OAR Box 1112 

Prepped by Ryan Dugan 

Document Number: 

28) ll-C-1f 

Docket Number: 

A-83-22 

Printed 4/16/2008 9:12:07AM Sheet 28 of 97 

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DESCRIPTION OF LEAD EXPOSURE MODEL 

W.F. Biller 

August 1983 
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DESCRIPTION OF LEAD EXPOSURE MODEL 

The lead exposure model accounts for lead compounds breathed 

into the lungs and the ingestion of lead contained in food, drink 

and other materials entering the mouth (e.g., soil, dust). The 

model described below is an application of the NAAQS Exposure Model 

(NEM) and was developed in a joint effort by members of EPA, PEDCo 

Environmental, GCA, and the writer. 

Cohort Description 

Following the general approach of NEM, the sensitive 

population living within a defined geographic area is divided into 

a finite number of classes referred to as cohorts. Let n^ is the 

number of sensitive individuals in the area which are represented 

by cohort k Then, the total population, N, of sensitive people is: 

(1) N • n-i + n, + + n S 

where S is the total number of cohort classes chosen to represent 

the sensitive population. 

The sensitive group for the purposes of NEM is young children 

under the age of seven. Another sensitive group of interest is 

unborn fetuses. However, since this group is not directly exposed 

to airborne or injested lead, its exposure will be modeled 

separately by estimating lead uptake via transplacental transfer. 

Another model, the physiological model, will be used to estimate 

the blood levels and distribution of lead among major body 

compartments in the sensitive groups. To account for the exposure 

to lead and accumulation of lead in the unborn fetus the exposure 

of the mother to lead will be estimated using NEM. The 
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physiological model will then be used to estimate the mother's 

blood lead levels. 

The following means of classifying the sensitive population 

into cohorts will be used: 

1. General - children up to seventh birthday 

2. Home Location - traffic density, point source contribution 

3. Age - in years, 0....6 

4. Season of Birth - winter, spring, summer, fall 

5. Socio/Economic Classification - two levels 

6. Age of Housing in Neighborhood - two levels 

7. Race - black/other 

The above descriptors serve to differentiate cohorts for both 

exposure to airborne lead and ingested lead. For exposure to 

airborne lead, these descriptors are only important to the extent 

that they result in a different pattern of movement through 

contaminated environments, since it is this pattern which causes 

differences in exposure. Thus descriptors #5 and 6# may not be as 

important to exposure to airborne lead as they are to ingested lead, 

Exposure to Airborne Lead 

The location of a given cohort during the period of any clock 

hour of a given day is represented by a human activity model based 

on the human activity information that is currently available. All 

possible locations can be classified into a finite number of 

classes determined by vehicular traffic density, general level of 

ambient lead concentrations contributed by point sources, and 

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microenvironment. Traffic density is classified into three levels: 

low, medium, high. Point source contribution is classified into 

four levels: none, low, medium, and high. The traffic density and 

point source contribution taken together will be said to define the 

neighborhood type. Five classes of microenvironments are defined 

to represent all possible locations within a given neighborhood 

type: outdoors near roadway, outdoors away from roadway, inside 

vehicle, indoors-residence, indoors other. 

A neighborhood type is defined by the pair of indices {i,j} 

where i and j refer to traffic density and point source contribution 

class respectively. The indices take the values 0,1,2,3 for none, 

low, medium, and high. The ambient lead levels associated with a 

neighborhood type will be assumed to have two sources, one that 

is associated primarily with vehicular traffic and the other 

which is associated with point sources of lead emissions. The 

total ambient lead level for the neighborhood type is the sum of 

the contributions from these two sources. The traffic density 

concentration component for the i-th density class is determined 

from air monitors located in neighborhoods where j = 0. 

The point source concentrations component is estimated using 

dispersion modeling. We have, therefore 

(2) C(i,j,h,d) = CT(i,j,h,d) + Cp(i,j,h,d) 

where C(i,j,h,d) is the hourly average lead concentration for a 

neighborhood type {i,j} for the hour h of day d. CT and Cp 

are the traffic density and point source components of the net 

concentration. 

