Physiologicomathematical model for studying human

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1 British Journl of ndustril Mediine 1986;43: Physiologiothetil odel for studying hun exposure to orgni solvents: kinetis of blood/tissue n-hexne onentrtions nd of 2,5-hexnedione in urine L PERBELLN, P MOZZO,2 F BRUGNONE,' A ZEDDE' Fro the nstitute of Ouptionl Mediine' nd Physil Helth Servie,2 Polilinio Borgo Ro, Veron, tly ABSTRAT The physiologiothetil odel with eight oprtents desribed llows the siultion of the bsorbtion, distribution, biotrnsfortion, exretion of n orgni solvent, nd the kinetis of its etbolites. The usul oprtents of the hun orgnis (vessel rih group, usle group, nd ft group) re integrted with the lungs, the etbolising tissues, nd three other oprtents deling with the etboli kinetis (biotrnsfortion, wter, nd urinry oprtents). The findings obtined by thetil siultion of exposure to n-hexne were opred with dt previously reported. The onentrtions of n-hexne in lveolr ir nd in venous blood desribed both in experientl nd ouptionl exposures provided substntil vlidtion for the dt obtined by thetil siultion. The results of the urinry exretion of 2,5-hexnedione given by the odel were in good greeent with dt lredy reported. The siultion of n exposure to n-hexne repeted five dys week suggested tht the solvent uultes in the ft tissue. The hlf life of n-hexne in ft tissue equlled 64 hours. The kinetis of 2,5-hexnedione resulting fro the odel suggest tht ouptionl exposure results in the presene of lrge ounts of 2,5-hexnedione in the body for the whole working week. Vrious thetil odels siulting the uptke, distribution, nd exretion of hexogenous heils in the body hve been proposed during the pst dedes. They re useful in ny fields of toxiology nd ediine. Fiserov-Bergerov desribed thetil odel for the kinetis of nestheti gses whih hs been extended to orgni solvents.1 Other odels hve been used by Sto et l,2 Fernndez et l,3 nd Droz et l4 to siulte the behviour of industril solvents in people ouptionlly or experientlly exposed. Mny interesting dt fro whih to prepre siilr physiologiothetil odels hve been reported by Fiserov-Bergerov.5 The phrokinetis of soe ntineoplsti drugs hve lso been reported by using differentil equtions integrted into thetil odel whih desribes the probble oveents of the substnes in the body oprtents.67 Rsey nd Andersen Aepted 3 Mrh 1986 proposed physiologilly bsed phrokineti odel to desribe the behviour of inhled styrene in rts nd to predit its kinetis in n.8 Droz suggested tht the thetil odels siulting solvent phrokinetis fter ouptionl exposure y be useful in estblishing the "biologil exposure index" of these produts, in studying the individul preters whih re ble to odify the solvent onentrtions in the tissues of exposed people, nd for further reserh into the reltion between the body onentrtions of the solvents nd their toxi effets.9 A tter whih hs been insuffiiently disussed in these thetil odels is tht of the biotrnsfortion of the inhled gses. Reently Andersen et l obtined soe interesting toxiokineti desriptions of the etbolis of inhled gses in nils1 nd these results re useful to oplete the bsi dt needed for the siulting odels. The present pper desribes thetil odel tht integrtes the dt bout the behviour of sol- 76 Br J nd Med: first published s /oe on 1 Noveber Downloded fro on 16 Deeber 218 by guest. Proteted by

