stewart hypothesis strong ion difference

Strong Ion Difference

Chris nickson.

• Oct 26, 2022

Strong Ion Difference and Stewart’s physicochemical approach to acid-base chemistry

• The quantitative approach to acid-base chemistry is also known as the physicochemical method or the Stewart approach
• Proposed by Canadian physiologist Peter Stewart in 1981
• It provides a mathematical explanation of the relevant variables that control H + in body fluids and their interactions
• The approach treats body fluids as a system that contains multiple interacting constituents and is based on the physical laws of aqueous solutions to write equations that describe how the variables interact.
• The Stewart approach shows that pH is not simply determined by the [H+] and [HCO 3 – ] (as in the Henderson-Hasselbach approach) but involves interactions of other variables, three of which are independent variables that control acidity.

DEPENDENT AND INDEPENDENT VARIABLES

Dependent variables are thought of as internal to the system; their values depend on the values of the independent variables and reflect the behaviour of the equilibrium reactions in the system. The independent parameters control acidity ([H+]) in arterial or venous plasma.

Dependent variables:

• HCO 3 –
• HA (weak acid)
• A – (weak anions)

Independent variables:

• ATOT (total weak non-volatile acids)
• SID (net Strong Ion Difference)

PHYSICAL LAWS UNDERPINNING THE PHYSICOCHEMICAL METHOD

The interactions among the variables in the system that determine pH obey the physical laws of aqueous solutions –

• maintenance of electrical neutrality
• dissociation equilibria for weak electrolytes (partially dissociated when dissolved in water)
• conservation of mass

Thus the influence of the independent variables can be predicted through 6 simultaneous equations:

• [H + ] x [OH – ] = K ‘w (water dissociation equilibrium)
• [H + ] x [A-] = KA x [HA] (weak acid equilibrium)
• [HA] + [A-] = [ATOT] (conservation of mass for “A”)
• [H + ] x [HCO 3 – ] = KC x pCO₂ (bicarbonate ion formation equilibrium)
• [H + ] x [CO32-] = K3 x [HCO 3 – ] (carbonate ion formation equilibrium)
• [SID] + [H+] – HCO 3 – -] – [A-] -[CO32-] – [OH – ] = 0 (maintenance of electrical neutrality)

STRONG ION DIFFERENCE

Strong ions are those ion that dissociate completely at the pH of interest in a particular solution. In blood at pH 7.4:

• strong cations are: Na + , K + , Ca 2+ , Mg 2+
• strong anions are: Cl - and SO 4 2-

Strong Ion Difference (SID) is the difference between the concentrations of strong cations and strong anions.

• SID = [strong cations] – [strong anions]
• apparent SID = SIDa = (Na + + K + + Ca 2+ + Mg 2+ ) – (Cl – + L-lactate + urate)
• Abbreviated SID = (Na + ) – (Cl – )

In normal human plasma the SID is 42 mEq/L (which suits fans of the Hitchhiker’s Guide to the Galaxy)

• the number of positive and negative ions in a solution must be equal (SID = 0), so there are unmeasured anions
• increased SID (>0) leads to alkalosis (increase in unmeasured anions)
• decreased SID (<0) acidosis
• given that SID is about 40mEq/L, plasma is normally slightly alkaline (any departure is roughly equivalent to the standard base-excess, although because SID doesn’t allow for Hb there is often a discrepancy)

The SID can be changed by two methods:

(1) Concentration change

• dehydration: concentrates the alkalinity and increases SID
• overhydration: dilutes the alkaline state (dilutional acidosis) and decreases SID

(2) Strong Ion changes

• Decreased Na + : decreased SID and acidosis
• Increased Na + : increased SID and alkalosis
• Increased Cl - : decreased SID and acidosis (NAGMA; occurs with normal saline as the relative increase in Cl - exceeds that of Na + )
• increased in organic acids with pKa < 4 (lactate, formate, ketoacids): decreased SID and acidosis (HAGMA))

Strong Ion Gap (SIG)

• SIG = SIDa – SIDe
• SIDa = apparent SID = calculation of {strong cations] – [strong anions] shown above
• SIDe = [A-] + [HCO 3 – ]
• Thus unmeasured anions will increase SIDa, but not SIDe, thus increasing SIG
• SIG is analogous to AGc (anion gap corrected for albumin) but has the advantage of less unmeasured components
• SIG is still suspectable to unmeasured cations (e.g. Li) and anions (e.g. myeloma)
• SIG suffers from imprecision due the acculumation of measurement errors in multiple individual components
• normal SIG may not be zero if calculated from the mid-range of individual hospital normal ranges for each component (likely due to systematic bias in measurement methods)
• high: increased unmeasured anions
• low: increased unmeasured cations
• independent of pH, albumin, PO4, Ca, Mg
• ATOT = total plasma concentration of inorganic phosphate, serum proteins and albumin (weak non-volatile acids)
• ATOT = [PiTOT] + [PrTOT] + [albumin]
• hypoproteinaemia = base excess
• at a molecular level, it is the concentration of CO₂, not the partial pressure which governs its effect on other molecules and ions
• However, in practice, our warm blood means that CO₂ is scarcely soluble and measured pCO₂ can be used to measure effect

CLASSIFICATION OF ACID-BASE DISORDERS

Respiratory causes

• increased or decreased PaCO 2

Non-respiratory causes

• Water excess: ↓ SID, ↓ [Na + ]
• Water deficit:↑ SID, ↑ [Na + ]
• ↓ SID, ↑ [Cl – ]
• ↑ SID, ↓ [Cl – ]
• ↓ SID, ↑ [XA – ]
• excess or deficit of inorganic phosphate
• excess or deficit of albumin

PROS AND CONS OF THE PHYSICOCHEMICAL METHOD

• acknowledgement of the importance of other factors controlling pH
• diminishes the importance of the HCO 3 – ion which is just a dependent variable
• based on physicochemical principles
• provides elegant explanations for phenomena such as the acidosis induced by normal saline administration
• SID only reflects plasma (whereas SBE reflects the whole body and the influence of Hb)
• SID is calculated from multiple measurements, leading to accumulation of measurement error
• lack of clinical correlation to validate the benefit
• standard base excess accuracy has been well validated and accepted in clinical correlation
• emerging chemistry research suggests that the Stewart approach may not be mechanistically correct in describing acid-base chemistry

References and links

Journal articles and textbooks

• Doberer D, Funk GC, Kirchner K, Schneeweiss B. A critique of Stewart’s approach: the chemical mechanism of dilutional acidosis. Intensive Care Med. 2009;35(12):2173-80. [ pubmed ]
• Gunjan Chawla, Gordon Drummond; Water, strong ions, and weak ions, Continuing Education in Anaesthesia Critical Care & Pain, 2008; 8(3):108–112, https://doi.org/10.1093/bjaceaccp/mkn017
• Knight C, Voth GA. The curious case of the hydrated proton. Acc Chem Res. 2012;45(1):101-9. [ pubmed ]
• Morgan TJ. The meaning of acid-base abnormalities in the intensive care unit: part III — effects of fluid administration. Crit Care. 2005;9(2):204-11. [ pubmed ] [ article ]
• Morgan TJ. The Stewart approach–one clinician’s perspective. Clin Biochem Rev. 2009;30(2):41-54. [ pubmed ] [ article ]
• Morgan TJ. What exactly is the strong ion gap, and does anybody care?. Crit Care Resusc. 2004;6(3):155-9. [ pubmed ] [ article ]
• Sirker AA, Rhodes A, Grounds RM, Bennett ED. Acid−base physiology: the ‘traditional’ and the ‘modern’ approaches. Anaesthesia. 2002;57(4):348-356. [ article ]
• Stewart PA. How to Understand Acid-Base. New York: Elsevier, 1981 (available at: http://www.acidbase.org/ )
• Stewart PA. Independent and dependent variables of acid-base control. Respir Physiol. 1978;33(1):9-26. [ pubmed ]
• Stewart PA. Modern quantitative acid-base chemistry. Can J Physiol Pharmacol. 1983;61(12):1444-61. [ pubmed ]
• Story DA, Poustie S, Bellomo R. Quantitative physical chemistry analysis of acid-base disorders in critically ill patients. Anaesthesia. 2001;56(6):530-3. [ pubmed ] [ article ]
• Kurtz I, Kraut J, Ornekian V, Nguyen MK. Acid-base analysis: a critique of the Stewart and bicarbonate-centered approaches. Am J Physiol Renal Physiol. 2008;294(5):F1009-31. [ pubmed ] [ article ]

FOAM and web resources

• Acid Base Physiology by Kerry Brandis
• EMCrit — Acid Base in the Critically Ill – Part I and Acid Base in the Critically Ill – Part II (2016)
• EMCrit — Acid Base Ep. 7 – Bicarb Updates, Quantitative Approach, and Prof. David Story (2018)
• How to interpret acid-base by Peter Stewart
• The Physicochemical approach to Acid-Base
• Acid Base Tutorial — Stewart’s Strong Ion Difference
• PulmCrit — The Great Lactate Debate Part 1: should we be counting protons or strong ions? by John Emille Kenny (2018)
• PulmCrit — The Great Lactate Debate Part 2: can we ‘myth-bust’ the strong ion approach? by John Emille Kenny (2018)
• PulmCrit — The Acidity of Normal Saline and the Stewart Approach by John Emille Kenny (2016)

Critical Care

Chris is an Intensivist and ECMO specialist at the  Alfred ICU in Melbourne. He is also a Clinical Adjunct Associate Professor at Monash University . He is a co-founder of the  Australia and New Zealand Clinician Educator Network  (ANZCEN) and is the Lead for the  ANZCEN Clinician Educator Incubator  programme. He is on the Board of Directors for the  Intensive Care Foundation  and is a First Part Examiner for the  College of Intensive Care Medicine . He is an internationally recognised Clinician Educator with a passion for helping clinicians learn and for improving the clinical performance of individuals and collectives.

