Further Stewart Notes

First, why not try a Google search?

And now for a few other thoughts ...

If we look at whole blood - a mix of red cells and plasma - then things become more complex. If we take a sample of blood with everything at equilibrium then we can look at the red cell and plasma as two separate compartments, which interact. In each compartment, Stewart's principles must apply - if we know the independent variables, we can calculate the dependent ones!

It is thus possible to work out what is happening in the red cell compartment, just as we did for the plasma compartment. Things are more tricky in the red cell compartment, as there is an enormous amount of weak acid (in the form of haemoglobin), and the behaviour of this weak acid is, to put it mildly, very complex. I'm not aware of anyone who has sat down and accurately applied Stewart's approach to the red cell.

How do the two compartments interact? As Stewart pointed out, there are only two ways that the compartments can interact:

1. by diffusion of CO2 across the red cell membrane (this is rapid, so the PCO2 in both compartments rapidly equilibrates);
2. by movement of strong ions (notably the chloride ion).

The traditional approach to acid-base concentrates on the Henderson-Hasselbalch (H-H) equation. This is simply a modification of one of the six equations we use in describing the relationship between the dependent variables we wish to calculate, and the independent variables that govern them. The H-H equation will of course always hold, but it cannot be used to explain the behaviour of dependent variables, which will be influenced by all of the independent variables in the acid-base system.

People who focus on the traditional approach are often vigorously critical of the physicochemical approach, but I have yet to read a valid mathematical criticism of Stewart's solution.

Note that there appear to be at least two "subdivisions" of the traditional approach - those who concentrate on plasma bicarbonate concentration as a measure of metabolic acid-base disturbance, and those who look at base excess as a measure of this disturbance. This is starkly illustrated by the lack of consensus in the Acid-base terminology document published in the Lancet way back when in 1965 (Lancet, 1965 2 1010-12).

Base Excess

How is base excess determined in a specimen of arterial blood? Formally, base excess is defined as "the amount of strong acid (or strong base) required to titrate whole blood to pH 7.40 at a standard PCO2 of 40mmHg". Note that no titration is done in real life - our 'blood gas machines' plug in measured values of Hb, pH and PCO2 and then use standardised algorithms to derive what base excess should be . It should be clear that base excess is the same as saying "How much do we have to change the SID in order to achieve a pH of 7.40?" - a 'traditionalist' will see this as "titrating strong acid/base"; a physicochemical fanatic will regard the strong ions administered with the "strong acid/base" as being the important component, as they reflect a change in SID!

cB'(B) = (1 - ctHb(B)*0.023) * (

ctHCO 3 -(P) +

pH(P) * ( 2.30 * ctHb(B) + 7.7) ) .. Equation 1

This looks intimidating, but all we are doing is saying that:

• cB'(B) is the change in the buffer content of whole blood (Base Excess);

• ctHb(B) is the haemoglobin content of whole blood;
• pH(P) is the corresponding change in plasma pH;

• HCO 3 -(P) is the change in bicarbonate content of plasma;

The 'NCCLS recommendations' (Scand J Clin Lab Invest 1996 56 S 224 89-106) use a slightly different algorithm from Siggaard-Andersen's:

cB'(B) = (1 - ctHb(B) * 0.014 ) * (

ctHCO3 -(P) +

pH(P)*(1.43 * ctHb(B) + 7.7) )

They take

pH as (pH - 7.40) and

ctHCO 3 - as (cHCO 3 - - 24.8). Siggaard-Andersen variously uses 24.4 and 24.1 as values for a normal bicarbonate, and 0.023 or 0.0205 as the coefficient where they use 0.014.

It is even more instructive to get Siggaard-Andersen's book and read his derivation of Equation 1 (pages 44-51). The first thing you will note is that he makes a fair number of assumptions, perhaps the most telling being that plasma protein concentrations are normal !

In addition he gives us equation 1 thus:

cB'(B) = (1 - ctHb(B)*0.023) * (

ctHCO 3 -(P) + ( 2.30 * ctHb)B) + 7.7) *

pH(P) ) .. His equation (15)

Fixing the errant parenthesis, we note that he derives his Equation (15) from the following two equations:

cB'(B) =

ctHCO 3 -(P) * (1 - ctHb(B)*0.0205) ) .. His equation (14)

and

dctHCO 3 -(P)/dpH(P) = -2.30 * ctHb(B) - 7.7 .. His Equation (11)

Even allowing for his sudden change from a coefficient of 0.0205 to 0.023, can you see how he does this? I unfortunately cannot!

