- Author:
- Soroush Safaei <ssaf006@aucklanduni.ac.nz>
- Date:
- 2019-03-06 21:20:11+13:00
- Desc:
- fixing the param
- Permanent Source URI:
- https://models.fieldml.org/workspace/4bd/rawfile/866c504b253f511a51609d674ff66944e702a8aa/Mm2_p2.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="Mm2">
<variable 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="inputDelay_2" units="amount"/>
<variable initial_value="0" name="inputDelay_3" units="amount"/>
<variable initial_value="0" name="inputDelay_4" units="amount"/>
<variable initial_value="0" name="inputDelay_5" units="amount"/>
<variable initial_value="0" name="glucoseFbDelay" units="amount"/>
<variable initial_value="0" name="glucosefeedback" units="amount"/>
<!-- blood flow-->
<variable name="k_flow" units="per_sec"/>
<!-- glucose in arterial blood-->
<variable initial_value="100" name="G_body" units="amount"/>
<!-- glucose feedback delay-->
<variable initial_value="100" name="GD_body" units="per_sec"/>
<!-- oxygen in arterial blood-->
<variable initial_value="100" name="O_2_body" units="amount"/>
<!-- oxygenated hemoglobin in arterial blood-->
<variable initial_value="100" name="oHb_body" units="amount"/>
<!-- deoxygenated hemoglobin in arterial blood-->
<variable initial_value="100" name="dHb_body" units="amount"/>
<!-- output signal-->
<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_GFB" units="amount_per_sec"/>
<variable name="v_ID2" units="amount_per_sec"/>
<variable name="v_ID3" units="amount_per_sec"/>
<variable name="v_ID4" units="amount_per_sec"/>
<variable name="v_ID5" units="amount_per_sec"/>
<!-- parameters-->
<variable initial_value="627.1792" name="k1_f" units="per_sec"/>
<variable initial_value="1381.9932" name="k1_b" units="per_amount_per_sec"/>
<variable initial_value="5.0587" name="k_basal" units="per_amount_per_sec"/>
<variable initial_value="102.6292" name="kflow_glucose" units="amount_per_sec"/>
<variable initial_value="2905.5532" name="k_y" units="dimensionless"/>
<variable initial_value="189.3795" name="k_metabolic" units="per_sec"/>
<variable initial_value="111.8459" name="k_m" units="amount"/>
<variable initial_value="11.67404" name="k_i2" units="per_amount2_per_sec"/>
<variable initial_value="1.3159" name="proportion_1" units="dimensionless"/>
<variable initial_value="0.0" name="proportion_2" units="dimensionless"/>
<variable initial_value="0.9575" name="k_ID" units="per_sec"/>
<variable initial_value="18641.1377" name="k_GFBD" units="per_sec"/>
<variable initial_value="11921.2175" name="k_GFB" units="per_sec"/>
<variable initial_value="0.9613" name="k_ID2" units="per_sec"/>
<variable initial_value="0.9484" name="k_ID3" units="per_sec"/>
<variable initial_value="0.9703" name="k_ID4" units="per_sec"/>
<variable initial_value="2687.7052" name="k_ID5" units="per_sec"/>
<!-- rate of releasing oxyhemoglobin into oxygen and deoxyhemoglobin-->
<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>
<!-- rate of binding oxygen and deoxyhemoglobin into oxyhemoglobin-->
<apply>
<eq/>
<ci>v1_b</ci>
<apply>
<times/>
<ci>k1_b</ci>
<ci>dHb</ci>
<ci>O_2</ci>
</apply>
</apply>
<!-- oxyhemoglobin influx-->
<apply>
<eq/>
<ci>vin_oHb</ci>
<apply>
<times/>
<ci>oHb_body</ci>
<ci>k_flow</ci>
</apply>
</apply>
<!-- oxyhemoglobin outflux-->
<apply>
<eq/>
<ci>vout_oHb</ci>
<apply>
<times/>