After finishing his medical degree at the University of Auckland, he continued post-graduate training in New Zealand as well as Australia’s Northern Territory, Perth and Melbourne. He has completed fellowship training in both intensive care medicine and emergency medicine, as well as post-graduate training in biochemistry, clinical toxicology, clinical epidemiology, and health professional education.

He is actively involved in in using translational simulation to improve patient care and the design of processes and systems at Alfred Health. He coordinates the Alfred ICU’s education and simulation programmes and runs the unit’s education website,  INTENSIVE .  He created the ‘Critically Ill Airway’ course and teaches on numerous courses around the world. He is one of the founders of the  FOAM  movement (Free Open-Access Medical education) and is co-creator of  litfl.com , the  RAGE podcast , the  Resuscitology  course, and the  SMACC  conference.

His one great achievement is being the father of three amazing children.

On Twitter, he is  @precordialthump .

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Physiology News Magazine

• Summer (June) 2021- Issue 122

An introduction to Stewart acid–base

Clinically useful or chemical bookkeeping.

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).

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.

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

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• Published: 02 July 2004

Science review: Quantitative acid–base physiology using the Stewart model

• E Wrenn Wooten 1  

Critical Care volume  8 , Article number:  448 ( 2004 ) Cite this article

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There has been renewed interest in quantifying acid–base disorders in the intensive care unit. One of the methods that has become increasingly used to calculate acid–base balance is the Stewart model. This model is briefly discussed in terms of its origin, its relationship to other methods such as the base excess approach, and the information it provides for the assessment and treatment of acid–base disorders in critically ill patients.

Introduction

Acid–base derangements are commonly encountered in the critical care unit [ 1 ], and there is renewed interest in the precise description of these disorders in critically ill patients [ 2 – 5 ]. This new interest has led to a renovation of the quantitative assessment of physiological acid–base balance, with increasing use of the Stewart model (strong ion difference [SID] theory) to calculate acid–base balance in the critically ill [ 2 , 3 , 6 , 7 ]. This method is discussed, particularly as it pertains to the metabolic component of acid–base derangements, as one of several approaches that may be used in the intensive care unit for quantitative evaluation. As with any mathematical model, a basic understanding of its principles is useful for proper application and interpretation.

• Stewart model

All equilibrium models of acid–base balance utilize the same basic concept. Under the assumption of equilibrium or a steady-state approximation to equilibrium, some property of the system (e.g. proton number, proton binding sites, or charge, among other possible properties) is enumerated from the distribution of that property over the various species comprising the system, according to the energetics of the system manifested through the relevant equilibrium constants of the various species under a given set of conditions [ 5 , 8 – 12 ]. This function is calculated at the normal values and then the abnormal values; from these the degree of change is obtained to give information about the clinical acid–base status of the patient. All of the apparently 'different' methods for assessing acid–base balance arise from this common framework [ 5 , 12 ].

In the Stewart method, charge is taken as the property of interest [ 7 , 11 , 13 ]. Using this property, acid–base status may be expressed for a single physiologic compartment, such as separated plasma, as follows [ 7 , 10 , 11 , 13 ]:

Plasma physiologic pH is then determined by the simultaneous solution of Eqn 1 and the Henderson-Hasselbalch Equation:

Where for human plasma pK' = 6.103. S = 0.0306 is the equilibrium constant between aqueous and gas phase CO 2 [ 16 , 17 ]. [HCO 3 - ] is the concentration of plasma bicarbonate in mmol/l, and PCO 2 is the partial CO 2 tension in Torr.

The standard technique for acid–base assessment [ 1 , 18 ] may be recognized as a subset of the Stewart model [ 14 ], in which the series in Eqn 1 is truncated at the first term to give the following:

SID = [HCO 3 - ]     (3)

In this approach the metabolic component of an acid–base disorder is quantified as the change in plasma bicarbonate concentration (Δ[HCO 3 - ]) [ 18 ], which by Eqn 3 is also equal to ΔSID. This method is often sufficient and has been used successfully to diagnose and treat countless patients, but it has also been criticized as not strictly quantitative [ 19 , 20 ]. [HCO 3 - ] depends upon the PCO 2 and does not provide complete enumeration of all species, because albumin and phosphate also participate in plasma acid–base reactions [ 15 , 17 , 20 , 21 ].

A more complete calculation may be undertaken for better approximation by including more terms in the series in Eqn 1. In addition, although

is a nonlinear function of pH, it can be approximated over the physiologic range by a more computationally convenient linear form, such that for plasma the following explicit expression is obtained [ 11 , 12 , 15 ]:

SID = [HCO 3 - ] + C Alb (8.0pH - 41) + C Phos (0.30pH - 0.4)     (4)

Equation 4 was obtained via a term by term summation over all of the buffer groups in albumin and of phosphoric acid, as performed by Figge and coworkers [ 15 , 21 ]. The theoretical basis for the validity of this approach is well established [ 8 ], and Eqn 4 has been shown to reproduce experimental data well [ 11 , 12 , 15 , 21 , 22 ]. Some authors have argued that the effects of plasma globulins should also be considered for better approximation [ 17 , 20 , 23 , 24 ], although other calculations suggest that the consideration of globulins would be of little clinical significance in humans [ 22 ].

Consideration of the change in SID using Eqn 4 between normal and abnormal states at constant albumin and phosphate concentrations gives the following:

ΔSID = Δ[HCO 3 - ] + (8.0C Alb + 0.30C Phos )ΔpH     (5)

Which is recognized to be of the same form and numerically equivalent to the familiar Van Slyke equation for plasma, yielding the plasma base excess (BE) [ 5 , 11 , 17 , 25 ]. Furthermore, Eqn 4 is of the same form as the CO 2 equilibration curve of the BE theory presented by Siggaard-Andersen [ 11 , 17 , 20 , 25 ]. The BE approach and the Stewart method are equivalent at the same level of approximation [ 11 , 12 , 26 ].

Strong ion gap

A widely used concept arising from the Stewart approach is the strong ion gap (SIG), which was popularized by Kellum [ 27 ] and Constable [ 28 ]. This relies upon a direct calculation of the SID as, for example, the following:

Where SID m is the measured SID [ 27 ]. This direct measurement is then compared with that generated via Eqn 4:

SIG = SID m - SID     (7)

This gives a higher level version of the familiar plasma anion gap [ 1 , 18 ]. Some publications have used the notation SID a (for SID apparent) to refer to the variable SID m calculated using Eq. 6, and SID e (SID effective) to refer to that calculated using Eqn 4 [ 2 , 3 , 15 , 27 ]. SIG has been shown to predict the presence of unmeasured ions better than the conventional anion gap [ 28 ], as might be expected, given that more variables are taken into account. Some unmeasured ions that are expected to contribute to the SIG are β-hydroxybutyrate, acetoacetate, sulfates, and anions associated with uremia [ 6 ].

Changes in noncarbonate buffer concentration

ΔSID expressed through the relationship of Eqn 5 unambiguously quantifies the nonrespiratory component of an acid–base disturbance in separated plasma [ 11 , 17 ], with the total concentrations of amphoteric species such as albumin and phosphate remaining constant [ 11 , 12 , 17 ]. An amphoteric substance is one that can act as both an acid and a base. Stewart and other investigators [ 4 , 7 , 29 – 33 ], though, have emphasized the role played by changes in the noncarbonate buffer concentrations in acid–base disorders. When the noncarbonate buffer concentrations change, the situation becomes more complex, and in general a single parameter such as ΔSID no longer necessarily quantifies the metabolic component of an acid–base disorder, and enough variables must be examined to characterize the disorder unambiguously. Examples below demonstrate this point when the concentrations of noncarbonate buffers change, through a pathologic process or through resuscitation.

