Location: Diabetes @ d8d113844ef7 / Original / 1-WholeBodyLevel.cellml

Author:
Soroush Safaei <ssaf006@aucklanduni.ac.nz>
Date:
2018-05-23 18:24:20+12:00
Desc:
finishing the BG model
Permanent Source URI:
https://models.physiomeproject.org/workspace/483/rawfile/d8d113844ef7bafbac5f25cf2c8fa89875c0297e/Original/1-WholeBodyLevel.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">
    <!-- in:  
 out: INS,G_t,vglucoseuptake-->
    <import xlink:href="Units-min.cellml">
        <units name="minute" units_ref="minute"/>
        <units name="l_per_kg" units_ref="l_per_kg"/>
        <units name="dl_per_kg" units_ref="dl_per_kg"/>
        <units name="per_minute" units_ref="per_minute"/>
        <units name="minute_kg_per_pmol" units_ref="minute_kg_per_pmol"/>
        <units name="mg" units_ref="mg"/>
        <units name="per_mg" units_ref="per_mg"/>
        <units name="mg_per_kg_minute" units_ref="mg_per_kg_minute"/>
        <units name="mg_l_per_kg_minute_pmol" units_ref="mg_l_per_kg_minute_pmol"/>
        <units name="mg_per_minute_pmol" units_ref="mg_per_minute_pmol"/>
        <units name="mg_per_kg" units_ref="mg_per_kg"/>
        <units name="pmol_dl_per_kg_mg" units_ref="pmol_dl_per_kg_mg"/>
        <units name="pmol_dl_per_kg_mg_minute" units_ref="pmol_dl_per_kg_mg_minute"/>
        <units name="pmol_per_kg" units_ref="pmol_per_kg"/>
        <units name="pmol_per_l" units_ref="pmol_per_l"/>
        <units name="mg_per_dl" units_ref="mg_per_dl"/>
        <units name="pmol_per_kg_minute" units_ref="pmol_per_kg_minute"/>
        <units name="l_per_mol_minute" units_ref="l_per_mol_minute"/>
        <units name="mol_per_l" units_ref="mol_per_l"/>
    </import>
    <import xlink:href="Parameters-min.cellml">
        <component component_ref="param1" name="param"/>
    </import>
    <component name="environment">
        <variable name="time" public_interface="out" units="minute"/>
    </component>
    <component name="state">
        <variable name="t" public_interface="in" units="minute"/>
        <!-- Parameters-->
        <!-- V_G: distribution volume of Glucose
 k_1: rate parameter
 k_2: rate parameter
 k_p1: extrapolated EGP at zero Glucose and Insulin
 k_p2: liver Glucose effectiveness
 k_p3: amplitude of insulin action on liver
 k_p4: amplitude of portal Insulin action on liver
 k_i:  delay between Insulin signal and Insulin action
 k_abs: rate of intestinal absorption
 k_gri: rate of grinding
 f: fraction of intestinal absorption appears in plasma
 BW: body weight
 D: ingested Glucose mass
 p_2U: rate constant of Insulin action on the peripheral Glucose utilisation
 V_I: distribution volume of Insulin
 gamma: transfer rate constant between portalvein & liver
 beta: pancreatic responsivity to Glucose
 alpha: delay between Glucose signal & Insulin secretion
 K: pancreatic responsivity to Glucose rate of change
 U_ii: Glucose insulin independent utilisation-->
        <variable name="V_G" public_interface="in" units="dl_per_kg"/>
        <variable name="k_1" public_interface="in" units="per_minute"/>
        <variable name="k_2" public_interface="in" units="per_minute"/>
        <variable name="U_ii" public_interface="in" units="mg_per_kg_minute"/>
        <variable name="k_p1" public_interface="in" units="mg_per_kg_minute"/>
        <variable name="k_p2" public_interface="in" units="per_minute"/>
        <variable name="k_p3" public_interface="in" units="mg_l_per_kg_minute_pmol"/>
        <variable name="k_p4" public_interface="in" units="mg_per_minute_pmol"/>
        <variable name="k_i" public_interface="in" units="per_minute"/>
        <variable name="k_max" public_interface="in" units="per_minute"/>
        <variable name="k_min" public_interface="in" units="per_minute"/>
        <variable name="k_abs" public_interface="in" units="per_minute"/>
        <variable name="k_gri" public_interface="in" units="per_minute"/>
        <variable name="f" public_interface="in" units="dimensionless"/>
        <variable name="b" public_interface="in" units="dimensionless"/>
        <variable name="d" public_interface="in" units="dimensionless"/>
        <variable name="BW" public_interface="in" units="kilogram"/>
        <variable name="D" public_interface="in" units="mg"/>
        <variable name="V_m0" public_interface="in" units="mg_per_kg_minute"/>
        <variable name="V_mX" public_interface="in" units="mg_l_per_kg_minute_pmol"/>
        <variable name="K_m0" public_interface="in" units="mg_per_kg"/>
        <variable name="p_2U" public_interface="in" units="per_minute"/>
        <variable name="part" public_interface="in" units="dimensionless"/>
        <variable name="V_I" public_interface="in" units="l_per_kg"/>
        <variable name="m_1" public_interface="in" units="per_minute"/>
        <variable name="m_2" public_interface="in" units="per_minute"/>
        <variable name="m_4" public_interface="in" units="per_minute"/>
        <variable name="m_5" public_interface="in" units="minute_kg_per_pmol"/>
        <variable name="m_6" public_interface="in" units="dimensionless"/>
        <variable name="K" public_interface="in" units="pmol_dl_per_kg_mg"/>
