Abstract
The determination of O_{2} consumption by using arteriovenous O_{2} content differences is dependent on accurate oxyhemoglobin saturation measurements. Because swine are a common experimental species, we describe the validation of COoximeter for porcinespecific oxyhemoglobin saturation. After developing a nonlinear mathematical model of the porcine oxyhemoglobin saturation curve, we made 366 porcine oxyhemoglobin saturation determinations with a calibrated bloodgas analyzer and a porcinespecific COoximeter. There was a high degree of correlation with minimal variability (r ^{2} = 0.99, SE of the estimate = 5.2%) between the mathematical model and the porcinespecific COoximeter measurements. BlandAltman comparison showed that the COoximeter measurements were biased slightly lower (−0.4 vol%), and the limits of agreement (±2 SD) were 0.7 and −1.5 vol%. This is in contrast to a 10–20 vol% error if humanspecific methods were used. The results show excellent agreement between the nonlinear model and COoximeter for porcinespecific oxyhemoglobin saturation measurements. In contrast, comparison of the porcinespecific oxyhemoglobin saturations with saturations obtained by using human methods highlights the necessity of speciesspecific measurement methodology.
 COoximetry
 oxyhemoglobin
 mathematical modeling
experimental work in hemodilution, systemic hypoxia, hemorrhage, and ischemiareperfusion routinely produces low levels of oxygenation and extremely low hemoglobin saturations. To obtain accurate data on global and regional O_{2} delivery and consumption during these conditions, the ability to measure or calculate speciesspecific oxyhemoglobin (HbO_{2}) saturation is required. Because of the known differences between human hemoglobin and that of other animal species used for scientific study, companies have developed COoximeter coefficient sets specific for some laboratory animals. As with other mammals, porcine hemoglobin has a significant sequence difference from human hemoglobin (57,19). These sequence differences alter the functional properties of hemoglobin and change the electrostatic interactions that modulate the O_{2} affinity (24). Subsequently, there is a difference in the HbO_{2} saturation characteristics of porcine and human blood as demonstrated by the decreased O_{2}affinity of porcine hemoglobin and the resulting increased 50% saturation with molecular oxygen (P_{50}) (2, 4,11, 15, 16, 22, 25). As with dogs and rats, this hemoglobin sequence difference results in differences in absorbance coefficients for the hemoglobin species at the specific COoximeter wavelengths. Thus relying on a human or other animal coefficient sets for the determination of HbO_{2} saturation will result in data that are not accurate. Although speciesspecific COoximeters are available for humans, dogs, and rats, the validation of an accurate porcinespecific COoximeter for laboratory use is currently lacking. To resolve this deficiency, we compiled laboratory hemoglobin saturation data that had previously only been used in classic Hill plots to graphically estimate the P_{50} of porcine hemoglobin (10, 15). These data were used to generate a descriptive mathematical model of the complete porcine HbO_{2}dissociation curve. In addition, using fresh porcine blood samples, Instrumentation Laboratories (IL) independently generated a porcinespecific coefficient set for direct measurement of HbO_{2} saturation using the IL 682 COoximeter. Subsequently, using fresh porcine blood obtained from instrumented anesthetized swine, we determined the HbO_{2} saturation determined by using the porcinespecific COoximeter and the HbO_{2}saturation calculated by using the porcine mathematical model. The agreement of these independent methods of porcine HbO_{2}saturation was compared with the HbO_{2} saturation determined by using a humanspecific HbO_{2} saturation methods. These studies highlight the potential for significant systematic error when incorrect measurement methodologies are applied to different species.
MATERIALS AND METHODS
Mathematical modeling of the porcine and human HbO_{2}dissociation curve.
