- Author:
- ssaf006 <ssaf006@aucklanduni.ac.nz>
- Date:
- 2019-06-06 20:47:37+12:00
- Desc:
- fixed the nvc model
- Permanent Source URI:
- http://models.cellml.org/workspace/4bd/rawfile/4e32e1754f465d7374b6a52d1371fba0a346c5c4/bondgraph/Mm3_p4.cellml
<?xml version='1.0'?>
<model name="metabolic_model" 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="amount" units_ref="amount"/>
<units name="per_amount" units_ref="per_amount"/>
<units name="per_sec" units_ref="per_sec"/>
<units name="amount_per_sec" units_ref="amount_per_sec"/>
<units name="per_amount_per_sec" units_ref="per_amount_per_sec"/>
<units name="per_amount2_per_sec" units_ref="per_amount2_per_sec"/>
</import>
<component name="Mm3">
<variable initial_value="0" name="t" units="second"/>
<variable name="stimulus" units="amount"/>
<variable initial_value="0" name="oHb" units="amount"/>
<variable initial_value="0" name="dHb" units="amount"/>
<variable initial_value="0" name="O_2" units="amount"/>
<variable initial_value="0" name="glucose" units="amount"/>
<variable initial_value="0" name="inputDelay" units="amount"/>
<variable initial_value="0" name="glucoseFbDelay" units="amount"/>
<variable initial_value="0" name="glucoseFbDelay_2" units="amount"/>
<variable initial_value="0" name="glucoseFbDelay_3" units="amount"/>
<variable initial_value="0" name="glucosefeedback" units="amount"/>
<variable name="k_flow" units="per_sec"/>
<variable initial_value="100" name="G_body" units="amount"/>
<variable initial_value="100" name="O_2_body" units="amount"/>
<variable initial_value="100" name="oHb_body" units="amount"/>
<variable initial_value="100" name="dHb_body" units="amount"/>
<variable name="y" units="dimensionless"/>
<variable name="v1_f" units="amount_per_sec"/>
<variable name="v1_b" units="amount_per_sec"/>
<variable name="vin_oHb" units="amount_per_sec"/>
<variable name="vout_oHb" units="amount_per_sec"/>
<variable name="vin_dHb" units="amount_per_sec"/>
<variable name="vout_dHb" units="amount_per_sec"/>
<variable name="vin_G" units="amount_per_sec"/>
<variable name="vout_G" units="amount_per_sec"/>
<variable name="vin_O2" units="amount_per_sec"/>
<variable name="vout_O2" units="amount_per_sec"/>
<variable name="v_basal" units="amount_per_sec"/>
<variable name="v_stim" units="amount_per_sec"/>
<variable name="input_1" units="amount_per_sec"/>
<variable name="v_ID" units="amount_per_sec"/>
<variable name="v_toGFBD" units="amount_per_sec"/>
<variable name="v_GFBD" units="amount_per_sec"/>
<variable name="v_GFBD2" units="amount_per_sec"/>
<variable name="v_GFBD3" units="amount_per_sec"/>
<variable name="v_GFB" units="amount_per_sec"/>
<!-- parameters-->
<variable initial_value="1.3952" name="k1_f" units="per_sec"/>
<variable initial_value="0.0011" name="k1_b" units="per_amount_per_sec"/>
<variable initial_value="174.588" name="k_basal" units="per_amount_per_sec"/>
<variable initial_value="2438.726" name="kflow_glucose" units="amount_per_sec"/>
<variable initial_value="297.9752" name="k_y" units="dimensionless"/>
<variable initial_value="19943.3114" name="k_metabolic" units="per_sec"/>
<variable initial_value="3.3201" name="k_m" units="amount"/>
<variable initial_value="2.1006" name="proportion_1" units="dimensionless"/>
<variable initial_value="0.0011" name="proportion_2" units="dimensionless"/>
<variable initial_value="7.083" name="k_ID" units="per_sec"/>
<variable initial_value="2603.4638" name="GD_body" units="per_sec"/>
<variable initial_value="19932.2693" name="k_GFBD" units="per_sec"/>
<variable initial_value="0.6959" name="k_GFBD2" units="per_sec"/>
<variable initial_value="0.6676" name="k_GFBD3" units="per_sec"/>
<variable initial_value="0.4752" name="k_GFB" units="per_sec"/>
<!--var k_i3: per_amount2_per_sec {init: ?};
this is added in order to have consistent units for v_stim; similar to Mm2-->
<!--reactions-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v1_f</ci>
<apply>
<times/>
<ci>k1_f</ci>
<ci>oHb</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v1_b</ci>
<apply>
<times/>
<ci>k1_b</ci>
<ci>dHb</ci>
<ci>O_2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>vin_oHb</ci>
<apply>
<times/>
<ci>oHb_body</ci>
