Location: Cardiovascular Circulation @ d0d05dca8689 / Mynard_Smolich_myocardium (copy).cellml

Author:
Soroush <ssaf006@aucklanduni.ac.nz>
Date:
2021-12-09 13:57:24+13:00
Desc:
changed the valve
Permanent Source URI:
https://models.cellml.org/workspace/4ac/rawfile/d0d05dca86894705e03d7bad752782f5354d166a/Mynard_Smolich_myocardium (copy).cellml

<?xml version='1.0' encoding='UTF-8'?>
<model name="Mynard_Smolich_myocardium" 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="m3_per_s2" units_ref="m3_per_s2"/>
        <units name="m6_per_J" units_ref="m6_per_J"/>
        <units name="per_m" units_ref="per_m"/>
        <units name="J_per_m3" units_ref="J_per_m3"/>
        <units name="J_per_m3_s" units_ref="J_per_m3_s"/>
        <units name="Js_per_m6" units_ref="Js_per_m6"/>
        <units name="Js2_per_m6" units_ref="Js2_per_m6"/>
        <units name="Js2_per_m5" units_ref="Js2_per_m5"/>
        <units name="J_per_s" units_ref="J_per_s"/>
        <units name="J_per_m6" units_ref="J_per_m6"/>
        <units name="Js_per_m3" units_ref="Js_per_m3"/>
        <units name="UnitValve" units_ref="UnitValve"/>
    </import>
    <component name="main">
        <variable initial_value="0.0" name="t" public_interface="in" units="second"/>
        <!-- Input pressures-->
        <variable name="P_in" public_interface="in" units="J_per_m3"/>
        <!--var P_in: J_per_m3 {init: 13300};-->
        <variable initial_value="65000" name="P_LV" units="J_per_m3"/>
        <variable initial_value="10" name="dPdT" units="J_per_m3_s"/>
        <variable initial_value="666.7" name="P_RA" units="J_per_m3"/>
        <!-- Computed intratissue pressures definitions-->
        <variable name="P_im1" units="J_per_m3"/>
        <variable name="P_im2" units="J_per_m3"/>
        <variable name="P_im3" units="J_per_m3"/>
        <variable name="dPim1_dt" units="J_per_m3_s"/>
        <variable name="dPim2_dt" units="J_per_m3_s"/>
        <variable name="dPim3_dt" units="J_per_m3_s"/>
        <!-- Parameters-->
        <variable initial_value="3.2503e-12" name="C_PA" units="m6_per_J"/>
        <variable initial_value="2.6664e8" name="L_PA" units="Js2_per_m6"/>
        <variable initial_value="5.3328e8" name="R_PA" units="Js_per_m6"/>
        <variable initial_value="2.6664e8" name="R_PV" units="Js_per_m6"/>
        <variable initial_value="6.3506e-11" name="C_PV" units="m6_per_J"/>
        <variable initial_value="5.8661e+09" name="R0m" units="Js_per_m6"/>
        <variable initial_value="7.0393e+09" name="R01" units="Js_per_m6"/>
        <variable initial_value="2.9330e+09" name="R02" units="Js_per_m6"/>
        <variable initial_value="2.7778e-07" name="V01" units="m3"/>
        <variable initial_value="8.8889e-07" name="V02" units="m3"/>
        <variable initial_value="1.0834e-11" name="C1" units="m6_per_J"/>
        <variable initial_value="2.1169e-10" name="C2" units="m6_per_J"/>
        <variable initial_value="0.75" name="gamma" units="dimensionless"/>
        <variable initial_value="0.55" name="cf1" units="dimensionless"/>
        <variable initial_value="1.28" name="rf1" units="dimensionless"/>
        <variable initial_value="0.68" name="cf2" units="dimensionless"/>
        <variable initial_value="1.12" name="rf2" units="dimensionless"/>
        <!-- State variables definitions-->
        <variable initial_value="100" name="P_PA" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0" name="Q_PA" public_interface="out" units="m3_per_s"/>
        <variable initial_value="100" name="P11" units="J_per_m3"/>
        <variable initial_value="100" name="P21" units="J_per_m3"/>
        <variable initial_value="100" name="P12" units="J_per_m3"/>
        <variable initial_value="100" name="P22" units="J_per_m3"/>
        <variable initial_value="100" name="P13" units="J_per_m3"/>
        <variable initial_value="100" name="P23" units="J_per_m3"/>
        <variable initial_value="100" name="P_PV" units="J_per_m3"/>
        <!-- Intermediate variables definitions-->
        <variable name="V11" units="m3"/>
        <variable name="V21" units="m3"/>
        <variable name="R11" units="Js_per_m6"/>
        <variable name="R21" units="Js_per_m6"/>
        <variable name="Rm1" units="Js_per_m6"/>
        <variable name="Q11" units="m3_per_s"/>
        <variable name="Qm1" units="m3_per_s"/>
        <variable name="Q21" units="m3_per_s"/>
        <variable name="V12" units="m3"/>
        <variable name="V22" units="m3"/>
        <variable name="R12" units="Js_per_m6"/>
        <variable name="R22" units="Js_per_m6"/>
        <variable name="Rm2" units="Js_per_m6"/>
        <variable name="Q12" units="m3_per_s"/>
        <variable name="Qm2" units="m3_per_s"/>
        <variable name="Q22" units="m3_per_s"/>
        <variable name="V13" units="m3"/>
        <variable name="V23" units="m3"/>
        <variable name="R13" units="Js_per_m6"/>
        <variable name="R23" units="Js_per_m6"/>
        <variable name="Rm3" units="Js_per_m6"/>
        <variable name="Q13" units="m3_per_s"/>
        <variable name="Qm3" units="m3_per_s"/>
        <variable name="Q23" units="m3_per_s"/>
        <variable name="Q_ima" units="m3_per_s"/>
