Drinking Water and Health, Volume 8: Pharmacokinetics in Risk Assessment (1987)

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PART V11 Summary: Prospectives and Future Directions

Prospective Predictions and Validations in Anticancer Therapy Jerry M. Collins I NTRODUCTION At first glance, the processes of anticancer drug development and en- vironmental risk assessment may not seem to have much conceptual over- lap. However, there is a strong common thread based upon the need to make decisions regarding allowable human exposure limits. In both cases, heavy reliance is placed upon interspecies toxicological comparisons. Risk assessment is based upon both mathematical models and experi- mental data. For example, the data might be the incidence of tumor formation in rodents following controlled laboratory exposures to a toxin. The role of the model is to predict the incidence of carcinogenesis in humans under a variety of occupational and/or environmental exposure conditions. The weakest link in this process is model validation. Due to ethical considerations, it is not usually possible to administer precise amounts of toxic chemicals to humans. If a human population develops an unusual form of cancer, epidemiologic detectives might be able to trace the source to a particular chemical. The human exposure data are estimated retrospectively in whatever fashion possible, but the uncertainty in these calculations is a major hurdle in quantitative analyses. Once a specific chemical becomes suspect, it would be possible to do a set of quantitative experiments in animals. Even if we accept these examples with their imprecise estimates of human exposure, the total data base for model validation is very small. Yet a variety of needs forces us to accept these models as the basis for 431

432 JERRY M. COLLINS major prospective decisions that have an impact upon the health of citizens and the economic well-being of corporations and communities. The preclinical toxicology phase of drug development shares some of the same facets as the safety testing of industrial pollutants or other po- tential environmental contaminants. For example, animals are used to determine a lethal dose, such as the lethal dose for 10% of the animals tested (LD~o). That estimate is then used to determine safety in humans. Perhaps the single largest difference between the development of anti- cancer drugs and the assessment of risks from environmental contaminants is that direct experimental evidence is obtained in humans that can be (rapidly) compared with data from animals. The treatment of a life-threatening disease requires a rather different set of risk-to-benefit decisions than considerations of maximally allowed pollutants. The drugs used for the treatment of cancer have narrower safety margins than those used for most other diseases. In general, the ratio of a therapeutic dose to a toxic dose approaches unity. DRUG DEVELOPMENT Drug development consists of a progression of steps (Table 1) that starts with the discovery of a new compound and ends with a clinical deter- mination of therapeutic utility. To begin human testing, a safe starting dose is needed. Establishment of a safe starting dose is one of the chief functions of preclinical toxicology studies. As reviewed by Grieshaber and Marsoni (1986), the current preclinical toxicology protocol for anti- cancer drugs provides the basis for a safe starting dose, tailored to potency in rodents. The human starting dose is 1/10 of the mouse ODD, expressed on a milligrams/square meter basis. Prior to human testing, this dose is confirmed in a second species. After the starting dose has been evaluated in patients, subsequent doses are escalated. Although there is always therapeutic intent when an anti- cancer drug is given to patients, the major scientific goal of initial clinical trials is to determine the acute, reversible toxicity. The endpoint of these phase I trials is called the maximum tolerated dose, or MTD. The MTD TABLE 1 Stages of Drug Development Name Function Preclinical Discovery Random or planned Screening Bioactivity Toxicology LD,o; organ sites Clinical Phase I Safety Phase II Activity Phase III Efficacy

Predictions and Validations in Anticancer Therapy 433 is used to establish the dose for more detailed efficacy studies in phase II testing. The procedure used for dose escalation must achieve a balance between the desire to escalate slowly enough to be safe and the desire to escalate fast enough to be efficient. The most commonly used procedure is known as the modified Fibonacci scheme (Goldsmith et al., 19751. The initial escalation is rapid (100%, or doubling of the dose); subsequent escalations narrow down until the 30-35% range is reached (Figure 11. In summary, there are two areas of risk assessment that are encountered in these early clinical trials: (1) selection of a safe starting dose, and (2) choosing the rate of dose escalation. A_ In O £ 3 _.' ~ O _ ~ _ ~ ~ a) Q ~ _' 2 - 0.7 - 0.5 - 0 0.1 O O 0 07 0.05 _ 0.03 10 - Doxorubicin 5 - 6-MP Daunomyctn Thalicarpine Acitnomycin D Vincristine AZQ - AMSA Teroxlrone x5 ~ Teroxirone Dlhydro-AC Carbo-Plat N—Methyl—For Hon~oHar ThioTEPA Triciribine - AnguidTne Triciribine x5 (I ~ — F-Ara-AMP— — Entry - F-Ara—AMP x5 30-352; 30-35% 30 - 35~; 30 - 357 30-352; 30-35% 30 - 35% 30 - 357 30-35% 40% 50% 67~; 1 00% FIGURE 1 Interspecies toxicity comparison. For these 17 anticancer drugs, the median MTD in humans was equal to the mouse LD~o, when both doses were expressed on a milligram/square meter basis. To compare toxicity on a milligram/kilogram basis, the ordinate was multiplied by 0.083. All drugs were given as single doses ( x 1) or as five daily doses ( x 5). Data in the second column are from Grieshaber and Marsoni (1986). Data in the first column were collected from information in the literature or on file in the Toxicology and Investigational Drug Branches, Division of Cancer Treatment, National Cancer Institute. As a reference, the modified Fibonacci escalation steps are shown in the third column. Adapted from Collins et al. (1986).

434 ~ ERRY M. COLLl NS COMPARISON OF HUMAN AND MURINE TOXICITY How well does this strategy work? In Figure 1, the ratio of (human MTD)/(mouse Log) is presented for a series of anticancer drugs (Collins et al., 19861. First, it is worth noting that this particular collection of interspecies toxicology data, although not exhaustive, probably exceeds any comparable compilation for environmental contaminants or other hu- man toxins. Rather than focusing on specific drugs at this stage, it is helpful to get some appreciation of the range of variation. It could be argued that there is considerable variation, even though the average is quite reasonable. It might also be reasonably argued, however, that this level of agreement is adequate for comparative purposes. A number of factors provide motivation to probe further. For example, patient safety might be improved by a better understanding of the sources of this vari- ation. Also, the efficiency of early clinical testing might be raised if the toxicologic variation could be related to measurable determinants, such as plasma levels. What are possible explanations for this variation in toxicity between mouse and man? Table 2 lists three possibilities: (1) differences in drug metabolism, elimination, and binding; (2) exposure time differences; and (3) target cell sensitivity differences. Elimination rates determine the drug exposure, or C x T. the area under the concentration versus time curve. The concept of C x T with regard to drug toxicity originated during World War I (Prentiss, 19371. German pharmacologists observed that mustard agents are equally toxic whether a high concentration is inhaled for a short time or a low concentration is inhaled for a long time. The essential feature is that the CxT is the determinant of effect rather than the absolute concentration itself. Most toxicologists have presented their dosing information in terms of milligrams/kilogram. Based upon the relationships between body surface area and body weight (Freireich et al., 1966), it is possible to interconvert dosing data between milligrams/square meter and milligrams/kilogram. For mice, the relationship is 1 m2 = 3 kg. For humans, it is 1 m2 = 37 kg. Empirically, either set of units can be used to present raw data. The use of body surface area has a distinct advantage, however, when toxicity TABLE 2 Potential Explanations for Variation in Toxicity Between Mouse and Man 1. Species differences in drug metabolism, elimination, and binding 2. Schedule dependency due to exposure time differences 3. Species differences in target cell sensitivity