Health effects arise from the accumulation of lead in the body. 

This accumulation is a dynamic phenomenon in which entering lead is 

distributed through the blood to bone and soft tissues of the body. 
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A continuous exchange occurs between these body 'compartments'. 

Lead is excreted from the body through several routes. The halflife of lead in the blood is about 30 days, in soft tissue the halflife is about 45 days and in the bone many years. To model the 

uptake of lead, the dynamic exchange of lead among the compartments 

and its excretion, it is sufficient to know the average exposure to 

lead over a twenty-four hour period. However, given that 

individuals move about, it is still necessary to take into account 

the activities of sensitive individuals over the course of the day 

in order to estimate their net or average exposure for the day. 

As will be shown, advantage can be taken of the sufficiency of 

the twenty-four exposure to greatly reduce the computational effort. 

If for a day d , Equation (2) holds for each hour, then we 

can write for a 1-hr average concentration at the neighborhood 

type {i,j} for hour h of day d: 

(3) C(i,j,h,d) = gT(i,h,d)CT(i,d) + gp (j ,h,d)Cp (j ,d) 

where gT and gp are factors relating the 24-hour 

concentrations CT and Cp for the day d to the 1-hour average 

concentrations for the hour h. 

To obtain the exposure concentration for a cohort k in a 

microenvironment m in the neigborhood type {i,j} we use the same 

procedure used in NEM: 

(4) CE(i,j,m,h,d,k) = aT(i,m,h,d)gT(i,h,d)CT(i,d) + 

ap(j,m,h,d)gp(j,h,d)Cp(j,d) + 

b(i,j,m,h,d) 

where the a values are transformation factors relating the 

traffic and point source neighborhood type concentrations to a 
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coefficient b represents a contribution from within the 

microenvironment which is independent of the lead concentration 

contributed by the neighborhood type. This term is, therefore, 

independent of the neighborhood type as it has been defined for 

this application. 

The 24-hour exposure concentration is given by: 

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(5) CE(d,k) = (1/24) z z [fi(i,j,m,h,d,k)aT(i,m,h,d)gT(i,h,d)CT(i,d) 

h=l i,j,m 

+ 6 (irJ/d,k)ap(j,m,h,d)gp(j,h,d)Cp(j,d) 

+ 6(i,j,m,h,d,k)b(m,h,d)] 

where: 

6 (i, j ,m,h,d,k) = 1 if cohort k is at {i,j,m} 

during hour h of day d. 

= 0 if cohort k not at {i,j,m}. 

Equation (5) can be rearranged to give: 

3 _ 3 

(6) CE(k,d) = Z aT(i,d,k)CT(i,d) + z ap (j ,d)Cp(j ,d) + 

i=0 j=0 

b(d,k) 

where: 

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(7) aT(i,d,k) = (1/24) Z I «(i,j,m,h,d,k)aT(i,m,h,d)gT(i,h,d) 

h=l j,m 

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(8) ap(j,d,k) = (1/24) j j 6(i,j,m,h,d,k)ap(j,m,h,d)gp(j,h,d) 

h=l i,m 

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(9) B(d,k) = (1/24) Z Z 6(i,j,m,h,d,k)b(m,h,d) 

h=l i,j,m 
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The significance of Equations (6) through (9) is that the terms 

a"T, i"p, and b can be made parameters of the model. That is, they 

can be evaluated prior to running the model for alternative 

standards. 

The expressions (7), (8), (9) appear more complex than they 

actually are. Since a cohort can only be at one location in any 

hour, most of the delta terms evaluate to zero. Furthermore, some 

of the appearance of complexity is the result of expressing the 

terms in the equations in their most general form. For a given 

application substantial simplification is likely. For example, for 

purposes of simplicity the concentration patterns gT and gp might 

all be set equal to one. If it is feasible to derive patterns from 

existing data, it may be determined that gT and gp are equal. It 

may also be practical to use a single pattern for all weekdays and 

another pattern for weekend days. It may be necessary to further 

adjust the weekday and weekend patterns for seasonal effects. Even 

in this case there would be a substantial simplification. 

