Location: BondGraph Basic @ 37dedd8a252b / BG Tutorial Fluid Systems / 0D / Shi Model / Circuation.cellml
- Author:
- Soroush Safaei <ssaf006@aucklanduni.ac.nz>
- Date:
- 2017-12-11 23:11:31+13:00
- Desc:
- minor changes
- Permanent Source URI:
- https://models.fieldml.org/workspace/43b/rawfile/37dedd8a252be14c4f9dac0db7618fc3b6763445/BG Tutorial Fluid Systems/0D/Shi Model/Circuation.cellml
<?xml version='1.0'?>
<model name="CardiovascularSystem" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#" xmlns:xlink="http://www.w3.org/1999/xlink">
<import xlink:href="Units.cellml">
<units name="m3" units_ref="m3"/>
<units name="m3_per_s" units_ref="m3_per_s"/>
<units name="J_per_m6" units_ref="J_per_m6"/>
<units name="J_s_per_m6" units_ref="J_s_per_m6"/>
<units name="J_s2_per_m6" units_ref="J_s2_per_m6"/>
<units name="J_per_s" units_ref="J_per_s"/>
<units name="J_per_m3" units_ref="J_per_m3"/>
<units name="J_s_per_m3" units_ref="J_s_per_m3"/>
<units name="UnitValve" units_ref="UnitValve"/>
</import>
<component name="environment">
<variable name="time" public_interface="out" units="second"/>
</component>
<!-------------- Systemic Circulation ------------//-->
<component name="Systemic">
<variable name="t" public_interface="in" units="second"/>
<!-- Constitutive Parameters-->
<variable initial_value="1.666525e+9" name="E_sas" units="J_per_m6"/>
<variable initial_value="0.08332625e+9" name="E_sat" units="J_per_m6"/>
<variable initial_value="0.0065e+9" name="E_svn" units="J_per_m6"/>
<variable initial_value="0.4e+6" name="R_sas" units="J_s_per_m6"/>
<variable initial_value="6.666e+6" name="R_sat" units="J_s_per_m6"/>
<variable initial_value="66.66e+6" name="R_sar" units="J_s_per_m6"/>
<variable initial_value="69.32744e+6" name="R_scp" units="J_s_per_m6"/>
<variable initial_value="10.0e+6" name="R_svn" units="J_s_per_m6"/>
<variable initial_value="0.008266e+6" name="L_sas" units="J_s2_per_m6"/>
<variable initial_value="0.2266474e+6" name="L_sat" units="J_s2_per_m6"/>
<!-- State Variables-->
<variable initial_value="13332.0" name="u_sas" public_interface="out" units="J_per_m3"/>
<variable initial_value="13332.0" name="u_sat" public_interface="out" units="J_per_m3"/>
<variable name="u_sar" public_interface="out" units="J_per_m3"/>
<variable name="u_scp" public_interface="out" units="J_per_m3"/>
<variable initial_value="0.0" name="u_svn" public_interface="out" units="J_per_m3"/>
<variable name="u_ra" public_interface="in" units="J_per_m3"/>
<variable initial_value="0.0" name="v_sas" public_interface="out" units="m3_per_s"/>
<variable initial_value="0.0" name="v_sat" public_interface="out" units="m3_per_s"/>
<variable name="v_sar" public_interface="out" units="m3_per_s"/>
<variable name="v_scp" public_interface="out" units="m3_per_s"/>
<variable name="v_svn" public_interface="out" units="m3_per_s"/>
<variable name="v_lv" public_interface="in" units="m3_per_s"/>
<!-- Constitutive Relations-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>u_sas</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<ci>v_lv</ci>
<ci>v_sas</ci>
</apply>
<ci>E_sas</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>u_sat</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<ci>v_sas</ci>
<ci>v_sat</ci>
</apply>
<ci>E_sat</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_sar</ci>
<apply>
<plus/>
<ci>u_scp</ci>
<apply>
<times/>
<ci>v_sar</ci>
<ci>R_sar</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_scp</ci>
<apply>
<plus/>
<ci>u_svn</ci>
<apply>
<times/>
<ci>v_scp</ci>
<ci>R_scp</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>u_svn</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<ci>v_sat</ci>
<ci>v_svn</ci>
</apply>