<ci>oHb</ci>
<ci>k_flow</ci>
</apply>
</apply>
<!-- deoxyhemoglobin influx-->
<apply>
<eq/>
<ci>vin_dHb</ci>
<apply>
<times/>
<ci>dHb_body</ci>
<ci>k_flow</ci>
</apply>
</apply>
<!-- deoxyhemoglobin outflux-->
<apply>
<eq/>
<ci>vout_dHb</ci>
<apply>
<times/>
<ci>dHb</ci>
<ci>k_flow</ci>
</apply>
</apply>
<!-- glucose influx-->
<apply>
<eq/>
<ci>vin_G</ci>
<apply>
<times/>
<ci>G_body</ci>
<ci>k_flow</ci>
</apply>
</apply>
<!-- glucose outflux-->
<apply>
<eq/>
<ci>vout_G</ci>
<apply>
<times/>
<ci>glucose</ci>
<ci>k_flow</ci>
</apply>
</apply>
<!-- oxygen influx-->
<apply>
<eq/>
<ci>vin_O2</ci>
<apply>
<times/>
<ci>O_2_body</ci>
<ci>k_flow</ci>
</apply>
</apply>
<!-- oxygen outflux-->
<apply>
<eq/>
<ci>vout_O2</ci>
<apply>
<times/>
<ci>O_2</ci>
<ci>k_flow</ci>
</apply>
</apply>
<!-- basal metabolism-->
<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>
<!-- metabolism during stimulation-->
<apply>
<eq/>
<ci>v_stim</ci>
<apply>
<times/>
<ci>inputDelay_5</ci>
<apply>
<power/>
<ci>O_2</ci>
<ci>proportion_2</ci>
</apply>
<ci>glucose</ci>
<ci>k_i2</ci>
</apply>
</apply>
<!-- delay state reactions-->
<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_GFB</ci>
<apply>
<times/>
<ci>glucosefeedback</ci>
<ci>k_GFB</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_ID2</ci>
<apply>
<times/>
<ci>inputDelay_2</ci>
<ci>k_ID2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_ID3</ci>
<apply>
<times/>
<ci>inputDelay_3</ci>
<ci>k_ID3</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_ID4</ci>
<apply>
<times/>
<ci>inputDelay_4</ci>
<ci>k_ID4</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_ID5</ci>
<apply>
<times/>
<ci>inputDelay_5</ci>
<ci>k_ID5</ci>
</apply>
</apply>
<!-- stimulus input signal-->
<apply>
<eq/>
<ci>stimulus</ci>
<piecewise>
<piece>
<cn cellml:units="amount">1</cn>
<apply>
<and/>
<apply>
<gt/>
<ci>t</ci>
<cn cellml:units="second">0.5</cn>
</apply>
<apply>
<lt/>
<ci>t</ci>
<cn cellml:units="second">1.0</cn>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="amount">0</cn>
</otherwise>
</piecewise>
</apply>
<!-- change in oxyhemoglobin level-->
<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>
<!-- change in deoxyhemoglobin level-->
<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>
<!-- change in oxygen level-->
<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>
<!-- change in glucose level-->
<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>
<!-- dealy state-->
<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>inputDelay_2</ci>
</apply>
<apply>
<minus/>
<ci>v_ID</ci>
<ci>v_ID2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>inputDelay_3</ci>
</apply>
<apply>
<minus/>
<ci>v_ID2</ci>
<ci>v_ID3</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>inputDelay_4</ci>
</apply>
<apply>
<minus/>
<ci>v_ID3</ci>
<ci>v_ID4</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>inputDelay_5</ci>
</apply>
<apply>
<minus/>
<ci>v_ID4</ci>
<ci>v_ID5</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>
<!-- glucose feedback to the blood flow-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>glucosefeedback</ci>
</apply>
<apply>
<minus/>
<ci>v_GFBD</ci>
<ci>v_GFB</ci>
</apply>
</apply>
<!-- 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>
<!-- output signal-->
<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>
