Dr Jon-Emile S Kenny, Health Sciences North Research Institute and Flosonics Medical, Ontario, Canada

https://doi.org/10.36866/122.26

Puissance de l’hydrogène or “power of hydrogen” is what I was taught to be the origin of pH; this is likely incorrect (Kenny and Goldfarb, 2012). In the early 20th century Sørensen, a Danish chemist studying beer- producing enzymatic reactions, quantified hydrogen ion concentration [H+] with the pH scale. Yet the derivation of pH in Sørensen’s manuscript arose from solving an equation with two unknowns (labeled p and q) such that the p in pH reflected mathematical notation rather than puissance. The power of protons [H+] in biological reactions cannot be over-emphasised. Waxing and waning [H+] alters enzymatic and cellular activity amongst other biological consequences. With acute effects on cardiovascular, respiratory and neurological function, severe pH changes are life-threatening, therefore, understanding acid–base disturbances in human health is critical.

The primary purpose of this brief review is to introduce the reader to an acid–base paradigm codified and quantified by the Canadian physical chemist Professor Peter Stewart. There are many excellent reviews for more in-depth reading (Rastegar, 2009; Kurtz et al., 2008; Story, 2004; Sirker et al., 2002). Stewart’s approach is gaining traction in clinical medicine – primarily amongst intensivists and anaesthesiologists. It is particularly useful when thinking about metabolic pH disturbances because it adopts a broader definition of acids and bases. Arguably, the Stewart approach better explains pH variation associated with albumin and chloride concentration changes. However, others posit that mechanistic cause-and- effect is lacking and Stewart’s formulation is merely chemical book-keeping. While this debate is likely to continue, the student of health sciences is likely to encounter the Stewart approach, so a basic understanding is warranted. Prior to outlining the fundamentals of Stewart’s concept, a cursory history of clinical acid–base is presented for context.

The traditional view of acid–base balance

At the turn of the 20th century, the definition of an acid, as championed by Naunyn, was somewhat of a conglomeration (Story, 2004). It included the description of an acid as something that, in water, elaborated protons – as per Arrhenius. But an acid also encompassed anions (e.g. chloride) based on what Faraday had previously conceived. Per this approach, electrolytes such as sodium and chloride are considered base and acid, respectively. Indeed, there is a direct line between Naunyn’s formulation to Van Slyke in 1920 and then Singer and Hastings in 1948 who coined the term “buffer base” (BB). BB is calculated as the difference between all of the completely dissociated cations (i.e. total base) and anions (i.e. total fixed acid) – a difference filled by buffer base, that is, bicarbonate and weak acid anions (e.g. albumin and phosphate). Of note, this general acid–base model (encompassing cations and anions) was the predominant clinical concept until the mid-20th century when it was supplanted by what is currently termed the “traditional” approach, described below.

However, at variance with the description above, another impression of clinical acid–base took shape – one with which most clinicians are familiar today. In 1909, Henderson combined equilibrium constants for the relationships between carbon dioxide [CO₂], water, carbonic acid, bicarbonate [HCO -] and [H+]. With this, Henderson advanced direct and indirect quantitative relationships between [H+], dissolved [CO₂] and [HCO -], respectively. Shortly thereafter, Hasselbalch incorporated Sørensen’s pH scale to derive the oft-taught Henderson–Hasselbalch equation (Fig. 1) (Kurtz et al., 2008; Sirker et al., 2002):

Here, pK is the acid dissociation constant (6.1), SCO₂ is the solubility coefficient for CO₂ (0.0307) and PₐCO₂ is the partial pressure of carbon dioxide in arterial blood. With this equation, the relationships between PₐCO₂, [HCO -] and blood pH were made objective. In addition, the calculation enabled the sense that respiratory and renal physiology modulated pH via ventilation (i.e. carbon dioxide tension) and bicarbonate balance, respectively. This “bicarbonate-centered” formulation also comported with the contemporary Bronsted–Lowry definition of an acid – a substance capable of proton donation.

