Location: Bond Graph Circulation @ dbdc7c5db2bc / BG_Modules.cellml
- Author:
- finbar <farg967@aucklanduni.ac.nz>
- Date:
- 2021-08-02 22:13:06+12:00
- Desc:
- Fixed alpha implementation in BG modules so that resistance can be modified globally and locally
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/673/rawfile/dbdc7c5db2bca9b0962298928e03cd0e9ecfeddd/BG_Modules.cellml
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//////////////////////////////////////////////////////////////////////////////////////////////////////-->
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<!--//////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////// input-BC Vessel ///////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////////////////-->
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<times/>
<cn cellml:units="dimensionless">8</cn>
<ci>mu</ci>
<ci>l</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R_v</ci>
<apply>
<divide/>
<cn cellml:units="second">0.01</cn>
<ci>C</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>length</ci>
<ci>l</ci>
</apply>
<apply>
<eq/>
<ci>E_m</ci>
<ci>E</ci>
</apply>
<apply>
<eq/>
<ci>radius</ci>
<ci>r</ci>
</apply>
<apply>
<eq/>
<ci>thickness</ci>
<ci>h</ci>
</apply>
<!-- Conservation Laws-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>u</ci>
<ci>u_d</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>v</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_g</ci>
<ci>rho</ci>
<ci>g</ci>
<ci>l</ci>
<apply>
<cos/>
<apply>
<divide/>
<apply>
<times/>
<ci>theta</ci>
<pi/>
</apply>
<cn cellml:units="dimensionless">180</cn>
</apply>
</apply>
</apply>
</apply>
<ci>I</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>u_C</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>v_in</ci>
<ci>v</ci>
</apply>
<apply>
<divide/>
<ci>C</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>u_C_d</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>v</ci>
<ci>v_out</ci>
</apply>
<apply>
<divide/>
<ci>C</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u</ci>
<apply>
<plus/>
<ci>u_C</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>R_v</ci>
<apply>
<minus/>
<ci>v_in</ci>
<ci>v</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_d</ci>
<apply>
<plus/>
<ci>u_C_d</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>R_v</ci>
<apply>
<minus/>
<ci>v</ci>
<ci>v_out</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--//////////////////////////////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////// output-BC Vessel ///////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////////////////-->
<component name="pp_BC_type">
<variable name="t" public_interface="in" units="second"/>
<!-- Constitutive Parameters-->
<variable initial_value="0.004" name="mu" units="Js_per_m3"/>
<variable initial_value="1050" name="rho" units="Js2_per_m5"/>
<variable initial_value="9.81" name="g" units="m_per_s2"/>
<variable name="beta_g" public_interface="in" units="dimensionless"/>
<variable name="theta" public_interface="in" units="dimensionless"/>
<variable name="E" public_interface="in" units="J_per_m3"/>
<variable name="E_m" public_interface="out" units="J_per_m3"/>
<variable name="l" public_interface="in" units="metre"/>
<variable name="length" public_interface="out" units="metre"/>
<variable name="h" public_interface="out" units="metre"/>
<variable name="thickness" public_interface="out" units="metre"/>
<variable name="r" public_interface="in" units="metre"/>
<variable name="radius" public_interface="out" units="metre"/>
<variable name="I" public_interface="out" units="Js2_per_m6"/>
<variable name="I_e" public_interface="out" units="Js2_per_m6"/>
<variable name="C" public_interface="out" units="m6_per_J"/>
<variable name="R" public_interface="out" units="Js_per_m6"/>
<variable name="R_v" public_interface="out" units="Js_per_m6"/>
<variable name="R_T" public_interface="in" units="Js_per_m6"/>
<variable name="R_T_2" public_interface="out" units="Js_per_m6"/>
<variable name="C_T" public_interface="in" units="m6_per_J"/>
<variable initial_value="0.2802" name="a" units="dimensionless"/>
<variable initial_value="-505.3" name="b" units="per_m"/>
