The Relation between the Ultrafiltrable Calcium Fraction and Blood pH and Concentrations of Total Plasma Calcium, Albumin, and Globulin

Department of Clinical Biochemistry, Flinders Medical Center, South Australia 5050, Australia
^a author for correspondence: fax 61-8-8374-0848, e-mail malcolm.cochran{at}flinders.edu.au

With the advent of various micropartition systems, typically as developed by Amicon, it became simple to ultrafilter serum and to obtain an apparent measure of the ultrafiltrable calcium fraction (UFCa). In studies of this type, evidence of strict monitoring of serum pH, known to affect calcium binding, was not generally reported (1)(2)(3)(4). An earlier study (5), attempted to control temperature and PCO₂, but in our hands the study was difficult to reproduce (unpublished). We have determined the UFCa values of 54 samples of whole blood at 37 °C at or near physiologic pH and sought an empirical relationship with more readily measured biochemical variables, which might enable us to predict UFCa from routine laboratory results. We were particularly interested in data in mild renal failure.

Although any aqueous solution is subject to control by the Henderson-Hasselbach relation, the relatively low pK (6.1) means that the buffering capacity near pH 7.4 is poor. Furthermore, modest changes in the PCO₂ have a minor effect on the HCO₃ concentration, for a marked effect on the pH. We found that the buffering capacity of whole blood allowed confidence in our procedure because the pH remained stable during handling. The Millipore® UFU 4 system allowed lateral filtration without the erythrocytes obstructing the membrane such that an ultrafiltrate of whole blood could be obtained.

We used Millipore UFU 4 10KNML systems, shortened to 20 mm by cutting off part of the upper reservoir. Initially, we loaded 1 mL of plasma, but in our final work, we used 1 mL of heparinized venous blood. In pilot experiments, we took 1-mL aliquots of a pooled serum sample (five specimens) and altered the pH by adding 0.1 mol/L HCl or 0.1 mol/L NaOH. The volumes added were 100, 80, 60, 40, 20, or 0 µL of HCl, respectively, and 20, 40, 60, or 80 µL of NaOH. When necessary, the added volume was made up to 100 µL, in each case with 0.1 mol/L NaCl. The starting pH was checked and ultrafiltrates were obtained without gassing.

We then took 1-mL portions of four gassed heparinized blood samples (see below) and observed the pH at 37 °C over 3 min while the samples were exposed undisturbed to air. We compared this with plasma from the same samples, treated likewise.

Our final approach was to rotate the blood sample in the collection tube, angled almost horizontally, in an electrical heating block at 37 °C, passing over it a mixture of 5.66% CO₂ and 4.64% O₂ in nitrogen for 3 min. The blood was transferred to the Millipore filter, which sat in a plastic serum tube shortened to 18 mm, and this in turn was put in the steel centrifuge tube, similarly warmed. A specially made nylon cap, with two small holes, plugged the top of the steel centrifuge tube, and the same gas was passed slowly through the system for 3 min, venting through the cap. The holes were sealed, and the sample was centrifuged at 1000g for 10 min in a fixed angle Centra-3® centrifuge (IEC) placed in an incubator at 37 °C; ~100 µL was thus obtained for estimation of calcium (UFCa). To test reproducibility, we used five blood samples, each divided into five portions. We obtained plasma from the same blood samples and ultrafiltered the corresponding 25 portions in an identical way to allow comparison.

We analyzed, in this way, 54 samples from patients chosen to include cases of mild renal failure. The pH, PCO₂, and ionized calcium (Ca²) of the gassed heparinized venous whole blood were measured before ultrafiltering. After filtering, the pH and PCO₂ in the residual blood (~90% of initial volume) were remeasured. The calcium concentration of the ultrafiltrate was determined using a Hitachi Boerhinger Mannheim 917 Automatic Analyzer (Hitachi).

The pH, PCO₂, and Ca² were measured in a Radiometer ABL 620 (Radiometer Medical A/S). A portion of each blood sample had been separated previously to allow estimation of plasma concentrations of total calcium (TCa), magnesium, phosphate (P), bicarbonate, sodium, potassium, chloride, albumin, total protein, and creatinine in the Hitachi 917. The ion gap and globulin were calculated. The [H] was calculated directly from the pH and was assumed to be H activity.

Statistical analysis used SPSS.

In pilot experiments, we confirmed that the UFCa from a sample of serum increased in a curvilinear fashion as the pH decreased from 7.77 to 6.87. Near the physiologic range, an ~1.2% change in UFCa resulted from each 0.02 pH unit change. When whole blood was exposed to air for 3 min, there was no measurable change in pH, but plasma became steadily alkalotic, with a >10% fall in [H] over 30 s and a >25% fall over 3 min. Measurement of calcium in ultrafiltrates of blood and plasma gave almost identical precision, the CVs being 1.28% and 1.31% respectively, but blood yielded significantly higher UFCa values, 1.06 ± 0.04 times greater (P <0.05). After the centrifugation process, the pH of blood had increased slightly but significantly, the initial mean pH 7.39 increasing to pH 7.42 afterward (P <0.0001), and the PCO₂ was comparably lower (mean of 39.4, falling to 35.6 mmHg).

Among the 54 samples, creatinine ranged from 0.052 to 1.055 mmol/L (mean, 0.260; median, 0.153); TCa from 1.96 to 2.80 mmol/L (mean, 2.34; SD, 0.204); UFCa from 1.18 to 1.68 mmol/L (mean, 1.41; SD, 0.125); Ca² from 1.0 to 1.36 mmol/L (mean, 1.20; SD 0.092); pH from 7.19 to 7.54 (median, 7.39) converted to [H] from 29 to 64 nmol/L (mean, 41; SD, 7.1); albumin from 17 to 44 g/L (mean, 34.3; SD, 7.8); and globulins from 17 to 53 g/L (mean, 35.1; SD, 6.8).

