INTRODUCTION

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CHARACTERIZATION OF ACID-BASE BALANCE in the body is of central importance in medicine, since it may provide valuable information about the status of a patient or provide clues about the underlying pathophysiology of a patient's disease process (16). Mathematical models of physiological acid-base balance help the clinician conceptualize the processes involved, in order to better diagnose and treat the patient.

Several models, algorithms, and methods have been proposed to evaluate clinical acid-base status. These have classically been divided into those that are based primarily on measured bicarbonate concentration ([HCO₃]) (16, 17) vs. those that use base excess (BE) (24) to evaluate nonrespiratory acid-base disorders. In the former approach, the anion gap (AG) and the change in anion gap (AG) are also calculated to gain further insight into the origins of a metabolic acid-base disturbance (5, 31).

More recently, Stewart and others (6-8, 13, 29) have popularized the use of the strong-ion difference (SID) method to describe acid-base. This is the same idea originally set forth by Singer and Hastings under the name "buffer base" (27). The SID is the sum of positive-ion concentrations minus the sum of negative-ion concentrations for those ions that do not participate in proton transfer reactions. The Stewart approach (29) is a very general physicochemical method that uses charge and mass balance to deduce an expression for proton concentration. Similarly, the BE method is another very general physicochemical approach, but one that uses proton balance to calculate changes in proton concentration by using the Van Slyke equation (25).

In the following sections, a general formalism for calculating total titratable acid and base is given, and it is shown that a linear approximation to the expression for total titratable base (C_B) yields the Van Slyke equation. Next, a similar equation is developed for SID, and it is shown that a linear approximation to the complete equation for SID has the same form as the Van Slyke equation. Mathematical relationships between the various parameters commonly used to assess acid-base status are then derived, yielding insight into the interrelationships between the different methods for assessing physiological acid-base balance.

	GENERAL THEORY

Glossary

AG'

Anion gap corrected for respiratory effects

AG

Change in anion gap (delta gap)

_j(i)

Fraction of species i with j protons bound

BE

Base excess

Buffer value

b_i

Constant that together with C_i determines C

C

Constant in linear approximation to complete equations

C

Concentration of proton acceptor sites of the carbonate buffers

C_B

Total titratable base

C_B

Change in C_B, including noncarbonate buffer base

C'_B

Change in C_B referenced to new buffer ion concentration C'_i

C_H

Total titratable acid

C_i

Analytical concentration of buffer ion species i

C'_i

New (abnormal) analytical concentration of buffer ion

D

[H⁺]  [OH]

_i

Average number of proton acceptor sites per molecule of species i

K_l(i)

Conditional molar equilibrium constant for the lth dissociation step of species i

_i

Average number of protons per molecule of species i

_max(i)

Maximum number of protons per molecule for species i

S

Equilibrium constant between dissolved CO₂ and CO₂ in the gas phase

SID

Strong-ion difference

SID_m

Strong-ion difference for measured ions

SID_u

Strong-ion difference for unmeasured ions

VSSB

Van Slyke standard bicarbonate

VSSB'

Van Slyke standard bicarbonate referenced to C'_i

_i

Average charge per molecule of species i

_max(i)

Maximum charge on species i

Minimum charge on species i

z_p

Charge on unmeasured positive ion p

z_q

Charge on unmeasured negative ion q

Acid-base equilibrium in aqueous solution has been exhaustively treated in the classic works of Ricci (18), Butler (2), and Kolthoff and Elving (14). Most recently, Guenther (10) has extended and simplified their work to give a master equation for solving complex acid-base problems

(1)

where C_H is total titratable acid and D is Ricci's difference function

(2)

Unless otherwise specified, parameters are expressed in terms of concentrations (indicated by brackets) rather than activities. _i is the average number of protons per molecule of species i. C_i is the analytical concentration of species i, the sum of all concentrations of subspecies, regardless of protonation state

(3)

where _max(i) is the maximum value of for species i and j(i) is the proton ligand number for species i.

