- Author:
- Soroush <ssaf006@aucklanduni.ac.nz>
- Date:
- 2018-06-07 18:16:45+12:00
- Desc:
- add
- Permanent Source URI:
- https://models.cellml.org/workspace/483/rawfile/2c3451dfbd0a114efbabe7f43d40c8172c5915f4/BondGraph/BG.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.cellml">
<units name="mmol_per_s" units_ref="mmol_per_s"/>
<units name="mol_per_s" units_ref="mol_per_s"/>
<units name="per_s" units_ref="per_s"/>
<units name="m3_per_s" units_ref="m3_per_s"/>
<units name="per_mol" units_ref="per_mol"/>
<units name="kg_per_mol" units_ref="kg_per_mol"/>
<units name="mM" units_ref="mM"/>
<units name="pM" units_ref="pM"/>
<units name="pmol" units_ref="pmol"/>
<units name="mmol" units_ref="mmol"/>
<units name="mM_per_s" units_ref="mM_per_s"/>
<units name="mM_per_mol" units_ref="mM_per_mol"/>
<units name="m3" units_ref="m3"/>
<units name="g_per_s" units_ref="g_per_s"/>
<units name="l_per_kg" units_ref="l_per_kg"/>
<units name="s_per_pmol" units_ref="s_per_pmol"/>
<units name="g_per_l" units_ref="g_per_l"/>
<units name="g_per_s_pM" units_ref="g_per_s_pM"/>
<units name="g_per_s_pmol" units_ref="g_per_s_pmol"/>
<units name="pmol_per_s" units_ref="pmol_per_s"/>
<units name="mmol_per_s_kg" units_ref="mmol_per_s_kg"/>
<units name="pM_per_s" units_ref="pM_per_s"/>
<units name="pmol_l_per_g_s" units_ref="pmol_l_per_g_s"/>
<units name="pmol_l_per_g" units_ref="pmol_l_per_g"/>
<units name="per_g" units_ref="per_g"/>
<units name="mmol_per_g" units_ref="mmol_per_g"/>
<units name="per_mM_s" units_ref="per_mM_s"/>
<units name="per_mM" units_ref="per_mM"/>
</import>
<component name="environment">
<variable name="time" public_interface="out" units="second"/>
</component>
<component name="state">
<variable name="t" public_interface="in" units="second"/>
<!-- State variable-->
<!-- q_G_pl: blood glucose
q_I_pl: plasma insulin
q_I_pe: peripheral insulin
k_gre: kidney extraction
k_cns: central nervous system uptake
k_is: insulin sensitivity
k_egp: endogenous glucose production
k_ra: glucose exogenous input
k_gsat: saturation of insulin mediated glucose uptake parameter
k_hs: hepatic secretion of insulin
k_bl: rate constant of insulin clearance through blood
k_isat: hepatic clearance parameter
k_ire: kidney clearance of insulin
k_diff: insulin diffusion between plasma and periphery
k_cell: insulin degradation by cell rate constant
k_end: insulin secretion
k_exo: delivered insulin exogenously
V_G_pl: volume of distribution of glucose in plasma
V_I_pl: blood plasma volume - distribution of plasma insulin
V_I_pe: interstitial fluid volume - distribution of peripheral insulin-->
<variable initial_value="0.0" name="q_G_pl" public_interface="out" units="mM"/>
<variable initial_value="0.0" name="q_I_pl" public_interface="out" units="mM"/>
<variable initial_value="0.0" name="q_I_pe" public_interface="out" units="mM"/>
<variable initial_value="78" name="q_G_sto1" public_interface="out" units="gram"/>
<variable initial_value="0.0" name="q_G_sto2" public_interface="out" units="gram"/>
<variable initial_value="0.0" name="q_G_gut" public_interface="out" units="gram"/>
<variable name="v_G_RE" public_interface="out" units="mM_per_s"/>
<variable name="v_G_EGP" public_interface="out" units="mM_per_s"/>
<variable name="v_G_RA" public_interface="out" units="mM_per_s"/>
<!--var v_G_RA1: mM_per_s {pub: out};-->
<variable name="v_G_abs" public_interface="out" units="g_per_s"/>
<variable name="v_G_empt" public_interface="out" units="g_per_s"/>
<variable name="v_G_gri" public_interface="out" units="g_per_s"/>
<variable name="v_G_CNS" public_interface="out" units="mM_per_s"/>
<variable name="v_G_idu" public_interface="out" units="mM_per_s"/>
<variable name="v_I_PE" public_interface="out" units="mM_per_s"/>