Predictions and Validations in Anticancer Therapy 435 comparisons are made across species. The physiological determinants of elimination rates (such as glomerular filtration rate or organ blood flow) tend to be highly correlated with body surface area. Thus, if the dose is expressed in milligrams/square meter and elimination rates (milliliter/min- ute/square meter) are identical in mice and men, then the drug exposure (C x T) will be the same in both species at the same dose. On the other hand, if the dose is expressed in milligrams/kilogram, the dose in humans that produces equal C x T will be 1/12th the mouse dose, because a correction must be made for body surface area differences. The factor of 12 is simply the ratio of body surface area constants, 37/3. Freireich et al. (1966), Skipper et al. (1971), and Schabel et al. (1983) have reported that with many anticancer drugs, toxicity observations carry across species on a milligram/square meter basis, as long as schedules are similar. They also were aware, however, that there are exceptions and that more complete exposure parameters such as C x T or plasma phar- macokinetics allow more useful comparisons of toxic or therapeutic re- sponses from experimental and clinical studies. Doxorubicin appears to be an example of metabolism/elimination dif- ferences. The MTD in man is fivefold greater than the LD~o in mice, on a milligram/square meter basis. Yet, as shown in Figure 2, there is con- siderable agreement between blood levels measured at equitoxic doses. It appears that humans are more tolerant than mice due to a higher clearance (milliliters/minute/square meter) for doxorubicin. FACTORS OTHER THAN C x T The second factor of possible importance is a difference in exposure times. For some drugs, there are threshold concentrations or time depen- dencies that are related to toxicity and/or mechanisms of action. For drugs with equal clearance values in mice and humans (milliliters/minute/square meter), Skipper and colleagues (1971) have made the point that a bolus dose of equal milligrams/square meter generally produces rather different time courses in mice and man (Figure 3~. If there is a threshold for action and a critical exposure time, where the threshold lies can give major differences in species response. For example, if the threshold in Figure 3 is set at 10-6 M, there is no effect in man. If the threshold is set at 10-7 M, however, the duration of effect is much longer in man than in mice. Note that the time course for doxorubicin (Figure 2) is an exception to the generalized pattern. In a classic study by Quinn et al. (1958) 29 years ago, the threshold effect was first demonstrated for the barbiturate hexobarbital. After a standard dose of 50 to 100 mg/kg was given to mice, rats, and rabbits,

436 JERRY M. COLLINS 10-5 o _' o ·_ 10-6 mu o c 10-7 r ~ At 10-8 - 7 - t O Mouse LD1 0 (1 8 mg/sq.m) t · Human MID (90 mg/sq.m) . _ _ ·. . .. . . l l 24 6 12 TIME (hours) FIGURE 2 Doxorubicin plasma concentrations in mice and humans at equitoxic doses. Human data were scaled from a 75-mg/m2 intravenous (i.v.) dose. Mouse data were scaled from a 75- mg/m2 dose given i.v. to CDFl mice. Reprinted with permission from Collins et al. (1986). there was substantial variation in the drug effectiveness. The times to awakening were 12, 90, and 49 min in mice, rats, and rabbits, respectively. When the plasma pharmacokinetics of hexobarbital were investigated, it was found that the three species exhibited rather different elimination rates, or plasma half-times. At the time of awakening, however, the plasma drug concentration was similar in all three species. Thus, this is an example of a species difference in drug effect that is determined by pharmacokinetic changes in exposure patterns. Studies in dogs did not give as clear a pattern as for the other three species. The first two reasons for the species variation in toxicology have been oriented toward plasma pha~acokinetics. The third factor essentially covers all explanations that are not related to the delivery of the drug to the site of action. There can be differences at the cellular level that de- termine species sensitivity. For example, if the drug needs to be activated

Predictions and Validations in Anticancer Therapy 437 inside the cell, there may be a species difference in activation capabilities. Fludarabine phosphate (F-Ara-AMP) has been found to have the largest difference in dose (10- to 30-fold) between the mouse LD~o and the human MID. This discrepancy is apparently an example of species differences in target cell sensitivity. The phosphate group on F-Ara-AMP makes the drug readily soluble, but it is rapidly cleaved to F-Ara-A in viva. Within 5 min following administration, only the F-Ara-A form can be detected in plasma. As shown in the plasma profiles following single doses of F-Ara-AMP (Figure 4), there is no obvious plasma pharmacokinetic ex- planation for the species difference in toxicity. In contrast to the situation for doxorubicin (in which equitoxic doses produced similar plasma drug concentrations), it can be seen from these data that the plasma concen- trations of the circulating species F-Ara-A are considerably different. Studies with bone marrow cultures in vitro indicate that human bone 10 ~5 ~ ~ Mouse-Man sample plot Skipper Concept 10 -6 S: o ·_ O 10-7 o \ \ \ \ \ Mouse \\ ~~i-------- Human ·.. \ \ \ . . 10-8 0 3 6 12 .. - , ·. . 24 TIME (hours) FIGURE 3 Idealized plasma concentrations in mice and humans following equal bolus doses (milligrams/square meter). Assume that volume of distribution (liters/kilogram) and clearance (milliliters/minute/square meter) are similar in both species. Adapted from Skipper et al. (1971).

438 ~ ERRY M. COLLI NS 1000 ~ lo: 100 o ._ Cat o ~ 10 of: 1 1 Ah\ - 452\ \ - titmouse LD10, 2600 mg/sq.m ~ ~` ` `^ - ~_¢, Human MTD, 260 mg/sq.m 1 ~ , . 0 240 480 720 TIME (minutes) FIGURE 4 F-Ara-A plasma concentrations in mice and humans at equitoxic doses. Mouse data are from Noker et al. (1983). Human data are from Malspeis (Minutes of the Phase I Working Group, Bethesda, Md., June 13-14, 1983). Reprinted with permission from Collins et al. (1986). marrow cells are intrinsically more sensitive to this particular compound than are mouse marrow cells (C. Poston et al., unpublished data). Because bone marrow suppression is the principal acute toxicity in viva, it appears that the species differences are due to target cell differences for this drug. SUMMARY OF DATA C x T information is listed for 12 anticancer drugs in Table 3. For the first nine of these drugs, the C x T ratio is a useful predictor of the relative toxicity in mice and humans. For S-azacytidine, doxorubicin (as already discussed), and teroxirone, the C x T ratio is far better than the dose ratio. For the next five drugs on this list, the C x T ratio was also a reasonable predictor, although it was about the same as the dose ratio. For thio- TEPA, the C x T ratio was also an improvement over the dose ratio.