Table 1 gives several examples for separated human plasma, including the normal values of case 1. Case 2 demonstrates a metabolic acidosis with constant noncarbonate buffer concentrations, in which the ΔSID of -10 mmol/l quantifies the metabolic component of the acid–base disorder [ 11 ], which has been described as a strong ion acidosis [ 4 ]. Case 3 gives values for the fairly common occurrence of isolated hypoproteinemia. This too gives a ΔSID of -10 mmol/l, although the total weak acid and weak base concentrations have both decreased [ 11 ]. The physiological interpretation of this condition in terms of acid–base pathology is the subject of debate [ 3 , 6 , 12 , 20 , 31 , 34 ]. Considering this to be an acid–base disorder, some authors would classify this case as hypoproteinemic alkalosis with a compensating SID acidosis [ 4 , 6 , 30 – 32 ]. More generally, this has been termed a buffer ion alkalosis with compensating strong ion acidosis [ 4 ]. If the mechanism of hypoalbuminemia is en bloc loss of charged albumin with counterions in tow, for example in nephrotic syndrome, then it seems dubious to describe this process as compensation in the usual physiologic sense. Also, note that both cases 2 and 3 have the same decrease in SID, but the individual in case 2 is expected to be quite sick with acidemia whereas the patient in case 3 is probably not acutely ill, except for the effects of low oncotic pressure.

Although it has been suggested that alkalosis can result from hypoproteinemia, with patients without adequate compensation becoming alkalemic [ 29 , 32 ], the idea of alterations in protein concentration as acid–base disorders per se has been questioned [ 3 , 20 ]. The concept of the normal SID changing as a function of protein concentration has been suggested [ 3 , 11 , 12 ]. In such an instance, ΔSID again quantifies the metabolic component of an acid–base disturbance, essentially renormalizing the noncarbonate buffer concentrations to the abnormal values [ 11 , 12 ]. This is basically what has been advocated in the past for BE [ 20 , 34 ], in which Eqn 5 uses the abnormal protein and phosphate concentrations for C Alb and C Phos [ 11 ]. Thus, the SID of 29 mmol/l in case 3 is said to be normal for the decreased albumin concentration [ 3 ], giving a ΔSID of 0 mmol/l. This individual will, however, be more susceptible to acidemia or alkalemia for a given derangement, as expressed through the molar buffer values and noncarbonate buffer concentrations, than would a normal individual [ 5 ]. If SID is not renormalized as described above, then BE and ΔSID differ by an added constant [ 11 , 12 ].

Another interesting issue is raised in the treatment of patients with intravenous albumin or other amphoteric species. Kellum previously pointed out that, based on the SID, one might think that albumin solutions with a SID of 40–50 mmol/l would be alkalinizing to the blood, even though their pH is close to 6.0 [ 35 ]. This apparent paradox is resolved by again realizing that, for amphoteric substances, one is not only changing the SID but also increasing both the total weak acid and weak base concentrations by increasing the total protein concentration [ 9 , 11 ]. This highlights the point made by Stewart concerning the necessity of considering all variables in assessing acid–base balance [ 7 , 13 ]. A complete calculation yields what is intuitively predicted – that such a solution is in fact acidifying to blood (unpublished data). One might further speculate that the administration of 'unbuffered' albumin to patients may contribute to the reason why this treatment has not been more successful in the critically ill [ 36 ]. Extensive quantitative discussions regarding the acid–base balance of administered fluids have typically not been given in publications on resuscitation with amphoteric colloids [ 36 – 39 ], although this is an issue that should be examined. Constable [ 40 ] recently gave a brief quantitative discussion of acid–base effects of giving various crystalloids.

Model for whole blood

Several points arise in the comparison of SID with BE, as has been performed in a number of studies [ 33 , 38 , 41 – 44 ]. This is in some respects a misplaced comparison, because BE represents a difference whereas SID does not [ 11 , 26 ]. The corresponding variable to SID in the BE formalism is the concentration of total proton binding sites, while the BE represents the change in this quantity from the normal value, and corresponds to ΔSID [ 11 , 12 , 17 , 26 ]. More significant, clinical studies using Stewart theory have calculated the separated plasma SID, while making comparison with the BE for whole blood or the standard base excess (SBE) [ 33 , 38 , 41 , 42 ], rather than the corresponding plasma BE. Furthermore, consideration of only the plasma compartment creates a potential source of error, because separated plasma versions of the Stewart method quantify only a portion of the acid–base disorder [ 12 , 17 , 45 ]. An equation for the SID of whole blood has recently been derived, partly to address this issue [ 12 ].

Where φ(E) is the hematocrit, C Hgb (B) is the hemoglobin concentration of whole blood, and C DPG (E) is the 2, 3-diphosphoglycerate concentration in the erythrocyte. Again, concentrations are in mmol/l, and one may multiply hemoglobin in g/dl by 0.155 to obtain hemoglobin in mmol/l. The normal 2, 3-diphosphoglycerate concentration in the erythrocyte is 6.0 mmol/l [ 12 ]. The 'P', 'B', and 'E' designations stand for plasma, whole blood, and erythrocyte fluid, respectively. The corresponding Van Slyke form has also been obtained, and is numerically identical to BE for whole blood [ 12 ].

The SBE, as mentioned above, is also widely used [ 3 , 17 , 20 , 25 ]. This parameter reflects the extracellular acid–base status and approximates the in vivo BE for the organism [ 17 , 20 , 25 ]. The Van Slyke equation for SBE approximates this situation via a 2:1 dilution of whole blood in its own plasma [ 17 , 20 , 25 ]. It should be borne in mind, therefore, that Eqn 4 may prove more concordant with clinical data than Eqn 8, since the plasma expression may produce values closer to the in vivo condition because of the distribution functions of various species across the whole organism [ 17 ].

Stewart theory and mechanism

Finally, the Stewart model is taken by some to be a mechanistic description of acid–base chemistry in which changes only occur by alteration in PCO 2 , SID, or noncarbonate buffer concentrations because these are the only true independent variables; changes never occur by addition or removal of H + to the system or by changes in [HCO 3 - ] because these are dependent variables [ 7 , 13 ]. It is said that because the Stewart theory provides mechanistic information, it is superior to the BE approach [ 3 , 35 , 46 , 47 ]. Support for this point of view is offered in the form of philosophic arguments regarding the nature of independence [ 7 , 13 ], as well as studies showing that the Stewart model accurately predicts what is observed experimentally [ 30 , 42 , 44 , 48 ]. However, like the BE approach and like any other method derived from considerations involving the calculation of interval change via the assessment of initial and final equilibrium states, the Stewart method does not produce mechanistic information [ 8 , 35 ]. These are basically bookkeeping methods. To believe otherwise risks falling prey to the computo , ergo est (I calculate it, therefore it is) fallacy. What is thus required for mechanistic understanding is the collection of actual mechanistic data, perhaps obtainable through isotopic labeling and kinetics experiments.

Both experimental and theoretical data have shown that the Stewart method is accurate for describing physiological acid–base status, and the use of the SIG potentially offers an improvement over the traditional anion gap, but because the Stewart method proceeds from the same common framework as the BE approach, it theoretically offers no quantitative advantage over BE at corresponding levels of approximation [ 11 , 12 , 26 , 35 , 49 ]. As such, it remains to be seen whether the renovation of acid–base assessment afforded by the Stewart approach constitutes a radical new architecture for understanding acid–base physiology, or whether it is simply a new façade.

Abbreviations

• base excess

albumin concentration

phosphate concentration

partial CO 2 tension

standard base excess

strong ion difference

strong ion gap.

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

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Traditional approach versus Stewart approach for acid–base disorders: Inconsistent evidence

Satoshi kimura.

1 Department of Anesthesiology and Resuscitation, Okayama University Hospital, Okayama, Japan

Muhammad Shabsigh

2 Department of Anesthesiology, The Ohio State University Wexner Medical Center, Columbus, OH, USA

Hiroshi Morimatsu

The traditional approach and the Stewart approach have been developed for evaluating acid–base phenomena. While some experts have suggested that the two approaches are essentially identical, clinical researches have still been conducted on the superiority of one approach over the other one. In this review, we summarize the concepts of each approach and investigate the reasons of the discrepancy, based on current evidence from the literature search.

In the literature search, we completed a database search and reviewed articles comparing the Stewart approach with the traditional, bicarbonate-centered approach to November 2016.

Our literature review included 17 relevant articles, 5 of which compared their diagnostic abilities, 9 articles compared their prognostic performances, and 3 articles compared both diagnostic abilities and prognostic performances. These articles show a discrepancy over the abilities to detect acid–base disturbances and to predict patients’ outcomes. There are many limitations that could yield this discrepancy, including differences in calculation of the variables, technological differences or errors in measuring variables, incongruences of reference value, normal range of the variables, differences in studied populations, and confounders of prognostic strength such as lactate.

Conclusion:

In conclusion, despite the proposed equivalence between the traditional approach and the Stewart approach, our literature search shows inconsistent results on the comparison between the two approaches for diagnostic and prognostic performance. We found crucial limitations in those studies, which could lead to the reasons of the discrepancy.

