Abstract
The strong ion approach provides a quantitative physicochemical method for describing the mechanism for an acidbase disturbance. The approach requires speciesspecific values for the total concentration of plasma nonvolatile buffers (A_{tot}) and the effective dissociation constant for plasma nonvolatile buffers (K
_{a}), but these values have not been determined for human plasma. Accordingly, the purpose of this study was to calculate accurate A_{tot} and K
_{a} values using data obtained from in vitro strong ion titration and CO_{2}tonometry. The calculated values for A_{tot} (24.1 mmol/l) andK
_{a} (1.05 × 10^{−7}) were significantly (P < 0.05) different from the experimentally determined values for horse plasma and differed from the empirically assumed values for human plasma (A_{tot} = 19.0 meq/l and K
_{a} = 3.0 × 10^{−7}). The derivatives of pH with respect to the three independent variables [strong ion difference (SID), Pco
_{2}, and A_{tot}] of the strong ion approach were calculated as follows:
 buffer value
 plasma pH
 strong ion difference
 strong ion gap
 anion gap
two physicochemical mechanistic acidbase models based on the strong ion approach have been developed to assess acidbase status: the strong ion model (35) and the simplified strong ion model (4). The strong ion approach requires speciesspecific values for the total concentration of plasma nonvolatile buffers (A_{tot}) and the effective dissociation constant for plasma nonvolatile buffers (K _{a}) (4, 32). Values for A_{tot} (14.9 or 15.0 mol/l) andK _{a} (2.1 or 2.2 × 10^{−7} eq/l) have been experimentally determined for equine plasma (4,32), but accurate values are unavailable for human plasma; thus it is difficult to apply the strong ion approach to acidbase disturbances in humans (14, 16). Wilkes (41) suggested that the values used for A_{tot} (17 meq/l) andK _{a} (3.0 × 10^{−7}) of human plasma are incorrect, and Lindinger and colleagues (20) preferred to use a higher value for A_{tot} (19 meq/l). Stewart (35) originally assigned an empirical value of 19 meq/l to A_{tot}.
The most widely used method to assign a value for A_{tot} of human plasma is calculation from the total protein concentration ([total protein]) (15, 20, 36), whereby
There appear to be three errors with this approach. First, the correct units for A_{tot} are millimoles per liter (instead of meq/l), where millimoles per liter refers to dissociable groups capable of donating or accepting a proton, because an assumption in the strong ion approach is that plasma nonvolatile buffer mass (and not charge) is conserved (see Eq. EA6
). Second, Eq. 1
purportedly calculates the net charge of nonvolatile plasma buffers (albumin, globulin, and phosphate), which equals A^{−} concentration ([A^{−}], 15.0 meq/l when pH = 7.40 andK
_{a} = 3.0 × 10^{−7}), instead of A_{tot} (which has units of mmol/l) (4,15). Because A_{tot} = [HA] + [A^{−}] (where [HA] is weak acid concentration and is uncharged), Eq. 1
must underestimate the true value of A_{tot} when A_{tot} is expressed in the correct units of millimoles per liter, inasmuch as rearrangement of Eq.EA3
provided
The most commonly used value for K _{a} of human plasma is 3.0 × 10^{−7}. This empirical value was first used by Stewart in 1983 (35), although Stewart used different K _{a} values (0.4 × 10^{−7}, 2.0 × 10^{−7}, and 4.0 × 10^{−7}) at other times (3335). AK _{a} value of 3.0 × 10^{−7}appears incorrect, inasmuch as in vitro CO_{2} tonometry of human plasma indicates maximal buffering at pH ∼7.1 (30). Because buffering is maximal when pH = pK _{a} (24, 37), the effectiveK _{a} value for human plasma should approximate 0.8 × 10^{−7} (pK _{a} = 7.1), rather than 3.0 × 10^{−7}(pK _{a} = 6.5).
