Predicting The Carboxyhemoglobin
Levels Resulting From
Carbon Monoxide Exposures
The Department of Environmental Medicine
Report No.: CRC APRAC CAPM-3-68 MCOW- ENVM- CO-73-1
JUNE, 1973
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PREDICTING THE CARBOX ^HEMOGLOBIN LEVELS
RESULTING FROM
CARBON MONOXIDE EXPOSURES
By
Jack E. Peterson, Ph.D.
Richard D. Stewart, M. D.
Following is an alphabitical list of those persons who
contributed information contained in this report:
Eleanor Bachand, R.N.
Edward D. Baretta, M.S.
Hugh C. Dodd, B.S.
Karen K. Donohoo, B.S.
Sally A. Graff, B.S.
Carl L. Hake, Ph. D.
Paul E. Newton, M.S.
Report No. : CRC APRAC CAPM-3-68 MCOW-ENVM- CO-73- 1
From the Department of Environmental Medicine, The Medical College of Wisconsin,
Allen-Bradley Medical Science Laboratory, 8700 West Wisconsin Avenue, Milwaukee,
Wisconsin 53226
Supported by Contract CRC-APRAC. Project No. CAPM--3-68, from the Coordinating
Research Council, Inc. , and the Environmental Protection Agency
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SUMMARY
Data from a series of human exposures to carbon monoxide were ana-
lyzed to determine the fit to the theoretical Coburn, Forster, Kane (CFK) equa-
tion as a function of experiment duration and CO concentration, exercise level,
and sex. The equation was found to predict carboxyhemoglobin (COHb) levels
for both men and women at exercise rates ranging from sedentary to 300 kp-m/
min when they were exposed to steady CO concentrations of 50, 100, and 200 ppm
for 0.33 to 5.25 hours. In addition, the equation accurately summed the results
of a discontinuous exposure to CO.
Methods for determining values of each of the variables in the CFK
equation were collected and a rational, efficient procedure for solving the equa-
tion by trial and error was outlined. The CFK equation was then used to prepare
a graph relating COHb saturation to exposure duration and concentration, and
also to describe the effect of several variables on the rate of CO uptake and
equilibrium COHb levels.
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INTRODUCTION
From the time of Orfila (who first established a relationship between
dose and effect), acute effects of toxins have been related to the dose admin-
istered by ingestion, by injection, and more recently, by skin absorption.
With the advent of inhalation experiments, however, the concept of, "dose"
(or the amount of material in the body - the body burden) became nebulus as
there was no simple relationship between dose and exposure parameters.
Consequently, effects of experimental inhalation exposures have been related
to concentration and to exposure duration instead of to body burden or dose.
If quantitative information is available on excretion of the material
administered (or on one of its metabolites), that data can often be described
by an empirical equation which can then be used to calculate a value propor-
tional to the total body burden. '*' > ) The main difficulty with this or any
other empirical approach is that while the results may be useful for interpo-
lation, they will not be useful for extrapolation to conditions other than those
of the experiment. Nevertheless, the empirical treatment of excretion data
to estimate body burden is an extremely important first step toward true
exposure integration.
The technique called the "time-weighted average" has been used in
lieu of true exposure integration and even has a more-or-less official
/4\
sanction. . v ' If an inhalation exposure is broken into time intervals, t,
each of a generally steady concentration, c, then the time-weighted average
(TWA) is found as:
TWA = Ect/Et (1)
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- 2 -
Use of equation 1 for estimating dose tacitly assumes that molecules
inhaled at the beginning of the exposure contribute to the total dose or body
burden equally with those molecules inhaled at the end of the exposure.
This assumption can be true only if none of the material is excreted during
the exposure or if each exhalation excretes 100% of the total body burden at
that time. Either of these conditions may be approached, but neither is likely
to be fulfilled for any real gas or vapor exposure, and therefore the TWA
cannot be an accurate representation of the dose received.
Even though the TWA based on "interval" sampling does not accurately
represent the dose, it does correspond,quite well to concentrations found by
cumulative air sampling methods. (A good cumulative air sampler operated
throughout an exposure does not "excrete" any of the trapped material. ) Fur-
thermore, methods to supplant the TWA have not been available, nor has
there been any tremendously pressing demand for their development. That
the TWA is used almost universally today to represent dose, testifies that
its errors are not large for most materials in comparison with other errors
inherent in the evaluation of inhalation hazards. But with the advent of auto-
mated general .area air samplers, personal "dosimeter samplers" and
computer data analysis and reduction, the "other errors inherent in the
evaluation of inhalation hazards" are becoming smaller. '^> "' Consequently,
'there is a demand for sumrna.tion or integration techniques capable of pro-
ducing numbers more truly representative of the dose received than the TWA
technique allows. Because they are based on experimental data, empirical
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- 3 -
methods of estimating man's body burden from excretion data will usually
give better results than the TWA. However, still better results can be
expected from models of uptake and excretion based on a good theoretical
approach. Of course, all models must be verified by experiment.
Carbon monoxide is almost the ideal gas for which to formulate a
theoretical uptake-excretion equation. Inhaled CO passes through the lungs
to the blood stream where it attaches firmly but reversibily to proteinaceous
material, chiefly hemoglobin. Its concentration in blood (as carboxyhemo-
globin, COHb) readily becomes high enough for accurate determination by
inexpensive methods while still being low enough to have no delaterious
effects. Furthermore, CO stays in the blood, does not react appreciably
with other materials, tissues or fluids, ''' and is excreted unchanged and
quantitatively through the lungs. The one minor complication is that CO is
produced in small quantities in the body and thus the blood always contains
a background endogenous level of COHb.
The rate of endogenous CO production is increased by some disease
states, specifically those which result in red cell destruction. Investigators
of this and other related phenomena have felt a need for a mathematical
model of the way the human body handles CO so that they could better under-
stand the effects of disease. None of the proposed models was particularly
successful until 1965 when Coburn, Forster and Kane published the derivation
of a new model. \°' They used this model successfully in a study of endogenous
CO production, but they did not study inhaled (exogenous) CO.
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-4-
Their model (the CFK equation) was tested by Peterson and Stewart in
1970 with data from the exposure of sedentary, male Caucasians \'>. Those
experiments included oxygen inhalation therapy, long and short-term exposure
to constant concentrations, a discontinuous exposure, and an exposure to a
steadily rising concentration. In all cases, the CFK equation "fit" the data
very well when average values were used for most of the subject-specific
variables. The purposes of the present study were to extend the testing of
the equation to include women as well as men at several exercise levels and
to extend the computer program used for solving the equation to treat as
variables several of the previously constant parameters.