        <variable name="Q_imv" units="m3_per_s"/>
        <variable name="Q_out" units="m3_per_s"/>
        <!-- Computed intratissue pressures calculations-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>P_im1</ci>
                <apply>
                    <times/>
                    <cn cellml:units="dimensionless">1.2</cn>
                    <cn cellml:units="dimensionless">0.167</cn>
                    <ci>P_LV</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>P_im2</ci>
                <apply>
                    <times/>
                    <cn cellml:units="dimensionless">1.2</cn>
                    <cn cellml:units="dimensionless">0.500</cn>
                    <ci>P_LV</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>P_im3</ci>
                <apply>
                    <times/>
                    <cn cellml:units="dimensionless">1.2</cn>
                    <cn cellml:units="dimensionless">0.833</cn>
                    <ci>P_LV</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>dPim1_dt</ci>
                <apply>
                    <times/>
                    <cn cellml:units="dimensionless">1.2</cn>
                    <cn cellml:units="dimensionless">0.167</cn>
                    <ci>dPdT</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>dPim2_dt</ci>
                <apply>
                    <times/>
                    <cn cellml:units="dimensionless">1.2</cn>
                    <cn cellml:units="dimensionless">0.500</cn>
                    <ci>dPdT</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>dPim3_dt</ci>
                <apply>
                    <times/>
                    <cn cellml:units="dimensionless">1.2</cn>
                    <cn cellml:units="dimensionless">0.833</cn>
                    <ci>dPdT</ci>
                </apply>
            </apply>
            <!-- Intermediate variables calculations-->
            <apply>
                <eq/>
                <ci>V11</ci>
                <apply>
                    <times/>
                    <ci>cf1</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <ci>P11</ci>
                                <ci>P_im1</ci>
                            </apply>
                            <ci>C1</ci>
                        </apply>
                        <ci>V01</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>V21</ci>
                <apply>
                    <times/>
                    <ci>cf1</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <ci>P21</ci>
                                <ci>P_im1</ci>
                            </apply>
                            <ci>C2</ci>
                        </apply>
                        <ci>V02</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R11</ci>
                <apply>
                    <times/>
                    <ci>rf1</ci>
                    <ci>R01</ci>
                    <apply>
                        <power/>
                        <apply>
                            <divide/>
                            <ci>V01</ci>
                            <ci>V11</ci>
                        </apply>
                        <cn cellml:units="dimensionless">2</cn>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R21</ci>
                <apply>
                    <times/>
                    <ci>rf1</ci>
                    <ci>R02</ci>
                    <apply>
                        <power/>
                        <apply>
                            <divide/>
                            <ci>V02</ci>
                            <ci>V21</ci>
                        </apply>
                        <cn cellml:units="dimensionless">2</cn>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Rm1</ci>
                <apply>
                    <times/>
                    <ci>R0m</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>gamma</ci>
                                <ci>R11</ci>
                            </apply>
                            <ci>R01</ci>
                        </apply>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <apply>
                                    <minus/>
                                    <cn cellml:units="dimensionless">1</cn>
                                    <ci>gamma</ci>
                                </apply>
                                <ci>R21</ci>
                            </apply>
                            <ci>R02</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Q11</ci>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>P_PA</ci>
                        <ci>P11</ci>
                    </apply>
                    <ci>R11</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Qm1</ci>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>P11</ci>
                        <ci>P21</ci>
                    </apply>
                    <ci>Rm1</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Q21</ci>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>P21</ci>
                        <ci>P_PV</ci>
                    </apply>
                    <ci>R21</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>V12</ci>
