Location: Blood HbO2 and HbCO2 Dissociation Curves @ f725b6864f22 / Figure03.cellml
- Author:
- nima <nafs080@aucklanduni.ac.nz>
- Date:
- 2020-10-29 09:32:37+13:00
- Desc:
- All the Cellml files, Sedml files and python scripts for figures are added
- Permanent Source URI:
- https://models.cellml.org/workspace/607/rawfile/f725b6864f22a00138a2c2455308142c8baba373/Figure03.cellml
<?xml version='1.0' encoding='UTF-8'?>
<model name="my_model" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
<!--Nima October 2020-->
<component name="main">
<!-- Parameters those are fixed in the model (i.e., water fractions, hemoglobin
concentration in RBCs, equilibrium constants, and Hill coefficient)-->
<variable initial_value="0.94" name="Wpl" units="dimensionless"/>
<!--fractional water space in plasma-->
<variable initial_value="0.65" name="Wrbc" units="dimensionless"/>
<!--fractional water space in RBCs-->
<variable initial_value="0.69" name="Rrbc" units="dimensionless"/>
<!--Gibbs-Donnan ratio across RBC membrane-->
<variable initial_value="5.18e-3" name="Hbrbc" units="dimensionless"/>
<!--hemoglobin concentration in RBCs;M-->
<variable initial_value="2.95e-5" name="K2" units="dimensionless"/>
<!--CO2 + HbNH2 equilibrium constant-->
<variable initial_value="1.0e-6" name="K2dp" units="dimensionless"/>
<!--HbNHCOOH dissociation constant; M-->
<variable name="K2p" units="dimensionless"/>
<!--kf2p/kb2p; 1/M-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>K2p</ci>
<apply>
<divide/>
<ci>K2</ci>
<ci>K2dp</ci>
</apply>
</apply>
</math>
<variable initial_value="2.51e-5" name="K3" units="dimensionless"/>
<!--CO2 + O2HbNH2 equilibrium constant-->
<variable initial_value="1.0e-6" name="K3dp" units="dimensionless"/>
<!--O2HbNHCOOH dissociation constant; M-->
<variable name="K3p" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>K3p</ci>
<apply>
<divide/>
<ci>K3</ci>
<ci>K3dp</ci>
</apply>
</apply>
</math>
<!--kf3p/kb3p; 1/M-->
<variable initial_value="2.63e-8" name="K5dp" units="dimensionless"/>
<!--HbNH3+ dissociation constant; M-->
<variable initial_value="1.91e-8" name="K6dp" units="dimensionless"/>
<!--O2HbNH3+ dissociation constant; M-->
<variable initial_value="2.7" name="nhill" units="dimensionless"/>
<!--Hill coefficient-->
<variable name="n0" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>n0</ci>
<apply>
<minus/>
<ci>nhill</ci>
<cn cellml:units="dimensionless">1.0</cn>
</apply>
</apply>
</math>
<!-- Variables those are privately fixed in the model with the standard
physiological values (i.e., pH0, pCO20, DPG0, Temp0)-->
<variable initial_value="100.0" name="pO20" units="dimensionless"/>
<!--standard O2 partial pressure in blood; mmHg-->
<variable initial_value="40.0" name="pCO20" units="dimensionless"/>
<!--standard CO2 partial pressure in blood; mmHg-->
<variable initial_value="7.24" name="pH0" units="dimensionless"/>
<!--standard pH in RBCs-->
<variable initial_value="4.65e-3" name="DPG0" units="dimensionless"/>
<!--standard 2;3-DPG concentration in RBCs; M-->
<variable initial_value="37.0" name="Temp0" units="dimensionless"/>
<!--standard temperature in blood;degC-->
<variable name="Fact" units="dimensionless"/>
<!--a multiplicative factor; M/mmHg-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Fact</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless" type="e-notation">1.0<sep/>-6</cn>
<ci>Wpl</ci>
</apply>
</apply>
</math>
<variable name="alpha_O2_0" units="dimensionless"/>
<!--solubility of O2 in water at 37 C; M/mmHg-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_O2_0</ci>
<apply>
<times/>
<ci>Fact</ci>
<cn cellml:units="dimensionless">1.37</cn>
</apply>
</apply>
</math>
<variable name="alpha_CO2_0" units="dimensionless"/>
<!--solubility of CO2 in water at 37 C; M/mmHg-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_CO2_0</ci>
<apply>
<times/>
<ci>Fact</ci>
<cn cellml:units="dimensionless">30.7</cn>
</apply>
</apply>
</math>
<variable name="O20" units="dimensionless"/>
<!--standard O2 concentration in RBCs; M-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>O20</ci>
<apply>
<times/>
<ci>alpha_O2_0</ci>
<ci>pO20</ci>
</apply>
</apply>
</math>