THE CFK EQUATION
The basic form of the CFK equation is as follows:
A[COHbl, - V_B - PT
c uu ro
_ = exp (-tA/V.B) (2)
- VCQB -
where:
A = Pr /M[O?Hbl
"
°2
B - 1 +
^/^ A
'O
M = Ratio of the affinity of blood for CO to that for O?
[O Hbl = milliliters of QZ per milliliter of blood
[COHb]t = milliliters of CO per milliliter of blood at time t
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- 5 -
[COHb] 0 = milliliters of CO per milliliter of blood at the
beginning of the exposure interval
p. = average partial pressure of oxygen in lung capillaries,
mm Hg
= rate of endogenous CO production ml/min
= diffusivity of the lung for CO, ml/(min) (mm Hg)
= barometric pressure minus the vapor pressure of
water at body temperature, mm Hg
= blood volume, ml
PT = partial pressure of CO in the inhaled air, mm Hg
V^ = alveolar ventilation rate, ml/min
t = exposure duration, min
exp = 2.7182 . . . the base of natural logarithms raised
to the power of the bracketed expression
In the original solution of this equation for exogenous exposure to CO, (9
all variables were considered constant except t, PL. [COHblt and PI,,.-. The
OO
remaining variables are not constant, however, and methods are needed for
their evaluation.
The Affinity Constant (M);
Several investigators have reported values for the ratio of the affinity
of hemoglobin for CO to that for ©2- This ratio varies widely between species,
and also varies from individual to individual. For man, values ranging from
about 150 to 300 have been used as "average" or "normal".
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- 6 -
Rodkey, et al' ' determined the ratio of the affinity for 13 male
and 2 female subjects in whole blood and hemoglobin solutions. The values
found ranged from 197 to 229, averaging 217.7, with a standard deviation
of 7. 32. An average of 218 appears to be appropriate for man.
Average Partial Pressure of Oxygen in Lung Capillaries (P^ ):
_ _ °2
Data for values of PC are extremely difficult to obtain. Coburn,
Forster, and Kane suggest a value of 100 mm Hg, and this is probably ade-
quate if the partial pressure of C>2 (?Q ) in the air that is breathed does not
L*
differ greatly from 150 mm Hg in air saturated with water at body tempera-
ture. However, if pure Q-^ is being breathed, or, if the exposure takes
place under a reduced or elevated total pressure (on a mountain or in a cais-
son, for instance), a value of 100 mm Hg for P~ will be incorrect.
°2
When the inhaled P.-. is greater than "normal", the value of Pr
°2 * C02
will be greater than 100 mm Hg. To determine an approximate value the
following technique appears reasonable:
For a barometric pressure, PR in (in mm of Hg), and a vapor
pressure of water at body temperature of 47 mm of Hg, the
partial pressure of oxygen in saturated inspired air (Pj )
L*
can be calculated from the fraction of oxygen in inspired air
(F'o):
Ln ^n
°2 °2
(PB - 47>
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- 7 -
If "normal" values are applied in this equation, the PIQ, is found to be
149 mm Hg. To reach the 100 mm Hg recommended for PCO in these circum-
stances, 49 must be subtracted. This number (49) represents the level of
CO? in alveolar air and also the effect of averaging over all lung capillaries.
If this value is reasonable under normal conditions, it should be in must
others and consequently,
When PIO? is less than 149 mm Hg, PCO2 wil1 be less than 10° mrn
At these lower values of PIQ? t^le relationship between the partial pressure
of oxygen in air and blood is no longer linear because hemoglobin cannot be
assumed to be saturated (or nearly so). The average partial pressure in lung
capillaries cannot be greatly different from that in mixed arterial blood, and
data for estima.ting oxygen partial pressure in arterial blood as a function of
inspired oxygen partial pressure are available. "*' These data were submitted
to a computerized regression program, resulting in:
_ 2
. 072- 0.00079 Pi02 + 0.000002515 PIO?)
where PlQ2 is the partial pressure of oxygen in the inhaled air in mm of Hg.
Rate of Endogenous CO Production
The normal rate of production of CO by the body is approximately
0.007 ml/min STPD. , but some diseases can cause an increase. (8)
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- 8 -
Diffusivity of the Lung for CO (DL ):
\J W .
Lung diffusivity varies with many conditions including the molecular
species, body size, rate of work, temperature, pressure, etc. In this case,
only the diffusivity of the lung for CO is of concern a.t an assumed normal
body temperature (37°C). Body size effects on diffusivity at rest were assem-
bled and graphed by Coburn. ' ' A regression equation for his data was
derived:
DL = l/[-0.0287 + 0. 1188/A]
(r = 0.994)
where Dj^ is diffusivity in ml CO/min-mm Hg and A is the body surface
area in m .
Similarly, data on the effect of work rate as indicated by the oxygen
consumption rate ' ' were submitted to a computer regression program.
The resulting equation is:
= l/[0.'l05 - 0.0246 log (VOJ]
2
(r = 0.775)
where VQ is the oxygen consumption rate in ml/min.
Blood Volume (VK);
The blood volume of average men is 74 ml per kilogram of body weight,
while that for women is 73 ml per kilogram. (14) Prolonged strenuous
exercise
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- 9 -
may increase these values. Coburn, Forster and Kane use a value of 5500
ml, which they assume to be average for all body weights.
Partial Pressure of Inhaled CO (Pj ):
Gas or vapor concentrations of interest are usually expressed in
parts per million by volume (ppm). Conversion to partial pressure is easily
done.
Pj _ = (ppm) (barometric pressure in mm Hg)/10
Alveolar Ventilation Rate (V"A):
If the total rate of ventilation, in ml/min, is V-r,, the dead space
(ml) is VD, and the respiration rate (min"1) is f, the alveolar ventilation
rate VA (ml/min, BTPS) is:
VA = VE - £VD (3)
Unfortunately, the dead space, V^, is not constant but increases with exercise.
At rest for normal men, VT-J is about 170 ml, but in heavy exercise may reach
350 ml. The relationship between dead space and total ventilatory rate
appears to be linear^5) so that equation 9 can be revised:
VA = V£ - f (132 + 0.067 V£)
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- 10 -
At low exercise rates, total lung ventilation increases linearly with
exercise, and also with the oxygen consumption rate, VQ , but begins to
L*
increase more rapidly at higher exercise rates. This rate increase varies
with each subject but on the average, a VQ of 1000 ml/min (STPD) requires
L*
a VE of approximately 22, 000 ml/min (BTPS).
