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Anal. Chem. 1983, 5 5 , 1098-1103
LITERATURE CITED (1) Rigamonti, R.; Marchettl, S. Aft/ Accad. Scl. Torlno, Cl. Scl. Fls., Mat. Nat. 1959,9 4 , 25. Chem. Abstr. 1963, 59, 14644e. (2) Berg, E. W.; Lau, E. Y. Anal. Chlm. Acta 1962,2 7 , 248. (3) Khan, M. A.; Morris, D. F. C. Chem. Ind. (London) 1968, 1802. (4) Iqbal, M.; Ejaz, J. J . Radloanal. Chem. 1975,27, 15. (5) Mojski, M. Talanta 1978, 25, 163. (6) Senlse, P.; Pitombo, L. R. M. Talanta 1964, 1 1 , 1185. Kiba, T.; Kiba, T. Bull. Chem. SOC.Jpn. 1970,4 3 , 2063. (7) Akaza, I.; (8) Mojski, M. Talanta 1960,2 7 , 7 . (9) Nlcolas, D. J. Rep.-Natl. Inst. Metall. (S.Afr.) 1974,Project no. 01374, 5th Dec. (10) Zoiotov, Yu. A.; Petrukhin, 0. M.; Shevchenko, V. N.; Dunlna, V. V.; Rukhadze. E. G. Anal. Chlm. Acta 1978, 100, 613. (11) Diamantatos, A. Anal. Chim. Acta 1973, 66,147. (12) Rakovskil, E. E.; Shvedova, N. V.; Berliner, L. D. J . Anal. Chem. USSR IEnal. Trans/.) 1974. 29. 1933. (13) Forsythe,:. H. W.; Magee,'R. J.; Wllson, C. L. Talanta 1960, 3,330. (14) Gregoire, D. C.;Chow, A. Talanta 1975,22, 453. (15) Berman, s. s.; McBryde, w. A. E. Can. J . Chem. 1958,36, 835. (16) Macnevin, W. M.; Crummett, W. B. Anal. Chem. 1953, 25, 1628.
AI-Bazi, S. J.; Chow, A. Talanfa 1982,2 9 , 507. Crowell, T. I.; Hanklns, M. G. J . Phys. Chem. 1969, 7 3 , 1380. Mason, W. R.; Gray, H. B. J . Am. Chem. SOC. 1968, 9 0 . 5721. Eiding, L. I.Acta Chem. Scand. 1970,2 4 , 1331, 1341, 1527. Elding, L. I.Inorg. Chlm. Acta 1978,28, 255. Swihart, D. L.; Mason, W. R. Inorg. Chem. 1970,9 , 1749. Hall, W. H.; Wilson, I. R. Aust. J . Chem. 1969,22,513. Mureinik, R. J. Inorg. Chlm. Acta 1975, 13, 127. (25) Hamon, R. F.; Khan, A. S.; Chow, A. Talanta 1982,29, 313. (26) Khan, A. S.Ph.D. Thesis, Chem. Dept., Univ. of Manitoba, 1982. (27) Mureinik, R. J.; Robb, W. Spectrochlm. Acta, Part A 1966,24A, 837. (28) Vorlicek, J.; Dolezal, J. 2. Anal. Chem. 1972,260, 369. Chem. Abstr. 1972, 7 7 , 1348282. (29) Jorgensen, C. K. Mol. Phys. 1959,2,309. (30) Ishida, K.; Kiriyama, T.; Kuroda, R. Anal. Chim. Acta 1968,41, 537. (17) (18) (19) (20) (21) (22) (23) (24)
RECEIVED for review December 22, 1982. Accepted February 8, 1983. This work was supported by the Natural Science and Engineering Research Council of Canada.
Automated System for the Absolute Measurement of Oxygen in Whole Blood Justin S. Clark" and Ming-Cheng Yen' Primary Children's Medical Center, 320 12th Avenue, Salt Lake City, Utah 84 103
A modlfled amperometrlc method for measurlng oxygen content In whole blood, which achleves absolute measurement accuracy equal to that of the Van Slyke manometrlc method, Is described. Absolute measurement accuracy Is achleved by an oxygen sensor nulllng technique that ellminates the influence of the characterlstlcsof the sensor from the oxygen measurement. The method is also characterized by a slmpllfylng continuous flow proportlonlng feature, which Improves the accuracy and reliablllty of the method by ellmlnatlng the requlrement of blood and dlluent volume meterlng by the operator. The results of a palred sample study showed no statistical dlfference between thls and the Van Slyke methods (mean dlfference = 0.005 vol % and standard devlatlon = 0.35 vol %). The advantages of thls method over the Van Slyke are malnly those provided by the design simplicity, which lends itself to microprocessor control. Those advantages Include ( 1) operator Independent accuracy and precldon, (2) reduced measurement tlme (4.5 mln), and (3) small sample slre (0.4 mL whlch can be reduced much further).
