fnviron. Sci. Techno/. 1986, 20, 916-923
(12) Berkson, J. Am. Stat. Assoc. J . 1953, 48, 565-597. (13) Blachman, M.; Lippmann, M. Am. Ind. Hyg. Assoc. J. 1974, 35, 311-326. (14) Kleinbaum, D. G.; Kupper, L. L. Applied Regression Analysis and Other Multivariable Methods; Duxbury Press:
North Scituate, MA, 1978. Received for review August 31,1984.Revised manuscript received June 6,1985.Accepted April 30,1986.This work was financially supported by U.S. EPA Contract 68-02-3431,
Biological Significance of Fluctuating Concentrations of Carbon Monoxide Bernard E. Saltzman” and Stanley H. Fox
Department of Environmental Health, University of Cincinnati, Cincinnati, Ohio 45267-0056 The biological significance of fluctuating concentrations is not well understood. Fluctuation patterns can be approximated as a Fourier series of sine waves of different amplitudes, periods, and phases. A theoretical equation was developed for relating carboxyhemoglobin levels in blood to sine wave exposure patterns of carbon monoxide. It was experimentallv validated for rabbits exr>osed to 50-350 ppm of CO in sine waves of periods from $7 to 280 min. Higher frequency carbon monoxide concentration fluctuations were more highly attenuated in the blood in accordance with the equation. The response may be viewed in a new perspective as a modification of the original fluctuation pattern by the transmittance of the “biological window”. A simplified method of evaluating “biologically effective” concentrations for different carbon monoxide fluctuation patterns is proposed. Although most exposures are to fluctuating concentrations of pollutants, environmental standards are generally expressed in terms of time weighted average and shortterm peak or ceiling concentrations. While using a mean value is a convenient approximation, it may be significantly in error for certain fluctuation patterns of exposures. Concentrations of carbon monoxide were utilized in this study of these relationships as an experimentally convenient model. The primary effect of this gas is to combine with hemoglobin in the blood with 210-250 times the affinity of oxygen and thus interfere with its oxygen transport. Extensive reviews of the scientific literature are available in the NIOSH (1)and EPA (2)criteria documents on carbon monoxide. A level of 5% carboxyhemoglobin (COHb) in blood has been recognized as undesirable. The current EPA standard for carbon monoxide is 35 ppm for 1h or 9 ppm for 8 h not to be exceeded more than once a year. The NIOSH recommended standard for industrial exposures is 35 ppm for an 8-h time weighted average and a ceiling concentration of 200 ppm. At 200 ppm an employee engaged in heavy work will reach 5% COHb in about 12 min, whereas it will take about 40 min for a sedentary employee. What is needed to protect people from fluctuating concentrations is a method for describing the almost infinite patterns of exposure and a measure of their biological importance. Saltzman suggested ( 3 , 4 )an approach based on the fact that any finite fluctuation pattern can be expressed as a series of sine and cosine waves, its discrete Fourier transform. In this study, carboxyhemoglobin was determined in the blood of rabbits at frequent intervals during the course of their exposures to carbon monoxide fluctuating in sine wave patterns of various periods. A theoretical equation relating carboxyhemoglobin and carbon monoxide concentrations was developed and validated. A simplified method for evaluating human exposures to fluctuating concentrations is proposed. 916
Environ. Sci. Technol., Vol. 20, No. 9, 1986
In the human lung, oxygen is absorbed in 3 X lo8 alveoli through membranes 0.35-2.5 ym thick into the blood in a capillary network of 90-m’ area (5). The rate of absorption is limited mainly by the diffusion process. Hemoglobin in the blood combines with oxygen and releases it in the tissues. Each molecule contains four atoms of iron and can engage in a reversible reaction with four molecules of oxygen. There are four different equilibrium constants for these reactions, all of which are affected by blood pH, which can change slightly with its COz content. The relationship between oxygen partial pressure and 02Hb % is sigmoidal. Venous blood enters the alveoli with an oxygen partial pressure of about 40 torr (75% 02Hb)and leaves 0.75 s later in a resting person with an oxygen partial pressure of 100 torr (97% 02Hb). During exercise the blood transit time may decrease to 0.34 s, and the air ventilation and oxygen diffusion rates increase. Carbon monoxide combines with greater affinity with hemoglobin in the same manner. It is not appreciably consumed in the tissues although perhaps 20% of the body store of carbon monoxide may be in combination with myoglobin in the muscles. Hatch (6),using the data of Forbes et al. (7), developed an equation for carboxyhemoglobin concentrations in 1952 that recognized the exponential nature of the CO uptake. This equation was