<ci>E_svn</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v_sas</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>u_sas</ci>
<ci>u_sat</ci>
</apply>
<apply>
<times/>
<ci>v_sas</ci>
<ci>R_sas</ci>
</apply>
</apply>
<ci>L_sas</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v_sat</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>u_sat</ci>
<ci>u_sar</ci>
</apply>
<apply>
<times/>
<ci>v_sat</ci>
<ci>R_sat</ci>
</apply>
</apply>
<ci>L_sat</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_svn</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_svn</ci>
<ci>u_ra</ci>
</apply>
<ci>R_svn</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_scp</ci>
<ci>v_sar</ci>
</apply>
<apply>
<eq/>
<ci>v_sar</ci>
<ci>v_sat</ci>
</apply>
</math>
</component>
<!-------------- Pulmonary Circulation ------------//-->
<component name="Pulmonary">
<variable name="t" public_interface="in" units="second"/>
<!-- Constitutive Parameters-->
<variable initial_value="0.74e+9" name="E_pas" units="J_per_m6"/>
<variable initial_value="0.035e+9" name="E_pat" units="J_per_m6"/>
<variable initial_value="0.0065e+9" name="E_pvn" units="J_per_m6"/>
<variable initial_value="0.266644e+6" name="R_pas" units="J_s_per_m6"/>
<variable initial_value="1.33322e+6" name="R_pat" units="J_s_per_m6"/>
<variable initial_value="6.666e+6" name="R_par" units="J_s_per_m6"/>
<variable initial_value="33.33e+6" name="R_pcp" units="J_s_per_m6"/>
<variable initial_value="0.08e+6" name="R_pvn" units="J_s_per_m6"/>
<variable initial_value="0.007e+6" name="L_pas" units="J_s2_per_m6"/>
<variable initial_value="0.2266474e+6" name="L_pat" units="J_s2_per_m6"/>
<!-- State Variables-->
<variable initial_value="4000.0" name="u_pas" public_interface="out" units="J_per_m3"/>
<variable initial_value="4000.0" name="u_pat" public_interface="out" units="J_per_m3"/>
<variable name="u_par" public_interface="out" units="J_per_m3"/>
<variable name="u_pcp" public_interface="out" units="J_per_m3"/>
<variable initial_value="0.0" name="u_pvn" public_interface="out" units="J_per_m3"/>
<variable name="u_la" public_interface="in" units="J_per_m3"/>
<variable initial_value="0.0" name="v_pas" public_interface="out" units="m3_per_s"/>
<variable initial_value="0.0" name="v_pat" public_interface="out" units="m3_per_s"/>
<variable name="v_par" public_interface="out" units="m3_per_s"/>
<variable name="v_pcp" public_interface="out" units="m3_per_s"/>
<variable name="v_pvn" public_interface="out" units="m3_per_s"/>
<variable name="v_rv" public_interface="in" units="m3_per_s"/>
<!-- Constitutive Relations-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>u_pas</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<ci>v_rv</ci>
<ci>v_pas</ci>
</apply>
<ci>E_pas</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>u_pat</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<ci>v_pas</ci>
<ci>v_pat</ci>
</apply>
<ci>E_pat</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_par</ci>
<apply>
<plus/>
<ci>u_pcp</ci>
<apply>
<times/>
<ci>v_par</ci>
<ci>R_par</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_pcp</ci>
<apply>
<plus/>
<ci>u_pvn</ci>
<apply>
<times/>
<ci>v_pcp</ci>
<ci>R_pcp</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>u_pvn</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<ci>v_pat</ci>
<ci>v_pvn</ci>
</apply>
<ci>E_pvn</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v_pas</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>u_pas</ci>
<ci>u_pat</ci>
</apply>
<apply>
<times/>
<ci>v_pas</ci>
<ci>R_pas</ci>
</apply>
</apply>
<ci>L_pas</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v_pat</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>u_pat</ci>