<variable initial_value="0.1324" name="c" units="dimensionless"/>
<variable initial_value="-11.14" name="d" units="per_m"/>
<variable name="alpha" public_interface="in" units="dimensionless"/>
<!-- State Variables-->
<variable name="u_in" public_interface="in" units="J_per_m3"/>
<variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
<variable name="u" public_interface="out" units="J_per_m3"/>
<variable initial_value="0.0" name="u_C" public_interface="out" units="J_per_m3"/>
<variable name="u_T" public_interface="out" units="J_per_m3"/>
<variable initial_value="0.0" name="v_T" public_interface="out" units="m3_per_s"/>
<variable name="u_out" public_interface="in" units="J_per_m3"/>
<variable initial_value="0.0" name="q_T" public_interface="out" units="m3"/>
<variable initial_value="0.0" name="int_control_sum" public_interface="out" units="Js_per_m6"/>
<variable name="R_T_wCont" public_interface="out" units="Js_per_m6"/>
<variable name="gain_int" public_interface="in" units="J_per_m9"/>
<variable name="v_nominal" public_interface="in" units="m3_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>h</ci>
<apply>
<times/>
<ci>r</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>a</ci>
<apply>
<exp/>
<apply>
<times/>
<ci>b</ci>
<ci>r</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>c</ci>
<apply>
<exp/>
<apply>
<times/>
<ci>d</ci>
<ci>r</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>I</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>rho</ci>
<ci>l</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>I_e</ci>
<apply>
<times/>
<ci>I</ci>
<cn cellml:units="dimensionless" type="e-notation">1<sep/>-6</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>C</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>l</ci>
</apply>
<apply>
<times/>
<ci>E</ci>
<ci>h</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">8</cn>
<ci>mu</ci>
<ci>l</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R_v</ci>
<apply>
<divide/>
<cn cellml:units="second">0.01</cn>
<ci>C</ci>
</apply>
</apply>
<!--R_T_2 = 4{dimensionless}*R_T;-->
<apply>
<eq/>
<ci>R_T_2</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>R_T_wCont</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>length</ci>
<ci>l</ci>
</apply>
<apply>
<eq/>
<ci>E_m</ci>
<ci>E</ci>
</apply>
<apply>
<eq/>
<ci>radius</ci>
<ci>r</ci>
</apply>
<apply>
<eq/>
<ci>thickness</ci>
<ci>h</ci>
</apply>
<!-- Conservation Laws-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>u_in</ci>
<ci>u</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>v</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_g</ci>
<ci>rho</ci>
<ci>g</ci>
<ci>l</ci>
<apply>
<cos/>
<apply>
<divide/>
<apply>
<times/>
<ci>theta</ci>
<pi/>
</apply>
<cn cellml:units="dimensionless">180</cn>
</apply>
</apply>
</apply>
</apply>
<ci>I</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>u_C</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>v</ci>
<ci>v_T</ci>
</apply>
<ci>C</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u</ci>
<apply>
<plus/>
<ci>u_C</ci>
<apply>
<times/>
<ci>R_v</ci>
<apply>
<minus/>
<ci>v</ci>
<ci>v_T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v_T</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>u</ci>
<ci>u_out</ci>
</apply>
<ci>u_T</ci>
</apply>
<apply>
<times/>
<ci>R_T_wCont</ci>
<ci>v_T</ci>
</apply>
</apply>
<ci>I_e</ci>
</apply>
</apply>
<!-- ode(u_T, t) = (v_T-u_T/(alpha*R_T_2))/C_T;-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_T</ci>
</apply>
<apply>
<minus/>
<ci>v_T</ci>
<apply>
<divide/>
<ci>q_T</ci>
<apply>
<times/>
<ci>C_T</ci>
<ci>R_T_2</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_T</ci>
<apply>
<divide/>
<ci>q_T</ci>
<ci>C_T</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>int_control_sum</ci>
</apply>
<apply>
<times/>
<ci>gain_int</ci>
<apply>
<minus/>
<ci>v_T</ci>
<ci>v_nominal</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R_T_wCont</ci>
<apply>
<times/>
<ci>alpha</ci>
<apply>
<plus/>
<ci>R_T</ci>
<ci>int_control_sum</ci>
</apply>
</apply>
</apply>
</math>
<!--ode(u_T, t) = (v_T-u_T/(alpha*R_T_2))/C_T;-->
</component>
<!--//////////////////////////////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////// output-BC Venous Vessel ////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////////////////-->