Porcine HbO_{2} saturation data generated by polarographic methods were combined with those generated by spectrophotometric methods for the generation of a mathematical models describing the full porcine HbO_{2} saturation curve. We compiled a database with a total of 213 porcine HbO_{2} saturation data points from 19 separate experimental series: 141 data points came from young adult porcine blood with normal 2,3diphosphoglycerate levels in which hemoglobin saturation was measured by spectrophotometric methods (15), and 71 of the HbO_{2} saturation data points were generated polarographically (4). Although the HbO_{2} saturation data were measured differently, the experimental methods in terms of incubation and equilibration with O_{2}, Pco _{2}, pH, and temperature (37°C) were identical. Thus the data were combined to mathematically model the complete O_{2} dissociation curve. Furthermore, there were 34 HbO_{2} values from 11 experimental series determined spectrophotometrically and 18 values determined polarographically from eight experimental series at the critical hypoxic range (Po _{2} = 0–25 Torr). Each of the 19 experimental series was assigned one zerosaturation value at an assumed Po _{2} = 0. The database also contained 6 values for Po _{2} ≥ 98 Torr (4).
Because O_{2} saturation of hemoglobin as a function of Po
_{2} is sigmoidal and can be described as a nonlinear rectangular hyperbola with cooperativity, we used a general nonlinear rectangular hyperbola mathematical model with an exponentiated variable to account for the sigmoidal nature of the HbO_{2} saturation (S) relationship (8). This model yielded an equation in the following general form
The mathematical model of the human HbO_{2}dissociation curve was derived from 135 single or mean observations relating Po _{2} and hemoglobin saturation in human blood at 37°C and pH 7.4 (2, 4, 9, 16, 18, 23).
IL 682 COoximeter coefficient determination for porcine blood.
Heparinized whole blood was obtained from Yorkshire swine (30–35 kg) and shipped overnight on ice to IL, where it was prepared for the determination of the porcine coefficient set for the IL 682 COoximeter. The animal coefficient set is an inverse 4 × 4 matrix of the relative absorption coefficients for the porcine blood at the IL 682 measuring wavelengths (535, 585, 594, and 626 nm). In brief, IL personnel used standard validated laboratory procedures (on file at IL) to produce and measure porcine blood samples that consisted of 100% HbO_{2}, 100% deoxyhemoglobin, 100% methemoglobin, and 100% carboxyhemoglobin. From these samples, IL determined the coefficient set for swine, which was subsequently programmed into the IL 682 COoximeter.
Construction of in vitro porcine HbO_{2} dissociation curve.
Gas tanks of 100% N_{2}, O_{2}, and CO_{2}were connected to a Cameron Instruments (CIC) gasmixing flowmeter that delivered the watersaturated gases in desired proportions to a CIC dual equilibrator (Cameron Instruments, Brownsville, TX). Six Yorkshire swine were used on separate days for these experiments. In preparation, they were anesthetized with halothane, intubated, and ventilated to maintain the arterial Pco _{2} at 40 Torr. After percutaneous placement of a 20gauge femoral arterial cannula, 3ml fresh heparinized blood samples were obtained and immediately added to each of the spinning chambers of the equilibrator. The equilibration conditions in the CIC dual equilibrator were targeted at 37.0°C, pH 7.40 (balanced by the addition of NaHCO_{3} or HCl), and a Pco _{2} of 40.0 Torr. The blood samples were equilibrated over a range of gas flows for N_{2}and O_{2} in a stepwise manner to produce Po _{2} ranging from 0 to 500 Torr. At each step, the blood samples were equilibrated for 3–5 min before 1 ml was withdrawn and analyzed on an IL 682 COoximeter programmed with porcine coefficients and a calibrated IL 1610 bloodgas analyzer. As the equilibrated samples were consumed from each chamber over 20–30 min, the blood in the equilibrating chamber was replenished with fresh heparinized blood from the anesthetized swine. After the final measurements at no O_{2} flow, complete deoxygenation was ensured by the addition of 20 mg sodium dithionite. Fresh human blood samples were used in similar methods to measure HbO_{2}saturation on an IL 682 programmed with human coefficients at Po _{2} levels ranging from 20 to 120 Torr. These measurements were used as a validation data set for the human mathematical modeling.
Statistical analysis.