Predictions and Validations in Anticancer Therapy 439 TABLE 3 The Mouse as a Quantitative Predictor of Human Toxicity: Comparison of Dose Ratio (milligram/square meter basis) and C x T Ratio for Human MID to Mouse LD1o Dose C x T Drug ratio ratio 1. 5-Azacytidine 6.5 (1.1) 2. Doxorubicin 5.0 0.8 3. Teroxirone 4.3 0.8 4. Diaziquone (AZQ) l.O (0-7) 5. Indicine-N-oxide 0.9 0.6 6. Amsacrine (AMSA) 0.8 1.3 7. Deoxycoformycin 0.7 1.1 8. Tiazofurin 0.7 0.9 9. Thio-TEPA 0.4 1.0 10. PALA 2.8 3.3 11. F-Ara-AMP 0.1 0.1 12. Dihydroazacytidine 1.2 0.3 There are also some drugs for which the C x T ratio was not an effective predictor of toxicity. For PALA, both the dose ratio and the C x T ratio were overly conservative; i.e., humans were threefold more tolerant than mice. A more serious case arises when man is less tolerant than mice. Two such cases were found in our survey. F-Ara-AMP was discussed above. Dihydroazacytidine was also a case in which man was less tolerant than mice, due to severe chest pain. As pointed out by Grieshaber and Marsoni (1986), it is not easy to pick up some toxicities in a mouse toxicology study. Thus, the use of C x T seems to be a useful starting point for under- standing differences in toxicity between mouse and man, but it is not completely accurate. Further work is ongoing at the National Cancer Institute that is exploring the use of C x T data to adjust escalation rates in phase I trials (Collins et al., 19861. CONCLUSIONS The development of new anticancer drugs generates a unique quanti- tative data base that can be used for interspecies comparisons of toxicity. In addition to serving as a collection of empirical toxicity data, the data base can be used for the testing of hypotheses regarding the fundamental determinants of toxicity. For example, the role of pharmacokinetics can be probed. Finally, the insights gained from analyses of past experience can be put to practical use in the form of improvements to the drug development process.

440 JERRY M. COLLINS ACKNOWLEDGM ENTS Substantial contributions have been made to the concepts and data presented in this paper by Dr. Robert Dedrick of the Division of Research Services, National Institutes of Health, and by the staff and contractors of the Division of Cancer Treatment, National Cancer Institute. Portions of this manuscript have been excerpted from Collins et al. (19861. REFERENCES Collins, J. M., D. S. Zaharko, R. L. Dedrick, and B. A. Chabner. 1986. Potential roles for preclinical pharmacology in phase I clinical trials. Cancer Treatment Rep. 70:73- 80. Freireich, E. J., E. A. Gehan, D. P. Rall, L. H. Schmidt, and H. E. Skipper. 1966. Quantitative comparison of toxicity of anticancer agents in mouse, rat, hamster, dog, monkey, and man. Cancer Chemother. Rep. 50:219-244. Goldsmith, M. A., M. Slavik, and S. K. Carter. 1975. Quantitative prediction of drug toxicity in humans from toxicology in small and large animals. Cancer Res. 35:1354- 1364. Grieshaber, C. K., and S. Marsoni. 1986. The relation of preclinical toxicology to findings in early clinical trials. Cancer Treatment Rep. 70:65-72. Noker, P. E., G. F. Duncan, S. M. L. El Dareer, and D. L. Hill. 1983. Disposition of 9-,B-D-arabinofuranosyl-2-fluoroadenine 5'-phosphate in mice and dogs. Cancer Treat- ment Rep. 67:445-456. Quinn, G. P., J. Axelrod, and B. B. Brodie. 1958. Species, strain, and sex differences in metabolism of hexobarbitone, amidopyrine, antipyrine and aniline. Biochem. Pharmacol. 1:152-159. Prentiss, A. M. 1937. Chemicals in War: A Treatise on Chemical Warfare. New York: McGraw-Hill. Schabel, F. M., Jr., D. P. Griswold, T. H. Corbett, and W. R. Laster, Jr. 1983. Increasing therapeutic response rates to anticancer drugs by applying the basic principles of phar- macology. Pharmacol. Ther. 20:283-305. Skipper, H. E., F. M. Schabel, Jr., L. B. Mellet, J. A. Montgomery, L. J. Wilkoff, H. H. Lloyd, and R. W. Brockman. 1971. Implications of biochemical, cytokinetic, phar- macologic and toxicologic relationships in the design of optimal therapeutic schedules. Cancer Chemother. Rep. 54:431-450.

The Application of Pharmacokinetic Data in Carcinogenic Risk Assessment Daniel Krewski, Duncan ]. Murdoch, and Jim R. Withey I NTRODUCTION The area of carcinogenic risk assessment has received considerable attention in recent years (Krewski and Brown, 1981), and continues to be a subject of much current debate (OSTP, 19851. Information on carcin- ogenic risks can be obtained by using epidemiological studies of human populations (Day, 1985) and toxicological experiments conducted in the laboratory (Bickis and Krewski, 19851. While epidemiological investi- gations can provide information on adverse health effects directly in man, experimental studies with animal models have the advantage of being able to predict potential health hazards in advance of actual human exposure, and thus continue to be widely used for identifying substances with car- cinogenic potential. The main disadvantage of toxicological testing is the ultimate need to translate test results obtained in animals to the human situation. Because laboratory tests are conducted at relatively high-dose levels to induce measurable rates of response in a small sample of experimental animals, it is often necessary to extrapolate these results to lower doses corre- sponding more closely to anticipated human exposure levels. Because the test species do not resemble the target species in all respects, it is also necessary to take into account interspecies differences when extrapolating between the animal model used and man. It may also be necessary to infer what would occur if the test compound were administered by a different route of exposure than that actually employed. Traditional approaches to interspecies extrapolation require the selection 441

442 DAN ~ EL KREWSK! ET AL. Of an appropriate scale for dose for which potency remains the same in animals and humans. For example, it may be assumed that potency is invariant across species when dose is expressed in amount per body weight per day or in amount per unit surface area. Empirical evidence to support the use of any particular scale, however, is limited (Mantel and Schnei- derman, 19751. Pharmacokinetic models can be used to describe the fate of chemical substances after they enter the body (Gehring, 1978; Withey, 1984), thereby providing useful information on the formation of the reactive metabolites responsible for the induction of toxic effects in individual tissues. These models can be used to describe the relationship between the dose admin- istered in toxicological tests and the dose delivered to the target tissue (Gehring and Blau, 19771. One of the first applications of pharmacokinetics to the problem of carcinogenic risk assessment was given by Cornfield (1977), who proposed a simple pharmacokinetic model with an irreversible detoxification step that predicts a threshold in the dose-response curve at steady state. Brown et al. (1978) subsequently noted that the threshold effect apparently as- sociated with this construct may not occur in practice because of the formation of some reactive metabolite during the approach to steady state and the possibility that detoxification may be reversible. Subsequent ap- plications of pharmacokinetics in risk assessment have been reviewed by Hoel (19851. The pharmacokinetic models employed in these applications generally envisage biological systems that consist of a small number of compart- ments, with interactions among these compartments described by a cor- responding set of differential equations. In contrast to such mathematical pharmacokinetic models, physiological pharmacokinetic models in which the body is considered to consist of a larger number of relevant physio- logical compartments have also been employed in recent years. Although they require detailed information on physiological and biochemical para- meters, such physiologically based pharmacokinetic models have also been used to predict the risk associated with exposure to specific substances such as styrene and methylene chloride (Ramsey and Andersen, 1984; Andersen et al., 1987) In this paper, we discuss the use of pharmacokinetic data in extrapolating the results of laboratory tests on carcinogenicity between doses, species, and routes of exposure. We begin with a brief review of the current status of carcinogenic risk assessment, and continue with an overview of both mathematical and physiologically based pharmacokinetic models. The use of mathematical pharmacokinetic models to describe the con- version of the administered dose of a xenobiotic to the dose delivered to the target tissue is then considered, and the implications of saturation

