## Abstract

The quantitative mechanistic acid-base approach to clinical assessment of acid-base status requires species-specific values for [A]_{tot} (the total concentration of nonvolatile buffers in plasma) and *K*_{a} (the effective dissociation constant for weak acids in plasma). The aim of this study was to determine [A]_{tot} and *K*_{a} values for plasma in domestic pigeons. Plasma from 12 healthy commercial domestic pigeons was tonometered with 20% CO_{2} at 37°C. Plasma pH, Pco_{2}, and plasma concentrations of strong cations (Na, K, Ca), strong anions (Cl, l-lactate), and nonvolatile buffer ions (total protein, albumin, phosphate) were measured over a pH range of 6.8–7.7. Strong ion difference (SID) (SID_{5} = Na + K + Ca − Cl − lactate) was used to calculate [A]_{tot} and *K*_{a} from the measured pH and Pco_{2} and SID_{5}. Mean (±SD) values for bird plasma were as follows: [A]_{tot} = 7.76 ± 2.15 mmol/l (equivalent to 0.32 mmol/g of total protein, 0.51 mmol/g of albumin, 0.23 mmol/g of total solids); *K*_{a} = 2.15 ± 1.15 × 10^{−7}; and p*K*_{a} = 6.67. The net protein charge at normal pH (7.43) was estimated to be 6 meq/l; this value indicates that pigeon plasma has a much lower anion gap value than mammals after adjusting for high mean l-lactate concentrations induced by restraint during blood sampling. This finding indicates that plasma proteins in pigeons have a much lower net anion charge than mammalian plasma protein. An incidental finding was that total protein concentration measured by a multianalyzer system was consistently lower than the value for total solids measured by refractometer.

- plasma pH
- strong ion difference
- anion gap
- metabolic acidosis

acid-base balance has traditionally been evaluated by using the Henderson-Hasselbalch equation (17, 18) to characterize four primary acid-base disturbances (i.e., respiratory acidosis and alkalosis, metabolic acidosis and alkalosis) (2, 10, 28) and by calculating the anion gap (AG) to estimate the unmeasured anion concentration (4, 7, 9, 23). Because the traditional Henderson-Hasselbalch approach is more descriptive than mechanistic (9) and fails to provide an accurate method for quantifying the unmeasured strong ion charge in animals with abnormal serum protein concentrations (4, 7, 10, 23, 28), alternative approaches to the clinical assessment of acid-base balance are required. A physicochemical approach derived from strong ion difference (SID) theory considers three independent variables (plasma SID, Pco_{2}, and plasma nonvolatile buffer ion concentration) to directly determine plasma pH. This approach differs in three important areas from the traditional bicarbonate centric application of the Henderson-Hasselbalch equation (13): *1*) acid-base balance is examined using a systems approach; *2*) a clear conceptual distinction is made between dependent variables {such as pH and bicarbonate concentration ([HCO_{3}^{−}])} and the independent variables; and *3*) the effects of protein concentration on acid-base balance are considered (10, 26, 28, 29). The strong ion approach characterizes six primary acid-base disturbances (i.e., respiratory acidosis and alkalosis, strong ion acidosis and alkalosis, nonvolatile buffer ion acidosis and alkalosis), and the unmeasured strong anion concentration is quantified by calculating the strong ion gap (SIG) (4, 13, 19).

The strong ion approach requires species-specific values for the total plasma concentration of nonvolatile weak acids ([A]_{tot}; i.e., the total concentration of plasma nonvolatile buffers: albumin, globulin, and phosphate) and the effective dissociation constant (*K*_{a}) for plasma nonvolatile buffers (8, 26). Values for [A]_{tot} and *K*_{a} have been experimentally determined in the plasma of horses (8, 27), humans (26), cats (21), dogs (6), and calves (5), and theoretically determined for the plasma of humans (11) and adult cattle (9). Values for [A]_{tot} and *K*_{a} of bird plasma are presently unavailable. The objective of the study was to experimentally determine [A]_{tot} and *K*_{a} values for avian plasma; to compare these values with [A]_{tot} and *K*_{a} values for the plasma of horses, calves, cats, dogs, and humans; and to calculate the net protein charge in bird plasma. This information will facilitate our understanding of acid-base abnormalities in birds.

