Location: BondGraph Basic @ ce87545e174b / BG Tutorial Fluid Systems / Circuation.cellml

Author:
Soroush Safaei <ssaf006@aucklanduni.ac.nz>
Date:
2017-08-15 18:22:15+12:00
Desc:
Adding the systemic circulation model
Permanent Source URI:
https://models.fieldml.org/workspace/43b/rawfile/ce87545e174bd4b8e9daf7f25f6298119f6d2220/BG Tutorial Fluid Systems/Circuation.cellml

<?xml version='1.0'?>
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    <units name="UnitP">
        <unit multiplier="133" units="pascal"/>
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        <unit exponent="-1" units="second"/>
    </units>
    <units name="UnitR">
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        <unit exponent="-1" units="UnitQ"/>
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    <units name="UnitC">
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        <unit units="UnitV"/>
    </units>
    <units name="UnitCV">
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        <unit exponent="-0.5" units="UnitP"/>
    </units>
    <units name="UnitL">
        <unit units="UnitP"/>
        <unit exponent="-1" units="UnitQ"/>
        <unit units="second"/>
    </units>
    <units name="UnitE">
        <unit units="UnitP"/>
        <unit exponent="-1" units="UnitV"/>
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    <units name="UnitV">
        <unit multiplier="0.001" units="litre"/>
    </units>
    <component name="main">
        <variable name="t" public_interface="out" units="second"/>
        <variable initial_value="1.0" name="T" units="second"/>
        <variable name="mt" units="second"/>
        <variable name="et_a" units="dimensionless"/>
        <variable name="et_v" units="dimensionless"/>
        <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="400" name="CV_ti" units="UnitCV"/>
        <variable initial_value="350" name="CV_pa" units="UnitCV"/>
        <variable initial_value="400" name="CV_mi" units="UnitCV"/>
        <variable initial_value="350" name="CV_ao" units="UnitCV"/>
        <variable name="E_lv" units="UnitE"/>
        <variable initial_value="2.5" name="E_lv_Max" units="UnitE"/>
        <variable initial_value="0.1" name="E_lv_Min" units="UnitE"/>
        <variable name="E_la" units="UnitE"/>
        <variable initial_value="0.25" name="E_la_Max" units="UnitE"/>
        <variable initial_value="0.15" name="E_la_Min" units="UnitE"/>
        <variable name="E_rv" units="UnitE"/>
        <variable initial_value="1.15" name="E_rv_Max" units="UnitE"/>
        <variable initial_value="0.1" name="E_rv_Min" units="UnitE"/>
        <variable name="E_ra" units="UnitE"/>
        <variable initial_value="0.25" name="E_ra_Max" units="UnitE"/>
        <variable initial_value="0.15" name="E_ra_Min" units="UnitE"/>
        <!-- parameters systemic-->
        <variable initial_value="0.003" name="R_sas" units="UnitR"/>
        <variable initial_value="0.05" name="R_sat" units="UnitR"/>
        <variable initial_value="0.5" name="R_sar" units="UnitR"/>
        <variable initial_value="0.52" name="R_scp" units="UnitR"/>
        <variable initial_value="0.075" name="R_svn" units="UnitR"/>
        <variable initial_value="0.002" name="R_pas" units="UnitR"/>
        <variable initial_value="0.01" name="R_pat" units="UnitR"/>
        <variable initial_value="0.05" name="R_par" units="UnitR"/>
        <variable initial_value="0.25" name="R_pcp" units="UnitR"/>
        <variable initial_value="0.0006" name="R_pvn" units="UnitR"/>
        <variable initial_value="0.000062" name="L_sas" units="UnitL"/>
        <variable initial_value="0.0017" name="L_sat" units="UnitL"/>
        <variable initial_value="0.000052" name="L_pas" units="UnitL"/>
        <variable initial_value="0.0017" name="L_pat" units="UnitL"/>
        <variable initial_value="0.08" name="C_sas" units="UnitC"/>
        <variable initial_value="1.6" name="C_sat" units="UnitC"/>
        <variable initial_value="20.5" name="C_svn" units="UnitC"/>
        <variable initial_value="0.18" name="C_pas" units="UnitC"/>
        <variable initial_value="3.8" name="C_pat" units="UnitC"/>
        <variable initial_value="20.5" name="C_pvn" units="UnitC"/>
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        <variable initial_value="30" name="u_pat" units="UnitP"/>
        <variable initial_value="0" name="u_pvn" units="UnitP"/>
        <variable initial_value="100" name="u_sas" units="UnitP"/>
        <variable initial_value="100" name="u_sat" units="UnitP"/>
        <variable initial_value="0" name="u_svn" units="UnitP"/>
        <variable name="u_ra" units="UnitP"/>
        <variable name="u_rv" units="UnitP"/>
        <variable name="u_la" units="UnitP"/>
        <variable name="u_lv" units="UnitP"/>
        <variable initial_value="1.0" name="u_ra_ini" units="UnitP"/>
        <variable initial_value="1.0" name="u_rv_ini" units="UnitP"/>
        <variable initial_value="1.0" name="u_la_ini" units="UnitP"/>
        <variable initial_value="1.0" name="u_lv_ini" units="UnitP"/>
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        <variable initial_value="0" name="v_pat" units="UnitQ"/>
        <variable name="v_pvn" units="UnitQ"/>
        <variable initial_value="0" name="v_sas" units="UnitQ"/>
        <variable initial_value="0" name="v_sat" units="UnitQ"/>
        <variable name="v_svn" units="UnitQ"/>
        <variable name="v_ti" units="UnitQ"/>
        <variable name="v_pa" units="UnitQ"/>
        <variable name="v_mi" units="UnitQ"/>
        <variable name="v_ao" units="UnitQ"/>
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        <variable initial_value="20" name="q_la" units="UnitV"/>
        <variable initial_value="500" name="q_lv" units="UnitV"/>
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        <variable initial_value="10.0" name="q_rv_ini" units="UnitV"/>
        <variable initial_value="4.0" name="q_la_ini" units="UnitV"/>
        <variable initial_value="5.0" name="q_lv_ini" units="UnitV"/>
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                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
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                    <divide/>
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                        <minus/>
                        <ci>v_pa</ci>
                        <ci>v_pas</ci>
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                    <ci>C_pas</ci>
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            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
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                    <divide/>
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                    <ci>C_pat</ci>
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            <apply>
                <eq/>
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                    <diff/>
                    <bvar>
                        <ci>t</ci>
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                    <divide/>
                    <apply>
                        <minus/>
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                <eq/>
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                        <ci>t</ci>
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                        <ci>v_sas</ci>
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                    <ci>C_sas</ci>
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                <eq/>
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                        <ci>t</ci>
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                    <divide/>
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                        <minus/>
                        <ci>v_sas</ci>
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                    <ci>C_sat</ci>
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                <eq/>
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                        <ci>t</ci>
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                    <divide/>
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                        <minus/>
                        <ci>v_sat</ci>
                        <ci>v_svn</ci>
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                    <ci>C_svn</ci>
