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Initial composition calculation to reach osmolarity equilibrium betwe…
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…en blood plasma and blood red cells
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@MarekMatejak
MarekMatejak committed Sep 30, 2023
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218 changes: 216 additions & 2 deletions Physiolibrary/Media.mo
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Expand Up @@ -17,8 +17,8 @@ package Media
"AnesthesiaVascularConductance",
"Angiotensin2","Renin","Aldosterone",
"H2O_P","Other_E"},
reference_X=X(),
SubstanceFlowNominal=X() ./ Constants.TimeScale,
reference_X=ArterialDefault,
SubstanceFlowNominal=ArterialDefault ./ Constants.TimeScale,
ThermoStates=Modelica.Media.Interfaces.Choices.IndependentVariables.phX,
reducedX=false,
singleState=true,
Expand Down Expand Up @@ -1231,6 +1231,219 @@ package Media
F := XE/ (XE + XP);
end formedElementsMassFraction;

model InitalComposition "To set mass fractions in blood"

input Types.Temperature T = 310.15;
input Types.Pressure p = 101325;
input Types.ElectricPotential v = 0;
input Real I=0;

input Types.VolumeFraction hematocrit = D_Hct "Hematocrit [ml/ml]";
input Types.Concentration tO2 = D_Arterial_O2 "Total oxygen in blood",
tCO2 = D_Arterial_CO2 "Total carbon dioxide in blood",
tCO = D_CO "Total carbon monoxide in blood",
tHb = D_Hb "Total hemoglobin in blood";
input Types.Fraction FMetHb=D_MetHb/D_Hb "Methemoglobin fraction",
FHbF=D_HbF/D_Hb "Foetal hemoglobin fraction";
input Types.Concentration tAlb = D_Alb "Total albumin in blood plasma";
input Types.MassConcentration tGlb = D_Glb "Total globulin in blood plasma";

input Types.Concentration tPO4 = D_PO4 "Total inorganic phosphate in blood plasma",
cDPG = D_DPG "Diphosphoglycerate in red cells",
glucose = D_Glucose "Glucose in blood plasma",
lactate = D_Lactate "Lactate in blood plasma",
urea = D_Urea "Urea in blood plasma",
aminoAcids = D_AminoAcids "Amino acids in blood plasma",
lipids = D_Lipids "Fatty acids in blood plasma",
ketoacids = D_Ketoacids "Keto acids in blood plasma",
BEox = D_BEox "Base excess of oxygenated blood";

input Types.MassConcentration
epinephrine(displayUnit="ng/L")=D_Epinephrine_MC "Epinephrine in blood plasma",
norepinephrine(displayUnit="ng/L")=D_Norepinephrine_MC "Norepinephrine in blood plasma";
input Types.Concentration
vasopressin(displayUnit="pmol/L")=D_Vasopressin "ADH in blood plasma";
input Real
insulin(displayUnit="mU/L")=D_Insulin_A "Insulin in blood plasma";
input Types.MassConcentration
glucagon(displayUnit="ng/L")=D_Glucagon_MC "Glucagon in blood plasma";
input Types.Concentration
thyrotropin(displayUnit="pmol/L")=D_Thyrotropin "Thyrotropin in blood plasma";
input Types.MassConcentration
thyroxine(displayUnit="ug/L")=D_Thyroxine_MC "Thyroxine blood plasma",
leptin(displayUnit="ug/L")=D_Leptin_MC "Leptin in blood plasma",
desglymidodrine(displayUnit="ug/L")=D_Desglymidodrine_MC "Desglymidodrine in blood plasma";
input Types.Fraction
alphaBlockers = D_AlphaBlockers_f "Alpha blockers efffect",
betaBlockers = D_BetaBlockers_f "Beta blockers efffect",
anesthesiaVascularConductance = D_AnesthesiaVascularConductance_f "Anesthesia vasodilatation efffect";
input Types.MassConcentration
angiotensin2(displayUnit="ng/L")=D_Angiotensin2_MC "A2 in blood plasma";
input Real renin(displayUnit="ng/mL/h")=D_Renin_PRA "Renin in blood plasma";
input Types.Concentration
aldosterone(displayUnit="nmol/L")=D_Aldosterone "Aldosterone in blood plasma";