<variable name="CO20" units="dimensionless"/>
<!--standard CO2 concentration in RBCs; M-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>CO20</ci>
<apply>
<times/>
<ci>alpha_CO2_0</ci>
<ci>pCO20</ci>
</apply>
</apply>
</math>
<variable name="Hp0" units="dimensionless"/>
<!--standard H+ concentration in RBCs; M-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Hp0</ci>
<apply>
<power/>
<cn cellml:units="dimensionless">10</cn>
<apply>
<minus/>
<ci>pH0</ci>
</apply>
</apply>
</apply>
</math>
<variable name="pHpl0" units="dimensionless"/>
<!--standard pH in plasma-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>pHpl0</ci>
<apply>
<minus/>
<ci>pH0</ci>
<apply>
<log/>
<ci>Rrbc</ci>
</apply>
</apply>
</apply>
</math>
<variable initial_value="26.8" name="P500" units="dimensionless"/>
<!--standard pO2 at 50% SHbO2; mmHg-->
<variable name="C500" units="dimensionless"/>
<!--standard O2 at 50% SHbO2; M-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>C500</ci>
<apply>
<times/>
<ci>alpha_O2_0</ci>
<ci>P500</ci>
</apply>
</apply>
</math>
<!-- Calculation of intermediate variables and the indices n1, n2, n3, and
n4 in the computations of SHbO2 & SHbCO2-->
<variable name="Wbl" units="dimensionless"/>
<!--fractional water space in blood-->
<variable initial_value="37.0" name="Temp" units="dimensionless"/>
<!--temperature in blood;degC-->
<variable initial_value="0.45" name="Hct" units="dimensionless"/>
<!--Hematocrit; volume fraction of blood occupied by RBCs-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Wbl</ci>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>Hct</ci>
</apply>
<ci>Wpl</ci>
</apply>
<apply>
<times/>
<ci>Hct</ci>
<ci>Wrbc</ci>
</apply>
</apply>
</apply>
</math>
<variable name="pHpl" units="dimensionless"/>
<!--pH in plasma-->
<variable initial_value="7.4" name="pH" units="dimensionless"/>
<!--pH in rbc-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>pHpl</ci>
<apply>
<minus/>
<ci>pH</ci>
<apply>
<log/>
<ci>Rrbc</ci>
</apply>
</apply>
</apply>
</math>
<variable name="pHpldiff" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>pHpldiff</ci>
<apply>
<minus/>
<ci>pHpl</ci>
<ci>pHpl0</ci>
</apply>
</apply>
</math>
<variable initial_value="40" name="pCO2" units="dimensionless"/>
<!--rbc pCo2,mmHg-->
<variable name="pCO2diff" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>pCO2diff</ci>
<apply>
<minus/>
<ci>pCO2</ci>
<ci>pCO20</ci>
</apply>
</apply>
</math>
<variable initial_value="0.5" name="pO2" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>pO2</ci>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</math>
<!--rbc pO2,mmHg-->
<variable initial_value="4.65e-3" name="DPG" units="dimensionless"/>
<!-- Concentration of 2,3-DPG in RBCs,M-->
<variable name="pHdiff" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>pHdiff</ci>
<apply>
<minus/>
<ci>pH</ci>
<ci>pH0</ci>
</apply>
</apply>
</math>
<!--*******-->
<variable name="DPGdiff" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>DPGdiff</ci>
<apply>
<minus/>
<ci>DPG</ci>
<ci>DPG0</ci>
</apply>
</apply>
</math>
<variable name="Tempdiff" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Tempdiff</ci>
<apply>
<minus/>
<ci>Temp</ci>
<ci>Temp0</ci>
</apply>
</apply>
</math>
<variable name="alpha_O2" units="dimensionless"/>
<!--solubility of O2 in water-->
<variable name="alpha_CO2" units="dimensionless"/>
<!-- //solubility of CO2 in water-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_O2</ci>
<apply>
<times/>
<ci>Fact</ci>
<apply>
<plus/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1.37</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">0.0137</cn>
<ci>Tempdiff</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.00058</cn>
<apply>
<power/>
<ci>Tempdiff</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_CO2</ci>
<apply>
<times/>
<ci>Fact</ci>
<apply>
<plus/>
<apply>
<minus/>
<cn cellml:units="dimensionless">30.7</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">0.57</cn>
<ci>Tempdiff</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.02</cn>
<apply>
<power/>
<ci>Tempdiff</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<variable name="pK1" units="dimensionless"/>
