This chapter is relevant to Section J1(iv) of the 2023 CICM Primary Syllabus, which expects the exam candidates to "explain the Henderson-Hasselbach (traditional) and the Stewart (physico-chemical) approach to acid-base". That the latter requires a 504-page book to explain is not lost on this author, as it renders the chances of his own undertaking much less reassuring. For most normal people, an indepth discussion of Stewart's method by its effects resembles an encounter with Cthulhu on a lost island in the Pacific. Since the publication of his scandalous manuscript in 1983, Peter Stewart's method of acid-base analysis has developed a cult-like following, attracted widespread criticism from clinicians, and driven countless critical care trainees to gibbering madness, with polynomial equations smeared in blood on the padding of their asylum cells.
In short, it is entirely normal to find this subject difficult. We are all reassured by this quote from Neil Soni, who was asked to review the second edition:
"I, like many, observed the appearance of the Stewart approach with curiosity, rapidly supplanted by apprehension as it became popular, and with anxiety when it became clear that one might be expected to explain or teach it to others."
Teach it to others? Forget about the others. This summary chapter represents an effort by the author to explain or teach it to himself, to stand half a chance of answering questions from his trainees. It is important to have no ego about it, as, to borrow again from Soni, "anyone who thinks they understand Stewart, and many do, needs to read this book." From this, it follows that it would be impossible to recommend the original book to the CICM exam candidate who needs less reading rather than more. Something else is clearly required. Sirker et al (2002) and D.A. Story (2016) do an excellent job, and Dubin et al (2007) bring the physicochemical approach together with the two traditional approaches.
Traditional Henderson-Hasselbalch approach:
- pH is determined by the interaction of pCO2 and HCO3-, based on the law of mass action.
- In this interpretation,
- CO2 is the determinant of respiratory acid-base balance
- HCO3- is the determinant of metabolic acid-base balance
- Because the concentration of HCO3- is dependent on both metabolic and respiratory factors, it cannot be used on its own, and workarounds exist:
- Empirically derived corrective formulae (eg. the Boston methods)
- Corrections for the presence of non-bicarbonate buffers (base excess, SBE)
Thus, acid-base disorders can be classified as:
- Respiratory acidosis due to increased PaCO2
- Respiratory alkalosis due to decreased PaCO2
- Metabolic alkalosis due to increased HCO3- or SBE
- Metabolic acidosis due to decreased HCO3- or SBE
- The traditional model has trouble with differentiating the causes of metabolic acidosis, which makes it necessry to calculate the anion gap and classify acidosis as:
- High anion gap acidosis due to the accumulation of non-volatile acidic anions
- Normal anion gap acidosis due to the loss of HCO3-
- pH depends on the interaction of several variables, based on:
- the law of conservation of mass
- the law of mass action (that governs the dissociation equilibria of all incompletely dissociated substances)
- Electroneutrality (the sum of all the positively charged ions must equal the sum of all the negatively charged ions)
- There are independent variables, which can be altered from outside the system:
- SID - the strong ion difference
- ATOT - the total weak acid concentration
- There are dependent variables which are altered by changes in the independent variables:
- Thus, changes in any of the independent variables can cause a change in pH and HCO3-, i.e. acidosis and alkalosis.
- All the independent variables must be known to calculate the dependent variables
Thus, acid-base disorders can be classified as:
- Respiratory: increased or decreased PaCO2
- SID changes:
- due to excess or deficit of water
- due to excess or deficit of strong ions
- ATOT changes: excess or deficit of inorganic phosphate or albumin
The terms "traditional" or "classical" evoke warm imagery of home-cooked farm-style, down-south, country baked goodness as well as something vaguely reminiscent of cracked marble and Greco-Roman antiquity, creeping with ivy-covered respect. referring to these methods using these words seems to generate only very positive and affirming feelings in those who wield these concepts with the effortlessness of long practice. It would probably be less popular if we called it the "early 20th century approach", the "non-quantitative approach", or "the approach that requires corrections with fudge factors".