expanded by Forester et al. (8) in 1954 to include 14 variables. Coburn et al. (9) developed a model that included endogenous CO production in 1965 and an equation for uptake from constant CO concentrations. Coburn’s equations have been very successful in fitting a wide range of CO uptake data, notable those of Peterson and Stewart (IO),and are in integral part of the NIOSH criteria document for its proposed CO standard (1). Goldsmith and Terzoghi (11)used an analysis similar to that of Hatch (6) to get numeric solutions for fluctuating exposures. Marcus (12)developed a computerized model based on the Coburn equation and fitted Goldsmith‘s data. He pointed out that individual variations in ventilation rate, anemia, smoking, etc. greatly affected the results. The parameters in the Coburn equation were evaluated as empirical equations, and the complex systems were numerically evaluated by computer with results presented in graphs showing effects of activity and smoking (13)and altitude (14).Other studies (15-18)developed empirical equations relating human percent carboxyhemoglobin to carbon monoxide concentrations and short exposure times. Carbon monoxide diffusion constants for brief exposures have been measured recently by using mass spectrometric techniques (19,2O).The diffusion capacity of the lower lung was reported (21)to be double or triple that of the upper lung because of its greater blood perfusion. The studies of the longer exposures required complex computer calculations to evaluate effects of each individual
0013-936X/86/0920-09 16$0 1.50/0
0 1986 American Chemical Society
concentration fluctuation pattern. Simplifications were required, and results could vary greatly according to the values assumed for the many parameters which differ among individuals, In the present study a theoretical equation was developed by using the same basic relationships as the Coburn equation. Simplifying assumptions also were required, which may require adjustments of the results. But the final equation required only two parameters, and it permitted an analytical solution for the effects of fluctuating concentration exposures. Moreover, the results may be readily comprehended as a modification of the original concentration pattern by the transmittance of the "biological window". Thus, its form is especially useful to evaluate the biological effects of different fluctuation patterns. This equation calculates the response to each component concentration fluctuation frequency separately. The inhaled carbon monoxide concentration in ppm volume units is assumed to be a sine wave for each frequency: CO (ppm) = M
+ A , sin
[ ;: ] -(t
-
to)
(l)
where M = mean CO concentration (ppm), A, = amplitude (ppm) of this component, t = time (min), t, = period of one cycle (rnin), and to = time of the first ascending midpoint of the wave (min). Since the sine wave may not start at zero on the time scale used, the term to was inserted to adjust for the initial relationship. The details of the derivation are given in Appendix I. The final equation is
where X t = percent carboxyhemoglobin at time t due to the mean and the fluctuation component, X o = initial percent carboxyhemoglobin,K = rate constant (min-l), and R = equilibrium ratio of CO (ppm)/COHb %. This equation can best be understood by considering the significance of each of the three terms on the right side separately. First, assume that the exposure is to a constant CO concentration, M , and that the initial carboxyhemoglobin concentration, Xo, and A , are zero. Thus, the second and third terms become zero. The first term describes the exponential rise of carboxyhemoglobin,X,. At infinite time (1- e-Kt)= 1,and for this case X , = M / R . Thus, R is the equilibrium ratio of constant CO (ppm)/ COHb %. If one now assumes exposure to a fluctuating concentration of carbon monoxide of amplitude A,, the second term describes the corresponding fluctuation component of carboxyhemoglobin concentrations. The amplitude of the latter is proportional to A , / R and to the additional amplitude transmittance factor, T, representing the other part of the denominator in the term:
T=
l/dl + (2x/Kt,)'
(3)
19
&13
Figure 1. Schematic drawing of system for generating sine wave concentrations of carbon monoxide. (1) Cylinder containing co; (2) reducing valve; (3) shut-off valve; (4) solenoid safety valve shut off; (5) vent valve; (6) water-filled 100-mL buret for pressure control (vented in hood); (7) asbestos plug for flow resistance; (8) mixing tube: (9) clean air inlet; (10) glovebox exposure chamber; (1 1) perforated distribution pipe for inlet air; (12) air lock; (13) outlet pipe; (14) blower; (15) outlet (vented in hood); (16) geared motor drive and adjustable crank arm; (17) piston pump periodically varying water level in (6); (18) water syringe for adjusting water level in (6); (19) safety pressure switch for shutting off CO in the absence of slight negative pressure in the exposure chamber.