Accurate A_{tot} and K _{a} values are required to apply the strong ion approach to acidbase disturbances in humans. Because the currently used values for A_{tot} andK _{a} appear to be incorrect, the purpose of this study was to calculate accurate A_{tot} andK _{a} values for human plasma. This was accomplished using four approaches: 1) graphical representation of the nonlinear relationship between plasma A_{tot} and pK _{a}, 2) calculation of plasma A_{tot} and K _{a}values using published data, 3) calculation of albumin A_{tot} and K _{a} values using published data, and 4) calculation of the albuminK _{a} value using the estimated pK _{a} values for the 14 dissociable amino acids that act as nonvolatile buffers at physiological pH. The calculated A_{tot} and K _{a} values for human plasma were then validated using two approaches: 1) data obtained from in vivo studies in humans and 2) published values for the buffer value (β) of human plasma. The results indicate that the currently used values for A_{tot}{2.43 × [total protein] (g/dl) = 17 meq/l (18, 25,40) or 19 meq/l (35)} andK _{a} (3.0 × 10^{−7}) of human plasma are incorrect.
MATERIALS AND METHODS
Graphical representation of the A_{tot}pK_{a}relationship for human plasma.
For normal human plasma at 37°C, pH = 7.40, Pco
_{2} = 40 Torr, and strong ion difference (SID^{+}) ≃ 41.7 meq/l (28, 31). The normal plasma HCO
Calculation of A_{tot} and K_{a} values for human plasma using published data.
Data were obtained from four in vitro studies: one set from SiggaardAndersen and Engel (29), one set from SiggaardAndersen (28), and two sets from Figge et al. (10). The first data set was obtained from an in vitro study involving hydrochloric acid, acetic acid, lactic acid, and sodium carbonate titration of human plasma at 38°C (29). The simplified strong ion equation (4) was applied as
The algebraic form of the simplified strong ion equation used inEq. 4
was selected, because it provided the narrowest confidence intervals for the estimates of A_{tot} andK
_{a} when pH was changed by strong ion titration. Data analysis was restricted to SID^{+} values from 30 to 56 meq/l, inasmuch as residual plots developed during nonlinear regression indicated deviation of fitted from actual values outside this range, presumably because the hypertonic solutions used for strong ion titration increased ionic strength, thereby altering the effective values for K
_{a} and the apparent equilibrium constant (K′_{1}) (28). As titration was accomplished at 38°C, temperatureadjusted values for S (0.0301 mmol · l^{−1} · Torr^{−1}) (1) and pK′_{1} (6.120) were used (12, 22). The calculated value for A_{tot}was indexed to the reported mean total protein concentration (7 g/dl). The calculated value for K
_{a} (obtained at 38°C) was corrected to 37°C using van't Hoff's equation
The second data set was obtained from an in vitro study involving hydrochloric acid and sodium hydroxide titration of human plasma at 38°C (28). Data analysis was completed as described previously. The calculated value for A_{tot} was indexed to the reported mean plasma protein concentration (6.98 g/dl). The calculated value for K _{a} (obtained at 38°C) was corrected to 37°C using van't Hoff's equation, as described previously.
The third and fourth data sets were obtained from an in vitro study involving CO_{2} tonometry of two human serum protein solutions (subjects A and B) performed at 37°C (10). The simplified strong ion equation (4) was applied in the following form
For each of the four data sets, nonlinear regression was used to solve simultaneously for A_{tot} and K _{a} using reported or derived values for pH, Pco _{2}, and SID^{+}, known values for S and pK′_{1}, the stated form of the simplified strong ion model, and Marquardt's expansion algorithm (PROC NLIN) (11, 27). Nonlinear regression simultaneously adjusts the estimated values for A_{tot} and K _{a} to provide the best fit of the model to the data. The sixfactor simplified strong ion model (4) was used for nonlinear regression, instead of the eightfactor strong ion model (35), because reducing the number of parameters in the model leads to more precise parameter estimates (11). Initial values for A_{tot} of 5–30 mmol/l in 5 mmol/l increments and for K _{a} of 0.5 × 10^{−7}–3.0 × 10^{−7} in 0.5 × 10^{−7} increments were used in the nonlinear regression procedure. The application of a coarse grid search spanning the likely values for A_{tot} and K _{a} facilitated accurate estimation of the values for A_{tot} andK _{a}. The final estimate for A_{tot} was indexed to total protein (all 4 data sets) and albumin (3rd and 4th data sets) concentrations. Because plasma albumin concentration was not stated in the first two data sets (28, 29), albumin concentration ([albumin]) was calculated as follows: [albumin] (g/dl) = 0.6 × [total protein] (g/dl). From the four data sets, overall estimates for A_{tot} andK _{a} were calculated as means ± SD.