Oxyhemoglobin Concentration ([O2Hb]):
If the concentration of COHb in the blood is low, [C^Hbl can be consid-
ered constant at a value determined by the individual's hemoglobin concentra-"
tion. At standard conditions (STPD, or 760 mm Hg, 0°C, dry), one gram of
hemoglobin will hold 1. 38 ml of oxygen. 'ifc)' The maximum number of ml of
C>2 per ml of blood is found as:
[02Hb]max = 1.38 Hb/100
where Hb is the hemoglobin concentration, g/100 ml. This value is, of
course, also the number of ml of CO per ml of blood at 100% saturation and
since both CO and Q-^ compete for sites on hemoglobin,oxyhemoglobin concen-
tration is never [Pz^-^max. ^ut something less. During and after an exposure
to CO, the value of [C^Hb] that must be used in equation 2 is actually [O2Hb]rna
[COHb] But, [COHblj. is the variable being determined; it appears on both
sides of the equation and in an exponent of e on one side.
Under these circumstances, no direct solution of equation 2 is possible,
and a "trial-and-error" method must be used but the "new" value of [COHb]j-
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- 11 -
must not be the previously calculated one or the solution may diverge. A
successful procedure is indicated in the following steps:
a. Assume a value for [COHb]t (such as zero) and find [O2Hb] =
- [COHb]t
b. Calculate a new value for [COHb]t using equation 2
c. Check to see if the difference between the old and new values
of [COHblt is acceptable. (A maximum difference of 0. 00001
may be used). If so, the problem is solved; if not, proceed
to step (d).
d. Set the "old" value of [COHb]t equal to the one found in step (b).
e. Calculate a new value of [O2Hb] using equation 4 and proceed
to step (b).
P =.Q D - R/(R + S)] (4)
where:
P = the new value of |"O2Hb]
R = the old value of [COHb]t
S = the old value of [O2Hb]
This procedure converges on a solution for all values of [COHb].,
but is most rapid if a good guess of the proper value of [COHbK can be made
in step (a).
Carboxyhemoglobin Concentration ([COHb]);
The concentration of COHb found in the previous step at time t is
expressed in ml of CO/ml blood. To convert this value to the more conven-
tional "percentage saturation", multiply by 100 and divide by [O2Hbl _ .
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. - 12 -
The value of [COHb] used in equation 2 may range from the nominal
for a non-smoker of about 0. 5 to 1. 5%, averaging .1. 2% saturation (about
0. 0024 ml CO. per ml blood) to the heavy smoker's 5 to 7% (about 0.012 ml/
CO /ml blood) to the concentration of [COHb], calculated by using equation 2.
By using the just-calculated value of [COHb~lt successively as the new value
of [COHb] , any exposure or any series of exposures to any concentration of
CO (including zero) for any time interval can be summed.
TESTING THE EQUATION*
In the previously reported use of the CFK equation for exogenous
CO exposure^ ' no attempt was made to individualize the subject - specific
variables. For the present study, all available data on each subject were
used and "average" values were used only in those cases where individual
data were not available. Specifically, data were available or were obtained
for 22 subjects on non-exposed COHb level, hemoglobin concentration, and
alveolar ventilation rate at several exercise levels. Data on height and
weight were used to calculate blood volume and resting lung diffusivity for CO.
Data specific to each subject will be found in Table I. Particularly
noteworthy is the variability of alveolar ventilation rates .when the subjects
were sedentary. Values of V ^ ranged from 6. 2 L/min to over 17 L/min,.
#Data were collected from several experiments, some previously published,
carried out by the staff and faculty of the Department of Environmental
Medicine, Medical College of Wisconsin.
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- 13 -
and the differences were apparently real. Values for hemoglobin, non-
exposed COHb level, blood volume and lung diffusivity did not vary as
greatly, and averaged to expected levels.
Volunteer subjects were exposed to CO in the chamber previously
described. Concentrations of CO varied from 50 to 200 ppm, and during any
single exposure the coefficient of variation (the standard deviation of concen-
trations expressed as a percentage of the mean) was less than 5%. Exposure
durations ranged from 0. 33 to 5. 25 hours.
Blood samples were obtained prior to exposure, periodically during
exposure, and in the post-exposure period, occasionally for several hours.
These samples were analyzed on an IL/ CO-Oximeter which was kept in
calibration and continually compared with samples analyzed by a gas chromato-
graphic method. '* '> Expired air samples were also used to confirm blood
levels when such confirmation was felt to be appropriate. All analytical
methods were in complete agreement throughout the study.
In all but experiment 51, when none of the subjects exercised, the
following protocol was used: Blood samples were obtained and the subjects
then entered the exposure chamber (the 20 x 20 x 8 ft. room previously
described)' °> in which the concentration of CO in air was being maintained.
After initial procedures which took from 10 to 18 minutes (carefully timed),
the first group of four people began a 45-minute ride on the bicycle ergometers
(Krogh Monark). Just prior to the end of that ride, blood samples were
obtained from the second group of four subjects through an arm-port in the
chamber door. When the first group finished, the second group began to ride
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-14-
while blood samples were obtained from the first group. When the second
group finished, blood samples were obtained from all subjects and then all
persons remained sedentary for the remainder of the exposure.
The ergometers were used at a constant pedal speed of 50 rpm (a
metronome was used to pace the subjects) and at loads of 1, 0. 5, and 1. 0
which resulted in work rates of 0 (WBL or working baseline), 150, and 300
kp-m/min. At a time near the end of each ride, the expired air was collected
for an accurately-timed two minutes, and during that period a count was made
of the number of respirations. The expired air volume and respiratory fre-
quency were later used to determine the alveolar ventilation rate with equa-
tion 3. The 2 to 6 determinations of V. were later averaged for each sub-
ject (Table I).
At least two expired air samples were collected from each subject
while he or she was sedentary. Ventilation rate and frequency were used to
determine the alveolar ventilation rate as during exercise.
All 22 subjects participated in sedentary experiments, but only 15
exercised. Most of the exercise work was done at the highest of the three
levels. In all, 11 experiments were performed at other than sedentary levels,
and of those, 8 were at the highest rate. All of the female subjects partici-
pated in the exercise studies.
