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Technical Briefs |
1 Department of Pathology and Laboratory Medicine, Hartford Hospital, Hartford, CT 06102; fax 860-545-3733, e-mail rburnett{at}attbi.com
The measurement of P50 in whole blood, defined as the oxygen tension corresponding to 50% oxygen saturation, gives a quantitative measure of hemoglobin oxygen affinity. The determination of P50 is useful for screening for hemoglobin variants in cases of unexplained anemia or erythrocytosis, both because it is easily performed and because many hemoglobin variants with abnormal oxygen affinity are "silent", i.e., not detectable with conventional electrophoretic techniques (1).
The determination of P50 previously required obtaining several points on the oxyhemoglobin dissociation curve. The procedure was seldom performed because of the labor and specialized apparatus required. However, it was suggested >25 years ago that P50 could be accurately calculated from single measurements of oxygen tension (Po2) and the corresponding oxygen saturation (So2) (2). Since then, an improved mathematical model of the oxyhemoglobin dissociation curve (3) has been incorporated into a guideline for the so-called "single-point" determination of P50 (4) that has been tested (5)(6) and subsequently approved by the IFCC. The single-point approach is based on the fact that a plot of log Po2 vs log[So2/(1 - So2)], the so-called Hill plot, is linear over a fairly wide interval. Therefore, if one knows both the slope and one point on the line, any other point on the line can be determined.
There have been different recommendations for the interval within which the single-point method is valid. Some studies have suggested that it can be used for oxygen saturations as low as 20% (5). The original IFCC guideline (4) specified saturations in the interval between 40% and 80%, and a subsequent IFCC document on definitions of quantities used in blood pH and gas analysis (7) extended the upper limit to 90% saturation. To facilitate the calculation, many blood gas analyzers incorporate an algorithm for P50 into the internal microprocessor, so that P50 can be printed automatically if the measured saturation is within an interval preset by the manufacturer. These intervals are chosen to correspond to the region of the Hill plot deemed to be close enough to a straight line that P50 can be accurately estimated. However, a more rigorous error analysis has not been performed. In using the single-point method for P50 with healthy volunteers in our laboratory, we noticed that results were much less reproducible at oxygen saturations of 
20% than at saturations of 70% or 80%, which inspired us to analyze the P50 algorithm to quantitatively determine the sensitivity of a calculated P50 to errors in the measured Po2 and So2.
If z is a function of two variables (x and y), which are measured with uncertainties 
x and y, then an upper limit for z (the resulting error in z) is given by (8):
 | (1) |
where the first term is the error in z resulting from error in the measured value of x, and the second term is the error in z resulting from error in the measured value of y.
The equation for P50 adopted by the IFCC is:
 | (2) |
The IFCC algorithm also includes factors to adjust the observed P50 to standard conditions of pH 7.40 and Pco2 = 5.33 kPa (40 mmHg); this is necessary for the use of P50 to screen for hemoglobin variants. However, errors in the measured pH and Pco2 produce small second-order errors in the calculated P50 and are not considered here.
Performing the necessary differentiation of Eq. 2
gives the following equations for the error in P50 resulting from errors in Po2 and So2, respectively:
 | (3) |
 | (4) |
Eqs. 3 and 4 apply to both systematic and random errors.
In the case of random error, the quantities P50, Po2, and So2 may be replaced with the corresponding SDs. The random error in P50 resulting from the combination of errors in Po2 and So2 is less than implied by Eq. 1
because the random errors will cancel each other to some extent. The expected random error is found by taking the square root of the sum of the squares of the individual components (8):
 | (5) |
A graphical representation of Eqs. 3, 4, and 5 for a normal P50 of 3.56 kPa (26.7 mmHg) is shown in Fig. 1A
; it was generated with representative estimates of random error in Po2 and So2 from our laboratory. The values used are 2 SD estimates of 0.23 kPa (1.7 mmHg) for Po2 and 0.02 for So2.