PK Data in Carcinogenic Risk Assessment 443 effects in the metabolic activation process for extrapolation to low doses are explored. It is noted that the concentration of the active form of the xenobiotic at the target tissue may vary over time, depending on the rates of absorption, distribution, and elimination, as well as the manner in which the exogenous level of exposure may change with time. The implications of these effects on estimates of carcinogenic risks are also considered. We conclude with a series of examples for which both bioassay and pharmacokinetic data are available that illustrate the concepts discussed in this paper. In particular, data on formaldehyde, vinyl chloride, and methylene chloride are used to compare risk estimates derived on the basis of administered and delivered doses. The use of physiologically based pharmacokinetic models to extrapolate between species and routes is also illustrated by using data on methylene chloride and perchloroethylene. Our conclusions concerning the potential application of pharmacokinetic data in carcinogenic risk assessment are then summarized. CARCINOGENIC RISK ASSESSMENT Models of Carcinogenesis Quantitative estimates of risk are generally derived by using a biolog- ically based mathematical model of the process of carcinogenesis. The Armitage-Doll multistage model is based on the assumption that a tumor will be induced following completion of a k-stage process, in which each stage corresponds to the occurrence of some fundamental biological event such as a mutation at a specific gene locus (Armitage, 19851. This model provides an adequate description of the age-specific tumor incidence rates for a variety of lesions that occur in the human population, with values of k generally in the range of 2 to 7. Other mathematical models can also be derived under different biolog- ical assumptions. Moolgavkar and Venzon (1979) and Moolgavkar and Knudson (1981), for example, postulated that two mutations each occur- ring at the time of cell division are necessary for a normal cell to become malignant. Unlike the multistage model, this model provides for effects on cell proliferation, which can increase the pool of initiated cells available for malignant transformation, as well as for normal tissue growth. Incor- poration of these additional factors yields a two-stage model that is suf- ficiently flexible to describe the age-specific tumor incidence rates for many forms of cancer. Because information on cell kinetics and tissue growth is not inherent in bioassay results, however, this must be obtained from separate studies.

444 DAN ~ EL KREWSK! ET AL. Risks at Low Doses To estimate the level of risk associated with exposure to low doses of carcinogenic substances, it is necessary to extrapolate downward from the high doses used in laboratory studies by using an assumed functional relationship between dose and response. Such extrapolations can depend strongly on the mathematical model of carcinogenesis that is employed (Krewski and Van Ryzin, 1981) because of differences in the shape of the dose-response curve implied at low doses. If attention is restricted to models for which the dose-response curve is linear at low doses, however, such differences become slight (Krewski et al., 19841. A number of arguments can be advanced in support of the hypothesis of low-dose linearity (Krewski et al., 1986; Murdoch et al., in press). For example, both the Armitage-Doll multistage model and the two-stage birth- death-mutation model of Moolgavkar and Knudson (1981) and Moolgav- kar and Venzon (1979) lead to low-dose linearity when the transition intensity functions between stages are linear functions of dose. In the absence of specific model assumptions, Crump et al. (1976) demonstrated low-dose linearity in a general class of additive background models in which the test agent is considered to combine in an additive fashion with an effective background dose of that same substance. Low-dose linearity also occurs with pharmacokinetic models in those cases in which all kinetic processes are linear at low doses, provided that the probability of tumor occurrence is proportional to the dose delivered to the target tissue in the low-dose region. The assumption of low-dose linearity in carcinogenic risk assessment is supported by the U. S. Office of Science and Technology Policy, which stated that "when data and information are limited, models or procedures which incorporate low dose linearity are preferred" (OSTP, 1985, p. 10378). Given the assumption of low-dose linearity, the estimation of carcin- ogenic risks at low levels of exposure essentially involves estimating the slope of the dose-response curve at the origin. This may be done by fitting the multistage model to the available data and computing upper confidence limits on risk in the low-dose region (Crump and Howe, 19841. Because these confidence limits are linear in the low-dose region, this is referred to as the linearized multistage model. This model is currently used by the Carcinogen Assessment Group of the Environmental Protection Agency for purposes of low-dose extrapolation (Anderson and the Carcinogen Assessment Group of the U.S. Environmental Protection Agency, 19831. Krewski et al. (1986) have proposed a different approach to linear extrapolation that avoids the need for the specific parametric assumptions underlying the multistage model. This procedure involves linear inter- polation between a lower confidence limit on the response rate in the

PK Data in Carci inogenic Risk Assessment 445 control group and an upper confidence limit on the response rate in any of the exposed groups in which the observed response rate is not signif- icantly different from that in the control group. The minimum (positive) slope then provides an upper confidence limit on the slope at the origin. In most cases, this model-free approach to linear extrapolation provides results similar to those based on the linearized multistage model. This method of robust linear extrapolation can be advantageous, however, in cases in which the multistage model provides a poor fit to the experimental data, as can occur when the dose-response curve tends to rise sharply at low doses and then plateau at higher doses. PHARMACOKINETIC MODELS Mathematical Pharmacokinetic Models The description of complex phenomena that occur in viva following exposure to a toxicant is accomplished with maximum simplification by means of mathematical equations derived from the conception of biological systems that consist of a small number of compartments. In this frame- work, the temporal relationship of the concentration of the xenobiotic in blood, plasma, urine, or expired air is usually modeled with multiexpo- nential equations consisting of two or three terms (Gibaldi and Perrier, 19751. This provides for the subsequent evaluation of the kinetic coeffi- cients associated with the pharrnacokinetic compartmental model. One of the first studies in which multiexponential equations were used to describe the temporal relationship of blood levels following a single dose involved acetone administered intravenously, per os, per rectum, or following intraperitoneal or subcutaneous injection (Widmark, 19191. Sub- sequently, mathematical equations were derived to describe the kinetics of accumulation after repeated dosing (Widmark and Tandberg, 1924~. Later developments in mathematical modeling addressed important is- sues involved in the assessment of pharmacological or toxic response, such as a quantitative evaluation of the nature of the dose-response re- lationship, the effects of different routes of administration, factors af- fecting uptake and elimination, and the role of metabolism with respect to the elicited response (Wagner, 1971~. Information on the kinetics of the processes of absorption, distribution, metabolism, and excretion of a xenobiotic has also permitted the calculation of such parameters as the interval required between doses to achieve rapid steady-state blood levels or to predict whether a particular exposure regimen results in an accu- mulation of the test substance in blood or body tissues (Dittert, 19771. The value of mathematical modeling has also been demonstrated in the interpretation of toxicity tests (Gehring, 1978; Hammer and Bozler,