Another name often used to refer to this cognitive framework is as the "Henderson-Hasselbalch method", even though the way it is commonly used these days does not resemble anything like what Henderson or Hasselbalch would have done. In fact it should be called the Van Slyke & Cullen approach, after the first clinical application of the pure chemistry of Henderson and Hasselbalch, or the Schwartz & Relman approach, after the authors whose influential 1963 paper, actually a critique of the Van Slyke & Cullen interpretation, most closely resembles the modern "traditionalist" approach to acid-base interpretation.
But first, because the author cannot help himself, a lengthy historical digression.
Even ten years prior to Henderson publishing his most influential research, the components necessary to describe the systems of buffering and compensation were already there, but not connected to one another because of various competing theoretical frameworks that prevented their importance from being fully appreciated. For example, in his 1909 article "Acidosis", Edmund Spriggs appeared aware of buffering and remarked that "in acid poisoning, the amount of carbon dioxide which can be extracted from the venous blood is much less than normal", but then goes on to dismiss the connection between CO2 and acid-base balance:
" the diminution of tho amount of carbon dioxide was due to other causes. ....Another possible reason is that when the tissues are poisoned by an excess of acid radicles their oxidation will be interfered with, and consequently less carbon dioxide will be formed."
Acid-base interpretation was at this stage entirely qualitative,and acidosis was classified into categories consisting of "poisoning by mineral acids", "deprivation of mineral salts", "loss of alkali", and "acidosis upon a diet consisting of protein and fat, and during a fasting period", i.e. ketoacidosis.
Lawrence Henderson, around 1908, gave us the equation that describes the relationship between the dissociation products of CO2 in water, which was originally
[H+] = k × [pCO2] / [HCO3-]
where k is the first dissociation constant of carbonic acid, which is 24 if you represent pCO2 in mmHg. This insight reshaped the subsequent years of acid-base research but could not really be integrated into bedside thinking because of the difficulty involved in collecting the necessary measurements with contemporary apparatus and making the maths appear clinically relevant to physicians (sounds familiar?). Then, in 1916, Karl Albert Hasselbalch, whose name the college misspelled in their syllabus document, took the Henderson equation and added a step where the [H+] would be represented as a logarithm, the concept of pH having only recently been invented by Sorensen. The new equation looked like this:
pH = pK + log [HCO3-]/ SCO2 ×[pCO2]
where the pK is the negative logarithm of the k dissociation constant and SCO2 is the solubility coefficient of CO2. Neither Henderson nor Hasselbalch had suggested much in the way of a practical method to use these relationships clinically, but in the next year Donald Van Slyke and Glenn Cullen took these equations and transformed them into an approach which described very clearly the central theory and the practical application of the Henderson-Hasselbalch equation to explaining human acid-base disturbances. In the shortest possible form, these were:
Van Slyke then divided the possible acid-base disturbances into what the bicarbonate and the pH does, i.e. each can be either high, normal or low, giving nine possible acid-base states (where the centre of the grid is a normal acid-base balance). The image below is from the original 1921 paper:
A low bicarbonate therefore represented a metabolic acidosis, and a high bicarbonate represented a metabolic alkalosis; and in this model, CO2 was purely the work of respiratory compensatory mechanisms. Therefore it was never really essential to measure the bicarbonate concentration directly, and at this stage the convention was to measure only the whole blood CO2 content, assuming that this would be representative of the bicarbonate concentration. The normal CO2 being 28.2 mmol/L, a higher content (33 mmol/L and above) was interpreted as an acidosis, and a lower content (24 mmol/L or below) was interpreted as alkalosis.
