Location: Blood HbO2 and HbCO2 Dissociation Curves @ f725b6864f22 / Figure01(1).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/Figure01(1).cellml
<?xml version='1.0' encoding='UTF-8'?>
<model name="my_model" xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#">
<!--Nima October 2020 (CellML version of the mathematical model of O2 and CO2 saturations of hemoglobin which was first developed by Ranjan K. Dash and James B. Bassingthwaighte in Matlab, Jsim and SBML-->
<units name="M">
<unit units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="per_M">
<unit exponent="-1" units="M"/>
</units>
<units name="mmHg">
<unit multiplier="133.322" units="newton"/>
<unit exponent="-2" units="metre"/>
</units>
<units name="M_per_mmHg">
<unit units="M"/>
<unit exponent="-1" units="mmHg"/>
</units>
<units name="C">
<unit units="celsius"/>
</units>
<component name="main">
<!-- Parameters those are fixed in the model (i.e., water fractions, hemoglobin
concentration in RBCs, equilibrium constants, and Hill coefficient)-->
<!--fractional water space in plasma-->
<variable initial_value="0.94" name="Wpl" units="dimensionless"/>
<!--fractional water space in RBCs-->
<variable initial_value="0.65" name="Wrbc" units="dimensionless"/>
<!--Gibbs-Donnan ratio across RBC membrane-->
<variable initial_value="0.69" name="Rrbc" units="dimensionless"/>
<!--hemoglobin concentration in RBCs;M-->
<variable initial_value="5.18e-3" name="Hbrbc" units="M"/>
<!--CO2 + HbNH2 equilibrium constant-->
<variable initial_value="2.95e-5" name="K2" units="dimensionless"/>
<!--HbNHCOOH dissociation constant; M-->
<variable initial_value="1.0e-6" name="K2dp" units="M"/>
<!--kf2p/kb2p; 1/M-->
<variable name="K2p" units="per_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>
<!--CO2 + O2HbNH2 equilibrium constant-->
<variable initial_value="2.51e-5" name="K3" units="dimensionless"/>
<!--O2HbNHCOOH dissociation constant; M-->
<variable initial_value="1.0e-6" name="K3dp" units="M"/>
<!--kf3p/kb3p; 1/M-->
<variable name="K3p" units="per_M"/>
<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>
<!--HbNH3+ dissociation constant; M-->
<variable initial_value="2.63e-8" name="K5dp" units="M"/>
<!--O2HbNH3+ dissociation constant; M-->
<variable initial_value="1.91e-8" name="K6dp" units="M"/>
<!--Hill coefficient-->
<variable initial_value="2.7" name="nhill" units="dimensionless"/>
<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)-->
<!--standard O2 partial pressure in blood; mmHg-->
<variable initial_value="100.0" name="pO20" units="mmHg"/>
<!--standard CO2 partial pressure in blood; mmHg-->
<variable initial_value="40.0" name="pCO20" units="mmHg"/>
<!--standard pH in RBCs-->
<variable initial_value="7.24" name="pH0" units="dimensionless"/>
<!--standard 2;3-DPG concentration in RBCs; M-->
<variable initial_value="4.65e-3" name="DPG0" units="M"/>
<!--standard temperature in blood;degC-->
<variable initial_value="37.0" name="Temp0" units="C"/>
<!--a multiplicative factor; M/mmHg-->
<variable name="Fact" units="M_per_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>
<!--solubility of O2 in water at 37 C; M/mmHg-->
<variable name="alpha_O2_0" units="M_per_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>
<!--solubility of CO2 in water at 37 C; M/mmHg-->
<variable name="alpha_CO2_0" units="M_per_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>
<!--standard O2 concentration in RBCs; M-->
<variable name="O20" units="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>
<!--standard CO2 concentration in RBCs; M-->
<variable name="CO20" units="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>
<!--standard H+ concentration in RBCs; M-->
<variable name="Hp0" units="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>
<!--standard pH in plasma-->
<variable name="pHpl0" units="dimensionless"/>
<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>
<!--standard pO2 at 50% SHbO2; mmHg-->
<variable initial_value="26.6" name="P500" units="mmHg"/>
<!--standard O2 at 50% SHbO2; M-->
<variable name="C500" units="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-->
<!--fractional water space in blood-->
<variable name="Wbl" units="dimensionless"/>
<!--temperature in blood;degC-->
<variable initial_value="37.0" name="Temp" units="dimensionless"/>
<!--Hematocrit; volume fraction of blood occupied by RBCs-->
<variable initial_value="0.45" name="Hct" units="dimensionless"/>
<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>
<!--pH in plasma-->
<variable name="pHpl" units="dimensionless"/>
<!--pH in rbc-->
<variable initial_value="6.68" name="pH" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>pH</ci>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
<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>
<!--rbc pCo2,mmHg-->
<variable initial_value="40" name="pCO2" units="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>
<!--rbc pO2,mmHg-->
<variable initial_value="80" name="pO2" units="mmHg"/>
<!-- Concentration of 2,3-DPG in RBCs,M-->
<variable initial_value="4.65e-3" name="DPG" units="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>
<!--solubility of O2 in water-->