2 Physiologiothetil odel for studying hun exposure to orgni solvents vents in the body oprtents with the results of the kinetis of their etbolites. The results suggested by the odel bout the distribution of n-hexne in the body oprtents nd of its in etbolite (2,5-hexnedione) re opred with the dt found in published reports nd disussed in onnetion with the neurotoxi effets of these produts. Mterils nd ethods We prepred thetil odel with the following eight oprtents (fig 1). (1) Lung oprtent where the solvent rrives vi inhltion nd rehes onentrtion tht lso depends on the solvent onentrtion in the lveolr ir, in the rteril blood, nd in the venous blood. (2) Vessel rih tissue oprtent (VRG) inluding the hert, brin, nd kidney. (3) Musle tissue oprtent (MG). (4) Ft tissue oprtent (FG). (5) nd (6) Liver tissue whih inludes two oprtents: one relting to the input nd output of n- hexne (tbolis of n-hexne) nd the other relting to the synthesis nd trnsfer of 2,5-HD. Q (lv) Q(lv) _,- (exh) Fig 1 Digr of the physiologiothetil odel used to siulte the pttern of distribution of n-hexne in the body nd of 2,5-HD urinry exretion. Sybols nd physiologil preters re reported in tbles nd 2 nd in text. 761 (7) Wter oprtent onerned with the body distribution of 2,5-HD. (8) Urine oprtent where 2,5-HD is exreted. No other routes of 2,5-HD exretion hve been onsidered. The sybols shown in fig 1 re defined in tbles 1 nd 2. All thetil odels desribing the behviour of solvents in the body re bsed on the two in hypotheses tht: (1) the solvent onentrtion instntneously rehes blne between lveolr ir nd rteril blood (physiologilly the blne is rehed very quikly) nd (2) the solvent onentrtion in venous blood is onsidered to be in onstnt nd dyni blne with the orresponding tissue onentrtions. The liver oprtent is theoretilly onsidered to be the only site t whih the synthesis of etbolites tkes ple. The rte onstnts (K) whih desribe the tbolis, synthesis, or trnsfer of the biotrnsfored produts re onsidered to be first order. Tble 1 Physiologil nd kineti preters used in the odel siulting hun exposure to n-hexne. Perentge vlues of the totlflow rte re shown in prentheses Tissue/blood Bloodflow prtition Volues () (i/in) oeffiient) VRG (55%) 5 MG (16%) 6-2 FG (4-4%) 13 Liver (25%) 6-5 VRG = Vessel rih tissue oprtent. MG = Musle tissue oprtent. FG = Ft tissue oprtent. V(lung) = Volue of lung tissue: 11. V(rt) = Volue of rteril blood: Q(t) = Blood flow rte: 6-3 /in. Q(lv) = Alveolr ventiltion: 6 /in. N = Blood/ir prtition oeffiient of n-hexne: -8. Kl = -3/in. K2 = -12/in. K3 = 9/in. K4 = 9/in. FR = Funtionl residul pity: Tble 2 Sybols nd bbrevitions used in desribing the toxiokineti odel nd in the thetil equtions (i) = onentrtion in oprtent (i) (g/l). Q(i) = Blood flow rte to oprtent (i) (1/in). V(i) = Volue of oprtent (i) (1). (rt) = Solvent onentrtion in rteril blood (g/). N(i) = Tissue/blood prtition oeffiient. (ven) = Solvent onentrtion in venous blood (g/). A(lung) = Aount of solvent in lung oprtent (g). (lung) = Solvent onentrtion in lung oprtent (g/l). (inh) = Environentl onentrtion of solvent (g/l). (exh) = Solvent onentrtion in expired ir (g/). A(l) = Aount of etbolite (2,5-HD) in etbolising tissue group (liver oprtent) (g). A(w) = Aount of etbolite (2,5-HD) in the wter oprtent (g). A(u) = Aount of etbolite (2,5-HD) in urine (g). Br J nd Med: first published s /oe on 1 Noveber Downloded fro on 16 Deeber 218 by guest. Proteted by

3 762 PARAMETERS FOR THE MATHEMATAL MODEL The following preters re needed to work with the thetil odel: the volue nd the blood flow to eh oprtent, the blood/ir nd tissue/blood solvent prtition oeffiients, nd the rte onstnts for solvent biotrnsfortion nd for the behviour of its etbolites in the body. For the ssignent of the volues nd the blood flows of the individul oprtents we hve used previously reported dt" 12; these physiologil preters re listed in tble 1. Vlues for the solubility of n-hexne in blood nd in hun tissues (blood/ir nd tissues/blood prtition oeffiients) were tken fro our experientl studies "in vitro" (tble 1). The solubility dt obtined in hun tissues were siilr to those found in rt tissues "in vivo,"'14 prt fro the liver/blood solubility whih, in rts, inresed throughout the exposure period. The preters of n-hexne biotrnsfortion nd of the distribution nd exretion of 2,5-hexnedione were ssigned ording to reports or lulted fro dt obtined by us in workers exposed to the solvent or ording to soe itertive tests on the thetil