446 DAN ~ EL KREWSK' ET AL. 1977) and in the interspecies extrapolation of data (Gillette, 1976; Reitz et al., 1978~. The interpretation and quantitation of precise mechanisms that actually occur within physiological compartments in the body, how- ever, are generally not possible by using mathematical pharmacokinetic models. Physiologically Based Pharmacokinetic Models One of the methods of examining the kinetics of absorption, distribution, metabolism, and excretion of a xenobiotic involves a description of the body as a series of relevant physiological compartments arranged as a system of parallel shunts between the venous and arterial blood supplies (Fiserova-Bergerova, 1983; Himmelstein and Lutz, 19791. Such models use basic physiological and biochemical information to determine the temporal relationships of disposition and distribution of an administered dose. Physiological information such as blood flow rates to each com- partment, the partition coefficients between the blood and organ tissues, and the volume of the compartment allows differential mass-balance equa- tions to be derived for each compartment. These equations describe the influx, outflow, accumulation, and disappearance of the test substance within the body. Physiologically based pharmacokinetic (PB-PK) models require infor- mation based on the anatomy and physiology of the test animal, the solubility of the test chemical in various organs, and biochemical constants for tissue binding and metabolism in specific organs (Ramsey and An- dersen, 19841. Three types of information are essential. First, partition coefficients are required to express the relative solubility of the compound in blood and various tissues in the model. Second, physiological constants are needed for tissue and organ volumes and for blood flow through these. Third, biochemical constants are used to define the rate coefficients for important biotransformation pathways. Partition coefficients can be obtained by direct measurement in the laboratory (Sato and Nakajima, 1979) or estimated from the partition coefficient between octanol and water. Tissue volumes and blood flows to various tissues or tissue groups can often be found in the existing literature (Sato and Nakajima, 19791. Allometric relationships have also been useful in this application (Adolph, 19491. Biotransformation data are usually obtained from in vivo and in vitro kinetic studies after the principal metabolic pathways have been identified qualitatively. Two limiting cases can be invoked to accommodate the pharmacokinetic behavior of most compounds. In the flow-limited model, the cell mem- brane transport rates are so rapid that the rate of blood flow is the limiting rate that determines the rate of uptake. In the membrane-limited model, on the other hand, cell membrane permeability is low compared with the

PK Data in Carcinogenic Risk Assessment 447 on the other hand, cell membrane permeability is low compared with the blood perfusion rate. Thus, the rate of uptake to a specific tissue is limited by the rate at which it crosses cellular membranes within that tissue. The pharmacokinetics of volatile hydrocarbons and halogenated hydro- carbons such as styrene, methylene chloride, bromochloromethane, and dibromomethane are best described by a flow-limited model (Andersen et al., 1984; McDougal et al., 1986; Ramsey and Andersen, 19841. The drugs thiopental, cytarabine, mercaptopurine, sulfobromophthalein, sali- cylate, lidocaine, adriamycin, digoxin, and methotrexate all show phar- macokinetic behavior that is best described by a membrane-limited model (tIimmelstein and Lutz, 19791. Both flow-limited and membrane-limited compartments can exist in the same model. The grouping of individual organs with similar blood flow, diffusion, and permeability properties into single compartments is flexible. For ex- ample, the adrenals, kidney, thyroid, brain, heart, and hepato-portal sys- tem are usually pooled into one compartment because their perfusion/ volume ratios are relatively high, facilitating their classification as a vessel- rich group (VRG). The muscles and skin are usually placed in the muscle group (MG), while adipose tissue and bone marrow form the fat group (FG). Compartments with a poor vascularity, such as bones, teeth, liga- ments, hair, and cartilage, are placed in a vessel-poor group (VPG), (Fiserova-Bergerova, 19831. PB-PK models not only allow a prediction of the temporal relationships of the tissue concentrations of a xenobiotic postdosing but also accom- modate physiological changes such as a change in blood flow or renal clearance for an individual subject. Interspecies and intersubject differ- ences, nonlinear metabolic kinetics, and differences in mechanisms of uptake (for example, as a consequence of altering the route of adminis- tration) can also be accommodated by the model. Effects in different species can be predicted by using PB-PK models developed in one species and scaling those constants such as metabolic rates that are often unknown for the target species. When available, how- ever, information on metabolism in the species of interest should be used. ADMINISTERED AND DELIVERED DOSES One of the potential applications of pharmacokinetics to risk assessment involves the use of pharmacokinetic models to determine the effective dose of compound of interest that reaches the target tissue. The dose delivered to the target tissue can then be used in place of the administered dose in an attempt to obtain more accurate estimates of risk. In this section, we explore the effects of using the delivered dose as a surrogate for the administered dose in predicting carcinogenic risks.

448 DAN ~ EL KR EWSK' ET AL. Curvilinear Dose Response Many xenobiotic compounds require some form of metabolic activation to exert their carcinogenic potential (Gehring and Blau, 19771. The amount of the reactive metabolite reaching the target tissue is influenced by the pharmacokinetic laws governing the overall activation process. When one or more steps in this process are saturable, the relationship between the dose d* delivered to the target tissue and the administered dose d can be nonlinear (Hoer et al., 19831. To explore the effects of metabolic activation in estimates of low-dose risks, consider the simple pharmacokinetic model for metabolic activation of a particular toxicant shown in Figure 1 (Krewski et al., 19861. Here, exposure occurs at a constant rate d. Once absorbed into the body, the toxin X can be either eliminated or activated to its reactive form Y. The reactive metabolite can then be eliminated or detoxified. It is assumed that the elimination of both X and Y follows first-order linear kinetics, whereas activation and detoxification are assumed to be enzymatically mediated processes following saturable Michaelis-Menten kinetics. At steady state, the dose d* of the reactive metabolite reaching the target tissue can be expressed as a function do = fade of the admin- istered dose. This simple model can be used to illustrate the impact of saturation effects on the relationship between the dose d* delivered to the target tissue and the administered dose d (Figure 21. When both activation and detoxification follow linear kinetics, do is proportional to d. If the detox- ification process is allowed to be saturable, d* is still proportional to d at low doses. Once the process saturates, however, the delivered dose do increases rapidly as a function of d. Conversely, if only the activation step is considered to be saturable, d* levels off in relation to d as saturation occurs. A combination of both these effects can occur when both activation and detoxification are saturable. U ptake TOXiCANT ~ Activation X , _ _ _ Elimination REACTIVE METABOLITE Elimination _ Zeroth Order Kinetics ~ Linear Kinetics i ~~ ~ ~ Michoelis-Menten Kinetics FIGURE 1 A simple compartmental model for metabolic activation. Detoxif ication

PK Data in Carcinogenic Risk Assessment 449 _ ~ 0 - 11 In o C] .= C] 0 0 _ _ - / / - ~ . / , . 0 5 Administered Dose d Both Saturable — Activation Saturable Detoxification Saturable ........... Both Linear FIGURE 2 Administered and delivered doses with saturable kinetics. 1 0 To assess the implications of saturable kinetics on linear extrapolation from high to low doses using the administered dose d, we conducted a computer simulation involving the four cases illustrated in Figure 2. In this investigation, the probability of tumor induction was assumed to satisfy the simple one-stage model P(d) = 1—exp (-Ad*), where the delivered dose is in turn a function d* = fade of the administered dose and A = 1. Because P(d) ~ Ad* for even moderately large values of d*, the dose-response curve is essentially linear on the delivered dose scale. Under linear kinetics, d* is proportional to d, in which case P(d) is also a linear function of d. Because d* is a nonlinear function of d in the presence of saturation effects, however, the dose-response curve P(d) is a nonlinear function of d when activation or detoxification is saturable. Using this model, experimental outcomes were generated with 50 ob- servations at each of the four dose levels d = 0, 1/4, 1/2, and 1 corre- sponding to current National Toxicology Program (NIP) recommendations for experimental design (NTP, 19841. (Without the loss of generality, the doses used here represent fractions of the maximum tolerated dose EMTD], the highest dose normally used in a carcinogen bioassay.) For each of the