input Types.MassFraction XH2O = D_H2O_B "Water in blood";
//input Types.MassConcentration H2O_plasma = D_BloodPlasmaWater "Water in blood plasma";
//input Types.MassConcentration H2O_ery = D_BloodFormedElementsWater "Water in blood red cells";

input Types.Concentration cNa_P = D_Na "Sodium in blood plasma";
input Types.Concentration cK_P = D_K "Potassium in blood plasma";
input Types.Concentration cNa_E = D_Na_RBC "Sodium in erythrocytes";
input Types.Concentration cK_E = D_K_RBC "Potassium in erythrocytes";

output Types.MassFraction X[nS];

// output Types.MassFraction XH2O;

protected
Types.Density density,plasmaDensity;
Types.Fraction plasmacrit;
Types.Concentration NSID;
Types.Fraction XE,XP,PMF;

Types.SpecificEnthalpy h = X*Physiolibrary.Media.Blood.specificEnthalpies_TpvI(T,p);
ThermodynamicState state = setState_phX(p, h, X) "State of blood";
Physiolibrary.Media.Blood.BloodGases bloodGases(
T=T,
state=state);

Types.MassFraction pct "Plasmacrit [kg/kg]";
Types.MassFraction hct "Hematocrit [kg/kg]";

Modelica.Units.SI.Molality fH2O_P "Amount of free H2O particles in 1 kg of blood plasma [mol/kg]";
Modelica.Units.SI.Molality x_P(start=1.2) "Amount of free particles in 1 kg of blood plasma [mol/kg]";
Modelica.Units.SI.Molality x_E(start=0.86) "Amount of free particles in 1 kg of blood erythrocytes [mol/kg]";

Types.MoleFraction aH2O_P,aH2O_E, aCl_P, aCl_E, aHCO3, aHCO3_E;
Types.MassConcentration H2O_plasma(start=D_BloodPlasmaWater) "Water in blood plasma";
Types.MassConcentration H2O_ery(start=D_BloodFormedElementsWater) "Water in blood red cells";

// debug of chloride shift:
Modelica.Units.SI.Concentration cCl_P = (aCl_P*x_P)*plasmaDensity "Chloride in blood plasma";
Modelica.Units.SI.Concentration cCl_E = (aCl_E*x_E)*formedElementsDensity(state) "Chloride in blood red cells";

Modelica.Units.SI.Concentration cHCO3_P = (aHCO3*x_P)*plasmaDensity "Bicarbonate in blood plasma";
Modelica.Units.SI.Concentration cHCO3_E = (aHCO3_E*x_E)*formedElementsDensity(state) "Bicarbonate in blood red cells";
algorithm
density := D_BloodDensity;
plasmaDensity := D_BloodPlasmaDensity;
plasmacrit := 1-hematocrit;
NSID := (1 - hematocrit) * (zAlbNAP * tAlb + zGlbNAP * tGlb + zPO4NAP * tPO4 + ztCO2NAP) + hematocrit * (zHbNAE * (tHb / hematocrit) + ztCO2NAE + zDPG*cDPG + zOtherE);