Thus Eq. 1 states that if one knows the total concentrations of all of the various species and their ligand numbers, the C_H can be calculated. The right side of Eq. 1 represents the bound titratable acid, whereas D is the net free titratable acid.

The _i can be calculated from the fraction of species _j(i) as

(4)

The _j(i) are calculated via

(5)

The _j(i) can in turn be recast as functions of [H⁺] and equilibrium constants K (see for example Ref. 10)

(6)

where the K_l(i)'s are conditional molar equilibrium constants (10) and K_l(i) is the lth step for the dissociation of H⁺ from species i. The symbol  is a standard mathematical notation denoting that a product of K_l(i) is taken over the prescribed limits. K₀ is defined to be unity. Also note that

(7)

From Eq. 1, therefore, changes in C_H can be separated conceptually into changes in the C_i or changes in pH. A related concept is the total titratable base C_B, which, by analogy with Eq. 1, is

(8)

where _i is the average number of proton acceptor sites per molecule of species i and is calculated by

(9)

Equations 1, 4, 8, and 9 yield the obvious relations

(10)

and

(11)

	PHYSIOLOGICAL ACID-BASE THEORY

To agree with the standard definitions employed in the usual treatment of physiological acid-base, Eq. 8 is used to calculate acid-base balance. Because of the crucial role of CO₂ equilibrium in physiology, it is useful to separate the carbonate and noncarbonate contributions to C_B

(12)

where the C_i and _i now refer to the noncarbonate buffers. This definition is retained throughout the rest of the calculations. C represents the carbonate contribution

(13)

where PrNHCOO is the carbamate derivative formed from interaction of CO₂ with protein (24). Under physiological conditions, the [CO²₃] and [PrNHCOO] terms are small and can be neglected. Similarly, the D term of Eq. 12 is small and can be neglected. Under these approximations, Eq. 12 becomes

(14)

Combining Eqs. 4, 9, and 14 gives

(15)

Differentiation of Eq. 15 with respect to pH yields

(16)

It turns out that because of the large number of buffer groups on plasma proteins _i/pH is approximately linear over the physiological pH range, so that Eq. 16, using Eq. 15, can be recast in integrated form as

(17)

The constant C depends on the concentrations and identities of the various species i and is given by

(18)

where b_i is a constant that depends on the difference between the pH at which the slope is determined and the negative base ten logarithm of the dissociation constant (pK ) of species i. Equation 17 is referred to as the Van Slyke equation (25).

Physiological pH is determined under the simultaneous solution of the Van Slyke equation and the Henderson-Hasselbalch equation (1a)

(19)

where pK' = 6.103 and S is the equilibrium constant between dissolved CO₂ and CO₂ in the gas phase and equals 0.0306 at 37°C, when H⁺ is in moles per liter, HCO₃ is in millimoles per liter, and PCO₂ is in Torr.

	SID THEORY

In 1983, Stewart published an article (29) in which he developed a quantitative model of acid-base, employing a parameter first used by Singer and Hastings (27). Stewart called this parameter the "strong-ion difference," whereas Singer and Hastings referred to this same parameter as "buffer base." The advantage of the buffer base parameter is that it is independent of changes in PCO₂.

Strong ions are defined as those that do not participate in acid-base reactions; that is, they are spectator ions. Ions that do involve net proton exchange are called buffer ions. The SID is, therefore, given by

(20)

where z_k is the charge on strong ion S_k. In terms of the physiological ions which are typically present, SID usually is

(21)

By virtue of the principle of electroneutrality, SID can also be calculated, in analogy to Eq. 12, by

(22)

where _i is the average charge per molecule for species i and is given by

(23)

_min(i) is the minimum possible charge for species i. Equation 22 is a more general form of the equations of Stewart (29) and Figge et al. (7). After neglecting the terms with small values under physiological conditions as before, Eq. 22 gives, in analogy with Eq. 14

(24)

In analogy with Eq. 15

(25)

Several additional relations are worth pointing out, including

(26)

Hence

(27)

and by similar arguments to those leading to Eq. 17

(28)

Note that Eq. 28 has the same general form as Eq. 17. Equation 28 is also an analytical expression for the simplified equation of Figge et al. (7). Combining Eqs. 15, 25, and 26 gives the additional relationship

(29)

where _max(i) is the maximum possible charge for species i.