A pre-exposure blood sample was obtained from each subject. In
the few cases where that data were lost, the average non-exposed level for
that subject was substituted. (These levels were determined during control
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- 15 -
experiments. ) This level was taken as the initial COHb level for use in
equation 2. The duration of an exposure segment for the subject under con-
sideration was then taken as the length of time he or she was exposed until
the next blood sample was taken.
Available then, were an initial level of COHb, and an actual final
level for that exposure segment. Using subject-specific and exposure-
specific parameters, equation 2 was used to calculate a predicted COHb
level. The actual and predicted levels were then used to form the statistics
necessary for their comparison. Then, the actual COHb level wa's used
as the initial COHb level for the next exposure segment. This procedure
was also followed for post-exposure data which were obtained. The statistics
were accumulated so that an examination could be made of the effects of the
experiment, of the subject, and of the exercise level on the ability of the
CFK equation to predict COHb concentrations. For this determination, both
the standard error and the correlation coefficient were used.
Table II contains a list of the experiments conducted, including the
nominal CO concentration and the number of subjects. (Dstails of each ex-
periment are in the appendix. ) These data show that there was no effect of
CO concentration on the fit of the CFK equation. This was so even in experi-
ment 51 where the concentration varied from 0 to 164 ppm.
Table IV is similar to Table II, except in this case the variable analyzed
was subject number. There was no evident sex bias and, in general, correlation
coefficients were high.
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- 16 -
Table V shows that the ability of the CFK equation to predict COHb
concentrations was not a function of exercise level as the .equation performed
equally,well at the high level of exercise an,d,with sedentary subjects. The
high exercise level (300 kp-m/min) was equivalent to an oxygen consumption
rate of about 1. 0 L/min, or to the energy expenditure of a man driving a
truck in traffic. This level is not high in comparison to that in. many athletic
endeavors, but ms.y be representative of the work being done during many
industrial exposures to CO. .
In experiment 51, the subjects were exposed,for 60 minutes to approxi-
mately 150 ppm CCX They then left the chamber for%30 minutes. While they
were gone the concentration was reduced to about 50 ppm so that when they
reentered they were exposed to the lower concentration. After an hour at
50 ppm they ag.ain left for 30 minutes while the concentration was increased.
to about 100 ppm in preparation for the final exposure hour..
Venous blood samples were obtained, every 20 minutes in the chamber,
at the end of each 30-minute period outside the chamber, and then twice at the
conclusion of the experiment. Details of this exposure will be found in Table III.
Values of COHb percentage saturation in experiment 51 for the seven subjects
(sedentary white males) were averaged and plotted against time in Fig. 1.
(Individual values will be found in the Appendix. ) The CFK equation was then
used to predict COHb levels for each subject at the end of each experimental
segment. An average value of 30 m]/min-mm Hg was used for DL, and
6000 ml/hr was assumed for VA! these data were not available for this group
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- 17 -
of people. In each case, the pre-exposure COHb level was used in equation 2
for [COHb]0, and then [COHb]t was calculated for a 20-minute exposure to
150 ppm. Then that value (not the actual level found) was used as the [COHb]o
for the next (164 ppm) segment, etc. For each exposure segment, the values
of [COHb]j- were averaged for the seven subjects and plotted in Figure I as
predicted values.
The remarkable ability of the CFK equation to sum exposures to CO
is well illustrated in Figure 1 . Only at the beginning and end of the first
30-minute period of non-exposure was the prediction in error by more than
0. 5% saturation. That error may well have been in the "actual" values as
indicated by the low slope of this curve over the first zero-exposure segment.
(All of the non-exposure segments should have about the same slope. ) Further-
more, after 90 minutes both actual and predicted values are very close; the
nature of this kind of prediction is that an early error tends to be propagated
and no propagation was seen. At any rate, the error was small, and the theor-
etical CFK equation was shown well able to sum the results of this type of
exposure.
CONCLUSIONS
The CFK equation appears to predict COHb levels as well for women
as it does for men even though the female subjects did absorb CO more rapidly
than did most of the male subjects. Furthermore, exercise sufficient to
increase the alveolar ventilation rate by a factor of about 2. 5 from sedentary
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- 18 -
levels did ii6t materially alter the fit of the equation to the data. Finally,, a'
discontinuous 'exposure to varying CO concentrations was summed with excep-
tionally good results. All of this information indicates that the CFK equation
is a good theoretical model of the uptake and'excretion'of carbon monoxide.
Because the model is based on a'theory which1 extensive 'experimentation
has yet to contradict, moderate extrapolation from the experimental'data
should be practical. On this basis Figure 2 was constructed, -relating per-
centage carboxyhemoglobin to exposure duration for a.series of CO concentra-
tions in ambient air and nominal values of other parameters. The lowest
concentration; 8. 7 pp'm,~ is equivalent to that allowed by the Environmental
Protection Agency to exist for eight hours in the ambierit'air 'no more often
than once per year; (1°) --No'human experimentation has been.-conducted at this
concentration.
A concentration of 50 ppm was chosen because this is the current
Threshold Limit Value (TLV) of the Ame'rican Conference of Governmental
Industrial Hygienists. (4) A level of 35 ppm was used b'ecause this concentra-
tion has been proposed as a new TLV: 100 ppm was the TLV for many years.
The remaining concentrations, 25, 200, 500 and 1000 ppm were chosen be-
cause human exposures have been conducted recently at these levels. '^J The
CFK equation was shown to fit' the resulting data very well. ('A graph similar
to Figure II was published previously. :(9) That graph is in error at*high levels
of COHb and long exposure durations :because [O2Hb] was regarded as a constant,
not a variable, in solving the CFK equation. )
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- 19 -
Information in.Figure 2 pertains to many CO exposures, but many
exposures also take,place under, other conditions. To. show the.relative effect
of some of the exposure and person.-specific parameters on CO uptake, Table
VI was; constructed. Values of % COHb .saturation were found by. solving
equation 2 using the parameter levels listed in Table VI. In each case, the
parameter indicated,was, the only one changed from the value indicated in
Figure,2.. Also, levels of each parameter were chosen to represent real but
extreme conditions which might be .encountered. Results of, this exercise
give at. least a/partial indication of the effect.of each parameter on.;the-uptake
of CO.