<!--pK of CO2 hydration reaction,-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>pK1</ci>
<apply>
<plus/>
<apply>
<minus/>
<cn cellml:units="dimensionless">6.091</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">0.0434</cn>
<ci>pHpldiff</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.0014</cn>
<ci>Tempdiff</ci>
<ci>pHpldiff</ci>
</apply>
</apply>
</apply>
</math>
<variable name="K1" units="dimensionless"/>
<!--Equilibrium constant for overall CO2 hydration reaction,M-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>K1</ci>
<apply>
<power/>
<cn cellml:units="dimensionless">10</cn>
<apply>
<minus/>
<ci>pK1</ci>
</apply>
</apply>
</apply>
</math>
<variable name="O2" units="dimensionless"/>
<!--M-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>O2</ci>
<apply>
<times/>
<ci>alpha_O2</ci>
<ci>pO2</ci>
</apply>
</apply>
</math>
<variable name="CO2" units="dimensionless"/>
<!--M-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>CO2</ci>
<apply>
<times/>
<ci>alpha_CO2</ci>
<ci>pCO2</ci>
</apply>
</apply>
</math>
<variable name="Hp" units="dimensionless"/>
<!--H+ concentration in RBCs,M-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Hp</ci>
<apply>
<power/>
<cn cellml:units="dimensionless">10</cn>
<apply>
<minus/>
<ci>pH</ci>
</apply>
</apply>
</apply>
</math>
<variable name="Hppl" units="dimensionless"/>
<!--H+ concentration in plasma,M-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Hppl</ci>
<apply>
<power/>
<cn cellml:units="dimensionless">10</cn>
<apply>
<minus/>
<ci>pHpl</ci>
</apply>
</apply>
</apply>
</math>
<!--*******-->
<variable name="Term1" units="dimensionless"/>
<variable name="Term2" units="dimensionless"/>
<variable name="Term3" units="dimensionless"/>
<variable name="Term4" units="dimensionless"/>
<variable name="Term10" units="dimensionless"/>
<variable name="Term20" units="dimensionless"/>
<variable name="Term30" units="dimensionless"/>
<variable name="Term40" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Term1</ci>
<apply>
<times/>
<ci>K2p</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>K2dp</ci>
<ci>Hp</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Term2</ci>
<apply>
<times/>
<ci>K3p</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>K3dp</ci>
<ci>Hp</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Term3</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Hp</ci>
<ci>K5dp</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Term4</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Hp</ci>
<ci>K6dp</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Term10</ci>
<apply>
<times/>
<ci>K2p</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>K2dp</ci>
<ci>Hp0</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Term20</ci>
<apply>
<times/>
<ci>K3p</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>K3dp</ci>
<ci>Hp0</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Term30</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Hp0</ci>
<ci>K5dp</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Term40</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Hp0</ci>
<ci>K6dp</ci>
</apply>
</apply>
</apply>
</math>
<variable name="Kratio10" units="dimensionless"/>
<variable name="Kratio11" units="dimensionless"/>
<variable name="Kratio12" units="dimensionless"/>
<variable name="Kratio20" units="dimensionless"/>
<variable name="Kratio21" units="dimensionless"/>
<variable name="Kratio22" units="dimensionless"/>
<variable name="K4dp" units="dimensionless"/>
<!--1/M-->
<variable name="K4tp" units="dimensionless"/>
<!--1/M-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Kratio10</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci>Term10</ci>
<ci>CO20</ci>
</apply>
<ci>Term30</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>Term20</ci>
<ci>CO20</ci>
</apply>
<ci>Term40</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Kratio11</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci>Term1</ci>
<ci>CO20</ci>
</apply>
<ci>Term3</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>Term2</ci>
<ci>CO20</ci>
</apply>
<ci>Term4</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Kratio12</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci>Term10</ci>