Calculation of A_{tot} and K_{a} values for human albumin using published data.
Data were obtained from an in vitro study involving CO_{2}tonometry of one human albumin solution at 37°C (Table A in Ref.10) and analyzed as stated previously for the two human serum protein solutions.
Calculation of human albumin K_{a} value using the pK_{a} values for dissociable amino acid groups.
Figge et al. (9) reanalyzed data from an earlier study (10) and identified 212 dissociable groups on human albumin that could be categorized into 6 different groups, with 5 groups having an “effective K _{a}” as follows: 1 carboxyterminus group, pK _{a} = 3.10; 98 Asp and Glu groups, pK _{a} = 4.00; 1 aminoterminus group, pK _{a} = 8.00; 1 Cys group, pK _{a} = 8.50; 18 Tyr groups, pK _{a} = 9.60; and 77 Arg and Lys groups, pK _{a} = 9.40. On the basis of data obtained from magnetic resonance imaging of human albumin (2) and an iterative computing routine, the remaining 16 His groups were assigned the following pK _{a} values: 4.85, 5.20, 5.76, 5.82, 6.17, 6.36, 6.73, 6.75, 7.01, 7.10, 7.12, 7.22, 7.30, 7.30, 7.31, and 7.49 (9). An apparent pK _{a}for human albumin was calculated from these data as the weighted mean average of the 12 dissociable His groups and 2 other dissociable groups (Cys and aminoterminus) that acted as nonvolatile buffer ions at physiological pH (pK _{a} = 7.4 ± 1.5) (4).
RESULTS
Graphical representation of the A_{tot}pK_{a}relationship for human plasma.
Equation 3 indicates that if K _{a} is empirically assigned the value of 3.0 × 10^{−7}(pK _{a} = 6.52), then A_{tot} = (41.7 − 22.9)[1 + 10^{(6.52 − 7.40)}] = 21.9 mmol/l, which differs in magnitude and units from the empirical value for A_{tot} (17.0 meq/l) calculated using Eq.1 with the assumption of a normal plasma protein concentration of 7.0 g/dl (Fig. 1) and differs in units from the value of 19 meq/l assigned by Stewart (35). Figure 1 also demonstrates that the empirical pK _{a} value (6.52) differs from the pH value for maximal buffering of human plasma (30), where pK _{a} = pH (24, 37). One or both of the empirically assigned values for A_{tot} andK _{a} must therefore be in error.
Calculation of A_{tot} and K_{a} values for human plasma using published data.
Analysis of the first data set containing 26 data points from strong ion titration at 38°C of plasma samples from 12 humans (29) provided the following equations: A_{tot}(mmol/l) = 3.88 × [total protein] (g/dl) (95% confidence interval for coefficient value = 3.87–3.89), andK _{a} = 0.938 × 10^{−7} (95% confidence interval = 0.934–0.942 × 10^{−7}).K _{a} at 37°C was calculated using van't Hoff's equation as 0.904 × 10^{−7}. A_{tot} in terms of plasma albumin concentration was calculated as follows: A_{tot} (mmol/l) = 6.47 × [albumin] (g/dl).
Analysis of the second data set containing 26 data points from strong ion titration at 38°C of plasma samples from 4 humans (28) provided the following equations: A_{tot}(mmol/l) = 3.59 × [total protein] (g/dl) (95% confidence interval for coefficient value = 3.58–3.60), andK _{a} = 1.004 × 10^{−7} (95% confidence interval = 0.994–1.014 × 10^{−7}).K _{a} at 37°C was calculated using van't Hoff's equation as 0.968 × 10^{−7}. A_{tot} in terms of plasma albumin concentration was calculated as follows: A_{tot} (mmol/l) = 5.98 × [albumin] (g/dl).