## MATERIALS AND METHODS

Twelve healthy domestic meat pigeons were acclimated for 5 days before the start of the blood sampling. The birds were physically restrained for venipuncture of the basilic vein of one wing. Five to ten milliliters of venous blood were thus collected into lithium-heparin vacuum tubes from each bird. One aliquot of whole venous blood was immediately analyzed anaerobically in duplicate on an automated blood-gas analyzer to characterize the normal values for this group of birds. The following parameters were measured simultaneously at 37°C (Statprofile M, NOVA Biomedical, Canada, Mississauga, Ontario): blood-gas analysis (pH, Pco_{2}) and determination of [Na^{+}], [K^{+}], [Ca^{2+}], [Cl^{−}], and [l-lactate^{−}] (where brackets denote concentration). Plasma was harvested from the remaining blood aliquot by centrifugation within 30 min of collection, and CO_{2} tonometry was performed on all samples within 60 min of collection. An untonometered plasma aliquot was analyzed in duplicate for determination of the strong cation magnesium and nonvolatile buffer ion (total protein, albumin, and inorganic phosphate) concentrations (Hitachi 911 with Roche reagents). Duplicate values from each bird were averaged, and the average was used from each parameter of each bird to calculate mean and SD of all birds (normal venous blood values).

#### CO_{2} tonometry of plasma.

Plasma samples were tonometered (model IL235, Instrumentation Laboratory, Lexington, MA) for 20 min at 37°C over a Pco_{2} range of 20–145 Torr and a pH range of 6.80–7.65 using a mixture of humidified 20% CO_{2} and 80% normal air alternating with 100% normal air as washout. Previous experience with tonometry has shown that the changes in Pco_{2} occur rapidly, and, therefore, individual samples were aspirated at empiric intervals anaerobically into a capillary tube and analyzed directly using the automated blood-gas analyzer, as detailed above. A total of 88 CO_{2} tonometered plasma samples were analyzed, representing four to nine tonometered samples from each bird. Pco_{2} varied from 20 to 145 Torr, yielding pH values between 6.8 and 7.8. All tonometered plasma samples were analyzed once for blood/plasma gas analysis (pH, Pco_{2}) and determination of [Na^{+}], [K^{+}], [Ca^{2+}], [Cl^{−}], and [l-lactate^{−}] simultaneously.

#### Calculation of SID.

A fixed value for SID during in vitro CO_{2} tonometry is one of the assumptions of the strong ion approach; SID is invariant over the physiological range of pH, because strong ions are fully dissociated at physiological pH (8, 26, 29). Therefore, all strong cation (Na^{+}, K^{+}, Ca^{2+}, Mg^{2+}) and strong anion (Cl^{−}, l-lactate) concentrations were assumed to be constant during CO_{2} tonometry, and an ionic equivalency using ion-selective potentiometry (Mg^{2+}) was assigned to those variables not measured. Accurate measurements of SID are difficult to obtain in plasma because of cumulative measurement error, presence of unknown strong anions (13, 19, 26), and differences in equipment and methodology used to measure strong ion concentrations (25). SID was initially calculated for each bird's titration using the following four formulas: SID_{3} = {([Na^{+}] + [K^{+}]) − [Cl^{−}]}; SID_{4} = {([Na^{+}] + [K^{+}]) − ([Cl^{−}] + [lactate])}; SID_{5} = {([Na^{+}] + [K^{+}] + [Ca^{2+}]) − ([Cl^{−}] + [l-lactate])}; SID_{6} = {([Na^{+}] + [K^{+}] + [Ca^{2+}] + [Mg^{2+}]) − ([Cl^{−}] + [lactate])}. Mean ± SD of all titrations of each bird was obtained as constants for each SID_{3–6} (data not shown) for use in linear regression analyses.