This factor causes greater attenuation of fluctuations having shorter periods, t,. The carboxyhemoglobin fluctuation sine wave lags that of the carbon monoxide by a part of the sine term, arc tan ( 2 ~ / K t , )This . approaches 90 deg as t, becomes smaller. Dividing the lag angle by 277, which is the angle of a complete period, gives the ratio of the lag time to the period: 1 tL/tp = - arc tan ( 2 ~ / K t , ) (4) 2T where t L = lag time for this component (rnin). The third term is an adjustment to the first two terms to make the value of the left side of the equation at t = 0 to be equal to Xo. Alternatively, if one assumes a high initial value of X o and exposure to clean air ( M = 0, A , = 0), then the first two terms on the right side drop out, and the third term describes the exponential decomposition of the carboxyhemoglobin as it releases carbon monoxide by the reversal of the uptake reaction. While this equation appears complex, it may be readily solved on a microcomputer. The small endogenous production of CO has been ignored in the derivation. It produces a small constant level (about 0.5% COHb in man) which may be added to that derived from eq 2. The biological half-life of the process, t b , in minutes is defined as tb
= 0.693/K
(5)
Equation 2 was experimentally validated for rabbits exposed to sine wave patterns of carbon monoxide exposure, as described in the following sections.
Experimental Section Carbon Monoxide Exposure System. The exposure chamber, Figure 1, was a modified glovebox, 10, with a volume of 385 L. An exhaust fan, 14, provided almost one air change per minute, and the chamber was maintained at a negative pressure of about 8 cm of H,O. Carbon monoxide was metered into the incoming air with an asbestos plug diffusion micrometering system described by Saltzman (22). The source of the gas was a cylinder, 1, containing 99% pure CO. An asbestos plug, 7, 16 mm diameter X 13 mm deep was connected to it at the output Environ. Sci. Technol., Vol. 20, No. 9, 1986
917
leg of a tee. The third leg of the tee, the waste gas leg, was immersed in water in a 100-mL graduated buret, 6. The cylinder valve was adjusted to produce a slow stream of bubbles in the buret. The upstream pressure on the plug, and, therefore, the rate of flow, was determined by the height of water over the waste outlet in the buret. To obtain a sinusoidal CO flow, the height of water in the graduated buret was varied by a piston pump, 17. The piston pump was driven in a sinusoidal manner by a rod attached to an adjustable crank, rotated at a very slow adjustable speed by a geared down motor, 16. The time for one revolution of the crank was adjusted to be the desired period of the sinusoidal fluctuation. The concentration in the chamber was monitored with a Model 1000 Ecolyzer and fluctuated between about 360 and 50 ppm with periods between 37 and 280 min. A continuous record of the CO exposure was made on a chart recorder. Each run was to a fluctuating concentration of a single period for one or more cycles. At the end of most runs, the rabbit was allowed to approach equilibrium with a constant concentration of carbon monoxide, which was then shut off. The subsequent washout was monitored to obtain the biological half-life of COHb. Subjects. Eight white New Zealand male rabbits, weighing 2.5-3.5 kg were exposed to carbon monoxide during the 11 runs. Most were used only once, but some were used a second time after a recovery period of at least 1 month. Blood Sampling Technique. The procedure of taking blood samples was somewhat critical. Initially, an attempt was made to implant a chronic intravenous catheter into the external jugular vein by using a method similar to that described by Hall et al. (23). However, the initial three catheters implanted did not remain patent during the 1-2-day recovery period before exposure. This technique was abandoned in favor of a catheter implanted into the central aural artery. A 23-gauge needle, with the hub removed and replaced by a P E 50 Teflon catheter tube, was inserted into the lumen of the central aural artery and taped carefully into place. Approximately 30 cm of tubing was used to conduct the blood out of the exposure chamber. Great care was used to ensure that the entrance angle into the artery that yielded the easiest flow was maintained. The rabbit was in a plastic lab-type restraint, with the ears immobilized by splints taped to the restraint. Outside the chamber, a 23-gauge needle with a three-way stopcock was inserted into the catheter. One sidearm was used to withdraw the heparinized saline filling the system between samples, and the other sidearm was used to withdraw blood samples. The volume withdrawn was kept as small as possible so as not to affect the rabbit. The system was backfilled with heparinized saline after each sample. COHb 5% Analysis Technique. After each sample was withdrawn, it was injected into a 2-cm3vacutainer, and immediately a 0.05-mL sample was diluted with 30 mL of 1:800 dilute ammonia solution. By use of the method described by Buchwald (24),this solution was divided into three parts. The first portion (I) was transferred into a 10-mL test tube which was completely filled and sealed. A 20-gauge needle was inserted through the stopper before it was used to seal the tube and withdrawn after. This allowed any trapped air on excess solution to escape. The second portion (11)was saturated with oxygen by bubbling the gas into it through a capillary at 50 mL/min for 15 min and then sealing it. The third portion (111)was saturated with CO (50 mL/min for 2 min) and sealed. When solution I1 was used as the zero absorbance reference solution, the 918
Environ. Sci. Technol., Vol. 20, No. 9, 1986
3501
-
300 E
g250.
