High Accuracy Determination of Calcium in Blood Serum by Isotope Dilution Mass Spectrometry L. J . Moore and L. A. Machlan Analytical Chemistry Diuision, Institute f o r Materials Research, National Bureau of Standards, Washington, D.C. 20234
An isotope dilution technique utilizing thermal ionization mass spectrometry has been developed for the accurate determination of calcium in synthetic and serum samples at the 100 pg!g level. Calcium was separated from a serum matrix by destruction of the organic matter with HCIO, and HN03followed by ionexchange separation from interferences using AG 50W-X8 100-200 mesh resin. A mass spectrometric isotopic analysis procedure was developed using a Ca(NO& solution deposited on Re sample filaments in a triple filament thermal ion source. The relative error between calculated and experimentally determined concentrations in synthetic calcium solutions was 5~0.1%. The 95% limit of error for a single analysis was -0.2% for synthetic and serum samples. A comparison of the isotope dilution data with concurrently determined atomic absorption data from several clinical and independent laboratories is presented.
A DETERMINATIONOF THE AMOUNT of calcium present in blood serum is one of the most useful and commonly employed diagnostic tools available to a physician. A mutual interest in and need for a standardized method for the determination of calcium have prompted the National Bureau of Standards and several clinical laboratories to cooperate in a N B S - C h i cal Chemistry Interaction Plan designed to evaluate and improve the accuracy of interlaboratory calcium analyses ( I ) . As part of the Interaction Plan, the Analytical Mass Spectrometry Section was called upon to develop an isotope dilution method for the absolute determination of calcium in a series of synthetic and serum samples. Concurrently, several participating clinical and independent laboratories were asked to analyze the same series of samples using an analysis protocol based on a previously published atomic absorption technique ( 2 ) . The primary function of the isotope dilution work was to provide a nearly bias-free and independent set of calcium concentrations to be used as a reference point, or target value, for the concentration values generated by atomic absorption. A comparison of the atomic absorption data with the isotope dilution target values for each set of analyses was then used as a measure of the laboratories’ progress toward an interlaboratory atomic absorption method accurate to i1 %. Mass spectrometric isotope dilution has been proved a viable tool for the accurate determination of trace quantities of selected elements in a variety of matrices. Accuracies of 0.5 % [95 % limit of error (L.E.) for a single analysis] are routinely available with a minimum investment of analytical development time. A careful control of the various factors affecting the accuracy of isotope dilution trace analyses can result in state-of-the-art accuracies of 0.1-0.25 (95 L.E., or tu). For example, recent analyses in this laboratory of Pb, U , Th, and TI in the NBS Trace Elements in Glass (Standard Reference Materials 610-619) have shown that accuracies (1) J. P. Cali, J. Mandel, L. J. Moore, and D. S . Young, Nar. Bur. Sfa17d.(US.), Spec. Pirhi., 260-36, 1972. (2) J. Pybus, F. J. Feldman, and G. N. Bowers, Jr., Cliiz. Cliem., 16, 998 (1970).
of 0.25z are possible, even for concentrations less than 1 PPm (3). However, the accurate measurement of calcium isotopes has been experimentally difficult ( 4 , 5 ) . Attempts by previous investigators to make a direct measurement of the natural 40Ca/44Caratio have been limited to precisions 2 0.5 (tc),in addition to probable systematic errors of undetermined magnitude. Most such measurements were made on relatively simple systems of pure or slightly altered CaCO,, and the errors represent the ability to reproducibly measure the natural ratios and were not susceptible to systematic errors possible from chemical processing. Recently the technique of double spiking has been employed to indirectly measure the 40Ca/44Ca ratio of a CaCO, shelf standard and geological samples with a precision (presumably c) of 0.2% (6). The technique described here permits a direct measurement of the natural 40Ca/44Cato 2% over a 10-minute period. The 2 % change in ratio occurs simultaneously with the rapid increase in signal intensity, making an accurate ratio measurement experimentally difficult during the 10-20 minute interval. Thus the initial portion of the curve is poorly defined. Once the stable region is reached at -30 minutes, the ratio usually changes less than 0.1 % for a 40-minute analysis. The accuracy of the calcium isotope measurements is shown in Table I1 for SRM 915, C a C 0 3 . To take maximum advantage of the electrometer linearity, the l0Ca was measured a t -4 X IO-" A, which left the natural 43Caand 46Caintensities at -5 x 10-14 A and -8 x IO-l4 A, respectively. Thus the accuracy of their measurement is largely due to the error in the measurement of small signals. Difficulty was experienced in producing a distortion-free base line over eight mass units due to reflected ion beams in the instrument. An error of -0.1 x 10-lb A in the base-line measurement could result in an error of -1 part in 800 for the @Caand -1 part in 500 for the 3Ca. The small error introduced in the 4oCa/44Ca and 4*Ca/44Ca measurements by slightly inconsistent sample fractionation patterns is augmented by the error associated with the measurement of isotopes with large mass differences (10% for 40Ca- 4Ca). Also the 95% L.E. for the 40Ca/44Cawas calculated using only four degrees of freedom ( t = 2.776) and the resultant error limit of -0.19% is probably conservative. More recent refinements of the analysis procedure indicate that consistent 40Ca/44Cameasurements 50.1 % (95 % L.E.) should be possible with this technique. The range (0.08%) of the three independent spike calibrations shown in Table 111, which were determined for the last series of serum analyses, approaches the ultimate accuracy obtainable for the isotope dilution analysis of calcium. Synthetic Samples. Two sets of synthetic calcium solutions were analyzed. The results of the first set are shown in Table IV. The initial concentrations were calculated according to Equation 1 as pg/g and corrected for blank contribution. These values were then converted to milliequivalents of calcium per liter of solution by applying the experimentally determined density for each concentration level.