#### Estimation of [A]_{tot} and K_{a}.

Measured values for pH and Pco_{2}, each bird's individual constant SID_{3–6}, the simplified strong ion electroneutrality equation (8), and the Marquardt nonlinear regression procedure (14) (PROC NLIN, SAS 8e, SAS Institute, Cary, NC) were used to simultaneously estimate values for [A]_{tot} and *K*_{a} for each bird. This required application of the simplified strong ion electroneutrality equation: (1) in which the net nonvolatile buffer ion concentration in plasma ([A^{−}]) was evaluated. To assist in estimating values for [A]_{tot} and *K*_{a}, *Eq. 1* was expressed in the following form: (2) using known values for solubility coefficient for CO_{2} (*S*) (0.0307 mmol·l^{−1}·mmHg^{−1}) (3) and −log of first dissociation constant of carbonic acid (p*K*_{1}) (6.120 at [NaCl] = 0.16 mmol/l) (15). Using the value of 6.120 for p*K*_{1} calculates actual plasma [HCO_{3}^{−}] in millimoles per liter at 37°C (24); likewise, the methods used to calculate SID_{3–6} provide a value in terms of concentration. This means that *Eq. 2* estimates a value for [A]_{tot} in terms of concentration (mmol/l) (8). Initial estimates for [A]_{tot} of 5–30 mmol/l in increments of 5 mmol/l and initial estimates for *K*_{a} of 0.1 × 10^{−7} to 3.0 × 10^{−7} in increments of 0.1 × 10^{−7} were used for the nonlinear regression procedure (14). For each pigeon's nonlinear regression procedure, the accuracy of the estimated values for [A]_{tot} and *K*_{a} were evaluated using the number of iterations required to converge to a solution, the *R*^{2} value, comparison of actual vs. predicted values for [HCO_{3}^{−}], calculation of standardized residuals, studentized residuals, Cook's distance, examination of residual plots (plot of the difference between measured and predicted [HCO_{3}^{−}] values on the *y*-axis vs. pH on the *x*-axis), and normal probability plots of the residuals (14); the *R*^{2} value was considered to be the most important measure of model fit. A value of *P* < 0.05 was regarded as significant. Means ± SD (all birds combined) of SID_{3–6}, [A]_{tot}, and *K*_{a} for all birds were calculated.

The calculated [A]_{tot} values for each bird were evaluated as the [A]_{tot} indexed to the total protein concentration ([A]_{tot-tp}), the [A]_{tot} indexed to the albumin concentration ([A]_{tot-alb}), and the [A]_{tot} indexed to total solids ([A]_{tot-ts}). Mean (±SD) values for [A]_{tot}, [A]_{tot-tp}, [A]_{tot-alb}, [A]_{tot-ts}, and *K*_{a} were determined.

Total solids as measured with a refractometer (Veterinary refractometer: Leica vet 360) were graphically compared with total protein estimation on an automatic analyzer (Hitachi 911 with Roche reagents) to examine agreement between the two methods.

#### Comparison of calculated and measured pH values.

pH was calculated from the measured value for SID and Pco_{2}, estimated values for [A]_{tot} (based on plasma albumin concentration) and *K*_{a}, known values for *S* (0.0307 mmol·l^{−1}·mmHg^{−1}) (3) and p*K*_{1} (6.120 at [NaCl] = 0.16 mmol/l) (15), and the simplified strong ion equation expressing pH as a function of the three independent factors (SID, Pco_{2}, [A]_{tot}) and three constants (*K*_{a}, *S*, p*K*_{1}) (8). The calculated pH value was regressed against the measured pH value using linear regression analysis, and the relationship was compared with the line of identity (14).

#### Comparison of [A]_{tot} and K_{a} values.

The estimated values for [A]_{tot} and *K*_{a} in plasma of birds were compared with results from studies using identical experimental methodology for plasma of calves (5), horses (8, 27), humans (26), cats (21), and dogs (6) by using an unpaired *t*-test. Because five multiple comparisons were being performed, the *P* value for significance was Bonferroni adjusted for the number of comparisons, producing a *P* <0.01 as significant.

#### Sensitivity of plasma pH and [HCO_{3}^{−}] to changes in SID, Pco_{2}, and [A]_{tot}.

Sensitivity of the dependent variables (plasma pH and [HCO_{3}^{−}]) to the three independent factors, SID, Pco_{2}, and [A]_{tot}, was conveyed by a spider plot (11), which graphically depicted the relationship between the dependent variables and percentage change in one independent factor, while the remaining two independent factors were held constant at typical values. The spider plots were created using *Eq. 1* solved for the dependent variable pH and [HCO_{3}^{−}] using mean SID and Pco_{2} values for the plasma of healthy pigeons (determined in this study) and estimated values for [A]_{tot} and *K*_{a} (29). In addition, the derivatives of pH and HCO_{3}^{−} with respect to the three independent factors (SID, Pco_{2}, [A]_{tot}) were then calculated using an Excel software program to provide an index of the sensitivity of plasma pH and HCO_{3}^{−} to changes in each of the independent factors at physiological pH.

## RESULTS

#### Blood and plasma analyses.

The values for venous blood from 12 meat pigeons are presented in Table 1. Mean sodium and chloride plasma concentrations of pigeons were comparable to dogs and were higher compared with humans (6, 26). Pigeons had high mean plasma [l-lactate] induced by manual restraint for blood sampling.