Data are presented as means ± SD. The linear regression analysis was used to determine the correlation between the IL 682 porcine hemoglobin saturation and the mathematical modelpredicted porcine saturations. Agreement between saturation measurements made by the IL 682 COoximeter and the porcine HbO_{2} saturations predicted by the mathematical model were evaluated by use of BlandAltman analysis (1, 17). In this analysis, the mean of the two measurements is plotted against the difference in the measurements. The limits of agreement of the two techniques is reported as the mean difference ± 2 standard deviations of the mean difference.
RESULTS
Mathematical modeling Hg dissociation curves using data sets.
At pH 7.4, 37°C, the following basic porcine HbO_{2}dissociation equation was obtained from the porcine data points (n = 213)
The descriptive modeling of the adult human O_{2}dissociation curve on the 135 published measurements performed at 37°C and pH 7.4 yielded the following equation
Po_{2} predicted and measured HbO_{2}saturation data.
We performed 366 separate porcine HbO_{2} saturation determinations on the IL 682 COoximeter. The temperature maintained in the dualchamber equilibrator was 37.1 ± 0.1°C. The Po _{2} values measured by the IL 1610 ranged from of 639 to 0 Torr. The measured pH was 7.41 ± 0.03, and Pco _{2} was 39.8 ± 0.08 Torr.
Figure 1 compares measured (IL 682 COoximeter) HbO_{2} saturation with the corresponding calculated hemoglobin saturations from the measured Po _{2} (IL 1610) for both porcine and human mathematical models. At a Po _{2} > 100 Torr, the human and porcine HbO_{2} dissociation curves are essentially identical. However, as the Po _{2}declines below 80 Torr, the IL 682 COoximetermeasured and the mathematical modelpredicted porcine HbO_{2} saturations are noticeably shifted to the right of the predicted human HbO_{2}saturations. Thus the porcine HbO_{2} saturation decrease more rapidly, resulting in a P_{50} at ∼33 Torr compared with the predicted human P_{50} of ∼26 Torr.
Figure 2 shows porcine HbO_{2}saturation measured with the IL 682 COoximeter with the HbO_{2} saturation calculated from the measured Po _{2} using the porcine and human model. When measured porcine HbO_{2} saturations are compared with saturations predicted by the porcine mathematical model, there is an extremely high degree of correlation between the data with minimal variability (r ^{2} = 0.99, SE of the estimate = 5.2%). Comparing measured HbO_{2} saturations with saturations predicted by the mathematical model of the human HbO_{2} saturation curve revealed a nonlinear pattern of correlation throughout the range of hemoglobin saturations in which measured porcine saturations were consistently lower than those predicted by the human mathematical model.
Figure 3 compares hemoglobin saturation differences with the use of porcine HbO_{2} saturation data obtained from the IL 682 COoximeter and the differences in that data with saturations predicted from the Po _{2} by the mathematical models in a BlandAltmanstyle plot. Figure 3 shows that, over the range of saturation measurements, IL 682 measurements were biased slightly lower (mean Hg saturation bias = −0.4%), and the limits of agreement (±2 SD) were 0.7 and −1.5%. In general, this shows a good agreement of the two methods for determining the O_{2} saturation of porcine hemoglobin. In contrast, the BlandAltman comparison of the IL 682measured porcine HbO_{2}saturation levels with the HbO_{2} saturation predicted by the human mathematical model shows an average overestimation of the percent porcine HbO_{2} saturation by the human HbO_{2}saturation model of 9.8 ± 6.6. Between HbO_{2}saturations of 60 and 30, these differences represent a 20–40% error in the saturation determination. These differences in the HbO_{2} saturation are significant because they occur at the physiologically relevant mixed venous O_{2} tensions of 40–25 Torr.
