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Number: 

# 28 ) ll-C-1 f Docket Number: 

# A-83-2 2

Printed 4/16/20089:12:07AM Sheet 28of 97 P. 1DESCRIPTIO N OF LEADEXPOSUR E MODEL

W.F . Bille r

Augus t 198 3P. 3

DESCRIPTIO

N O F LEA DEXPOSURE MODE L Th e lea dexposur e mode l account s fo r lea dcompound s breathe d int o th e lung s an

dth e ingestio

no f lea

dcontainedi

nfood , drin

k an dother material s enterin g th e mout h(e.g. , soil , dust) . Th e mode l describedbelo w i s a napplicatio

no f th e NAAQ S Exposur e Mode l (NEM ) an

dwa s develope di

na join t effor t b

y member s o f EPA , PEDC o Environmental , GCA , an dth e writer . Cohor t Descriptio

n Followin

g th e genera l approachof NEM , th e sensitiv

e populatio

nlivin g withi na define

dgeographi c area i s divide dint o a finit e number o f classe s referre dt o a s cohorts . Le t n ^ i s th e numbe r of sensitiv e individual s i

nth e area whichare represented b y cohor t kThen , th e tota l population , N , o f sensitiv e peopl e is : (1 ) N• n-

i + n , + + n S wher e S i s th

e tota l number of cohor t classe s chosent o represent th e sensitiv

e population . The sensitiv

e grou pfo r th e purpose s of NEM

i s youn

g children under th

e ag e of seven . Anothe r sensitiv e grou pof interes t i s unbor nfetuses . However , sinc e thi s grou pi s not directl y

expose d to airborn

e o r injeste

dlead , it s exposur e wil l b e modeled separatel y

b y estimatin

g lea duptak e vi a transplacenta l transfer . Anothe r model , th

e physiologica l model , wil l b e use dto estimat e th e bloo dlevel s an

ddistributio

no f lea

damon g majo r bod

y compartment s inth e sensitiv

e groups . T o accoun t fo r th e exposur e t o lea dan daccumulationo f lea di nth e unbor nfetu s th

e exposur e o f th e mothe r t o leadwil l b e estimate dusing NEM . Th eP. 4

physiologica l mode l wil l the n be use d t o estimat e th e mother' s bloo d lead levels . Th e followin g mean s o f classifying th e sensitiv e populatio n int o cohort s wil l be used : 1 . Genera l - childre n u p t o sevent h birthday 2 . Hom e Locatio n - traffi c density , poin t sourc e contributio n 3 . Ag e - i n years , 0.... 6 4 . Seaso n o f Birt h- winter , spring , summer , fal l 5 . Socio/Economi c Classificatio n - tw o level s 6 . Ag e o f Housin g i n Neighborhoo d - tw o level s 7 . Rac e - black/othe r Th e abov e descriptor s serv e t o differentiat e cohort s fo r bot h exposur e t o airborn e lead an d ingeste d lead . Fo r exposur e t o airborn e lead , thes e descriptor s ar e onl yimportan t t o the exten t tha t theyresul t i n a differen t patter n o f movemen t through contaminate d environments , sinc e i t i s thi s patter n whic h cause s difference s i n exposure . Thu s descriptor s # 5 an d 6 # ma yno t be a s importan t t o exposur e t o airborn e lead a s theyar e t o ingeste d lead ,

Exposur e t o Airborn e Lead Th e locatio n o f a give n cohor t during th e perio d o f an ycloc k hou r o f a give n da yi s represente d b ya huma n activit ymode l base d o n th e huma n activit yinformatio n tha t i s currentl yavailable . Al l possibl e location s ca n be classifie d int o a finit e numbe r o f classe s determine d b yvehicula r traffi c density , genera l leve l o f ambien t lead concentration s contribute d b ypoin t sources , an d

2 VP. 5

microenvironment . Traffi c densit yi s classifie d int o thre e levels : low , medium , high . Poin t sourc e contributio n i s classifie d int o four levels : none , low , medium , an d high . Th e traffi c densit yan d poin t sourc e contributio n take n togethe r wil l be sai d t o defin e th e neighborhoo d type . Fiv e classe s o f microenvironment s ar e define d t o represen t al l possibl e location s withi n a give n neighborhoo d type : outdoor s nea r roadway , outdoor s awa yfromroadway , insid e vehicle , indoors-residence , indoor s other . Aneighborhoo d typ e i s define d b ythe pai r o f indice s {i,j } wher e i an