<ci>alpha_CO2_0</ci>
<ci>pCO2</ci>
</apply>
<ci>Term30</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>Term20</ci>
<ci>alpha_CO2_0</ci>
<ci>pCO2</ci>
</apply>
<ci>Term40</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>K4dp</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>Kratio10</ci>
<apply>
<power/>
<ci>O20</ci>
<ci>n0</ci>
</apply>
</apply>
<apply>
<power/>
<ci>C500</ci>
<ci>nhill</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>K4tp</ci>
<apply>
<divide/>
<ci>K4dp</ci>
<apply>
<power/>
<ci>O20</ci>
<ci>n0</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Kratio20</ci>
<apply>
<divide/>
<ci>Kratio10</ci>
<ci>K4tp</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Kratio21</ci>
<apply>
<divide/>
<ci>Kratio11</ci>
<ci>K4tp</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Kratio22</ci>
<apply>
<divide/>
<ci>Kratio12</ci>
<ci>K4tp</ci>
</apply>
</apply>
</math>
<variable name="P501" units="dimensionless"/>
<!--mmHg-->
<variable name="P502" units="dimensionless"/>
<!--mmHg-->
<variable name="P503" units="dimensionless"/>
<!--mmHg-->
<variable name="P504" units="dimensionless"/>
<!--mmHg-->
<variable name="C501" units="dimensionless"/>
<!--M-->
<variable name="C502" units="dimensionless"/>
<!--M-->
<variable name="C503" units="dimensionless"/>
<!--M-->
<variable name="C504" units="dimensionless"/>
<!--M-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>P501</ci>
<apply>
<plus/>
<apply>
<minus/>
<cn cellml:units="dimensionless">26.8</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">21.279</cn>
<ci>pHdiff</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">8.872</cn>
<apply>
<power/>
<ci>pHdiff</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>P502</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">26.8</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">0.0428</cn>
<ci>pCO2diff</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless" type="e-notation">3.64<sep/>-5</cn>
<apply>
<power/>
<ci>pCO2diff</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>P503</ci>
<apply>
<minus/>
<apply>
<plus/>
<cn cellml:units="dimensionless">26.8</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">795.633533</cn>
<ci>DPGdiff</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">19660.8947</cn>
<apply>
<power/>
<ci>DPGdiff</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>P504</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">26.8</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">1.4945</cn>
<ci>Tempdiff</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.04335</cn>
<apply>
<power/>
<ci>Tempdiff</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.0007</cn>
<apply>
<power/>
<ci>Tempdiff</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>C501</ci>
<apply>
<times/>
<ci>alpha_O2_0</ci>
<ci>P501</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>C502</ci>
<apply>
<times/>
<ci>alpha_O2_0</ci>
<ci>P502</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>C503</ci>
<apply>
<times/>
<ci>alpha_O2_0</ci>
<ci>P503</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>C504</ci>
<apply>
<times/>
<ci>alpha_O2</ci>
<ci>P504</ci>
</apply>
</apply>
</math>
<variable name="n1" units="dimensionless"/>
<variable name="n2" units="dimensionless"/>
<variable name="n3" units="dimensionless"/>
<variable name="n4" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>n1</ci>
<piecewise>
<piece>
<cn cellml:units="dimensionless">1.0</cn>
<apply>
<lt/>
<apply>
<abs/>
<apply>
<minus/>
<ci>pH</ci>
<ci>pH0</ci>
</apply>
</apply>
<cn cellml:units="dimensionless" type="e-notation">1.0<sep/>-6</cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<log/>
<ci>Kratio21</ci>
</apply>
<apply>
<times/>
<ci>nhill</ci>
<apply>
<log/>
<ci>C501</ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<ci>pH</ci>
<ci>pH0</ci>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>n2</ci>
<piecewise>
<piece>
<cn cellml:units="dimensionless">1.0</cn>
<apply>
<lt/>
<apply>
<abs/>
<apply>
<minus/>
<ci>pCO2</ci>
<ci>pCO20</ci>
</apply>
</apply>
<cn cellml:units="dimensionless" type="e-notation">1.0<sep/>-6</cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<log/>