        <variable name="alpha" public_interface="in" units="per_minute"/>
        <variable name="beta" public_interface="in" units="pmol_dl_per_kg_mg_minute"/>
        <variable name="gamma" public_interface="in" units="per_minute"/>
        <variable name="G_b" public_interface="in" units="mg_per_dl"/>
        <variable name="I_b" public_interface="in" units="pmol_per_l"/>
        <variable name="S_b" public_interface="in" units="pmol_per_kg_minute"/>
        <!-- State variables-->
        <!-- G_p:  Glucose mass in plasma & rapidly equilibrating tissues
 G_t:  Glucose mass in slowly equilibrating tissues
 G:    Glucose concentration in plasma
 EGP:  endogenous Glucose production
 Ra:   Glucose rate of appearance in plasma
 E:    renal excretion
 U_id: Glucose insulin dependent utilisation
 U_ii: Glucose insulin independent utilisation
 EGP:  endogenous Glucose production
 I_1:  delayed Insulin signal
 I_d:  delayed Insulin signal
 I_po: Insulin amount in portal vein
 Ra:     Glucose rate of appearance in plasma
 Q_sto1: Glucose mass in first stomach compartment
 Q_sto2: Glucose mass in second stomach compartment
 Q_gut:  Glucose mass in intestine
 Q_sto:  Glucose mass in stomach
 k_empt: rate constant of gastric emptying
 U_id:  Insulin dependent Glucose uptake
 U_idm: Insulin dependent Glucose uptake by the muscle tissue
 INS:   Insulin in interstitial fluid
 vglucoseuptake: Glucose uptake by the adipose tissue
 I:   Insulin concentration in plasma
 I_p: Insulin mass in plasma
 I_l: Insulin mass in liver
 S:   Insulin secretion
 HE:  Insulin hepatic extraction
 Y: aux state for Insulin secretion
 S: Insulin secretion to beta cells
 S_po: Insulin secretion to portal vein-->
        <variable initial_value="178" name="G_p" public_interface="out" units="mg_per_kg"/>
        <variable initial_value="135" name="G_t" public_interface="out" units="mg_per_kg"/>
        <variable initial_value="4.5" name="I_l" public_interface="out" units="pmol_per_kg"/>
        <variable initial_value="1.25" name="I_p" public_interface="out" units="pmol_per_kg"/>
        <variable initial_value="78000" name="Q_sto1" public_interface="out" units="mg"/>
        <variable initial_value="0" name="Q_sto2" public_interface="out" units="mg"/>
        <variable initial_value="0" name="Q_gut" public_interface="out" units="mg"/>
        <variable initial_value="25" name="I_1" public_interface="out" units="pmol_per_l"/>
        <variable initial_value="25" name="I_d" public_interface="out" units="pmol_per_l"/>
        <variable initial_value="0" name="INS" public_interface="out" units="pmol_per_l"/>
        <variable initial_value="3.6" name="I_po" public_interface="out" units="pmol_per_kg"/>
        <variable initial_value="0" name="Y" public_interface="out" units="pmol_per_kg_minute"/>
        <variable name="G" public_interface="out" units="mg_per_dl"/>
        <variable name="I" public_interface="out" units="pmol_per_l"/>
        <variable name="HE" public_interface="out" units="dimensionless"/>
        <variable name="m_3" public_interface="out" units="per_minute"/>
        <variable name="Q_sto" public_interface="out" units="mg"/>
        <variable name="k_empt" public_interface="out" units="per_minute"/>
        <variable name="a" public_interface="out" units="per_mg"/>
        <variable name="c" public_interface="out" units="per_mg"/>
        <variable name="Ra" public_interface="out" units="mg_per_kg_minute"/>
        <variable name="EGP" public_interface="out" units="mg_per_kg_minute"/>
        <variable name="V_mmax" public_interface="out" units="mg_per_kg_minute"/>
        <variable name="U_idm" public_interface="out" units="mg_per_kg_minute"/>
        <variable name="U_id" public_interface="out" units="mg_per_kg_minute"/>
        <variable name="S" public_interface="out" units="pmol_per_kg_minute"/>
        <variable name="S_po" public_interface="out" units="pmol_per_kg_minute"/>
        <variable initial_value="0.0" name="E" public_interface="out" units="mg_per_kg_minute"/>
        <variable name="vglucoseuptake" public_interface="in" units="mg_per_kg_minute"/>
        <!-- Conservation laws-->
        <!-- Glucose Kinetics-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>G_p</ci>
                </apply>
                <apply>
                    <plus/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <apply>
                                    <plus/>
                                    <ci>EGP</ci>
                                    <ci>Ra</ci>
                                </apply>
                                <ci>U_ii</ci>
                            </apply>
                            <ci>E</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>k_1</ci>
                            <ci>G_p</ci>
                        </apply>
                    </apply>
                    <apply>
                        <times/>
                        <ci>k_2</ci>
                        <ci>G_t</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>G_t</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <plus/>
                        <apply>