Thus, by the mid 20th century, clinical acid–base physiology was motored by the Henderson–Hasselbalch equation and propelled “trans-Atlantic debates” as to how pH disturbances are best judged (Rastegar, 2009). In Denmark, during the polio epidemic, Bjørn Ibsen realised that patients were dying not of alkalosis, as initially thought, but rather PₐCO₂ retention – which led to bicarbonate elevation. This insight was followed by the base excess (BE) calculation, proposed by Professor Siggaard-Andersen. BE is the amount of [H+] titration needed to return in vitro blood pH to 7.4 at a PₐCO₂ of 40 mmHg. Across the Atlantic, however, Professor William Schwartz and Professor Arnold Relman argued that in vitro BE is problematic because it ignores whole body kinetics (e.g. the role of interstitial buffering) and chronic, renal compensatory responses (Schwartz and Relman, 1963). Thus, they proposed “rules of thumb” to help guide the clinician (e.g. for every 10 mmHg PₐCO₂ elevation, bicarbonate increases by 1 mEq/L acutely). Despite their different interpretations, both the “Copenhagen” and “Boston” schools of thinking were grounded by the Henderson–Hasselbalch perspective.

What distinguishes Stewart acid-base from the traditional approach?

A key criticism of the traditional, bicarbonate- centred approach is that it is merely a mathematical description of pH and fails to provide any mechanistic insight into rising and falling [H+]. For example, the isohydric principle predicts that the [H+] (and therefore pH) may be expressed by the ratio of any weak acid–conjugate base pair in a biological solution. Thus, blood pH could be equally well described by the ratio of HPO₄2– to H₂PO₄ –; in other words, in terms of pH there is nothing unique about bicarbonate (Story, 2004). Consequently, the Henderson–Hasselbalch equation may lead clinicians into a “computo; ergo, est” fallacy (I calculate it; therefore, it is) (Wooten, 2004).

In response to these perceived shortcomings, Peter Stewart proposed a quantitative acid–base analysis in the late 1970s that is argued to provide true cause-and-effect relationships between independent and dependent variables, respectively (Stewart, 1978). In his formulation, there are 3 independent variables that clinically mediate both [H+] and [HCO₃-]:
1. PₐCO₂

2. The total weak acid concentration [A ] (e.g. albumin, phosphate)

3. The strong ion difference [SID]

Accounting for the law of mass conservation, electroneutrality and equilibrium constants for all incompletely dissociated species in biological solution, Stewart derived a fourth- order polynomial equation expressing [H+] as directly related to PₐCO₂ and ATOT and inversely to SID (Sirker et al., 2002).

SID is the difference between strong cations and strong anions in solution. “Strong” denotes how completely a species dissociates in a particular solution. In blood, the predominant strong ions are sodium [Na+] and chloride [Cl-] with small contributions from potassium [K+], magnesium [Mg2+] and calcium [Ca2+] (see Table 1). As SID may be simplified to [Na+] less [Cl-], its value is approximately +40 mEq/L in humans. For example, looking at a metabolic panel, you might see a [Na+] of 140 mEq/L and [Cl-] of 100 mEq/L. To think of how SID changes pH, keep in mind the imposition of electroneutrality in Stewart’s system of equations. If PₐCO₂ and ATOT were kept constant, but the SID diminished from +40 mEq/L to +25 mEq/L (e.g. hyperchloraemia from normal saline resuscitation), then the concentration of negatively charged, dependent species like bicarbonate would fall and positively charged, dependent species like protons would rise by mass action; thus, pH decreases.

The key to Stewart’s paradigm is that both [H+] and [HCO -] are completely at the mercy of the three independent variables noted above. PₐCO₂, ATOT and SID independently define the boundaries within which [H+] and [HCO -] dependently settle in the system. When sodium bicarbonate is administered intravenously, [H+] falls not because of the addition of the dependent [HCO -]; addition of the strong cation sodium raises the SID, which is the independent variable. On the other hand, intravenous hydrochloric acid (HCl) elevates [H+] not because of the dependent proton within HCl; the strong anion chloride shrinks the SID, which is directly responsible for diminished pH.