We used UFCa as the observed variable and regressed this on the other measured variables as predictors, except for magnesium, which was considered separately. We thought that the most useful predictors were likely to be TCa, albumin (alb), globulin (glob), and [H], but that ion gap or phosphate might represent complexing radicals. Using TCa, alb, glob, and H, we obtained:

The P value of each of the coefficients was <0.0005, except for glob, which was <0.005.

Including ion gap or phosphate contributed nothing useful. Excluding glob reduced the correlation, r= 0.647, and increased the value of the constant. Using HCO₃ as a surrogate for H only slightly decreased the significance of the 4-variable equation, r = 0.705; but the constant, which also carried a large variance, became a major determinant (0.647 mmol/L). We obtained the same 4-variable equation when we used SPSS to build the optimal relationship by systematically rejecting variables with nonsignificant partial correlation coefficients or by adding in predictors and accepting the simplest, most significant correlation. The standardized coefficients (beta) yielded values of 1.08 for TCa, -0.60 for alb, 0.38 for H, and -0.22 for glob.

When we used our equation to predict a UFCa value for each case and obtained the difference between observed and predicted, these residuals were scattered randomly when plotted against the predicted UFCa.

Because we had measured the [Ca²] directly, we could also test the ability of the data to predict this value. We found the optimal equation was:

All P values of the coefficients were <0.0005. Inclusion of glob decreased the significance of the overall equation and, furthermore, introduced a substantial value for the constant. Similarly, we could see how [Ca²] was related to UFCa. We found:

When Ca²was used to predict UFCa, taking the iongap into account, the equation was:

The P values of the coefficients were <0.0005 for Ca² and <0.01 for the ion gap. The constant was not significantly different from zero. The standardized coefficient (beta) for Ca² was 0.752 and for ion gap was 0.240. The effect of pH should have been implicit in the [Ca²] and including [H] was of negligible benefit to the equation.

The parathyroid responds, albeit weakly, to Mg²; therefore, it was possible that this ion would influence the setting of the Ca² and, indirectly, the UFCa. However, incorporation of Mg (mean, 0.85 mmol/L; SD, 0.15) into our partial analyses had no helpful influence on any regression coefficients that we tested.

Knowledge of the calcium filtered at the glomerulus would be important in understanding renal calcium physiology, which is why we had set out to find an empirical relationship between the UFCa and commonly measured variables.

Near pH 7.4, the concentration of trivalent phosphate, which binds calcium predominantly, is low (6), and moreover, this concentration decreases sensitively as pH falls. Thus, any potential effect of phosphate on the UFCa might have been nullified in samples where there was acidosis. Magnesium did not appear in the analysis as an influence on either the UFCa or Ca².

The use of whole blood ensured good control of pH during the procedure, although a small decrease in PCO₂ was seen. We could not explain this by leakage of gas from our system nor by oxidation of the metal holder. It would be expected that the erythrocytes would continue to take up the CO₂ via carbonic anhydrase and also as carbamate, given the low O₂ atmosphere. We can only speculate as to the cause of our finding that plasma ultrafiltered by the same procedure always gave a slightly lower UFCa value.

The UFCa was approximated as the Ca² plus a constant, as would be expected. The variability of this constant obviously would have reflected the range of concentrations of dissociated, filterable moieties, such as calcium citrate, bicarbonate, and phosphate, which are crudely represented by the ion gap. More surprisingly, the Ca² was not as good a predictor of the UFCa as TCa. The standardized coefficients for [Ca²] and ion gap were both inferior to those for TCa. However, given the merit of its simplicity, Ca² and ion gap might be considered more practical predictors of UFCa than TCa, proteins, and arterial pH. Although the standardized venous [Ca²] of the ion-sensitive electrode would not exactly correspond to the fraction in arterial blood pH that would determine the glomerular UFCa, in practice it is likely to be a satisfactory approximation.

Nordin et al. (7) devised an ingenious way of predicting both UFCa and Ca², using data obtained in a large series of healthy middle-aged women (7). Our observed values (as X_UF or X_Ca) reasonably predicted that obtained from his iterative method (as Y_Nor), although with a rather high degree of uncertainty (r):

The difference is easily explained. First, the hypothesis of Nordin et al. (7) depends on Ca², which is the major component of UFCa, being held stable in a healthy population, whereas in renal failure it is likely to be variable. Second, at values <24 mmol/L, HCO₃ in our series was a surrogate for [H]. We could not assume an unaffected pH and simply regard HCO₃ as a possible complexing agent.

In fact, it is impossible to determine the true glomerular UFCa without micropuncture, because the average glomerular capillary protein concentration is higher than in peripheral plasma as a result of the continuous loss of filtered plasma water. Nevertheless, our equation does allow the arterial pH to be taken into account, which avoids approximations from empirical ultrafiltration procedures, whether they were carried out in a standardized physiologic atmosphere or not. We found that the influence of increasing protein concentration was twice that of lowering the [H]. Given that the average increase (8) in protein concentration in the glomerulus is ~10%, our estimate might be systematically increased. However, the Donnan effect counters much of this and probably obviates need for correction (9)(10).

From the results, we have therefore developed a relatively simple equation to predict the UFCa within ± 0.12 mmol/L at 95% confidence from commonly estimated biochemical variables. We plan to see whether our method to calculate UFCa, which requires the concentrations of total Ca, alb, glob, and arterial blood pH, will provide a tool to give insights into the altered tubular handling of calcium in early renal failure.

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