	METHODS

Theoretical simulations of acid-base balance in plasma, using the mathematical models above, were performed. In accordance with the results of Figge et al. (7), it was assumed that albumin and phosphate were sufficient to account for all of the noncarbonate buffer activity of plasma.

C_B vs. pH, SID vs. pH, and [HCO₃] vs. pH curves for different values of PCO₂ for both the SID and C_B cases were calculated. Microsoft Excel 97 running on a Compaq Deskpro computer equipped with a Pentium II processor was used for the calculations. pH was stepped in 0.01-unit increments to calculate the dependent variable. An ionic strength of 0.17 for plasma was assumed (1a), and activity coefficients were calculated from the Davies equation (4) at 37°C. This gave activity coefficients of f₁ = 0.75, f₂ = 0.31, and f₃ = 0.072 for ions with charges of ±1, ±2, and ±3, respectively. Concentrations of buffer ions are expressed in millimoles per liter.

Acid dissociation constants for the ionizable groups on albumin were those determined by Figge et al. (7, 8), and it was further assumed that the constants in their study were determined via concentrations for the protein but activity for H⁺. Carbonate and phosphate equilibrium constants were obtained from Refs. 1a and 21, respectively. The relevant equilibrium constants are listed in Table 1. For albumin, _max(i) = 212 and _min(i) = 118; for phosphate, _max(i) = 3 and _min(i) = 3.

The designation "normal plasma" within Figs. 1-5 and text denotes plasma with C_i for albumin of 0.66 mM (4.4 g/dl) and C_i for phosphate of 1.16 mM (3.6 mg/dl). The normal values for pH, PCO₂, and [HCO₃] are assumed to be 7.40, 40.0 Torr, and 24.25 mM, respectively, corresponding to a C_B = 101 mM and a SID = 39 mM. The constant C was calculated from Eq. 18 and the above values to give 110 mM for normal plasma, with a corresponding b_i of 160 for albumin and 3.3 for phosphate.

	ACID-BASE PARAMETERS AT CONSTANT NONCARBONATE BUFFER CONCENTRATION

Equation 12 represents an exact expression for C_B, subject to several caveats. First, since protein conformation is pH dependent, the K_l(i) will also be pH dependent, especially outside the physiological pH range. Second, as noted before, the K_l(i) values used here are really pseudoequilibrium constants, since they were not all determined directly; some were determined as parameters fitted to a model and others were assigned "average values" (7, 8). Finally, some authors have previously pointed out that, in general, the notions of both C_B and SID are somewhat ill-defined, since it depends on pH whether a given species behaves as a strong ion or a buffer ion (23, 26). In practice, however, there is very little ambiguity over the physiological pH range; therefore, these parameters may actually be regarded as well defined under physiological conditions. For the purposes of calculation, what is required is that all of the species that are involved in net proton transfer over the pH range of interest must be included in the right side of Eq. 8 or 22. With these approximations in mind, the behavior of the functions under various physiological perturbations can be considered.

Over the physiological pH range between pH = 6.8 and 7.8, Eq. 14 is often plotted as [HCO₃] vs. pH at constant C_B. Equation 19 is also plotted on the same graph for various PCO₂ values, as shown in Fig. 1. Equation 14 is seen to be nearly a straight line over this same pH range and can therefore be approximated by Eq. 17. The theoretical error introduced through the use of the linear approximations rather than the complete equations was found to be <1.0 mM over the pH range from 6.0 to 8.0.