<component name="pp_vBC_type">
<variable name="t" public_interface="in" units="second"/>
<!-- Constitutive Parameters-->
<variable initial_value="0.004" name="mu" units="Js_per_m3"/>
<variable initial_value="1050" name="rho" units="Js2_per_m5"/>
<variable initial_value="9.81" name="g" units="m_per_s2"/>
<variable name="beta_g" public_interface="in" units="dimensionless"/>
<variable name="theta" public_interface="in" units="dimensionless"/>
<variable name="E" public_interface="in" units="J_per_m3"/>
<variable name="E_m" public_interface="out" units="J_per_m3"/>
<variable name="l" public_interface="in" units="metre"/>
<variable name="length" public_interface="out" units="metre"/>
<variable name="h" public_interface="out" units="metre"/>
<variable name="thickness" public_interface="out" units="metre"/>
<variable name="r" public_interface="in" units="metre"/>
<variable name="radius" public_interface="out" units="metre"/>
<variable name="I" public_interface="out" units="Js2_per_m6"/>
<variable name="I_e" public_interface="out" units="Js2_per_m6"/>
<variable name="C" public_interface="out" units="m6_per_J"/>
<variable name="R" public_interface="out" units="Js_per_m6"/>
<variable name="R_v" public_interface="out" units="Js_per_m6"/>
<variable name="R_T" public_interface="in" units="Js_per_m6"/>
<variable name="C_T" public_interface="in" units="m6_per_J"/>
<variable initial_value="0.2802" name="a" units="dimensionless"/>
<variable initial_value="-505.3" name="b" units="per_m"/>
<variable initial_value="0.1324" name="c" units="dimensionless"/>
<variable initial_value="-11.14" name="d" units="per_m"/>
<!-- State Variables-->
<variable name="u_in" public_interface="in" units="J_per_m3"/>
<variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
<variable name="u" public_interface="out" units="J_per_m3"/>
<variable initial_value="0.0" name="u_C" public_interface="out" units="J_per_m3"/>
<variable initial_value="0.0" name="v_T" public_interface="out" units="m3_per_s"/>
<variable name="u_out" public_interface="in" units="J_per_m3"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>h</ci>
<apply>
<times/>
<ci>r</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>a</ci>
<apply>
<exp/>
<apply>
<times/>
<ci>b</ci>
<ci>r</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>c</ci>
<apply>
<exp/>
<apply>
<times/>
<ci>d</ci>
<ci>r</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>I</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>rho</ci>
<ci>l</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>I_e</ci>
<apply>
<times/>
<ci>I</ci>
<cn cellml:units="dimensionless" type="e-notation">1<sep/>-6</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>C</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>l</ci>
</apply>
<apply>
<times/>
<ci>E</ci>
<ci>h</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">8</cn>
<ci>mu</ci>
<ci>l</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R_v</ci>
<apply>
<divide/>
<cn cellml:units="second">0.01</cn>
<ci>C</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>length</ci>
<ci>l</ci>
</apply>
<apply>
<eq/>
<ci>E_m</ci>
<ci>E</ci>
</apply>
<apply>
<eq/>
<ci>radius</ci>
<ci>r</ci>
</apply>
<apply>
<eq/>
<ci>thickness</ci>
<ci>h</ci>
</apply>
<!-- Conservation Laws-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>u_in</ci>
<ci>u</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>v</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_g</ci>
<ci>rho</ci>
<ci>g</ci>
<ci>l</ci>
<apply>
<cos/>
<apply>
<divide/>
<apply>
<times/>
<ci>theta</ci>
<pi/>
</apply>
<cn cellml:units="dimensionless">180</cn>
</apply>
</apply>
</apply>
</apply>
<ci>I</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>u_C</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>v</ci>
<ci>v_T</ci>
</apply>
<ci>C</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u</ci>
<apply>
<plus/>
<ci>u_C</ci>
<apply>
<times/>
<ci>R_v</ci>
<apply>
<minus/>
<ci>v</ci>
<ci>v_T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v_T</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>u</ci>
<ci>u_out</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">3.0</cn>