Disregarding my mathematical ineptitude, we note that assumptions such as a normal plasma protein concentration are unlikely to hold in critically ill patients. The Van Slyke equation may hold in normals, but we should use it with caution in the critically ill!

Also note that there are many other variants of 'Base Excess' in the literature, some advocating use of Base Excess calculated to account for the whole extracellular fluid volume:

BE ecf = cHCO 3 - - 24.8 + 16.2*(pH - 7.4)

Wilkinson (Crit Care Med 1979 7(6) 280-1) uses a different formula, attributed to Severinghaus:

BE = 37 * e ((pH-7.4) + 0.345 * Y)/(0.55 - 0.09 * Y) - 1

where Y = ln (PCO 2 / 40)

The Nottingham Physiology Simulator (BJA 1998 81 327-32) uses a different variant of our first BE ecf equation:

BE ecf = cHCO 3 - - 24 + 11.6 *(pH - 7.4)

and so the confusion continues..

Some articles reviewed

Here are a few 'Stewart-related' papers we considered worth reading a few years ago. Some might now be a little dated!

• Metabolic acidosis in the critically ill: Lessons from physical chemistry
Kellum JA. Kidney International 1998 53 S66 S81-86.

John Kellum has published extensively on the Stewart approach.

• Here he shows how the Stewart approach accounts for the tendency of critically ill patients to develop acidosis when resuscitated with large volumes of normal saline (or other fluids with a low SID).
• He also looks at why high lactate levels need not necessarily be associated with 'acidaemia' and how recently we have begun to appreciate that high lactate levels in the critically ill are not necessarily always bad! (There are one or two typos in the text). The author reminds us how ignorant we still are about sources of and reasons for hyperlactataemia in the critically ill.
• He then gives an approach to "unexplained anions".

(

I've often found that most authors explain this concept inadequately. The basic idea is that electroneutrality must be maintained . If we have a difference in the activities of positively charged and negatively charged ions, this difference or 'gap' must be made up by additional negative ions. The negative ions that normally make up the 'gap' expressed as the Strong Ion Difference are bicarbonate, albumin, and phosphate. Let's take a normal individual. First we look at the things that go to make up the strong ion difference (all values in mEq/l). Let's say for argument's sake that the serum sodium is 137, the potassium 4, the ionised calcium 2.2, magnesium 1 and chloride 107, so the SID is very nearly 37 mmol/l. If the bicarbonate is 26 mmol/l, then clearly there are 11 mmol/l of negative ions that must be made up by other ions. If in our normal individual the albumin is say 46 g/l and the phosphate is 1, we can estimate their contribution by 0.2 * [Albumin] + 1.5 * [Phosphate], which works out to 10.7 mmol - so the SID is, as we would expect, almost completely made up by the negative charge on bicarbonate, phosphate and albumin. The critically ill may not be as fortunate as our normal example - a residual 'gap' would indicate that charge is being made up by unmeasured negative ions. This gap is what Kellum refers to as the 'Strong Ion Gap' - it's simply the difference between the actual, calculated SID (SID a ) and the SID you would have expected based on the concentrations of bicarbonate, albumin and phosphate - which he terms the SID e .

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• Finally, he emphasises that when we give sodium bicarbonate, it's really the influence of the sodium ions on the SID that changes the pH - the bicarbonate ions are irrelevant. With a large strong ion gap or high serum sodium concentration, bicarbonate therapy is clearly often inappropriate! He also briefly considers treatment of metabolic alkalosis.

Kellum has recently published several other articles. These include a review of Determinants of blood pH in health and disease (Kellum JA, Crit Care 2000 4 6-14), in which he explores the physicochemical approach in some detail. He also reviews some convenient rules of thumb, for example:

• In the setting of metabolic acidosis, the expected PCO 2 is 1.5 * the bicarbonate + 8 (± 5). A deviation from this suggests a mixed picture - that is, a respiratory component to the acid-base derangement. The corresponding 'rule' for metabolic alkalosis is PCO 2 = 0.7 * bicarbonate + 21.
• There are similar guidelines for assessing respiratory disorders, but these differ as to whether the derangement is acute or chronic. The estimates for serum bicarbonate are:  Disorder HCO 3 - Acute respiratory acidosis 24 + (PCO 2 - 40)/10 Chronic respiratory acidosis 24 + (PCO 2 - 40)/3 Acute respiratory alkalosis 24 + (40 - PCO 2 /5) Chronic respiratory alkalosis 24 + (40 - PCO 2 /2)