#### Calculation of SID.

Much larger differences in the mean value for SID_{3–6} were observed compared with other species (dogs, horses, cats, and ruminants) (Table 2). The larger differences in SID_{3–6} values were mainly due to the high plasma [l-lactate] in pigeons (Table 1).

#### Estimation of [A]_{tot} and K_{a}.

The *R*^{2} values for nonlinear regression models using SID_{5} and SID_{6} were >0.990, indicating excellent fit to the data, whereas the *R*^{2} values using SID_{3} and SID_{4} were always numerically lower (data not shown). Mean ± SD values for [A]_{tot} and *K*_{a} derived from SID_{3}, SID_{4}, SID_{5}, and SID_{6} indicated that the estimates derived from SID_{5} and SID_{6} were more precise (Table 2). Either pair of [A]_{tot} and *K*_{a} values derived from SID_{5} and SID_{6} would be suitable; however, we selected those derived from SID_{5} for further evaluation because the SD value for *K*_{a} was numerically smaller.

#### Comparison of calculated and measured pH values.

Calculation of pH from the measured values for the three independent factors (SID_{5}, Pco_{2}, [A]_{tot}) and three constants (*K*_{a}, *S*, p*K*′_{1}) indicated excellent agreement between calculated and measured pH values over a physiologically large range of pH (6.83–7.68; *R*^{2} = 0.974, Fig. 1). The slope (0.981) and intercept (0.132) for the linear regression equation relating calculated pH to measured pH were similar to the line of identity (slope = 1, *P* = 0.23; intercept = 0, *P* = 0.27).

#### Comparison of [A]_{tot} and K_{a} values.

The [A]_{tot} values of pigeon plasma were lower than that of cat, calf, human, dog, and equine plasma (Table 3). In contrast, the *K*_{a} values were similar to those of horse plasma but higher (*P* < 0.001) than those for dog, cat, calf, and human plasma.

#### Sensitivity of plasma pH and [HCO_{3}^{−}] to changes in SID, Pco_{2}, and [A]_{tot}.

Analysis of the spider plots revealed that pigeon plasma pH was most sensitive to changes in SID (Fig. 2) at physiological pH. Likewise, analysis of the spider plots depicted that pigeon plasma [HCO_{3}^{−}] was most sensitive to changes in SID at physiological pH (Fig. 3).

#### Net protein charge for model with SID_{5}.

Net protein charge has two components: nonvolatile buffer ion charge and SID charge. The value for [A^{−}] at pH = 7.43 reflects the net negative buffer ion charge of protein and phosphate; [A^{−}] = [A]_{tot}/(1 + 10^{− pH}) = 7.8 mmol/l/(1 + 10^{6.67 − 7.43}) = 6.65 meq/l (assuming nondissociated portion of the weak acids) is uncharged, A^{−} has a valence of −1, and p*K*_{a} is the negative logarithm to base 10 of the calculated *K*_{a} value. Because the net negative buffer ion charge of phosphate at pH = 7.43 approximates 0.96 meq/l (0.8 × [phosphate]; Table 1), the nonvolatile buffer ion charge of protein was 6.65 − 0.96 ≈ 6 meq/l. The true value for SID calculated using algebraic rearrangement of *Eq. 2* when pH = 7.43 (Table 1), Pco_{2} = 41.4 Torr (Table 1), [A]_{tot} = 7.8 mmol/l (Table 2), and *K*_{a} = 2.15 × 10^{−7} (Table 2) is 33.5 meq/l, which approximated the value for SID_{5} (32.8 meq/l; Table 1). This result suggests that plasma proteins have a SID charge of approximately zero; net protein charge, therefore, results primarily from nonvolatile buffer ion charge and approximates 6 meq/l.

#### The normal Gamble gram of birds.

Figure 4 demonstrates the composition of the normal Gamble gram of bird plasma based on the results of 12 healthy meat pigeons (Table 1).

#### Concentration of total solids (refractometer) and total protein concentrations.

Figure 5 shows relationship between total protein concentration and total solids as measured with refractometry.

## DISCUSSION

Use of the strong ion approach to evaluate acid-base status requires species-specific values for [A]_{tot} and *K*_{a} (26). In this study, mean values for [A]_{tot} (0.32 mmol/g of total protein or 0.51 mmol/g of albumin; or 0.23 mmol/unit of total solids) and *K*_{a} (2.15 × 10^{−7}) were experimentally established for plasma of meat pigeons.