d j refe r t o traffi c densit yan d poin t sourc e contributio n clas s respectively . Th e indice s tak e th e value s 0,1,2, 3 fo r none , low , medium , an

d high . Th e ambien t lead level s associate d wit ha neighborhoo d typ e wil l b e assume d t o hav e tw o sources , on e tha t i s associate d primaril ywit h vehicula r traffi c an d the othe r whic hi s associate d wit hpoin t source s o f lead emissions . Th e tota l ambien t lead leve l fo r th e neighborhoo d typ e i s the su mo f th e contribution s fromthes e tw o sources . Th e traffi c densit y concentratio n componen t fo r the i-t h densit yclas s i s determine d fromai r monitor s locate d i n neighborhood s wher e j = 0 . Th e poin t sourc e concentration s componen t i s estimate d using dispersio n modeling . W e have , therefor e (2 ) C(i,j,h,d ) = C T (i,j,h,d ) + C p (i,j,h,d ) wher e C(i,j,h,d ) i s the hourl yaverag e lead concentratio n fo r a neighborhoo d typ e {i,j } fo r th e hour ho f dayd . C T an d C p ar e th e traffi c densit yan d poin t sourc e component s o f the ne t concentration . Healt heffect s aris e from the accumulatio n o f lead i n th e body . Thi s accumulatio n i s a dynami c phenomeno n i n whic hentering lead i s distribute d throughth e bloo d t o bon e an d sof t tissue s o f the body .P. 6

Acontinuou s exchang e occur s betwee n thes e bod y'compartments' . Lea d i s excrete d fro mth e bod ythroug hsevera l routes . Th e half

lif e o f lea d i n th e bloo d i s abou t 3 0 days , i n sof t tissu e th e half

lif e i s abou t 4 5 day s an d i n th e bon e man yyears . T o mode l th e uptak e o f lead , th e dynami c exchang e o f lea d amon g th e compartment s an d it s excretion , i t i s sufficien t t o kno wth e averag e exposur e t o lea d ove r a twenty-fou r hou r period . However , give n tha t individual s mov e about , i t i s stil l necessar yt o tak e int o accoun t th e activitie s o f sensitiv e individual s ove r th e cours e o f th e da y i n orde r t o estimat e thei r ne t o r averag e exposur e fo r th e day . A s wil l b e shown , advantag e ca n b e take n o f th e sufficienc yo f th e twenty-fou r exposur e t o greatl yreduc e th e computationa l effort . I f fo r a da yd , Equatio n (2 ) hold s fo r eac hhour , the n w e ca n writ e fo r a 1-h r averag e concentratio n a t th e neighborhoo d typ e {i,j } fo r hou r h o f da yd : (3 ) C(i,j,h,d ) = g T (i,h,d)C T (i,d ) + g p ( j ,h,d)C p ( j ,d ) wher e g T an d g p ar e factor s relatin g th e 24-hou r concentration s C T an d C p fo r th e da yd t o th e 1-hou r averag e concentration s fo r th e hou r h . T o obtai n th e exposur e concentratio n fo r a cohor t k i n a microenvironmen t m i n th e neigborhoo d typ e {i,j } w e us e th e sam e procedur e use d i n NEM : (4 ) C E (i,j,m,h,d,k ) = a T (i,m,h,d)g T (i,h,d)C T (i,d ) +

a p (j,m,h,d)g p (j,h,d)Cp(j,d ) +

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

wher e th e a value s ar e transformatio n factor s relatin g th e traffi c an d poin t sourc e neighborhoo d typ e concentration s t o aP. 7

coefficien t b represent s a contributio n fro mwithi n th e microenvironmen t whic hi s independen t o f th e lea d concentratio n contribute d b

yth e neighborhoo d type . Thi s ter mis , therefore , independen t o f th e neighborhoo d typ e a s i t ha s bee n define d fo r thi s application . Th e 24-hou r exposur e concentratio n i s give n by :

2 4 (5 ) C E (d,k ) = (1/24 ) zz[fi(i,j,m,h,d,k)a T (i,m,h,d)g T (i,h,d)C T (i,d ) h= l i,j, m

+ 6 (irJ/d,k)a p (j,m,h,d)g p (j,h,d)C p (j,d )

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

where : 6 (i , j ,m,h,d,k ) = 1 i f cohor t k i s a t {i,j,m } durin g hou r ho f da yd .

