Bench-to-bedside review: Fundamental principles of acid-base physiology

Complex acid–base disorders arise frequently in critically ill patients, especially in those with multiorgan failure. In order to diagnose and treat these disorders better, some intensivists have abandoned traditional theories in favor of revisionist models of acid–base balance. With claimed superiority over the traditional approach, the new methods have rekindled debate over the fundmental principles of acid–base physiology. In order to shed light on this controversy, we review the derivation and application of new models of acid–base balance.


Introduction: Master equations
All modern theories of acid-base balance in plasma are predicated upon thermodynamic equilibrium equations. In an equilibrium theory, one enumerates some property of a system (such as electrical charge, proton number, or proton acceptor sites) and then distributes that property among the various species of the system according to the energetics of that particular system. For example, human plasma consists of fully dissociated ions ('strong ions' such as Na + , K + , Cland lactate), partially dissociated 'weak' acids (such as albumin and phosphate), and volatile buffers (carbonate species). C B , the total concentration of proton acceptor sites in solution, is given by Where C is the total concentration of carbonate species proton acceptor sites (in mmol/l), C i is the concentration of noncarbonate buffer species i (in mmol/l), ei is the average number of proton acceptor sites per molecule of species i, and D is Ricci's difference function (D = [H + ] -[OH -]). Equation 1 may be regarded as a master equation from which all other acid-base formulae may be derived [1].
Assuming that [CO 3 2-] is small, Eqn 1 may be re-expressed: Similarly, the distribution of electrical charge may be expressed as follows: Where SID + is the 'strong ion difference' and Z i is the average charge per molecule of species i.
The solution(s) to these master equations require rigorous mathematical modeling of complex protein structures. Traditionally, the mathematical complexity of master Eqn 2 has been avoided by setting ∆C i = 0, so that ∆C B = ∆[HCO 3 -]. The study of acid-base balance now becomes appreciably easier, simplifying essentially to the study of volatile buffer equilibria.

Stewart equations
Stewart, a Canadian physiologist, held that this simplification is not only unnecessary but also potentially misleading [2,3]. In 1981, he proposed a novel theory of acid-base balance based principally on an explicit restatement of master In traditional acid-base physiology, [A TOT ] is set equal to 0 and Eqn 11 is reduced to the well-known Henderson-Hasselbalch equation [5,6]. If this simplification were valid, then the plot of pH versus log PCO 2 ('the buffer curve') would be linear, with an intercept equal to log [HCO 3 -]/K′ 1 × SCO 2 [7,8]. In fact, experimental data cannot be fitted to a linear buffer curve [4]. As indicated by Eqn 11, the plot of pH versus log PCO 2 is displaced by changes in protein concentration or the addition of Na + or Cl -, and becomes nonlinear in markedly acid plasma (Fig. 1). These observations suggest that the Henderson-Hasselbalch equation may be viewed as a limiting case of the more general Stewart equation. When [A TOT ] varies, the simplifications of the traditional acid-base model may be unwarranted [9].

The Stewart variables
The Stewart equation (Eqn 10) is a fourth-order polynomial equation that relates [H + ] to three independent variables ([SID + ], [A TOT ] and PCO 2 ) and five rate constants (K a , K′ w , K′ 1 , K 3 and SCO 2 ), which in turn depend on temperature and ion activities (Fig. 2) [2,3].

Strong ion difference
The first of these three variables, [SID + ], can best be appreciated by referring to a 'Gamblegram' (Fig. 3 Where [A -] is the concentration of dissociated weak noncarbonic acids, principally albumin and phosphate.