ANALYTICAL CHEMISTRY, VOL. 44, NO. 14, DECEMBER 1972
Table IV. Concentration of Calcium in Synthetic CaC03 Solutions, meq/liter Relative Sample Operator 1 Operator 2 Average Calculated error 1
4.093 4.072 4.071 4.066 4.071 4.075
4.083 4. 08ga 4.083 4.081 4.075 4.073
4.088 4,081 4.077 4.074 4.073 4.074
4.075
4.081
4.078
5.173 5.174 5.180 5.176 5.179 5 . 192a
5.180 5.183 5.187 5.180 5.183 5.192
5.177 5.178 5.183 5.178 5.181 5.192
5.179
5.184
5.182
41 60 60A 99 99A
5.867 5.859 5.867 5.875 5.852
5.874 5.876 5.870 5.865 5.867
5.871 5.868 5.869 5.870 5.859
Average
5,864
5.870
5.867
1A 20 20A 120 120A
Average 21 21A 61 61A 80
80A Average
95% L.E.
4.083
0.12
5.186
0.08
Table VI. Concentration of Calcium in Serum, meq/liter. Effect of Inhomogeneous Sampling Sample Isotope dilution 501-C 501-D 508-C 508-D 516-c 516-D
Isotope ratios determined in duplicate. Error estimated as plus or minus the range of individual aliquots. Sampling is the dominant error for these results. The 95% L.E. for the isotope dilution analysis of calcium is ?E0.20%, as shown in Table V.
Table VII. Concentration of Calcium in Bovine Serum, meq/liter Sample Isotope dilution 621 624 625
5.867
605 608 609
~ k 0 . 3 5 % ~& 0 . 2 2 z *
660 662 669
Average 215 215A 242 242A
203A 263 266
3.590
0.08
4.892
a
4.887
6.377
6.375
5.023 5.728 5.74P 5.729
Average
5.733
95% L.E. 1 0 . 2 1 z b Isotope ratios determined in duplicate. Error expressed as 95% L.E. for a single analysis.
0.10
6.374 6.369 6.388
Average
a
641 643 645
4.895 4.896 4.891 4.887
Average
95% L.E.
3.593
4.294 5.015 5.023 5 .032R
Average
3.593 3.591 3.594
3,570 4.294 4.293 4.294
Average
Table V. Concentration of Calcium in Synthetic CaC03 Solutions (Na and K Added), meq/liter Isotope Relative Sample dilution Calculated error 23 1 235 276
3.569 3.573 3.569
Average
0 .00
Isotope ratios determined in duplicate. Error expressed as 95% L.E. for a single analysis.
a
4.106 4.096 4.096 4.096. 4.136 4.14P Average 4.112 i 1.12zh3c
0.03
10.20%.
Error expressed as 95% L.E. for a single analysis.
The 95 % L.E. (tu) was calculated for each operator by ratioing each experimental concentration in a given concentration level to the average value for that level. The deviations from unity were then used to evaluate tu over all concentration levels using 16 degrees of freedom. A difference in the 95 2 L.E. between operators is a reflection of each operator’s ability to reproducibly control inter-analysis fractionation of the calcium isotopes. Although two independent sets of analyses are often useful in detecting systematic operator bias, there was no detectable bias and each operator’s values were averaged to obtain the final concentration value for each level. A comparison with the theoretical value calculated from gravimetric data shows a consistent absolute accuracy 5 -0.1 %.