:200.
0
z 01500
oloo' 0
50
351
0
0
u
* I 0
-
0
OL
0;
1
I
I
60
1
,
-1
120 180 TIME, minuter
240
Figure 2. Run 1. Exposure of a rabbit to 300 ppm of CO for 120 min, followed by pure air. (---) CO (ppm); (-) (COHb % ) fitted curve; ( 0 ) experimental values of (COHb %), t .
350t 35t
ot
I
60
I
I
I
l
I
l
120 180 TIME, minuter
240
'
Flgure 3. Run 2. Exposure of a rabbit to sine wave input of CO (mean = 207.5 ppm, amplitude = 87.5 ppm, period = 36.8 min) for 155 min, then to 287 ppm for 39 min, and then to pure air. (- -) CO (ppm); (-) (COHb YO)fitted curve; ( 0 )experimental values of (COHb %), t .
-
360b
300
-
35k
I? E250-
;zoo. 150V
100. V
50
-
01
L 60
120
240 TIME, mlnules 180
300
. & 380
Figure 4. Run 10. Exposure of a rabbit to sine wave input of CO (mean 185 ppm, amplitude 125 ppm, period 180 min) for 300 min, then to 310 ppm for 30 min, and then to pure air. ( - - - ) CO (ppm); (-) (COHb % ) fitted curve; (0)experimental values of (COHb %), t .
absorbances of solutions I and I11 were measured in a double-beam scanning spectrophotometer from wavelengths 460 to 400 nm. Percent COHb was calculated as the ratio of the peak absorbance of portion I over that of I11 multiplied by 100. The absorbance measurements were carried out on the evening of the run. Analysis and Discussion of Experimental Data Table I presents a summary of the data obtained in 11
runs. Each run included 20-30 determinations of carboxyhemoglobin concentrations. After the best fit of eq 2 to the data was obtained, in a few cases a few outlying points were discarded and constants K and R were recalculated. The table lists values of biological half-life t b calculated from K by eq 5 and values of R and lists the number of points used in the final fitting and the square root of the mean square deviation. Figures 2-4 illustrate the data for runs 1,2, and 10. The dashed lines show the ppm of CO, the points show the experimental values of
COHb % and t , and the solid lines show the calculated COHb % from eq 2 by using the best-fit values of K and
R.
l o
I
The calculation of the values of K and R to best fit the data, which was essential to the method, was a difficult problem because of the complexity of eq 2. It was done by computer using a modified simplex procedure (25). Since other convenient methods are not available and the procedure is not well-known, it is outlined in Appendix 11, together with its limitations. Figures 3 and 4 clearly show that higher frequencies of CO fluctuations are more attenuated than lower frequencies, as predicted. The respective values of t /tb were 36,8121.09 = 1.74 and 180129.58 = 6.09. Tke corresponding values of T calculated from eq 3 (after replacing K with its equivalent value of t b from eq 5) were 19% and 56%. For values of (tp/tb) < 1, very little of these fluctuations ( 0 01
02
04
08 I
. .2 . ,
1 .
J . h L A J L t . .
4
6
8 10
.Id-.... 1
20
I
1
sigmoidal rather than linear. Stewart et al. published (18) a slightly curved equilibrium relationship derived from paired alveolar breath and venous blood samples from 56 fire fighters. The curve indicated average values of R of 6.0 for the range 0-15% COHb and 7.3 for the range of 0-30% COHb. The NIOSH criteria document ( 1 ) presented a chart of equilibrium values for human exposures which indicated an R value of about 6 for levels up to 100 ppm (16% COHb) increasing to 16 at extrapolated data for 1000 ppm (63% COHb). A linear approximation in Appendix I was required to obtain a differential equation that could be integrated. It should be noted that if carbon monoxide is removed from the blood by processes other than reverse equilibrium diffusion in the lung, the in vivo equilibrium ratio R may differ from the in vitro equilibrium ratio of CO (ppm)/COHb 70. The values of the rate constant K and of the equilibrium ratio R are similar for most animal species and man. The in vitro reaction rates for rabbit blood have been reported to be much slower than those for other animal species (28). But the in vivo kinetic rates include the additional factors of pulmonary diffusion and blood circulation rates. The major purpose of this study, however, was not to determine the numerical values applicable to man but to develop a simplified methodology for evaluating the various concentration fluctuation patterns, as will be proposed. Transmittances of t h e “Biological Window” and t h e “Sampling Window”
The variance of the concentration of carbon monoxide in a fluctuating pattern is the sum of the variances of the component frequencies. The experimental study indicated how the higher frequencies were more attenuated. A simple approach to evaluating different patterns is to modify them according to the variance transmittance pattern of the biological window. This is obtained by squaring the amplitude transmittance, eq 3, and combining the result with eq 5 to yield
where vb = variance transmittance factor of the biological window. When fluctuating concentrations are time-averaged, a similar attenuation effect occurs. A theoretical calculation (3) that averaged sine waves developed the relationship:
v, = (t,2/2&,2)[1
- cos (2xta/t,)l
(7)
where V , = variance transmittance factor of the “timeaveraged sampling window” and t , = averaging time. This 920
Environ. Sci. Technol., Vol. 20, No. 9, 1986
0 V
01
40 60
R A T I O C Y C L E P E R l O D l A V E R A G l N G T I M E OR B I O L O G I C A L H A L F L I F E
Flgure 5. Variance transmittance factors. (-) Factor for the “timeaveraged sampling window” vs. the ratio of pollutant fluctuation period, t,, to averaging time, fa; (---) factor for the “biological window” vs. the ratio of tp to biological half-life, t,; (-) lost fraction of variance when t , = t b vs. ratio t p l t b ; (+++)lost fraction of variance when t , = tb vs. ratio t,lt,.