Though Schwartz & Relman (1963) are occasionally credited with pointing out that "CO2 cannot be regarded exclusively as index of respiratory disturbances, nor can the bicarbonate content be considered solelt a reflection of metabolic disorders", in fact for the forty years between their paper and Van Slyke, plenty of other work had been done to reconcile the dependence of bicarbonate on CO2 with its Ptolemaic centrality as the main determinant of metabolic acid-base balance. Of these, one stand-out was the concept of whole-blood buffer base by Singer & Hastings (1948). They complained that measuring the CO2 content of blood as the surrogate for bicarbonate would not yield the full picture, and pointed out that haemoglobin also did a lot of the buffering in blood. Ergo, we should also measure the pH (or bicarbonate) and the haematocrit to assess whole blood buffering, they proposed. The resulting value, the buffering capacity of whole blood in mEq/L, had a normal value of about 50 mEq/L. Using this reasoning the authors had constructed a monstrous nomogram, presented here for people who think that the Stewart method is too complex:
The mentally frail author of this website had lost several hitpoints in psychic damage from trying to parse this graphic, but apparently physicians in the 1950s had stronger constitutions and were able to apply these concepts at the bedside (eg. Yeomans et al, 1952, who created this much more helpful graphic and used whole blood buffer base measurements to guide the treatment of six patients, or at least to explain their deterioration). At this stage in history we seem to have consistent references to recognisable terms in acid-base physiology, such as "respiratory acidosis" and "metabolic acidosis", but
Singer & Hastings already recognised that the oxygen content of the blood determined its buffering capacity because of the properties of haemoglobin. The answer to this came from Copenhagen, where Jørgensen & Astrup suggested that we should aim to standardise all buffer capacity measurements to some pre-agreed-upon pO2 and pCO2 values, as well as to a consistent temperature (as this also affects the oxygen-haemoglobin association kinetics). The resulting parameter, the concentration of bicarbonate in plasma of fully oxygenated blood at 38°C, when the pCO2 is 40 mmHg , referred to as "standard bicarbonate", had a value range of 21-23 mmol/L. It is still available as a reported measurement from ABG analysers, particularly from the Radiometer series of devices, as the company was founded in Demark and the development of their first commercial blood gas machines was influenced extensively by Poul Astrup and his colleagues.
The main advantage of this value was that it appeared to be independent of respiratory disturbances. As the O2 and CO2 were artificially normalised, all respiratory badness was eliminated, the authors asserted, leaving behind only the titratable acid generated by metabolic disease. However, one major complaint about the use of this standardised bicarbonate value was that, unlike with the whole-blood buffer base, the total amount of acid or base added to the blood could not be estimated from the measurement, because it was taken from plasma bicarbonate only, whereas in whole blood some of the buffering is also done by haemoglobin. A work-around was proposed by Astrup (1960), where the deviation of the standard bicarbonate value from normal was multiplied by 1.2 to correct for the additional amount of buffering by fully oxygenated haemoglobin. The resulting value, which Astrup referred to as "base excess", did represent the full buffering capacity of whole blood, or rather the total amount of acid or base added to it. This method gained popularity very rapidly, as it allowed the metabolic contribution to acidosis to be easily separated from the respiratory, making it easier to classify acid-base disorders and to estimate their severity. In this interpretation, a low base excess was a metabolic acidosis, a raised base excess was a metabolic alkalosis, and CO2 was a separate independent variable which described respiratory acid-base perturbations.
Schwartz & Relman (1963) mostly complained that the base excess method measured the variables in vitro and in plasma, whereas the bufering happened in the entire body. When arterial CO2 increases, the plasma bicarbonate increases about three times more than the extracellular fluid bicarbonate, and the newly generated bicarbonate diffuses into to the extracellular fluid, which means that the buffering power of whole blood in vivo is approximately the same as if it were diluted with extracellular fluid, down to a haemoglobin concentration of about 1/3rd. In an answer to this, the concept of the "standard" base excess was developed, which corrected the base excess value again, this time to account for the fact that the haemoglobin in the blood does a lot of the buffering for the rest of the extracellular fluid, even though it is not physically present in that fluid. Specifically, the measurement was corrected to a haemoglobin value of about 50g/L.