odel. Figure 1 shows both the tissue body oprterits nd the shee tht desribes the tbolis of n- hexne in the etbolising tissues (dispperne of n-hexne), the prodution of 2,5-HD in the etbolising tissues (liver), nd its trnsfer fro the liver into the wter oprtent nd into the urinry oprtent. A siilr ethod for etbolite studies ws proposed by Wgner.'5 The rte onstnt, K1, desribes the dispperne of n-hexne, K2 represents the onstnt rte of synthesis of 2,5-HD into the liver oprtent, K3 is the rte onstnt desribing the trnsfer of 2,5-HD fro the liver into the hydri oprtent, nd K4 is the rte onstnt for the urinry exretion of the 2,5-HD. The biotrnsfortion rte of n-hexne is fst in the liver oprtent t n environentl exposure of bout 1 pp (36 g/3). Hildebrnd nd Andersen who studied n-hexne etbolis indiretly by esuring the dispperne of n-hexne fro exposure ges regrdless of the prodution of n-hexne etbolites,'6 found tht the V x of the n-hexne etbolis ould be estited t 8-3 g/kg/h nd tht the k orresponded to n environentl n-hexne exposure of 163 pp (587 g/3). n ouptionl exposure to 1 pp (36 g/3) of n-hexne, we n estite n lveolr n-hexne uptke of -6 g/kg/h, whih is less thn one tenth the etbolis veloity (V x) of n-hexne in rts (8-3 g/kg/h); (n-hexne uptke i = x R x VA x t/kg with i = environentl onentrtion (36 Mg/l), R = lveolr retention (2%),'7 VA = lveolr venti- Perbellini, Mozzo, Brugnone, Zedde ltion (1 /in), t = tie in inutes, kg = body weight (7 kg)). n other words, ssuing tht V x in n is siilr to tht in rts, the ount of n- hexne bsorbed during n ouptionl exposure to 1 pp is uh less thn n be tully biotrnsfored. n experientl exposure only onentrtions higher thn 36 g/3 see to be ble to sturte the etboli tivity of the rt liver.'8 Bering in ind ll these onsidertions in the thetil odel we used etbolising rte onstnt of n-hexne K equl to 3. A siilr vlue ws used by Rsey nd Andersen for the etbolising rte onstnt of styrene.8 K4 is the urinry exretion rte of 2,5-HD fro the hydri oprtent. Soe dt lredy published"9 nd other dt olleted by us fro the urinry 2,5-HD kinetis in workers ouptionlly exposed to n-hexne, enbled us to estite the en hlf life of 2,5-HD in the urine to be bout hours, whih ens K4 ner to 9. Aong the nuerous produts eerging fro the etbolis of n-hexne in rt, rbbit, onkey, nd n, 2- nd 3-hexnols re the in urinry etbolites in nils, nd 2,5-HD is the in urinry etbolite in n.22' n experientl nils treted with 14-hexne22 3-4% of the dose ws eliinted s 14-O2 in the breth nd 4-5% s unidentified etbolites in the urine. This suggests tht n-hexne is highly etbolised opound (7-9%). Provided tht the urinry n-hexne etbolites tully identified in n turn out to orrespond only to bout 1-2% of the bsorbed n- hexne,'9 it follows tht 2,5-HD represents only sll ount of the biotrnsfored n-hexne nd we used rte onstnt of 2,5-HD synthesis whih is bout one thirtieth of tht for n-hexne tbolis (K2 = -12). K3 is the rte onstnt of the relese of 2,5-HD fro the liver into the wter oprtent. We bore in ind tht the highest point of the urinry exretion rte of 2,5-HD ws rehed three to four hours fter the end of exposure both in nils nd in n.'9 2 Moreover, the en exretion of 2,5-HD in workers exposed to 36 pg/l of n-hexne for eight hours ws found to equl 2 8 g in 24 hours.'9 On the bsis of these onsidertions nd fter itertive estitions on the thetil odel, we ssued tht K3 equlled 9. The set of differentil equtions used in the odel is given in the ppendix. Results The venous blood onentrtions of n-hexne fter exposures to 36 nd 72 g/3 for four hours lulted fro the odel re shown in figure 2. The open Br J nd Med: first published s /oe on 1 Noveber Downloded fro on 16 Deeber 218 by guest. Proteted by