<ci>Kratio22</ci>
</apply>
<apply>
<times/>
<ci>nhill</ci>
<apply>
<log/>
<ci>C502</ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<log/>
<ci>CO20</ci>
</apply>
<apply>
<log/>
<ci>CO2</ci>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>n3</ci>
<piecewise>
<piece>
<cn cellml:units="dimensionless">1.0</cn>
<apply>
<lt/>
<apply>
<abs/>
<apply>
<minus/>
<ci>DPG</ci>
<ci>DPG0</ci>
</apply>
</apply>
<cn cellml:units="dimensionless" type="e-notation">1.0<sep/>-6</cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<log/>
<ci>Kratio20</ci>
</apply>
<apply>
<times/>
<ci>nhill</ci>
<apply>
<log/>
<ci>C503</ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<log/>
<ci>DPG0</ci>
</apply>
<apply>
<log/>
<ci>DPG</ci>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>n4</ci>
<piecewise>
<piece>
<cn cellml:units="dimensionless">1.0</cn>
<apply>
<lt/>
<apply>
<abs/>
<apply>
<minus/>
<ci>Temp</ci>
<ci>Temp0</ci>
</apply>
</apply>
<cn cellml:units="dimensionless" type="e-notation">1.0<sep/>-6</cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<log/>
<ci>Kratio20</ci>
</apply>
<apply>
<times/>
<ci>nhill</ci>
<apply>
<log/>
<ci>C504</ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<log/>
<ci>Temp0</ci>
</apply>
<apply>
<log/>
<ci>Temp</ci>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
<variable name="Term5" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Term5</ci>
<apply>
<times/>
<apply>
<power/>
<apply>
<divide/>
<ci>Hp0</ci>
<ci>Hp</ci>
</apply>
<ci>n1</ci>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci>CO20</ci>
<ci>CO2</ci>
</apply>
<ci>n2</ci>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci>DPG0</ci>
<ci>DPG</ci>
</apply>
<ci>n3</ci>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci>Temp0</ci>
<ci>Temp</ci>
</apply>
<ci>n4</ci>
</apply>
</apply>
</apply>
</math>
<!--% Calculation of Hill coefficients (KHbO2 and KHbCO2); O2 and CO2 saturations
% of hemoglobin (SHbO2 and SHbCO2); and O2 and CO2 contents in blood. These
% are computed as functions of pO2 and pCO2. Also compute the concentrations
% of all the components of HbO2 and HbCO2.-->
<variable name="K4p" units="dimensionless"/>
<variable name="KHbO2" units="dimensionless"/>
<variable name="KHbCO2" units="dimensionless"/>
<variable name="SHbO2" units="dimensionless"/>
<variable name="SHbCO2" units="dimensionless"/>
<variable name="O2free" units="dimensionless"/>
<variable name="O2bound" units="dimensionless"/>
<variable name="O2total" units="dimensionless"/>
<variable name="O2content" units="dimensionless"/>
<variable name="CO2free" units="dimensionless"/>
<variable name="CO2bicarb" units="dimensionless"/>
<variable name="CO2bound" units="dimensionless"/>
<variable name="CO2total" units="dimensionless"/>
<variable name="CO2content" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>K4p</ci>
<apply>
<times/>
<ci>K4dp</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>O2</ci>
<ci>O20</ci>
</apply>
<ci>n0</ci>
</apply>
<ci>Term5</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>KHbO2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>K4p</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>Term2</ci>
<ci>CO2</ci>
</apply>
<ci>Term4</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>Term1</ci>
<ci>CO2</ci>
</apply>
<ci>Term3</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>KHbCO2</ci>
<apply>
<divide/>
<apply>
<plus/>
<ci>Term1</ci>
<apply>
<times/>
<ci>Term2</ci>
<ci>K4p</ci>
<ci>O2</ci>
</apply>
</apply>
<apply>
<plus/>
<ci>Term3</ci>
<apply>
<times/>
<ci>Term4</ci>
<ci>K4p</ci>
<ci>O2</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>SHbO2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>KHbO2</ci>
<ci>O2</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>KHbO2</ci>
<ci>O2</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>SHbCO2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>KHbCO2</ci>
<ci>CO2</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>KHbCO2</ci>
<ci>CO2</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>O2free</ci>
<apply>
<times/>
<ci>Wbl</ci>
<ci>alpha_O2</ci>