Kellum also published an interesting article that explains acid-base changes on cardiopulmonary bypass using the physiochemical approach. This was published together with several other Stewart stalwarts, including Rinaldo Bellomo and Matthew Hayhoe. (Crit Care Med 1999 27(12) 2671-7). They reach the rather counter-intuitive conclusion that the metabolic acidosis associated with cardiopulmonary bypass is not contributed to by the splanchnic circulation! A related study (this time by Hayhoe, Bellomo et al, Int Care Med 1999 25 680-5) shows that the metabolic acidosis asociated with CPB using polygeline pump prime is mostly due to iatrogenic increases in sodium chloride concentration {lowered SID}, together with unmeasured anions {polygeline}. Kellum and Bellomo also collaborated a few years ago (J Appl Physiol 1995 78(6) 2212-7) looking at hepatic anion flux in acute endotoxaemia in dogs - they found that the liver is the big producer of (undetermined) anions in early sepsis.

Note that Kellum derives much of his approach to the strong ion gap from Figge Mydosh and Fencl (J Lab Clin Med 1992, 120(5) 713-9). Their Appendix B gives a formula for expected SID:

SID e = [HCO 3 -] + [Alb x-] + [Pi y-]

A least-squares fit provided the following formula:

SID e = 1000 * Kc1 * PCO 2 /10 -pH + 10 * [Alb] * (0.123 * pH - 0.631) + [Pi tot ] * (0.309 * pH - 0.469).

Note that total phospate ([Pi tot ) is measured in mmol/l; albumin in g/dl, PCO 2 in mmHg, and Kc1 is 2.46*10 -11 (Eq/l)2 mmHg -1

In a later article (Figge et al, Crit Care Med 1998 26(11) 1807-10) they suggest a much simpler method of adjusting the anion gap for hypoalbuminaemia - simply add to the observed anion gap 0.25 times the change in albumin from the expected value (in g/L).

• Unmeasured anions identified by the Fencl-Stewart method predict mortality better than base-excess, anion gap and lactate in patients in the pediatric intensive care unit
Balasubramanyan N, Havens PL, Hoffman GM. Crit Care Med 1999 27 8 1577-81.

In a substantial number of patients (n=255), the association between serum lactate, mortality, and three estimates of "unmeasured anions" were compared. The three estimates were:

1. Base excess ( < -5 being taken as abnormal)
2. Anion gap ( Na + K - Cl - total carbon dioxide, > 17 abnormal)
3. A corrected base excess based on the Stewart approach (with modifications from Fencl & Leith, and Gilfix and colleagues), considered significant (post hoc) if <= -5.

The authors use equations derived by Fencl, Leith and Gilfix to correct the base excess in three ways:

1. correction for the 'free water effect';
2. correction for 'changes in chloride';
3. correction for changes in albumin;
The correction is to subtract from the BE calculated from 'standard bicarbonate' the following values:
1. 0.3 * (Na - 140)
2. 102 - (Cl * 140)/Na
3. 0.34 * (45 - Albumin g/l)

The authors demonstrate quite convincingly that approaches to metabolic acidosis which do not compensate for the effects of albumin and other interfering variables, are less adequate in predicting mortality than a compensated approach. A fairly good study.

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Note that, as mentioned above, base excess is a derived value. A recent study (Critical Care Medicine 2000 Aug, 28 2932-6) claims to have clinically validated the Van Slyke equation. Unfortunately this study makes no mention of alterations in serum albumin concentration, although normal blood was subjected to various combinations of added strong base, added strong alkali, lactate and variations in PCO 2 , with impressive stability of base excess as a measure of metabolic acid-base disturbance. I was intrigued to see that this study did not use the equation recommended by the NCCLS, but stuck to the original Van Slyke equation!
Playing round with my Java applet, one finds that for different concentrations of albumin the slope of the pH versus SID curve varies, suggesting that extrapolating from normals to the critically ill might be inappropriate!

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• Analytic calculation of physiological acid-base parameters in plasma
Wooten EW. J. Appl Physiol 1999 86(1) 326-34.