Introduction

Originally, Henderson 1 recognized that carbon dioxide and bicarbonate were key elements of carbonate mass action. Hasselbalch 2 developed it into the negative logarithmic pH notation. Henderson–Hasselbalch equation considers bicarbonate one of the strongest buffers and determinants of pH in our physiologic system. In order to separate metabolic and respiratory components in acid–base disorders, the concept of base excess (BE) was first introduced by Siggaard-Andersen et al. 3 and became the head of the Copenhagen school. On the other hand, exploiting the flaw of using in vitro concept of BE in a living organism, Schwartz and Relman 4 developed the bicarbonate-centered approach setting out the relationship between partial pressure of carbon dioxide (pCO 2 ) and bicarbonate ion (HCO 3 – ) in vivo, which became the center of the Boston school. The difference of the two approaches for metabolic components generated the “great trans-Atlantic acid-base debate” between the Boston school and the Copenhagen school. 5

In the late 1900s, Peter Stewart questioned the bicarbonate-centered approach and the base excess method for acid-base phenomenon. 6 – 8 In his concept, each variable is classified as a dependent or independent factor in determining the H + concentration of a solution, resulting in pH through the dissociation of water, in order to maintain electrical neutrality. 9 , 10 Although both the BE approach and the Stewart approach were developed in physio-chemical terms, the Stewart approach is sometimes called “physicochemical,” “modern,” or strong ion approach. 6 , 7 In contrast, the bicarbonate-centered approach and the base excess approach are called “traditional approach.” 11 Currently, most of the modern blood gas analyzers report both HCO 3 − and BE for many clinicians to use the traditional approach.

Since then, both the traditional and the Stewart approaches have been relevant subjects for clinical and research discussions. While some experts have suggested that the two approaches are essentially identical, 12 , 13 clinical researches have still been conducted and discussed which approach has a better performance as a diagnostic or prognostic tool. In this review, we summarize the concepts of each approach and investigate the reasons of this discrepancy, based on current evidence from the literature search, despite the proposed identity.

The traditional approach

Bicarbonate-centered (“boston”) approach.

In the early 1900s, an acid was defined as a substance that is capable of donating hydrogen to a solution, and a base was defined as a substance capable of accepting hydrogen from a solution. Henderson 2 first recognized that bicarbonate is a unique and important buffer, which has the ability to bind or release hydrogen ions in a solution to keep the pH relatively constant, in a physiologic system at constant pCO 2 . Henderson–Hasselbalch equation provides a simple relationship among the respiratory parameter (pCO 2 ), the non-respiratory parameter bicarbonate (HCO 3 – ), and the overall acidity parameter (pH). 14

Based on the equation, Schwartz and Relman 4 developed the CO 2 /HCO 3 – approach predicting the nature of acid–base disorders. Although it is relatively easy to understand and to apply in clinical settings, there are some weaknesses we need to consider. Since there are non-bicarbonate buffers such as albumin and hemoglobin, a change in bicarbonate concentration does not always reflect the total amount of non-respiratory acids or bases. 15 Furthermore, the equation listing pCO 2 and bicarbonate as determinants of pH can mislead their interdependence.

BE and standard BE (“Copenhagen”) approach

In 1948, Singer and Hastings 16 introduced the concept of the buffer base, which is the sum of all plasma buffer anions and is composed of bicarbonate ion and non-volatile, weak acid buffers (mainly albumin and phosphate). It is shown that a change in a buffer base corresponds to a change in the metabolic component of acid–base balance and develops into the BE methodology. 17 , 18

In 1960, Siggaard-Andersen et al. 3 , 19 measured the plasma bicarbonate concentration at a fixed temperature and partial pCO 2 and compared the difference between their results and a reference value. When corrected by a constant, this difference yields the BE, which represents the amount of acid or alkali that must be added to 1 L of oxygenated blood, exposed in vitro to a pCO 2 of 40 mmHg to achieve the average normal pH of 7.40. 19 , 20

Blood BE measures the metabolic component that is independent from the respiratory component and incorporates the effect of hemoglobin as a buffer. 19 , 20 The most commonly used formula for calculating the BE is the Van Slyke equation, developed by Siggaard-Andersen 19

The BE equation suffers from inaccuracy in vivo with changes in pCO 2 , possibly due to equilibration across the entire extracellular fluid space, which is composed of whole blood and interstitial fluid. 7 , 21 , 22 Therefore, the equation was modified to “Standardize” the effect of hemoglobin on CO 2 titration in order to improve the accuracy in vivo 7

However, the standard base excess (SBE) is still slightly subject to pCO 2 change. 7 Furthermore, this equation assumes normal non-buffer ion levels; however, a decrease in albumin or phosphate, which is commonly encountered in intensive care unit (ICU), results in more unstable SBE. 7 , 8 In addition, the BE and SBE methods are unable to detect complicated acid–base disorders or identify different types of metabolic acidosis.

The anion gap (AG), the difference between unmeasured plasma anions and the unmeasured plasma cations, 8 is an additional diagnostic tool to assess the metabolic components of the acid–base equilibrium. Albumin and phosphate, one of the circulatory proteins, mainly account for the AG under normal conditions. The rest of the possible candidates are composed of urate, lactate, ketone bodies, sulfate, salicylates, penicillins, citrate, pyruvate, and acetate. 23 , 24

This additional diagnostic tool provides new insight to the traditional approach, classifying metabolic acidosis into normal AG acidosis and high AG acidosis. However, severe pH disturbances and changes in the concentration of serum albumin, which behaves as an anion, have a significant impact on the AG. 25 , 26 Those disadvantages lower the sensitivity and specificity of this diagnostic tool to detect metabolic acidosis.

A noticeable attempt to improve the practical AG was the introduction of the corrected anion gap (AGc). The most popular AGc is “albumin-corrected” AG. For each 10 g/L decrement in the serum albumin concentration, the AG is expected to decrease by 2.5 mmol/L and needs to be corrected to compensate for abnormality of serum albumin concentration. 8 However, this AGc attributes a fixed negative charge to albumin, taking no consideration for pH effects on the imidazole groups of albumin. 7 In addition, this AGc ignores the phosphate contribution to all of the weak acids that might need to be considered. 27 – 29

Stewart approach

Concept of the stewart approach.

Stewart 9 , 10 questioned the traditional approach for acid–base equilibrium evaluation. He modeled a solution that contained a complex mixture of ions of constant charge over the physiological pH range (strong ions), non-volatile proton donor/acceptors which transfer H + within the physiological pH range (weak acid/base), and the volatile bicarbonate–CO 2 buffer system. 8 Key aspect of Stewart’s concept was the classification of each variable as dependent or independent in determining the H + concentration of the solution. In his theory, there are three responsible variables to independently determine the dissociation of water, and consequently the hydrogen ion concentration, in order to maintain electrical neutrality: (1) strong ion difference (SID), (2) total concentration of weak acids (A TOT ), and (3) partial pCO 2 of the solution. 8 , 30 Thus, in the Stewart’s approach, metabolic disorders are the results of changes in SID or A TOT . 7 , 31

Apparent SID and effective SID

Apparent SID (SIDa) represents the difference between measured strong cations and strong anions. 7 With the development of devices capable of detecting “unmeasured” ions (which we could not measure routinely), current calculation of the SIDa contains the following ions 7

where Na denotes sodium, K denotes potassium, Ca denotes calcium, Mg denotes magnesium, and Cl denotes chloride.

On the other hand, SID calculated to account for electrical neutrality is viewed as the effective SID (SIDe). 7 The SIDe can be calculated as the sum of bicarbonate and weak acids ([A – )), mainly albumin and phosphate 8

where Alb denotes albumin and Pi denotes inorganic phosphate

Although the law of electrical neutrality in the body requires SIDa and SIDe to be equal, failure to measure the concentration of all strong and weak ions in plasma yields a gap between the two. Thus, SIG, the difference of SIDa and SIDe, quantifies [unmeasured anions] – [unmeasured cations] of both strong and weak ions. 7

One of the theoretical advantages of SIG over AG is the pure representation of unmeasured ions. Although both AG and SIG represent unmeasured ions, the “unmeasured” ions derived from AG are composed of [Mg 2+ ], [Ca 2+ ], [A – ] (mainly albumin and phosphate), [Lactate – ], and [other ions] clinicians do not routinely measure, whereas the unmeasured ions expressed by the SIG are composed of just [other ions]. While normal AG ranges from 7 to 17 mEq/L when using [K + ] for the calculation, SIG is close to zero in normal situations. 8 Although the albumin-corrected AG eliminates the effect of hypo/hyper albuminemia, the gap still persists.

