Location: Diabetes @ 825df3f39a72 / BondGraph / UoC.cellml

Author:
Soroush <ssaf006@aucklanduni.ac.nz>
Date:
2018-06-07 18:09:31+12:00
Desc:
asd
Permanent Source URI:
https://models.physiomeproject.org/workspace/483/rawfile/825df3f39a72b546827370455ce78eeb605703b1/BondGraph/UoC.cellml

<?xml version='1.0'?>
<model name="main1" 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-min.cellml">
        <units name="minute" units_ref="minute"/>
        <units name="mmol" units_ref="mmol"/>
        <units name="mmol_per_min" units_ref="mmol_per_min"/>
        <units name="mmol_per_min_kg" units_ref="mmol_per_min_kg"/>
        <units name="mM" units_ref="mM"/>
        <units name="mM_per_min" units_ref="mM_per_min"/>
        <units name="per_mM_min" units_ref="per_mM_min"/>
        <units name="per_mM" units_ref="per_mM"/>
        <units name="per_min" units_ref="per_min"/>
        <units name="l_per_kg" units_ref="l_per_kg"/>
    </import>
    <component name="environment">
        <variable name="time" public_interface="out" units="minute"/>
    </component>
    <component name="state">
        <variable name="t" public_interface="in" units="minute"/>
        <!-- State variables-->
        <!-- q_G: blood glucose
 q_I: plasma insulin
 q_Q: peripheral insulin
 p_G: kidney extraction
 CNS: central nervous system uptake
 S_I: insulin sensitivity
 EGP: endogenous glucose production
 P_ex: glucose exogenous input
 V_G: volume of distribution of glucose in plasma
 V_P: blood plasma volume - distribution of plasma insulin
 V_Q: interstitial fluid volume - distribution of peripheral insulin
 alpha_G: saturation of insulin mediated glucose uptake parameter
 x_L: hepatic secretion of insulin
 n_L: rate constant of insulin clearance through blood
 alpha_I: hepatic clearance parameter
 n_K: kidney clearance of insulin
 n_I: insulin diffusion between plasma and periphery
 n_c: insulin degradation by cell rate constant
 u_en: insulin secretion
 u_ex: delivered insulin exogenously-->
        <variable initial_value="0.0" name="q_G" public_interface="out" units="mM"/>
        <variable initial_value="0.0" name="q_Q" public_interface="out" units="mM"/>
        <variable initial_value="0.0" name="q_I" public_interface="out" units="mM"/>
        <variable initial_value="0.003" name="p_G" public_interface="out" units="per_min"/>
        <variable initial_value="0.033" name="EGP" public_interface="out" units="mmol_per_min_kg"/>
        <variable initial_value="0.0104" name="P_ex" public_interface="out" units="mmol_per_min"/>
        <variable initial_value="0.088" name="CNS" public_interface="out" units="mmol_per_min_kg"/>
        <variable initial_value="0.0" name="u_ex" public_interface="out" units="mmol_per_min"/>
        <variable name="u_en" units="mM_per_min"/>
        <variable initial_value="0.75" name="m_body" public_interface="out" units="kilogram"/>
        <variable name="m_brain" units="kilogram"/>
        <variable initial_value="0.045" name="V_P" public_interface="out" units="l_per_kg"/>
        <variable initial_value="0.289" name="V_Q" public_interface="out" units="l_per_kg"/>
        <variable initial_value="0.56" name="V_G_frac" public_interface="out" units="l_per_kg"/>
        <variable initial_value="0.67" name="x_L" public_interface="out" units="dimensionless"/>
        <variable initial_value="1e-7" name="S_I" public_interface="out" units="per_mM_min"/>
        <variable initial_value="0.0258" name="n_c" public_interface="out" units="per_min"/>
        <variable initial_value="0.034" name="n_K" public_interface="out" units="per_min"/>
        <variable initial_value="0.025" name="n_I" public_interface="out" units="per_min"/>
        <variable initial_value="0.39" name="n_L" public_interface="out" units="per_min"/>
        <variable initial_value="0.0" name="alpha_G" public_interface="out" units="per_mM"/>
        <variable initial_value="0.0017" name="alpha_I" public_interface="out" units="per_mM"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>m_brain</ci>
                <apply>
                    <times/>
                    <cn cellml:units="dimensionless">0.14</cn>
                    <ci>m_body</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_en</ci>
                <piecewise>
                    <piece>
                        <apply>
                            <plus/>
                            <apply>
                                <minus/>
                                <cn cellml:units="mM_per_min">1.5</cn>
                            </apply>
                            <apply>
                                <times/>
                                <cn cellml:units="per_min">1.9</cn>
                                <ci>q_G</ci>
                            </apply>
                        </apply>
                        <apply>
                            <gt/>
                            <apply>
                                <plus/>
                                <apply>
                                    <minus/>
                                    <cn cellml:units="mM_per_min">1.5</cn>
                                </apply>
                                <apply>
                                    <times/>
                                    <cn cellml:units="per_min">1.9</cn>
                                    <ci>q_G</ci>
                                </apply>
                            </apply>
                            <cn cellml:units="mM_per_min">4.2</cn>
                        </apply>
                    </piece>
                    <piece>
                        <cn cellml:units="mM_per_min">4.2</cn>
