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AIRLEAD - BLOOD LEAD MODELS
Donald A. McCaughran, Ph.D.
Presented at the International Conference of Heavy Metals in the Environment Toronto, Ontario October 27-31> 1975
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The relationship between air lead and blood lead has received considerable attention by researchers because of the possible health hazard of airborne lead from the burning of leaded gasoline. Several models1*2, for the relationship have
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been proposed, but not generally accepted by the scientific community because of unrealistic underlying assumptions and .inadequate data used In parameter estimation.
Data that can be used in building models are generally from two different sources, lead chamber studies9*1*, and epidemiological studies5*6'7. The lead chamber studies are Important for an understanding of the basic phenomenon but cannot be used' to predict blood lead from air lead levels in the environment, because city residents may not have the same exposure levels as lead chamber residents although the
* lead chamber and average ambient air concentrations may be equal. It was decided, therefore, to build models of blood lead response to both controlled and natural environmental airborne lead. An attempt was made to incorporate into the models several realistic assumptions.
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MODEL X: Abrupt air lead change (controlled environment) Male and McCaughran (1972) present a simple compartment
model for the rate of change of blood lead with time for indivl duals subjected to abrupt change in air lead concentrations in controlled environment experiments.
wheres
dLB dt = A
Sp
Lg is the blood lead concentration (g/100 ml blood)
A is the average intake rate of lead into the blood from all sources (pg/100 ml blood/day).
Bp is the average removal rate of lead from the blood by all mechanisms (ug/100 ml blood/day).
Solving this equation and reparameterizing yielded the
following model for the average blood level (p(t)) at time t.
p(t)
fHn He - (He-Hn) exp|-||(t-t0)}
for t<t. for t0t<tf
Hn + (He-Hn) exp|--(t-tf)|[^1 - exp|-||(tf -tjjj for t>t4
and limp(t) = He
where:
An is the average pre*-experimental intake rath of lead into the blood
Ae is the average experimental intake rate of lead into the blood
Hn is the pre-experimental blood lead level
He is the asymptotic (equilibrium) lead level for blood under experimental conditions
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The fact that the blood lead levels of city dwellers, exposed to reasonably constant concentration of air lead, do not rise continuously over their lives argues strongly for an equilibrium blood level. The data collected in the Albany study4 also show that blood leads had or were in the process of reaching an equilibrium level.
The parameters of the model were estimated from the Albany study4 data. The blood lead concentrations of nine individuals living in an average of 10.9yg/m3 air lead and ten individual's living in an average of 3.2pg/m3 were used. Individuals were selected that had a sufficient number of observations to provide valid estimates of the parameters. The data and fitted model for several subjects of the study are shown as an example in Pig. l,2,&3.The data show that several subjects had not reached equilibrium conditions when the experiment was terminated. Values of the equilibrium level (He) and the pre-experiment level (Hn) estimated from the data are given in Table 1.
MODEL II: Steadystate Air Lead-Blood Lead Models Several attempts have been made to obtain a relationship
between ambient air lead and blood lead1*2*5*8 . in several papers1*8 the data were treated statistically by fitting a straight line to the log1Q transformed air lead (LA) and blood lead (LnP ) concentration values. The basic model in these treatmerits was ;
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1o s 10l b = G + b 1o s 10LA
c, b are constants
or exponentiating both sides of the equation;
where d w (10)c
This model implies:
i when air lead is zero blood lead is zero*
ii the rate of change of blood lead with changing air lead is
b-l
which shows that the rate of change in blood lead is propor
tional to a power of air lead when b > 1 and inversely pro
portional to a power of the blood lead if b < 1 and constant
if b * 1. iii no maximum blood lead value is approached as the air
lead gets extremely concentrated.
implication i is not true since lead is known to reach
the blood from dietary sources. No data are available to
validate Implications ii and iii.
Knelson, J.H. et. al. (1972)z attempted to model the blood
lead-air lead relationship using the Albany study4 data. The
model was of the form
Lfi m + b log10(BB)
m, b constants
where BB iiVR'Dlcr9
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L = air lead concentration V * pulmonary retention R * lead fraction retained D days of exposure The variables V and R were assigned the arbitrary values of 15m9 and 37# respectively. Several problems arise with models of this kind; 1 The model can only be used over the range of air leads in the study since the model predicts unreal values of blood lead at small air lead values (Lfi -*--as LA + 0). ii The variables V and R are parameters and must be estimated and cannot be assigned arbitrary values. The two models so far presented have ignored an important piece of scientific information; that blood lead concentration is greater than zero in the absence of air lead due to dietary sources. The only Justification for the log-log model is that when air lead-blood lead data are plotted they appear slightly curvilinear and a log transform is applied to linearize the data so that simple linear regression may be employed. This is done for statistical convenience. Without a complete understanding of the pathways taken by dietary and airborne lead a truly realistic model cannot be constructed but a curvilinear model which acknowledges dietary blood lead is scientifically more acceptable than the previously mentioned models.
