Physiologically Based PharmacokineticAnalyses of Simple MixturesKannan Krishnan,',2 Harvey J. Clewell lII,' and Melvin E. Andersen2'41Departement de Medecine du Travail et d'Hygiene du Milieu, Faculte de Medecine, Universite de Montreal,Montreal, Canada; 2Chemical Industry Institute of Toxicology, Research Triangle Park, North Carolina;3ManTech Environmental Technology Inc., Dayton, Ohio; 4Current address: Health Effects Research Laboratory,U.S. EPA, Research Triangle Park, North Carolina

Exposure to multiple chemicals may cause significant alterations of tissue dose of the toxic moiety of one or more of the individual chemicals.The change in target tissue dose of a chemical present in simple mixtures can be predicted when the determinants of disposition of each chemical,and the mechanism of toxicokinetic interaction between chemicals are understood at a quantitative level. Determinants of disposition includephysiological (e.g., breathing rates, cardiac output, tissue volumes, blood flow rates), biochemical (e.g., kinetic constants for metabolism and proteinbinding), and physicochemical factors (e.g., blood:air and tissue:blood partition coefficients). Mechanisms of toxicokinetic interactions refer to themanner in which coexposure alters these determinants of disposition as compared to exposure to the individual chemicals. Interactions betweenchemicals can be described quantitatively with physiologically based pharmacokinetic (PBPK) models, which integrate these mechanisticdeterminants and permit prediction of alterations in tissue dose for various exposure situations by computer simulation. PBPK modeling studies ofbinary chemical interactions conducted so far indicate that inhibitory rather than potentiating metabolic interactions are more likely to be observedduring multiple chemical exposures. As PBPK models of representative binary, tertiary and quaternary mixtures are developed, it will becomeincreasingly possible to draw reliable conclusions about the risk associated with human exposure to chemical mixtures. -Environ Health Perspect102(Suppl 9):151-155 (1994)

Key words: physiological pharmacokinetics, PBPK modeling, chemical mixtures, toxicokinetic interaction

IntroductionMultichemical exposure is the rule ratherthan the exception in both the general andoccupational environments. Simultaneousor sequential exposure to multiple chemi-cals may alter the toxicokinetics and/ortoxicodynamics of one or all of them. Thiscan lead to a quantitative alteration of thetoxicity predicted based on the summationof the effects of the components. Toxi-cokinetic interactions occur when the tissuedose of the active chemical per unit of ex-posure is altered by co-exposure to otherchemicals. Toxicodynamic interactionsoccur when tissue response to a unit tissuedose of the active chemical is altered by co-exposure to other chemicals. When interac-tions occur among components of achemical mixture, the mechanistic basis ofsuch interactions should be understood at aquantitative level to conduct risk assess-mnent for the chemical mixture. The uncer-tainties arising from changes in the

toxicokinetics of the components can be

This article was presented at the IV EuropeanISSX Meeting on Toxicological Evaluation of ChemcialInteractions: Relevance of Social, Environmental andOccupational Factors held 3-6 July 1992 in Bologna,Italy.

Address correspondence to Dr. Melvin E.Andersen, MD #74, HERL-US EPA, ResearchTriangle Park, NC 27711. Telephone (919) 541 0077.

addressed by developing physiologicallybased pharmacokinetic models of chemicalmixtures which can be used for dose, route,and species extrapolations of target tissueconcentrations of the toxic moieties. Thispaper presents a short overview of thebasics of physiologically based pharmacoki-netic modeling and some examples of itsuse in the mechanistic analyses of toxicoki-netic interactions occurring in chemicalmixtures.

Physiologically BasedPharmacokinetic ModelingPhysiologically based pharmacokinetic(PBPK) modeling is the process of develop-ing mathematical descriptions of theuptake and disposition of chemicals inwhich the interrelationships among thecritical biological determinants aredescribed as realistically as possible. In thePBPK modeling approach, the body isdivided into a number of tissue compart-ments (Figure 1), each of which is definedby appropriate volume, blood flow ratesand solubility characteristics. The compart-ments may represent a single tissue or agrouping of tissues that have similar bloodflow and solubility characteristics. In thePBPK models, the rate of tissue uptake of achemical is described either as a blood flowlimited uptake or limited by diffusion fromblood into the tissue (1). For blood flow

Qalv e a vCinh fe calv

QC , Qc_

Time

pharmacokinetic model for styrene. Q terms are air andblood flow rates; C terms are concentrations. Theseare indexed to individual tissue compartments: fat (f),muscle (n), richly perfused tissues (r) and liver (I).Effluent venous concentrations have a double letteredsubscript. 0aiv and Qt are alveolar ventilation and car-diac output. The subscripts inh, alv, art, and yen signifyinhaled air, exhaled air, arterial blood, and venousblood, respectively. Kinetic constants for liver metabo-lism are Vmax (maximum rate of metabolism) and Km(binding affinity of the substrate with metabolizingenzyme). From Ramsey and Anderseti (28), reproducedwith permission of Academic Press.