<variable name="alpha_O2" units="M_per_mmHg"/>
<!--solubility of CO2 in water-->
<variable name="alpha_CO2" units="M_per_mmHg"/>
<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>
<!--Equilibrium constant for overall CO2 hydration reaction,M-->
<variable name="K1" units="dimensionless"/>
<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>
<!--M-->
<variable name="O2" units="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>
<!--M-->
<variable name="CO2" units="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>
<!--H+ concentration in RBCs,M-->
<variable name="Hp" units="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>
<!--H+ concentration in plasma,M-->
<variable name="Hppl" units="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="per_M"/>
<variable name="Term2" units="per_M"/>
<variable name="Term3" units="dimensionless"/>
<variable name="Term4" units="dimensionless"/>
<variable name="Term10" units="per_M"/>
<variable name="Term20" units="per_M"/>
<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="M"/>
<variable name="Kratio21" units="M"/>
<variable name="Kratio22" units="M"/>
<!--1/M-->
<variable name="K4dp" units="dimensionless"/>
<!--1/M-->
<variable name="K4tp" units="per_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>
<!--mmHg-->
<variable name="P501" units="mmHg"/>
<!--mmHg-->
<variable name="P502" units="mmHg"/>
<!--mmHg-->
<variable name="P503" units="mmHg"/>
<!--mmHg-->
<variable name="P504" units="mmHg"/>
<!--M-->
<variable name="C501" units="M"/>
<!--M-->
<variable name="C502" units="M"/>
<!--M-->
<variable name="C503" units="M"/>
<!--M-->
<variable name="C504" units="M"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>P501</ci>
<apply>
<plus/>
<apply>
<minus/>
<cn cellml:units="dimensionless">26.765</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">26.80</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">26.78</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">26.75</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="per_M"/>
<variable name="KHbO2" units="per_M"/>
<variable name="KHbCO2" units="per_M"/>
<variable name="SHbO2" units="dimensionless"/>
<variable name="SHbCO2" units="dimensionless"/>
<variable name="O2free" units="M"/>
<variable name="O2bound" units="M"/>
<variable name="O2total" units="M"/>
<variable name="O2content" units="M"/>
<variable name="CO2free" units="M"/>
<variable name="CO2bicarb" units="M"/>
<variable name="CO2bound" units="M"/>
<variable name="CO2total" units="M"/>
<variable name="CO2content" units="M"/>
<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>
<!-- var a: dimensionless {init: 1};-->
<variable name="t" units="second"/>
<!-- ode(a, t) = 1{dimensionless};-->
<!-- M, // free O2 in plasm-->
<variable name="O2freepl1" units="M"/>
<!-- ml/dL, // mL free O2 per 100 mL plasma, orig had no units.-->
<variable name="O2freepl2" units="dimensionless"/>
<!-- M, // free O2 in RBCs-->
<variable name="O2freerbc1" units="M"/>
<!-- ml/dL; // mL free O2 per 100 mL RBCs, orig had no units.-->
<variable name="O2freerbc2" units="dimensionless"/>
<!-- M, // bound O2 in RBCs-->
<variable name="O2boundrbc1" units="M"/>
<!-- ml/dL, // mL bound O2 per 100 mL RBCs, orig had no units.-->
<variable name="O2boundrbc2" units="dimensionless"/>
<!-- M, // free CO2 in plasma-->
<variable name="CO2freepl1" units="M"/>
<!-- ml/dL, // mL CO2 per 100 mL plasma, orig had no units.-->
<variable name="CO2freepl2" units="dimensionless"/>
<!-- M, // free CO2 in RBCs-->
<variable name="CO2freerbc1" units="M"/>
<!-- ml/dL, // mL CO2 per 100 mL RBCs, orig had no units.-->
<variable name="CO2freerbc2" units="dimensionless"/>
<!-- M, // bicarb in plasma-->
<variable name="CO2bicarbpl1" units="M"/>
<!-- ml/dL, // mL bicarb per 100 mL plasma, orig had no units.-->
<variable name="CO2bicarbpl2" units="dimensionless"/>
<!-- M, // bicarb in RBCs-->
<variable name="CO2bicarbrbc1" units="M"/>
<!-- ml/dL, // mL bicarb per 100 mL RBCs, orig had no units.-->
<variable name="CO2bicarbrbc2" units="dimensionless"/>
<!-- M, // bound CO2 in RBCs-->
<variable name="CO2boundrbc1" units="M"/>
<!-- ml/dL;// mL bound CO2 per 100 mL RBCs, orig had no units. -->
<variable name="CO2boundrbc2" units="dimensionless"/>
<!-- M, // HbNH2 concentration in RBCs, M-->
<variable name="HbNH2" units="M"/>
<!-- M, // HbNH3+ concentration in RBCs, M-->
<variable name="HbNH3p" units="M"/>
<!-- M, // O2HbNH2 concentration in RBCs, M-->
<variable name="O2HbNH2" units="M"/>
<!-- M, // O2HbNH3+ concentration in RBCs, M-->
<variable name="O2HbNH3p" units="M"/>
<!-- M, // HbNHCOOH concentration in RBCs, M-->
<variable name="HbNHCOOH" units="M"/>
<!-- M, // HbNHCOO- concentration in RBCs, M-->
<variable name="HbNHCOOm" units="M"/>
<!-- M,// O2HbNHCOOH concentration in RBCs, M-->
<variable name="O2HbNHCOOH" units="M"/>
<!-- M,// O2HbNHCOO- concentration in RBCs, M-->
<variable name="O2HbNHCOOm" units="M"/>
<!-- O2 saturation of hemoglobin from kinetics, unitless-->
<variable name="SHbO2kin" units="dimensionless"/>
<!-- O2 saturation of hemoglobin from kinetics, unitless-->
<variable name="SHbCO2kin" units="dimensionless"/>
<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>