                <apply>
                    <times/>
                    <ci>cf2</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <ci>P12</ci>
                                <ci>P_im2</ci>
                            </apply>
                            <ci>C1</ci>
                        </apply>
                        <ci>V01</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>V22</ci>
                <apply>
                    <times/>
                    <ci>cf2</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <ci>P22</ci>
                                <ci>P_im2</ci>
                            </apply>
                            <ci>C2</ci>
                        </apply>
                        <ci>V02</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R12</ci>
                <apply>
                    <times/>
                    <ci>rf2</ci>
                    <ci>R01</ci>
                    <apply>
                        <power/>
                        <apply>
                            <divide/>
                            <ci>V01</ci>
                            <ci>V12</ci>
                        </apply>
                        <cn cellml:units="dimensionless">2</cn>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R22</ci>
                <apply>
                    <times/>
                    <ci>rf2</ci>
                    <ci>R02</ci>
                    <apply>
                        <power/>
                        <apply>
                            <divide/>
                            <ci>V02</ci>
                            <ci>V22</ci>
                        </apply>
                        <cn cellml:units="dimensionless">2</cn>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Rm2</ci>
                <apply>
                    <times/>
                    <ci>R0m</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>gamma</ci>
                                <ci>R12</ci>
                            </apply>
                            <ci>R01</ci>
                        </apply>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <apply>
                                    <minus/>
                                    <cn cellml:units="dimensionless">1</cn>
                                    <ci>gamma</ci>
                                </apply>
                                <ci>R22</ci>
                            </apply>
                            <ci>R02</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Q12</ci>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>P_PA</ci>
                        <ci>P12</ci>
                    </apply>
                    <ci>R12</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Qm2</ci>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>P12</ci>
                        <ci>P22</ci>
                    </apply>
                    <ci>Rm2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Q22</ci>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>P22</ci>
                        <ci>P_PV</ci>
                    </apply>
                    <ci>R22</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>V13</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <ci>P13</ci>
                            <ci>P_im3</ci>
                        </apply>
                        <ci>C1</ci>
                    </apply>
                    <ci>V01</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>V23</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <ci>P23</ci>
                            <ci>P_im3</ci>
                        </apply>
                        <ci>C2</ci>
                    </apply>
                    <ci>V02</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R13</ci>
                <apply>
                    <times/>
                    <ci>R01</ci>
                    <apply>
                        <power/>
                        <apply>
                            <divide/>
                            <ci>V01</ci>
                            <ci>V13</ci>
                        </apply>
                        <cn cellml:units="dimensionless">2</cn>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R23</ci>
                <apply>
                    <times/>
                    <ci>R02</ci>
                    <apply>
                        <power/>
                        <apply>
                            <divide/>
                            <ci>V02</ci>
                            <ci>V23</ci>
                        </apply>
                        <cn cellml:units="dimensionless">2</cn>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Rm3</ci>
                <apply>
                    <times/>
                    <ci>R0m</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>gamma</ci>
                                <ci>R13</ci>
                            </apply>
                            <ci>R01</ci>
                        </apply>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <apply>
                                    <minus/>
                                    <cn cellml:units="dimensionless">1</cn>
