the specific formulae as used on our website

the specific formulae used in our programme

the mass equilibrium constants

(at 37 °C and physiological ionic strength)

water dissociation

Kw' = 4.4*10^-14(mol/l)²

CO₂ + water to bicarbonate dissociation

KC' = 2.44*10^-11(mol/l)²/mmHg
(derived from Henderson-Hasselbalch pK 6.1 and solubility coefficient of 0.0307(mmol/l)/mmHg for CO₂)

bicarbonate to carbonate dissociation

K3' = 5.5*10^-11mol/l

(changed from 6 to 5.5*10^-11mol/l, or 11*10^-11Eq/l,
personal communication from James Figge, 20090220, see also:
J.Figge's website, note 18.)

the dissociation constant for trometamol

Kt' = 10^-7.82Eq/l

the formulae

bicarbonate in mmol/l:
(actual, not standard bicarbonate)
[H⁺] * [HCO₃^-] = K_C * P_CO2 * 10^pH * 7600 (with P_CO2 in kPa)

(the Henderson-Hasselbalch equation solved for bicarbonate)

apparent SID in mEq/l:
SID_app = [Na⁺] + [K⁺] + 2*[Ca²⁺] + 2*[Mg⁺] - [Cl^-]

(the Strong Ion Difference based on the measured strong ions, without lactate)
(even the protein bound calcium and magnesium are electrically balanced by negative albumin charges, that is why their full ionisation values are taken into the equation, contrary to what you will find in most publications.)

effective SID in mEq/l:
SID_eff = [HCO₃^-] + [albumin^-] + [H₂PO₄^-] + [HPO₄^2-] - [trometamol⁺]

(the Strong Ion Difference based on the measured weak ions)

"unknown anions" (XA) in mEq/l:
(also known as the "strong ion gap" or SIG)
[XA] = SID_app - SID_eff

(because of the way we chose to calculate the SID_app the normal range for this value tends to be 4 to 8mEq/l.
this strongly depends on the normal values for the basic measurements at your institution! to check this put the mean values for your local normal value ranges into the formulae for SID_app and SID_eff and calculate the resulting SIG.)

anionic charge of albumin in mEq/l:
[albumin^-] = [total albumin]*(pH*0.123 - 0.631) (total albumin in g/l)
according to Figge J, Mydosh T, Fencl V, 1992

anionic charge of phosphate in mEq/l:
[phosphate^-] = [total phosphate]*(pH*0.309 - 0.469) (total phosphate in mmol/l)
according to Figge J, Mydosh T, Fencl V, 1992

kationic charge of trometamol (tham) in mEq/l:
[tham⁺] = [total tham]*[H⁺]/([H⁺] - 10^-7.82) (total trometamol in mmol/l)

(for our calculations we assume homogeneous distribution of tham across all of the extracellular space - this is not completely correct, of course, as the substance eventually distributes into the intracellular space, too. our programmes cannot simulate time-dependent pharmacokinetcis, though.)

the anion gap (AG) in mEq/l:
AG = [Na⁺] + [K⁺] - [Cl^-] - [HCO₃^-]

the anion gap corrected for albumin level (AG_corr) in mEq/l:
AG_corr = [Na⁺] + [K⁺] - [Cl^-] - [HCO₃^-] + 2.5*(42-[albumin])

serum osmolality in mosmol/l:
osm = 2*([Na⁺] + [K⁺] + [Ca²⁺] + [Mg⁺]) - [albumin^-] + [urea] + [glucose] + [ethanol]

a van Slyke type of osmolality calculation

this is different from the common form of calculating serum osmolality. the reasoning behind this is that virtually all the kations are small entities with an osmolality of 1osmol/ mol and tend to be accompanied by an equal number of small anions, with the important execption of the anionic charge of albumin, which is why this charge is substracted from the doubled sum of the kationic osmolar contribution.
Donald van Slyke put it like this, in 1923: osmolality in plasma water is 2[BA]+[BP], where BA represents "base" - meaning kations in that time's terminology - accompanied by small molecular anions, and BP corresponds to "base" accompanied by protein anionic moieties.