-
lr! n I
TIME, m i n u t e r Figure 6. Calculations for time-averaged values of carbon monoxide concentrations in run 2, in which a rabbit was exposed to CO fluctuations with a period of 36.8 min. Averaging time = biological half-life = 21.1 min, R = 15.33. ( - - - ) Actual CO (ppm); (.-) time-averaged CO (ppm); (-) (COHb % ) fitted curve; ( 0 )experimental values of (COHb %), t . 351
350f
300 I! E250
-
v200.
:
150-
0
1000
50
0.
80
120
180
2 4 0
300
360
TIME, rnlnula#
Figure 7. Calculations for time-averaged values of carbon monoxide concentrations in run 10, in which a rabbit was exposed to CO fluctuations with a period of 180 min. Averaging time = 30.0 min, biological half-life = 29.6 min, and R = 11.89. (---) Actual CO (ppm); time-averaged CO (ppm); (--) (COHb YO)fitted curve; ( 0 )expert. imental values of (COHb YO), (.e.)
differs from the preceding equation because it does not involve kinetic relationships, but merely averaging of fluctuations. Figure 5 is a plot of eq 7 (solid line) and 6 (dashed line). If t , = t b , it can be seen that although time averaging attenuates a range of high-frequency fluctuations, those that are greatly suppressed are also not substantially transmitted into biological systems by the biological window. The lost fraction, calculated as the product (1 V,) vb, is shown by the dotted line. The maximum loss is 3 . 1 % at a ratio of t , / t b equal to 3.3. The (+) line shows losses when t , = l / g t b , with a maximum loss of only 0.88%. Thus, any value of averaging time equal to or less than the biological half-life may be safely used without significant loss of biologically transmitted fluctuations from the data. Calculation of “Biologically Effective” Concentrations of Carbon Monoxide
It is evident that the biological effects should relate to the internal concentration of a pollutant (or its product) rather than to its external concentration. For a time-averaged period at a constant concentration of carbon monoxide, eq 2 reduces to
where X,= internal concentration at the beginning of the period, X,= internal concentration at time t , and t = time from beginning of step (ranging from 0 to ta). The application of the window transmittance hypotheses and of eq 8 produces results in good agreement with the experimental data. Results for two runs are shown in Figures 6 and 7 on the basis of averaging times equal to
the experimentallydetermined half-lives. The dashed lines show the actual exposures, the dotted lines show timeaveraged values for successive periods, and the solid line shows carboxyhemoglobinconcentrations calculated from eq 8. The experimental points for measured carboxyhemoglobin fit the solid lines quite well, whereas they deviate widely from the external concentration pattern. Inspection of the figures suggested that straight line segments for each time interval would fit almost as well. This simplified the calculations to evaluating X only at the end of each interval. Application of this simplification to the data shown in Figure 6 yielded a root mean square deviation of the calculated from the 36 experimental values of 1.20 COHb %, which was actually less than the 1.52 COHb % determined for the 32 points in the calculation for the unaveraged sine wave portion. The same method applied to the data shown in Figure 7 yielded an RMS deviation from the 31 experimental values of 1.42 COHb %, compared to 1.66 COHb % in the 24 points for unaveraged data in the sine wave portion. The slightly better precision was not surprising, since the extra points included for these stepwise calculations were in the region of exposure to zero CO concentrations and, thus, were not subject to experimental errors from the sine wave generation system. The simplified method thus gave a good approximation of the internal concentrations. It is more convenient to relate environmental standards to biologically effective external concentrations, rather than to internal concentrations. We can define two new terms as follows: Y=RX (9) -0.693ta F=1-etb
Where Y = biologically effective external concentration that would be at in vivo equilibrium with internal concentration X and F = biological response fraction at the end of a time-averaging interval. We can then derive the following from eq 8-10: Yi = FM, + (1- flYi-1 (11) where Yi = biologically effective external concentration at the end of the ith interval, Mi = time-averaged external concentration during the ith interval, and Yi-l = biologically effective external concentration at the end of the previous internal. This equation provides a simple means of converting time-averaged measurements M I ,M,, M3, ... M,, to biologically effective values Y l , Y2,Y3,... Y,.The value of F is calculated from eq 10. The initial value Yo is estimated, and each value of Y then may be calculated as the simple weighted average of two terms from eq 11. Any error in the estimated value of Yobecomes negligible after the sum of the averaging times exceeds three biological half-lives. It can be seen that although averaging times shorter than the biological half-life produce greater variations in the values of M , the corresponding lower values of F attenuate the variations and produce essentially the identical pattern of biologically effective concentrations as that produced for an averaging time equal to the biological half-life. The ranges of the results can be visualized as between the solid lines in Figures 6 and 3 and between those in Figures 7 and 4. It should be clearly understood that the calculation of biologically effective concentrations must be based on an accepted average value of biological half-life (e.g., tb = 2 h). These and other evaluations obviously are affected by the actual values, which vary with activity and individuals.