450 DAN ~ EL KREWSK! ET AL. Both Saturable Actn. Saturable (target - . 022) (1 argot - 19) L Detox. Saturable Both Linear (Target - .0048) (Target - t) 4~ D o ~ .5 > _ E :' Cat o . ~ . .1 . ~-Y I, 1 ..oo 1 .01 .1 ~ 10 1 O Upper Con f idence Limit on Slope FIGURE 3 Cumulative distribution of upper confidence limits on low-dose slope based on robust linear extrapolation. Arrows indicate target slopes. four cases depicted in Figure 2, 1,000 sets of experimental data were generated, and a 95% upper confidence limit on the slope of the dose- response curve at the origin was calculated by using robust linear extrap- olation. The cumulative distributions of these upper confidence limits on the low-dose slope are shown in Figure 3. Under linear kinetics, the dose-response curve is essentially linear, and the values are tightly clustered near the true value of unity. In the two cases in which the detoxification process is saturable, however, the upper confidence limits are well in excess of the target slopes. When only the activation process is saturable, on the other hand, all of the values lie below the true slope of 19. This latter result is due to the steepness of the dose-response curve in the low-dose region, and is less pronounced if lower doses are included in the experimental design. For example, inclu- sion of a group of 50 animals at a dose of 1/32 of the MTD gave simulated confidence limits ranging from 8.5 to 23, as compared with the range of 2. 1 to 3.6 in Figure 3. Whittemore et al. (1986) showed that the biases in the confidence limits can be reduced if information about the phar- macokinetics is available.

PK Data in Carcinogenic Risk Assessment 451 Time-Dependent Exposure In the preceding section, the dose delivered to the target tissue was constant over time because exposure was by continuous infusion, with the system assumed to be in steady state. If steady state has not been achieved, or if the level of exposure d (tJ varies with time t, the delivered dose d*(t) is time dependent. To illustrate this, consider the simple compartmental model shown in Figure 4. Here, exposure can occur at a constant rate d or intermittently at different points in time. Once absorbed, the toxin X can be either eliminated or detoxified. As in the previous model, elimination is pre- sumed to follow linear kinetics, whereas detoxification can be a saturable process. Because metabolic activation of the toxin is not required, our interest is in the concentration d*(t) of the toxin in the target tissue over time t. The temporal profile of the dose delivered to the target tissue is shown in Figure Sa for four different exposure scenarios under the assumption that the detoxification process is nonsaturable (Withey and Murdoch, 19871. Curve A presents the case of continuous inhalation exposure to a constant dose d = 60 ~g/h over an 8-h working day. In this case, a plateau or steady-state level is achieved following 30 min of exposure, with clearance being essentially complete within 1.S h following the ter- mination of exposure. The systemic availability, or area under the con- centration-time curve, is 19 . 3 ~gh/ml. Uptake TOXICANT X Elimination FIGURE 4 A simple compartmental model for a direct-acting toxicant. Detoxification

452 DAN ~ EL KREWSK' ET AL. 40 30 a) — o E _ 20 - Il~ D 1 a) a) '. I a, to . ~ : \ ., 'a.'.\ , so 60 a) En ~ o E _ 40 a) ._ a) 20 4 Time t (hours) b. Saturable Detoxification \ \ \ o \ ;` \ i` 1 , ~ ~ , \ . a. Linear Detoxification l . - ~ c ~ , 11 ll . 1 i' ~ 1 : . ':' 16 l l 16 1: I. ~ . . A. . 8 . ~ " ale' "" , ~ . 10 o ~ 6 8 to Time t (hours) FIGURE 5 Time-dependent exposure patterns with saturable kinetics. Curve B is derived so as to have the same total administered dose of 480 fig following 16 equal oral doses of 30 fig given every 30 min. assuming that there is instantaneous absorption. Curves C and D are similar, corresponding to exposures every 2 h and once at the beginning of the day, respectively. Because the kinetics are nonsaturable, the sys-

PK Data in Carcinogenic Risk Assessment 453 TABLE 1 Systemic Availability Gag in/ml) Under Linear and Saturable Detoxification Number of Doses Detoxification (leg in/ml) Linear Saturable Continuous 16 4 19.3 19.3 19.3 19.3 36.4 38.9 63.6 193.7 temic availability under these three exposure regimens is the same as under the regimen shown in curve A. Even though the systemic availability is identical under all four exposure scenarios, the peak tissue concentrations vary appreciably. The higher peak exposures associated with the regimens shown in curves C and D may be expected to lead to more severe acute toxic effects than from the lower peak exposures in the regimens shown in curves A and B. as occurs, for example, with hydrogen sulfide (Evans, 19671. As demonstrated in the next section, however, this may not be the case with carcinogenic effects. Saturation of detoxification or other elimination processes can substan- tially increase systemic availability (Figure Sb). With saturation effects chosen to approximate the linear detoxification at low doses assumed previously, systemic availability is nearly doubled in the case of continuous infusion with a Michaelis constant of 5 ~g/ml (Table 11. With a single oral dose, saturation increases the area under the concentration-time curve by 10-fold. Risks with Time-Dependent Exposure Patterns The risk associated with exposure to a carcinogenic substance may depend not only on the total dose experienced over a period of time but also on the pattern of exposure during that period. For example, under a multistage model in which only the first stage is dose dependent, exposure early in life is more effective than exposure later in life (Day and Brown, 19801. Conversely, if only the last stage is dose related, exposure later in life will be of greater concern. To explore the effects of time-dependent exposure patterns, consider a multistage model in which only one stage is dose dependent. As shown in the Appendix, the carcinogenic risk associated with a delivered dose d*(t) over O < t < T will be the same as that for an equivalent constant dose of

454 DANIEL KREWSK! ET AL. T dT = J d*(t) w(t) aft, o (1) where w (t) is a weighting function depending on which stage of the model is affected. For example, consider a six-stage model, in which only the first stage is dose dependent, and a constant dose d* over the first quarter of an individual's expected lifetime followed by no exposure thereafter (Figure 6). Because dosing late in life is relatively ineffective, the equiv- alent constant dose dT is close to the actual dose d*(t) that reaches the target tissue during the period of exposure. Note that a simple time- weighted average dose T dT = J d*(t)dtlT o (2) is notably lower than the equivalent constant dose, and hence would underestimate the risk corresponding to the actual exposure pattern. A1- though the degree of such underestimation is in general no more than k- fold, where k denotes the number of stages in a multistage model with a single dose-dependent stage, this result cannot be guaranteed with other _ .Height Function -. Actu ,1 Dose . . Equivalent Dose Average Dose Birth Death Time t FIGURE 6 Equivalent constant dose with time-dependent exposure (six-stage model, with the first-stage being dose dependent).