<ci>u_pvn</ci>
</apply>
<apply>
<times/>
<ci>v_pat</ci>
<ci>R_pat</ci>
</apply>
</apply>
<apply>
<times/>
<ci>v_pat</ci>
<ci>R_pcp</ci>
</apply>
</apply>
<apply>
<times/>
<ci>v_pat</ci>
<ci>R_par</ci>
</apply>
</apply>
<ci>L_pat</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_pvn</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>u_pvn</ci>
<ci>u_la</ci>
</apply>
<ci>R_pvn</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_pcp</ci>
<ci>v_par</ci>
</apply>
<apply>
<eq/>
<ci>v_par</ci>
<ci>v_pat</ci>
</apply>
</math>
</component>
<!-------------- Heart ------------//-->
<component name="Heart">
<variable name="t" public_interface="in" units="second"/>
<!-- Constitutive Parameters-->
<variable name="mt" units="second"/>
<variable name="et_a" units="dimensionless"/>
<variable name="et_v" units="dimensionless"/>
<variable initial_value="1.0" name="T" units="second"/>
<variable initial_value="0.92" name="Tpwb" units="dimensionless"/>
<variable initial_value="0.09" name="Tpww" units="dimensionless"/>
<variable initial_value="0.3" name="Ts1" units="dimensionless"/>
<variable initial_value="0.45" name="Ts2" units="dimensionless"/>
<variable initial_value="34.6427e-6" name="CV_ra" units="UnitValve"/>
<variable initial_value="30.3124e-6" name="CV_rv" units="UnitValve"/>
<variable initial_value="34.6427e-6" name="CV_la" units="UnitValve"/>
<variable initial_value="30.3124e-6" name="CV_lv" units="UnitValve"/>
<variable name="E_lv" units="J_per_m6"/>
<variable initial_value="0.3333e+9" name="E_lv_Max" units="J_per_m6"/>
<variable initial_value="0.01333e+9" name="E_lv_Min" units="J_per_m6"/>
<variable name="E_la" units="J_per_m6"/>
<variable initial_value="0.03333e+9" name="E_la_Max" units="J_per_m6"/>
<variable initial_value="0.02e+9" name="E_la_Min" units="J_per_m6"/>
<variable name="E_rv" units="J_per_m6"/>
<variable initial_value="0.15332e+9" name="E_rv_Max" units="J_per_m6"/>
<variable initial_value="0.01333e+9" name="E_rv_Min" units="J_per_m6"/>
<variable name="E_ra" units="J_per_m6"/>
<variable initial_value="0.03333e+9" name="E_ra_Max" units="J_per_m6"/>
<variable initial_value="0.02e+9" name="E_ra_Min" units="J_per_m6"/>
<!-- State Variables-->
<variable initial_value="133.32" name="u_ra_0" units="J_per_m3"/>
<variable initial_value="133.32" name="u_rv_0" units="J_per_m3"/>
<variable initial_value="133.32" name="u_la_0" units="J_per_m3"/>
<variable initial_value="133.32" name="u_lv_0" units="J_per_m3"/>
<variable name="u_ra" public_interface="out" units="J_per_m3"/>
<variable name="u_rv" units="J_per_m3"/>
<variable name="u_la" public_interface="out" units="J_per_m3"/>
<variable name="u_lv" units="J_per_m3"/>
<variable name="u_sas" public_interface="in" units="J_per_m3"/>
<variable name="u_pas" public_interface="in" units="J_per_m3"/>
<variable name="v_ra" units="m3_per_s"/>
<variable name="v_rv" public_interface="out" units="m3_per_s"/>
<variable name="v_la" units="m3_per_s"/>
<variable name="v_lv" public_interface="out" units="m3_per_s"/>
<variable name="v_svn" public_interface="in" units="m3_per_s"/>
<variable name="v_pvn" public_interface="in" units="m3_per_s"/>
<variable initial_value="4.0e-6" name="q_ra_0" units="m3"/>
<variable initial_value="10.0e-6" name="q_rv_0" units="m3"/>
<variable initial_value="4.0e-6" name="q_la_0" units="m3"/>
<variable initial_value="5.0e-6" name="q_lv_0" units="m3"/>
<variable initial_value="20.0e-6" name="q_ra" units="m3"/>
<variable initial_value="500.0e-6" name="q_rv" units="m3"/>
<variable initial_value="20.0e-6" name="q_la" units="m3"/>
<variable initial_value="500.0e-6" name="q_lv" units="m3"/>
<!-- Elastance Functions-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>mt</ci>