KFlgure 8. Modified simplex method for iterative fitting of equation parameters K and R to maximize Z. Simplex triangle ABC represents the first triad of pairs of values of K and R . I n this case the second triad would be triangle P,AB. Successive estimates are labeled P’, P’I,, Prlr..05, Pf’lI-o,5.
Different sets of values may be calculated for individuals doing hard, light, and sedentary work. These relationships have important implications for the relationships between the environmental standards for peak concentrations entirely contained within different time-averaging periods. We may define the biologically effective standard as the external concentration that would be in equilibrium with the maximum allowable internal concentration. Applying eq 11 with the assumption that Yi-l is negligible, we obtain where M a = environmental standard for peak external concentration averaged for time a, Y,= biologically effective concentration standard, and Fa = biological response factor for averaging time a. Two hours may be taken as an average value of tP for carbon monoxide. The EPA standard for an 8-h timeaveraged value is 9 ppm. If one assumes a fairly uniform concentration M during this period of four biological half-lives, then eq 11 indicates that the final value of Y approaches M , and 9 ppm thus may be taken as a value of Y,.To calculate a corresponding standard for a 1-h peak period, we enter ta/tb = ‘I2 in eq 10, yielding F = 0.2929. Then from eq 12, Ma = 910.2929 = 30.7 ppm. This is not too different from the EPA 1-h standard at 35 ppm. Different peak internal concentrations can of course result from different concentration patterns during an 8-h period, even if all have a 9 ppm average. Thus, the 8-h standard is only an approximation.
Conclusions The experimental system was successfully developed for determining the transmittance of the biological window. The sine wave exposure approach presented a new perspective for future experimentation. Other studies of fluctuating concentrations of carbon monoxide have analyzed only relatively few sets of data. A substantial amount of new information has been obtained. The ability to describe these data with only two experimentalparameters, K and R, rather than with a complex set of simultaneous equations, was a substantial simplification. Further, work may clarify the variations of the parameters under various conditions. Environ. Sci. Technol., Vol. 20, No. 9, 1986
921
The major result of this study was the experimental validation of eq 2 as a reasonable approximation. This led to a means of evaluating the biological significance of different fluctuation patterns of carbon monoxide which was greatly simplified and required only simple arithmetical operations in eq 11. These methods should be applicable to other pollutants following simple first-order kinetic relationships. In a further extension of this work, a mathematical model for health risk assessment of fluctuating concentrations was developed (29). Acknowledgments Valuable comments were received from E. J. O'Flaherty. Appendix (I) Absorption of Fluctuating Concentrations of Carbon Monoxide. The basic equations relating COHb % to CO concentrations may be derived as follows from mass balance and mass transfer relationships:
v
In order to integrate this differential equation, certain simplifying approximations may be made. In eq 17b, (O2),/(OZHb)$ is taken as a constant, although at high values of (COHb), the value of (O,Hb), must decrease somewhat. Since equilibrium is reached in the alveoli within a small fraction of the time of passage of the blood through the capillaries, the average carboxyhemoglobin (COHb), concentration is taken as equal to a constant fraction, f , of the exiting concentration. Thus (COHb), = f(C0Hb)
(19)
where (COHb) = average carboxyhemoglobin concentration in blood leaving the alveoli (mL of CO/mL of blood). Also, percent carboxyhemoglobin, denoted by X , is taken as a more convenient variable:
dQ = -[(CO)i - (CO),] dt
(13)
lO-,Xr(HbT) = (COHb)
dQ = 6OD[(CO), - (CO),] dt
(14)
dQ = Vb d(C0Hb)
(15)
where (HbT) = total hemoglobin (g/mL of blood) and r = milliliters of CO which can combine with 1g of (HbT). Finally, we convert the inhaled carbon monoxide concentrations from partial pressure to ppm units:
P
