ci>v_B_lArm2</ci>
<ci>v_B_lArm3</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_lArmVein</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>E_B_lArmVein</ci>
<ci>q_B_lArmVein</ci>
</apply>
<apply>
<times/>
<ci>rho</ci>
<ci>g</ci>
<ci>z_lArm</ci>
<apply>
<cos/>
<ci>theta_rad</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<variable name="v_B_lArm1" units="L_per_s"/>
<variable name="v_B_lArm2" units="L_per_s"/>
<variable name="v_B_lArm3" units="L_per_s"/>
<variable initial_value="6000" name="R_B_lArm1" units="kPa_s_per_L"/>
<variable initial_value="1000" name="R_B_lArm2" units="kPa_s_per_L"/>
<variable initial_value="1000" name="R_B_lArm3" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_B_lArm1</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_AA</ci>
<ci>u_B_lArm</ci>
</apply>
<ci>R_B_lArm1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_B_lArm2</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_lArm</ci>
<ci>u_B_lArmVein</ci>
</apply>
<ci>R_B_lArm2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_B_lArm3</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_lArmVein</ci>
<ci>u_B_RA</ci>
</apply>
<ci>R_B_lArm3</ci>
</apply>
</apply>
</math>
<!-- Right arm-->
<variable initial_value="0.5" name="q_B_rArm" units="litre"/>
<variable initial_value="0.5" name="q_B_rArmVein" units="litre"/>
<variable name="u_B_rArm" units="kPa"/>
<variable name="u_B_rArmVein" units="kPa"/>
<variable initial_value="20" name="E_B_rArm" units="kPa_per_L"/>
<variable initial_value="20" name="E_B_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_B_rArm</ci>
</apply>
<apply>
<minus/>
<ci>v_B_rArm1</ci>
<ci>v_B_rArm2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_rArm</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>E_B_rArm</ci>
<ci>q_B_rArm</ci>
</apply>
<apply>
<times/>
<ci>rho</ci>
<ci>g</ci>
<ci>z_rArm</ci>
<apply>
<cos/>
<ci>theta_rad</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_B_rArmVein</ci>
</apply>
<apply>
<minus/>
<ci>v_B_rArm2</ci>
<ci>v_B_rArm3</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_rArmVein</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>E_B_rArmVein</ci>
<ci>q_B_rArmVein</ci>
</apply>
<apply>
<times/>
<ci>rho</ci>
<ci>g</ci>
<ci>z_rArm</ci>
<apply>
<cos/>
<ci>theta_rad</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<variable name="v_B_rArm1" units="L_per_s"/>
<variable name="v_B_rArm2" units="L_per_s"/>
<variable name="v_B_rArm3" units="L_per_s"/>
<variable initial_value="6000" name="R_B_rArm1" units="kPa_s_per_L"/>
<variable initial_value="1000" name="R_B_rArm2" units="kPa_s_per_L"/>
<variable initial_value="1000" name="R_B_rArm3" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_B_rArm1</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_AA</ci>
<ci>u_B_rArm</ci>
</apply>
<ci>R_B_rArm1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_B_rArm2</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_rArm</ci>
<ci>u_B_rArmVein</ci>
</apply>
<ci>R_B_rArm2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_B_rArm3</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_rArmVein</ci>
<ci>u_B_RA</ci>
</apply>
<ci>R_B_rArm3</ci>
</apply>
</apply>
</math>
<!-- Left leg-->
<variable initial_value="0.5" name="q_B_lLeg" units="litre"/>
<variable initial_value="0.5" name="q_B_lLegVein" units="litre"/>
<variable name="u_B_lLeg" units="kPa"/>
<variable name="u_B_lLegVein" units="kPa"/>
<variable initial_value="20" name="E_B_lLeg" units="kPa_per_L"/>
<variable initial_value="20" name="E_B_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_B_lLeg</ci>
</apply>
<apply>
<minus/>
<ci>v_B_lLeg1</ci>
<ci>v_B_lLeg2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_lLeg</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>E_B_lLeg</ci>
<ci>q_B_lLeg</ci>
</apply>
<apply>
<times/>
<ci>rho</ci>
<ci>g</ci>
<ci>z_lLeg</ci>
<apply>
<cos/>
<ci>theta_rad</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_B_lLegVein</ci>
</apply>
<apply>
<minus/>
<ci>v_B_lLeg2</ci>
<ci>v_B_lLeg3</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_lLegVein</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>E_B_lLegVein</ci>
<ci>q_B_lLegVein</ci>
</apply>
<apply>
<times/>
<ci>rho</ci>
<ci>g</ci>
<ci>z_lLeg</ci>
<apply>
<cos/>
<ci>theta_rad</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<variable name="v_B_lLeg1" units="L_per_s"/>
<variable name="v_B_lLeg2" units="L_per_s"/>
<variable name="v_B_lLeg3" units="L_per_s"/>
<variable initial_value="6000" name="R_B_lLeg1" units="kPa_s_per_L"/>