X[i("H2O_P")] := (plasmacrit*H2O_plasma)/density;
X[i("H2O_E")] := (hematocrit*H2O_ery)/density;
X[i("O2")] := (tO2*O2.MolarWeight)/density;
X[i("CO2")] := (tCO2*CO2.MolarWeight)/density;
X[i("CO")] := (tCO*CO.MolarWeight)/density;
X[i("Hb")] := (tHb*Constants.MM_Hb)/density;
X[i("MetHb")] := FMetHb*X[
i("Hb")];
X[i("HbF")] := FHbF*X[i("Hb")];
X[i("Alb")] := plasmacrit*(tAlb*Constants.MM_Alb)/
density;
X[i("Glb")] := plasmacrit*tGlb/density;
X[i("PO4")] := plasmacrit*(tPO4*PO4.MolarWeight)/
density;
X[i("DPG")] := hematocrit*(cDPG*Constants.MM_DPG)/
density;
X[i("Glucose")] := plasmacrit*(glucose*Constants.MM_Glucose)
/density;
X[i("Lactate")] := plasmacrit*(lactate*Constants.MM_Lactate)
/density;
X[i("Urea")] := plasmacrit*(urea*Constants.MM_Urea)
/density;
X[i("AminoAcids")] := plasmacrit*(aminoAcids*
Constants.MM_AminoAcids)/density;
X[i("Lipids")] := plasmacrit*(lipids*Constants.MM_Lipids)
/density;
X[i("KetoAcids")] := plasmacrit*(ketoacids*
Constants.MM_KetoAcids)/density;
X[i("Na_P")] := plasmacrit*(cNa_P*Na.MolarWeight)/density;
X[i("K_P")] := plasmacrit*(cK_P*K.MolarWeight)/density;
X[i("Na_E")] := hematocrit*(cNa_E*Na.MolarWeight)/density;
X[i("K_E")] := hematocrit*(cK_E*K.MolarWeight)/density;
X[i("Cl")] := -((NSID - BEox)-plasmacrit*(cNa_P+cK_P)-hematocrit*(cNa_E+cK_E))*Cl.MolarWeight/density "where blood SID = NSID - BEox";
X[i("Epinephrine")] := plasmacrit*(epinephrine)/
density;
X[i("Norepinephrine")] := plasmacrit*(
norepinephrine)/density;
X[i("Vasopressin")] := plasmacrit*(vasopressin*
Constants.MM_Vasopressin)/density;
X[i("Insulin")] := plasmacrit*(6e-9*insulin*
Constants.MM_Insulin)/density
"conversion factor for human insulin is 1 mU/L = 6.00 pmol/L";
X[i("Glucagon")] := plasmacrit*(glucagon)/density;
X[i("Thyrotropin")] := plasmacrit*(thyrotropin*
Constants.MM_Thyrotropin)/density;
X[i("Thyroxine")] := plasmacrit*(thyroxine)/
density;
X[i("Leptin")] := plasmacrit*(leptin)/density;
X[i("Desglymidodrine")] := plasmacrit*(
desglymidodrine)/density;
X[i("AlphaBlockers")] := 1e-6 * alphaBlockers;
X[i("BetaBlockers")] := 1e-6 * betaBlockers;
X[i("AnesthesiaVascularConductance")] :=
1e-6 * anesthesiaVascularConductance;
X[i("Angiotensin2")] := plasmacrit*(angiotensin2)/
density;
X[i("Renin")] := plasmacrit*(1e-12*0.6*11.2*renin)/
density
"conversion factor from PRA (ng/mL/h) to DRC (mU/L) is 11.2, μIU/mL (mIU/L) * 0.6 = pg/mL";
X[i("Aldosterone")] := plasmacrit*(aldosterone*
Constants.MM_Aldosterone)/density;

PMF := plasmacrit * plasmaDensity/density;
XP := X[i("H2O_P")] + X[i("CO2")] + X[i("Alb")] + X[i("Glb")] + X[i("Glucose")] +
X[i("PO4")] + X[i("Lactate")] + X[i("Urea")] + X[i("AminoAcids")] + X[i("Lipids")] + X[i("KetoAcids")];
XE := XP*(1-PMF)/PMF;
X[i("Other_E")] := XE - (X[i("H2O_E")] + X[i("Hb")] + X[i("DPG")]);

equation
XH2O = X[i("H2O_P")] + X[i("H2O_E")];

aH2O_P = aH2O_E "osmolarity";

aH2O_P = state.X[i("H2O_P")]*Chemical.Interfaces.Incompressible.specificAmountOfParticles(Substances.Water,T,p,v,I) / (pct*x_P);
aH2O_E = state.X[i("H2O_E")]*Chemical.Interfaces.Incompressible.specificAmountOfParticles(Substances.Water,T,p,v,I) / (hct*x_E);

pct = plasmaMassFraction(state);
hct = formedElementsMassFraction(state);

fH2O_P = state.X[i("H2O_P")]*Chemical.Interfaces.Incompressible.specificAmountOfParticles(Substances.Water,T,p,v,I)/pct "Amount of free H2O particles in 1 kg of blood plasma [mol/kg]";