How does the Stewart acid–base formalism change how we think about metabolic disturbances?

Considering the traditional, bicarbonate- centred approach and Stewart’s model, one sees that PₐCO₂ is an independent mediator of pH for both. Therefore, in arterial blood, respiratory disturbances may be thought of similarly in either formulation. As a consequence, the crucial distinction between the two models is the treatment of metabolic disorders. In fact, a “corrected” Henderson–Hasselbalch equation has been proposed to include the true independent acid–base variables as follows (Kurtz et al., 2008):

While the effect of PₐCO₂ is the same as the traditional model, falling SID (e.g. hyperchloraemia) or rising ATOT (A- is the conjugate anion of ATOT) diminishes pH (i.e. increases [H+]). Conversely, rising SID (e.g. hypochloraemia) and falling ATOT both elevate pH.

While an in-depth description of metabolic alkalosis (Goldfarb and Kenny, 2019) is far beyond the intent of this brief primer, from Equation 2 above we see that increased SID and/or decreased ATOT raise pH per the Stewart approach. The most common clinical causes of metabolic alkalosis are vomiting and diuresis. Both of these scenarios are marked by chloride loss, via the upper GI tract and kidneys, respectively; these processes raise the SID. Additionally, Stewart’s model invites the clinician to consider loss of ATOT as a mechanism of alkalosis, for example severe hypoalbuminaemia in critically ill patients (Story, 2004).

With respect to metabolic acidosis, confusion may arise given the important distinction between the “anion gap” (AG) and “strong ion gap” (SIG) in the traditional and Stewart approaches, respectively. Both gaps, ultimately, alert the clinician to the footprint of unaccounted anions in the blood; clandestine anions narrow the differential diagnosis of a metabolic acidosis. While both gaps are predicated upon electroneutrality, the fundamental difference between the AG and SIG is how anions are grouped during book-keeping (Fig. 2).

The AG considers the difference between positive and negative charges only – agnostic to how fully dissociated or not the charged species is. The normal AG is almost entirely occupied by the negatively-charged albumin and, therefore, should always be corrected for by the patient’s albumin concentration. As such, an AG of 12 could be quite elevated in a patient with very low albumin.

The SIG, however, partitions charged species into “strong” (e.g. sodium, potassium, chloride) and “weak” (e.g. albumin, bicarbonate, phosphate); the net balance between these two groupings should be zero when there are no hidden anions. These ionic factions are referred to as apparent SID (i.e. SIDₐ) and effective SID (i.e. SIDₑ), respectively (Fig. 2) (Rastegar, 2009). In the calculation of SIDₑ below, the three terms account for the concentration of bicarbonate, albumin and phosphate. Note that with this approach, albumin “correction” is built into the calculation, as opposed to the traditional, AG method. Also note how closely SIDₑ relates to buffer base, described above. Elevation of either AG or SIG should prompt a search for ketones, uraemia, lactate or toxic alcohols.

Association or causation?

While the proponents of Stewart formalism argue that his equations are mechanistic rather than descriptive, critics maintain that Stewart’s approach suffers from the same computo; ergo, est fallacy levied against traditionalists. Macroscopic electroneutrality, Stewart’s critics argue, is a good way to tally charged species, but it does not necessarily speak to any underlying cause-and-effect process (Kurtz et al., 2008). Further, electroneutrality may be violated. Consider oxidative phosphorylation, where the inner mitochondrial membrane is acidified without any clear change in SID or ATOT (Kurtz et al., 2008). How does the Stewart paradigm account for this ubiquitous physiochemical event?