Figure 2 shows that equilibrium is approached very slowly at low
concentrations, taking about 24 hours at 25 ppm and below. On the other
hand, equilibrium is complete in about 8 hours at 1000 ppm. Therefore, in
Table VI, the 1000 ppm column at 480 minutes is representative of the effect
at equilibrium of any (except CO concentration) of the parameter changes.
Only barometric pressure and oxygen concentration appear to have any great
effect on COHb levels at equilibrium. All of these parameters, on the other
hand, exert at least some effect on the rate at which equilibrium is approached.
As parameters were varied one at a time in constructing Table VI,
the effects of varying two or more at once are not apparent. Experimentation
with equation 2 shows that such effects can be much more than additive,
especially where the rate of CO uptake is concerned. For instance, a fire
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-20-
in an enclosed space will result in a low oxygen; concentration and a .high
level. , The high CD-? level can, in turn, cause mor6 'rapidr:respirati'6n and'
therefore, .a high V.. A combination of 10% oxygen, a VV of 25 L/min, and
a CO concentration of only 1000 ppm can be found to result in- a COHb level of
57. 1% in 60 minutes (the equilibrium value in this case'is 82. 5%).
Even though' the CFK equation has not been completely tested at all
levels of all parameters (and such testing is, in fact, impossible), present
indications are that it describes uptake and excretion of CO very well. This
equation appears .suitable for general use in predicting the consequences of
specific circumstances as well as for summing more ore less long-term
exposures to varying concentrations.
ACKNOWLEDGMENT
The exercise studies could not have been done without the active assis-
tance and cooperation of Mrs. Karen Donohoo, Mrs. Sally Graff, and Mr.
Paul Newton. Their help is gratefully acknowledged.
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TABLE I
SUBJECT INFORMATION
Subject
1
6
7
8
9
10
11 9
12 9
219
22
25
29
31
32
33
40
58
59
COHb
0.89
1.36
0. 71
1. 19
0. 69
1. 50
0. 79
0. 58
0. 86
0.89
1. 02
0. 93
1. 05
1.39
1.39
1. 20
1.4
1. 3
Hb
g/100 ml
17.06
17.45
14.41
14. 17
16. 10
16. 93
13. 92
14.43
13. 63
15. 27
16. 07
14. 70
15. 82
16.66
16. 42
14. 54
15. 96
16. 54
ml
5213
6223
5213
5718
5718
7400
3716
4645
4380
4709
5214
4877
5550
6593
4204
5348
5381
5247
VA in ml/min. ..nT -
** 1 j
Sed. WBL .150 300 CO
6233
17057
13721
10714
12939
10334
8424
9770
9025 10388
6518 10876
7461 13893
10513 19630
10888 11423
7426 18845
7710 9614
-_
-_
2Q480
29021
25619
19665
24516
27441
15946
20188
12918 21886
17439 21189
20798 24440
20332 25924
16514 20513
16710 25525
17176 23816
__
-_
33.0
--
23.7
25.7
30. 5
28. 1
30. 2
38. 6
22. 0
--
continued.
-------
TABLE 1, SUBJECT INFORMATION - continued
Subject
60
63
64
65
COHb
%
1.4
2.3
1. 5
1.3
Hb
g/100 ml
15.86
15.07
15.45
15. 30
VK VA in rnl/min. DT
D A -L-ipO
ml Sed. WBL 150 300 ^^
5886 -- -- -- -- .'""--
4541
4877 -- --'
5886
Average
-------
TABLE II
Fit of. the CFK Equation
As a Function of Experiment
Experiment Number Nominal Minutes of Total Standard Correlation
Number of Subjects ppm CO Exposure Segments Error Coefficient
1
2
3
6
7
10
41
43
44
47
50
51
8
8
8
8
7
8
7
7
7
7
6
7
100
50
200
50
200
100
200
200
200
200
200
**
315
300
310
290
265
265
274
270
268
255
270
240
32
24
24
55
47
55
21
21
21
21
18
90
1.
0.
3.
0.
1.
1.
3.
1.
1.
1.
2.
0.
23
60
13
.68
72
06
10
92
47
56
31
58
0. 94
0. 94
0. 95
0.84
0.92
0.88
0. 96
0.99
0.98
0.96
0.97
0.90
**Fluctuating concentration. See Table III
-------
TABLE III
Fluctuating Concentrations in Experiment 51
Segment
1
2
3
4
5
6
7
8
9
10
11
12
13
Duration,
min.
20
20
20
30
20
20
20
30
20
20
20
15
15
CO Concentration,
ppm
150
164
142
0
45
52
49
0
105
88
122
0
0
-------
TABLE IV
Fit of the CFK Equation
To Exercise Data for Individual Subjects
Subject
No.
1
6
7
8
9
10
119
129
21 9 .
22
25
29
31
32
33
40
58
59
60
Segments
21
29
30
30
30
27
35
35
15
15
15
15
15
12
15
12
13
13
13
Standard
Error
0.74
1.97
2. 20
1.21
1.36
0.81
1. 54
1. 22
2. 52
1.95
1.93
2.69
2.45
1.28
2.09
0. 60
0. 79
0. 58
0. 55
Correlation
Coefficient
0. 9892
0. 9075
0.9352
0.9782
0. 9701
0. 9832
0. 9573
0. 9758
0. 9287
0. 9436
0. 9550
0. 9587
0.9623
0. 9723
0. 9459
0. 9123
0.7909
0. 9158
0. 9183
-------
TABLE 4, continued
Subject
No.
63
64
65
Segments
13
13
13
Standard
Error
0. 68
0. 54 '
0. 56
Correlation
Coefficient
0.8338 ;
'0.9101 '
0. 9084
-------
TABLE V
Fit of CFK Equation
at Four Exercise Levels
Exercise Correlation
Level Segments ' Standard Error Coefficient
Sed. 344 1.53 0.9712
WBL 7 1.34 0.9553
150 13 2.55 0.7929
300 61 1.02 0.9654
-------
TABLE VI
Effect of Various Parameters on COHb Saturation
(Values are % COHb Levels Calculated from the CFK Equation
by Changing Only the Indicated Parameter. )
Parameter
Nominal (Fig. II)
PB = 400 mmHg
PB = 600 mmHg
PB = 1500 mmHg
VA = 15 L/min.
VA = 50 L/min.
VA = 100 L/min.