4 Physiologiothetil odel for studying hun exposure to orgni solvents 1- )4 jq 413 l 2 GD x Vio,/l Exposure tie ( hours ) 8 Fig 2 Venous blood onentrtions of n-hexne during nd fter exposure to the solvent. Dt suggested by the thetil odel (. : exposure to 36 g/3; -._-.-. :exposure to 72 g/r3) nd dt found by Veulens et l23 (: exposure to 36 g/3; : exposure to 72 g/r3). nd filled irles re dt reported by Veulens et l during nd fter experientl hun exposures.23 The venous blood onentrtions of n-hexne in people exposed to 72 g/3 for four hours, with en lung ventiltion of 1-4 1/in, rnged, on verge, between 334 nd 368 pg/l during exposure nd were siilr to those suggested by our odel. The venous onentrtions obtined fro the siulted exposure to 36 g/3 were bout 1% lower thn those found by Veulens et l.23 Figure 2 lso shows the trend of the blood n-hexne onentrtions fter the end of exposure. The experientl vlues found fter the end of exposure23 fll little ore slowly thn those given by the odel. Figure 3 shows the trend of the n-hexne onentrtions in venous blood, in lveolr ir, nd in the vrious oprtents (prt fro ft), when en exposure to n-hexne equl to 36 g/3 for workshift (four hours in the orning nd four in the fternoon) is siulted. After the beginning of exposure, the n-hexne onentrtions rise rpidly: within 3 inutes tissue onentrtions re ore thn 7% of the onentrtion tht they will reh t the end of the workshift (only usle tissues need longer tie to pproh these levels beuse of their lrge volue). During the iddy work brek (one hour), the n- hexne onentrtions in venous blood, in lveolr ir, in the VRG, nd in the liver quikly fll to 5-18% of the vlue found t the end of the first four hours of exposure. When work begins gin, the blood nd tissue onentrtions quikly return to high level Z : r r r r r r y vv vvy V v 1V r 1 r r = VRG =MG = Liver v = \knous btood = Atveolr r r F Exposure tie (hours ) Fig 3 n-hexne onentrtions in vrious oprtents suggested by odel: exposure to solvent equls 36 g/r3 forfour + four hours with workbrek lsting one hour. nd t the end of exposure, the lveolr ir, venous blood, VRG, nd MG show n-hexne levels equl respetively to 82%, 62-5%, 82-8%, nd 67-3% of the sturtion level. At the end of exposure the n-hexne onentrtion in venous blood orresponds to 182 pg/l. On ny osions we hve heked the n-hexne onentrtions in the workples of nuerous workers nd siultneously obtined venous blood sples t the end of exposure to nlyse the solvent onentrtion; fig 4 surises our experiene in this field. The lose reltion between the two preters suggests tht n exposure to 36 g/3 of n-hexne orresponds to en blood onentrtion of 176 pg/l. As y be seen, the result suggested by the odel (182 pg/) is siilr to tht found in the workers ouptionlly exposed to n-hexne. The lveolr onentrtions of n-hexne (whih re lwys in onstnt blne with rteril blood onentrtions) 6 inutes fro the beginning of exposure, orrespond to 77-5% of the-exposure onentrtions nd inrese to 83-3% t the end of exposure (fig 3). These dt onfir our previous reserh on workers '7 nd suggest tht the lveolr onentrtion (prt fro brief period fter the beginning of exposure) shows liner reltion with the environentl onentrtion. n the liver oprtent (fig 3) the n-hexne level rehes onentrtion equl to 5 pg/l (27% of the sturtion onentrtion) beuse of the rpid biotrnsfortion of the solvent in this oprtent. When exposure eses (fig 3) the n-hexne onen- r r r 763 Br J nd Med: first published s /oe on 1 Noveber Downloded fro on 16 Deeber 218 by guest. Proteted by

5 o * P- ) Y= 529X-14 9 r=*94 n=62 p<1 *. ** 5 O*'.... *,'~~~~. S.... R * 4. Perbellini, Mozzo, Brugnone, Zedde. *.... * 1 1 -,. _.... Fig 4 Reltion between environentl nd venous blood onentrtions of n-hexne. Dt obtined t end of four + four hours workshift. trtions fll in ll the oprtents: within 1 hours fter the end of exposure the venous blood nd lveolr onentrtions reh suh low vlues thn they re diffiult to detet by norl ethods of nlysis. The n-hexne ft onentrtion rises ontinuously during exposure nd rehes vlue of 2578 pg/l t the end. This vlue is higher thn tht of the other tissues but orresponds to only 6-9% of its