The manometric method, introduced by Van Slyke and Neil1 in 1924 (I), is an absolute method and the accepted standard for measuring oxygen content in blood. Oxygen is chemically released from hemoglobin and extracted in a vacuum space where it is brought to a chosen volume. The total pressure of this volume is measured. The oxygen is then chemically removed from the gas phase; the total pressure of the gas phase with oxygen absent is remeasured and subtracted from the previous measurement. The volume a t standard conditions corresponding to this pressure difference is calculated by use of the standard gas laws. The method is quite reproducible; however, it has been criticized for a 'Present address: Department of Anesthesiology, 3C 205, University of Utah Medical Center, Salt Lake City, UT 84112.
number of shortcomings (2-4)which include: (1) time requirement (15 min) for each determination, (2) tediousness of the procedure, and (3) extensive skill and experience requirement of technicians. The development of the galvanic method (5) in 1961 was directed toward eliminating the shortcomings of the Van Slyke manometric method. The galvanic method uses a galvanic cell to reduce the oxygen which has been driven out of the blood into the gas phase. Because the reduction process of the galvanic cell is specific to oxygen, the integral of the current output is a direct measure of the total oxygen reduced. If all blood oxygen were reduced by the galvanic cell, the method could rightly have absolute method status having an equal or better position than the manometric method. In practice, however, design constraints apparently have not permitted such an instrument to reduce all the oxygen; the integrated output of the galvanic cell is dependent on the rate of oxygen delivery to the cell (6). The method therefore relies on calibrations and must accept the systematic differences which can exist between calibration and measurement. The amperometric method was first introduced by Baumberger (7) in 1940;however, its practical implementation had to await the membrane covered amperometric sensor developed by Clark in 1956 (8). The principle of the amperometric method differs from both the manometric and galvanic methods in that oxygen, rather than being driven chemically from the hemoglobin into the gas phase for measurement, is instead driven from the hemoglobin into a water-based diluent where it exists as physically dissolved oxygen. The blood oxygen content is therefore directly determined from the concentration of physically dissolved oxygen which is measured by an amperometric electrode. As with the galvanic method, the amperometric method was developed and promoted as a method which eliminated or reduced the shortcomings of the Van Slyke manometric method. Analysis times have been reported between 3 and 6 min (9, IO), and there is less operator dependence. However, the reported methods rely on the calibration of the oxygen elec-
0003-2700/83/0355-1098$01.50/00 1983 American Chemical Societv
ANALYTICAL CHEMISTRY, VOL. 55, NO. 7, JUNE 1983
trode and, like the galvanic method, must accept the possibility of systematic differences between calibration and measurement. The problem of making absolute measurements with electrodes was addressed by Malmstadt and Pardue (11)who in 1961 reported a nulling technique for a potentiometric method for the measurement of glucaee. The method employed similar electrodes sensitive to the same species in contact with the sample solution and a reference solution, respectively. The concentration of this species of the reference solution was adjusted to maintain a null potential between the two electrodes. In 1962, Blaedel and Hicks (12) described an instrument for measuring glucose which kept sample and reagent manipulation by the technician it0 a minimum through use of a flowing system. Then in 1965, Blaedel and Laessig (13) reported an automated continuous titrator which combined continuous mixing of the sample, buffer, and reagent with an electrode nulling principle using a single electrode. For achieving atbsolute accuracy, the single electrode approach has the obvious advantage over the dual electrode approach in that the single electrode is identical with itself regardless of changes in its characteristics. A potential disadvantage of the single electrode approach is that the comparison between the sample solution and reference cannot be made simultaneously but must be made serially, allowing some potential error in null detection due to sensor drift. Described in this paper is an automatic amperometric method for measurement of blood oxygen content which utilizes (1) continuous mixing of the blood sample with the reagent and (2) nulling of a single electrode by changing the oxygen concentration of the reference solution. Allowance is made for electrode drift during the nulling procedure. Arguments are presented to show that this method is equal or superior to the Van Slyke manometrilc method in terms of absolute accuracy.