Consideration of A TOT alternations for acid–base disorders is another key aspect of this approach compared to the traditional one. 7 , 31 A TOT , representing all non-bicarbonate buffers, is made up of mainly serum albumin and other minor charges such as phosphate and globulins. 7 , 31 In the Stewart approach, an increase in A TOT would result in metabolic acidosis and a decrease would result in metabolic alkalosis. 7

There is a controversy over the existence of A TOT acidosis/alkalosis. 32 , 33 Although observations in vitro show that alterations in albumin concentration can affect acidity, there is no credible demonstration that the living organism, especially the liver, regulates albumin to maintain acid–base homeostasis. 30 One of the explanations is that the theoretical slight weak acid loss secondary to hypoproteinemia is compensated for by a decrease in SID (adjusted SID) without changes in pH, HCO 3 – , and BE as commonly seen in ICU, rather than a complex acid–base disorder such as a mixed metabolic acidosis/hypoalbuminemic alkalosis. 20 , 34 , 35

Although the traditional approach and the physicochemical approach originated from different concepts as mentioned above, their mathematical comparison showed very few differences once model coefficients are estimated in the consistent manner. 12 Representation of the bicarbonate buffers is almost identical, and representation of non-bicarbonate buffering in the van Slyke equation can be derived from the equations of Stewart. Representation of electrical neutrality comes from the preservation of charge equation described by Singer and Hastings. 16 For both approaches, measurement of plasma protein concentration is essential if unmeasured anions are to be distinguished from protein buffers. 12 However, many clinical researches have still been conducted on which method is more informative and useful in clinical situations, and there has been no consistent conclusion. In order to find the reasons of the consistency, we conducted a literature search focusing on two main comparisons: diagnostic and prognostic performance of those approaches.

Literature search

The PubMed Database was initially searched from inception to 15 November 2016 to compare the physicochemical approach with the traditional approach. The search was performed with the relevant medical subject heading terms and strategies: ((SID) OR (strong ion gap)) AND ((AG) OR (BE)). References of selected publications were individually inspected for additional articles that might have been omitted or overlooked in the electronic database search.

The inclusion criteria for the review were (a) studies using both approaches for the same population and (b) studies comparing the diagnostic and/or predictive abilities directly or indirectly. Studies using the traditional methods with AG but without AGc were excluded because non-corrected AG lacks consideration of abnormal albumin concentration commonly seen in the ICU, and many studies already have shown that the simple AG cannot detect acid–base disorders that the Stewart method can identify. 36 – 39 Nonhuman studies, case reports, abstracts, and unpublished or any studies in which full text was not available were excluded.

Our electrical literature search revealed 192 studies. One hundred and five nonhuman studies, case reports, abstracts, or otherwise irrelevant studies were excluded. Among 87 potentially relevant articles, we exclude 41 studies that did not compare the two approaches as for diagnostic and/or predictive performance and 29 studies that did not calculate corrected AG for the comparison. Thus, the remaining 17 articles were included in this review. Eight studies compared their diagnostic abilities and 12 articles compared their prognostic performances ( Table 1 ).

Differences in studied population, measured ions, calculation of variables, and references among articles comparing the two approaches.

ICU: intensive care unit; AGc: corrected anion gap; BE: base excess; SBE: standard base excess; SID: strong ion difference; SIDe: effective strong ion difference; SIG: strong ion gap; SIGc: corrected strong ion gap; Mg: magnesium; Ca: calcium; Alb: albumin; Pi: inorganic phosphate; Lac: lactate; HCO 3 : bicarbonate; AUROC: area under receiver operating characteristic curve; ROC: receiver operating characteristic; N/A: not applicable; OR: odds ratio; CI: confidential interval; SD: standard deviation.

Inconsistent results on the superiority of one approach over the other approach

While 10 studies have shown the potential superiority of the Stewart approach, 6 , 27 – 29 , 40 , 44 , 46 , 48 – 50 four articles failed to show the superiority of the physicochemical approach over the traditional one, 33 , 41 – 43 and three articles even showed greater strength of the traditional method than the modern one. 24 , 45 , 47

Reasons for inconsistent results on diagnostic performance

Our literature search shows a discrepancy over the ability to detect acid–base disturbances on diagnostic performance of the two approaches. There are several possible explanations for the discordance. The first thing to be mentioned is the calculation of each variable in both approaches. Table 1 shows there are many differences in inclusive ions, especially lactate, phosphate, and magnesium ion, of each calculation of AGc and SIG among the studies. In addition, cumulative differences or errors in each variable should be considered. As each mathematical equation contains more measurement, there could be greater variability in the parameters, such as SIDa, SIDe, and SIG in Stewart approach, because the differences are exaggerated via complicated mathematical calculations. 51 As shown by Matousek et al., 12 there should be no difference between the approaches from a mathematical perspective. However, it is true only when the same ions are measured and taken into account and each measurement is accurate. Those differences of each calculation and potential cumulative errors could lead to the discordance about the usefulness as a diagnostic tool between the two approaches.

Another potential reason is technological differences or errors in measuring each variable. Morimatsu et al. 52 showed that chloride measurements, made with point-of-care blood gas and electrolyte analyzers, differed significantly from those made using central laboratory biochemistry analyzers, resulting in different SID values and assessments of the acid–base status. Nguyen et al. 51 compared two central laboratory analyzers for electrolyte measurement and reported that the biochemistry laboratory analyzers have large differences from each other. It should be noted that 12 of 17 articles in our review measured electrolytes using central laboratory analyzers, many of which are currently using diluted blood sample and indirect ion selective electrodes in order to measure the electrolytes, rather than blood gas analyzers ( Table 1 ). Measurements by this method are affected by hypoalbuminemia and could be inaccurate compared with the ones measured by blood gas analyzers. 53 Studies that used indirect ion selective electrodes could lead to wrong calculation and acid–base interpretation, which could make an implausible conclusion. Thus, interpretation of the results in papers comparing these approaches needs attention on the analyzer that each study used. We found a wide variety of machines and technologies used to measure pH, pCO 2 , and electrolytes in those articles, which could be one of the reasons for the inconsistent results on this topic.

Reference value of each parameter is another problem. The dependency on site recommends reference value should be determined in each institution. 46 However, our review showed that while only five studies collected healthy controls for the reference, 33 , 40 , 46 , 49 , 50 other studies used pre-determined numbers, 29 , 41 , 44 , 45 , 48 and the method for reference value selection in those studies was not specified. 6 , 24 , 27 , 28 , 42 , 43 These incongruences of reference value due to arbitrary choice may cause a variety of discordant results. As there is no consensuses on the normal range of each variable, especially in the Stewart approach, we recommend that future researchers collect healthy controls for reference in each research institute.

We also need to pay attention to the differences in the normal result range between the two approaches in these studies, since more than one parameter in each method aims to represent the same concept. For example, Boniatti et al. defined normal SBE as −5 to +5 and normal SIDe as 38–42 mEq/L. Since changes in BE represent changes in SIDe if A TOT is normal, 8 the large difference of normal range (10 vs 4) could mislead the interpretation. This sort of “unfair” comparison might be one reason of the inconsistent results.

Studied populations need another consideration. Several studies showed that patients with renal failure, 54 liver diseases, 55 sepsis and trauma 56 often have accumulations of unmeasured anions. However, Dubin et al. 33 and Ho et al. 47 reported patient demographics in their studies; the percentage of patients with shock, acute renal failure, and hepatic failure was only 13%, 13%, and 4%, respectively, in one study, and liver diseases were only 2% in the other. A study by Cusack et al. 41 included a high proportion of post-elective surgery patients, who generally have low severity of illness and low mortality. Hucker et al. 43 did not provide details about reasons for admission, patients’ illness severity, or the underlying medical conditions of patients in their accident and emergency department. For patients with severe illness, measuring more ions and involving them into variables such as AG and SIG could demonstrate their potential ability to detect unmeasured anions, revealing more detailed acid–base disturbances, no matter which approach is used. For populations with a small number of severe patients, measuring more ions would not be needed for detailed analysis of acid–base disorders. Thus, the combination of variety of the studied populations and the aforementioned differences of calculation in each variable among those studies could be one of the reasons of their inconsistent results.

Reasons for inconsistent results on prognostic performance

Those factors as the potential reasons for inconsistent results on diagnostic performance could also yield a controversy about the prognostic performance of the two approaches. Some authors have investigated the predictive value of the traditional approach and the physicochemical Stewart approach, mainly, AGc versus SIG. One of their questions is “Is there any association between AGc or SIG and outcomes?” or “Can AGc or SIG levels be used as a marker of poor outcomes?” Here the difference of measured and involved ions in each calculation could again mislead the conclusion. Simple comparison of AGc with SIG does not always answer these particular questions. Although both parameters represent unmeasured ions, consideration of lactate for AGc and SIG depends on each individual study. A bulk of evidence has shown that the level of lactate is associated with poor prognosis. 57 , 58 If we would like to simply compare the prognostic abilities of the two approaches, the contribution of lactate should be removed from their equations. Only five of all 17 articles remove the effect of lactate from their calculations of AGc and SIG.

It is not only lactate but also other ions, such as magnesium, that need to be considered when comparing the two methods. The changes in magnesium concentration are usually so small that they may usually be neglected, but this simplification is not applicable if the changes are significant. Theoretically, an increased level of magnesium reduces the AG, increases SID, and does not change SIG. There are no studies so far that compare these approaches for patients with abnormal serum magnesium concentrations. Thus, radical question of the comparison should not be “Is there any association between AGc or SIG and outcomes?” but “Is there any association between unmeasured anions that we does not measure in clinical practice and outcomes?” In order to answer this question directly, we need to exclude the contribution of lactate and other measured ion.