                            <minus/>
                            <ci>U_id</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>k_1</ci>
                            <ci>G_p</ci>
                        </apply>
                    </apply>
                    <apply>
                        <times/>
                        <ci>k_2</ci>
                        <ci>G_t</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>G</ci>
                <apply>
                    <divide/>
                    <ci>G_p</ci>
                    <ci>V_G</ci>
                </apply>
            </apply>
            <!-- Insulin Kinetics-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>I_p</ci>
                </apply>
                <apply>
                    <plus/>
                    <apply>
                        <minus/>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <ci>m_2</ci>
                            </apply>
                            <ci>I_p</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>m_4</ci>
                            <ci>I_p</ci>
                        </apply>
                    </apply>
                    <apply>
                        <times/>
                        <ci>m_1</ci>
                        <ci>I_l</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>I_l</ci>
                </apply>
                <apply>
                    <plus/>
                    <apply>
                        <minus/>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <ci>m_1</ci>
                            </apply>
                            <ci>I_l</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>m_3</ci>
                            <ci>I_l</ci>
                        </apply>
                    </apply>
                    <apply>
                        <times/>
                        <ci>m_2</ci>
                        <ci>I_p</ci>
                    </apply>
                    <ci>S</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>I</ci>
                <apply>
                    <divide/>
                    <ci>I_p</ci>
                    <ci>V_I</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>HE</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <ci>m_5</ci>
                        </apply>
                        <ci>S</ci>
                    </apply>
                    <ci>m_6</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>m_3</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>HE</ci>
                        <ci>m_1</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <ci>HE</ci>
                    </apply>
                </apply>
            </apply>
            <!-- Glucose Rate of Appearance-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>Q_sto1</ci>
                </apply>
                <apply>
                    <times/>
                    <apply>
                        <minus/>
                        <ci>k_gri</ci>
                    </apply>
                    <ci>Q_sto1</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>Q_sto2</ci>
                </apply>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <ci>k_empt</ci>
                        </apply>
                        <ci>Q_sto2</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>k_gri</ci>
                        <ci>Q_sto1</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>Q_gut</ci>
                </apply>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <ci>k_abs</ci>
                        </apply>
                        <ci>Q_gut</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>k_empt</ci>
                        <ci>Q_sto2</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Q_sto</ci>
                <apply>
                    <plus/>
                    <ci>Q_sto1</ci>
                    <ci>Q_sto2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>k_empt</ci>
                <apply>
                    <plus/>
                    <ci>k_min</ci>
                    <apply>
                        <times/>
                        <apply>
                            <divide/>
                            <apply>
                                <minus/>
                                <ci>k_max</ci>
                                <ci>k_min</ci>
                            </apply>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                        <apply>
                            <plus/>
                            <apply>
                                <minus/>
                                <apply>
                                    <tanh/>
                                    <apply>
                                        <times/>
                                        <ci>a</ci>
                                        <apply>
                                            <minus/>
                                            <ci>Q_sto</ci>
                                            <apply>
                                                <times/>
                                                <ci>b</ci>
                                                <ci>D</ci>