As mentioned in PHYSIOLOGICAL ACID-BASE THEORY, physiological pH is determined by the simultaneous solution of the Van Slyke equation (Eq. 17) and the Henderson-Hasselbalch equation (Eq. 19); that is, at their crossing points, as shown in the case of human plasma plotted in Fig. 1. This type of plot has been called a Davenport diagram (3).

View larger version (24K): [in this window] [in a new window]   Fig. 1.   Davenport diagram comprising bicarbonate concentration [HCO3] vs. pH graphs of Eq. 14 (straight lines) and PCO2 vs. pH graphs of Eq. 19 (curved lines). Movement between labeled points along various lines corresponds to different types of acid-base disturbances, as explained in text. Line containing points A and B is for normal plasma with total titratable base (CB) = 101 mM, whereas that containing C and D represents a metabolic acidosis with change in concentration of buffer ion species i (Ci) = 0 mM. The y-displacement between points A and D is the change in the Van Slyke standard bicarbonate (VSSB = 10 mM), which in this case is also equal to base excess (BE), change in CB (CB), and change in strong-ion difference (SID). Dotted line almost superimposed over the line containing A and B is a [HCO3] vs. pH graph of the Van Slyke equation (Eq. 17).

The Van Slyke equation shows how [HCO₃] changes with PCO₂ at a constant concentration of noncarbonate buffer, so that C_i remains constant while _i increases or decreases. This change in [HCO₃], for example moving from point A to B in Fig. 1, is due to the PCO₂/[HCO₃] equilibrium and represents a pure respiratory derangement. Metabolic disturbance at constant PCO₂ is illustrated by the move from B to C in Fig. 1, in which the entire Van Slyke curve is shifted with a concomitant change in C_B.

These changes are described under constant noncarbonate buffer (C_i = 0) using Eq. 17 by

(30)

where  represents the buffer value

(31)

 can be calculated by a term-by-term differentiation of Eq. 4 or by fitting the data to a straight line. The data of Figge et al. (7) used here give a molar buffer value (_i/ pH) of 8.3 for albumin. The original data of Tanford et al. (30) give a molar buffer value 8.0. The molar buffer value of phosphate is calculated to be 0.29, compared with 0.309 given by Siggaard-Andersen and Fogh-Andersen (26). The corresponding theoretical and experimental (26) values of  for albumin are 5.5 and 5.3 mM, respectively, whereas the theoretical and experimental (26) values of  for phosphate are 0.34 and 0.36 mM, respectively. If the K_l(i) values are defined in terms of activity for protons and concentration for the remaining species, the calculated values are identical to the experimental values.

Pure respiratory disturbances, those with C_B = 0, give a [HCO₃] of

(32)

whereas metabolic disturbances are calculated via Eq. 30, which can be conceptualized in two ways. The first is as a calculation of the C_B, which is the BE as compared with the normal value. The second is to focus on the right side of Eq. 30 and to think of  · pH as a correction term to the measured [HCO₃], which corrects for changes in PCO₂ (respiratory effects). The correction term corrects the [HCO₃] to what it would be at pH = 7.40 (point D of Fig. 1). The [HCO₃] when corrected to pH = 7.40 is called the "Van Slyke standard bicarbonate," and the corresponding change in [HCO₃] is the change in Van Slyke standard bicarbonate (VSSB) or VSSB (23, 25). The VSSB is illustrated by the difference between points A and D in Fig. 1. Since the two lines in Fig. 1 are parallel

(33)

The equation for SID (Eq. 24) when plotted in a [HCO₃] vs. pH coordinate system at constant SID gives a plot identical to Fig. 1, recognizing that the slopes and y-intercepts will be the same but that SID and C_B differ by a constant (Eq. 29). The straight-line plots in Fig. 1 also show how [HCO₃] varies with PCO₂ at constant SID. The same arguments apply to SID that apply to the C_B case above, so that

(34)

and, therefore

(35)

as stated in Siggaard-Andersen's treatise (24) and also as concluded by Schlichtig (19). Figure 2 shows how SID and C_B vary as a function of pH for normal plasma and a metabolic acidosis. As will be shown in ACID-BASE PARAMETERS AT VARIABLE NONCARBONATE BUFFER CONCENTRATIONS, the equalities of Eq. 35 break down if the noncarbonate buffer concentration does not remain constant.