<variable initial_value="1000" name="R_B_lLeg2" units="kPa_s_per_L"/>
<variable initial_value="1000" name="R_B_lLeg3" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_B_lLeg1</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_AA</ci>
<ci>u_B_lLeg</ci>
</apply>
<ci>R_B_lLeg1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_B_lLeg2</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_lLeg</ci>
<ci>u_B_lLegVein</ci>
</apply>
<ci>R_B_lLeg2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_B_lLeg3</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_lLegVein</ci>
<ci>u_B_RA</ci>
</apply>
<ci>R_B_lLeg3</ci>
</apply>
</apply>
</math>
<!-- Right leg-->
<variable initial_value="0.5" name="q_B_rLeg" units="litre"/>
<variable initial_value="0.5" name="q_B_rLegVein" units="litre"/>
<variable name="u_B_rLeg" units="kPa"/>
<variable name="u_B_rLegVein" units="kPa"/>
<variable initial_value="20" name="E_B_rLeg" units="kPa_per_L"/>
<variable initial_value="20" name="E_B_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_B_rLeg</ci>
</apply>
<apply>
<minus/>
<ci>v_B_rLeg1</ci>
<ci>v_B_rLeg2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_rLeg</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>E_B_rLeg</ci>
<ci>q_B_rLeg</ci>
</apply>
<apply>
<times/>
<ci>rho</ci>
<ci>g</ci>
<ci>z_rLeg</ci>
<apply>
<cos/>
<ci>theta_rad</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_B_rLegVein</ci>
</apply>
<apply>
<minus/>
<ci>v_B_rLeg2</ci>
<ci>v_B_rLeg3</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_rLegVein</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>E_B_rLegVein</ci>
<ci>q_B_rLegVein</ci>
</apply>
<apply>
<times/>
<ci>rho</ci>
<ci>g</ci>
<ci>z_rLeg</ci>
<apply>
<cos/>
<ci>theta_rad</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<variable name="v_B_rLeg1" units="L_per_s"/>
<variable name="v_B_rLeg2" units="L_per_s"/>
<variable name="v_B_rLeg3" units="L_per_s"/>
<variable initial_value="6000" name="R_B_rLeg1" units="kPa_s_per_L"/>
<variable initial_value="1000" name="R_B_rLeg2" units="kPa_s_per_L"/>
<variable initial_value="1000" name="R_B_rLeg3" units="kPa_s_per_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_B_rLeg1</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_AA</ci>
<ci>u_B_rLeg</ci>
</apply>
<ci>R_B_rLeg1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_B_rLeg2</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_rLeg</ci>
<ci>u_B_rLegVein</ci>
</apply>
<ci>R_B_rLeg2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_B_rLeg3</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_B_rLegVein</ci>
<ci>u_B_RA</ci>
</apply>
<ci>R_B_rLeg3</ci>
</apply>
</apply>
</math>
<!-- Total volumes of blood in torso, brain, limbs and combination-->
<variable name="q_B_heartTot" units="litre"/>
<variable name="q_B_lungTot" units="litre"/>
<variable name="q_B_renalTot" units="litre"/>
<variable name="q_B_gutTot" units="litre"/>
<variable name="q_B_brainTot" units="litre"/>
<variable name="q_B_limbTot" units="litre"/>
<variable name="q_Blood" units="litre"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>q_B_heartTot</ci>
<apply>
<plus/>
<ci>q_B_LV</ci>
<ci>q_B_RV</ci>
<ci>q_B_LA</ci>
<ci>q_B_RA</ci>
<ci>q_B_AA</ci>
<ci>q_B_PA</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_B_lungTot</ci>
<apply>
<plus/>
<ci>q_B_lung</ci>
<ci>q_B_pulmVein</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_B_renalTot</ci>
<apply>
<plus/>
<ci>q_B_lGlomerulus</ci>
<ci>q_B_rGlomerulus</ci>
<ci>q_B_lPeritubular</ci>
<ci>q_B_rPeritubular</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_B_gutTot</ci>
<apply>
<plus/>
<ci>q_B_celiac</ci>
<ci>q_B_supMes</ci>
<ci>q_B_stomach</ci>
<ci>q_B_spleen</ci>
<ci>q_B_pancreas</ci>
<ci>q_B_intestine</ci>
<ci>q_B_colon</ci>
<ci>q_B_portalVein</ci>
<ci>q_B_liver</ci>
<ci>q_B_musTorso</ci>
<ci>q_B_musTorsoVein</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_B_brainTot</ci>
<apply>
<plus/>
<ci>q_B_brain</ci>
<ci>q_B_brainVein</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_B_limbTot</ci>
<apply>
<plus/>
<ci>q_B_lArm</ci>
<ci>q_B_lArmVein</ci>
<ci>q_B_rArm</ci>
<ci>q_B_rArmVein</ci>
<ci>q_B_lLeg</ci>
<ci>q_B_lLegVein</ci>
<ci>q_B_rLeg</ci>
<ci>q_B_rLegVein</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_Blood</ci>
<apply>
<plus/>
<ci>q_B_heartTot</ci>
<ci>q_B_lungTot</ci>
<ci>q_B_renalTot</ci>
<ci>q_B_gutTot</ci>
<ci>q_B_brainTot</ci>
<ci>q_B_limbTot</ci>
</apply>
</apply>
</math>
</component>
</model>