                                            </apply>
                                        </apply>
                                    </apply>
                                </apply>
                                <apply>
                                    <tanh/>
                                    <apply>
                                        <times/>
                                        <ci>c</ci>
                                        <apply>
                                            <minus/>
                                            <ci>Q_sto</ci>
                                            <apply>
                                                <times/>
                                                <ci>d</ci>
                                                <ci>D</ci>
                                            </apply>
                                        </apply>
                                    </apply>
                                </apply>
                            </apply>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>a</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="dimensionless">2.5</cn>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">1</cn>
                            <ci>b</ci>
                        </apply>
                        <ci>D</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>c</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="dimensionless">2.5</cn>
                    <apply>
                        <times/>
                        <ci>d</ci>
                        <ci>D</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Ra</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>f</ci>
                        <ci>k_abs</ci>
                        <ci>Q_gut</ci>
                    </apply>
                    <ci>BW</ci>
                </apply>
            </apply>
            <!-- Glucose Production-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>I_1</ci>
                </apply>
                <apply>
                    <times/>
                    <apply>
                        <minus/>
                        <ci>k_i</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>I_1</ci>
                        <ci>I</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>I_d</ci>
                </apply>
                <apply>
                    <times/>
                    <apply>
                        <minus/>
                        <ci>k_i</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>I_d</ci>
                        <ci>I_1</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>EGP</ci>
                <apply>
                    <minus/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>k_p1</ci>
                            <apply>
                                <times/>
                                <ci>k_p2</ci>
                                <ci>G_p</ci>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>k_p3</ci>
                            <ci>I_d</ci>
                        </apply>
                    </apply>
                    <apply>
                        <times/>
                        <ci>k_p4</ci>
                        <ci>I_po</ci>
                    </apply>
                </apply>
            </apply>
            <!-- Glucose Uptake-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>INS</ci>
                </apply>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <ci>p_2U</ci>
                        </apply>
                        <ci>INS</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>p_2U</ci>
                        <apply>
                            <minus/>
                            <ci>I</ci>
                            <ci>I_b</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>V_mmax</ci>
                <apply>
                    <times/>
                    <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <ci>part</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>V_m0</ci>
                        <apply>
                            <times/>
                            <ci>V_mX</ci>
                            <ci>INS</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>U_idm</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>V_mmax</ci>
                        <ci>G_t</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>K_m0</ci>
                        <ci>G_t</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>U_id</ci>
                <apply>
                    <plus/>
                    <ci>U_idm</ci>
                    <ci>vglucoseuptake</ci>
                </apply>
            </apply>
            <!-- Insulin Secretion-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>I_po</ci>
                </apply>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <ci>gamma</ci>
                        </apply>
                        <ci>I_po</ci>
                    </apply>
                    <ci>S_po</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>Y</ci>
                </apply>
                <apply>