Vb = 1000 ml
Vb = 2000 ml
Vb = 7000 ml
[COHb]Q = 2%
[COHb]Q = 7%
DL = 10 ml/min-mmHg
DL = 50 ml/min-mmHg
% 02 = 10
% O2 = 100
Hb = 10 g/ 100 ml
Hb = 20 g/100 ml
60-Minute
Exposure
PPM CO
8. 7
0. 93
0. 96
0. 94
0. 39
1. 00
1. 08
1, 11
1. 30
1. 11
0. 90
1.94
6. 13
0. 90
0. 94
1. 02
0. 44
0. 99
0. 90
35
1. 58
1. 54
1. 58
0. 83
2. 14
2. 82
3. 07
3. 82
2. 67
1. 43
2. 60
6.77
1. 37
1.65
1.71
0. 87
1.93
1.40
1
1
1
1
2
3
4
5
3
1
2
7
1
2
2
1
2
1
50
.96
. 88
. 94
. 08
.79
.81
. 17
. 23
. 55
.73
.97
. 14
.63
.06
. 10
. 11
.46
.69
100
3. 20
3. 00
3. 14
1. 90
4. 95
7. 06
7. 80
9.82
6. 47
2. 72
4.21
8. 36
2. 52
3.41
3.42
1.93
4. 25
2. 64
1000
25. 0
22.8
24.4
15.5
40. 2
52.4
55.2
59.6
49. 5
20. 3
25.9
29. 7
18.2
27. 0
26.8
15. 5
34.4
19.5
480-Minute
8.7
1. 42
1.69
1. 51
0. 23
1.47
1. 47
1. 47
1.63
1.61
1.34
1.73
3. 00
1. 37
1.43
2. 25
0.25
1. 52
1. 33
35
4. 48
5. 03
4. 69
0. 84
5. 22
5. 45
5. 47
5.65
5. 55
4. 06
4. 77
5. 97
3. 90
4. 61
6.71
0. 90
5.07
3. 98
PPM
50
6. 18
6.89
6.46
1. 18
7.25
7. 59
7. 62
7.79
7.66
5. 58
6.46
7.61
5.31
6. 38
9.21
1. 27
7.01
5.46
Exposure
CO
100
11.6
12.9
12.1
2.30
13.5
14. 1
14. 1
14.3
14. 1
10.5
11.8
12.9
9.91
12.0
17.3
2.47
13. 1
10.2
1000
61.4
68.7
63.9
18. 9
62.2
62.2
62.2
62. 2
62. 2
60.4
61.4
61. 5
59.6
61.7
81.2"
20. 0
62. 1
60.2
-------
o
7.0,
3 6.O
o
c
!5
5.O.
Predicted by CFK equation
(Average of 7 subjects)
^Actual values
(Average of 7 subjects)
3O 6O 9O 12O I5O I8O 2IO 24O 27O
Exposure duration, minutes
Figure I Average carboxyhemoglobin levels of subjects in
experiment 51 compared with values calculated by
using the CFK equation.
-------
s 750mm Hg
100
c so!
O 70.
.£ 60.
O 50.
2 40.
(j> 30.
20-
o
o>
o
0)
.c
o
o
0)
o
10
9
8
7
6
5.
4.
3
2-
VA = GOOOml/min
Vb = 5500ml
M =218
DL =30tnl/min - mmHg
[COHbJ0 = 0.8%
Vco= 0.007 ml/min
1000 ppm
500ppm
10 2345 6789100 2 34567891000 2 34 5000
Exposure duration, minutes
Figure II Carboxyhemoglobin levels for man as a function of
exposure duration and of the CO concentration as
determined by solving the CFK equation.
-------
REFERENCES
1. LANGHAM, W. H. , Determination of Internally Deposited Radio-
active Isotopes from Excretion Analysis, Amer. Ind. Hyg.
a, 17:305-318, 1956.
2. LIPPMANN, M. , L. D. Y. ONG, and W.. B. HARRIS, The Signifi-
cance of Urine Uranium Excretion Data, Amer. Ind. Hyg.
Ass oc^J., , 2j>:43-54, 1964.
3. DIVINCENZO, G. D. , F. J. YANNO, and B. D. AST1LL, Human
and Canine Exposures to Methyl ene Chloride Vapor, Amer. jnd.
Hyg. Assoc._J., 33:125-135, 1972.
4. American Conference of Governmental Industrial Hygienists,.
Threshold Limit Values fr2, American Conference of Govern-
___
mental Industrial Hygienists, 1014 Broadway, Cincinnati, Ohio 45202,
1972.
5. PETERSON, J. E.., H. R. HOYLE, E. J. SCHNEIDER, Appli-
cation of Computer Science to Industrial Hygiene, Amer. Ind.
Hyg. Assoc. J. . 27, March-April, 1966.
6. BARETTA, E. D. , R. D. STEWART, J. E. MUTCHLER,
Monitoring Exposures to Vinyl Chloride Vapor: Breath Analysis
and Continuous. Air Sampling, Amer. Ind. Hyg. Assoc. J. ,
3^:537-544, Nov. -Dec., 1969.
7. LUOMANMAKI, K. , R. F. CO3URN., Effects of Metabolism and
Distribution of Carbon Monoxide on Blood and Body Stores, Am.
J. Physiol.. 2J_7:354-363, 1969.
8. CO3URN, R. F. , R. E. FORSTER, P. B. KANE, Considerations of
the Physiology and Variables that Determine the Blood Carboxy-
hemoglobin Concentration in Man, J_. _ Clin. Invest. , 41; 1899- 1910,
1965. ~
9. PETERSON, J. E. , R. D. STEWART, Absorption and Elimination
of Carbon Monoxide in Inactive Young Men, Arch, of Environ.
Health, JJ_1; 165- 171, August, 1970.
10. RODKEY, F. L. , J. D. O'NEAL, H. A. COL,L,TSON, Oxygen and
Carbon Monoxide Equilibria of Huma.n Adult Hemoglobin at Atmo-
spheric and ELevated Pressure, Blood, 33:57-65, 1969.
-------
- 2 -
11. ROUGHTON, F. J. W. , Transport of Oxygen and Carbon Dioxide,
H^dbppk_o^'Pjijr_s_iolo^, Section 3, J_:8i9, W. O. Fenn and H.
Rahn, Eds., Amer. Phys. Society, Washington, D. C. , 1964.
12. CO3URN, R. E., Diffusion of Gases, Hfn3bj^kjDf_Pjiysjolog_y_,
Section 3, J_:86l, W. O. Fenn and H. Rahn, Eds., Amer.