PK Data in Carcinogenic Risk Assessment 455 models such as the birth-death-mutation model discussed earlier (Murdoch and Krewski, 19871. These results can be used to evaluate the risks associated with the time- dependent exposure patterns discussed above. Because clearance from the target tissue following cessation of exposure is sufficiently rapid so as to preclude bioaccumulation, systemic availability following repeated daily exposures is obtained simply by multiplying the values in Table 1 by the number of days during which exposure takes place. Because the weight function wk ~ can be treated as a constant over a short period of time, such as a single day, it follows from Equation 1 that the equivalent constant dose is nearly proportional to the area under the concentration-time curve for a single day. In the absence of bioaccumulation, systemic availability thus provides a good measure of delivered dose on which estimates of carcinogenic risk can be based. APPLICATIONS In the previous sections of this paper, we have explored the application of the delivered dose concept in carcinogenic risk assessment in general terms. In this section, we consider several compounds that have dem- onstrated carcinogenic potential in long-term bioassays and for which some pharmacokinetic information on delivered dose is also available. These latter data permit a comparison estimate of low-dose cancer risks based on administered and delivered doses, and may also facilitate extrapolation between different species and routes of exposure. FormatUehyde Formaldehyde has been shown to induce cancerous lesions in the nasal cavity of both rats and mice, predominantly squamous cell carcinomas (Albert et al., 1982; Swenberg et al., 19801. In addition to these bioassay results, information on delivered dose is available in the form of covalent binding to respiratory mucosal DNA in rats (Casanova-Schmitz et al., 19841. Assuming that covalently bound formaldehyde is associated with neoplastic change, these data can be used to evaluate the impact of the use of the delivered rather than the administered dose in predicting cancer risks at low doses. For purposes of illustration, consider the data on tumor incidence fol- lowing inhalation exposure of 6 in/day, 5 days/week for 24 months shown in Table 2, as previously considered in this context by Starr and Buck (19841. Experimental data on covalently bound formaldehyde as reported by Starr and Buck (1984) are also shown. These results indicate that the relationship between the delivered and administered doses is nonlinear,

456 DAN ~ EL KREWSK' ET AL. TABLE 2 Squamous Cell Carcinomas of the Nasal Cavity Induced in Male and Female Rats Exposed to Formaldehyde Covalently Bound Administered Formaldehyde Dose (ppm) (nmol/mg) Tumor Incidence 0.0 0.0 0/160(0%) 0.3 0.002 2.0 0.022 0/160 (0%) 5.6 0.212a 2/160 (1.3%) 6.0 0.233 10.0 0.406 14.3 0.600a 87/160 (52.5%) 15.0 0.631 aBased on linear interpolation between adjacent points. with a marked increase in the level of covalent binding above administered doses of 2 ppm (Figure 71. The dose-response curve for squamous cell carcinomas is also highly nonlinear on either the administered or delivered dose scale, with a large number of tumors observed only in the high-dose group. Although the relationship between the delivered and administered doses is unknown below 2 ppm, the data are not inconsistent with a linear relationship in this region with a slope of approximately 0.01 nmol/mg/ ppm. Under this assumption, robust linear extrapolation on the delivered dose scale leads to an upper confidence limit on the slope of the dose- response curve at the origin of 0.23 mg/nmol, equivalent to a slope of 0.0023 ppm-i = 0.01 nmol/mg/ppm x 0.23 mg/nmol on the adminis- tered dose scale. The corresponding value based on linear extrapolation directly on the administered dose scale is 0.0089 ppm-~. Given the as- sumption that covalent binding provides a relevant measure of delivered dose, the upper limit based on delivered dose is roughly fourfold lower than that based on administered dose. Viny' Chloride Vinyl chloride monomer (VCM) is known to induce a variety of tumors in rats, mice, and hamsters at diverse sites (Maltoni et al., 19811. In one study, male and female Sprague-Dawley rats were exposed to doses up to 10,000 ppm of VCM by inhalation 4 in/day, 5 days/week over a period of 1 year. The occurrence of angiosarcomas of the liver is summarized in Table 3. Note that these results indicate that the incidence of these lesions does not continue to increase at doses above 2,500 ppm.

PK Data in Carcinogenic Risk Assessment 457 .O c a) cat _ 5 .E ~ - 0 Z IL ~ ~ _ 0 0 m ~ _ _ c a) Cd lo 0 ·0 . — .— . — . — .. . . - . - .. .. . — 10 15 Administered Dose (ppm) FIGURE 7 Covalently bound formaldehyde in respiratory mucosal DNA in rats. Although VCM is known to form a number of different metabolites, Gehring et al. (1978) noted that the total amount d* of VCM metabolized in the liver appeared to depend on the level of exposure d via the Michaelis- Menten equation: Vd d* = K+ d' TABLE 3 Angiosarcomas Induced in Male and Female Sprague-Dawley Rats Exposed to Vinyl Chloride Monomer (3) Administered Dose (ppm) Metabolized VCM (~g/4 h) Tumor Incidence 0 0 0/461 (0%) 1 17 0/118 (0%) 5 84 0/119(0%) 10 164 1/119 (0.8%) 25 395 5/120 (4.2%) 50 739 15/354 (4.2%) 100 1,309 1/120 (0.8%) 150 1,761 6/119 (5.0%) 200 2,129 15/120 (10.0%) 250 2,434 3/59 (5.1%) 500 3,413 6/60 (10.0%) 2,500 5,029 13/60 (21.7%) 6,000 5,402 13/59 (22.0%) 10,000 5,520 7/70 (11.7%)

458 DANIEL KREWSK! ET AL. where V = 8,558 ~g/6 h is the estimated maximum velocity, and K = 336 ppm is the estimated Michaelis constant at which half the maximum velocity is achieved. Under this model, saturation effects are apparent only at administered doses on the order of several hundred ppm or higher (Figure 81. At lower doses, the amount metabolized per unit of exposure to VCM is approximately VIK = 25.5 ~g/6 h/ppm. In this example, the dose-response curve is apparently linear at doses below 200-SOO ppm on either the administered or delivered dose scale. Because of this, robust linear extrapolation based on delivered dose, which focuses primarily on data in this dose range, leads to an upper confidence limit on the low-dose slope of 0.00034 (1lg/4 h)-~, corresponding to 0.0058 ppm-i = 0.00034 (1lg/4 h)-i x 25.5 ~/6 h/ppm x (4 h/6 h) on the administered dose scale. This value is virtually identical to the value of 0.0056 ppm- ~ obtained by using the administered dose. Methylene Chloride and PerchIoroethylene Andersen et al. (1987) used a PB-PK model to assess the risk to humans of exposure to methylene chloride, also know as dichloromethane or DCM. Mice exposed to 2,000 and 4,000 ppm of DCM by inhalation 6 in/day, 5 days/week, demonstrated an excess of hepatocellular adenomas/carcino- mas as compared with unexposed controls (NTP, 19861. An earlier study conducted by the National Coffee Association (EPA, 1985), in which mice were exposed to DCM in drinking water at concentrations leading ~ 1 ~o - ~D t_ ~ O 03 D ~ 5 ~ — :~: o ........... .. ...................... o o o -o Administered Dose (ppm) FIGURE 8 Metabolized vinyl chloride monomer in rats. 5000

PK Data in Carcinogenic Risk Assessment 459 to exposures of up to 250 mg/kg/day, showed no increase in the incidence of liver tumors (Table 4~. The flow-limited PB-PK model shown in Figure 9 has been employed by Andersen et al. (1987) to explore this apparent inconsistency between routes of exposure and to allow extrapolation to humans. The paths on the right-hand side of the figure represent flows of arterial blood, while those on the left-hand side represent flows of venous blood. The lung has been divided into a first compartment in which gas exchange takes place, and a second compartment in which metabolism occurs. DCM adminis- tered in drinking water is assumed to pass through the gastrointestinal (GI) tract directly into the liver. There are two paths involved in the metabolism of DCM: the saturable mixed-function oxidase (MPO) path, and the essentially linear glutathione- S-transferase (GST) path. Because the mechanism of carcinogenesis of DCM is not known, three possible dose metameters were considered: the parent compound itself, the rate of metabolism of DCM in the MFO path, and the rate of metabolism of DCM in the GST path. The latter two were used as surrogates for metabolite formation. This model can be used to derive estimates of concentration of DCM and the rates of each of the two paths in the liver (Table 41. It can be seen that the rate of the MFO path is comparable in the two studies, whereas the other two measures of delivered dose are much higher in the inhalation experiment than in the drinking water experiment, as are the corresponding tumor incident rates. This can be taken as evidence that the MFO path is not responsible for tumor induction. Because the rate of delivery of the parent compound is proportional to the rate of the GST path, effects of the parent compound cannot be distinguished from those TABLE 4 Hepatocellular Adenomas/Carcinomas Induced in Female Mice Exposed to Methylene Chlonde Delivered Dose Route of Parent Administration Administered MFO Path GST Path Compound Tumor (dose units) Dose (g/liter/day) (g/liter/day) (ma in/liter) Incidence Drinking water 0 0.0 0.000 0.0 6/100 (6%) (mg/kg/day) 60 1.3 0.003 1.3 4/100 (4%) 125 2.8 0.007 2.9 2/50 (4%) 185 4.0 0.011 4.6 5/50 (10%) 250 5.4 0.016 6.4 3/50 (6%) Inhalation 0 0.0 0.00 0 3/50 (6%) (ppm) 2,000 3.6 0.85 360 16/48 (33%) 4,000 3.7 1.80 770 40/48 (83%)