Likewise, it may also be reasonable to set aT and ap equal to 

each other. In earlier applications of NEM the 'a' factor was 

generally not a function of time of day or day of week. If so in 

the present case, the expressions would be simplified. It may, of 

course, be necessary to distinguish between weekdays and weekend 

days and to take into account seasonal differences. 

The neighborhood type concentrations are obtained from a base 

set of data. The traffic density concentrations are obtained from 

air monitors in the study area. Missing data are filled in using 

techniques described in earlier NEM reports. The point source data 

are obtained from dispersion modeling of the study area. The 

rollback methods used in previous applications of NEM can be 
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applied to both the traffic density and point source base 

concentrations to produce a set of concentrations corresponding to 

other conditions, such as attainment of a NAAQS. In the case of 

the point source data, the dispersion models could be used to 

determine how the base data would vary under the imposition of 

alternative standards, and this derived correlation used to modify 

the base data for different NAAQS's. Note, however, that it is the 

sum of the traffic density concentration and point source 

concentration that must be rolled back. In the simplest case, both 

might be rolled back the same fractional amount. However, it is 

likely in actual practice that each would be rolled back to to a 

different degree. Note, also, that it is the 30 day or higher time 

averaged concentrations that will be rolled back. The appropriate 

time averaged concentration can be calculated from the base data. 

It is necessary to also compute the weight of lead breathed 

into the lungs by each cohort in a given day. If V(i,j ,m,h,d,k) is 

the volume of dry air inhaled in one hour while cohort k is at 

location {i,j,m}, then the weight of lead in the inhaled air for a 

day is given by the following equations: 

3 3 

(10) WE(k,d) = z A£(i,d,k)CT(i,d) + j Ajf (j ,d)Cp (j ,d) + 

i=0 j=0 

Bw<d,k) 

where: 

(11) AS(i,d,k) = 

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Z Z 6(i,j,m,h,d,k)aT(i,m,h,d)V(i,j,mfJi,d,k)gT(i,h,d) 

h=l j,m 

(12) A?(j,d,k) = 

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Z Z 6(i,j,m,h,d,k)ap(j,m,h,d)V(i,j,m,h,d,k)gp(j,h,d) 

h=l j,m 
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(13) Bw(d,k) = Z Z 6(i,j,m,h,d,k)V(i,j,m,h,d,k)b(m,h,d) 

h=l i/j,m 

Alternatively, and with less accuracy, the 24-hour volume of 

air breathed could be determined separately: 

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(14) V(d,k) z Z 6(i,J,m,h,d,k)V(i,j,m,h,,d,k) 

h=l i,j,m 

Then 

(15) WE(d,k) = V(d,k)CE(d,k) 

Exposure to Ingested Lead 

Hour by hour tracking of cohorts through neighborhood types 

and microenvironments is well suited to estimating exposure to 

airborne pollutants since the exposure is continuous when a cohort 

is breathing polluted air. On the other hand, contaminants are not 

ingested continuously and the environment a cohort is in at the time 

of a particular incidence of ingestion may have little relevance. 

Contaminated dust picked up on food, clothing, or the body in one 

environment may finally be ingested when the cohort is in another 

environment. Nor is it certain that it will be ingested at all. 