Finally, we cannot forget the effect of fluids used for resuscitation, which lead to iatrogenic acidosis. Hayhoe et al. 59 found 40% of acidosis were attributed to the use of polygeline, which acts as an acid resulting in increased unmeasured circulating anions. Similarly, gelatin-derived colloids have also been found to iatrogenically increase the SIG due to increased unmeasured anions. 59 None of the studies included in our review provided detailed information about the type and volume of administered resuscitation fluids. This iatrogenically fluid-induced increment of SIG and metabolic acidosis in less critical patients is not expected to have many adverse outcomes, and therefore, the prognostic value of these indices of the Stewart approach could be wrongly affected.

Although the traditional approach and the Stewart approach are seen as complementary giving the same information about the acid–base phenomena despite their different concepts, our literature search shows inconsistent results on the comparison between the traditional approach and the physicochemical approach for their diagnostic and prognostic performance. Many studies to date have crucial limitations in comparing these approaches. Those limitations are considered the reasons for the discrepancy in clinical researches.

Declaration of conflicting interests: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding: The author(s) received no financial support for the research, authorship, and/or publication of this article.

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Anion Gap and Stewart's Strong Ion Difference

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In metabolic acidosis, for every molecule of acid produced, a molecule of bicarbonate is replaced by another anion. However, the law of electroneutrality dictates that the sum of positive charges is exactly balanced by the negative charges. The anion gap quantifies this apparent difference between total cation concentration and total anion concentration. Stewart's hypothesis clarifies the role of the lungs, kidneys, liver and gut in acid–base control. According to Stewart's hypothesis, the alkalosis is not caused by loss of hydrogen ions because there is an inexhaustible supply of H+ ions from the dissociation of water. Measurement of chloride concentration is important: if the chloride is low or normal and there is metabolic acidosis, unmeasured ions such as lactic acid and ketoacids may be present in blood and is indicated by the strong ion gap. The classification of acid–base disturbances according to derangements of independent variables provides a better understanding of the primary clinical problem and helps direct treatment.

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Strong ions, weak acids and base excess: a simplified Fencl–Stewart approach to clinical acid–base disorders †

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D. A. Story, H. Morimatsu, R. Bellomo, Strong ions, weak acids and base excess: a simplified Fencl–Stewart approach to clinical acid–base disorders † , BJA: British Journal of Anaesthesia , Volume 92, Issue 1, January 2004, Pages 54–60, https://doi.org/10.1093/bja/aeh018

Background. The Fencl–Stewart approach to acid–base disorders uses five equations of varying complexity to estimate the base excess effects of the important components: the strong ion difference (sodium and chloride), the total weak acid concentration (albumin) and unmeasured ions. Although this approach is straightforward, most people would need a calculator to use the equations. We proposed four simpler equations that require only mental arithmetic and tested the hypothesis that these simpler equations would have good agreement with more complex Fencl–Stewart equations.

Methods. We reduced two complex equations for the sodium–chloride effect on base excess to one simple equation: sodium–chloride effect (meq litre –1 )=[Na + ]–[Cl – ]–38. We simplified the equation of the albumin effect on base excess to an equation with two constants: albumin effect (meq litre –1 )=0.25×(42–[albumin]g litre –1 ). Using 300 blood samples from critically ill patients, we examined the agreement between the more complex Fencl–Stewart equations and our simplified versions with Bland–Altman analyses.

Results. The estimates of the sodium–chloride effect on base excess agreed well, with no bias and limits of agreement of –0.5 to 0.5 meq litre –1 . The albumin effect estimates required log transformation. The simplified estimate was, on average, 90% of the Fencl–Stewart estimate. The limits of agreement for this percentage were 82–98%.

Conclusions. The simplified equations agree well with the previous, more complex equations. Our findings suggest a useful, simple way to use the Fencl–Stewart approach to analyse acid–base disorders in clinical practice.

Br J Anaesth 2004; 92 : 54–60

Accepted for publication: July 18, 2003

A challenge in clinical acid–base assessment is to analyse the size of the acid–base change and the underlying physiological mechanisms. 1   2 Base excess is a single variable used to quantify the metabolic (non‐respiratory) component of a patient’s acid–base status. Several research groups 3 – 5 have combined the base excess approach with the Stewart approach to acid–base physiology. 6 To combine these approaches, 5 these groups examined the base excess effects of two of Stewart’s independent variables: the strong ion difference and the total weak acid concentration. Balasubramanyan and colleagues 5 called this approach to base excess the Fencl–Stewart approach.

Gilfix and colleagues 4 used the work of Figge and colleagues 7 and Fencl’s unpublished work 8 to derive five equations to estimate the base excess effects of the strong ion difference and the total weak acid concentration. In plasma, sodium and chloride are the principal components of the extracellular strong ion difference, 6 and albumin is the principal extracellular weak acid. 9 While this approach is reasonably simple, most people would need a calculator to use the five equations.

We believe that these equations, used to estimate the sodium–chloride effect on base excess, can be simplified. Balasubramanyan and colleagues 5 simplified the Fencl–Stewart albumin equation. Work by Figge’s group 9 has further modified the Fencl–Stewart equation for the base excess effect of albumin. 8 This equation can also be simplified in the same way that Balasubramanyan simplified the older equation. 5 We proposed four simpler equations that require only simple mental arithmetic for clinical use.

We tested the hypothesis that the simplified estimates of the base excess effects of the plasma sodium–chloride concentration and the plasma albumin concentration have sufficiently strong agreement with the Fencl–Stewart estimates 3   4 to be used clinically. We used blood samples from critically ill adults to test this hypothesis.

Data were collected from intensive care unit records at the Austin and Repatriation Medical Centre, a tertiary referral hospital affiliated with the University of Melbourne. All samples were taken from arterial cannulae in patients requiring intensive care. No additional sampling was required. The Austin and Repatriation Medical Centre Human Research Ethics Committee waived the need for informed consent.

Arterial blood samples were collected in heparinized blood‐gas syringes (Rapidlyte; Chiron Diagnostics, East Walpole, MA, USA) and analysed in the intensive care unit blood‐gas analyser (Ciba Corning 865; Ciba Corning Diagnostics, Medfield, MA, USA). The analyser made measurements at 37°C. Nursing staff from the intensive care unit who had been taught to use the machine by support staff performed the analysis. Samples were not stored on ice. We collected data on the pH, partial pressure of carbon dioxide and the standard base excess.

For each data set, a further sample was drawn at the same time from the same arterial cannula using a vacuum technique with lithium heparin tubes or clot‐activating tubes (Vacuette; Greiner Labortechnik, Kremsmunster, Austria). These samples were sent to the hospital core laboratory in the Division of Laboratory Medicine. Plasma and serum underwent multicomponent analysis (Hitachi 747; Roche Diagnostics, Sydney, Australia). Scientific staff from the hospital clinical chemistry department analysed the samples. Samples were not stored on ice. We collected data on the plasma or serum concentrations of sodium, chloride and albumin.

Fencl divided the effect of strong ion difference on base excess into sodium and chloride effects. This group calculated the base excess effects of changes in free water on the sodium concentration and changes in the chloride concentration: 4   5   8

sodium effect (meq litre –1 )=0.3×([Na + ]–140)(1)

chloride effect (meq litre –1 )=102–([Cl – ]×140/[Na + ]).(2)

Sodium and chloride are the principal contributors to the strong ion difference. 6 The sum of the sodium and chloride effects will give the Fencl–Stewart estimate of the strong ion difference effect on base excess:

sodium–chloride effect (meq litre –1 )=0.3×([Na + ]–140)+102–([Cl – ]×140/[Na + ]).(3)

Separately estimating the base excess effects of changes in free water and changes in chloride provides useful information. These separate effects, however, do not need to be quantified initially to determine the effect of the sodium–chloride component of the effect of strong ion difference on base excess. Changes in the difference in sodium and chloride can be used to calculate directly the major changes in the strong ion difference. As the strong ion difference is decreased the blood becomes more acidic. 6

We proposed that the calculation of the strong ion difference effect on base excess could be simplified. From the reference range in our laboratory, the median value for sodium is 140 mmol litre –1 and that for chloride is 102 mmol litre –1 . Therefore the median difference is 38 mmol litre –1 . The measured sodium–chloride difference minus 38 mmol litre –1 will be an estimate of the change in the strong ion difference. For sodium and chloride, 1 millimole equals 1 milliequivalent.