= 0 i f cohor t k no t a t {i,j,m} . Equatio n (5 ) ca n b e rearrange d t o give :

3 _

3 (6 ) C E (k,d ) = Z a T (i,d,k)C T (i,d ) + za p ( j ,d)C p ( j ,d ) +

i= 0 j= 0

b(d,k ) where : 2 4 (7 ) a T (i,d,k ) = (1/24 ) Z I «(i,j,m,h,d,k)a T (i,m,h,d)g T (i,h,d ) h= l j, m 2 4 (8 ) a p (j,d,k ) = (1/24 ) j j 6(i,j,m,h,d,k)a p (j,m,h,d)g p (j,h,d ) h= l i, m 24 (9 ) B(d,k ) = (1/24 ) Z Z 6(i,j,m,h,d,k)b(m,h,d ) h= l i,j, mP. 8

Th e significanc e o f Equation s (6 ) through (9 ) i s tha t the term s a" T , i" p , an

d b ca n be mad e parameter s o f the model . Tha t is , they

can be evaluate d prio r t o running th e mode l fo r alternativ e standards . Th e expression s (7) , (8) , (9 ) appea r mor e comple x than they actuall yare . Sinc e a cohor t ca n onl ybe a t on e locatio n i n an y hour , mos t o f the delt a term s evaluat e t o zero . Furthermore , som e o f th e appearanc e o f complexit yi s th e resul t o f expressing th e term s i n th e equation s i n thei r mos t genera l form . Fo r a give n applicatio n substantia l simplificatio n i s likely . Fo r example , fo r purpose s o f simplicit yth e concentratio n pattern s g T an d g p migh t al l b e se t equa l t o one . I f i t i s feasibl e t o deriv e pattern s from existin g data , i t ma ybe determine d tha t g T an d g p ar e equal . I t ma yals o b e practica l t o us e a singl e patter n fo r al l weekday s an d anothe r patter n fo r weekend days . I t ma ybe necessaryt o furthe r adjus t th e weekda yan d weekend pattern s fo r seasona l effects . Eve n i n thi s cas e ther e woul d be a substantia l simplification . Likewise , i t ma yals o b e reasonabl e t o se t a T an d a p equa l t o eac hother . I n earlie r application s o f NE M th e 'a ' facto r wa s generall yno t a functio n o f tim e o f dayo r dayo f week . I f s o i n th e presen t case , th e expression s woul d be simplified . I t may , o f course , b e necessaryt o distinguis hbetwee n weekday s an d weekend day s an d t o tak e int o accoun t seasona l differences . Th e neighborhoo d typ e concentration s ar e obtaine d froma bas e se t o f data . Th e traffi c densit yconcentration s ar e obtaine d from ai r monitor s i n th e stud yarea . Missin g dat a ar e fille d i n using technique s describe d i n earlie r NE M reports . Th e poin t sourc e dat a ar e obtaine d fromdispersio n modelin g o f th e stud yarea . Th e rollbac k method s use d i n previou s application s o f NE M ca n beP. 9

applie d t o bot hthe traffi c densit yan d poin t sourc e bas e concentration s t o produc e a se t o f concentration s corresponding t o othe r conditions , suc ha s attainmen t o f a NAAQS . I n th e cas e o f th e poin t sourc e data , the dispersio n model s coul d be use d t o determin e ho wthe bas e dat a woul d varyunde r the impositio n o f alternativ e standards , an d thi s derive d correlatio n use d t o modif y th e bas e dat a fo r differen t NAAQS's . Note , however , tha t i t i s the su m o f th e traffi c densit yconcentratio n an d poin t sourc e concentratio n tha t mus t be rolle d back . I n th e simples t case , bot h migh t b e rolle d bac k the sam e fractiona l amount . However , i t i s likel yi n actua l practic e tha t eac hwoul d b e rolle d bac k t o t o a differen t degree . Note , also , tha t i t i s th e 3 0 dayo r highe r tim e average d concentration s tha t wil l be rolle d back . Th e appropriat e tim e average d concentratio n ca n be calculate d fromthe bas e data . I t i s necessaryt o als o comput e th e weigh t o f lead breathe d int o th e lung s b

yeac hcohor t i n a give n day . I f V(i, j ,m,h,d,k ) i s th e volum e o f dr yai r inhale d i n on e hou r whil e cohor t k i s a t locatio n {i,j,m} , the n th e weigh t o f lead i n th e inhale d ai r for a dayi s give n b

ythe followin g equations : 3 3 (10 ) W E (k,d ) = zA£(i,d,k)C T (i,d ) + j Aj f ( j ,d)C p ( j ,d ) +

i= 0 j= 0

B w <d,k ) where : (11 ) AS(i,d,k ) =

2 4 Z Z 6(i,j,m,h,d,k)a T (i,m,h,d)V(i,j,m f Ji,d,k)g T (i,h,d ) h= l j, m (12 ) A?(j,d,k ) =