THEORY This method, to be referred to as the flow proportioning method (abbreviated by FP), differs from previously reported amperometric methods for measuring oxygen content of blood in two principle aspects: 1. Volumetric dilution of the blood sample with carbon monoxide (CO) equilibrated saline (or a ferricyanide solution) is replaced by flow proportioning, a continuous process in which blood and CO equilibrated saliine are independently pumped by a common junction where mixing occurs prior to entering an oxygen sensor. The mixing ratio is equal to the ratio of saline flow to blood flow. 2. Measurements1 of oxygen partial pressure of the blood/saline mixture by a calibrated oxygen sensor are replaced by a nulling technique in which the oxygen sensor is used to indicate matching between the oxygen partial pressure of the blood/saline mixture and saline whose oxygen partial pressure is known and controlled to provide the match. P r i n c i p l e of Oper,ation. The principle of the FP method is presented in Figure 1. Blood is pushed anaerobically by a pump past the junction T after having been placed in the blood reservoir. Saline at a flow rate 30 times higher than that of blood is pushed through tonometer I (where CO equilibration occurs) and past the junction T where mixing with blood takes place prior to entering the oxygen sensor. The sensor response to the blood/saline mixture corresponding to the middle portion of the blood sample (avoiding end contaminations) is stored by the microprocessor which then proceeds to prepare a saline sample that produces the same sensor response as that produced by the blood/saline mixture. The microprocessor accomplishes this task by producing through the gas mixer the desired gas mixture which is fed into tonometer I1 such that the saline in it contains the same
1099
SALINE
BLOOD RESERVOIR
Figure 1. Simpllfled dlagram of flow proportioning (FP) method for measuring oxygen content in blood.
oxygen partial pressure as that of the blood/saline mixture. The saline which is directed to tonometer I1 (with the valve activated) is pushed to the oxygen sensor at the same flow rate as that of the blood/saline mixture. The oxygen of this solution is measured and compared to the stored oxygen of the blood/saline mixture. If the difference in oxygen of these two solutions exists, the gas mixer is readjusted until the nulling of sensor reading is achieved. The oxygen fraction provided by the gas mixer at the null condition is the percent oxygen contained in the blood/saline mixture. Maintaining the same flow rate for the oxygen sensor is a precaution taken to ensure that for a given oxygen partial pressure, the response of the sensor to both solutions (the saline nulling solution and the 1/30 blood/saline solution which has an electrode response indistinguishable from saline) is identical. A second precaution is taken to correct for systematic differences due to any sensor drift occurring during the short interval between the blood/saline measurement and nulling process. Sensor drift, if present, is measured during the null procedure. M a t h e m a t i c a l D e v e l o p m e n t . At junction T, the mass balance of oxygen gives
CO,($B
+ Co,csPs = CO,(B/SPB+ Fs)
(1)
where Co,is the oxygen content in the unit of volume percent (vol %), F is the flow rate (mL/min), and the subscripts S and B refer to saline and blood, respectively. Since saline is saturated with carbon monoxide before mixing, CO,(s) is zero. Equation 1 thus becomes
By definition, the oxygen content of a diluent is equivalent to the product of the oxygen partial pressure and the oxygen solubility of that diluent. Substituting the oxygen solubility and the oxygen partial pressure terms into eq 2 gives
in which CO,(~) is the oxygen content of blood (vol %), A is the Bunson oxygen solubility coefficient of the blood/saline mixture, PO,is the oxygen partial pressure of the blood/saline mixture (mmHg), and FB and Fs are the flow rates of blood and saline, respectively (mL/min). (The factor 100 converts the content units from volume per volume to volume per 100 volumes, vol %I. At the null condition, the oxygen partial pressure of the blood/saline mixture is equal to the oxygen partial pressure of the gas mixer which is related to the oxygen gas fraction of the mixer Cfo,) and barometric pressure (BP) by Po, = fO,(BP - 47) (4) where 47 is the vapor pressure in mmHg of water a t the
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tonometer temperature of 37 "C. Substituting eq 4 into eq 3 gives
In order to establish the FP method as an absolute method, we now must show that eq 5 involves only physical measurements and physical constants. The flow rates FB and Fs and the barometric pressure are physical measurements which can be determined to the accuracy required by the oxygen content measurement. We will now show that the oxygen solubility (A) of the blood/saline mixture (with the presence of dissolved CO) contains two physical constants (flow rates and salt concentrations) which determine the value of A to an accuracy required by any practical oxygen content measurement. By mass balance, X is related to the blood saline oxygen solubilities and flow rates as follows (see Appendix
I):
