Anthology on Base Excess

O.Siggaard-Andersen, 1994-05-31 (revised 2004-01-25)

Definition of base excess and concentration of titratable hydrogen ion:

Base Excess is defined as the negative value of the concentration of titratable hydrogen ion in blood or plasma, i.e. it may be determined directly experimentally. The endpoint of titration is pH = 7.40 at pCO2 = 5.3 kPa at T = 37.0 °C.

When the initial pH is below 7.40 the titration is carried out with a strong hydrogen ion binder (e.g. NaOH), and the result is a positive value for the concentration of titratable hydrogen ion, indicating an excess of titratable hydrogen ion. When the initial pH is above 7.4 the titration is carried out with a strong hydrogen ion donor (e.g. HCl), and the result is a negative value for the concentration of titratable hydrogen ion, indicating a deficit of titratable hydrogen ion.

In principle the titration should be carried out without changing any other components than H+ (and Cl-) and CO2; the effect of adding H2O or Na+  (together with OH-) during the titration should be evaluated and corrected for. The concentration of total oxygen should be constant.

With opposite sign base excess equals the concentration of titratable hydrogen ion. Since hydrogen ion is the chemical component of interest, the author now prefers to use this quantity rather than base excess. Unfortunately the term base excess does not directly indicate that the quantity refers to hydrogen ions or hydrogen ion binding groups. The term base formerly referred to cations, and unfortunately often it still does.

Direct titration must be considered to be the reference method. In practice the concentration of titratable hydrogen ion is determined by calculation based on a knowledge of the titration curve of blood or plasma together with the actual pH.

Definition of extracellular fluid and a model of the extracellular fluid:

The extracellular fluid including the blood is not accessible for direct sampling. Therefore the titration must be based on a model of the extended extracellular fluid, obtained by diluting the arterial blood with its own plasma to obtain a buffer value similar to the average buffer value of the total extracellular fluid (including blood). Empirically this is achieved by a three fold dilution of the blood. The base excess of the extracellular fluid is constant during acute in-vivo changes in pCO2 and hence the best parameter of a pure metabolic (non-respiratory) acid-base disturbance. It is often called the Standard Base Excess.

The Van Slyke equation for whole blood:

In actual practice the concentration of titratable hydrogen ion, ctH+B, is determined by calculation. The most recent version of the Van Slyke equation can be found in the OSA computer program, which is constantly updated, and freely available from the authors (Mads and Ole Siggaard-Andersen).

ctH+B = – (1 – ctHbB/ctHb°) · [(cHCO3-P – cHCO3-°)  + βB · (pHP – pH°)]

ctHbB:  the concentration of total hemoglobin in blood.

ctHb° =  43 mmol/L, an empirical constant accounting for plasma-erythrocyte bicarbonate distribution.

cHCO3-P =  αCO2P · pCO2 · antilog(pHP – pK), concentration of bicarbonate in plasma.

αCO2P = 0.23 (mmol/L)/kPa, solubility coefficient of CO2 in plasma at T°.

pCO2: carbon dioxide tension in blood.

pHP: pH of the plasma phase.

pK  = 6.10, the (-log) equilibrium constant for the CO2 /HCO3- equilibrium in plasma.

cHCO3-° = 24.5 mmol/L, reference bicarbonate concentration at pH°, pCO2°, and T °.

pH° = 7.40, the reference pH value.

pCO2° = 5.33 kPa, the reference pCO2 value.

T° = 37 °C, a standard temperature to which all the other quantities refer.

βB = βmHb° · ctHbB + βP, buffer value of non-bicarbonate buffers in blood.

βmHb° = 2.3, apparent molar buffer value of hemoglobin (monomer) in whole blood.

βP = βmAlb° · cAlbP + βwGlb° · ρGlbP + βmPO4° · cPO4,  buffer value of non-bicarbonate buffers in plasma, default value: βP° = 7.7 mmol/L.

βmAlb° = 8.0, molar buffer capacity of albumin.

cAlbP: concentration of albumin in plasma; default value 0,65 mmol/L.

βwGlb° = 0.075 mol/kg, apparent specific buffer capacity of plasma globulins.