Phys. Society, Washington, D. C.., 1964.
13. Ibid, page 862.
14. SJOSTRAND, T. , Blood V olume, Handbook of Physiology, Section
2, j_:53. W. F. Hamilton and P. Dow, Eds., Amer. Phys.
Society, Washington, D. C. , 1962.
15. ASMUSSEN, E., Muscular Exercise, Handbook of Physiology,
Section 3, 2^961, W. O. Fenn and H. Rahn, Eds., American
Phys. Society, Washington, D. C., 1965.
16. ROUGHTON, F. J. W. , op. cit. , page 770
17. PORTER, K. , and D. H. VOL.MAN, Flame lonization Detection of
Carbon Monoxide by Gas Chromatogr.aphic Analysis, Anal. Chem. ,
24:748, 1962.
18. STEWART, R. D. , J. E. PETERSON,'E. D. BARETTA, R. T.
BACHAND, M. J. HOSKO, and A. A. HERRMANN, Experimental
Human Exposure to Carbon Monoxide, A^rch. of^Envi._ron± Health,
21_:154-164, August, 1970.
19. Cpde_of_F_eji_e_r_a_l_Regulatipn£, Chapter IV, Title 42, Part 410. 8.
-------
APPENDIX
-------
EXPERIMENT 1
Actual Carboxyhemoglobin Saturation at the Conclusion
of Each Exposure Segment
Cone. ,
pprn
Dur.,
min.
1
S 6
u
b 7
j
e 8
c
t 9
10
N
o. 11
12
0
0
0.9
1.6
0. 1
0. 5
0.4
1. 1
0.7
0.2
98.4
12
--
--
--
_ _
-- -
101.8
45
2.6
2.9
2.9
5.0*
4. 2*
4. 2*
3.7
5.6*
100..5
45
6.2*
5.7*
6. 1*
6.1
6. 1
5.2
8. 2* .
7.4
101.23
213
9.9
8.7
8.9
10. 1
9.9
8.7
11.0
11.1
1.4
30
8.5
8.0
--
-- .
--
_ _
9.1
8.7
1.. 4
30
8.0
7; 7
--
--
--
_ _
7. 5
7.7
:Exercise at 300 kp-m/min.
-------
EXPERIMENT 2
Actual Carboxyhemoglobin Percentage Saturation
at the Conclusion of Each Exposure Segment.
Cone. ,
ppm
Dur. ,
min.
1
S 6
U
B 7
J
E 8
C
T 9
N 10
U
M 11
B
E 12
R
0
0
1. 2
2. 0
0. 5
0. 9
0. 2
0. 7
0. 3
0. 4
49. 5
12
_
50. 6
45
3 . 1 *
2.7
2.6*
3.2--:-
1. 9
2. ! =
1. 9
1.6
51. 1
45
4. 2
3. 7*
3. 2
3. 9
3.4*
3. 5
4. 7*
4. 1*
50. 6
198
5. 5
5. 0
5. 1
6. 2
5. 1
5.8
6.7
6.2
''Exercise at 300 kp-m/min.
-------
EXPERIMENT 3
Actual Carboxyhemoglobin Percentage Saturation
at the Conclusion of Each Exposure Segment
Cone. ,
ppm
Dur. ,
min.
1
S 6
U
B 7
J
E 8
C
T 9
N 10
U
M 11
B
E 12
R
0
0
1. 1
2. 1
1.0
1.2
0.7
1.2
0.7
0.3
198.6
10
--
- -
199.4
45
8.8*
5.4
8. 0*
7. 9*
4.8
6.2=:=
5.4
5.9
198.4
45
11. 1
9. 5*
10.1
10.5
10. 7*
9.1
1 3 . 0*
12. 3*
196. 5
210
15. 8
14. 2
15. 5
16.6
18.0
15. 1
17. 8
17. 8
-
* Exercise at 300 kp-m/min.
-------
EXPERIMENT 6
Actual Carboxyhemoglobin Percentage Saturation
at the Conclusion of Each Exposure Segment
Cone. ,
ppm
Dur. ,
min.
1
S 6
U
B 7
J
E 8
C
T 9
N 10
U
M 11
B
E 12
R
0
0
0. 8
1. 9
0 .3
1. 2
0.2
1.8
1. 2
0. 1
47. 4
12
_ _
47.8
45
2. 6=:=
3. 1
2. 5*
2. 9*
2. 1
3. 3*
2. 8
1.9
48. 0
45
4. 0
3.8*
3. 2
3. 5
4. 0=:-
3.7
4. 7*
3. 7*
49. 7
188
5. 3
5. 4
4. 4
5.8
4. 8
6. 2
6. 0
4.3
0.7
30
5.0
5.6
4. 4
5. 7
5.7
6. 2
5. 4
4. 6
1.0
30
5. 0
5. 0
4. 4
5. 1
4. 2
5. 2
4.8
4. 2
0. 3
60
_ _
4. 3
4.8
3. 8
3. 7
3. 5
0. 7
60
--
_ _
4. 0
4.4
3.6.
3. 1
2.6
0. 7
60
--
2. 2
3.9
3. 5
2. 7
2.8
* Exercise at 300 kp-m/min.
-------
EXPERIMENT 7
Actual Carboxyhemoglobin Percentage Saturation
at the Conclusion of Each Exposure Segment
Cone. ,
ppm
Dur.,
min.
6
S 7
U
B 8
J
E 9
C
T 10
N 11
U
M 12
B
E
R
0
0
1.5
0.7
1.3
0.3
1.9
0.9
0.9
199.8
10
_ _
--
_ _
- - -
202.7
45
5.6
7. 5*
9. 5*
5.4
8.8*
6.2
6.5
201. 6
45
9. 9*
10.3
12.6
12. 5*
11.2
14. 9*
14.3*.
202. 1
165
15.4
16. 5
18. 3
17.3
17. 0 .
. 20. 0
19.2
0
30
14. 1
14. 6
16.3
15.2
15.2
16.6
16.8
0. 3
30
13. 5
13.4
14. 7
13.5
14.2
14.8
15. 0
0
60
12. 1
--
--
13.0
11.8
9.7
0.3
60
10. 1
_ _
--
--
11.3
9.3
7.6
0
60
9. 1
--
--
10. 1
7.7
7.3
* Exercise at 300 kp-m/min.
-------
EXPERIMENT 10
Actual Carboxyhemoglobin Percentage Saturation
at the Conclusion of Each Exposure Segment
Cone. ,
ppm
Dur. ,
min.