<ci>R_T</ci>
<ci>v_T</ci>
</apply>
</apply>
<ci>I_e</ci>
</apply>
</apply>
</math>
</component>
<!--/////////////////////////////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////// Junctions //////////////////////////////////////////////
/////////////////////////////////////////////////////////////////////////////////////////////////////-->
<!-- Bifurcation-->
<component name="pv_jII_type">
<variable name="t" public_interface="in" units="second"/>
<!-- Constitutive Parameters-->
<variable initial_value="0.004" name="mu" units="Js_per_m3"/>
<variable initial_value="1050" name="rho" units="Js2_per_m5"/>
<variable initial_value="9.81" name="g" units="m_per_s2"/>
<variable name="beta_g" public_interface="in" units="dimensionless"/>
<variable name="theta" public_interface="in" units="dimensionless"/>
<variable name="E" public_interface="in" units="J_per_m3"/>
<variable name="E_m" public_interface="out" units="J_per_m3"/>
<variable name="l" public_interface="in" units="metre"/>
<variable name="length" public_interface="out" units="metre"/>
<variable name="h" public_interface="out" units="metre"/>
<variable name="thickness" public_interface="out" units="metre"/>
<variable name="r" public_interface="in" units="metre"/>
<variable name="radius" public_interface="out" units="metre"/>
<variable name="I" public_interface="out" units="Js2_per_m6"/>
<variable name="C" public_interface="out" units="m6_per_J"/>
<variable name="R" public_interface="out" units="Js_per_m6"/>
<variable name="R_v" public_interface="out" units="Js_per_m6"/>
<variable initial_value="0.2802" name="a" units="dimensionless"/>
<variable initial_value="-505.3" name="b" units="per_m"/>
<variable initial_value="0.1324" name="c" units="dimensionless"/>
<variable initial_value="-11.14" name="d" units="per_m"/>
<!-- State Variables-->
<variable name="u_in" public_interface="in" units="J_per_m3"/>
<variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
<variable name="u" public_interface="out" units="J_per_m3"/>
<variable initial_value="0.0" name="u_C" public_interface="out" units="J_per_m3"/>
<variable name="v_out_1" public_interface="in" units="m3_per_s"/>
<variable name="v_out_2" public_interface="in" units="m3_per_s"/>
<!-- Constitutive Relations-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>h</ci>
<apply>
<times/>
<ci>r</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>a</ci>
<apply>
<exp/>
<apply>
<times/>
<ci>b</ci>
<ci>r</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>c</ci>
<apply>
<exp/>
<apply>
<times/>
<ci>d</ci>
<ci>r</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>I</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>rho</ci>
<ci>l</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>C</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>l</ci>
</apply>
<apply>
<times/>
<ci>E</ci>
<ci>h</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">8</cn>
<ci>mu</ci>
<ci>l</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R_v</ci>
<apply>
<divide/>
<cn cellml:units="second">0.01</cn>
<ci>C</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>length</ci>
<ci>l</ci>
</apply>
<apply>
<eq/>
<ci>E_m</ci>
<ci>E</ci>
</apply>
<apply>
<eq/>
<ci>radius</ci>
<ci>r</ci>
</apply>
<apply>
<eq/>
<ci>thickness</ci>
<ci>h</ci>
</apply>
<!-- Conservation Laws-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>u_in</ci>
<ci>u</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>v</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_g</ci>
<ci>rho</ci>
<ci>g</ci>
<ci>l</ci>
<apply>
<cos/>
<apply>
<divide/>
<apply>
<times/>
<ci>theta</ci>
<pi/>
</apply>
<cn cellml:units="dimensionless">180</cn>
</apply>
</apply>
</apply>
</apply>
<ci>I</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>u_C</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>v</ci>
<ci>v_out_1</ci>
</apply>
<ci>v_out_2</ci>
</apply>
<ci>C</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u</ci>
<apply>
<plus/>
<ci>u_C</ci>
<apply>
<times/>
<ci>R_v</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>v</ci>
<ci>v_out_1</ci>
</apply>
<ci>v_out_2</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!-------------------------------------------------------------------------------//