<variable name="v_I_DEG" public_interface="out" units="mM_per_s"/>
<variable name="v_I_END" public_interface="out" units="mM_per_s"/>
<variable name="v_I_EXO" public_interface="out" units="mM_per_s"/>
<variable name="v_I_RE" public_interface="out" units="mM_per_s"/>
<variable name="v_I_HE" public_interface="out" units="mM_per_s"/>
<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_I_pl" public_interface="out" units="l_per_kg"/>
<variable initial_value="0.289" name="V_I_pe" public_interface="out" units="l_per_kg"/>
<variable initial_value="0.56" name="V_G_pl" public_interface="out" units="l_per_kg"/>
<variable initial_value="0.00005" name="k_gre" public_interface="out" units="per_s"/>
<variable initial_value="0.00055" name="k_egp" public_interface="out" units="mmol_per_s_kg"/>
<variable initial_value="0.0001733" name="k_ra" public_interface="out" units="mmol_per_s"/>
<variable initial_value="0.001467" name="k_cns" public_interface="out" units="mmol_per_s_kg"/>
<variable initial_value="0.67" name="k_hs" public_interface="out" units="dimensionless"/>
<variable initial_value="0.01667e-7" name="k_is" public_interface="out" units="per_mM_s"/>
<variable initial_value="0.00043" name="k_cell" public_interface="out" units="per_s"/>
<variable initial_value="0.0005667" name="k_ire" public_interface="out" units="per_s"/>
<variable initial_value="0.0004167" name="k_diff" public_interface="out" units="per_s"/>
<variable initial_value="0.0065" name="k_bl" public_interface="out" units="per_s"/>
<variable initial_value="0.0" name="k_gsat" public_interface="out" units="per_mM"/>
<variable initial_value="0.0017" name="k_isat" public_interface="out" units="per_mM"/>
<variable initial_value="0.0" name="k_EXO" public_interface="out" units="mmol_per_s"/>
<variable name="k_END" units="mM_per_s"/>
<variable name="a" public_interface="out" units="per_g"/>
<variable name="c" public_interface="out" units="per_g"/>
<variable initial_value="0.00093" name="k_max" public_interface="out" units="per_s"/>
<variable initial_value="0.00013" name="k_min" public_interface="out" units="per_s"/>
<variable initial_value="0.00095" name="k_abs" public_interface="out" units="per_s"/>
<variable initial_value="0.00093" name="k_gri" public_interface="out" units="per_s"/>
<variable initial_value="0.9" name="f" public_interface="out" units="dimensionless"/>
<variable initial_value="0.82" name="b" public_interface="out" units="dimensionless"/>
<variable initial_value="0.01" name="d" public_interface="out" units="dimensionless"/>
<variable initial_value="78" name="BW" public_interface="out" units="kilogram"/>
<variable name="k_empt" public_interface="out" units="per_s"/>
<variable initial_value="78" name="D" public_interface="out" units="gram"/>
<variable initial_value="5.551" name="mol_gram" units="mmol_per_g"/>
<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>k_END</ci>
<piecewise>
<piece>
<apply>
<plus/>
<apply>
<minus/>
<cn cellml:units="mM_per_s">0.025</cn>
</apply>
<apply>
<times/>
<cn cellml:units="per_s">0.0317</cn>
<ci>q_G_pl</ci>
</apply>
</apply>
<apply>
<gt/>
<apply>
<plus/>
<apply>
<minus/>
<cn cellml:units="mM_per_s">0.025</cn>
</apply>
<apply>
<times/>
<cn cellml:units="per_s">0.0317</cn>
<ci>q_G_pl</ci>
</apply>
</apply>
<cn cellml:units="mM_per_s">0.07</cn>
</apply>
</piece>
<piece>
<cn cellml:units="mM_per_s">0.07</cn>
<apply>
<leq/>
<apply>
<plus/>
<apply>
<minus/>
<cn cellml:units="mM_per_s">0.025</cn>
</apply>
<apply>
<times/>
<cn cellml:units="per_s">0.0317</cn>
<ci>q_G_pl</ci>
</apply>
</apply>
<cn cellml:units="mM_per_s">0.07</cn>
</apply>
</piece>
</piecewise>
</apply>