An interesting finding was that the [A]_{tot} value of pigeon plasma was lower than that of cat, calf, human, dog, and equine plasma (Table 3) and that the *K*_{a} values were similar to horse plasma but higher to those for dog, cat, calf, and human plasma. Because the main determinants of [A]_{tot} and *K*_{a} are the plasma albumin concentration and number and mean p*K*_{a} value of histidine residues on albumin (6, 8, 9, 11, 21, 26), it is not surprising that values for [A]_{tot} and *K*_{a} of avian plasma are different from those of mammalian plasma. As a group, the albumin and total protein concentrations in avian plasma are much lower than those of mammalian plasma (Table 3) (16); however, when [A]_{tot} was indexed to the albumin ([A]_{tot-alb}) or total protein concentration ([A]_{tot-tp}), the values for avian plasma were similar to mammalian values. This indicates that the main reason for the low [A]_{tot} value of pigeon plasma is the low plasma albumin and total protein concentrations. Differences in the *K*_{a} value of avian plasma and most mammalian species were most likely due to small differences in the mean p*K*_{a} value of histidine moieties on albumin.

The mean AG was ∼13 meq/l, comprising 7 meq/l of l-lactate and 6 meq/l of plasma protein charge. The AG in healthy pigeons differs from that in small-animal species (dog, cat), because the AG of pigeons reflects the plasma protein concentration and the [l-lactate]; the latter was increased markedly due to restraint for blood sampling and represents a “restraint artifact.” Our results suggest that the normal AG of an unrestrained pigeon is ∼7 meq/l, assuming a normal [l-lactate] of 1 mmol/l (28).

A useful clinical application of SID theory is calculation of the SIG instead of the AG (4, 10). The SIG provides an estimate for the difference between the unmeasured strong anion charge (mostly due to l-lactate, d-lactate, sulfate, nonesterified fatty acids, ketoacids, pH-independent protein and phosphate charge, and very few other strong anions) and unmeasured strong cation charge (Ca^{2+}, Mg^{2+}). The SIG is also referred to as the difference between a measured SID and an effective SID (26). Total protein or albumin concentrations can be used to calculate [A]_{tot} for calculation of the SIG. Based on estimated values for [A]_{tot} and *K*_{a}, the following equations for calculating SIG (in meq/l) in the plasma of pigeons are proposed: (3) where [total protein] is in g/l and the AG (in meq/l) = ([Na^{+}] + [K^{+}]) − ([Cl^{−}] + [HCO_{3}^{−}]). The major component of SIG in pigeons is l-lactate (Table 1), and this equation may be used to estimate the [l-lactate] in laboratories where lactate measurements are not available.

A worrisome observation was the discrepancy between total protein plasma concentrations (Hitachi 911^{e}) and total protein concentrations estimated by refractometer as total solids. Normally there is excellent agreement between refractometer readings of total solids and biuret estimation of total protein concentrations in domestic species (12). The literature on correlation for avian biuret plasma protein concentrations compared with total solid estimation varies, and some studies showed good agreement (chicken, turkey, duck) (1, 22), whereas one study in pigeons showed poor to no agreement that was attributed to interference by high concentrations of other refractive compounds in plasma, such as chromagens, lipids, and glucose (16, 20). The exact cause of the difference is not known. Physiologically, the higher total protein concentrations estimated by refractometry appear to make sense. This aspect needs further investigation.

We did not measure plasma urate concentration in the pigeons. Failure to account for the urate concentration in plasma could theoretically lead to an error in estimating SID, because the p*K*_{a} of uric acid is 5.6; urate, therefore, is categorized as a strong anion at physiological pH (8). However, the serum urate concentration in birds is <0.8 mmol/l, with the normal range for *Columba livia* (pigeon) being 0.15–0.77 mmol/l (16). The plasma urate concentration is, therefore, quantitatively small relative to the measurement error in SID and can, therefore, be ignored.

In conclusion, application of the experimentally determined values for [A]_{tot}, *K*_{a}, and net protein charge of pigeon plasma should improve our understanding of the mechanism for complex acid-base disturbances in critically ill pigeons.

## GRANTS

Funding for this project was obtained from Pet Trust Ontario Veterinary College, University of Guelph, Guelph, Canada.

## Footnotes

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked “

*advertisement*” in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

- Copyright © 2006 the American Physiological Society