Exposure to airborne contaminants is different. If an individual 

is in an environment containing polluted air, it can be presumed he 

is continuously exposed to the pollutant. Consequently, it is 

suggested that exposure to ingested lead be keyed directly to the 

cohort, that is, to the the descriptive factors that define a 

cohort. 
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Thus: 

(16) Wj(d,k) •***• Z w0(u,d,k) + Z wg(v,d,k) 

u v 

Where"Wj is the average weight of lead ingested by cohort k during 

day d. The WQ and Wg represent contributions from pathways which 

are independent and dependent, respectively, of the NAAQS. The 

indices u and v represent the different pathways to ingestion for 

each of the two classes. The index d is included to take into account 

any short term or long term trends with time. That is, there may be 

weekday/weekend trends, seasonal trends, or longer trends such 

as reduced use of lead soldering in the manufacture of 

metal food containers. Or the imposition of a NAAQS may cause a 

slow reduction of ingested lead from the ws-type pathways. 

The cohort designation takes into account differences in 

ingestion rate resulting from such factors as age of the child, 

socio/economic status, age of housing in the neighborhood, etc. 

It is likely that Equation 16 can be simplified by summing over 

the u indices prior to input to the exposure model. In the case of 

the pathways dependent on the NAAQS designation, it may be possible 

to combine pathways with similar dependencies. If v indexes the 

combined pathways: 

(17) Wx(d,k) = U0(d,k) + z Us(v,d,k) 

v 

It is necessary to model the dependency of the NAAQS dependent 

pathways. It is assumed that lead from these pathways is primarily 

particulate from vehicle emissions and point sources which has 

settled on surfaces and the top layers of soil. In this manner it 
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has been generally incorporated into dust and soil in the 

environment. It will be assumed that the addition of lead to dust 

and soil by these mechanisms is offset to some degree by removal 

mechanisms. These can be mechanisms such as simple dilution with 

dust or soil which contains no lead or lesser amounts of lead, 

leaching by rain water, or washing away by rain water. 

The deposition rate will be assumed to be proportional to the 

average concentration of lead in ambient air. The latter quantity 

will then be related to a NAAQS. The removal process is more 

complicated. A common feature of many removal processes is that the 

rate of removal increases with increasing concentrations of the 

material being removed. Simple dilution and inefficient leaching 

processes work in this manner. In this case the simplest assumption 

is that the rate of removal is proportional to the concentration of 

lead in the dust or soil. Another simple alternative is that the 

material is being removed at a fixed rate independent of the 

concentration present. This might be true of leaching processes in 

which the leaching material becomes saturated with the contaminant 

being leached during each application. 

In the case that the removal rate is partially proportional to 

the concentration and partially independent of concentration we have 

the following: 

(18) dCs/dt = raCa - R - qCs 

Cs is the concentration of lead in the soil or duet at time t. 

Ca is the annual average atmospheric concentration of lead. The 

term ra Ca represents the rate of increase in lead in soil and 

dust due to deposition from traffic and point sources. The term R 

is the rate of loss due to factors which are independent of 

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concentration. The third term on the right side of the equation 

is the rate of change in concentration due to those factors which 

are influenced by concentration. Equation (18) is easily 

integrated to give: 

(19) Cs = C°exp(-qt) + (1/q)(raCa~ R)(1 - exp(qt)) 

where Ca is the initial concentration of lead. If raCa is 

greater than R, the system will eventually reach a steady state 

concentration equal to (1/q) (raCfl - R) which is dependent on the 

NAAQS. If the term q is very small or zero, meaning that there 

is little to no dependence of the removal rate on the existing 

concentration, Equation 19 becomes: 

(20) Cs = (raCa - R)t 

That is, the concentration will either be increasing or decreasing 

linearly, depending on the which of the two terms, rflCa or R, is 

larger. There will be no steady state if k is zero. If k is 

very small, a very long time would be required to reach the 

steady state. 