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KRISHNAN ETAL.

limited uptake, the rate of change in theamount of a chemical in the tissue (dAt/dt)is described with a mass balance differentialequation, which accounts for the roles oftissue blood flow rates (Q,), arteriovenousconcentration difference (C6-Ct), and tis-sue metabolismdA4t/dt = Qt (Ca7(,) - d4met/dt

[1]Metabolism in individual tissues or tis-

sue groups can be included by addingappropriate terms, to account for theamount lost by metabolism, which mightbe a first or second order process (e.g., glu-tathione conjugation), or a saturableprocess (e.g., cytochrome P450 mediatedoxidation) as followsdAmetldt = Vm. Cvt/(Km+C,+,) + KfCvtVt

[2]where

Vmax = Maximum enzymatic reaction rate(mg/hr)

Km = Michaelis constant for enzymaticreaction (mg/I)

Kf = First order rate constant (hr-1)Vt = Volume of the tissue (1)

The total amount of the chemical inthe tissue (At) then is calculated by inte-grating the mass balance differentialequation (Equation 1). The tissue concen-tration of the chemical at any time is calcu-lated by dividing the amount in the tissueby tissue volume.

Three types of parameters are requiredto develop PBPK models: physiological(e.g., alveolar ventilation rate, blood flowrate, tissue volumes, glomerular filtrationrate), biochemical (e.g., Vmax, Km) andphysicochemical (e.g., blood:air and tis-sue:blood partition coefficients). Partitioncoefficients of volatile organic chemicalscan be determined by vial equilibration(2). Physiological parameters can beobtained from biomedical literature (3).Biochemical parameters related to metabo-lism and protein binding can be deter-mined either in vitro or u,sing noninvasivein vivo exposure techniques such as gasuptake and exhaled breath techniques formetabolic parameters (4). Once formu-lated by integrating the information onanimal physiology, rate constants forkinetic processes and partition coefficients,the PBPK model can be used to simulatethe kinetic behavior of a chemical in thetest species for a variety of exposure scenar-

This type of PBPK model has beendeveloped for a number of individualchemicals (4). The principal application ofthis biologically and mechanistically basedapproach is in the prediction of target tis-

sue dose of the toxic parent chemical or itsreactive metabolite. Using the tissue doseof the toxic moiety of a chemical in riskassessment provides a better basis of relat-ing to the observed toxic effects than theexternal exposure concentration (5).Because PBPK models facilitate the predic-tion of target tissue dose in people, theycan help reduce the uncertainty associatedwith the conventional extrapolation proce-dures (6).

PBPK Modeling of SimpleMixturesWhen animals and people are exposed totwo chemicals there may or may not be aninteraction between the chemicals. Toxicinteractions result from the modulation ofthe toxicokinetics and/or toxicodynamicsof one chemical by another. Toxicokineticinteractions involve modulation of theabsorption, distribution, metabolism, andexcretion of one chemical by another viaalterations in the physicochemical, physio-logical, and biochemical parameters. PBPKmodeling studies of chemical mixtures cansignificantly improve our ability to investi-gate mechanisms of toxic interactions invivo in a quantitative manner, and can beused to conduct dose, route, and speciesextrapolations of the target tissue dose ofthe toxic moieties of the chemicals in themixture.

For PBPK modeling of binary mix-tures, the influence of one chemical on theother should be considered in terms of thealteration of critical biological determi-nants of disposition by the coexposure.Combined chemical exposures may affect(a) physicochemical parameters, (b) physi-ological parameters and (c) biochemicalparameters, which necessarily determinethe disposition ofboth chemicals, and theirtarget tissue dose.

