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Air Lead~Blood Lead Models Donald A* HcCaughrart1
Two air lead-blood lead models have been constructed:
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Da model to describe the increase in blood lead from an ~ abrupt increase in air lead as experienced by persons in
controlled environment experiments} 2) a model to describe . the contribution to the blood of airborne lead in the
environment. 1, Abrupt Increase Model
This model describes the average change in blood lead Concentration following an abrupt change in the concentra" tion of airborne lead- The avwage rate of change of blood lead is described by
ft * A ~ B|i
A is the average intake rate into the blood from all
sources (pg/lQQ ml)
Bp is the average removal rate from the blood from all
sources (yg/100 ml)
>
Solving and reparametrizing, the model for the average
blood lead concentration at time t Is: Lp for t < tq (pre-exposure)
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Lg -- (I * Ip) expC- (t * tp)}
l*(t) *<
for tp < t < tf (during exposure)
Ip + (lg * lp)exp(-
}{I-xp{ |~~{tp*t0)}}
for t > t^ (post exposure)
X University of Washington, Seattle, Washington.
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Lg * lim y{t) Is. the average asymptotic blood level for the *'*"** ftlven exposure level (pg/100 ml),
Lp is the average blood lead concentration prior to expo* sure to the nw air lead concentration (ug/lOQ ml).
Ap is the average Intake rate pre- and post-exposure (ug/XOO ml/day3.v
Ag is the averafsf? intake rate during exposure (pg/100 ml/day), The data from Albany prisoner study of Coulston, et al?
are used for parameter estimation. The model describes the data- for individuals extremely well. .11.; Blood Lead-Environmental Air Lead Hodel
v The model describes the average stable blood lead con* calibration of- persons exposed to constant levels of ,,airbopne lead* The model proposed for the rate of change in steady state blood lead concentration with changing air
concentration is;
Lg * blood lead concentration
VK<Lt L^ * air lead concentration
Thif%ssumptlorts are?
1) jA maximum rate of intake through the lungs is approach-
0td as the air lead concentration increases, due to the.
finite internal surface area of the lungs.
2) At the maximum rate of intake the body is capable of
removing lead from the blood at a similar rate, i.e., a maximum equilibrium blood lead concentration is
reached (Lg).
3) When * 0
the blood lead concentration
due to dietary sources.
Solving the above equation results in
'B
t*E
-
-C2-LA c*
cx , Cp are parameters.
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{ammeter estimates for men were derived for the
Albany Study using the asymptomatic level (Lg) for each
individual and from the average air lead and blood lead values for the women in the "7-City Study" of Tepper and
Levin*to produce a model for U.S. women*
The model predicts the average blood lead concentra
tion for U.S. women in several ambient air lead concentra
tions to be;
Mean Air Lead (us/m*)
Blood lead (ur/lQO ml?
0 15.75 1 16*41. 2 17.05 3 17.68 k 18.31 5 18.92 The Soldsmlth-Hexter** model and the model of KneIson,
etal? are reviewed; the assumptions in both models are
considered unrealistic since both models are undefined at
zero' .air lead concentration and both models Imply that blood lead concentration has no upper bound.
^^^Coulston, P Qolberg, L., Griffin, T*, and Russell,
CvAlbany Medical College. Final Report, June 1972,
February 1973*
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'Tapper, L. B. and Levin* L, S. College of Medicine,
University of Cincinnati, Pinal Report, 1972.
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^ '**.5f gGoldsmith, J, R, and Heater, A. c. Science, 15$:196?'vi *Xnelson, J. H*, Johnson, R. J., Coulston, F.,
Golberg, L., and Griffin, T, Proceedings of the Inter- - ' /*- * national Symposium on the Environmental Health Aspects of
Lead* 1972*
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