                    <times/>
                    <apply>
                        <minus/>
                        <ci>alpha</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>Y</ci>
                        <apply>
                            <times/>
                            <ci>beta</ci>
                            <apply>
                                <minus/>
                                <ci>G</ci>
                                <ci>G_b</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>S</ci>
                <apply>
                    <times/>
                    <ci>gamma</ci>
                    <ci>I_po</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>S_po</ci>
                <apply>
                    <plus/>
                    <ci>Y</ci>
                    <apply>
                        <divide/>
                        <apply>
                            <times/>
                            <ci>K</ci>
                            <apply>
                                <plus/>
                                <apply>
                                    <minus/>
                                    <apply>
                                        <minus/>
                                        <apply>
                                            <minus/>
                                            <apply>
                                                <plus/>
                                                <ci>EGP</ci>
                                                <ci>Ra</ci>
                                            </apply>
                                            <ci>E</ci>
                                        </apply>
                                        <ci>U_ii</ci>
                                    </apply>
                                    <apply>
                                        <times/>
                                        <ci>k_1</ci>
                                        <ci>G_p</ci>
                                    </apply>
                                </apply>
                                <apply>
                                    <times/>
                                    <ci>k_2</ci>
                                    <ci>G_t</ci>
                                </apply>
                            </apply>
                        </apply>
                        <ci>V_G</ci>
                    </apply>
                    <ci>S_b</ci>
                </apply>
            </apply>
        </math>
    </component>
    <connection>
        <map_components component_1="param" component_2="state"/>
        <!-- Glucose Kinetics-->
        <map_variables variable_1="V_G" variable_2="V_G"/>
        <map_variables variable_1="k_1" variable_2="k_1"/>
        <map_variables variable_1="k_2" variable_2="k_2"/>
        <map_variables variable_1="U_ii" variable_2="U_ii"/>
        <!-- Insulin Kinetics-->
        <map_variables variable_1="V_I" variable_2="V_I"/>
        <map_variables variable_1="m_1" variable_2="m_1"/>
        <map_variables variable_1="m_2" variable_2="m_2"/>
        <map_variables variable_1="m_4" variable_2="m_4"/>
        <map_variables variable_1="m_5" variable_2="m_5"/>
        <map_variables variable_1="m_6" variable_2="m_6"/>
        <!-- Ra-->
        <map_variables variable_1="k_max" variable_2="k_max"/>
        <map_variables variable_1="k_min" variable_2="k_min"/>
        <map_variables variable_1="k_abs" variable_2="k_abs"/>
        <map_variables variable_1="k_gri" variable_2="k_gri"/>
        <map_variables variable_1="f" variable_2="f"/>
        <map_variables variable_1="b" variable_2="b"/>
        <map_variables variable_1="d" variable_2="d"/>
        <map_variables variable_1="BW" variable_2="BW"/>
        <map_variables variable_1="D" variable_2="D"/>
        <!-- EGP-->
        <map_variables variable_1="k_p1" variable_2="k_p1"/>
        <map_variables variable_1="k_p2" variable_2="k_p2"/>
        <map_variables variable_1="k_p3" variable_2="k_p3"/>
        <map_variables variable_1="k_p4" variable_2="k_p4"/>
        <map_variables variable_1="k_i" variable_2="k_i"/>
        <!-- Glucose Uptake-->
        <map_variables variable_1="V_m0" variable_2="V_m0"/>
        <map_variables variable_1="V_mX" variable_2="V_mX"/>
        <map_variables variable_1="K_m0" variable_2="K_m0"/>
        <map_variables variable_1="p_2U" variable_2="p_2U"/>
        <map_variables variable_1="part" variable_2="part"/>
        <map_variables variable_1="I_b" variable_2="I_b"/>
        <!-- Insulin Secretion-->
        <map_variables variable_1="K" variable_2="K"/>
        <map_variables variable_1="alpha" variable_2="alpha"/>
        <map_variables variable_1="beta" variable_2="beta"/>
        <map_variables variable_1="gamma" variable_2="gamma"/>
        <map_variables variable_1="S_b" variable_2="S_b"/>
        <map_variables variable_1="G_b" variable_2="G_b"/>
    </connection>
    <connection>
        <map_components component_1="environment" component_2="state"/>
        <map_variables variable_1="time" variable_2="t"/>
    </connection>
</model>