where dQ = milliliters of carbon monoxide absorbed in incremental time dt (min), V = average air flow through the lungs (mL/min) under saturated humidity conditions, (CO) = average partial pressure of carbon monoxide (torr) under saturated humidity conditions, i, e, and c = subscripts representing inhaled, exhaled, and alveolar capillary locations, respectively, P = ambient barometric pressure (torr), D = CO diffusion and mass transfer coefficient (mL/(s.torr)) (Dis multiplied by 60 to convert the time units to min), v b = total blood volume (mL), and d(C0Hb) = increment of carboxyhemoglobin concentration in the blood, expressed as milliliters of CO per milliliter of blood. Equation 15 assumes that the body store of CO is essentially entirely in the blood. A small portion may be stored in the tissue, as previously mentioned. Use of an "effective" blood volume may approximately compensate for this without complicating the equations. Since (CO)i and (CO), are the partial pressures of interest, (CO), can be eliminated by equating the right halves of eq 13 and 14 and solving for (CO),:
This value may be entered in eq 14. The reaction between carbon monoxide and oxyhemoglobin in the alveoli may be expressed by the Haldane relationship: CO -t O2Hb
COHb
+02
where B = equilibrium constant (210 to 250 in man), (OJ, = average partial pressure of oxygen in the alveolar capillaries (torr) (COHb), = average concentration of carboxyhemoglobin (mL of CO/mL of blood), and (O,Hb), = average concentration of oxyhemoglobin (mL of Oz/mL of blood). Hence
922
Combining eq 14-16 and 17b and rearranging yield
Environ. Sci. Technol., Vol. 20,
No. 9, 1986
(20)
CO (ppm) = 106(CO)i/P (21) Combining eq 1 and 18-21 and rearranging yield the final differential equation:
where K
f(oz),/(O,Hb)$Vb[(P/fi
+ (1/6OD)]
R = 104r(H bT)f(0,),/ P(0,Hb) $
(23)
(24)
This first-order, first degree differential equation may be solved by multiplying by the integrating factor eKt. The final solution is eq 2. (11) Modified Simplex Method for Determining Parameters K and R of Equation 2. A pair of values for K and R was chosen and inserted in eq 2. The mean square was determined of the deviations between the experimental COHb % values and the values of COHb Yo calculated from the equation. The function 2 was defined as the reciprocal of this value, and the purpose of the procedure was to maximize 2 by an iterative procedure: 2 = n/C[(COHb%)i - (COHb%)i,,p]2
(25)
i=l
where n = number of points to be fitted, each at a different time, (COHb%)i = carboxyhemoglobin calculated from eq 2 by using the selected parameters K and R and the time corresponding to the point, and (COHb%)i,,p = carboxyhemoglobin experimentally measured for the same point in time. This procedure was repeated for two more pairs of K and R. The three points, A, B. and C, shown as a simplex triangle in Figure 8, represent these selected pairs in a field of K and R illustrating hypothetical values of 2. The point with the highest calculated 2 is labeled A, and the one with the lowest 2 is labeled C. These points should be selected so that they are not on a straight line. The computer next calculates the coordinates of the next estimated pair of K , R values (labeled P in the figure) by
moving away from the worst point, C, using the following rules: (1)Calculate M as the midpoint of AB. (2) Calculate p1as M + LO~GE.Calculate zp1. (3a) If 2, > Zpl,then abandon PI and calculate as M - 0.5m.Calculate ZPq5. (3b) If 2, > Zpl > Zc, then abandon PI and calculate as M 0 . 5 E . Calculate Zpo,s. (3c) If ZA > Zpl > ZB, then retain PI. (3d) If Zpl > Z A , then calculate Pl.s as M + 1.8m. Calculate Z,,,. If Zpl, > ZA,then abandon PI. Otherwise abandon Pl,& (4)Of the four points A, B, C, and P, discard the one with the lowest Z value and relabel the remaining ones A, B, and C, as before, in descending order of their Z values. Then go to step 1. The computer was programmed to tabulate the successive values of K and R and corresponding 1/Z values. The latter declined with the newly selected points, and the program was stopped when the mean square deviation appeared minimized to the desired degree of accuracy. The automatic expansion and contraction of the simplex triangle as presented made the procedure almost automatic. It was convenient and easily programmable on a microcomputer. No difficulty was experienced with this application. However, under some conditions the method may fail, and there is no guarantee that the best solution will be obtained for certain relationships. This may be clarified by viewing Figure 8 as a topographic map of values of Z for different pairs of values of K and R. It is possible that several peaks may exist and that the simplex triangle will center on one that is not the highest. This can be checked by repeating the procedure with a new set of three initial points in a different area. An empirical check of the validity of the solutions was the reasonably low root mean square deviations of the fitted lines from the experimental points, as shown in Table I and Figures 2-4. It was noted that slight errors in the experimental data could result in substantial changes in the resulting calculated values of K and R. Registry No. CO, 630-08-0.