Physicocemical ParametersDuring combined exposure scenarios, onechemical may alter the solubility character-istics of another chemical. For example,cyanide forms complexes with essentialmetals resulting in a change in their tissueconcentrations and distribution pattern(7-10) due to changes in solubility andstability (11,12). Similarly, various dithio-carbamates form lipophilic complexes withinorganic lead, enhancing lead uptakeacross the blood-brain barrier, thus causinga greater accumulation in the lipid-richbrain compartments (13). However, thetissue:air and blood:air partition coeffi-cients of certain volatile organic chemicalshave been found to remain unaltered dur-

ing combined exposures (14). Thesechemicals still interact by mechanisms thatinvolve changes in the biochemical andphysiological parameters.

Physiological ParametersPhysiological parameters include tissue vol-umes (Vt), breathing rates (Qp), cardiacoutput (Qc), blood flow rates (Qt),glomerular filtration rate (GFR), etc. If onechemical in a simple mixture alters one ofthe physiological parameters, then thatchemical can be expected to alter the dis-position and target tissue dose of othercomponents in the mixture (15). Forexample, repeated administration of phe-nobarbital causes enlargement of the liver(i.e., increases the model parameter V),and alters liver blood flow rates (in addi-tion to altering the biochemical parame-ters). Ethanol causes alterations of hepaticblood flow rates (Q I) and cadmium altersthe GFR. Hydrogen sulfide and hydrogencyanide at low exposure concentrationscause increases in Qp, thus increasing therespiratory uptake (and therefore thetoxicity) of other chemicals. For theseobservations to be incorporated into a phy-siological modeling framework to predicttheir effect on the disposition of otherchemicals, dose-response information (e.g.,Ql, Qp, 4, GFR versus exposure concen-tration) is needed. With environmentalchemicals, the most common single mech-anism of interaction investigated in suchdetail appears to be the modulation of bio-chemical parameters (15).

Biochemical ParametersBiochemical parameters include the rateconstants of metabolism, and the affinitiesand capacities of protein binding. Theeffects of combined exposure to chemicalson their metabolism might be a result oftheir competition for enzymatic bindingsites, or might be due to one chemicalinducing the enzyme system implicated inthe metabolism of the other.

Enzyme induction has been modeledby taking into account the altered Vma. orKf due to treatment with the inducer.Induction should not alter the Km if thesame isoform is induced. Andersen et al.(16) modeled the effect of prior adminis-tration of styrene (1000 ppm for 6 hr/dayfor 4 days) or phenobarbital (80 mg/kg/dayfor 4 days prior to styrene exposure) on themetabolism of styrene. Pretreatment withphenobarbital increased the Vm. by a fac-tor of six; styrene pre-exposures increasedVma, by a factor of 2. These observationswere consistent with a role for a high affin-

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PBPKANALYSES OFSIMPLE MIXTURES

nij Pretreated

.~80

x 60 StyrenePretreated

Eu 20 -/ Pretreated

0 10 20 30 40

BLOOD STYRENE CONCENTRATION(mg/L)

Figure 2. Relationship between the rate of uptake ofstyrene from inhaled air and the arterial blood concen-tration of styrene at the end of a 6-hr exposure.Pretreatments used were pyrazole, 320 mg/kg, 30 minbefore initiating exposure, and phenobarbital, 80mg/kg/day on each of 4 days preceding styrene expo-sure. The styrene pretreatment was daily exposure to1000 ppm for 6 hr on each of the 4 days before testexposure to the various concentrations. From Andersenet al. (16) with permission of the Academic Press.

ity enzyme in the metabolism of styrene,and indicated that the inducer pretreat-ments did not enhance styrene metabolismat low exposure concentrations (

KRISHNAN ETAL.

101

lx ~~~~00000O 10

00 12 2A 36 48 6.0

TIME (hr)

Figure 5. trans-1,2-Dichloroethylene uptake by groupsof three F-344 rats placed in a closed, recirculatedchamber with starting concentrations of 12, 8, or 5ppm. Experimental data are shown as symbols andmodel simulations are presented as solid lines. Thesystematic discrepancy between the model and thedata provided an indication that the simple descriptionof metabolism in the model was inadequate for thischemical. From Clewell and Andersen (25); with per-mission of the National Academy of Sciences.