                        <apply>
                            <leq/>
                            <apply>
                                <plus/>
                                <apply>
                                    <minus/>
                                    <cn cellml:units="mM_per_min">1.5</cn>
                                </apply>
                                <apply>
                                    <times/>
                                    <cn cellml:units="per_min">1.9</cn>
                                    <ci>q_G</ci>
                                </apply>
                            </apply>
                            <cn cellml:units="mM_per_min">4.2</cn>
                        </apply>
                    </piece>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_G</ci>
                </apply>
                <apply>
                    <plus/>
                    <apply>
                        <minus/>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <ci>p_G</ci>
                            </apply>
                            <ci>q_G</ci>
                        </apply>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>S_I</ci>
                                <ci>q_G</ci>
                                <ci>q_Q</ci>
                            </apply>
                            <apply>
                                <plus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <apply>
                                    <times/>
                                    <ci>alpha_G</ci>
                                    <ci>q_Q</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <divide/>
                        <apply>
                            <minus/>
                            <apply>
                                <plus/>
                                <ci>P_ex</ci>
                                <apply>
                                    <times/>
                                    <ci>EGP</ci>
                                    <ci>m_body</ci>
                                </apply>
                            </apply>
                            <apply>
                                <times/>
                                <ci>CNS</ci>
                                <ci>m_brain</ci>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>V_G_frac</ci>
                            <ci>m_body</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_I</ci>
                </apply>
                <apply>
                    <plus/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <apply>
                                <divide/>
                                <apply>
                                    <times/>
                                    <apply>
                                        <minus/>
                                        <ci>n_L</ci>
                                    </apply>
                                    <ci>q_I</ci>
                                </apply>
                                <apply>
                                    <plus/>
                                    <cn cellml:units="dimensionless">1</cn>
                                    <apply>
                                        <times/>
                                        <ci>alpha_I</ci>
                                        <ci>q_I</ci>
                                    </apply>
                                </apply>
                            </apply>
                            <apply>
                                <times/>
                                <ci>n_K</ci>
                                <ci>q_I</ci>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>n_I</ci>
                            <apply>
                                <minus/>
                                <ci>q_I</ci>
                                <ci>q_Q</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <divide/>
                        <ci>u_ex</ci>
                        <apply>
                            <times/>
                            <ci>V_P</ci>
                            <ci>m_body</ci>
                        </apply>
                    </apply>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">1</cn>
                            <ci>x_L</ci>
                        </apply>
                        <ci>u_en</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_Q</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <times/>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>n_I</ci>
                                <ci>V_P</ci>
                            </apply>
                            <ci>V_Q</ci>
                        </apply>
                        <apply>
                            <minus/>
                            <ci>q_I</ci>
                            <ci>q_Q</ci>
                        </apply>
                    </apply>
                    <apply>
                        <divide/>
                        <apply>
                            <times/>
                            <ci>n_c</ci>
                            <ci>q_Q</ci>
                        </apply>
                        <apply>
                            <plus/>
                            <cn cellml:units="dimensionless">1</cn>
                            <apply>
                                <times/>
                                <ci>alpha_G</ci>
                                <ci>q_Q</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <connection>
        <map_components component_1="environment" component_2="state"/>
        <map_variables variable_1="time" variable_2="t"/>
    </connection>
</model>