This author has provided a review of the various approaches, comparing the 'traditional' approach with the Stewart one, and coming to the broad conclusion that change in SID and change in total titratable base are of similar utility. He also points out the limitations of the Van Slyke equation. A tiring read, but his approach appears thorough and substantial!

• Rapid Saline Infusion Produces hyperchloremic acidosis in patients undergoing gynecologic surgery
Scheingraber S, et al. Anesthesiology 1999 90 1265-70.

Metabolic acidosis resulted from infusion of large volumes of normal saline, but not Ringer's lactate. Fairly convincing support for the Stewart approach!

• Hypoproteinaemia, strong-ion difference, and acid-base status in critically ill patients
Wilkes, P. J Appl Physiol 1998 84(5) 1740-8.

This observational study suggests that the hypoalbuminaemia we so often see in critically ill patients is accompanied by a compensatory drop in [SID]. He makes interesting reference to the 'alpha-stat' hypothesis, and to trouble with demonstrating electrical neutrality!

• Modeling the effects of proteins on pH in plasma
Watson PD. J Appl Physiol 1999 86(4) 1421-7.

Philip Watson has explored refinements of the Stewart approach in detail. His single-association-constant model has the merit of being both simple and accurate.

• Lactated Ringer's is superior to normal saline in a model of massive hemorrhage and resuscitation
Healey MA, et al J Trauma 1998 45(5) 894-1003

Not only acidosis, but survival was considerably worse in rats subject to massive haemorrhage and then resuscitated with normal saline + washed red cells, when compared with those resuscitated with Ringer's + washed red cells. Another victory for Stewart?

• Much of the December 1999 issue of Current Opinion in Critical Care (Vol 5 No 6) is devoted to the Stewart approach.
Rinaldo Bellomo (with Claudio Ronco) has done a magnificent job of getting together a number of controversial, mainly Stewart-orientated articles. These include:
• 'Acid base-physiology in the post-Copernican era' - another stirling contribution from John Kellum (p 429);
• 'The acid-base physiology of crystalloid solutions' - by David Story and Rinaldo Bellomo (p 436)
• 'The acid-base physiology of colloid solutions' - Frank Liskaser and Story again (p 440);
• 'The effects of continuous hemofiltration on acid-base physiology' (Han Kim Tan and Bellomo, p 443), 'The acid-base effects of peritoneal dialysis' (Feriani et al, p 448), and 'The acid-base effects of acute hemodialysis' (M Leblanc, p 468);
• 'The pathogenesis of lactic acidosis in sepsis' (Bellomo and Ronco, p452), and 'The etiology and significance of metabolic acidosis in trauma patients' (Kaplan et al, p 458);
• 'The pathogenesis of acid-base changes during cardiopulmonary bypass' (Hayhoe et al, p 464).

Stewart - Ready for Prime Time?

There is little doubt in my mind that the Stewart approach makes sense, and provides a slightly better model of how acid-base works than does the conventional approach. I believe that Stewart provides a refinement of the conventional approach. Under many, perhaps most circumstances, the 'old-fashioned' approach works fine, but we should be aware of the exceptions (gross volume dilution with fluids which have a low SID; hypoalbuminaemia in association with metabolic acidosis) and invoke the physicochemical approach in these circumstances. This new approach also helps us explain how our therapeutic interventions work.

Much still needs to be done. We need a viable model based on physicochemical principles that can be consistently shown to be as good as or better than the older models. Ideally this model should also extend to assessment of whole blood acid-base status, and even allow us to predict whole-body pH changes in response to therapeutic interventions.

In addition, each clinician who makes therapeutic decisions should appreciate the limitations of the model they are using. He/she should also relate the model to the limitations in laboratory estimation of the numbers that go into the model. For example, in the hospital where I currently work, the standard deviation of the estimates of serum sodium concentration is 3 mmol/l. I don't believe I can trust a serum sodium of "170 mmol/l" as I have seen a repeat estimate on the same specimen come out as "177 mmol/l"! We have also known since 1977 that small variations in sampling technique may have profound effects on arterial blood gas analysis - Hansen and Simmons (ARRD 1977 115 1061-3) found substantial reductions in PCO 2 related to heparinisation of arterial blood gas samples. Be careful when you plug the numbers you obtain into any model, and then make dramatic alterations in clinical management based on small numbers, especially where there may be multiple sources of error! This point is well made by Swenson in an otherwise rather humdrum editorial that you can read online.

Use both Stewart and conventional approaches with caution!