DISCUSSION
The important new information presented in this paper is the development of a convenient, but solely descriptive, mathematical model for nonlinear estimation of porcine HbO_{2} saturation and the agreement with a porcinespecific COoximeter for laboratory determination of fractional HbO_{2} saturation. We developed this as a descriptive nonlinear cooperative rectangular hyperbola that describes the saturation curve accurately at both extremely low and high Po _{2} as well as in the physiological Po _{2} ranges. Because this is an entirely pragmatic and descriptive approach, the model does not have implications for the regulation of O_{2} binding by hemoglobin. However, for the first time, our model describes the entire saturation curve accurately, both at extremely low and high Po _{2} as well as in the middle. This accurate description and measurement of porcine HbO_{2} saturation is important because swine are frequently used for experimental situations (hemodilution, systemic hypoxia, ischemiareperfusion, or resuscitation) that routinely produce extremely low or high blood oxygenation levels that result in extremely very low or near 100% hemoglobin saturations. To estimate with acceptable accuracy the delivery and consumption of O_{2} under such conditions, a complete HbO_{2} dissociation curve and measurement modality is required. The importance of accurate speciesspecific measurement techniques is demonstrated in the differences in the porcinespecific HbO_{2} saturation and saturation determined by use of humanspecific methods.
One other purpose of this study was to validate the IL 682 COoximeter for accurate measurement of porcine HbO_{2} saturation. The validation of the IL 682 measurements is based on a BlandAltman statistical method for evaluating differences in measurements obtained on the same samples by two different measurement techniques (1,17). This method evaluates the mean difference between the two methods over the range of interest (estimated bias) and the variability of the measurements (standard deviation) around the mean difference. The mean difference ± 2 SD is defined as the “limits of agreement.” If no significant differences in data outcomes are produced between the two measurements within the range of interest, the methods can be used interchangeably. Because the existing methods of measuring porcine HbO_{2} saturation are extremely time consuming, we modeled the entire adult human and porcine O_{2}dissociation curves on the basis of data compiled from the literature by using published data from Bartels and Harms (4) and both published and unpublished data from Kim and Duhm (15). This produced nonlinear cooperative mathematical models that were not based on the original Hill formula and are, therefore, purely descriptive. The models were nonlinear rectangular hyperbolas with positive cooperativity that described the HbO_{2} saturation for both adult humans and swine with high fidelity; they were also well defined at Po _{2} = 0 Torr and proved to be accurate at physiological extremes, i.e., both at low (<20 Torr) and high (>100 Torr) Po _{2} levels. We compared the predicted model data with directly measured values by using COoximetry. This validation produced essentially identical curves over the entire Po _{2} range of clinical and experimental interest. From Fig. 3 there is a close agreement of HbO_{2}saturation measured with the IL 682 COoximeter and the mathematical model of porcine HbO_{2} saturation. In addition, the limits of agreement (±1.1%, 2 SD) between the two methods would not be expected to cause any appreciable error in the calculation of O_{2} content or O_{2} consumption. Overall, the measured HbO_{2} saturation is slightly lower than the HbO_{2} saturation predicted by the mathematical model (−0.4% mean bias). However, this difference and the limited variability shown by the limits of agreement are experimentally and physiologically insignificant.