                                    <ci>gamma</ci>
                                </apply>
                                <ci>R23</ci>
                            </apply>
                            <ci>R02</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Q13</ci>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>P_PA</ci>
                        <ci>P13</ci>
                    </apply>
                    <ci>R13</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Qm3</ci>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>P13</ci>
                        <ci>P23</ci>
                    </apply>
                    <ci>Rm3</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Q23</ci>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>P23</ci>
                        <ci>P_PV</ci>
                    </apply>
                    <ci>R23</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Q_ima</ci>
                <apply>
                    <plus/>
                    <ci>Q11</ci>
                    <ci>Q12</ci>
                    <ci>Q13</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Q_imv</ci>
                <apply>
                    <plus/>
                    <ci>Q21</ci>
                    <ci>Q22</ci>
                    <ci>Q23</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Q_out</ci>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>P_PV</ci>
                        <ci>P_RA</ci>
                    </apply>
                    <ci>R_PV</ci>
                </apply>
            </apply>
            <!-- These are the ODEs        -->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>P_PA</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>Q_PA</ci>
                        <ci>Q_ima</ci>
                    </apply>
                    <ci>C_PA</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>Q_PA</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>P_in</ci>
                            <ci>P_PA</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>Q_PA</ci>
                            <ci>R_PA</ci>
                        </apply>
                    </apply>
                    <ci>L_PA</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>P11</ci>
                </apply>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <apply>
                            <minus/>
                            <ci>Q11</ci>
                            <ci>Qm1</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>cf1</ci>
                            <ci>C1</ci>
                        </apply>
                    </apply>
                    <ci>dPim1_dt</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>P21</ci>
                </apply>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <apply>
                            <minus/>
                            <ci>Qm1</ci>
                            <ci>Q21</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>cf1</ci>
                            <ci>C2</ci>
                        </apply>
                    </apply>
                    <ci>dPim1_dt</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>P12</ci>
                </apply>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <apply>
                            <minus/>
                            <ci>Q12</ci>
                            <ci>Qm2</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>cf2</ci>
                            <ci>C1</ci>
                        </apply>
                    </apply>
                    <ci>dPim2_dt</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>P22</ci>
                </apply>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <apply>
                            <minus/>
                            <ci>Qm2</ci>
                            <ci>Q22</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>cf2</ci>
                            <ci>C2</ci>
                        </apply>
                    </apply>
                    <ci>dPim2_dt</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>P13</ci>
                </apply>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <apply>
                            <minus/>
                            <ci>Q13</ci>
                            <ci>Qm3</ci>
                        </apply>
                        <ci>C1</ci>
                    </apply>
                    <ci>dPim3_dt</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>P23</ci>
                </apply>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <apply>
                            <minus/>
                            <ci>Qm3</ci>
                            <ci>Q23</ci>
                        </apply>
                        <ci>C2</ci>
                    </apply>
                    <ci>dPim3_dt</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>P_PV</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>Q_imv</ci>
                        <ci>Q_out</ci>
                    </apply>
                    <ci>C_PV</ci>
                </apply>
            </apply>
        </math>
    </component>
</model>