<!-- Glucose Kinetics-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_G_pl</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>v_G_RA</ci>
<ci>v_G_EGP</ci>
</apply>
<ci>v_G_RE</ci>
</apply>
<ci>v_G_CNS</ci>
</apply>
<ci>v_G_idu</ci>
</apply>
</apply>
<!-- Glucose Rate of Appearance-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_G_sto1</ci>
</apply>
<apply>
<minus/>
<ci>v_G_gri</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_G_sto2</ci>
</apply>
<apply>
<minus/>
<ci>v_G_gri</ci>
<ci>v_G_empt</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_G_gut</ci>
</apply>
<apply>
<minus/>
<ci>v_G_empt</ci>
<ci>v_G_abs</ci>
</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>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/>
<apply>
<plus/>
<ci>q_G_sto1</ci>
<ci>q_G_sto2</ci>
</apply>
<apply>
<times/>
<ci>b</ci>
<ci>D</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<tanh/>
<apply>
<times/>
<ci>c</ci>
<apply>
<minus/>
<apply>
<plus/>
<ci>q_G_sto1</ci>
<ci>q_G_sto2</ci>
</apply>
<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>v_G_gri</ci>
<apply>
<times/>
<ci>k_gri</ci>
<ci>q_G_sto1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_G_empt</ci>
<apply>
<times/>
<ci>k_empt</ci>
<ci>q_G_sto2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_G_abs</ci>
<apply>
<times/>
<ci>k_abs</ci>
<ci>q_G_gut</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_G_RA</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>v_G_abs</ci>
<apply>
<times/>
<ci>V_G_pl</ci>
<ci>m_body</ci>
</apply>
</apply>
<ci>f</ci>
<ci>mol_gram</ci>
</apply>
</apply>
<!-- Endogenous Glucose Production-->
<apply>
<eq/>
<ci>v_G_EGP</ci>
<apply>
<divide/>
<ci>k_egp</ci>
<ci>V_G_pl</ci>
</apply>
</apply>
<!-- Glucose Uptake-->
<apply>
<eq/>
<ci>v_G_RE</ci>
<apply>
<times/>
<ci>k_gre</ci>
<ci>q_G_pl</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_G_CNS</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k_cns</ci>
<ci>m_brain</ci>
</apply>
<apply>
<times/>
<ci>V_G_pl</ci>
<ci>m_body</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_G_idu</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k_is</ci>
<ci>q_G_pl</ci>
<ci>q_I_pe</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>k_gsat</ci>
<ci>q_I_pe</ci>
</apply>
</apply>
</apply>
</apply>
<!-- Insulin Kinetics-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_I_pl</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>v_I_END</ci>
<ci>v_I_EXG</ci>
</apply>
<ci>v_I_HE</ci>
</apply>
<ci>v_I_RE</ci>
</apply>
<ci>v_I_PE</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_I_pe</ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>v_I_PE</ci>
<ci>V_I_pl</ci>
</apply>
<ci>V_I_pe</ci>
</apply>
<ci>v_I_DEG</ci>
</apply>
</apply>
<!-- Insulin Secretion-->
<apply>
<eq/>
<ci>v_I_END</ci>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>k_hs</ci>
</apply>
<ci>k_END</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_I_EXO</ci>
<apply>
<divide/>
<ci>k_EXO</ci>
<apply>
<times/>
<ci>V_I_pl</ci>
<ci>m_body</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_I_PE</ci>
<apply>
<times/>
<ci>k_diff</ci>
<apply>
<minus/>
<ci>q_I_pl</ci>
<ci>q_I_pe</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_I_RE</ci>
<apply>
<times/>
<ci>k_ire</ci>
<ci>q_I_pl</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_I_HE</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k_bl</ci>
<ci>q_I_pl</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>k_isat</ci>
<ci>q_I_pl</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_I_DEG</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k_cell</ci>
<ci>q_I_pe</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>k_gsat</ci>
<ci>q_I_pe</ci>
</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>