where As and AB are the Bunson oxygen solubilities of saline and blood, respectively. Note that AB is the oxygen solubility of blood without oxygen hemoglobin binding. The oxygen solubility of saline As is determined by the following relationships given by Sendroy, Dillon, and Van Slyke (14): As = A, - 6C (7) in which A, is the Bunson oxygen solubility of water a t 37 "C (a physical constant), 6 is the solubility depression per unit concentration of sodium chloride (NaC1) in water a t 37 "C, and C is the NaCl concentration in moles per liter of water. For human blood, the ratio AB/As is so close to unity (i.e,, 0.98) (15) that a flow ratio FB/(Fs+ FB) equal t o 1/30 or less ensures that this term in eq 6 can be neglected. (Neglecting the term [FB/(Fs FB)](l- AB/As) affects eq 6 by less than 0.06% .) Eliminating this term from eq 6 and combining eq 5 , 6 , and 7 provide the final equation for calculating oxygen content
+
Equation 8 shows that the oxygen content measurement is determined by the physical constants A, and 6 as well as the fundamental measurements of flow, oxygen fraction (by gas mixer), barometric pressure, and knowledge of the salt concentrations of the saline diluent. Therefore, we conclude that the FP method should provide absolute measurement of oxygen content. EXPERIMENTAL SECTION Apparatus. A more detailed block diagram of the system is shown in Figure 2. A Gilson Minipuls 2 multichannel peristaltic pump (Gilson, Gilson Medical Electronics, Middleton, WI) provided the fast flow Fsand slow flow FB pumping operation. Since the flows from such pumps are not very precise, thermal flow measuring devices were placed in series with the pump channels. The outputs of these devices are monitored by the microprocessor. Calibration is accomplished volumetrically by timing the filling of glass pipets (5 mL and 0.2 mL) connected to the output of the waste line and the input of the blood injection port. Such calibrations are accurate to 0.1 %; however, electronic drift of the flow measuring devices reduced the accuracy to &0.5% when calibration intervals were reduced t o 24 h. The tonometers are comprised of six parallel Silastic Medical-Grade tubings (0.0635 cm 0.d. X 0.0305 cm i.d. X 63.5 cm length, Dow Corning, Midland, MI) contained in aluminum enclosures. Tonometer I is connected to the CO gas tank (Air Products, Allentown, PA) and tonometer I1 is connected t o the gas mixer. The gas mixer, developed for other purposes in this
Flgure 2. Detalled diagram of flow proportioning (FP) method for measurlng oxygen content in blood.
laboratory, has an absolute accuracy exceeding 0.05% (16). The blood reservoir and mixing coil are constructed from nylon tubing (0.0787cm i.d. X 0.165 cm 0.d.). The reservoir has a volume of 0.15 mL; the mixing coil has a volume of 0.3 mL. The oxygen sensor is a commercial electrode (Technicon PN 041-13039) housed in a stainless steel cuvette for efficient temperature control. The oxygen electrode, cuvette, mixing coil, and both tonometers are temperature controlled to 37 & 0.1 "C. The controller is a Mostek BO microcomputer system (Mostek, Carrollton, TX) with a 12 bit A/D converter (Burr-Brown SDM 853) and CRT (Infoton) key board terminal. System Operation. When the system is first turned on, it is initialized by entering the barometric pressure through the terminal and calling a microprocessor controlled two-point electrode calibration; slope and intercept calibration constants are calculated and stored. With the saline inlet to the blood injection port disconnected, a blood oxygen content measurement is initiated by manually injecting 0.4 mL of blood into the blood reservoir, followed by reconnection of the saline inlet to the blood injection port. From this point on, the analysis process is automatic. Blood is continuously driven into the mixing coil at the rate FB (0.08 mL/min) where it is mixed continuously with CO-equilibratedsaline which enters the mixing coil from tonometer I at the faster rate Fs (2.40 mL/min). The mixing coil provides uniform mixing of blood and saline and sufficient time to ensure displacement (by CO) of virtually all combined oxygen from hemoglobin to the dissolved phase prior to reaching the oxygen sensor. The initial and final quarters of the blood/saline mixture which arrive at the electrode are ignored to avoid contamination errors. However, the electrode output during the time the middle portion of the mixture is in the electrode is received by the microprocessor. The electrode output is averaged and an estimate of oxygen partial pressure of the blood/saline mixture is computed from the average electrode value, using the calibration data previously stored in the system. The nulling process is initiated by setting the gas mixer to provide the oxygen gas fraction which corresponds to the calculated estimate of the oxygen partial pressure of the blood/saline mixture. Valves 1 and 2 are then energized to cause saline, equilibrated at this oxygen partial pressure, to enter the oxygen electrode-maintaining the same flow conditions as the previous blood/saline mixture. The output of the electrode from the tonometered saline is now used as a new calibration point (close to the blood/saline oxygen value) for recalibrating the slope calibration parameter. With the new slope parameter, the oxygen partial pressure of the blood/saline mixture is recalculated. If the difference between this recalculated value and the previous calculation lies outside the error band, the gas mixer is reset to this latest calculated value of the blood/saline oxygen partial pressure and the cycle is repeated until the accuracy criteria of the system is met. The system then completes the blood washout in preparation for the next blood sample. The accuracy criteria of the nulling process is set by the operator by entering a percent error limit into the system. With normal electrode function, no more than two settings of the gas mixer