<apply>
<minus/>
<ci>t</ci>
<apply>
<times/>
<ci>T</ci>
<apply>
<floor/>
<apply>
<divide/>
<ci>t</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>et_a</ci>
<piecewise>
<piece>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<cos/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<pi/>
<apply>
<plus/>
<apply>
<minus/>
<ci>mt</ci>
<apply>
<times/>
<ci>Tpwb</ci>
<ci>T</ci>
</apply>
</apply>
<ci>T</ci>
</apply>
</apply>
<apply>
<times/>
<ci>Tpww</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<and/>
<apply>
<geq/>
<ci>mt</ci>
<cn cellml:units="second">0</cn>
</apply>
<apply>
<leq/>
<ci>mt</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<plus/>
<ci>Tpwb</ci>
<ci>Tpww</ci>
</apply>
<ci>T</ci>
</apply>
<ci>T</ci>
</apply>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="dimensionless">0</cn>
<apply>
<and/>
<apply>
<gt/>
<ci>mt</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<plus/>
<ci>Tpwb</ci>
<ci>Tpww</ci>
</apply>
<ci>T</ci>
</apply>
<ci>T</ci>
</apply>
</apply>
<apply>
<leq/>
<ci>mt</ci>
<apply>
<times/>
<ci>Tpwb</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</piece>
<piece>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<cos/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<pi/>
<apply>
<minus/>
<ci>mt</ci>
<apply>
<times/>
<ci>Tpwb</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>Tpww</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<and/>
<apply>
<gt/>
<ci>mt</ci>
<apply>
<times/>
<ci>Tpwb</ci>
<ci>T</ci>
</apply>
</apply>
<apply>
<leq/>
<ci>mt</ci>
<ci>T</ci>
</apply>
</apply>
</piece>
</piecewise>
</apply>
<apply>
<eq/>
<ci>et_v</ci>
<piecewise>
<piece>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<cos/>
<apply>
<divide/>
<apply>
<times/>
<pi/>
<ci>mt</ci>
</apply>
<apply>
<times/>
<ci>Ts1</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<and/>
<apply>
<geq/>
<ci>mt</ci>
<cn cellml:units="second">0</cn>
</apply>
<apply>
<leq/>
<ci>mt</ci>
<apply>
<times/>
<ci>Ts1</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</piece>
<piece>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<cos/>
<apply>
<divide/>
<apply>
<times/>
<pi/>
<apply>
<minus/>
<ci>mt</ci>
<apply>
<times/>
<ci>Ts1</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<minus/>
<ci>Ts2</ci>
<ci>Ts1</ci>
</apply>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<and/>
<apply>
<gt/>
<ci>mt</ci>
<apply>
<times/>
<ci>Ts1</ci>
<ci>T</ci>
</apply>
</apply>
<apply>
<leq/>
<ci>mt</ci>
<apply>
<times/>
<ci>Ts2</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="dimensionless">0</cn>
<apply>
<and/>
<apply>
<gt/>
<ci>mt</ci>
<apply>
<times/>
<ci>Ts2</ci>
<ci>T</ci>
</apply>
</apply>
<apply>
<lt/>
<ci>mt</ci>
<ci>T</ci>
</apply>
</apply>
</piece>
</piecewise>
</apply>
<apply>
<eq/>
<ci>E_ra</ci>
<apply>
<plus/>
<ci>E_ra_Min</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>et_a</ci>
<apply>
<minus/>
<ci>E_ra_Max</ci>
<ci>E_ra_Min</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>E_rv</ci>
<apply>
<plus/>
<ci>E_rv_Min</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>et_v</ci>
<apply>
<minus/>
<ci>E_rv_Max</ci>
<ci>E_rv_Min</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>E_la</ci>
<apply>
<plus/>
<ci>E_la_Min</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>et_a</ci>
<apply>
<minus/>
<ci>E_la_Max</ci>
<ci>E_la_Min</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>E_lv</ci>
<apply>
<plus/>
<ci>E_lv_Min</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>et_v</ci>
<apply>
<minus/>
<ci>E_lv_Max</ci>
<ci>E_lv_Min</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<!-- Constitutive Relations-->
<apply>
<eq/>
<ci>v_ra</ci>
<piecewise>