2 4 Z Z 6(i,j,m,h,d,k)a p (j,m,h,d)V(i,j,m,h,d,k)g p (j,h,d ) h= l j, mP.1 0

2 4 (13 ) B w (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 , an

d wit hles s accuracy , th e 24-hour volum e o f ai r breathe d coul d be determine d separately : 2 4 (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 The n (15 ) W E (d,k ) = V(d,k)C E (d,k ) Exposur e t o Ingeste d Lead Hou r b yhour tracking o f cohort s throughneighborhoo d type s an d microenvironment s i s wel l suite d t o estimatin g exposur e t o airborn e pollutant s sinc e the exposur e i s continuou s whe n a cohor t i s breathing pollute d air . O n th e othe r hand , contaminant s ar e no t ingeste d continuousl yan d the environmen t a cohor t i s i n a t th e tim e o f a particula r incidenc e o f ingestio n ma yhav e littl e relevance . Contaminate d dus t picke d u p o n food , clothing , o r th e bod yi n on e environmen t ma yfinall yb e ingeste d whe n the cohor t i s i n anothe r environment . No r i s i t certai n tha t i t wil l be ingeste d a t all . Exposur e t o airborn e contaminant s i s different . I f an individua l i s i n an environmen t containing pollute d air , i t ca n be presume d h e i s continuousl yexpose d t o the pollutant . Consequently , i t i s suggeste d tha t exposur e t o ingeste d lea d be keye d directl yt o th e cohort , tha t is , t o th e the descriptiv e factor s tha t defin e a cohort .P.1 1

Thus :

(16 ) Wj(d,k ) •***• Z w 0 (u,d,k ) + Z w g (v,d,k ) u v Where"W j i s th e averag e weigh t o f lea d ingeste d b ycohor t k durin g dayd . Th e W Q an

d W g represen t contribution s from pathway s whic h ar e independen t an

d dependent , respectively , o f the NAAQS . Th e indice s u an

d vrepresen t the differen t pathway s t o ingestio n fo r eac ho f the tw o classes . Th e inde x d i s include d t o tak e int o accoun t anyshor t ter mo r lon g ter mtrend s wit h time . Tha t is , ther e ma yb e weekday/weeken d trends , seasona l trends , o r longe r trend s suc h a s reduce d us e o f lead soldering i n th e manufactur e o f meta l foo d containers . O r th e impositio n o f a NAAQ S ma ycaus e a slo wreductio n o f ingeste d lead fromth e w s -typ e pathways . Th e cohor t designatio n take s int o accoun t difference s i n ingestio n rat e resulting fromsuc hfactor s a s ag e o f the child , socio/economi c status , ag e o f housing i n th e neighborhood , etc . I t i s likel ytha t Equatio n 1 6 ca n b e simplifie d b ysummin g ove r the u indice s prio r t o inpu t t o th e exposur e model . I n th e cas e o f the pathway s dependen t o n th e NAAQ S designation , i t ma ybe possibl e t o combin e pathway s wit hsimila r dependencies . I f vindexe s the combine d pathways :

(17 ) W x (d,k ) = U 0 (d,k ) + z U s (v,d,k ) v I t i s necessaryt o mode l the dependenc yo f the NAAQ S dependen t pathways . I t i s assume d tha t lead fromthes e pathway s i s primaril y particulat e fromvehicl e emission s an d poin t source s whic hha s settle d o n surface s an d th e to p layer s o f soil . I n thi s manne r i tP.1 2

ha s bee n generall yincorporate d int o dus t an d soi l i n th e environment . I t wil l be assume d tha t the additio n o f lead t o dus t an d soi l b

ythes e mechanism s i s offse t t o som e degre e b yremova l mechanisms . Thes e can b e mechanism s suc h a s simpl e dilutio n wit h dus t o r soi l whic hcontain s n o lea d o r lesse r amount s o f lead , leaching b