Strong ion gap
The strong ion gap (SIG), the difference between [SID + ] a and [SID + ] e , may be taken as an estimate of unmeasured ions: Unlike the well-known anion gap (AG = [Na + ] [10], the SIG is normally equal to 0. SIG may be a better indicator of unmeasured anions than the AG. In plasma with low serum albumin, the SIG may be high (reflecting unmeasured anions), even with a completely normal AG. In this physiologic state, the alkalinizing effect of hypoalbuminemia may mask the presence of unmeasured anions [11][12][13][14][15][16][17][18]. Although thermodynamic equilibrium equations are independent of mechanism, Stewart asserted that his three independent parameters ([SID + ], [A TOT ] and PCO 2 ) determine the only path by which changes in pH may arise (Fig. 4). Furthermore, he claimed that [SID + ], [A TOT ] and PCO 2 are true biologic variables that are regulated physiologically through the processes of transepithelial transport, ventilation, and metabolism ( Fig. 5).

Base excess
In contrast to [SID + ], the 'traditional' parameter base excess (BE; defined as the number of milliequivalents of acid or base that are needed to titrate 1 l blood to pH 7.40 at 37°C while the PCO 2 is held constant at 40 mmHg) provides no further insight into the underlying mechanism of acid-base disturbances [20,21]. Although BE is equal to ∆SID + when nonvolatile buffers are held constant, BE is not equal to ∆SID + when nonvolatile acids vary. BE read from a standard nomogram is then not only physiologically unrevealing but also numerically inaccurate (Fig. 2) [1,9].

The Stewart theory: summary
The relative importance of each of the Stewart variables in the overall regulation of pH can be appreciated by referring to a 'spider plot' (Fig. 6). pH varies markedly with small changes in PCO 2 and [SID + ]. However, pH is less affected by perturbations in [A TOT ] and the various rate constants [19].  Reproduced with permission from Corey [9].

Figure 3
Gamblegram -a graphical representation of the concentration of plasma cations (mainly Na + and K + ) and plasma anions (mainly Cl -, HCO 3 and A -). SIG, strong ion gap (see text).
In summary, in exchange for mathematical complexity the Stewart theory offers an explanation for anomalies in the buffer curve, BE, and AG.

The Figge-Fencl equations
Based on the conservation of mass rather than conservation of charge, Stewart SID + , strong ion difference.

Figure 6
Spider plot of the dependence of plasma pH on changes in the three independent variables ( [19].
When plasma β is low, the ∆pH is higher for any given BE than when β is normal.
The β may be regarded as a central parameter that relates the various components of the Henderson-Hasselbalch, Stewart and Figge-Fencl models together (Fig. 7). When noncarbonate buffers are held constant:

The Wooten equations
Acid-base disorders are usually analyzed in plasma. However, it has long been recognized that the addition of hemoglobin [Hgb], an intracellular buffer, to plasma causes a shift in the buffer curve (Fig. 8) [26]. Therefore, BE is often corrected for [Hgb] using a standard nomogram [20,21,27].
Wooten [28] With C alb and C Hgb expressed in g/dl and C phos in mg/dl.
In summary, the Wooten model brings Stewart theory to the analysis of whole blood and quantitatively to the level of titrated BE.

Application of new models of acid-base balance
In order to facilitate the implementation of the Stewart approach at the bedside, Watson [29] has developed a computer program (AcidBasics II) with a graphical user interface (Fig. 9). One may choose to use the original Stewart or the Figge-Fencl model, vary any of the rate constants, or adjust the temperature. Following the input of the independent variables, the program automatically displays all of the independent variables, including pH, [HCO 3 -] and [A -]. In addition, the program displays SIG, BE, and a 'Gamblegram' (for an example, see Fig. 3).
One may classify acid-based disorders according to Stewart's three independent variables. Instead of four main acid-base disorders (metabolic acidosis, metabolic alkalosis, respiratory acidosis, and respiratory alkalosis), there are six disorders based on consideration of PCO 2 , [SID + ], and [A TOT ] ( Table 1). Disease processes that may be diagnosed using the Stewart approach are listed in Table 2.  Table 3.