x_P =fH2O_P +
aCl_P*x_P +
(
state.X[i("Na_P")]/Na.MolarWeight +
state.X[i("K_P")]/K.MolarWeight +
state.X[i("CO2")]/CO2.MolarWeight +
state.X[i("Alb")]/Constants.MM_Alb +
state.X[i("Glb")]/Constants.MM_Glb +
state.X[i("Glucose")]/Constants.MM_Glucose +
state.X[i("PO4")]/PO4.MolarWeight +
state.X[i("Lactate")]/Constants.MM_Lactate +
state.X[i("Urea")]/Constants.MM_Urea +
state.X[i("AminoAcids")]/Constants.MM_AminoAcids +
state.X[i("Lipids")]/Constants.MM_Lipids +
state.X[i("KetoAcids")]/Constants.MM_KetoAcids)/pct "Amount of free particles in 1 kg of blood plasma [mol/kg]";

x_E =
aCl_E*x_E +
(state.X[i("H2O_E")]*Chemical.Interfaces.Incompressible.specificAmountOfParticles(Substances.Water,T,p,v,I) +
state.X[i("K_E")]/K.MolarWeight +
state.X[i("Na_E")]/Na.MolarWeight +
state.X[i("Hb")]/Constants.MM_Hb +
state.X[i("DPG")]/Constants.MM_DPG)
/hct "Amount of free particles in 1 kg of intracellular fluid in erythrocytes [mol/kg]"; //+ 0.03

aHCO3 = bloodGases.cHCO3 / (x_P*plasmaDensity);
aHCO3_E = bloodGases.cHCO3_E / (x_E*formedElementsDensity(state));

aHCO3*aCl_E = aCl_P*aHCO3_E "Chloride shift";
state.X[i("Cl")] = (aCl_P*x_P)*Cl.MolarWeight*pct + (aCl_E*x_E)*Cl.MolarWeight*hct "Mass fraction of Cl- in blood";

end InitalComposition;
end Blood;

package Water "Incompressible water with constant heat capacity"
Expand Down Expand Up @@ -2383,6 +2596,7 @@ Modelica source.

constant Types.Concentration D_BloodPlasmaWater=932.75 "Default free particles of water in blood plasma";
constant Types.Concentration D_BloodFormedElementsWater=694 "Default free particles of water in blood formed elements";
constant Types.MassFraction D_H2O_B = 0.7342409 "Mass fraction of water in blood";

end InitialValues;
end Media;
2 changes: 1 addition & 1 deletion Physiolibrary/package.mo
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Expand Up @@ -49,7 +49,7 @@ package Physiolibrary "System biology, integrative physiology and pathophysiolog
<li><a href=\"modelica://Physiolibrary.UsersGuide.Connectors\">Connectors</a></li>
<li><a href=\"modelica://Physiolibrary.UsersGuide.Contact\">Contact</a> </li>
</ul>
<p><br>The origin of this Modelica Physiolibrary was in the first version of our HumMod Golem Edition model implementation, where it was called HumMod.Library. As the successors of Guyton&apos;s Medical Physiology School write, the original HumMod model is &ldquo;The best, most complete, mathematical model of human physiology ever created&rdquo;.</p>
<p><br>The origin of this Modelica Physiolibrary was in the first version of our HumMod Golem Edition model implementation, where it was called HumMod.Library. As the successors of Guyton&apos;s Medical Physiology School write, the original HumMod model was &ldquo;The best, most complete, mathematical model of human physiology ever created&rdquo;.</p>
<p>We are also developing many types of smaller physiological models for use in medical education, so it was essential to separate this library from our HumMod Modelica implementation. This separation improves the quality of the next HumMod release and provides a useful Modelica library to modelers in this bioscience.</p>
<p>The library contains only carefully-chosen elementary physiological laws, which are the basis of more complex physiological processes.</p>
<p><br>Physiology is a very progressive discipline, that examines how the living body works. And it is no surprise that all processes in the human body are driven by physical laws of nature. The great challenge is to marry old empirical experiments with the &ldquo;new&rdquo; physical principles. Many teams and projects in the word deal with this formalization of physiology, for example: Physiome, SBML, EuroPhysiome, VPH, CellML etc. It is our hope that this library helps this unflagging effort of physiologists to exactly describe the processes.</p>
Expand Down

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