ANALYTICAL CHEMISTRY, VOL. 55, NO. 7, JUNE 1983
are required to provide accuracy within the precision limitations of the system. Normally, only one setting is required to meet this accuracy criteria. For this situation, the total measurement and washout time equals 4.5 min. The potential for systematic error due to electrode drift occurring during the shoiet time between the blood/saline measurement and the nulling process is eliminated by mathematical correction based on drift measurement during the nulling process. The drift is Calculated by linear regression analysis of 48 s of data following 40 s (six sensor time constants) of steady-state conditions applied to the electrode. However, since normal electrode drift is negligible (less than 0.2% /min) over this relatively short period, this provision ha9 significance only when the sensor is abnormally noisy. When the system noise is too large to meet the accuracy criteria that has been entered, the operator is alerted. Test of Assumption I: Identical Sensor Response to Saline Containing: Nitrogen and to Saline Containing Carbon Monoxide. It is assumed that the oxygen sensor responds identically to saline containing dissolved carbon monoxide and to saline containing dissolved nitrogen for the same partial pressure of oxygen. To test the adequacy of this assumption, the Fs output of the pump was connected to tlhe input of tonometer I and the output of FB was connected to the input of tonometer 11. The input of both channels was saline; however, tonometer I1 was supplied with 100% oxygen while tonometer I was alternately supplied with carbon monoxide and nitrogen. Comparison of the sensor responses to the two states was analyzed by using a paired t test. Test of Ass~~mptioiu 11: Identical Sensor Response to Saline and Blood/Saline Mixture. To test this assumption, the same test configuration was used as in the above study except that the liquid slupplying tonometer I was varied instead of the gas. The input to Fswas alternately valved between saline and a blood/saline mixture (one part blood to 30 parts saline). Tonometer I1 was supplied with 100% oxygen and tonometer I was supplied with carbon monoxide. Comparison of the sensor response for the two states was analyzed by using a paired t test. Determination of Oxygen Solubility aif Saline. The oxygen solubility of saline was measured with respect to distilled water by placing the input to Fs in saline and valving the input to FB between distilled water and saline. The output of FS was connected directly to the input of tonometer I (supplied with carbon monoxide) and tbe output of FB was connected directly to the input of tonometer 11. With saline being pumped through i o nometer 11, the gas mixer was set to provide 100% oxygen, simulating the oxygen measurement of a saline sample having a known POz equal to barometric pressure minus the partial pressure of water vapor. The saline in tonometer I1 was then replaced with distilled water, and the gas mixer fraction required to produce a null with the previous measurement was cletermined. The ratio of the gas mixer fractions, so obtained, is related to the saline and the water oxygen solubilities (at 37 "C) by the following equation (see Appendix I][):
where As and A, are the Bunson oxygen solubilities of saline and ) Poz(s)represent the gas mixer water, respectively,and F ' O , ~ ~ sand Oz partial pressure outputs for water/saline mixture and saline, respectively. Tlhe fractional depression coefficient 6 is then calculated from eq 7 . Reproducibility Determination of Oxygen Content Measurements. Both patient and dog blood samples were used for this study. Arterial and venous samples were about equally represented. Ten milliliters of blood was collected into a syringe containing 0.2 mL of sodium heparin (1000 units/mL) and six glass spheres (0.305 cm diameter). The blood was mixed for 2 min by shaking. Five milliliters was then quickly transferred to a second syringe, which also contained six glass spheres. The syringes with the divided samples were then placed in ice for 30 min before performing a paired sample determination to ensure that both samples had reached temperature equilibrium. One of the syringes was then randomly selected and its blood was mixed for 5 min while being brought to room temperature. The blood was then inserted into the blood reservoir to initiate the
1101
oxygen content measurement. At this point, the other syringe was removed from the ice and was mixed for 5 min while being brought to room temperature, using the same procedure as for the previous sample. At the end of this period the apparatus had completed the measurement and clean out cycle of the first sample. The second blood sample was then inserted to start the second oxygen content measurement. Fifty-six pairs were measured over the period of a week. Comparisons to the Van Slyke Manometric Method. For the Van Slyke comparisons, the same blood handling technique was used. However, because of the significant differences in analysis times of the two methods and geographical distances (2 miles) between analyzers, it was impractical to maintain the same timing control for this study as was achieved for the reproducibility study. The protocol was therefore modified