Another also entirely reasonable complaint about the SBE method was that the patient whose SBE was elevated because of chronic hypercapnia was considered to have a "metabolic alkalosis" as well as a "respiratory acidosis", which was viewed as a paradox, as it implied that some degree of metabolic alkalosis was normal. The recognition of exactly what amount of "normal" acidosis and alkalosis was therefore required, and this - the opponents of the SBE approach argued - could not be determined from anything other than empirical measurements. To borrow an extreme example from Schwartz & Relman, using the SBE method in patients who have a severe respiratory acidosis (pCO2 of 80mmHg) as well as a severe metabolic acidosis (bicarbonate of 29 mmol/L, whereas it was supposed to be about 40), could theoretically yield a SBE value of 0.0 mEq/L (all fine and normal) while the pH was actually 7.18.
Clearly some sort of correction factor was required to help clinicians decide what SBE or bicarbonate value would be appropriate in any given situation. These correction factors were ultimately derived from measurements in healthy volunteers and chronic outpatients by Dell and Winters (1967) and Brackett et al (1969). The result was a system of mathematical correction "fudge factors", generously referred to as "rules", which to this day bedevil the CICM exam candidate. A set is available for both bicarbonate and base excess, depending on which parameter one feels the most comfortable with using.
The anion gap seems to have developed as a means of detecting lactic acidosis in an era when one could not conveniently measure lactate. In fact there was no real way of directly measuring any of the non-volatile organic acids that could titrate the bicarbonate- CO2 balance, which made it difficult to identify and manage situations where patients had multiple simultaneous metabolic acid-base disturbances. The first instance of anyone using the term "anion gap" seems to have been Jurgenson & Whitehouse (1969) who used to explain a severe acidosis in a patient with DKA, whose ketosis resolved but whose acidosis persisted. Lactate, they concluded, must have been responsible, as the anion gap remained elevated even as the ketones disappeared.
It is hard to track down how and when the anion gap happened by the normal mechanisms available to the author which mostly consist of tracking references back through the literature until the first mention of a term is recorded. Jurgenson & Whitehouse were obviously pioneers in using the term "anion gap" because they used it with quotation marks, but they presented it as a well-established concept already, referencing a work by E.E Carlson from the same year. Also in 1969, Howard Bleich used the anion gap in creating a very early computerised system for the evaluation of acid-base disturbances, inscribed into some kind of ancient Talmudic machine code and offered to the 36-bit spirit of a GE-635 mainframe. Again the concept was used and not explained, as if everyone already knew what it was, but none of the references used by the author specifically mention it. Looking back, the idea that the law of electroneutrality could be used to guess the unmeasured anion composition of body fluids can be traced back as far as the earliest work by James Lawder Gamble from 1936 (he of the Gamblegrams), but it did not appear to have widespread popularity at that time, and was absent from the literature.
In short, it appears the anion gap became a well-accepted concept at some stage in 1969, such that by 1973 it was already the subject of flame wars in the pages of the Lancet. It was still powerless to detect a "third" disorder, however, as it did not formally permit the appreciation of an elevated buffer capacity coexisting with a new acidosis. This became possible with the delta gap (Wrenn, 1990) and the delta ratio (Salem, 1992) which compared the change in the anion gap to the change in bicarbonate, maintaining the centrality of bicarbonate to the thinking process. Metabolic alkalosis was also classified in terms of different mechanisms of bicarbonate gain (Seldin & Rector, 1972) where "maintenance factors" such as bicarbonate concentration due to the contraction of extracellular volume or potassium deficiency increasing hydrogen ion secretion in the renal tubule were blamed for the alkalinisation of the body fluids.
At this stage in history we now had something resembling the modern interpretation system for acid-base disturbances, which was now able to discriminate the disorders into metabolic and respiratory, as well as "compensated" and "uncompensated", and to offer an empirically derived method of determining whether the compensation was appropriate or not, as well as a method to discriminate between different contributions from anions to the acid-base balance.