sturtion onentrtion. Figure 5 shows the behviour of the n-hexne onentrtions in ft tissue when dily exposure of eight hours to 36 g/3, for five dys week, for two weeks, is siulted. The gret solubility of n-hexne in this tissue ens tht the solvent tends to uulte nd the body burden of n-hexne nnot be entirely eliinted if exposure is not interrupted for severl dys (t lest 1 dys sine the hlf life of n-hexne in ft tissue orresponds to bout 64 hours). i- 6 o , n - Hexne environentl onentrtion (,Ug Ml) At the end of the seond week of exposure, when the xiu level of the solvent in the ft oprtent (996 pg/l) is rehed, the ft burden of n-hexne orresponds to 26-6% of the sturtion level. Figure 6 shows the en urinry exretion rte of 2,5-HD during 24 hours in group of 13 shoe ftory workers who were ouptionlly exposed to n- hexne for eight hours. The dt were obtined s previously desribed'9 nd neessitted the esureent of environentl exposure nd the olletion of ll urine sples during 24 hour period. During exposure the exretion rte of 2,5-HD inreses progressively nd ontinues for three to four hours fter exposure hs esed. Subsequently the exretion rte flls slowly to the level found t the end of exposure. The results suggested by the odel fit the en results obtined fro the workers. n fig 6 the dotted lines represent the results obtined fro the Br J nd Med: first published s /oe on 1 Noveber Downloded fro on 16 Deeber 218 by guest. Proteted by

6 Physiologiothetil odel for studying hun exposure to orgni solvents 1 9.' v UV r -r-9-.~. _ Dys Fig 5 n-hexne onentrtions rehed in ft tissue during siulted exposure to 36 g/3, for eight hours dy, for five dys week, for two weeks.? 12 91, L 6 ' :.... odel when K2 equl to 9 nd -16 (insted of -12) is used. Siulting n exposure to 36 g/3 for eight hours dy for five dys, the 2,5-HD exretion rte will be siilr to tht shown in fig 7. After the first exposure, the urinry exretion rte of 2,5-HD reins high, lthough with wide flututions; only on Mondy orning, before work strts, is the 2,5-HD exretion rte so low tht its quntifition is unertin. n the se figure the urinry ount of 2,5-HD (g/24h) exreted during eh week dy is L Exposure tie (hours) Mondy -Tuesdy- Fig 6 Urinry exretion rte of 2,5-HD in group of shoe ftory workers exposed to n-hexne during workshift. Men vlue is represented by blk irle (stndrd devition by vertil strokes). Dt suggested by thetil odel (.-_._._.) orrespond well to en exretion rte of 2,5-HD. Dotted lines bove nd below en re obtined using K2 equl to -16 nd 9 respetively..94- Z,- 3- td.5.l D n.2,.t. t :...1 t,..1 t :..: g124h Mon Tue Wed Thur Fri St Sun 765 Fig 7 Urinry exretion rte of 2,5-HD suggested by odel with siulted exposure to n-hexne to 36g/3 for eight hours for five dys week. Totl ount of 2,5-HD dily exreted is lso shown..1 Br J nd Med: first published s /oe on 1 Noveber Downloded fro on 16 Deeber 218 by guest. Proteted by

7 766 reported. On Mondy this vlue is uh lower thn on the lst working dy of the week. Disussion The objetive of the present work ws to inrese knowledge of the toxiology of n-hexne by interpreting experientl dt olleted in industril workers with the help of thetil odel. The biologil exposure index (BE) is ttrting the ttention of industril hygienists nd soe vlues hve been reently suggested by the AGH.2" Mthetil odels n be useful in the study of ouptionl exposure, n opleent field studies nd experientl exposures, nd n help to understnd the uptke, distribution, nd exretion of vrious produts. They re helpful when it is neessry to study the tie of biologil spling or the physil worklod in the solvent uptke or the body burden during different types of exposure (short nd high or onstnt or repeted). The odel used here to siulte the kinetis of n-hexne nd of 2,5-HD gives ny results whih re siilr to those lredy reported. The lveolr nd venous blood onentrtions of n-hexne suggested by the thetil odel re siilr to those obtined in experientl