ρGlbP: mass concentration of globulins in plasma.

βmPO4° = 0.309, molar buffer capacity of phosphate ion at pH°.

cPO4: concentration of inorganic phosphate in plasma.

βP ≈ βwPr° · ρPrP.

βwPr° = 0.11 mol/kg, specific buffer capacity of total protein in plasma.

ρPrP: mass concentration of total protein in plasma; default value 70 g/L.

The Van Slyke equation for plasma:

If ctHbB = 0, then the equation for whole blood gives titratable hydrogen ion in plasma.

The Van Slyke equation for extracellular fluid:

ctH+Ecf is calculated by replacing ctHbB with the overall extracellular hemoglobin concentration, defined as  ctHbEcf = ctHbB · VB/VEcf, where VEcf includes VB. ctHbEcf is estimated as ctHbEcf = ctHbB/3.

When the hemoglobin concentration or hematocrit is measured, as it is with modern pH-blood gas analyzers combined with a CO-oximeter, it is recommended to take the patient hemoglobin into account for derivation of ctHbEcf. If the blood hemoglobin concentration is unknown, then a default value of 9 mmol/L is used, i.e. ctHbEcf = 3 mmol/L. If the hematocrit (FEryB) is measured, the hemoglobin concentration may be estimated as:

ctHbB = FEryB · ctHbEry°, where ctHbEry° = 20 mmol/L.

Annotated bibliography

The symbols used in the following annotated bibliography are the more recent systematic symbols not the symbols used in the original publications.

1. Singer RB, Hastings AB. An improved clinical method for the estimation of disturbances of the acid-base balance of human blood. Medicine (Baltimore) 1948; 27: 223-42.

Introduce buffer base (cBB+) and delta buffer base (ΔcBB+), using the old terminology, where a base is a cation and an acid an anion:

cBB+         :=  (cNa+ + cK+ + 2 · cCa2+ + 2 · cMg2+) – (cCl- + cHCO3- + 2 · cSO42- + cOrg-)

ΔcBB+     :=  cBB+ cBB+Normal,

where cBB+Normal is the concentration of buffer base in plasma or whole blood after adding or removing HCl so that pH = 7.40 and pCO2 = 5.33 kPa. cBB+ may apply to plasma (serum) and oxygenated whole blood.

Buffer acid (BA) is the concentration of buffer anions:

cBA-         :=  cHCO3- + cPr- + cHb-

Due to the law of electro-neutrality buffer base and buffer acid must be identical.           

Buffer base was calculated as buffer acid, using an alignment nomogram with scales for pH, pCO2, cHCO3P, ctCO2B or ctCO2P, FEryB, sO2Hb, and cBB+. The pH, pCO2, cHCO3-P, ctCO2P scales are identical with the much employed Van Slyke & Sendroy nomogram.

The purpose of introducing buffer base was to obtain a measure of a metabolic acid-base disturbance, i.e. a measure of accumulation of non-volatile acid or base in the plasma or whole blood. Unfortunately buffer base increases with increasing hemoglobin concentration and plasma protein concentration, even at normal pH and pCO2.  For this reason Singer and Hastings recommended ΔcBB+ as a measure of a metabolic acid-base disturbance.

2. Siggaard-Andersen O, Engel K. A new acid-base nomogram. An improved method for calculation of the relevant blood acid-base data. Scand J Clin Lab Invest 1960; 12: 177-86.

Introduce and define base excess as the concentration of titratable base (cBase). The definition differed from the current with respect to the following parameters: T° = 38 °C, pH° = 7.38, pO2° > 80 kPa (equilibration with CO2/O2 mixtures), ensuring  sO2Hb near 100 %.

cBase corresponds to ΔcBB- although they are defined differently.

The base excess was calculated using a curve nomogram with pH and (log) pCO2 on the axes and scales for cHCO3-, cBB- and cBase. A double scale for cBB-Normal as a function of ctHbB added on the cBB- scale. The nomogram was especially suitable for the CO2 equilibration method of Astrup.