A change in the sodium–chloride component of the strong ion difference will change the base excess directly. Therefore our simplified version of the equation for the sodium–chloride effect on base excess is:

sodium–chloride effect (meq litre –1 )=[Na + ]–[Cl – ]–38.(4)

Albumin is the principal contributor to the plasma total weak acid concentration. The effect of albumin on the base excess is due to the anionic effect of albumin. Figge and colleagues 9 developed a pH‐dependent formula for the anionic effect of albumin:

albumin anionic effect (meq litre –1 )=(0.123×pH–0.631)×albumin (g litre –1 ).(5)

Changes in the concentration of albumin will cause changes in the anionic effect of albumin. Changes in the anionic effect of albumin will change the base excess. As the albumin concentration is decreased the blood becomes more alkaline. We calculated the Fencl–Stewart estimates for the base excess effects of albumin. We used the most recent estimates of the effects of albumin ionization: 8

albumin effect (meq litre –1 )=(0.123×pH–0.631)×[42–albumin (g litre –1 )].(6)

We simplified this equation by using a single pH of 7.40:

albumin effect (meq litre –1 )=0.28×[42–albumin (g litre –1 )].(7)

To facilitate calculation at the bedside we further simplified the equation by using the constant of 0.25. This allows the simple mathematics of dividing the difference in albumin concentrations by 4. Therefore the simplified equation became:

albumin effect (meq litre –1 )=0.25×[42–albumin (g litre –1 )].(8)

Statistical analysis

Data were collected from patient charts and the hospital computer system. Data were stored on a computer spreadsheet (Excel, Microsoft, Seattle, WA, USA). All statistical calculations were done with Statview software (Abacus Concepts, Berkeley, CA, USA).

We used the limits of agreement method of Bland and Altman 10   11 to determine the agreement between the Fencl–Stewart and simplified estimates of the albumin and strong ion difference effects on base excess. We proposed that a bias of ±1 meq litre –1 and limits of agreement of bias ±2 meq litre –1 were acceptable for clinical use of the simplified equations. That is, the greatest difference between two estimates would be 3 meq litre –1 . Data were analysed for the overall group and three subgroups: an acidaemic group (pH <7.35), a reference range group (pH 7.35–7.45) and an alkalaemic group (pH >7.45). We used these groups to examine the possibility that different acid–base states may affect the agreement.

Where the difference between the estimates varied with the average of the two estimates (heterodasticity), the relationship was analysed with correlation statistics. If the correlation were statistically significant, at a P value of <0.05, the data were log‐transformed. The limits of agreement statistics were reported as proportions because a log minus a log is the ratio of the antilogs. 10

We analysed the relative risk of death where the standard base excess, sodium–chloride effect or unmeasured ion effect was less than –5 meq litre –1 . The effect of albumin was almost always alkalinizing; therefore we calculated the relative risk of death of an albumin effect on base excess greater than 5 meq litre –1 . We assumed the increase in mortality risk was statistically significant if the 95% confidence interval for the risk ratio did not include 1. We used Confidence Interval Analysis software (BMJ Books).

Three hundred pairs of data were collected from 300 adult patients. The median age of the patients was 65 yr (range 12–94 yr). The median Simplified Acute Physiology Score (SAPS II) score 12 was 17 (range 2–40). The median risk of death calculated from the SAPS II was 26% (range 0–96%).

The agreement between the Fencl–Stewart and simplified estimates was analysed for the entire set of 300 samples (Figs 1 and 2 ) and for the three subgroups: pH <7.35 (acidaemic), pH 7.35–7.45 (reference range) and pH >7.45 (alkalaemic) (Tables 1 , 2 and 3 ).

There was strong agreement between the Fencl–Stewart and simplified estimates of the sodium–chloride effect. There was no bias and the limits of agreement were from –0.5 to 0.5 meq litre –1 (Fig. 1 ). There was an apparent pattern in the data points (Fig. 1 ); however, the cause and importance of this pattern are unclear. The agreement was similar in the three subgroups classified according to pH (Tables 2 and 3 ).

The agreement between the Fencl–Stewart and the simplified estimates of the albumin effect varied with the average effect. This correlation had an R 2 of 0.47 and a P value of <0.001. The data were log‐transformed and analysed again. The log transformation removed the correlation between the difference of the estimates and the average value (Fig. 2 ). After log transformation there was good agreement between the Fencl and simplified estimates of the albumin effect. The simplified estimate was, on average, 90% of the Fencl estimate. The limits of agreement for this percentage were 82–98%. The results were similar in the three pH subgroups, with the best agreement in the acidaemic group (Tables 2 and 3 ).

The relative risk of death was greater when either the standard base excess or the unmeasured ion effect was less than –5 meq litre –1 . A sodium–chloride effect on base excess less than –5 meq litre –1 or an albumin effect greater than 5 meq litre –1 was not associated with an increased risk of death (Table 4 ).

We studied 300 blood samples from 300 critically ill adults. When analysing the acid–base status of these samples we used sodium–chloride as the principal component of the plasma strong ion difference 6 and albumin as the principal component of the plasma total weak acid concentration. 9 We found that the simplified equations to estimate the base excess effects of plasma sodium–chloride concentration and plasma albumin concentration agreed well with more complex equations used in other studies. 4   5   8 Furthermore, we found good agreement in the three subgroups classified according to pH.

Balasubramanyan and colleagues 5 simplified an earlier version of the equation for the albumin effect. 4 These researchers, however, did not examine the agreement of the simplified equation with the more complex Fencl–Stewart version. 4 One strength of our study is that we used the most recent versions of the Fencl equations. 8 Furthermore, we used a large number of samples from different patients with a wide range of acid–base disorders, including some with increased plasma lactate (another strong ion) 5 or increased plasma phosphate (another important weak acid). 9 Another strength is that we avoided overestimating the strength of agreement attributable to mathematical linking. 13 We avoided this problem by using the limits of agreement approach of Bland and Altman. 10   11

In unpublished work, Fencl 8 proposed a method of combining base excess and the Stewart approach 6 to acid–base physiology and disease. This approach was designed to facilitate clinical application of the Stewart approach. We suggest the following simplified version of the Fencl method. 4   5

Four variables are determined (standard base excess and the base excess effects of sodium–chloride, albumin and unmeasured ions) using the following four equations:

standard base excess (mmol litre –1 =meq litre –1 ) from a blood gas machine;

sodium–chloride effect (meq litre –1 )=[Na + ]–[Cl – ]–38;(4)

albumin effect (meq litre –1 )=0.25×[42–albumin (g litre –1 )];(8)

unmeasured ion effect (meq litre –1 )=standard baseexcess–sodium–chloride effect–albumin effect.(9)

These four variables, with the partial pressure of carbon dioxide, allow physicians to examine the base excess effects of the principal components of Stewart’s independent factors: carbon dioxide, strong ion difference (sodium–chloride) and total weak acid concentration (albumin). The strong ion difference effect can be further analysed with the separate Fencl–Stewart equations for sodium and chloride. 4 The unmeasured ions may be strong ions, such as sulphate and acetate, 14 or weak acids, such as phosphate and polygeline. 15

These equations require four input variables: the base excess and the plasma concentrations of sodium, chloride and albumin. By using the plasma sodium and chloride concentrations and the simplified sodium–chloride equation we can estimate the base excess effects of electrolyte changes from i.v. fluid therapies. 16   17 For example, Scheingraber and colleagues 16 studied acid–base changes during major gynaecological surgery. Patients received 0.9% saline or lactated Ringer’s solution. The saline group had a greater metabolic acidosis, as shown by a more negative base excess. One cause of this acidosis was a decreased strong ion difference. The Scheingraber group showed that these changes in base excess and strong ion difference occurred in parallel but they did not quantify the effect. The method described in our study allows easy quantification of the effects of changes in plasma sodium and chloride (strong ion difference) on base excess (Table 5 ).

Analysis of the fourth variable, plasma albumin concentration, is useful in the intensive care unit and in the perioperative setting. In addition to the acidifying effects of saline, Scheingraber and colleagues also found an intraoperative decrease in plasma albumin concentration in both their groups. 16 They speculated that this decrease in albumin would affect the base excess, but did not quantify the effect. Decreased plasma albumin leads to a decreased total weak acid concentration that produces a metabolic alkalosis. 3 Using a different method, Figge and colleagues 18 developed the same constant (0.25) to quantify the effect of changes in plasma albumin on the anion gap, as we did for the effects on base excess. Our work supports this finding because the physiology is the same: changes in the anionic effect of albumin will alter both the base excess and the anion gap. 19 Decreased plasma albumin concentration is common in critically ill patients. 20 The method described in our study allows easy quantification of the effects of changes in plasma albumin (total weak acid concentration) on base excess (Table 5 ).

Using an approach similar to ours, Balasubramanyan’s group 5 studied critically ill children. In a subgroup of 66 children, they found that a base excess effect of unmeasured ions more negative than –5 meq litre –1 was an important predictor of mortality. Our approach simplifies estimation of the unmeasured ion effect on base excess by simplifying the calculations for the effects of the strong ion difference and the total weak acid concentration. Among 300 patients, we found that an unmeasured ion effect on base excess less than –5 meq litre –1 increased the risk of death by 50%. The risk of death with a standard base excess less than –5 meq litre –1 was increased by 100%. There was, however, considerable overlap in the 95% confidence intervals for the relative risk of death for the unmeasured ion effect and the standard base excess. Furthermore, similar changes in the base excess effects of sodium–chloride and albumin did not increase the relative risk of death. These findings suggest that it is the unmeasured ion component of the base excess that is the important clinical marker for mortality.