Analysis of the third data set containing 12 data points from 4 sets of CO_{2}tonometered human serum samples for subject A at 37°C (10) provided the following equations: A_{tot} (mmol/l) = (3.38 ± 0.82) × [total protein] (g/dl) or (5.57 ± 1.54) × [albumin] (g/dl), andK _{a} = (0.84 ± 0.50) × 10^{−7}.
Analysis of the fourth data set containing 30 data points from 10 sets of CO_{2}tonometered human serum samples for subject B at 37°C (10) provided the following equations: A_{tot} (mmol/l) = (2.92 ± 0.46) × [total protein] (g/dl) or (4.76 ± 0.65) × [albumin] (g/dl), andK _{a} = (1.40 ± 0.67) × 10^{−7}.
The values (means ± SD) of the four data sets indicated that, at 37°C, A_{tot} (mmol/l) = (3.44 ± 0.40) × [total protein] (g/dl) or (5.72 ± 0.72) × [albumin] (g/dl), K _{a} = (1.05 ± 0.25) × 10^{−7}, and pK _{a} = 6.98 (95% confidence interval = 6.81–7.26). For a normal plasma protein concentration of 7.0 g/dl, A_{tot} = 24.1 ± 2.8 mmol/l. The 95% confidence interval for the calculated A_{tot} (in mmol/l) and pK _{a} values included the line depicting the nonlinear relationship between A_{tot} and pK _{a} and the pH value (7.1) for maximal buffering of human plasma (when pK _{a} = pH) (30) but did not include the values empirically assumed for human plasma (Fig. 1). The calculated A_{tot} and K _{a} values were significantly different from the experimentally determined values (4) for horse plasma: A_{tot} = 15.0 ± 2.8 mmol/l (t = 4.56, P < 0.0025), andK _{a} = (2.22 ± 0.32) × 10^{−7} (t = 6.47, P < 0.0005).
Calculation of A_{tot} and K_{a} values for human albumin using published data.
Analysis of data from CO_{2} tonometry of a solution containing albumin and no globulin at 37°C (10) provided the following equations: A_{tot} (mmol/l) = 4.60 × [albumin] (g/dl) (95% confidence interval for coefficient = 3.20–10.00), K _{a} = 1.40 × 10^{−7} (95% confidence interval = 0.50–3.14 × 10^{−7}), and pK _{a} = 6.85 (95% confidence interval = 6.50–7.30). The calculated value was similar to that predicted by Reeves (K _{a} = 1.77 × 10^{−7}) for canine albumin at 37.5°C (23).
Calculation of K_{a} for human albumin using the pK_{a} values for dissociable amino acid groups.
Reanalysis of data in an earlier study involving titration of human albumin produced an apparent pK _{a} for albumin of 7.17 (9): pK _{a} = [1 × (6.17 + 6.36 + 6.73 + 6.75 + 7.01 + 7.10 + 7.12 + 7.22 + 7.30 + 7.30 + 7.31 + 7.49) + (1 × 8.00) + (1 × 8.50)]/14. The estimated pK _{a} value was within the 95% confidence interval (6.50–7.30) for the K _{a}value of human albumin calculated previously using nonlinear regression.
Validation of calculated A_{tot} and K_{a} values using in vivo data.
The calculated values for A_{tot} andK
_{a} of human plasma were applied to data obtained from an in vivo study involving six humans with acute respiratory acidosis and alkalosis (8). Plasma pH was calculated using the simplified strong ion equation (4)
For the in vivo validation data set, pH ranged from 7.26 to 7.66, Pco
_{2} from 15 to 62 Torr, and SID^{+}from 38.5 to 49.2 meq/l. When the calculated values for A_{tot} (24.1 mmol/l) and K
_{a} (1.05 × 10^{−7}) were used, an excellent correlation between pH_{calc} and pH_{meas} was observed (r = 0.94; Fig. 2), and the regression equation relating pH_{calc} to pH_{meas} was not significantly different from the line of identity
The calculated A_{tot} and K _{a} values were also applied to the mean values of 219 arterial blood samples obtained from 91 human patients in a critical care population, providing SID^{+} = 38.2 meq/l, Pco _{2} = 41.1 Torr, [total protein] = 5.32 g/dl, and pH = 7.424 (40). Solving Eq. 7 using the stated values for SID^{+}, Pco _{2}, and total protein concentration and the calculated values for A_{tot} (3.44 × [total protein], g/dl) and K _{a} (1.05 × 10^{−7}) provided a predicted pH value of 7.422 (a difference of 0.002). In contrast, the solution of Eq. 7 using the empirical values for A_{tot} (2.43 × [total protein], g/dl) andK _{a} (3 × 10^{−7}) provided a predicted pH value of 7.454 (a difference of 0.030), and solution ofEq. 7 using Stewart's empirical values for A_{tot}(19 meq/l) and K _{a} (3.0 × 10^{−7}) provided a predicted pH value of 7.363 (a difference of 0.059).