View larger version (18K): [in this window] [in a new window]   Fig. 2.   Graphs of CB and strong-ion difference (SID) vs. pH of Eqs. 14 and 24 for normal plasma with [HCO3] = 24.25 mM (solid lines a and c) and for a metabolic acidosis (arrows) with Ci = 0 mM and [HCO3] = 14.25 mM (dotted lines b and d). CB = SID, and their differences are pH independent.

Siggaard-Andersen and others have previously argued (22, 26) that BE, as a parameter by itself, is the most relevant arbiter of whether there is a net metabolic acid-base disturbance and to what degree; however, examination of the change in the concentrations of other ions can also give additional diagnostic information. The parameter most often used for extracting that information is the anion gap AG (5).

The AG is usually defined as

(36)

and it is generally interpreted as the "unmeasured anions," although in actuality the AG is

(37)

where the sums extend over the unmeasured positive ions p and the unmeasured negative ions q. The AG, therefore, represents the opposite of the net unmeasured charge concentration. Because the net unmeasured negative charge is typically much greater than the unmeasured positive charge, AG is positive. Whether the AG is low, normal, or high helps the clinician by dividing the differential diagnosis into those associated with low, normal, or high gaps, as has been described in Refs. 5, 16, and 17.

The "delta gap" (AG) is used to uncover mixed metabolic disturbances (17, 31). It is given by

(38)

where AG is calculated from measured values via Eq. 36, and the constant 12 mM represents the normal value for the gap. If the AG does not equal the [HCO₃] calculated from

(39)

where [HCO₃] represents the measured value and the constant 24 mM represents the normal bicarbonate value, then a mixed metabolic disorder is present. This mixed nonrespiratory disorder will be made up of two disorders with different AGs, for example, a metabolic alkalosis from vomiting and a metabolic acidosis from diabetic ketoacidosis.

Equations 17 and 28 show how to incorporate a similar analysis into the BE and Stewart approach. SID can be divided into measured and unmeasured components, as suggested by Jones (12) and by Figge et al. (7).

(40)

where SID_m is the measured SID and SID_u is the unmeasured SID. Hence, using Eq. 30

(41)

This is the delta gap for a metabolic disturbance, remembering that the BE at constant C_i represents the change in [HCO₃] corrected for respiratory effects. The AG' is the difference between the measured SID and the VSSB. Therefore, if AG' = BE = 0, then there is no net disturbance. If AG' = 0 and BE  0, then there is a "measured ion-compensated" disturbance, for example, a hyperchloremic metabolic acidosis. If AG' = BE, then there is a differential diagnosis consistent with the presence of "unmeasured ions," for example, a wide gap metabolic acidosis. Finally, if AG' is between 0 and BE, then there is a mixed delta gap problem with both measured ion-compensated and unmeasured ion disturbances present.

These concepts are illustrated graphically in Fig. 3, showing the AG' in the BE formalism and how SID changes with metabolic disturbances, through a change in SID_m or SID_u, or potentially both.

View larger version (24K): [in this window] [in a new window]   Fig. 3.   A plot analogous to a Davenport diagram is shown for [HCO3] vs. pH of Eq. 24 (solid straight lines). PCO2 vs. pH graphs of Eq. 19 (curves) are also plotted. Upper solid straight line represents normal plasma with a SID = 39 mM, whereas lower solid straight line represents a metabolic acidosis with Ci = 0 mM and VSSB = 15 mM. SIDam is the measured SID for normal plasma, in this case [Na+]  [Cl] = 36 mM. SIDbm is the measured SID for a "measured ion-compensated" disorder with change in anion gap corrected for CO2 effects (AG') = 0 mM. AG'1 = 12 mM and AG'2 = 12 mM are AGs in BE formalism, as explained in text. Distance between points A and B represents AG' for an "unmeasured ion" disturbance with AG' = BE = 15 mM.