yrai n water , o r washin g awa yb yrai n water . Th e depositio n rat e wil l be assume d t o be proportiona l t o the averag e concentratio n o f lead i n ambien t air . Th e latte r quantit y wil l the n be relate d t o a NAAQS . Th e remova l proces s i s mor e complicated . Acommo n featur e o f manyremova l processe s i s tha t th e rat e o f remova l increase s wit h increasing concentration s o f the materia l being removed . Simpl e dilutio n an d inefficien t leaching processe s wor k i n thi s manner . I n thi s cas e th e simples t assumptio n i s tha t th e rat e o f remova l i s proportiona l t o th e concentratio n o f lead i n th e dus t o r soil . Anothe r simpl e alternativ e i s tha t th e materia l i s being remove d a t a fixe d rat e independen t o f th e concentratio n present . Thi s migh t be tru e o f leaching processe s i n whic hth e leaching materia l become s saturate d wit h the contaminan t being leache d during eac happlication . I n the cas e tha t th e remova l rat e i s partiall yproportiona l t o the concentratio n an d partiall yindependen t o f concentratio n w e hav e th e following :

(18 ) dC s /d t = r a C a - R - qC s C s i s th e concentratio n o f lead i n th e soi l o r due t a t tim e t . C a i s the annua l averag e atmospheri c concentratio n o f lead . Th e ter mr a C a represent s th e rat e o f increas e i n lea d i n soi l an d dus t du e t o depositio n fromtraffi c an d poin t sources . Th e termR i s th e rat e o f los s du e t o factor s whic har e independen t o f

1 0P.1 3

concentration . Th e third ter mo n the righ t sid e o f the equatio n i s th e rat e o f chang e i n concentratio n du e t o thos e factor s whic h ar e influence d b

yconcentration . Equatio n (18 ) i s easil y integrate d t o give : (19 ) C s = C°exp(-qt ) + (1/q)(r a C a ~ R)( 1 - exp(qt) ) wher e C a i s th e initia l concentratio n o f lead . I f r a C a i s greate r than R , th e systemwil l eventuall yreac ha stead ystat e concentratio n equa l t o (1/q ) (r aC f l - R ) whic h i s dependen t o n th e NAAQS . I f the termqi s verysmal l o r zero , meanin g tha t ther e i s littl e t o n o dependenc e o f th e remova l rat e o n th e existin g concentration , Equatio n 1 9 becomes : (20 ) C s = (r a C a - R) t Tha t is , th e concentratio n wil l eithe r b e increasing o r decreasing linearly , depending o n th e whic h o f th e tw o terms , r fl C a o r R , i s larger . Ther e wil l b e n o stead ystat e i f k i s zero . I f k i s ver ysmall , a ver ylon g tim e woul d b e require d t o reac h th e stead ystate . Th e C a ter mca n b e calculate d fro mth e 24-hou r lea d concentration s fo r th e cohort' s hom e neighborhood . Th e ingestio n rat e Vj(v,k,d ) woul d be : (21 ) V!(v,k,d ) = ri (v,k,d)C s (v ) Combinin g Atmospheri c an d Ingestiv e Exposure s Th e atmospheri c an d ingestiv e exposure s o f sensitiv e individual s t o lead wil l b e outpu t separatel yb yth e model . I n fact , th e physiologica l mode l wil l requir e tha t theyb e treate d

1 1P. M

separatel ysinc e th e efficienc ywit hwhic hlea d i s absorbe d int o th e bloo d i s differen t fo r th e tw o routes . I t is , nevertheless , instructiv e t o combin e th e tw o measure s int o a tota l exposur e fo r a 24-hour period . Th e necessarycommo n measure s fo r doing thi s hav e alread

ybee n develope d above . W e hav e therefor e

W TE (d,k ) = W E (d,k ) + Wj.(d,k ) Wher e Wm E i s the combine d exposur e expresse d a s weigh t o f lead pe r 24-hour s an

d th e individua l component s W E an d W j ar e define d i n Equation s (15 ) an d (17 ) respectively .

Dynamic s o f Exposur e Mode l Becaus e the physiologica l mode l wil l b e operatin g o n th e output s o f the exposur e mode l the mode l wil l follo weac h chil d cohor t fromthe tim e o f conceptio n t o it s sevent hbirthday . Eac h chil d cohor t wil l b e treate d a s conceive d a t th e beginning o f a quarter . Birt hwil l occu r thre e quarter s ( 9 months ) later . Befor e birt hther e i s n o direc t exposur e t o lead an d consequentl yonl yth e exposur e o f the mothe r wil l be followe d during thi s period . Th e physiologica l mode l wil l tak e int o accoun t th e buil d u p o f lead i n th e fetu s during thi s perio d base d o n th e mother' s exposur e an d th e level s o f lead i n he r bod ycompartments . Direc t exposur e o f th e chil d wil l b e take n int o accoun t fromth e tim e o f birt ht o th e sevent hbirthday . Ideally , eigh t year s o f 24-hou r lea d concentration s i n ambien t ai r wil l b e use d b yth e model . Lackin g this , a singl e yea r t o severa l year s o f dat a coul d b e use d repetitiousl yt o obtai n severa l year s o f data . Trend s du e t o th e impositio n o f emissio n control s