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            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
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                    <ci>v_pas</ci>
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                <apply>
                    <divide/>
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                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u_pas</ci>
                            <ci>u_pat</ci>
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                        <apply>
                            <times/>
                            <ci>v_pas</ci>
                            <ci>R_pas</ci>
                        </apply>
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                    <ci>L_pas</ci>
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            <apply>
                <eq/>
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                    <divide/>
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                        <minus/>
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                            <apply>
                                <minus/>
                                <apply>
                                    <minus/>
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                                    <times/>
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                            <apply>
                                <times/>
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                            <times/>
                            <ci>v_pat</ci>
                            <ci>R_par</ci>
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                    <ci>L_pat</ci>
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            <apply>
                <eq/>
                <ci>v_pvn</ci>
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                    <divide/>
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                        <minus/>
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                        <ci>u_la</ci>
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            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_sas</ci>
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                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u_sas</ci>
                            <ci>u_sat</ci>
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                        <apply>
                            <times/>
                            <ci>v_sas</ci>
                            <ci>R_sas</ci>
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            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
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                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <apply>
                                    <minus/>
                                    <ci>u_sat</ci>
                                    <ci>u_svn</ci>
                                </apply>
                                <apply>
                                    <times/>
                                    <ci>v_sat</ci>
                                    <ci>R_sat</ci>
                                </apply>
                            </apply>
                            <apply>
                                <times/>
                                <ci>v_sat</ci>
                                <ci>R_scp</ci>
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                        <apply>
                            <times/>
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                            <ci>R_sar</ci>
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                    <ci>L_sat</ci>
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                <eq/>
                <ci>v_svn</ci>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>u_svn</ci>
                        <ci>u_ra</ci>
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                    <ci>R_svn</ci>
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                            <floor/>
                            <apply>
                                <divide/>
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                                <ci>T</ci>
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            <!-- Heart Flow-->
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                            <times/>
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                                    <apply>
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                                        <ci>u_rv</ci>
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                            <ci>u_rv</ci>
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                            <lt/>
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                            <ci>u_rv</ci>
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                <ci>v_pa</ci>
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                        <apply>
                            <times/>
                            <ci>CV_pa</ci>
                            <apply>
                                <root/>
                                <apply>
                                    <abs/>
                                    <apply>
                                        <minus/>
                                        <ci>u_rv</ci>
                                        <ci>u_pas</ci>
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                            <ci>u_pas</ci>
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                            <ci>u_pas</ci>
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                        <apply>
                            <times/>
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                            <apply>
                                <root/>
                                <apply>
                                    <abs/>
                                    <apply>
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                                        <ci>u_lv</ci>
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                            <geq/>
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                            <ci>u_lv</ci>
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                            <lt/>
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                            <ci>u_lv</ci>
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                <eq/>
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                            <times/>
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                            <apply>
                                <root/>
                                <apply>
                                    <abs/>
                                    <apply>
                                        <minus/>
                                        <ci>u_lv</ci>
                                        <ci>u_sas</ci>
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                            <geq/>
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                            <ci>u_sas</ci>
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                            <lt/>
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                <eq/>
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                    <diff/>
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                <eq/>
                <apply>
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                <eq/>
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                                    <divide/>
                                    <apply>
                                        <times/>
                                        <cn cellml:units="radian">3.14159</cn>
                                        <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/>
                                        <cn cellml:units="radian">3.14159</cn>
                                        <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>
        </math>
    </component>
</model>