nd ouptionl exposures. The urinry 2,5-HD exretion found in workers exposed to n-hexne ws lso orretly siulted by the thetil lultions. This vlidtion of the odel llows us to think tht other siultions will lso provide soe dt with good pproxition to those found in vivo. The dt on the kinetis of n-hexne in the ft tissues re prtiulrly interesting. The odel suggests n-hexne t /2 in the ft tissue equl to 64 hours; it follows fro this tht the solvent uultes in the ft oprtent nd the unexposed period of the weekend is not long enough to llow the oplete exretion of the solvent fro the ft tissues.> The oplete exretion of n-hexne fro ft tissue needs ore thn 1 dys with no further exposure. After ouptionl exposure, the oplete relese of n- hexne fro the ft is not possible during the weekend but requires long bsenes fro work. Siilr results were obtined experientlly with other industril solvents whose blood/ft distribution oeffiient is ore thn 5.25 Another useful piee of infortion suggested by the odel reltes to the lveolr nd venous blood n-hexne onentrtions whih, 16 hours fter 36 g/3 exposure for eight hours, re so low tht their detetion is not possible with the usul ethods. Moreover, it is iprobble tht the sll ount of n-hexne in these biologil sples would be relible for orret evlution of previous exposure. The results onerning the urinry exretion rte of Perbellini, Mozzo, Brugnone, Zedde 2,5-HD, obtined with the odel re in good greeent with the dt obtined fro subjets exposed t work. The inferene bout repeted exposures with progressive inrese of the urinry 2,5-HD during the working week is supported by our previous dt'9 nd by those of Arfioli et l26 nd wt et l.27 These uthors found tht 2,5-HD is present in urine sples olleted 16 hours fter exposure to n-hexne (on the orning fter) nd tht t the end of the working week, the urinry 2,5-HD onentrtions re higher thn on the first dy of the week (if the exposure is the se). f we onsider urinry exretion of 1 l/in the odel suggests tht on Mondy evening t the end of n exposure to n-hexne 36 g/3 for eight hours, the 2,5-HD urinry onentrtion is equl to 1 2 g/l (if the urine is olleted in single sple); t the end of the workshift on Fridy (with repeted nlogous exposure during the other weekdys) the 2,5-HD urinry onentrtion rehes 3-2 g/l. Mutti et l found tht urinry 2,5-HD onentrtion of 3 g/g of retinine orresponded to en exposure of 5 pp (18 g/3).28 Siilr dt were found by us2' nd by wt et l27 in other groups of workers, but none of the studies onsidered the possibility of n uultion of urinry 2,5-HD during the week. Other studies will be neessry to define the BE of 2,5-HD fter exposure to n-hexne but the dt suggested by the odel should prove useful in this respet. The uultion of 2,5-HD in the body nd in the urine provides n iportnt ftor in understnding the ehniss of the neurotoxiity of n-hexne nd of other solvents tht give rise to 2,5-HD; oreover, ny ftors tht odify the body kinetis of this produt will lso odify its toxi effets on the peripherl nervous syste. Appendix Tissue oprtents-the rte ofhnge of n-hexne within the three oprtents (FG, MG, VRG), where the solvent does not undergo ny biotrnsfortion or exretion, is estited s the differene between the ount of the solvent whih rehes the oprtent in the rteril blood nd the ount of the solvent whih leves the oprtent in the venous blood. Bering in ind tht the venous blood onentrtions eerging fro eh oprtent re governed by the tissue/blood prtition oeffiients of the solvent, the differentil eqution whih expresses the rte of n-hexne hnge in the individul oprtents is: d(i)/dt = Q(i)/V(i)((rt)-(i)/N(i)) (1) Venous blood onentrtion-n the ixed venous blood rehing the lungs the onentrtion of n- hexne is lulted s the su totl of the venous Br J nd Med: first published s /oe on 1 Noveber Downloded fro on 16 Deeber 218 by guest. Proteted by