+
Literature Cited (1) National Institute for Occupational Safety and Health Criteria for a Recommended Standard-Occupational Exposure to Carbon Monoxide; Pub. No. (HSM) 73-11000, U.S. Department of Health, Education and Welfare: Washington, DC, 1972. (2) National Air Pollution Control Administration Air Quality Criteria for Carbon Monoxide; NAPCA Publication No.
AP-62, U.S. Department of Health, Education and Welfare: Washington, DC, 1970. (3) Saltzman, B. E. J. Air. Pollut. Control Assoc. 1970,20,660. (4) Saltzman, B. E. U S . Environ. Prot. Agency, Res. Dev., [Rep.]EPA 1974, EPA-650/4-74-038,11-1-11-13. (5) Montcastle, V. B., Ed. Medical Physiology, 13th ed; C. V. Mosby Co: St. Louis, MO, 1976; pp 1382-1387. (6) Hatch, T. F. Arch. Ind. Hyg. Occup. Med. 1952, 6, 1. (7) Forbes, W. H.; Sargent, F.; Roughton, F. J. W. Am. J. Physiol. 1945, 143, 594. (8) Forester, R. E.; Fowler, W. S.; Bates, D. V. J. Clin. Invest. 1954,33, 1128. (9) Coburn, R. F.; Forester, R. E.; Kone, P. B. J.Clin. Invest. 1965,21, 1899. (10) Peterson, J. E.; Stewart, R. D. Arch. Environ. Health 1970, 21, 165. (11) Goldsmith, J. R.; Terzoghi,J. Arch. Environ. Health 1963, 7, 33. (12) Marcus, A. H. Atmos. Environ. 1980,14,841; 1981,15,1776. (13) Joumard, R., et al. Environ. Health Perspect. 1981,41,277. (14) Collier, C. R.; Goldsmith, J. R. Atmos. Environ. 1983, 17, 723. (15) Stewart, R. E.; Fisher, T. N.; Baretta, E. D.; Herrmann, A. A. Arch. Environ. Health 1973, 26, 1. (16) Jones, R. M.; Fagan, R. Arch. Environ. Health 1975, 30, 1984. (17) Peterson, J. E.; Stewart, R. D. Am. Ind. Hyg. Assoc. J. 1972, 33, 293. (18) Stewart, R. D., et al. J. Am. Med. Assoc. 1976, 235, 390. (19) Jones, H. A.; Clark, J. C.; Davies, E. E.; Forester, R. E.; Hughes, J. M. B. J. Appl. Physiol. 1972, 52, 109. (20) MacIntyre, N. R.; Nadel, J. A. J. Appl. Physiol. 1982,52, 1487. (21) Meyer, M.; Lessner, W.; Scheid, P.; Piiper, J. J. Appl. Physiol. 1981, 51, 571. (22) Saltzman, B. E. Anal. Chem. 1961, 33, 1100. (23) Hall, L. L., et al. Lab. Anim. Sci. 1974, 24, 79. (24) Buchwald, H. Am. Ind. Hyg. Assoc. J. 1969, 30, 514. (25) Deming, S. N.; Morgan, S. L. Anal. Chem. 1973, 45, 279A-283A. (26) Commins, B. T., et al. Zntercomparison of Measurement of Carboxyhemoglobinin Different European Laboratories and Establishment of the Methodology for the Assessment of COHb Levels in Exposed Populations;Health and Safety Directorate; Doc. V/F/1315/77e, Commission of the European Communities: Luxembourg, May, 1977. (27) Holland, R. A. B. Gen. Physiol. 1965, No. 2, 199-200. (28) Holland, R. A. B. Respir. Physiol. 1969, 7, 30-42, 43-63. (29) Saltzman, B. E. Am. Znd. Hyg. Assoc. J., in press.
Received for review December 17, 1984. Revised manuscript received October 21, 1985. Accepted April 21, 1986. This work was supported in part by National Institute of Environmental Health Sciences Grants ES 00159 and IF 22 ES 02844.
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