3. Siggaard-Andersen O. The pH, logpCO2 blood acid-base nomogram revised. Scand J Clin Lab Invest 1962; 14: 598-604.

The curve nomogram for calculating cBase was revised on the basis of titrations of whole blood and plasma with HCl and NaHCO3 keeping cNa+P constant thereby maintaining the osmolality more constant.

Base Excess was redefined to refer to titration to pH° = 7.40 at pCO2 = 5.33 kPa and T°= 38 °C without specifying the pO2.

4. Siggaard-Andersen O. Blood acid-base alignment nomogram. Scales for pH, pCO2, base excess of whole blood of different hemoglobin concentrations, plasma bicarbonate, and plasma total-CO2. Scand J Clin lab Invest 1963; 15: 211-7.

The curve nomogram was transformed into an alignment nomogram similar to the Singer & Hastings nomogram. Calculations of cBase on the basis of measured pH, pCO2, and ctHb was easier with the alignment nomogram than with the curve nomogram.

The base excess was defined as in the previous reference without specifying the pO2 or sO2. In other words, the base excess value of the blood refers to the actual oxygen saturation unless it is specified that the value refers to completely oxygenated blood.

The difference between the two was calculated using a whole-blood-Haldane-coefficient of 0.48 (mol/mol) (which is higher than the present value of 0.3).

5. Siggaard-Andersen O. Acute experimental acid-base disturbances in dogs. An investigation of the acid-base and electrolyte content of blood and urine. Scand J Clin Lab Invest 1962; 14, Suppl 66: 1-20.

It was shown that cBaseB and cBaseP both change (in opposite direction) during acute in-vivo changes in pCO2. This confirms (forgotten) data of Shaw & Messer from 1932. The variation in whole blood and plasma base excess is due to a redistribution of hydrogen ions between the well buffered blood and the less buffered interstitial fluid.

6. Siggaard-Andersen O. The acid-base status of the blood (thesis). Scand J Clin Lab Invest 1963; 15, Suppl 70: 1-134.

The base excess was defined as in the previous two references. It was specified that the titration should be carried out at the actual oxygen saturation. In analyses of venous blood, however, it will often be of more interest to know the base excess value for oxygenated blood, this corresponding to the value for arterial blood (provided that the oxygen saturation of the arterial blood is nearly 100 %).

This paper contains the first derivation and publication of the base excess equation. The equation allows calculating cBase from pH, cHCO3-P, and ctHbB (Eqns. 15 + 16, p 47 and 49). The following parameters differed from our present: T°  = 38 °C, βmHb° = 2.51, βP° = 8.2 mmol/L.

The equation was based on parallel and linear CO2 equilibration curves in a pH, cHCO3- coordinate system (also called a Davenport diagram).

7. Siggaard-Andersen O. Acid/base disturbances (letter). Lancet 1964; I: 1104.

Prompted by a question from Dr. Selwin Crawford and Dr. Holaday this letter explains in great detail why the base excess should be redefined to refer to the actual hemoglobin oxygen saturation and the original specification about complete oxygenation of the hemoglobin omitted from the definition.

It is completely logical and consistent with the Haldane effect that the base excess of an oxygenated blood sample is lower than the base excess of the deoxygenated sample. Oxygenating the blood from a deoxygenated state corresponds to adding some acid, namely the acid generated when the hemoglobin binds oxygen.

8. Siggaard-Andersen O. Titratable acid or base of body fluids. Ann NY Acad Sci 1966; 133: 41-58.

The paper gives a thorough discussion of the base excess concept and the base excess equation. The following parameters differed from the current:  T° = 38 °C, βmHb° = 2.63, βP° = 9.5 mmol/L.

9. Astrup P, Campbell EJM, Chinard FP, Nahas GG, Siggaard-Andersen O, Winters RW. Report of ad hoc committee on acid-base terminology. In Nahas GG (ed). Current Concepts of Acid-Base Measurement. Ann NY Acad Sci 1966; 133: 251-8.

Base excess was redefined with respect to the standard temperature, which was changed from 38 °C to 37 °C, i.e. T° = 37 °C.

10. Siggaard-Andersen O. Therapeutic aspects of acid-base disorders. In Evans FT, Gray TC (eds). Modern Trends in Anaesthesia. Butterworths, Margate, 1966: 99-131.