	ACID-BASE PARAMETERS AT VARIABLE NONCARBONATE BUFFER CONCENTRATION

When the concentrations of buffer ions C_i change, the relationships between the acid-base parameters discussed above also change. Using Eq. 15, the change in C_B due only to the change in C_i can be calculated by assuming that [HCO₃], PCO₂, and pH are held constant at their normal values

(42)

Here, _i is understood to be evaluated at pH = 7.40. Alternatively, using the linear approximation of Eq. 17

(43)

The change in titratable base due only to C_i is illustrated graphically in Fig. 4.

View larger version (20K): [in this window] [in a new window]   Fig. 4.   Graphs of CB and SID vs. pH drawn using Eqs. 14 and 24 for normal plasma with [HCO3] = 24.25 mM (solid lines a and c) and for a case with same values except albumin concentration = 0.33 mM (dotted lines b and d). Both the slopes and y-displacement change, so that CB  SID, and their differences are pH dependent. Line e represents a metabolic acidosis in the setting of hypoproteinemia calculated from Eq. 14 by using same values as for line b, except [HCO3] = 14.25 mM. The y-displacement between points A and B is the total CB for this case.

The total change in C_B when the above variables are not held constant is

(44)

or in the linear approximation

(45)

Again, this is shown graphically in Fig. 4.

The relevant analogous equations for SID can be derived in the same way to give

(46)

for the change due to C_i alone and for the total change

(47)

In their linear approximations

(48)

and

(49)

The SID due only to a change in C_i is also illustrated in Fig. 4.

Under variations in noncarbonate buffer concentration, the VSSB is calculated in the linear approximation via

(50)

as shown graphically in Fig. 5. Here C'_i represents the new (different from normal) C_i. C'_B is interpreted as the BE referenced to the new buffer ion concentration C'_i (dotted line in Fig. 5). C'_B will, of course, be equal to the correspondingly defined SID'.

View larger version (27K): [in this window] [in a new window]   Fig. 5.   Davenport diagram ([HCO3] vs. pH) for normal plasma (solid straight line containing point A), metabolic acidosis for Ci = 0 mM and VSSB = 10 mM (solid straight line containing point B), plasma with normal values except albumin concentration = 0.33 mM (dashed line containing point A), and the same corresponding metabolic acidosis with albumin concentration = 0.33 mM (dotted line containing point C). C'B, change in CB referenced to new buffer ion concentration C'i.

It should be clear from Eqs. 44, 47, and 50 that the equalities of Eq. 35 no longer hold. In fact, Eq. 29 shows that in general for C_i  0 

(51)

and, therefore, in general

(52)

whereas, in general

(53)

	DISCUSSION

Disagreement about the best parameter to describe acid-base balance in the body has dominated this area of physiology for more than three decades (1, 20, 22, 26). For the most part, the disagreement has been between advocates of the Boston method employing measured [HCO₃] and the Copenhagen method employing BE. This controversy has, in fact, been given a name "The Great Trans-Atlantic Acid-Base Debate" (1). Recently, on another front, Stewart and others (11, 28, 29) have argued that SID is the best parameter for expressing acid-base derangements and have even suggested that the very concept of pH be abandoned.

The limitations of the Boston method have been eloquently discussed by Severinghaus (22). The basic problem with this method is that the effects of buffer ions are not taken into account directly, and thus changes in [HCO₃] are treated as independent of PCO₂. In reality, though, [HCO₃] changes acutely as a function of PCO₂, which is purely due to the chemical equilibrium and independent of any compensation by the kidneys. As a result, changes in bicarbonate due to nonrespiratory causes may be underestimated or overestimated. This same approach also examines changes in ion concentration via AG and AG to obtain additional information; however, these variables are also subject to the same problem, since [HCO₃] is also involved in their calculation.