from that of the previous study, permitting a maximum difference of 90 min between the measurements of a duplicate pair. In order to ensure that no significant systematic error was introduced into the study by this much uncertainty in the timing of measurements, the nonused portions of five samples were randomly selected from the study and maintained in ice for an additional 24 h. The oxygen content of these samples was then reanalyzed by the FP method and compared to the earlier measurements. An approximately equal number of arterial and central venous blood samples was obtained from patients for this study. The statistical significance of the difference between the two methods was determined with a paired t test. Comparisons of precision were determined by applying a linear regression to the data and calculating the standard error of the estimate. RESULTS AND DISCUSSION Effect of Nitrogen Substituting for Carbon Monoxide in the Nulling Procedure. Ten paired measurements of oxygen content of saline were performed, modified as described in the methods section. One measurement of the pair used carbon monoxide saturated saline as the diluent; the second measurement used nitrogen saturated saline as the diluent. The measured average paired difference (CO - N,) was 0.04%, the standard deviation was 0.27%. These results show no evidence of a systematic difference between nitrogen and carbon monoxide substitutions in the saline diluent (Student t test); however, a statistical uncertainty (95% confidence) of 0.2% exists due to the limited size of the sample set. Effect of Saline Substitution for Blood/Saline Mixture in the Nulling Procedure. Six paired measurements of oxygen content of saline were performed, modified as described in the methods section. One measurement of the pair used a blood/saline mixture as the diluent; the second measurement used saline as the diluent. The measured average paired difference (blood/saline - saline) was 0.03 % ; the standard deviation was 0.12%. Again, there is no significant difference between the saline and blood/saline mixture measurements. Saline Oxygen Solubility Measurement. From 14 measurements, the ratio of &/XW (saline/water oxygen solubility ratio) was found to be 0.9515 f 0.0008. By use of the Bunson oxygen solubility coefficient of water of 0.02386 (15), the Bunson oxygen solubility coefficient in saline equals 0.02270 f 0.00002. From eq 7, 6 was calculated to be 0.31 f 0.01 which is not statistically different from measurements reported by Sendroy et al. (14). Just as the Van Slyke method depends critically on the precise knowledge of the value of the gas constant R, the FP method as well as other amperometric methods depend critically on precise knowledge of the oxygen solubility of the diluent-in this case saline. Some ambiguity exists between oxygen solubility data for saline as it appears in the handbooks and the references cited by the handbooks (14, 15). We, therefore, felt that it was important to measure the oxygen solubility of saline and determine the fractional depression coefficient, 6.
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Reproducibility Study. The results of 56 paired blood samples, measured consecutively by the FP method showed that the mean difference (second measurement - first measurement) was 0.0045 vol % and the linear regression was second vol % = 0.993 first vol % + 0.116 vol % with the correlation coefficient r = 0.9985 and the standard deviation = 0.21 vol %. The mean difference is not significantly different from zero, indicating that no significant memory or hysteresis exists in the measuring apparatus. The standard deviation for individual measurements equals the standard deviation for paired samples divided by 2lIz, 0.15 vol %. For the average value of 16 vol %, the coefficient of variation equals 0.94%. Van Slyke Comparison Study. The five paired sample study designed to measure the rate of oxygen loss of iced samples showed an average loss of 0.06 vol % for 24 h with a standard deviation of 0.08 vol %. Statistical analysis (95% confidence limits of the Student t distribution) places the uncertainty of oxygen loss a t 0.17 vol % per 24 h, or 0.96% per 24 h. (The average value of the five sample pairs was 17.7 vol %.) An uncertainty limited to *0.1% is acceptable for the Van Slyke comparison study. Errors due to sample degradation with time were therefore maintained within this range by adhering to the 2 h limit for measurements of iced paired samples. The 32 duplicate blood samples, one sample measured by the Van Slyke manometric method and its duplicate measured by the FP method, produced a mean difference (FP method - Van Slyke) of 0.0056 vol % with a standard deviation of 0.35 vol %-a result which is not statistically different from zero by paired t test. The linear regression was FP vol '70 = 0.993 Van Slyke vol % + 0.109 vol % with r = 0.9964. The FP method fits the definition of an absolute method in that no standards are required for calibration, even though the method uses an oxygen sensor which is a relative measuring device. This result is produced because the oxygen sensor is used only as a null indicator. Comparisons are made between the solution which requires measurement and a nearly identical solution whose oxygen partial pressure is modified until the null condition is achieved. (Provision is made to correct for potential systematic error due to sensor drift.) The value of the oxygen partial pressure