We have reduced five Fencl–Stewart equations to four simpler equations. We have maintained good agreement with the previous, more complex equations. These simple equations may allow easy, direct application of Stewart’s independent factors to clinical work both inside and outside the operating room. We propose these equations as bedside clinical tools rather than as tools for detailed physiological research. Future studies should examine the importance of each of the base excess effects on patient outcome.

Funding was provided by the Research Fund, Department of Anaesthesia, Austin and the Repatriation Medical Centre, Heidelberg, Victoria, Australia.

Fig 1 Bland–Altman plot, for 300 samples, of the differences in sodium–chloride effect on base excess between the Fencl–Stewart (FS) and simplified methods ( y axis), and the average of the two methods: (Fencl–Stewart+simplified)/2. The full lines are the limits of agreement and the dashed line is the bias. The y axis represents our proposed upper limits of agreement of bias ±2 meq litre –1 .

Fig 2 Bland–Altman plot, for 300 samples after log transformation, of the differences in estimates of the albumin effect on base excess between the Fencl–Stewart (FS) and simplified methods ( y axis), and the average of the two methods: (Fencl–Stewart+simplified)/2. The full lines are the limits of agreement and the dashed line is the bias.

Plasma acid–base variables for three subgroups. Median (range)

Subgroup analysis for sodium–chloride and albumin effects on base excess. Median (range)

Limits of agreement between the Fencl–Stewart and simplified estimates for three subgroups

Relative risk of death. *Compared with patients with a base excess or base excess effect equal to or greater than –5 meq litre –1 ; **compared with patients with an albumin base excess effect of equal to or less than 5 meq litre –1

Clinical example of the simplified Fencl–Stewart approach. An acid–base assessment of a patient after anaesthetic induction and after 2 h of major gynaecological surgery. Normal saline was used as the intraoperative fluid. Data are the average values from Scheingrabber et al . 16 In this patient, after 2 h of surgery most of the metabolic acidosis can be explained by a decrease in the strong ion difference secondary to an increase in plasma chloride. This is partly offset by a decrease in the total weak acid concentration (albumin). Unmeasured ions are unimportant in this acidaemia. These changes follow the infusion of about 6 litres of 0.9% sodium chloride. *Sodium–chloride effect on base excess (meq litre –1 )=[Na + ]–[Cl – ]–38; **albumin effect on base excess (meq litre –1 )=0.25×(42–[albumin] g litre –1 ); ***unmeasured ion effect (meq litre –1 )=standard base excess–(sodium–chloride effect)–albumin effect

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Author notes

1Department of Anaesthesia, and 2Department of Intensive Care, Austin and Repatriation Medical Centre, Heidelberg, Victoria 3084, Australia

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Utility of Stewart's strong ion difference as a predictor of major injury after trauma in the ED

Affiliation.

• 1 Department of Emergency Medicine, SUNY Downstate and Kings County Hospital, Brooklyn, NY 11203, USA.
• PMID: 17920981
• DOI: 10.1016/j.ajem.2007.02.031

Introduction: Base deficit (BD) is a validated surrogate for lactate in injured patients and correlates with trauma severity. Stewart proposed a more comprehensive measure of acidosis based on the strong ion difference (SID) (SID = Na + K + Mg + Ca - CL - lactate [mEq/L]). We compared operating characteristics of BD, anion gap (AG), and SID in identifying major injury in emergency department (ED) trauma patients.

Methods: This was a retrospective review. Major injury was defined as Injury Severity Score > or =15, blood transfusions, or significant drop in hematocrit. Receiver operating characteristic curves compared BD, AG, and SID in differentiating major from minor injuries.

Results: The study included 1181 patients. Both BD and SID were significantly (P = .0001) different after major vs minor injury (mean difference, 3.40; 95% confidence interval, 2.70-4.00 and mean difference, 2.50; 95% confidence interval, 1.90-3.10, respectively). Receiver operating characteristic curves were minimally different from one another (P = .0035).

Conclusion: Stewart's SID can identify major injury in the ED.

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Strong ions, weak acids and base excess: A simplified Fencl-Stewart approach to clinical acid-base disorders

Research output : Contribution to journal › Article › Research › peer-review

Background. The Fencl-Stewart approach to acid-base disorders uses five equations of varying complexity to estimate the base excess effects of the important components: the strong ion difference (sodium and chloride), the total weak acid concentration (albumin) and unmeasured ions. Although this approach is straightforward, most people would need a calculator to use the equations. We proposed four simpler equations that require only mental arithmetic and tested the hypothesis that these simpler equations would have good agreement with more complex Fencl-Stewart equations. Methods. We reduced two complex equations for the sodium-chloride effect on base excess to one simple equation: sodium-chloride effect (meq litre -1 )=[Na + ]-[CI]-38. We simplified the equation of the albumin effect on base excess to an equation with two constants: albumin effect (meq litre -- )=0.25×(42-[albumin]g litre -1 ). Using 300 blood samples from critically ill patients, we examined the agreement between the more complex Fencl-Stewart equations and our simplified versions with Bland-Altman analyses. Results. The estimates of the sodium-chloride effect on base excess agreed well, with no bias and limits of agreement of -0.5 to 0.5 meq litre -1 . The albumin effect estimates required log transformation. The simplified estimate was, on average, 90% of the Fencl-Stewart estimate. The limits of agreement for this percentage were 82-98%. Conclusions. The simplified equations agree well with the previous, more complex equations. Our findings suggest a useful, simple way to use the Fencl-Stewart approach to analyse acid-base disorders in clinical practice.

• Chemistry, analytical
• Complications, acid-base disorders
• Intensive care

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• 10.1093/bja/aeh018

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• Link to publication in Scopus

T1 - Strong ions, weak acids and base excess

T2 - A simplified Fencl-Stewart approach to clinical acid-base disorders

AU - Story, David A.

AU - Morimatsu, H.

AU - Bellomo, R.

PY - 2004/1/1

Y1 - 2004/1/1

N2 - Background. The Fencl-Stewart approach to acid-base disorders uses five equations of varying complexity to estimate the base excess effects of the important components: the strong ion difference (sodium and chloride), the total weak acid concentration (albumin) and unmeasured ions. Although this approach is straightforward, most people would need a calculator to use the equations. We proposed four simpler equations that require only mental arithmetic and tested the hypothesis that these simpler equations would have good agreement with more complex Fencl-Stewart equations. Methods. We reduced two complex equations for the sodium-chloride effect on base excess to one simple equation: sodium-chloride effect (meq litre-1)=[Na+]-[CI]-38. We simplified the equation of the albumin effect on base excess to an equation with two constants: albumin effect (meq litre--)=0.25×(42-[albumin]g litre-1). Using 300 blood samples from critically ill patients, we examined the agreement between the more complex Fencl-Stewart equations and our simplified versions with Bland-Altman analyses. Results. The estimates of the sodium-chloride effect on base excess agreed well, with no bias and limits of agreement of -0.5 to 0.5 meq litre-1. The albumin effect estimates required log transformation. The simplified estimate was, on average, 90% of the Fencl-Stewart estimate. The limits of agreement for this percentage were 82-98%. Conclusions. The simplified equations agree well with the previous, more complex equations. Our findings suggest a useful, simple way to use the Fencl-Stewart approach to analyse acid-base disorders in clinical practice.

AB - Background. The Fencl-Stewart approach to acid-base disorders uses five equations of varying complexity to estimate the base excess effects of the important components: the strong ion difference (sodium and chloride), the total weak acid concentration (albumin) and unmeasured ions. Although this approach is straightforward, most people would need a calculator to use the equations. We proposed four simpler equations that require only mental arithmetic and tested the hypothesis that these simpler equations would have good agreement with more complex Fencl-Stewart equations. Methods. We reduced two complex equations for the sodium-chloride effect on base excess to one simple equation: sodium-chloride effect (meq litre-1)=[Na+]-[CI]-38. We simplified the equation of the albumin effect on base excess to an equation with two constants: albumin effect (meq litre--)=0.25×(42-[albumin]g litre-1). Using 300 blood samples from critically ill patients, we examined the agreement between the more complex Fencl-Stewart equations and our simplified versions with Bland-Altman analyses. Results. The estimates of the sodium-chloride effect on base excess agreed well, with no bias and limits of agreement of -0.5 to 0.5 meq litre-1. The albumin effect estimates required log transformation. The simplified estimate was, on average, 90% of the Fencl-Stewart estimate. The limits of agreement for this percentage were 82-98%. Conclusions. The simplified equations agree well with the previous, more complex equations. Our findings suggest a useful, simple way to use the Fencl-Stewart approach to analyse acid-base disorders in clinical practice.

KW - Chemistry, analytical

KW - Complications, acid-base disorders

KW - Intensive care

UR - http://www.scopus.com/inward/record.url?scp=0346336778&partnerID=8YFLogxK

U2 - 10.1093/bja/aeh018

DO - 10.1093/bja/aeh018

M3 - Article

C2 - 14665553

AN - SCOPUS:0346336778

SN - 0007-0912

JO - British Journal of Anaesthesia

JF - British Journal of Anaesthesia