1 2P.1 5

coul db e buil t int o th

e dat a throug

hth e us e of rollbackprocedures . I f there are n

o significant trend s i nambien t lea

dlevel s over th e seve nyea r perio do f th e computation , another substantia l saving s i

ncomputationa l effor t wil l b e realized . I nthi s cas e durin g th e exposur e computationw e ca neffectivel y

dropth

e distinctio

no f cohort s b

y age , an

dconsider onl y

th e quarter i

n whic hthe

y wer e bor

n(o r conceived ) a s distinguishin g them . A

t th e completiono f th

e calculatio

nw e ca ndevelopseparat e exposur e distribution s fo

r childrenat a givenag e u pt o thei r seventh birthday . Withi na give nyea r th e exposur e distribution s fo r childrenbor

ni ndifferen t quarter s of th e yea r ca nb e weightedt o account fo

r effect s of seaso no nbirthrate . Thes e exposur e distribution s ca

nthe nb e weightedb

y th e numbe r o f childreni nth e populatio

ni neac hof thes e year s t o obtai non e yea r exposur e distribution s fo

r childrenu

pt o thei r seventhbirthday . I f ther e ar e strong trend s inambien t level s o f leadove r the perio do f interest , th

e yearly

exposur e distribution s woul db e differen t fo

r eac hyear . I f th

e exposur e distribution s wer e wanted fo r a particular year , th e computationwoul dhav e t o b e startedseven year s earlie r an

da ne w se t o f cohort s starte dineac hquarte r o f eachsucceedin

g yea r throug

hth e en do f th e year o f interest . The computationa l burde nwoul dtherefor e b e substantiall y

greater tha

n th e n o tren dcas e discussedi nth e precedin

g paragraph . I t i s likel y

tha t bot

hcase s wil l b

e o f interest . The firs t cas e woul dlikel y

pertai ni

na standard s objectiv e analysis , whil e th e secon dcas e woul dlikely pertai ni

na standard s impac t analysis . Not e tha t b

y thi s methodo f calculationwe ax e not , strictl y speaking , followin

g a singl e chil dcohor t over sixyear s an dnin e months . B

y ou r cohor t definitio nwe are dealin

g wit ha ne

w cohor t ever y 3 months . Alternatively , th e computationca

nb e vieweda s dealin g wit ha singl e chil dcohor t fro m conceptiont o it s seventh

1 3P.1 6

birthdayan

d the n dividing the singl e cohor t int o 2 7 subcohort s a t th e en d o f the computatio n fo r the purpos e o f developing exposur e an d bod yburde n distributions . Th e exposure s o f pregnan t wome n woul d onl yb e tracke d during th e nin e mont hperio d o f pregnancy . Thi s present s n o difficultie s fo r the exposur e portio n o f the model . I n th e cas e o f the physiologica l mode l assumption s wil l hav e t o b e mad e abou t the distributio n o f lead amon g bod ycompartment s a t th e beginning o f th e pregnancy . Thi s distributio n wil l generall yvarywit h th e cohort . Outpu t fromth e Exposur e Mode l Th e lead exposur e mode l wil l outpu t th e followin g distribution s o f exposur e ove r a on e yea r period : 1 . Exposur e t o 2 4 hr averag e ai r lead concentration s (yg/m*** ) 2 . Exposur e t o inhale d lead (yg/24hrs ) 3 . Exposur e t o ingeste d lead (yg/24hrs ) 4 . Tota l exposur e t o lead , inhale d + ingeste d ( yg/24hrs )

Eac ho f th e abov e distribution s i s expresse d i n thre e forms : 1 . Tota l numbe r o f exposure s a t o r abov e a give n exposur e leve l 2 . Numbe r o f peopl e expose d a t o r abov e a give n leve l 3 . Numbe r o f peopl e experiencing thei r pea k exposur e a t a give n leve l i n a on e yea r period . Distribution s ca n appl yt o th e tota l sensitiv e populatio n o r an y subse t o f cohorts , a s fo r exampl e childre n i n thei r firs t year .

WilliamF . Bille r 8/29/8 3

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