required to produce the null condition is determined accurately by flow proportioning which is an absolute measurement. This principle requires that the oxygen partial pressures of both solutions be identical at the null point, a condition which is assured by flow control and chemical composition of the nulling solution. This expectation was specifically verified experimentally. The only literature value the F P method needs is the oxygen solubility of water (the equivalent parameter for the Van Slyke method is the gas constant, R). The FP method's ability to measure the oxygen solubility of the diluent has been demonstrated; results reported in standard handbooks have been confirmed. With this background of preparation, we feel that the favorable comparison of the FP method and the Van Slyke method should have been expected and is evidence that no significant systematic errors existed with either method during the comparison study. The advantages of this method over the Van Slyke method are mainly those provided by a design which lends itself to microprocessor control. These advantages include (1)operator independent accuracy and precision, (2) reduced measurement time, and (3) smaller sample size (which can be scaled down much further). However, the Van Slyke method has the inherent capability to measure contents of any blood gas for which chemical means exist to selectively remove it from all other gas components. To achieve this same purpose, the F P method requires an electrode which is specific to each par-
ticular blood gas whose content is to be measured. However, in practice, there is only one gas of medical interest other than oxygen; that gas is carbon dioxide. An electrode specific to dissolved carbon dioxide is commonly available which provides the capability of expansion to include this gas as demonstrated by the work of Harabin and Farhi (17). While other blood oxygen content analytical methods (referred to in the background section of this paper) have also been developed to overcome some or all of the disadvantages of the Van Slyke method, the principal advantage offered by the FP method over these methods is the inherent accuracy which equals that of the Van Slyke. The FP method can be modified by using pump flow control in place of the gas mixer to provide the null condition. However, to achieve an accuracy performance equal to or greater than the Van Slyke method, flow control using peristaltic pumps (used by Blaedel and Laessig ( 1 3 ) )is inadequate. Liquid-tight syringe pumps, controlled by stepping motors, would be adequate when properly designed; however, such pumps are not commercially available. GLOSSARY barometric pressure (mmHg) NaCl concentration (equiv/L of water) oxygen content (volume percent; vol %) oxygen content of blood (vol %) oxygen content of blood/saline mixture (vol %) oxygen content of saline (vol % ) flow rate of blood and saline, respectively (mL/min) oxygen fraction of gas mixer oxygen partial pressure of blood/saline mixture (mmHg) gas mixer oxygen partial pressure output for saline and water/saline mixture, respectively (mmHg) oxygen partial pressure in tonometer I1 fractional oxygen depression coefficient for NaCl in water at 37 "C Bunson oxygen solubility of blood/saline mixture a t 37 "C Bunson oxygen solubility of blood at 37 "C Bunson oxygen solubility of saline a t 37 "C Bunson oxygen solubility of water at 37 OC ACKNOWLEDGMENT We are grateful to Ivan Jensen for the oxygen content determinations by the Van Slyke method and to Charles Cochran for constructing the apparatus. APPENDIX I. Derivation of the Blood/Saline Oxygen Solubility Coefficient. The derivation of eq 6 is based on the assumption that the oxygen content of a mixture of two solutions at a given partial pressure of oxygen is the sum of the oxygen contents the solutions would have had before mixing if equilibrated at that same partial pressure of oxygen. Although such a condition of linearity is not absolutely true, it serves as an adequate approximation over small ranges. (We have verified that it is true for mixtures of CO saturated blood and saline over the range of values measured by the FP method.) Therefore, by mass balance we have
Po,X(F,
+ Fs) = P o 2 X ~ F+ ~P0,XsFs
(10)
where X is the oxygen solubility of the blood/saline mixture, AB and As are the oxygen solubilities of the blood and the saline, respectively, FB and Fs are the flow rates of the blood and the saline, respectively, and Po, is the partial pressure of oxygen of the mixture. Dividing eq 10 by (FB+ Fs)Po,one has
Anal. Chem. 1983, 55, 1103-1107
Rearranging terms, eq 11 becomes eq 6. TI. Derivat,ion of the Saline Oxygen Solubility Coefficient. By mass balance the following equation is given for the saline/saline mixture:
FB~SPCMT) = (FB + Fs)Wo2(s)
(12)
where Po2(T)is the oxygen partial pressure in tonometer I1 and the rest of the parameters are described in the text. Mass balance for the saline/water mixture i s given by FBxWP02(T)
= (FBAW
FSh3)P02(W/S)
(13)
(Note: The tested assumption of linearity made above in Appendix I is ,also implied in this equation.) Dividing eg 12 by eq 13 we have
_ --
(FB
+ FS)xSP02(S)
(FBxW + FS)POz(W/S)
(14)
Dividing the numerator and the denominator of the right hand side of eq 14 by Xs and rearranging terms, eq 9 is produced. Registry No. Oxygen, 7782-44-7. LITERATURE CITED (1) Van Slyke, D. D.; Nelll, J. M. J. Blol. Chem. 1924, 61, 523-573. (2) Nevllle, J. R. J. AppE. Physiol. 1960, 15,717-722.