Example
Consider a hypothetical 'case 1' with pH = 7.30, PCO 2 = 30.0 torr, [HCO 3 -] = 14.25 mmol/l, Na 2+ = 140 mEq/l, K + = 4 mEq/l, Cl -= 115 mEq/l, and BE = -10 mEq/l. The 'traditional' interpretation based on BE and AG is a 'normal anion gap metabolic acidosis' with respiratory compensation. The Stewart interpretation based on [SID + ] e and SIG is 'low [SID + ] e /normal SIG' metabolic acidosis and respiratory compensation. The Stewart approach 'corrects' the BE read from a nomogram for the 0.6 mEq/l acid load 'absorbed' by the noncarbonate buffers. In both models, the differential diagnosis for the acidosis includes renal tubular acidosis, diarrhea losses, pancreatic fluid losses, anion exchange resins, and total parenteral nutrition (Tables 2 and 3). Now consider a hypothetical 'case 2' with the same arterial blood gas and chemistries but with [albumin] = 1.5 g/dl. The Available online http://ccforum.com/content/9/2/184

Figure 8
The effect of hemoglobin (Hb) on the 'buffer curve': (left) in vitro and (right) in vivo. PCO 2 , partial CO 2 tension. Reproduced with permission from Davenport [26]. 'traditional' interpretation and differential diagnosis of the disorder remains unchanged from 'case 1' because BE and AG have not changed. However, the Stewart interpretation is low [SID + ] e /high SIG metabolic acidosis and respiratory compensation. Because of the low β, the ∆pH is greater for any given BE than in 'case 1'. The Stewart approach corrects BE read from a nomogram for the 0.2 mEq/l acid load 'absorbed' by the noncarbonate buffers. The differential diagnosis for the acidosis includes ketoacidosis, lactic acidosis, salicylate intoxication, formate intoxication, and methanol ingestion (Tables 2 and 3).

Summary
All modern theories of acid-base balance are based on physiochemical principles. As thermodynamic state equations are independent of path, any convenient set of parameters (not only the one[s] used by nature) may be used to describe a physiochemical system. The traditional model of acid-base balance in plasma is based on the distribution of proton acceptor sites (Eqn 1), whereas the Stewart model is based on the distribution of electrical charge (Eqn 2). Although sophisticated and mathematically equivalent models may be derived from either set of parameters, proponents of the 'traditional' or 'proton acceptor site' approach have advocated simple formulae whereas proponents of the Stewart 'electrical charge' method have emphasized mathematical rigor. and PCO 2 . These variables may define a biologic system and so may be used to explain any acid-base derangement in that system. In return for mathematical complexity, the Stewart model 'corrects' the 'traditional' computations of buffer curve, BE, and AG for nonvolative buffer concentration. This may be important in critically ill, hypoproteinuric patients.

Conclusion
Critics note that nonvolatile buffers contribute relatively little to BE and that a 'corrected' AG (providing similar information to the SIG) may be calculated without reference to Stewart theory by adding about 2.5 × (4.4 -[albumin]) to the AG.
To counter these and other criticisms, future studies need to demonstrate the following: the validity of Stewart's claim that his unorthodox parameters are the sole determinants of pH in plasma; the prognostic significance of the Stewart variables; the superiority of the Stewart parameters for patient management; and the concordance of the Stewart equations  AcidBasics II. With permission from Dr Watson. with experimental data obtained from ion transporting epithelia.
In the future, the Stewart model may be improved through a better description of the electrostatic interaction of ions and polyelectroles (Poisson-Boltzman interactions). Such interactions are likely to have an important effect on the electrical charges of the nonvolatile buffers. For example, a detailed analysis of the pH-dependent interaction of albumin with lipids, hormones, drugs, and calcium may permit further refinement of the Figge-Fencl equation [25].
Perhaps most importantly, the Stewart theory has reawakened interest in quantitative acid-base chemistry and has prompted a return to first principles of acid-base physiology.

Competing interests
The author(s) declare that they have no competing interests.