<piece>
<apply>
<times/>
<ci>CV_ra</ci>
<apply>
<root/>
<apply>
<minus/>
<ci>u_ra</ci>
<ci>u_rv</ci>
</apply>
</apply>
</apply>
<apply>
<geq/>
<ci>u_ra</ci>
<ci>u_rv</ci>
</apply>
</piece>
<piece>
<cn cellml:units="dimensionless">0</cn>
<apply>
<lt/>
<ci>u_ra</ci>
<ci>u_rv</ci>
</apply>
</piece>
</piecewise>
</apply>
<apply>
<eq/>
<ci>v_rv</ci>
<piecewise>
<piece>
<apply>
<times/>
<ci>CV_rv</ci>
<apply>
<root/>
<apply>
<minus/>
<ci>u_rv</ci>
<ci>u_pas</ci>
</apply>
</apply>
</apply>
<apply>
<geq/>
<ci>u_rv</ci>
<ci>u_pas</ci>
</apply>
</piece>
<piece>
<cn cellml:units="dimensionless">0</cn>
<apply>
<lt/>
<ci>u_rv</ci>
<ci>u_pas</ci>
</apply>
</piece>
</piecewise>
</apply>
<apply>
<eq/>
<ci>v_la</ci>
<piecewise>
<piece>
<apply>
<times/>
<ci>CV_la</ci>
<apply>
<root/>
<apply>
<minus/>
<ci>u_la</ci>
<ci>u_lv</ci>
</apply>
</apply>
</apply>
<apply>
<geq/>
<ci>u_la</ci>
<ci>u_lv</ci>
</apply>
</piece>
<piece>
<cn cellml:units="dimensionless">0</cn>
<apply>
<lt/>
<ci>u_la</ci>
<ci>u_lv</ci>
</apply>
</piece>
</piecewise>
</apply>
<apply>
<eq/>
<ci>v_lv</ci>
<piecewise>
<piece>
<apply>
<times/>
<ci>CV_lv</ci>
<apply>
<root/>
<apply>
<minus/>
<ci>u_lv</ci>
<ci>u_sas</ci>
</apply>
</apply>
</apply>
<apply>
<geq/>
<ci>u_lv</ci>
<ci>u_sas</ci>
</apply>
</piece>
<piece>
<cn cellml:units="dimensionless">0</cn>
<apply>
<lt/>
<ci>u_lv</ci>
<ci>u_sas</ci>
</apply>
</piece>
</piecewise>
</apply>
<apply>
<eq/>
<ci>u_ra</ci>
<apply>
<plus/>
<ci>u_ra_0</ci>
<apply>
<times/>
<ci>E_ra</ci>
<apply>
<minus/>
<ci>q_ra</ci>
<ci>q_ra_0</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_rv</ci>
<apply>
<plus/>
<ci>u_rv_0</ci>
<apply>
<times/>
<ci>E_rv</ci>
<apply>
<minus/>
<ci>q_rv</ci>
<ci>q_rv_0</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_la</ci>
<apply>
<plus/>
<ci>u_la_0</ci>
<apply>
<times/>
<ci>E_la</ci>
<apply>
<minus/>
<ci>q_la</ci>
<ci>q_la_0</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_lv</ci>
<apply>
<plus/>
<ci>u_lv_0</ci>
<apply>
<times/>
<ci>E_lv</ci>
<apply>
<minus/>
<ci>q_lv</ci>
<ci>q_lv_0</ci>
</apply>
</apply>
</apply>
</apply>
<!-- Conservation Laws-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_ra</ci>
</apply>
<apply>
<minus/>
<ci>v_svn</ci>
<ci>v_ra</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_rv</ci>
</apply>
<apply>
<minus/>
<ci>v_ra</ci>
<ci>v_rv</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_la</ci>
</apply>
<apply>
<minus/>
<ci>v_pvn</ci>
<ci>v_la</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_lv</ci>
</apply>
<apply>
<minus/>
<ci>v_la</ci>
<ci>v_lv</ci>
</apply>
</apply>
</math>
</component>
<!-------------- Mapping ------------//-->
<connection>
<map_components component_1="Heart" component_2="Systemic"/>
<map_variables variable_1="u_sas" variable_2="u_sas"/>
<map_variables variable_1="v_svn" variable_2="v_svn"/>
<map_variables variable_1="v_lv" variable_2="v_lv"/>
<map_variables variable_1="u_ra" variable_2="u_ra"/>
</connection>
<connection>
<map_components component_1="Heart" component_2="Pulmonary"/>
<map_variables variable_1="u_pas" variable_2="u_pas"/>
<map_variables variable_1="v_pvn" variable_2="v_pvn"/>
<map_variables variable_1="u_la" variable_2="u_la"/>
<map_variables variable_1="v_rv" variable_2="v_rv"/>
</connection>
<connection>
<map_components component_1="environment" component_2="Heart"/>
<map_variables variable_1="time" variable_2="t"/>
</connection>
<connection>
<map_components component_1="environment" component_2="Systemic"/>
<map_variables variable_1="time" variable_2="t"/>
</connection>
<connection>
<map_components component_1="environment" component_2="Pulmonary"/>
<map_variables variable_1="time" variable_2="t"/>
</connection>
</model>