8 Physiologiothetil odel for studying hun exposure to orgni solvents 767 onentrtions eerging fro ll the oprtents da(w)/dt = A(l)K3 - A(w)K4 (9) ording to the following forul: Urine oprtent-the rte of hnge of 2,5-HD in (ven) = (E Q(i)(rt)/N(i))/Q(t) (2) the urine is estited by the ount of the etbolite Pulonry oprtent-the onentrtion of n- eerging fro the wter oprtent: hexne in the lung oprtent depends on the da(u)/dt = A(w)K4 (1) ount of solvent inhled, the ount of solvent The syste of siultneous differentil equtions ws reoved by the pulonry rteril blood, on the solved using the Runge-Kutt-Gill ethod of integrtion written in Bsi on M24 Olivetti personl o- ount of solvent brought by ixed venous blood fro the tissues to the lungs, nd on the ount of puter. solvent expired. Aording to this, the rte of hnge of n-hexne in the pulonry oprtent is given s: da(lung)/dt = Q(lv)(inh) + (ven)q(t) - Q(lv)(lv) - (rt)q(t) (3) As the pulonry oprtent onsists of the lung tissue, the residul funtionl pity (RF), nd the rteril blood, the ount of solvent present in the lung oprtent y be expressed s follows: A(lung) = (lung)v(lung) + (rt)v(rt) + (FR)FR (4) Sine (lung) = (rt), (lv) = (RF) nd (RF) = (rt)/n, equtions (3) nd (4) y be expressed s: d(rt)/dt = l/(v(lung) + V(rt) + FR/N)(Q(lv)(inh) + (ven)q(t) - Q(lv)(rt)/N-(rt)Q(t)) (5) By inserting (for the evlution of the venous blood onentrtion of the solvent) eqution (2) into (5) we obtin: d(rt)/dt = (l/(v(lung) + V(rt) + FR/N))(Q(lv)(inh) + (i)q(i)(i)/n(i) - Q(lv)(rt)/N-(rt)Q(t)) (6) whih gives the rte of hnge of the rteril blood n-hexne onentrtion. Liver oprtents-the liver inludes, fro the thetil point of view, two oprtents: one for n-hexne nd the other for its etbolites. The rte of.hnge,of -n;hexne in the liver is given by eqution (1) with the insertion of the biotrnsfortion n-hexne rte onstnt K1: d(1)/dt = 1/V(l)((Q(1)(rt) Q(l)(l)/N(l))-(l)Kl (7) The ount of the 2,5-HD present in the liver depends on the n-hexne liver onentrtion, on the rte of synthesis of 2,5-HD (K2), nd on the eliintion rte of the 2,5-HD (K3) fro the liver into the wter oprtent: da(l)/dt = (l)v(l)k2 -Y(8)K3 (8) Wter oprtent-the ount of the 2,5-HD present in the wter oprtent is given by the differene between the ount rriving fro the liver oprtent nd the ount exreted in the urine: This work ws in prt supported by the tlin Ntionl Reserh ounil (NR): finlised projet on preventive nd rehbilittive ediine, subprojet SP5, Toxiologil Risk, grnt No Referenes Fiserov-Bergerov V, Vlh J, Singhl K. Siultion nd predition of uptke, distribution nd exhltion of orgni solvent. Br J nd Med 1974;31: Sto A, Nkji T, Fujiwr Y, Mury N. A phrokineti odel to study the exretion of trihloroethylene nd its etbolites fter n inhltion exposure. Br J nd Med 1977;34: Fernndez JG, Droz PO, Hubert BE, peros JR. Trihloroethylene exposure. Siultion of uptke, exretion, nd etbolis using thetil odel. Br J nd Med 1977;34: Droz PO, Guellein MP. Hun styrene exposure. V. Developent of odel for biologil onitoring. nt Arh Oup Environ Helth 1983;53: Fiserov-Bergerov V. Modeling ofinhltion exposure to vpors: uptke, distribution, nd eliintion. Vols -. levelnd: R Press, n, Bishoff KB, Dedrik RL, Zhrko DS, Longstreth JA. Methotrexte phrokinetis. J Phr Si 1971;6: Hielstein KJ, Lutz RJ. A review of the pplitions of physiologilly bsed phrokineti odeling. J Phrokinet Biophr 1979;7: Rsey J, Andersen ME. A physiologilly bsed desription of the inhltion phrokinetis of styrene in rts nd huns. Toxiol Appl Phrol 1984;73: Droz PO. The use of siultion odels for setting BEs for orgni solvents. Ann A onf nd Hyg 1985;12: Andersen ME. A physiologilly bsed toxiokineti desription of the etbolis of inhled gses nd vpors: nlysis t stedy stte. Toxiol Appl Phrol 1981;6: Eger El. Anestheti uptke nd tion. Bltiore: Willis nd Wilkins o, Mpleson WW. irultion-tie odels of the uptke of inhled nesthetis nd dt for quntifying the. Br J Anesth 1973;45: Perbellini L, Brugnone F, rett D, Mrnelli G. Prtition oeffiient of soe industril liphti hydrorbons (5-7) in blood nd hun tissues. Br J nd Med 1985;42: Bohlen P, Shlunegger UP, Luppi E. Uptke nd distribution of hexne in rt tissues. Toxiol Appl Phrol 1973;25: Wgner JG. Method for estiting rte onstnts for bsorption, etbolis, nd eliintion fro urinry exretion dt. J Phrol Si 1967;56: Hilderbrnd RL, Andersen ME. n vivo kineti onstnts for the etbolis of inhled hydrorbon toxints s deterined by gs uptke ethods. Toxiologist 1981;1:86-7. Br J nd Med: first published s /oe on 1 Noveber Downloded fro on 16 Deeber 218 by guest. Proteted by