The base excess equation was given with the following constants, which are very close to the current values:

βmHb°         = 2.26,

βP°              = 8.0 mmol/L,

cHCO3-°      = 24 mmol/L,

αCO2       = 0.225 (mmol/L)/kPa.

The concept "extracellular" base excess was introduced in this paper for the first time as being the most relevant parameter of a metabolic acidosis or alkalosis being independent of acute in vivo changes in pCO2.

Definition: The concentration of titratable base minus the titratable acid, when titrating the extracellular fluid (Ecf = blood plus interstitial fluid) to an arterial blood plasma pH of 7.40 at a pCO2 of 5.33 kPa at 37 °C.

The buffer value of Ecf can be estimated from the mean hemoglobin concentration of the extracellular fluid, distributing the red cells evenly throughout it.

Calculated using a standard value of: ctHbEcf° = 3.1 mmol/L.

11. Siggaard-Andersen O. An acid-base chart for arterial blood with normal and pathophysiological reference areas. Scand J Clin Lab Invest 1971; 27: 239-45.

cBaseEcf is calculated (approximately) by projecting the pH, pCO2 point in the acid-base chart to the scale for extracellular base excess. Projections to the base excess scale are made along the slanting lines of the chart. These base excess lines represent so-called vivo CO2 equilibration curves. The slope of the lines has been determined experimentally by several authors by CO2 inhalation or hyperventilation. The slope depends on the buffer value of the extracellular fluid, which is largely dependent on the hemoglobin concentration of the extracellular fluid calculated as ctHbEcf = ctHbB · VB/VEcf. In the chart the slope corresponds to a hemoglobin concentration of 3.7 mmol/L, i.e. ctHbEcf° = 3.7 mmol/L.

12. Siggaard-Andersen O. The acid-base status of the blood. 4th revised ed. Munksgaard, Copenhagen and Williams & Wilkins, Baltimore, 1974; pp 229.(ISBN 87 16 01567 3).

The book gives a thorough update on base excess (p 12) and buffer base (p 27) and the base excess equation (p 51). The equation uses all the current constants with the exception of a pK = 6.105 giving a cHCO3° = 24.1 mmol/L.

13. Siggaard-Andersen O. The Van Slyke equation. Scand J Clin Lab Invest 1977; 36, Suppl 146: 15-20.

It was proposed here for the first time to name the important base excess equation the Van Slyke equation to honor Donald D. Van Slyke's outstanding contributions to pH and blood gases. More specifically he introduced the quantity "buffer value" and in 1921 he showed that the CO2 equilibration curve in a pH, cHCO3- diagram is practically a straight line, the slope of which represents the buffer value of the non-bicarbonate buffers.

In this paper the constants of the equation are virtually identical with our most recent values.

14. Siggaard-Andersen O, Rørth M, Strickland DAP. The buffer value of plasma, erythrocyte fluid and whole blood. NBS Special Publication 1977; 450: 11-9.

Gives the most recent values for βmHb° and βP°.

The cause of some of the differences in buffer values reported in the literature is the fact that the buffer value of hemoglobin and of plasma proteins varies with the pH. The value at pH=7.4 is somewhat lower than a mean value for the pH interval 6.8 to 7.8.

15. Siggaard-Andersen O. Acid-base algorithms. NBS Special Publication 1977; 450: 21-6.

Gives a thorough description of the Van Slyke equation, including an alternative equation based on initial calculation of the erythrocyte pH.

16. Siggaard-Andersen O, Siggaard-Andersen M. The oxygen status algorithm: a computer program for calculating and displaying pH and blood gas data. Scand J Clin Lab Invest 1990; 50, Suppl 203: 29-45.

This paper describes a computer program, which is freely available from the authors and continuously updated. The most recent version contains a description of the most recent version of the Van Slyke equation as given in the introduction here.

17. Siggaard-Andersen O, Fogh-Andersen N. Base excess or buffer base (strong ion difference) as measure of a non-respiratory acid-base disturbance. Acta Anaestesiol Scand 1995: 39: Suppl. 107, 123-128.