Studies of Gas and Electrolyte Equilibria in The Blood, part 5: Factors Controlling the Electrolyte and Water Distribution in The Blood, J. Biol. Chem., Jul 1923; 56: 765 - 849, the specific reference being to page 778 )

the mathematics behind predicting pH changes:
read more!

the mass equilibrium constants (at 37 °C and physiological ionic strength)
water dissociation	Kw' = 4.4*10^-14(mol/l)²
CO₂ + water to bicarbonate dissociation	KC' = 2.44*10^-11(mol/l)²/mmHg (derived from Henderson-Hasselbalch pK 6.1 and solubility coefficient of 0.0307(mmol/l)/mmHg for CO₂)
bicarbonate to carbonate dissociation	K3' = 5.510^-11mol/l (changed from 6 to 5.510^-11mol/l, or 11*10^-11Eq/l, personal communication from James Figge, 20090220, see also: J.Figge's website, note 18.)
the dissociation constant for trometamol	Kt' = 10^-7.82Eq/l

the formulae
bicarbonate in mmol/l: (actual, not standard bicarbonate) [H⁺] * [HCO₃^-] = K_C * P_CO2 * 10^pH * 7600 (with P_CO2 in kPa) (the Henderson-Hasselbalch equation solved for bicarbonate)
apparent SID in mEq/l: SID_app = [Na⁺] + [K⁺] + 2[Ca²⁺] + 2[Mg⁺] - [Cl^-] (the Strong Ion Difference based on the measured strong ions, without lactate) (even the protein bound calcium and magnesium are electrically balanced by negative albumin charges, that is why their full ionisation values are taken into the equation, contrary to what you will find in most publications.)
effective SID in mEq/l: SID_eff = [HCO₃^-] + [albumin^-] + [H₂PO₄^-] + [HPO₄^2-] - [trometamol⁺] (the Strong Ion Difference based on the measured weak ions)
"unknown anions" (XA) in mEq/l: (also known as the "strong ion gap" or SIG) [XA] = SID_app - SID_eff (because of the way we chose to calculate the SID_app the normal range for this value tends to be 4 to 8mEq/l. this strongly depends on the normal values for the basic measurements at your institution! to check this put the mean values for your local normal value ranges into the formulae for SID_app and SID_eff and calculate the resulting SIG.)
anionic charge of albumin in mEq/l: [albumin^-] = [total albumin](pH0.123 - 0.631) (total albumin in g/l) according to Figge J, Mydosh T, Fencl V, 1992
anionic charge of phosphate in mEq/l: [phosphate^-] = [total phosphate](pH0.309 - 0.469) (total phosphate in mmol/l) according to Figge J, Mydosh T, Fencl V, 1992
kationic charge of trometamol (tham) in mEq/l: [tham⁺] = [total tham]*[H⁺]/([H⁺] - 10^-7.82) (total trometamol in mmol/l) (for our calculations we assume homogeneous distribution of tham across all of the extracellular space - this is not completely correct, of course, as the substance eventually distributes into the intracellular space, too. our programmes cannot simulate time-dependent pharmacokinetcis, though.)
the anion gap (AG) in mEq/l: AG = [Na⁺] + [K⁺] - [Cl^-] - [HCO₃^-]
the anion gap corrected for albumin level (AG_corr) in mEq/l: AG_corr = [Na⁺] + [K⁺] - [Cl^-] - [HCO₃^-] + 2.5*(42-[albumin])
serum osmolality in mosmol/l: osm = 2*([Na⁺] + [K⁺] + [Ca²⁺] + [Mg⁺]) - [albumin^-] + [urea] + [glucose] + [ethanol] a van Slyke type of osmolality calculation this is different from the common form of calculating serum osmolality. the reasoning behind this is that virtually all the kations are small entities with an osmolality of 1osmol/ mol and tend to be accompanied by an equal number of small anions, with the important execption of the anionic charge of albumin, which is why this charge is substracted from the doubled sum of the kationic osmolar contribution. Donald van Slyke put it like this, in 1923: osmolality in plasma water is 2[BA]+[BP], where BA represents "base" - meaning kations in that time's terminology - accompanied by small molecular anions, and BP corresponds to "base" accompanied by protein anionic moieties. Studies of Gas and Electrolyte Equilibria in The Blood, part 5: Factors Controlling the Electrolyte and Water Distribution in The Blood, J. Biol. Chem., Jul 1923; 56: 765 - 849, the specific reference being to page 778 )


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