1103
(3) Laver, M. B.; Murphy, A. J.; Seifen, A.; Radford, E. P.,Jr. J. Appl. Physioi. 1965, 20, 1063-1069. (4) Kllngenmaier, C. H.; Behar, M. G.; Smith, T. C. J. Appl. Physlol. 1969, 26. 653-655. (5) Bates, D. V.; Harkness, E. V. Can J . Blochem. Physiol. 1961, 39, 991-999. (6) Clerbaux, Th.; Gerets, G.; Frans, A. J. Lab. Clin. Med. 1973, 82, 342-348. (7) Baumberger, J. P. Am. J. Physiol. 1940, 129,308. (8) Clark, L. C.,Jr. Trans. Am. SOC. Artif. Intern. Organs 1956, 2 , 41-48. (9) Llnden, L. J.; Ledsome, J. R.; Norman, J. B r . J. Anaesth. 1965, 3 7 , 77-88. (IO) Tazawa, H. J. Appl. Physlol. 1970, 29 (3), 414-416. (11) Malmstadt, H. V.; Pardue, H. L. Anal. Chem. 1961, 33, 1040-1047. (12) Blaedel, W. J.; Hlcks, G. P. Anal. Chem. 1962, 3 4 , 388-394. (13) Blaedel, W. J.; Laesslg, R. H. Anal. Chem. 1965, 3 7 , 1255-1260. (14) Sendroy, J., Jr.; Dlllon, R . T.; Van Slyke, D. D. J. Blol. Chem. 1934, 105,597-632. (15) Altamn, P. L.; Dlttmer, D. S. “Biological Handbooks: Respiration and Circulation”; Federation of Amerlcan Societies Experimental Biology: Bethesda, MD, 1971; pp 16-18. (16) Wallace, W. D.; Clark, J. S.;Cutler, C. A. Anal. Chem. 1961, 53, 2313-231 a. (17) Harabln, A. L.; Farhi, L. E. J. Appl. Physlol.: Respir., Environ. Exerclse Physlol. 1978, 44 (5), 818-820.
RECEIVED for review August 10, 1982. Resubmitted January 31, 1983. Accepted March 3, 1983. This research was supported by National Heart, Lung and Blood Institute, Grants HL-20351 and HL-21445.
Kinetic Spectrum Method for Analysis of Simultaneous, First-Order Reactions and Application to Copper(I I) Dissociation f rom Aquatic Macromolecules Dean L. Olsoin and Mark S. Shuman* Department of Environmental Sciences and Engineering, School of Public Health, University of North Carolina, Chapel Hiii, North Carolina 27514
A nonllnear dlfferential rate method tlhat requires no prior knowledge of rate constants, lnltlal concentrations, or number of components Is developed to analyze multicomponent, flrst-order or pseudo-flrst-order reactlone. The method glves a klnetlc spectrum with peak maxlma correspondlng to rate constants and peak areas equal to inltlal concentratlons of components. Complete resolutlon of two components requires a rate constant ratio greater than about 40. The method was applied to a study of Cu( I I ) dlssoclatlon from estuarlne humlc material In whlch a Cu(I1)-humic mixture was reacted wlth a colorlmetrlc reagent and absorbance followed from 50 ms to 1835 s. The klnetlc spectrum showed bound Cu(I1) dlstrlbuted In two regions over a wide range of rate constants. About 43 % of the total Cu( I I ) dlssoclated In times greater than 50 ms correspondlng to rate Constants 5 4 0 s-’.
Graphical extrapolation and multiple proportions are the two differential reaction rate methods frequently used for kinetic analysiri of mixtures (1,2). These methods are commonly applied to binary systems and are occasionally extended to kinetic analysis of rnore than two components. Graphical extrapolation requires that one component react nearly to completion before the other component reacts significantly, and the method of multiple proportions requires an inde-
pendent estimate of the rate constants. These methods cannot be readily adapted to the analysis of mixtures for which neither the number of components nor the rate constants are known. Graphical extrapolation is sometimes used in such cases, but fitting data to straight line segments becomes rather arbitrary without prior knowledge of the number of components and the relative values of the rate constants. Dissolved organic materials in natural waters are poorly characterized, polydisperse macromolecules possessing multiple metal binding sites. Estimation of the metal dissociation rate constant for each of these sites reduces to the problem of analyzing a multicomponent mixture for which the dissociation mechanisms, relative rate constants, and the nature and number of binding sites are unknown. Cu(I1) dissociation rate constants have been estimated electrochemically with a rotated electrode (3-5), but this technique has a rather narrow experimental time range. The photometric method described here was developed to broaden the time range and is based on monitoring the appearance of a colored complex, Cu(PAR),, where PAR is the reagent 4-(2-pyridylazo)resorcinol. PAR was chosen because it forms a strong, water-soluble Cu(I1) complex of simple stoichiometry with a large molar absorptivity (6). The rate of Cu(PAR), appearance depends on the rate of Cu(I1) dissociation from multiple sites on the macromolecules. A “kinetic spectrum” method was used to plot the distribution of binding sites which gives a series of peaks with
0003-2700/83/0355-1103$01.50/0 -. A 0 1983 Amerlcan Chemical Soclety
