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.cellml.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>