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The following assumptions are suggested for the construc tion of an air lead-blood lead model.
1. Blood lead concentration should Increase as air lead concentration increases.
2. At nero air lead concentration the blood will contain lead from dietary sources.
3. At any particular air lead level an equilibrium between input of lead to the blood and removal of lead from the blood is finally reached.
4. As the air lead concentration gets large (L^ -* ") a maximum intake rate is reached since the intake mechanisms are finite.
5. The rate of change in lead intake decreases as the maximum rate of intake is approached.
Assumptions 3, 4, and 5 provide the curvilinear shape to the model and imply that a maximum blood concentration is approached as air lead concentrations become extremely large. Having an asymptotic blood concentration will have little effect on the model in the range of air leads encountered in ambient or in occupational situations*
These assumptions are implicit in the following model for the rate of change of blood lead concentration as a function of air lead concentrationj
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- OCLg - Lb), La - o ->I^ - Ld
C is a constant Lp, is the maximum (asymptotic) blood lead
* concentration (g/100 ml) Ln is the blood lead concentration from
u dietary sources. Solving the above differential equation yields the blood lead concentration model;
"2 l a
VeLe - (tE -
This model can be used to represent the blood lead-air lead concentration relationship for a particular individual or for the average relationship of a group of individuals.
Parameter Estimation The data needed for parameter estimation for an individual
is a set of air lead-blood lead concentration values obtained from an individual living for long periods of time at a yariety of air lead concentrations. The individual should have a constant dietary lead intake and must live at each air lead concentration level long enough for the equilibrium blood lead value to be reached. The air lead concentrations should be measured by personal samples to obtain the most accurate measure of the mean daily air lead contribution to the individual's respiratory air. The wide range of air lead concentrations is necessary for estimating Lg accurately. If the estimated model
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is only going to bo used for predicting blood lead values at
ambient environmental levels an accurate estimate of the asympto
tic level (Lg) is not necessary since a 20 yg/lOOml error in Lg
for example will introduce no more than a 1 yg/100ml error in
blood lead at 10 yg/M3 air lead. Increased variability in blood
lead values will result if the dietary lead varies and will lead
to a decrease in the precision of the estimates.
If estimates of the average of a population are desired
then data as indicated must be collected from a randomly selected
group of individuals from the population of interest.
No data that fits the described criteria are available.
The best data set for parameter estimation was found in a study
by Williams M.K., King, E., and Walford, J. (1969). The data
are from an industrial source, therefore the lead particles
may be somewhat different than those found in the environment.
The air lead was only measured during the working day and hence
is an overestimate of the daily average air lead exposure.
In any case the relative exposure between people is probably
correct and the data are of sufficient range (8 yg/Ms to 298 yg/M3)
to get reasonably good estimates of the parameters. The esti
mates are,
A
Lg * 89.102 yg/lOOml (asymptotic level)
Lg ** 24.632 yg/lOQml (dietary level)
A* c2 0.006535
The proportion of variability accounted for by the model;
Ra * 0,846.
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The data with the estimated model are presented in figure 4.
An attempt was then made to find a set of data suitable
for parameter estimation for the environmental air lead-blood
lead relationship. The problem with all data sets investigated1*8 *
is that the range of air lead concentrations is too small to
obtain meaningful estimates of Lg. The individual variability
in blood lead measurements over the small range of air lead
values was so great the Azar et.al.6, ( 1972
) were
not able to show a significant relationship with the log-log
model using thirty subjects! The same problem occurred with
the data from Tepper, L.B., and Levin, L.S. (1972)5.
However, parameter estimates were obtained for women using
Tepper, L.B., and Levin, L.S. (1972) and from the estimated
equllbrlum blood lead values (He) from Male, L. and McCaughran,
D.A. (1972). The parameter estimates for the women ftrej
A
Lg = 5^.65 ug/lOOml (asymptotic level)
LD * 15.75 yg/lOOml (dietary level)
C2 - 0.017
Since only two air lead concentrations were used in the
Albany study** and we had three parameters to estimate LD was
estimated separately from pre-exposure values and the other two
parameters were obtained by nonlinear least squares. The
estimates arej
Lg " 55.00 ug/lOOml
Lp - 19.71 yg/100mT
C2 * 0.071
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Figure 5 shows the data and the estimated models and the data and model of Goldsmith and Hexter1.