The whole point of this enormously wasteful historical digression was to bring together all the factors that resulted in the formation of the modern "physiological" approach, demonstrating that each step along the way was a kludge to repair the shortcomings of the fundamental premise. The most generously favourable interpretation of this is probably to say that the incremental growth in our understanding of this subject was slow, but we needed to have immediate clinical applications, and so our models were necessarily based on incomplete theories, and had to be updated rather than replaced because clinicians were already familiar with a specific framework and did not feel safe changing practice abruptly. The best discussion that summarises the principles of this "physiological" approach is probably something like Berend (2014), and a simplified point-form version can be expressed as follows:
The "base excess" variant of the "physiological" approach to acid-base is essentially the same series of conceptual steps, up until the very last one. Instead of applying correction factors to eliminate the contribution from compensation and establish the presence of a second disorder, the use of the base excess allows the contribution from raised CO2 to be eliminated so that only "metabolic" reasons remain for the change in the buffering capacity of the blood. This does nothing to eliminate the need for corrective formulae, but it does simplify those formulae, which is not nothing (especially when the main argument against the competing method is an attack on its complexity).
Peter A. Stewart is widely quoted to have produced this theory in 1981, but that was actually the publication date for his first book, and the original work outlining his theory was presented in 1977 at the XXVII International Congress of Physiological Sciences in Strasbourg. This was a fascinating move. On one hand, he clearly knew he was stepping into a minefield. The opening lines of his presentation refer to acid-base chemistry as "an emotionally charged area of science". The scientific climate of the time was highly volatile, characterised by senior scholars exchanging invective across the Atlantic, to the extent that the variables of one school were forbidden from the textbooks and blood gas machines of the other. Anybody raising their head above the parapet would have to have been prepared to defend their ideas in violent confrontation. Indeed, the physicochemical approach was dismissed by both the Copehnagen school and the Boston school as they continued to disagree with each other. It is therefore remarkable that between this publication and until his death in 1993 Stewart published only two articles and one brief book outlining his theory, as if refusing to get involved in the mudslinging. In all fairness, the citations of his last paper (now counting over 1600) did not really begin to gain momentum until well after his death, in the early 2000s.
The Stewart interpretation does not use anything novel or excessively abstract, and in fact has basically everything in common with the traditional approach. To massively oversimplify the premise of the physicochemical approach:
Water dissociation␣equilibrium [H+][OH–] = K′W
Weak acid dissociation equilibrium [H+][A–] = KA[HA]
Conservation of mass for weak acid A [HA] + [A–] = [ATOT]
Bicarbonate−carbon dioxide equilibrium [H+][HCO3–] = M × pCO2
Bicarbonate-carbonate␣equilibrium [H+][CO32–]␣= N × [HCO3–]
Thus, acid-base disorders can be classified as:
Thus, there are six main acid base disturbances recognised by this model:
Even though the comfortably familiar term "metabolic" is absent from these classifications, the "classical" metabolic acid-base disturbances can still line up reasonably well with the physicochemical ones, and can be presented in a table as follows:
|"Classical" acid-base disorder
|Corresponding physicochemical disorder
|Respiratory acidosis (raised CO2)
|Respiratory acidosis (raised CO2)
|Respiratory alkalosis (depressed CO2)
|Respiratory alkalosis (depressed CO2)
High anion gap metabolic acidosis
High ATOT acidosis
Normal anion gap metabolic acidosis
Low SID acidosis
High SID alkalosis
Low ATOT alkalosis
These seem very similar, the jaded reader might complain. What, functionally, are the differences here? Well. The interpretations differ enough that under several circumstances different answers might be generated to the question "Why is the patient's pH low", and these may lead to slightly different management strategies. The respiratory disorders are rather uncontroversial, and we can ignore them. The most important sources of conflict are NAGMA and metabolic alkalosis.