1
S 6
U
B 7
J
E 8
C
T 9
N 10
U
M 11
B
E 12
R
0
0
1. 1
2. 1
0. 8
1. 3
0. 7
2. 6
1. 7
0.6
94. 9
8
_ _
92.7
45
4. 4*
3.4
4. 5*
4. 9*
4.2
4. 9*
3.8
2. 9
95. 5
45
6.0
6. 5*
7.0
6.3
7.0*
6.4
8.8*
7. 1*
96. 0
167
9. 5
8.5
9.3
9. 1
9.6
9.4
10. 9
10. 5
2.6
30
8.6
8.6
8.6
8. 5
9.4
9. 3
9.5
9.2
0.8
30
8. 1
7. 6
8.2
8.0
8.0
8.6
8.4
7.8
0.8
60
_ _
5.2
6.3
5.6
_ _
5. 0
5.2
0
60
_ _
7. 1
7.0
6.6
.
5.6
5.6
0
60
_ _
4. 6
5. 0
4. 5
_ _
4. 7
4.4
* Exercise at 300 kp-m/min.
-------
EXPERIMENT 41
Actual Carboxyhemoglobin Percentage Saturation
-at the Conclusion of Each Exposure Segment
Cone. ,
ppm
Dur.,
min.
21
S 22
U
B 25
J
E 29
C
T 31
N 32
U
M 33
B
E
R
0
0
0.8
0. 9
0.8
0.8
0.8
0.9
0.8
190.4
30
--
. »
193.5
45
4.9
4.2
4.4
4.2
5. 6*
5.7*
5.7*
200. 8
45
10.0*
8. 6*
8.6*
8. 9*.
8.0
8.2
8.0
201. 1
154
16.8
15.5
14.6
16. 0
15.6
14. 9
15.2
-
--'Exercise at 150 kp-m/min.
-------
EXPERIMENT 43
Actual Carboxyhemoglobin Percentage Saturation
at the Conclusion of Ea ch Exposure Segment
Cone. ,
ppm
Dur. ,
min.
21
S 22
U
B 25
J
E 29
C
T 31
N 32
U
M 33
B
E
R
0
0
0. 9
1.1
1. 2
1. 3
1. 1
1.4
1.7
199.2
14
--
_ _
205. 5
45
8. 1
6.8
6.2
7.0
6. 7*
6.7*
8.2*
201. 9
45
13. 2*
10. 9*
10. 6*
11.7*
9.8
9.4
10.3
214. 3
166
19. 0
17.6
17. 0
19. 1
16. 2
15. 8
16.7
* Exercise at 0. 0 kp-m/min. (working baseline)
-------
EXPERIMENT 44
Actual Carboxyhemoglobin Percentage Saturation
at the Conclusion of Each Exposure Segment
Cone.,
ppm
Dur.,
min.
S 21
U
B 22
J
E 25
C
T 21
N 31
U
M 32
B
E 33
R
0
0
1. 1
1. 1
0.7
0.9
1.0
3.0
1.8
182.8
10
--
_ _
185.9
45
6.4
5.6
6.2
5.6
8. 0*
9.4*
9. 6*
207. 5
45
15. 6*
13.4*
12.8*
13.2*
11.2
12.6
13.2
199.0
168
19.6
17.7
18.2
18.6
17.2
17. 1
18.3
* Exercise at 300 kp-m/min.
-------
EXPERIMENT 47
Actual Carboxyhemoglobin Percentage Saturation
at the Conclusion of Each Exposure Segment
Cone. ,
ppm
Dur. ,
min.
S 21
U
B 22
J
E 25
C
T 29
N 31
U
M 32
B
E 33
R
0
0
1. 5
1. 4
1. 5
1. 1
1.2
1. 4
1.8
186. 8
10
_ _
191.4
4.5
13.0*
12.2*
10. 9*
.10.4*
6. 1
5.8
6.9
198. 5
45
16. 0
16.2
14. 8
13. 0
12.4*
11.6*
14. 8*
200. 5
155
19. 9
18.7
18. 0
18.2
17. 7
17.6
19.2
* Exercise at 300 kp-m/min.
-------
EXPERIMENT 50
Actual Carboxyhemoglobin Percentage Saturation
at the Conclusion of Each Exposure Segment
Cone. ,
ppm
Dur. ,
min.
S 21
U
B 22
J
E 25
C
T 29
N 31
U
M 33
B
E
R
0
0
0.8
1.4
1.2
0.6
1.0
1.8
206.3
15
--
_ _.
201.8
45
8.8*
8.4*
8. 0*
9. 0*
5.1
6.8
193.8
45
12.1
11.4
10. 6
12.5
10. 0*
12.4*
196.7
170
16.8
16. 1
15.2
17. 1
15. 5
16.7
-.-Exercise at 150 kp-m/min.
-------
EXPERIMENT 51
Actual Carboxyhemoglobin Saturation at the
Conclusion of Each Exposure Segment
Cone. ,
ppm
Dur. ,
min.
Sub. No.
40
58
59
60
63
64
65
0
0
1.2
1. 4
1. 3
1. 4
2. 3
1. 5
1.3
149. 0
20
2. 2
1. 9
2.3
2.6
3. 5
3.0
2. 5
163. 5
20
3. 5
2. 8
3.2
3. 3
4. 3
4. 0
3. 4
142. 8
20
4. 5
3.6
3.9
4. 1
5. 0 .
4. 5
4.0
0
30
4.2
3. 4
4. 1
4. 0
5. 1
4.3
3. 8
45.0
20
5. 3
3. 8
4.6
5. 0
6.0
5. 1
4.7
51. 8
20
4.8
4. 1
4. 7
4.8
6. 0
5. 4
5. 1
49. 0
20
5.6
4. 7
5.1
5.2
6.0
5.5
5.2
0
30
5. 0
4.5
4. 8
5. 0
5. 5
5.2
4.4
105. 1
20
6.0
5. 1
5.6
5.8
6.4
6.0
5.4
87. 8
20
6.4
5. 3
6.2
6. 2
6.6
6.6
6.4
122.4
20
7.0
5. 1
6.7
6.9
7. 5
7.0
6.5
0
15
5. 7
6. 3
6. 4
7. 0
6. 5
6.0
0
15
5.6
5. 6
6. 1
6. 3
6.6
6. 3
5. 9
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