The Ca term can be calculated from the 24-hour lead 

concentrations for the cohort's home neighborhood. The ingestion 

rate Vj(v,k,d) would be: 

(21) V!(v,k,d) = ri(v,k,d)Cs(v) 

Combining Atmospheric and Ingestive Exposures 

The atmospheric and ingestive exposures of sensitive 

individuals to lead will be output separately by the model. In 

fact, the physiological model will require that they be treated 

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separately since the efficiency with which lead is absorbed into 

the blood is different for the two routes. It is, nevertheless, 

instructive to combine the two measures into a total exposure for 

a 24-hour period. The necessary common measures for doing this 

have already been developed above. We have therefore 

WTE(d,k) = WE(d,k) + Wj.(d,k) 

Where WmE is the combined exposure expressed as weight of lead 

per 24-hours and the individual components WE and Wj are defined 

in Equations (15) and (17) respectively. 

Dynamics of Exposure Model 

Because the physiological model will be operating on the 

outputs of the exposure model the model will follow each child 

cohort from the time of conception to its seventh birthday. Each 

child cohort will be treated as conceived at the beginning of a 

quarter. Birth will occur three quarters (9 months) later. Before 

birth there is no direct exposure to lead and consequently only the 

exposure of the mother will be followed during this period. The 

physiological model will take into account the build up of lead in 

the fetus during this period based on the mother's exposure and the 

levels of lead in her body compartments. Direct exposure of the 

child will be taken into account from the time of birth to the 

seventh birthday. 

Ideally, eight years of 24-hour lead concentrations in ambient 

air will be used by the model. Lacking this, a single year to 

several years of data could be used repetitiously to obtain several 

years of data. Trends due to the imposition of emission controls 

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could be built into the data through the use of rollback procedures. 

If there are no significant trends in ambient lead levels over 

the seven year period of the computation, another substantial 

savings in computational effort will be realized. In this case 

during the exposure computation we can effectively drop the 

distinction of cohorts by age, and consider only the quarter in 

which they were born (or conceived) as distinguishing them. At the 

completion of the calculation we can develop separate exposure 

distributions for children at a given age up to their seventh 

birthday. Within a given year the exposure distributions for 

children born in different quarters of the year can be weighted to 

account for effects of season on birth rate. These exposure 

distributions can then be weighted by the number of children in the 

population in each of these years to obtain one year exposure 

distributions for children up to their seventh birthday. 

If there are strong trends in ambient levels of lead over the 

period of interest, the yearly exposure distributions would be 

different for each year. If the exposure distributions were wanted 

for a particular year, the computation would have to be started seven 

years earlier and a new set of cohorts started in each quarter of 

each succeeding year through the end of the year of interest. The 

computational burden would therefore be substantially greater than 

the no trend case discussed in the preceding paragraph. 

It is likely that both cases will be of interest. The first 

case would likely pertain in a standards objective analysis, while 

the second case would likely pertain in a standards impact analysis. 

Note that by this method of calculation we axe not, strictly 

speaking, following a single child cohort over six years and nine 

months. By our cohort definition we are dealing with a new cohort 

every 3 months. Alternatively, the computation can be viewed as 

dealing with a single child cohort from conception to its seventh 

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birthday and then dividing the single cohort into 27 subcohorts at 

the end of the computation for the purpose of developing exposure 

and body burden distributions. 

The exposures of pregnant women would only be tracked during 

the nine month period of pregnancy. This presents no difficulties 

for the exposure portion of the model. In the case of the 

physiological model assumptions will have to be made about the 

distribution of lead among body compartments at the beginning of 

the pregnancy. This distribution will generally vary with the 

cohort. 

Output from the Exposure Model 

The lead exposure model will output the following distributions 

of exposure over a one year period: 

1. Exposure to 24 hr average air lead concentrations (yg/m***) 

2. Exposure to inhaled lead (yg/24hrs) 

3. Exposure to ingested lead (yg/24hrs) 

4. Total exposure to lead, inhaled + ingested ( yg/24hrs) 

Each of the above distributions is expressed in three forms: 

1. Total number of exposures at or above a given exposure level 

2. Number of people exposed at or above a given level 

3. Number of people experiencing their peak exposure at a given 

level in a one year period. 

Distributions can apply to the total sensitive population or any 

subset of cohorts, as for example children in their first year. 

William F. Biller 

8/29/83 

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