<ci>pO2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>O2bound</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>Hct</ci>
<ci>Hbrbc</ci>
<ci>SHbO2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>O2total</ci>
<apply>
<plus/>
<ci>O2free</ci>
<ci>O2bound</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>O2content</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2225.6</cn>
<ci>O2total</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>CO2free</ci>
<apply>
<times/>
<ci>Wbl</ci>
<ci>alpha_CO2</ci>
<ci>pCO2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>CO2bicarb</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>Hct</ci>
</apply>
<ci>Wpl</ci>
</apply>
<apply>
<times/>
<ci>Hct</ci>
<ci>Wrbc</ci>
<ci>Rrbc</ci>
</apply>
</apply>
<ci>K1</ci>
<ci>alpha_CO2</ci>
<ci>pCO2</ci>
</apply>
<ci>Hppl</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>CO2bound</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>Hct</ci>
<ci>Hbrbc</ci>
<ci>SHbCO2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>CO2total</ci>
<apply>
<plus/>
<ci>CO2free</ci>
<ci>CO2bicarb</ci>
<ci>CO2bound</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>CO2content</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2225.6</cn>
<ci>CO2total</ci>
</apply>
</apply>
</math>
<variable name="t" units="second"/>
<variable name="O2freepl1" units="dimensionless"/>
<!-- M, // free O2 in plasm-->
<variable name="O2freepl2" units="dimensionless"/>
<!-- ml/dL, // mL free O2 per 100 mL plasma, orig had no units.-->
<variable name="O2freerbc1" units="dimensionless"/>
<!-- M, // free O2 in RBCs-->
<variable name="O2freerbc2" units="dimensionless"/>
<!-- ml/dL; // mL free O2 per 100 mL RBCs, orig had no units.-->
<variable name="O2boundrbc1" units="dimensionless"/>
<!-- M, // bound O2 in RBCs-->
<variable name="O2boundrbc2" units="dimensionless"/>
<!-- ml/dL, // mL bound O2 per 100 mL RBCs, orig had no units.-->
<variable name="CO2freepl1" units="dimensionless"/>
<!-- M, // free CO2 in plasma-->
<variable name="CO2freepl2" units="dimensionless"/>
<!-- ml/dL, // mL CO2 per 100 mL plasma, orig had no units.-->
<variable name="CO2freerbc1" units="dimensionless"/>
<!-- M, // free CO2 in RBCs-->
<variable name="CO2freerbc2" units="dimensionless"/>
<!-- ml/dL, // mL CO2 per 100 mL RBCs, orig had no units.-->
<variable name="CO2bicarbpl1" units="dimensionless"/>
<!-- M, // bicarb in plasma-->
<variable name="CO2bicarbpl2" units="dimensionless"/>
<!-- ml/dL, // mL bicarb per 100 mL plasma, orig had no units.-->
<variable name="CO2bicarbrbc1" units="dimensionless"/>
<!-- M, // bicarb in RBCs-->
<variable name="CO2bicarbrbc2" units="dimensionless"/>
<!-- ml/dL, // mL bicarb per 100 mL RBCs, orig had no units.-->
<variable name="CO2boundrbc1" units="dimensionless"/>
<!-- M, // bound CO2 in RBCs-->
<variable name="CO2boundrbc2" units="dimensionless"/>
<!-- ml/dL;// mL bound CO2 per 100 mL RBCs, orig had no units. -->
<variable name="HbNH2" units="dimensionless"/>
<!-- M, // HbNH2 concentration in RBCs, M-->
<variable name="HbNH3p" units="dimensionless"/>
<!-- M, // HbNH3+ concentration in RBCs, M-->
<variable name="O2HbNH2" units="dimensionless"/>
<!-- M, // O2HbNH2 concentration in RBCs, M-->
<variable name="O2HbNH3p" units="dimensionless"/>
<!-- M, // O2HbNH3+ concentration in RBCs, M-->
<variable name="HbNHCOOH" units="dimensionless"/>
<!-- M, // HbNHCOOH concentration in RBCs, M-->
<variable name="HbNHCOOm" units="dimensionless"/>
<!-- M, // HbNHCOO- concentration in RBCs, M-->
<variable name="O2HbNHCOOH" units="dimensionless"/>
<!-- M,// O2HbNHCOOH concentration in RBCs, M-->
<variable name="O2HbNHCOOm" units="dimensionless"/>
<!-- M,// O2HbNHCOO- concentration in RBCs, M-->
<variable name="SHbO2kin" units="dimensionless"/>
<!-- O2 saturation of hemoglobin from kinetics, unitless-->
<variable name="SHbCO2kin" units="dimensionless"/>
<!-- O2 saturation of hemoglobin from kinetics, unitless-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>HbNH2</ci>
<apply>
<divide/>
<ci>Hbrbc</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>Term1</ci>
<ci>CO2</ci>
</apply>
<ci>Term3</ci>
<apply>
<times/>
<ci>K4p</ci>