-----------------------------------------------------------------------------//-->
<!-- Merging-->
<component name="vv_jII_type">
<variable name="t" public_interface="in" units="second"/>
<!-- Constitutive Parameters-->
<variable initial_value="0.004" name="mu" units="Js_per_m3"/>
<variable initial_value="1050" name="rho" units="Js2_per_m5"/>
<variable initial_value="9.81" name="g" units="m_per_s2"/>
<variable name="beta_g" public_interface="in" units="dimensionless"/>
<variable name="theta" public_interface="in" units="dimensionless"/>
<variable name="E" public_interface="in" units="J_per_m3"/>
<variable name="E_m" public_interface="out" units="J_per_m3"/>
<variable name="l" public_interface="in" units="metre"/>
<variable name="length" public_interface="out" units="metre"/>
<variable name="h" public_interface="out" units="metre"/>
<variable name="thickness" public_interface="out" units="metre"/>
<variable name="r" public_interface="in" units="metre"/>
<variable name="radius" public_interface="out" units="metre"/>
<variable name="I" public_interface="out" units="Js2_per_m6"/>
<variable name="C" public_interface="out" units="m6_per_J"/>
<variable name="R" public_interface="out" units="Js_per_m6"/>
<variable name="R_v" public_interface="out" units="Js_per_m6"/>
<variable initial_value="0.2802" name="a" units="dimensionless"/>
<variable initial_value="-505.3" name="b" units="per_m"/>
<variable initial_value="0.1324" name="c" units="dimensionless"/>
<variable initial_value="-11.14" name="d" units="per_m"/>
<!-- State Variables-->
<variable name="v_in_1" public_interface="in" units="m3_per_s"/>
<variable name="v_in_2" public_interface="in" units="m3_per_s"/>
<variable name="u" public_interface="out" units="J_per_m3"/>
<variable initial_value="0.0" name="u_C" public_interface="out" units="J_per_m3"/>
<variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
<variable name="u_d" public_interface="out" units="J_per_m3"/>
<variable initial_value="0.0" name="u_C_d" public_interface="out" units="J_per_m3"/>
<variable name="v_out_1" public_interface="in" units="m3_per_s"/>
<variable name="v_out_2" public_interface="in" units="m3_per_s"/>
<!-- Constitutive Relations-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>h</ci>
<apply>
<times/>
<ci>r</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>a</ci>
<apply>
<exp/>
<apply>
<times/>
<ci>b</ci>
<ci>r</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>c</ci>
<apply>
<exp/>
<apply>
<times/>
<ci>d</ci>
<ci>r</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>I</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>rho</ci>
<ci>l</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>C</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>l</ci>
</apply>
<apply>
<times/>
<ci>E</ci>
<ci>h</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">8</cn>
<ci>mu</ci>
<ci>l</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R_v</ci>
<apply>
<divide/>
<cn cellml:units="second">0.01</cn>
<ci>C</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>length</ci>
<ci>l</ci>
</apply>
<apply>
<eq/>
<ci>E_m</ci>
<ci>E</ci>
</apply>
<apply>
<eq/>
<ci>radius</ci>
<ci>r</ci>
</apply>
<apply>
<eq/>
<ci>thickness</ci>
<ci>h</ci>
</apply>
<!-- Conservation Laws-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>u</ci>
<ci>u_d</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>v</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_g</ci>
<ci>rho</ci>
<ci>g</ci>
<ci>l</ci>
<apply>
<cos/>
<apply>
<divide/>
<apply>
<times/>
<ci>theta</ci>
<pi/>
</apply>
<cn cellml:units="dimensionless">180</cn>
</apply>
</apply>
</apply>
</apply>
<ci>I</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>u_C</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>v_in_1</ci>
<ci>v_in_2</ci>
</apply>
<ci>v</ci>
</apply>
<apply>
<divide/>
<ci>C</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>u_C_d</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>v</ci>
<ci>v_out_1</ci>
</apply>
<ci>v_out_2</ci>
</apply>
<apply>
<divide/>
<ci>C</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u</ci>
<apply>
<plus/>
<ci>u_C</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>R_v</ci>
