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:
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).
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!
What equation is used to calculate base excess? This equation has been termed the "Van Slyke equation" (See Scand J Cl Lab Invest Supp 77 37(146) 15-20, also Siggaard-Andersen, 1974). It tells us that:
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);
pH(P) is the corresponding change in plasma pH;
HCO _{3 }^{-}(P) is the change in bicarbonate content of plasma;
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..
Here are a few 'Stewart-related' papers we considered worth reading a few years ago. Some might now be a little dated!
John Kellum has published extensively on the Stewart approach.
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 }.
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:
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).
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:
The authors use equations derived by Fencl, Leith and Gilfix to correct the base excess in three ways:
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.
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!
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!
Metabolic acidosis resulted from infusion of large volumes of normal saline, but not Ringer's lactate. Fairly convincing support for the Stewart approach!
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!
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.
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?
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!
Date of First Publication: 1999 | Date of Last Update: 2006/10/24 | Web page author: Click here |