Table V contains the results of the second set, which was a closer synthetic approximation to the serum samples and required the addition of an ion-exchange step to separate the sodium and potassium. The concentrations and the 95% L.E. of 0.20 were calculated as in the first series. A slight improvement in the operator’s ability to control isotope fractionation is reflected in the lower limit of error. In addition the absolute accuracy of 6 0 . 1 % is indicative that no systematic chemical bias was introduced by the addition of a n ionexchange step in the analytical procedure. Serum Samples. The first two sets of serum analyses performed during the Interaction Plan were alternately perturbed by erratic blank and sampling problems. Bacteriological action in the serum produced samples with suspended particulate matter that was filtered during sample withdrawal with the syringe. An example of the nonrepresentative sampling due to a n inhomogeneous sample is shown in Table VI. Three ampoules from one concentration level were subsampled in duplicate (C&D) and analyzed by isotope dilution. While ampoules 501 and 508 are internally and mutually consistent, they differ collectively from ampoule 516 (which is internally consistent) by -1 %.
ANALYTICAL CHEMISTRY, VOL. 44, NO. 14, DECEMBER 1972
2295
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1.0. 95% LE.
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95% 1.E.
I
11 T
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-4 CONEtNIYIlONI 2 3 I 2 3 1 2 3 1 2 3 1 2 3 1 2 3 I 2 3 LhBOMTORY
A
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F
H
CONCfNIRl~OMl231l231 1 2 3 1 1 2 1 1 1 2 3 1 1 2 3 1 1 2 3 1 LABOUTORI
A
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Figure 4. Relative error of AA analyses with respect to the isotope dilution (ID) values shown in Table IV for synthetic calcium solutions. Arrows indicate I.D. 95 % limit of error for a single analysis ( 1 0 . 2 %)
Figure 5. Relative error of AA analyses with respect to the ID concentrations shown in Table V for bovine serum samples. Arrows indicate I.D. 95% limit of error for a single analysis (i0.2 %)
Samples supplied by the CDC were analyzed to obtain the data shown in Table VII. A calculation of the 95% L.E. yielded +0.21%, as compared to the 95% L.E. of 1 0 . 2 0 %in the second series of synthetic samples. The blank for the serum samples was reduced to a negligible 0.03 of the total amount of calcium per sample. Comparison with Atomic Absorption Data. The expense, time, and technical expertise required for accurate isotope dilution analysis prohibit its widespread application as a routine tool for clinical calcium analyses. However, its efficacy as an absolute measure of the agreement among inter-laboratory atomic absorption (AA) analyses is illustrated in Figures 4 and 5. Data from the first synthetic analyses were used to calculate the relative error of the AA analyses by laboratories A through H as shown in Figure 4. Each pair of deviations represents the same ampoule (concentration level) analyzed separately a t one-week intervals. While no detailed statistical treatment of the deviations is presented here ( I ) , it is obvious that systematic biases and random errors of up to several per cent exist among the laboratories as well as with respect to the isotope dilution “true” value. Only one AA laboratory approaches the absolute accuracy of 0.1 available from isotope dilution.
Figure 5 illustrates similarly calculated relative errors of the AA data when compared to the I D data for the serum analyses of Table VII. Although no calculated serum concentrations were available for comparison with the experimental ID values, the 95 % L.E. remained constant at i 0 . 2 %. Thus the relative error for the average of each concentration level with respect to the “true” value should be -0.1 as for the synthetic samples. Fluctuation of the concentrations determined by AA by more than -0.1 % should therefore be detectable. As a comparison of Figures 4 and 5 reveals, several laboratories do exhibit apparent systematic shifts a t the 0.25 % level and above, which are easily detected by using the ID value as a reference.
2296
z,
ACKNOWLEDGMENT
The authors gratefully acknowledge the NBS Office of Standard Reference Materials for providing the atomic absorption data used for comparison. Acknowledgment is also given to J. R . Moody, T. J. Murphy, and K. M. Sappenfield for sample preparation and E. L. Garner and W. R. Shields for mass spectrometric assistance and discussion. RECEIVED for review May 30,1972. Accepted July 27,1972.
ANALYTICAL CHEMISTRY, VOL. 44, NO. 14, DECEMBER 1972