9 Brugnone F, Perbellini L, Grigolini L, Apostoli A. Solvent exposure in shoe upper ftory.. n-hexne nd etone onentrtion in lveolr nd environentl ir nd in blood. nt Arh Oup Environ Helth 1978;42: Bker TS, Rikert DE. Dose-dependent uptke, distribution, nd eliintion of inhled n-hexne in the Fisher-344 rt. Toxiol Appi Phrol 1981;61: Perbellini L, Brtolui GB, Brugnone F, De Ros E, Vlentini F. 11 2,5-esndione nel ontrollo biologio dell'esposizione professionle n-esno. Med Lv 1985;76: Perbellini L, Antini M, Brugnone F, Frontli N. Urinry exretion of n-hexne etbolites. A oprtive study in rt, rbbit nd onkey. Arh Toxiol 1982;5: Perbellini L, Brugnone F, Fggionto G. Urinry exretion of the etbolites of n-hexne nd its isoers during ouptionl exposure. Br J nd Med 1981;38: Bus JS, Deyo D, ox M. Disposition of rdiotivity in rts fter ute inhltion exposure to 14-n-hexne. Toxiologist 1981;1: Veulens H, Vn Ve E, Jnsses H, Msshelein R, Leplt A. Vnouver style All nusripts subitted to the Br J nd Med should onfor to the unifor requireents for nusripts subitted to bioedil journls (known s the Vnouver style). The Br J nd Med, together with ny other interntionl bioedil journls, hs greed to ept rtiles prepred in ordne with the Vnouver style. The style (desribed in full in Br MedJ, 24 Februry 1979, p 532) is intended to stndrdise requireents for uthors. Referenes should be nubered onseutively in the order in whih they re first entioned in the text by Arbi nuerls bove the line on eh osion the referene is ited (Mnson' onfired other reports ). n future referenes to ppers subitted to the Br J nd Med should inlude: the nes of ll uthors if there Perbellini, Mozzo, Brugnone, Zedde Experientl hun exposure to n-hexne: study of the respirtory uptke nd eliintion, nd of n-hexne onentrtions in peripherl venous blood. nd Arh Oup Environ Helth 1982;49: Aerin onferene of Governentl ndustril Hygienists. Threshold liit vlues for heil substnes nd physil gents in the work environentl nd biologil exposure indies with intended hnges for ininnti: AGH, Engstron J. Styrene in subutneous dipose tissues fter experientl nd industril exposure. Snd J Work Environ Helth suppl 1978;2: Arfioli, Bvzzno P, Binlni P, et l. Utilizzzione del 2,5-esndione urinrio nel onitorggio biologio degli esposti n-esno.48 ongr Nz So tl Med Lv giene And. Pvi Sept 1985, Monduzzi (Bologn) wt M, Tkeuhi Y, Hisng N, On Y. A study on biologil onitoring of n-hexne exposure. nt Arh Oup Environ Helth 1983;51: Mutti A, Flzoi M, Luertini S, et l. n-hexne etbolis in ouptionlly exposed workers. Br J nd Med 1984;41: re six or less or, if there re ore, the first three followed by et l; the title of journl rtiles or book hpters; the titles of journls bbrevited ording to the style of ndex Medius; nd the first nd finl pge nubers of the rtile or hpter. Exples of oon fors of referenes re: 1 nterntionl Steering oittee of Medil Editors. Unifor requireents for nusripts subitted to bioedil journls. Br Med J 1979;1: 'Soter NA, Wssern S, Austen KF. old urtiri: relese into the irultion of histine nd eosinophil heotti ftor of nphylxis during old hllenge. N EnglJ Med 1976;294: Weinstein L, Swrtz MN. Pthogeni properties of invding iro-orgniss. n: Soden WA Jr, Soden WA, eds. Pthologi physiology: ehnisns ofdisese. Phildelphi: W B Sunders, 1974: Br J nd Med: first published s /oe on 1 Noveber Downloded fro on 16 Deeber 218 by guest. Proteted by