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The error curve for Po2 shows that the uncertainty in P50 increases steadily as Po2 decreases, as expected from the form of Eq. 3
and in accordance with our observations in the laboratory. When Po2 is equal to P50, the errors in the two quantities are also equal. On the other hand, the error curve for So2 shows that uncertainty in P50 increases at both high and low values of So2, and the minimum error is achieved when So2 is 50%, i.e., when Po2 equals P50. [Only Po2 values are shown on the abscissas in Fig. 1
to avoid clutter. Corresponding values for So2 were calculated from an expression for the standard oxyhemoglobin dissociation curve (3)].
The uppermost line in Fig. 1A
shows the random error in P50 as expressed by Eq. 5
. It is shown that, for the 2 SD error estimates chosen for Po2 and So2, the resulting uncertainty in P50 is minimized at a Po2 of 5.33 kPa (40 mmHg) where the 2 SD range is equal to approximately ± 0.2 kPa (1.5 mmHg).
Systematic error should also be considered. Eqs. 3 and 4 also apply to systematic error, but the error in P50 resulting from systematic errors in Po2 and So2 is found by simple addition rather than by the square root of the sum of squares. This will give a worst-case estimate. (It is assumed that the direction of a systematic error is not known because if it were, it could be corrected.) The systematic error in P50 that would result from a 0.13 kPa (1 mmHg) bias in Po2 and a 0.005 bias in So2 is shown in Fig. 1B
. The uppermost line shows the combined error, again assuming that the error components are in the same direction. With these assumptions, the minimum bias in P50 is 0.12 kPa (0.9 mmHg) at a Po2 of 6.3 kPa (47 mmHg), and the bias increases to >0.27 kPa (2 mmHg) at low Po2.
The expected total error in P50 resulting from the combination of these random and systematic components is shown in Fig. 1C
. The shapes of the error curves will change somewhat if different values are used for the estimated errors in Po2 and So2; we feel the data shown here represent reasonable estimates for the instruments used in our laboratory. With these assumptions, it is seen from Fig. 1C
that to minimize error in P50, the Po2 (and So2) of the sample need to be within a fairly narrow range. Specifically, the Po2 should be in the range of 4.0–7.3 kPa (30–55 mmHg), which corresponds to a So2 range of 58–88%. This upper limit is not significantly different from the most recent IFCC recommendation for single-point determinations (7), but the lower limit is higher than has been previously recommended. Although the Hill plot is linear well below 58% oxygen saturation, the error in calculated P50 increases rapidly below this point primarily because of the propagation of error in measured Po2. Fortunately, this does not present a practical problem in P50 measurement because venous blood drawn into an evacuated tube typically has a saturation of 
58%. If it does not, the saturation is easily increased by drawing the blood into a syringe and then drawing in some air and mixing well (4).
It is recommended that the following points be observed to minimize error in P50 determinations:
The value of P50 determined from an excellent mathematical model of the oxyhemoglobin dissociation curve under standard conditions of 37 °C, pH 7.40, Pco2 = 5.33 kPa (40 mmHg), and a 2,3-diphosphoglycerate concentration of 5.0 mmol/L is 3.56 kPa (26.7 mmHg) (3). Considering the total error curves in Fig. 1C
, we feel a prudent estimate of the 95% confidence interval in our laboratory is ± 0.4 kPa (±3 mmHg), which makes our reference interval 3.16–3.96 kPa (23.7–29.7 mmHg). This is in good agreement with the reference interval proposed by Kwant et al. (5), but is wider than suggested in the IFCC guideline (4). Much of the observed variation in P50 values in reference populations probably results from random and systematic errors in the measurement procedure, although interindividual variation in 2,3-diphosphoglycerate concentrations in blood also contributes. Ideally, as suggested in the IFCC guideline, each laboratory should determine its own reference interval for P50. Alternatively, an error analysis can be performed in the manner described here to estimate a lower bound for a 95% confidence interval.
References
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) and PO2 (
). Top curve (•) shows the random error from both sources combined. (B), error in P50 resulting from systematic error in measured SO2 (