<apply>
<minus/>
<apply>
<plus/>
<ci>v_in_1</ci>
<ci>v_in_2</ci>
</apply>
<ci>v</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_d</ci>
<apply>
<plus/>
<ci>u_C_d</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>R_v</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>v</ci>
<ci>v_out_1</ci>
</apply>
<ci>v_out_2</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!-- Vein Merging-->
<component name="vp_jII_type">
<variable name="t" public_interface="in" units="second"/>
<!-- Constitutive Parameters-->
<variable initial_value="0.004" name="mu" units="Js_per_m3"/>
<variable initial_value="1050" name="rho" units="Js2_per_m5"/>
<variable initial_value="9.81" name="g" units="m_per_s2"/>
<variable name="beta_g" public_interface="in" units="dimensionless"/>
<variable name="theta" public_interface="in" units="dimensionless"/>
<variable name="E" public_interface="in" units="J_per_m3"/>
<variable name="E_m" public_interface="out" units="J_per_m3"/>
<variable name="l" public_interface="in" units="metre"/>
<variable name="length" public_interface="out" units="metre"/>
<variable name="h" public_interface="out" units="metre"/>
<variable name="thickness" public_interface="out" units="metre"/>
<variable name="r" public_interface="in" units="metre"/>
<variable name="radius" public_interface="out" units="metre"/>
<variable name="I" public_interface="out" units="Js2_per_m6"/>
<variable name="C" public_interface="out" units="m6_per_J"/>
<variable name="R" public_interface="out" units="Js_per_m6"/>
<variable name="R_v" public_interface="out" units="Js_per_m6"/>
<variable initial_value="0.2802" name="a" units="dimensionless"/>
<variable initial_value="-505.3" name="b" units="per_m"/>
<variable initial_value="0.1324" name="c" units="dimensionless"/>
<variable initial_value="-11.14" name="d" units="per_m"/>
<!-- State Variables-->
<variable name="v_in_1" public_interface="in" units="m3_per_s"/>
<variable name="v_in_2" public_interface="in" units="m3_per_s"/>
<variable name="u" public_interface="out" units="J_per_m3"/>
<variable initial_value="0.0" name="u_C" public_interface="out" units="J_per_m3"/>
<variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
<variable name="u_out" public_interface="in" units="J_per_m3"/>
<!-- Constitutive Relations-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>h</ci>
<apply>
<times/>
<ci>r</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>a</ci>
<apply>
<exp/>
<apply>
<times/>
<ci>b</ci>
<ci>r</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>c</ci>
<apply>
<exp/>
<apply>
<times/>
<ci>d</ci>
<ci>r</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>I</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>rho</ci>
<ci>l</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>C</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>l</ci>
</apply>
<apply>
<times/>
<ci>E</ci>
<ci>h</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">8</cn>
<ci>mu</ci>
<ci>l</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R_v</ci>
<apply>
<divide/>
<cn cellml:units="second">0.01</cn>
<ci>C</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>length</ci>
<ci>l</ci>
</apply>
<apply>
<eq/>
<ci>E_m</ci>
<ci>E</ci>
</apply>
<apply>
<eq/>
<ci>radius</ci>
<ci>r</ci>
</apply>
<apply>
<eq/>
<ci>thickness</ci>
<ci>h</ci>
</apply>
<!-- Conservation Laws-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>u</ci>
<ci>u_out</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>v</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_g</ci>
<ci>rho</ci>
<ci>g</ci>
<ci>l</ci>
<apply>
<cos/>
<apply>
<divide/>
<apply>
<times/>
<ci>theta</ci>
<pi/>
</apply>
<cn cellml:units="dimensionless">180</cn>
</apply>
</apply>
</apply>
</apply>
<ci>I</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>u_C</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>v_in_1</ci>
<ci>v_in_2</ci>
</apply>
<ci>v</ci>
</apply>
<ci>C</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u</ci>
<apply>
<plus/>
<ci>u_C</ci>
<apply>
<times/>
<ci>R_v</ci>
<apply>
<minus/>
<apply>
<plus/>
<ci>v_in_1</ci>
<ci>v_in_2</ci>
</apply>
<ci>v</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
</model>