<ci>k_flow</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>vout_oHb</ci>
<apply>
<times/>
<ci>oHb</ci>
<ci>k_flow</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>vin_dHb</ci>
<apply>
<times/>
<ci>dHb_body</ci>
<ci>k_flow</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>vout_dHb</ci>
<apply>
<times/>
<ci>dHb</ci>
<ci>k_flow</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>vin_G</ci>
<apply>
<times/>
<ci>G_body</ci>
<ci>k_flow</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>vout_G</ci>
<apply>
<times/>
<ci>glucose</ci>
<ci>k_flow</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>vin_O2</ci>
<apply>
<times/>
<ci>O_2_body</ci>
<ci>k_flow</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>vout_O2</ci>
<apply>
<times/>
<ci>O_2</ci>
<ci>k_flow</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_basal</ci>
<apply>
<times/>
<ci>k_basal</ci>
<apply>
<power/>
<ci>O_2</ci>
<ci>proportion_1</ci>
</apply>
<ci>glucose</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_stim</ci>
<apply>
<times/>
<ci>inputDelay</ci>
<apply>
<power/>
<ci>O_2</ci>
<ci>proportion_2</ci>
</apply>
<ci>glucose</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>input_1</ci>
<apply>
<times/>
<ci>k_metabolic</ci>
<ci>stimulus</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_ID</ci>
<apply>
<times/>
<ci>k_ID</ci>
<ci>inputDelay</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_toGFBD</ci>
<apply>
<times/>
<ci>GD_body</ci>
<ci>glucose</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_GFBD</ci>
<apply>
<times/>
<ci>glucoseFbDelay</ci>
<ci>k_GFBD</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_GFBD2</ci>
<apply>
<times/>
<ci>glucoseFbDelay_2</ci>
<ci>k_GFBD2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_GFBD3</ci>
<apply>
<times/>
<ci>glucoseFbDelay_3</ci>
<ci>k_GFBD3</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_GFB</ci>
<apply>
<times/>
<ci>glucosefeedback</ci>
<ci>k_GFB</ci>
</apply>
</apply>
<!--ODEs-->
<apply>
<eq/>
<ci>stimulus</ci>
<piecewise>
<piece>
<cn cellml:units="amount">1</cn>
<apply>
<and/>
<apply>
<gt/>
<ci>t</ci>
<cn cellml:units="second">0.0</cn>
</apply>
<apply>
<lt/>
<ci>t</ci>
<cn cellml:units="second">0.5</cn>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="amount">0</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>oHb</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<ci>v1_b</ci>
<ci>v1_f</ci>
</apply>
<ci>vin_oHb</ci>
</apply>
<ci>vout_oHb</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>dHb</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<ci>v1_f</ci>
<ci>v1_b</ci>
</apply>
<ci>vin_dHb</ci>
</apply>
<ci>vout_dHb</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>O_2</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>v1_f</ci>
<ci>v1_b</ci>
</apply>
<apply>
<times/>
<ci>v_basal</ci>
<ci>proportion_1</ci>
</apply>
</apply>
<apply>
<times/>
<ci>v_stim</ci>
<ci>proportion_2</ci>
</apply>
</apply>
<ci>vin_O2</ci>
</apply>
<ci>vout_O2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>glucose</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>vin_G</ci>
<ci>vout_G</ci>
</apply>
<ci>v_basal</ci>
</apply>
<ci>v_stim</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>inputDelay</ci>
</apply>
<apply>
<minus/>
<ci>input_1</ci>
<ci>v_ID</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>glucoseFbDelay</ci>
</apply>
<apply>
<minus/>
<ci>v_toGFBD</ci>
<ci>v_GFBD</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>glucoseFbDelay_2</ci>
</apply>
<apply>
<minus/>
<ci>v_GFBD</ci>
<ci>v_GFBD2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>glucoseFbDelay_3</ci>
</apply>
<apply>
<minus/>
<ci>v_GFBD2</ci>
<ci>v_GFBD3</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>glucosefeedback</ci>
</apply>
<apply>
<minus/>
<ci>v_GFBD3</ci>
<ci>v_GFB</ci>
</apply>
</apply>
<!--the blood flow-->
<apply>
<eq/>
<ci>k_flow</ci>
<apply>
<divide/>
<ci>kflow_glucose</ci>
<apply>
<plus/>
<ci>k_m</ci>
<ci>glucosefeedback</ci>
</apply>
</apply>
</apply>
<!--outputsignal-->
<apply>
<eq/>
<ci>y</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k_y</ci>
<ci>oHb</ci>
</apply>
<ci>dHb</ci>
</apply>
</apply>
</math>
</component>
</model>