<ci>O2</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>Term2</ci>
<ci>CO2</ci>
</apply>
<ci>Term4</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>HbNH3p</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>HbNH2</ci>
<ci>Hp</ci>
</apply>
<ci>K5dp</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>O2HbNH2</ci>
<apply>
<times/>
<ci>K4p</ci>
<ci>O2</ci>
<ci>HbNH2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>O2HbNH3p</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>O2HbNH2</ci>
<ci>Hp</ci>
</apply>
<ci>K6dp</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>HbNHCOOH</ci>
<apply>
<times/>
<ci>K2p</ci>
<ci>CO2</ci>
<ci>HbNH2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>HbNHCOOm</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>K2dp</ci>
<ci>HbNHCOOH</ci>
</apply>
<ci>Hp</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>O2HbNHCOOH</ci>
<apply>
<times/>
<ci>K3p</ci>
<ci>CO2</ci>
<ci>O2HbNH2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>O2HbNHCOOm</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>K3dp</ci>
<ci>O2HbNHCOOH</ci>
</apply>
<ci>Hp</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>SHbO2kin</ci>
<apply>
<divide/>
<apply>
<plus/>
<ci>O2HbNH2</ci>
<ci>O2HbNH3p</ci>
<ci>O2HbNHCOOH</ci>
<ci>O2HbNHCOOm</ci>
</apply>
<ci>Hbrbc</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>SHbCO2kin</ci>
<apply>
<divide/>
<apply>
<plus/>
<ci>HbNHCOOH</ci>
<ci>HbNHCOOm</ci>
<ci>O2HbNHCOOH</ci>
<ci>O2HbNHCOOm</ci>
</apply>
<ci>Hbrbc</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>O2freepl1</ci>
<apply>
<times/>
<ci>Wpl</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>Hct</ci>
</apply>
<ci>alpha_O2</ci>
<ci>pO2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>O2freepl2</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2225.6</cn>
<ci>O2freepl1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>O2freerbc1</ci>
<apply>
<times/>
<ci>Wrbc</ci>
<ci>Hct</ci>
<ci>alpha_O2</ci>
<ci>pO2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>O2freerbc2</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2225.6</cn>
<ci>O2freerbc1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>O2boundrbc1</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>Hct</ci>
<ci>Hbrbc</ci>
<ci>SHbO2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>O2boundrbc2</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2225.6</cn>
<ci>O2boundrbc1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>CO2freepl1</ci>
<apply>
<times/>
<ci>Wpl</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>Hct</ci>
</apply>
<ci>alpha_CO2</ci>
<ci>pCO2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>CO2freepl2</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2225.6</cn>
<ci>CO2freepl1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>CO2freerbc1</ci>
<apply>
<times/>
<ci>Wrbc</ci>
<ci>Hct</ci>
<ci>alpha_CO2</ci>
<ci>pCO2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>CO2freerbc2</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2225.6</cn>
<ci>CO2freerbc1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>CO2bicarbpl1</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>Wpl</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>Hct</ci>
</apply>
<ci>K1</ci>
<ci>alpha_CO2</ci>
<ci>pCO2</ci>
</apply>
<ci>Hppl</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>CO2bicarbpl2</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2225.6</cn>
<ci>CO2bicarbpl1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>CO2bicarbrbc1</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>Wrbc</ci>
<ci>Hct</ci>
<ci>Rrbc</ci>
<ci>K1</ci>
<ci>alpha_CO2</ci>
<ci>pCO2</ci>
</apply>
<ci>Hppl</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>CO2bicarbrbc2</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2225.6</cn>
<ci>CO2bicarbrbc1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>CO2boundrbc1</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>Hct</ci>
<ci>Hbrbc</ci>
<ci>SHbCO2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>CO2boundrbc2</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2225.6</cn>
<ci>CO2boundrbc1</ci>
</apply>
</apply>
</math>
</component>
</model>