Observe, the different ways of thinking about what each team would probably refer to as "hyperchloraemia":
Traditional interpretation: The primary problem is that the bicarbonate has been lost. It was either suctioned out of the NJ tube, lost via poor renal conservation (eg in RTA) or excreted as diarrhoea. To maintain electroneutrality, intracellular chloride is displaced to the extracellular space by Gibbs-Donnan equilibria, which is why the chloride is so high. When exogenous chloride is given intravenously (eg. saline), it ... well. Some authors authoritatively report that the exogenous chloride displaces bicarbonate into the cells, whereas others suggest that the saline has diluted the bicarbonate buffer. Either way, to fix this situation, we need to administer sodium bicarbonate to replace the bicarbonate that was lost/diluted/displaced from the extracellular fluid. Or, if you are European, the extra bicarbonate will contribute to the total buffering capacity of the blood and return the negative base excess to some more normal value.
Physicochemical interpretation: The primary problem is that the SID has decreased, whether as the result of sodium loss (such as through diarrhoea) or chloride gain (such as through normal saline administration). The resulting change in the concentration of strong ions has resulted in a decreased net cationic charge in the solution, and therefore a change in the dissociation equilibrium of the self-ionisation of water, favouring more H+ activity. The resulting fall in pH shifted the Henderson-Hasselbalch equilibrium and decreased the ratio of HCO3- to CO2 and H2O, which is the reason the bicarbonate is low. To fix this situation, we need to administer sodium bicarbonate to replace sodium, as this will increase the strong ion difference. Or remove chloride, if you can do that selectively.
Validity of these interpretations is difficult to test. Which version is correct? Unfortunately each seem to be supported by some experimental evidence. For example, Doberer et al (2012) performed some in vitro experiments to determine whether the low-SID-induced increase in water self-ionisation causes dilutional acidosis. They added saline to some bicarbonate solution, observed that the solution becomes acidified, and attributed this change to the dilution of the bicarbonate and the addition of some H+ from the diluent water. The SID did change, of course, and as expected the addition of pure water changed the SID (and the acidity) by exactly the same amount, but the interpretation offered for this was "classical" and therefore the SID was dismissed as "only an algebraic necessity or marker of dilution".
How would you separate the effects of dilution from the effects of SID change? Well, one might point to the effects of infusing different fluids. For example, if dilution of the extracellular fluid was responsible for the acidaemia that follows, then surely all diluents should produce the same level of acidaemia? This worked for Doberer et al (2012) because they used zero-SID water and saline as diluents, but we also have other fluids available, and those fluids with a high SID (Hartmanns, Plasmalyte) appear to alkalinise the body fluid instead. Still, depending on one's bias, this is again a situation amenable to a "classical" interpretation; all you'd need to do is classify the lactate and acetate as "bicarbonate precursors" and complain that the alkalinising effects of the Plasmalyte are due to the generation of new bicarbonate molecules. Sure, the SID changes, but that's just maths, you might say.
So, what if we give a high-SID solution that does not incorporate a "bicarbonate precursor"? Ke et al (2013) produced exactly this sort of study by giving sodium octanoate as the infused fluid. Octanoic acid is a medium-chain fatty acid which is not a "strong ion" but which is also not an immediate source of bicarbonate, as it takes some time to undergo beta-oxidation. The investigators found that the pH and bicarbonate both increased following the infusion of sodium octanoate, whereas the saline created a decrease in both. Bicarbonate generation should not have occurred, and the dilution would have been the same for both fluids; the only thing that differed was the SID.
But then, some might say the octanoate in this experiment acted as a de facto bicarbonate precursor anyway, as it could theoretically have undergone rapid metabolism. What about if we manipulate the SID more directly? Zanella et al (2019) used electrodialysis to selectively remove chloride, and nothing else, from the bloodstream of mechanically ventilated pigs with lactic or respiratory acidosis (down to a pH of 7.15). By dropping their chloride by 26 mmol over 6 hours the authors were able to renormalise the pH completely. No other anions were introduced or extracted, and the animals were ventilated in a manner that would not have permitted any compensation. In other words, the investigators manipulated an independent variable of the physicochemical interpretation, and demonstrated that the dependent variables were affected. Cove & Kellum (2020) immediately used this to flay the classical method of acid-base interpretation, fending off increasingly desperate counterattacks from loyalists.