The main reason for the close agreement of these two different methods of porcine HbO_{2} saturation is related to the accuracy of the primary measurements. The measurements made by the IL 682 COoximeter are derived from the porcinespecific coefficient set stored in memory. This coefficient set is an inverse 4 × 4 matrix of the relative absorption coefficients at the measuring wavelengths of the IL 682 COoximeter. The IL 682 COoximeter uses this coefficient set and the absorption of the sample at the COoximeter wavelengths to calculate a fractional HbO_{2} saturation by dividing the HbO_{2} saturation by the sum (100%) of the oxy, deoxy, carboxy, and methemoglobin saturation. The coefficient set is derived from porcine blood by using standard techniques by IL personnel (data on file with IL). In brief, the absorption coefficients for oxy, deoxy, carboxy, and methemoglobin for porcine blood at the set wavelengths are determined by measuring a sample containing only one hemoglobin species. The absolute accuracy of the absorption coefficients for the individual hemoglobin is related to the assumptions made by IL in the protocols that generate the data for the calculation of the coefficients for the IL 682 COoximeter. Those protocols use fresh animal blood to generate “pure” hemoglobin species to determine the absorbance characteristics. However, pure deoxyhemoglobin is still potentially contaminated by the unknown small amount of carboxyhemoglobin in the fresh blood sample. The accuracy of the pure carboxyhemoglobin absorbance at the four wavelengths is limited by the amount of methemoglobin in the original sample. Finally, the accuracy of the absorbance characteristics of 100% HbO_{2} is limited by the small amounts of carboxy and methemoglobin in the fresh sample. Before calculation of the coefficient set, the IL protocols correct the saturation measurements for the residual levels of carboxy and methemoglobin. However, the polarographic and spectrophotometric experiential data used for modeling accounted only for oxy and deoxyhemoglobin and do not measure or modify for contamination by carboxy and methemoglobin. Although the small amount of these contaminants inherent in the fresh porcine blood has a small effect on the overall calculations, it does limit the absolute accuracy of the COoximeter and the original measurements by Kim and Duhm (15) and Bartels and Harms (4). Another potential small source of error in the measurement of the HbO_{2} saturation in the porcine blood is the use of HCl to correct the pH to 7.4. Because Cl competes for binding sites with 2,3bisphosphoglycerate and CO_{2}, it can decrease HbO_{2} affinity (20, 21). However, in this experiment the swine were anesthetized, ventilated, and maintained normothermic between arterial blood sampling. In addition, because the pH of the fresh arterial blood from the swine ranged between 7.39 and 7.42, pH correction was infrequent. Thus, although not fully documented, the impact of changes in the Cl content on the IL 682 measured HbO_{2} saturation was probably minimal.
The second purpose of this study was to estimate the error incurred, if human O_{2} dissociation curves are used in porcine experiments. There are substantial differences between the human and the porcine saturation data in the Po _{2} for venous blood samples. The magnitude of this difference is illustrated in the calculation of O_{2} content for regional or global O_{2} consumption. Because the HbO_{2} saturation is a major factor in the determination of O_{2} content [(1.34 · Hb · HbO_{2}saturation) + (0.003 · Po _{2})], the differences in the HbO_{2} saturation and thus the O_{2} content determined by using the human methodology for porcine HbO_{2} saturation can be quite large. On the other hand, the differences in calculated arterial O_{2} contact are small (0.5%) because the porcine HbO_{2} saturation is overestimated by the human methodology difference <0.5 vol% at Po _{2} levels >100 Torr. However, if the Po _{2} of the venous blood is 40 or 30 Torr, i.e., in the physiological range, the HbO_{2} saturation derived from human methods is overestimated by 11.0 and 15.9 vol%, respectively. This leads to an overestimation of the venous O_{2} content in the porcine blood with normal Hb levels (10 g/dl) by 1.5 and 2.1 ml/dl, respectively. In these examples, the systematic error leads to an underestimation in the arterialvenous O_{2} content difference by 30.3 and 27.5%, respectively. This error is further compounded by the multiplication of the arterial and venous O_{2} content difference by the flow rate in the calculation of either regional or global O_{2} consumption. In addition, if the HbO_{2} saturation measurements are used to calculate the cardiac output by the Fick method, erroneously high HbO_{2} saturation measurements determined for porcine blood by using humanspecific methods will result in a 45 and 43% overestimation in the cardiac output at venous Po _{2} levels of 40 or 30 Torr, respectively.
Acknowledgments
This work was supported in part by the Office of Naval Research, The Office of Research and Development, Medical Research Service, Department of Veterans Affairs, and the Walter Reed Army Institute of Research.
Footnotes

The opinions or assertions contained herein are the private views of the authors and are not to be construed as reflecting the views of the Department of the Army, the Department of Defense, or the Department of Veterans Affairs.

Address for reprint requests and other correspondence: P. D. Mongan, Dept. of Anesthesiology, Uniformed Services Univ. of the Health Sciences, 4301 Jones Bridge Rd., Bethesda, MD 20814 (pmongan{at}usuhs.mil).

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.

First published October 18, 2002;10.1152/japplphysiol.00710.2002
 Copyright © 2003 the American Physiological Society