On the other hand, a recent electrodialysis study established that both respiratory and metabolic acidosis could be corrected by selectively removing chloride (Zanella et al., 2020)! Per the Stewart model, this is explained by rising SID – leading editorialists to declare the “end of the bicarbonate era” (Cove and Kellum, 2020). While debate is likely to continue, when used correctly, both models lead to similar clinical predictions (Rastegar, 2009).

Conclusion

As Stephen King noted, “sooner or later, everything old is new again.” Peter Stewart’s description of clinical acid–base in the late 1970s resonates with both buffer base and Naunyn’s thinking in the early 1900s. Consequently, in the 1950s the Henderson– Hasselbalch approach was considered “modern” with respect to the older notion including anions and cations as mediators of pH. These schools have reversed over the last 40 years after Stewart provided a quantifiable framework based upon conservation of mass, electroneutrality and mass action that holds “strong ions” as independent determinants of [H+]. While Stewart’s theoretical approach is embraced as mechanistic, others argue that like Henderson–Hasselbalch, Stewart’s equations do not offer cause-and-effect and are equally descriptive. Whether the student chooses to follow the traditional or Stewart approach to clinical acid–base, the following general guidelines are worthwhile:

1. Look at the pH first
2. Search for cryptic anions, even if there is primary alkalaemia
3. Remember albumin
4. Keep an open mind
5. Treat the patient, not the numbers

Disclosures

Dr Kenny is the cofounder and Chief Medical Officer of Flosonics Medical. He is the creator and author of a free haemodynamic curriculum at heart-lung.org.

References

Cove M and Kellum JA (2020). The end of the bicarbonate era? A therapeutic application of the Stewart approach. American Journal of Respiratory and Critical Care Medicine 201(7), 757–758. https://doi.org/10.1164/rccm.201910-2003ED

Goldfarb DS and Kenny J-E S (2019). Chapter 79 – Metabolic alkalosis. In: Lerma EV et al. (eds.) Nephrology Secrets (Fourth Edition). Elsevier.

Kenny J-E and Goldfarb DS (2012). Capital punishment: what is the appropriate abbreviation for partial pressure of a gas? The American Journal of the Medical Sciences 344(3), 255–256. https://doi.org/10.1097/MAJ.0b013e318253a09c

Kurtz I et al. (2008). Acid-base analysis: a critique of the Stewart and bicarbonate-centered approaches. American Journal of Physiology – Renal Physiology 294, F1009-F1031. https://doi.org/10.1152/ajprenal.00475.2007

Rastegar A (2009). Clinical utility of Stewart’s method in diagnosis and management of acid-base disorders. Clinical Journal of the American Society of Nephrology 4(7), 1267–1274. https://doi.org/10.2215/CJN.01820309

Schwartz WB and Relman AS (1963). A critique of the parameters used in the evaluation of acid-base disorders: whole-blood buffer base and standard bicarbonate compared with blood pH and plasma bicarbonate concentration. New England Journal of Medicine 268, 1382–1388. https://doi.org/10.1056/NEJM196306202682503

Sirker A et al. (2002). Acid−base physiology: the ‘traditional’ and the ‘modern’ approaches. Anaesthesia 57, 348–356. https://doi.org/10.1046/j.0003-2409.2001.02447

Stewart PA (1978). Independent and dependent variables of acid-base control. Respiration Physiology 33(1), 9–26. https://doi.org/10.1016/0034-5687(78)90079-8

Story DA (2004). Bench-to-bedside review: A brief history of clinical acid–base. Critical Care 8, 253–258. https://doi.org/10.1186/cc2861

Wooten EW (2004). Science review: Quantitative acid–base physiology using the Stewart model. Critical Care 8, 448–452. https://doi.org/10.1186/cc2910

Zanella A et al. (2020). Extracorporeal chloride removal by electrodialysis. A novel approach to correct acidemia. American Journal of Respiratory and Critical Care Medicine 201, 799–813. https://doi.org/10.1164/rccm.201903-0538oc