101

.0tA 100

V0 10- . 1,0.0 1.5 3.0 4.5 6.(

TIME (hr)

Figure 6. 1,2-Dichloroethylene uptake by groups ofthree F-344 rats placed in a closed, recirculated cham-ber with starting concentrations of 12, 8, or 5 ppm.Experimental data are shown as symbols and modelsimulation is presented as solid lines. In this case, themodel description accounted for enzyme inactivation byreactive metabolites assumed to be produced duringthe metabolism of trans-dichloroethylene. From Clewelland Andersen (25) with permission of the NationalAcademy of Sciences.

inhibitory chemical (equivalent to hexane)needs to have a low partition coefficientand be rapidly eliminated by exhalation atcessation of the co-exposure period. Themetabolized component (equivalent toMnBK) should have a greater solubilityand persist in the body after the exposure ishalted. To facilitate the study, metabolite(equivalent to HD) should readily be mea-surable. Clewell and Andersen (6) devised

a mixture of isoflurane (ISO) and dibro-momethane (DBM). DBM, a tissue-solu-ble vapor, is metabolized to carbonmonoxide. During exposure ISO inhibitsDBM conversion to CO. After exposureISO is eliminated more rapidly than DBMand CO production is enhanced. The com-plex behavior of carboxyhemoglobin, likethat of HD, occurs due to differentialblood:air partition coefficients of the com-peting substrates (Figure 4).

Inhibitory metabolic interactionsbetween trichloroethylene and dichloroeth-ylene, benzene and toluene, and m-xyleneand toluene have also been described witha physiological modeling approach(21-23). In these studies, the metabolicrate constants for each chemical were firstdetermined by conducting gas uptake stud-ies with individual chemicals, and then themetabolic inhibition constants were deter-mined by conducting another series of gasuptake studies with both chemicals. Thebinary chemical gas uptake data indicatingaltered uptake of both chemicals duringcoexposures were analyzed with a PBPKmodel to test various hypotheses of inhibi-tory interaction (e.g., competitive, non-competitive, uncompetitive). These studiesconsidered the metabolic rate constants tobe time-invariant. There are instanceswhere such a description may not be suffi-cient, especially where inactivation ofmetabolizing enzymes occurs during theexposure.

Andersen et al. (24) found that thedecline in the gas uptake chamber concen-tration of both cis- and trans- 1,2-dichloro-ethylene could not be described with time-invariant metabolic constants (Figure 5).This indicated that the maximum rate ofmetabolism was decreasing during exposureto these compounds. The gas uptake datawas successfully described by a PBPKmodel in which the rate of enzyme inacti-vation was proportional to a second orderrate constant (Kd) times the square of theinstantaneous rate of metabolism (Figure6). The square dependence on instanta-neous metabolic rate indicated an interac-tion between a reactive metabolite and theenzyme-substrate complex in the rate limit-ing step for enzyme inactivation (25,26).Of the two chloroethylenes, the trans iso-mer is a much better suicide inhibitor thanthe cis isomer (Kd: 400 vs 1.2). Inhibition

by trans-1,2-dichloroethylene occurs at lowexposure levels (5 ppm), and may be signif-icant in various exposure situations.

Future DirectionsBinary chemical mixtures are a great sim-plification of the real world situations. Thetoxicokinetics and toxicodynamics of twointeracting chemicals might further bealtered by other components in morecomplex mixtures. With multichemicalmixtures, some components may act inde-pendently, neither interfering with norbeing modified by other chemicals, whereasothers might interfere with and modify thetoxicity of other chemicals. With environ-mental chemicals, toxic interactions mainlyappear to involve alteration of biochemicalparameters (15). If metabolic inhibitoryinteraction occurs among the componentsof a multichemical mixture, the modelingof such a phenomenon can be accom-plished by approaches similar to those uti-lized for binary chemical mixtures (27).

Another area that deserves more consid-eration is the role of multiple forms ofcytochrome P450 each of which maymetabolize a given chemical with distinctaffinity and capacity. PBPK modeling ofmultiple chemicals metabolized to varyingextents by several isoenzymes will be morecomplicated with various mixed type inhi-bitions, rendering the discriminationbetween mechanistic descriptions difficult.

In summary, physiologically basedmodeling approaches facilitate predictionsof change in the target tissue concentra-tions of toxic moiety of chemicals presentin simple mixtures, when the mechanismsof disposition and interaction are under-stood at a quantitative level. The PBPKanalyses of simple mixtures conducted todate indicate that the effects of enzymeinactivators, such as trans-1,2-dichlo-roethylene, are likely to be observedin occupational and perhaps in certainenvironmental exposure situations. On thecontrary, the interactive effects of enzymeinducers such as ethanol and styrene will beimportant only at much higher exposureconcentrations. As PBPK models of repre-sentative binary, tertiary and quaternarymixtures are developed, it will becomeincreasingly possible to draw reliable con-clusions about the risk associated withhuman exposures to chemical mixtures.

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