Validation of calculated A_{tot} and K_{a} values using β of human plasma.
Equation EA8
produced the following relationship between nonvolatile buffer concentration (A_{tot}, in mmol/l), β (the Van Slyke buffer value, in meq/l), pH, and pK
_{a}
DISCUSSION
The findings of this study indicate that the currently used A_{tot} and K _{a} values for human plasma are incorrect and that speciesspecific values for A_{tot} andK _{a} are required when the strong ion approach is applied to acidbase disturbances.
It is customary to perform a sensitivity analysis after use of nonlinear regression to estimate values for one or more factors in a model. The sensitivity of the dependent variable to changes in input variables can be conveyed by a spider plot (39), which graphically depicts the relationship between the dependent variable and percent change in one input factor while the remaining input factors are held constant at their normal values. The spider plot (Fig.3), based on the eight factors in Stewart's strong ion model (35), graphically indicated that plasma pH was most sensitive to changes in SID^{+} and was more sensitive to changes in A_{tot} than to changes inK _{a}. The latter finding was recently reported by Watson (40).
The tangent to each line in the spider plot reflects the sensitivity of human plasma pH to that factor. With the use of the simplified strong ion model equation (Eq. 7
), the derivatives of pH with respect to the three independent factors (SID^{+}, Pco
_{2}, and A_{tot}) of the strong ion approach were calculated to provide an index of the sensitivity of pH to changes in each of the independent factors
A clinically important problem is identifying and quantifying the presence of strong anions in plasma that are not routinely measured, such as lactate, βhydroxybutyrate, acetoacetate, and uremic anions. Shortly after Stewart developed the strong ion approach, it was evident that calculating the difference between measured and predicted strong ion difference would provide a method for quantifying the unmeasured strong ion concentration in plasma (15). This led to definition of the strong ion gap (SIG) by Kellum and colleagues in 1995 (17, 18), where the SIG is the difference between the charge assigned to unmeasured strong cations and anions. Calculation of the SIG for human plasma was based on an electroneutrality equation developed by Figge et al. in 1992 (9), whereby
Solving Eq. 2
using the calculated A_{tot} and pK
_{a} values indicated that [A^{−}] = 17.5 meq/l and that the net negative charge of human plasma protein was therefore 15.3 meq/l, because normal phosphate charge is 2.2 meq/l. This estimate for net protein charge was greater than that obtained by van Leeuwen in 1964 (12.6 meq/l, [A^{−}] = 14.8 meq/l) (36) and Figge et al. in 1992 (12.0 meq/l, [A^{−}] = 14.2 meq/l) (9); however, the higher net protein charge estimate provided a better fit to the simplified strong ion electroneutrality equation (4): SID^{+} − HCO
Stewart's strong ion model states that plasma pH is a function of eight factors [SID^{+}, Pco
_{2}, A_{tot}, K′_{1}, S,K
_{a}, the apparent equilibrium dissociation constant for HCO
Footnotes

Address for reprint requests and other correspondence: P. D. Constable, Dept. of Veterinary Clinical Medicine, College of Veterinary Medicine, University of Illinois, 1008 W. Hazelwood Dr., Urbana, IL 61802 (Email: pconstable{at}uiuc.edu).

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 Copyright © 2001 the American Physiological Society
Appendix
The electroneutrality equation from the simplified strong ion model (Eq. 7 in Ref. 4) provided
Combination of Eqs. EA2
and
EA4
and algebraic rearrangement provided