Discussion The analysis of the Albany study4 data points out the
tremendous variability between individual response to increases in air lead exposure. The range in blood lead Increase for the 3.2 yg/M3 exposure was 3*89 to 9*78 yg/lOOml and 13*64 to 26.20 yg/100ml for the 10.9 yg/M8 exposure. This large vari ability can in part be explained by the variability in the dietary lead levels. The average increase when the model was fitted to the data on all subjects together was 8.71 for 3.2 yg/M3 exposure and 19.49 yg/lOOm! for the 10.9 yg/M9 exposure. These increases are considerably higher than any previously demonstrated, The use of this data to estimate the parameters in the air leadblood lead model is of little consequence since there are only three air lead values in the study, pre-exposure, 3*2 yg/M3 and 10.9 yg/M3. Lead chamber studies using artificially produced lead particles have dubious applications to the ambient airblood lead relationship in any case.
The air lead concentrations in Williams et. al. (1969) are an overestimation of the average daily air lead exposure concentrations since the samplers were only worn while at work. A conservative estimate of the average daily exposure would be to assume that one third of the day the individuals were exposed to the values reported in the study and the other 2/3
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of the day the exposure was 0.0 ug/M9, The only parameter estimate that changes is C2, it now becomes 3Cg. The predicted average blood concentrations will be overestimated since the individuals in the study were probably exposed to some air lead while not at work. The estimated average blood leads based on the model with parameters estimated from the Albany study*, the Williams et.al, study7 and the 7-City study5 are given in Table 2.
The estimates of Lg and C2 obtained from the 7-City study are imprecise. The problem is that to obtain good estimates of the parameter Lg, blood lead values at high air lead values (>50 ug/M3) are needed, but since high air lead values never occur in the environment no good estimate of the asymptotic level can be obtained. The other problem with fitting models to environmental data is the large variability in blood lead values.' It can be shown from the duplicate samples taken from a number of subjects in the 7-City study7 that the variability in analytic error accounts for 79.65!! of the total variability. The remaining variability comes from differences in actual exposure, dietary lead, smoking habits and physiological differences.
No extrapolation should be made from the Albany model to the environmental air lead situation. The lead particles are from a different source which may effect their intake rate. In addition, although an individual resides in a city with a particular average daily air lead concentration the real exposure
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concentration Is probably much lower. For this reason the type of data collected by Azar5 et.al. is extremely valuable, it is unfortunate, however, that a larger sample was not obtained and a more realistic model used in the analysis.
It is felt that the model for the air lead-blood lead relationship presented is realistic and gives an adequate model for prediction when sufficiently large air lead values are available for parameter estimation. However, since the environmental air lead concentrations are small and the increase in blood lead concentration is so small that an increase cannot be detected with most data sets available, strictly empirical models such as a straight line with a non-zero intercept or a second degree function would give an adequate description of the relationship. The fact that in epidemological studies a small percentage of people have blood lead concentrations somewhat higher than the average indicates that they are exposed to lead from sources other than ambient air lead and the total removal of all lead from the air would not decrease their blood lead concentration more than a few micrograms per 100 mis. of blood.
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References
1. Goldsmith, J.R., Hexter, -A.C.; Respiratory Exposure to Lead: Epidemiological Experimental Dose-response Relation ships, Science, 158: 132-13*1 6 October, 1967*
2. Knelson, J,H., Johnson, R.J., Coulston, F., Golberg, L., Griffin, T.: Proceedings of the International Symposium on Environmental Health Aspects of Lead, October 2-6, 1972, Amsterdam: 391-401.
3. Kehoe, R.A.: The Metabolism of Lead in Man in Health and Disease. The Harben Lectures. Jour. Roy, Inst, Public Health 24:81; 101-129-i 177, 1961.
4^ Coulston, F., Golberg, L. Griffin, T., Russell, 0.: The Effects of Continuous Exposure to Airborne Lead. Exposure of Men to Particulate Lead, II at a level of 10.9 Pg/M3, IV at a level of 3.2 pg/M3. Institute of Experimental Pathology and Toxicology, Albany Medical College, Albany, New York. Final Report, June 1972, February 1973-
5. Tapper, L.B., Levin, L.S.i A survey of Air and Population Lead Levels in Selected American Communities. Department of Environmental Health, College of Medicine, University of Cincinnati, Cincinnati, Ohio. 'Final Report 1972*
6. Azar, A., R.D. Snee, and K. Habibi: An Epidemiologic Approach to Community Air Lead Exposure Using Personal Air Samplers, p, 254 in Environmental Quality and Safety, Supplement Volume II; Lead, Academic Press, New York, 1975-
7* Williams, M.K., King, E. and Walford,J,; An Investiga tion of Lead Absorption in an Electric Accumulator Factory with the Use of Personal Samplers, British Journal of Industrial Medicine. 26, 202-216, 1969.
8. Male, L. and McCaughran, D.A.: A Model to Describe the Effect on Blood Lead Concentration of an Abrupt Change in Air Lead Concentration. Report dated November 1972 to Industrial BIO-TEST Laboratories. Northbrook, Illinois.
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