Buffer base (cBB+) by Singer and Hastings was reintroduced years later by Stewart with the name strong ion difference and the acronym SID (Stewart PA. Modern quantitative acid-base chemistry. Can J Physiol Parmacol 1983: 61: 1444-61). Stewart called this “an approach to acid-base which revolutionizes our ability to understand, predict and control what happens to hydrogen ions in living systems”.

SID is defined as the sum of the concentrations of all aprote cations minus the sum of the concentrations of all aprote anions in the blood plasma. It is not defined for whole blood nor extended extracellular fluid. In the physiological pH range aprote cations (i.e. non-buffering cations) are Na+, K+, Ca2+, and Mg2+. Aprote anions are Cl-, SO42-, lactate ions, and several other organic anions.

SID is numerically equal to the sum of the concentrations of buffer anions minus the sum of the concentrations of buffer cations. Buffer anions are HCO3-, net albumin anion, and phosphate ion. The concentration of buffer cations is negligible. This may be called buffer base in the modern terminology where a base is a hydrogen ion binding group.

SID calculated according to the definition is sometimes called SID-measured, while SID calculated as the concentration of buffer anions is called SID estimated.

SID-estimated may in principle be determined directly experimentally as the negative value of the concentration of titratable hydrogen-ion in the plasma. The endpoint pH should be the isoionic (isoelectric) pH of albumin (ca. 4,7) at a pCO2 of zero. The titration should be carried out with a strong hydrogen ion donor (e.g. HCl). With this endpoint all the bicarbonate and all net albumin-anions would be titrated and virtually all the phosphate ions.

In essence both base excess and SID, with opposite sign, indicate the concentration of titratable hydrogen ion, the only difference being the endpoint of titration. I prefer an endpoint pH = 7.40 at pCO2 = 5.3 kPa at T = 37°C, because this is a natural physiological reference point.

Those who prefer to titrate the plasma to the isoionic pH of albumin must remember that an increased SID value need not indicate a metabolic alkalosis, - it may also be due to an increased albumin concentration. Some authors prefer to consider any increase in SID an indication of a metabolic alkalosis, and any increase in albumin concentration a "hyperalbuminemic acidosis". In other words they redefine metabolic acidosis and alkalosis as being synonymous with low, respectively high, SID. Furthermore, increase or decrease in albumin concentration are considered special kinds of acidosis/alkalosis.

Hydrogen ions cannot be added or removed from the system without a concomitant anion or exchanging cation (law or electro-neutrality). The "base excess approach" may be said to focus on the hydrogen ions, whereas the "SID approach" focuses on the associated anion or cation.

Having measured an excess or deficit of hydrogen ions in the blood, it is important to try to identify the accompanying anion or exchanging cation. However, this does not necessarily allow any conclusion about the pathophysiological process. For example, an excess of hydrogen ions associated with an increase in chloride ion (hyperchloremic acidosis) might indicate addition of hydrochloric acid (by ingestion or infusion), but it is more likely that it is due to a loss of sodium bicarbonate (e.g. intestinal) associated with an addition of sodium chloride (e.g. saline infusion).


Base excess is defined as the titratable base of the blood or plasma or model of the extracellular fluid when titrating to pH = 7.40 at pCO2 = 5.33 kPa at 37 °C (at constant concentration of total oxygen). Direct titration must therefore be considered to be the reference method.

For practical reasons it is more convenient to calculate the base excess either with a nomogram or with an arithmetic equation. For many years the base excess was always calculated with the curve nomogram or the alignment nomogram. The nomograms are now largely replaced by computer calculation and generally the calculation is based on some version of the Van Slyke equation.

No equation can claim to be completely consistent with the reference method. However, all equations should give a base excess of zero if the pH and pCO2 are 7.40 and 5.33 kPa, respectively, at 37 °C. Significant differences between different equations generally arise only when the base excess deviates considerably from the normal, in which case a difference of a few millimoles per liter is clinically irrelevant.

I think it is useful that the IFCC or other standardizing organizations recommend an equation as being clinically acceptable, but there should be room for alternative equations, which may be preferred for one reason or another, as long as they are clinically adequate.