The BE approach is an attempt to correct for respiratory changes in [HCO₃]. A point of confusion is that the definition of BE is nebulous. BE implies, and is stated in the literature to be, the change in total titratable base, C_B (24, 25). The term BE is also used synonymously with VSSB. As demonstrated in ACID-BASE PARAMETERS AT VARIABLE NONCARBONATE BUFFER CONCENTRATION, however, the equivalence is justified only if C_i is constant or if the standard reference state is changed to that with the new buffer ion concentration C'_i. That section alluded to a situation in which pH, [HCO₃], and PCO₂ conceivably could all be normal while the noncarbonate buffer concentration may not be normal. As demonstrated in Fig. 4, because of the large number of buffer groups on a protein, small absolute changes in protein concentration will have large accompanying changes in C_B or SID. This may be true even within the normal albumin reference range. Also, as seen in Fig. 4, the change in SID for such a case will be smaller than the change in C_B. Siggaard-Andersen and Fogh-Andersen have suggested (26) that changes in protein concentration should not be considered acid-base disorders, and have considered the Stewart approach problematic in that regard. The calculations in ACID-BASE PARAMETERS AT VARIABLE NONCARBONATE BUFFER CONCENTRATIONS demonstrate the same potential problem with BE when defined as C_B.

By comparison, because the Van Slyke equation is fairly flat over the physiological pH range, VSSB is relatively constant with changes in buffer ion concentration. Figure 5 shows that the error introduced by using C_i to calculate VSSB rather than C'_i to calculate VSSB' will usually be less than ±1 mM. In addition, although many find the characterization of metabolic disturbances in terms of AG and AG behavior useful, advocates of the BE approach tend to denigrate the use of these two parameters (26), and so extracting information about ion disturbances other than H⁺ is not dealt with in the BE approach. As demonstrated in ACID-BASE PARAMETERS AT CONSTANT NONCARBONATE BUFFER CONCENTRATIONS, however, the concept of the AG and AG can be recast within the framework of the BE and Stewart formalisms to give the same useful information.

Stewart and his followers (28, 29) advocate the description of acid-base status in terms of SID, C_i, and PCO₂, based on the claim that these are the only independent variables of acid-base physiology. It bears pointing out, however, that SID is a surrogate variable for the difference in analytic concentrations between strong base and strong acid, the variables found in the standard treatments of acid-base equilibrium from the 1950s. The very same calculations of acid-base balance can be made, yielding the very same results, without explicit inclusion of spectator ions in the calculation (2, 10, 14, 18).

The Stewart approach has mainly found utility via the work of Figge et al. (7, 8), who calculated SID from pH, C_i, and PCO₂, basically from Eq. 24. The only difference is that Figge et al. include the small terms D and [CO²₃] in their calculations and they also calculate the carbonate terms from pH and PCO₂ (7). Next, they calculate SID_u from the difference between SID_m and SID, including [Na⁺], [K⁺], [Mg²⁺], [Ca²⁺], [Cl], and [lactate] in their calculation of SID_m. The value for SID_u is then interpreted clinically much like the AG. This model has been tested both in vitro (6-8) and in vivo (9, 15) and found to give reliable predictions.

The central relationship linking the BE concept with the Stewart approach is Eq. 27, which states that the rate of change in charge with respect to pH is equal to the rate of change in protonation with respect to pH. From that principle comes the fact that C_B and SID are the same within an added constant and that BE and SID are also the same within an added constant.

The foregoing discussion should clarify the debate about whether SID or BE is a better measure of acid-base disturbance in plasma. They are really two different kinds of parameter; one represents a change in concentration and the other does not. SID, as a stand-alone parameter, does not seem that useful and is certainly no more useful than C_B or C_H from a theoretical standpoint. Similarly, BE is no more or less useful than SID, but BE and SID seem to be more relevant parameters, since they do represent the deviations from normal, which is what one is usually concerned about practically.

Conclusions