460 DAN ~ EL KREWSK' ET AL. I.:. _ Gas Exchange 1 Lung Metabolism . . . ~ . .. . .; ... ......... . .. . .. ._ .... . ..... .% .... ...... .... .. . ....... .................... ..... - ............. ;;; ........ .... .. . ..,... .; ... ·,., x ~ ... ~~ .. N. -., A---,, %, ~ ~~ RICHLY PERFUSED ~ : ~ . . . .. ... ... r ~ . . ' ~ Y. -::: ~ ~ ~ .~.; -: ·.~::$:'~ ::: ~ · -: :: :: .: ·:: ::-: t:::'·:::: :- ~ :.:: :.: :: :~ SLOWLY PERFUSED :: ~ ~ ~ I G. 1. TRACT FIGURE 9 A physiologic phaImacokinetic model for methylene chloride (Andersen et al., 1987). of the GST path. Nonetheless, on the basis of other biochemical consid- erations, Andersen et al. (1987) concluded that the GST surrogate is the most appropriate predictor of tumor incidence. Based on the GST path, the delivered dose in the high-dose groups is approximately 100 times higher in the inhalation study than in the drinking

PK Data in Carcinogenic Risk Assessment 461 water study, as compared with the tenfold difference indicated by using the administered doses. This is due to the fact that the doses in the inhalation study were all well above the level necessary to saturate the MFO path, leading to a high rate of activity in the GST path (figure 10), whereas those in the drinking water study were not. An upper confidence limit on the risk at low doses for female mice can be calculated by using robust linear extrapolation based on the delivered dose data from the inhalation study in Table 4 to be 0.56 (g/liter/day) - I. At low doses, the rate of the GST path is approximately 0.036 mg/liter/ day/ppm, so that the low-dose slope on the administered dose scale is 2.0 x 1o-s Pam-. Working directly on the administered dose scale, the low-dose slope value would be 2.4 x 1O-4 ppm-~, which is 12 times higher. To extrapolate to humans, we follow the results of Andersen et al. (1987) and assume that the GST surrogate has the same potency across species on a body weight scale. Calculation of the amount of GST surrogate formed in humans requires determination of the human values of the model parameters by allometric scaling or, preferably, by experimental mea- surement. In the present example, Andersen et al. (1987) calculated many of the physiological constants and the rates of the GST path allometrically, but determined the metabolic constants involved in the saturable MFO pathway expenmentally. The calculation also requires specification of the dosing regimen. At low doses, inhalation of methylene chloride for 6 h 150 as - J _ ~ 100 - a) - ce o 50 3 CO CO C, o / / / - / 100 200 300 400 Administered Dose (ppm) FIGURE 10 GST activity in the liver in mice due to 6-in/day exposure to methylene chloride.

462 DAN ~ EL KREWSK! ET AL. daily results in GST rate per part per million of about 0.012 mg/liter/day/ ppm, one-third of the rate for mice. Thus, the 95% upper confidence limit on the low-dose slope for humans is 6.7 x 10-6 ppm-i, which is 36 times less than the corresponding value for mice calculated on the basis of the administered dose. It is worth noting that this ratio does not apply to all dosing routes. For example, when drinking water exposure is modeled as continuous infusion to the liver, human GST activity per unit dose is 0.16 (mg/liter/day)/(mg/ kg/day). This is about 3 times higher than that of mice, rather than 3 times lower as calculated above for inhalation exposure. C. Chen and J. N. Blancato (this volume) used a similar physiological pharmacokinetic model to assess the risks of exposure to perchloroethylene (PCE). Their model had no lung metabolism compartment, because one path in the liver was assumed to account for all metabolism and to produce the active metabolite. Its rate was used as the dose surrogate. Species equivalence on surface area, body weight, liver volume, and air concen- tration scales were all considered. In each case, the use of the metabolized dose produced estimates of human risks 5-10 times lower than calculations based on the administered dose. SUMMARY AND CONCLUSIONS The process of carcinogenic risk assessment based on the results of toxicological experiments conducted in the laboratory involves certain assumptions, such as that of low-dose linearity when extrapolating from high to low doses. By using a simple mathematical pharmacokinetic model for metabolic activation in which the probability of tumor induction is proportional to the delivered dose, it was shown with a computer simu- lation that saturation effects in metabolic activation resulting in a curvi- linear dose response can have an impact on estimates of low-dose risk obtained by linear extrapolation. In particular, saturation of detoxification processes can result in an appreciable overestimation of risk, whereas saturation of activation processes can lead to some underestimation of risk. The most accurate estimates of risk are obtained with a linear dose response. These effects were further evaluated by using existing data on formal- dehyde and vinyl chloride monomer, using covalent binding to DNA in the nasal mucosa and the level of metabolism in the liver as possible measures of delivered dose, respectively. With formaldehyde, low-dose risks predicted on the basis of delivered dose were a factor of 4 lower than those obtained by using the administered dose level, because of the nonlinear relationship between the delivered and administered doses within the experimental dose range. Because VCM metabolism is nearly pro- portional to the level of exposure at low to moderate doses, estimates of

PK Data in Carcinogenic Risk Assessment 463 low-dose risk based on either the delivered or administered dose scale were virtually identical. The dose delivered to the target tissue may vary with time, depending on both the exposure regimen and metabolic activation. By using a simple mathematical compartmental model based on linear kinetics, it was dem- onstrated that exposure regimens with different dosing intervals having the same systemic availability lead to different peak concentrations in the target tissue. In the absence of bioaccumulation, however, it was noted that under the multistage model of carcinogenesis, the area under the concentration-time curve is a better predictor of carcinogenic risk than are peak concentrations. Carcinogenic risk assessment can also require extrapolations between different routes of exposure and from the animal model used to humans. This can be done with PB-PK models. With methylene chloride and perchloroethylene, it was noted that estimates of low-dose risks in humans using predictions of dose delivered to the target tissue based on such models can be substantially lower than traditional estimates based on the use of the administered dose level. In conclusion, pharmacokinetic models can be used to obtain more accurate estimates of risk at low doses through the use of the dose delivered to the target tissue as a surrogate for the administered dose in toxicological studies, particularly when the response of interest is roughly proportional to the delivered dose. Predictions of the internal tissue dose for other routes of exposure can be obtained by using PB-PK models, provided that measurements of the physiological and biochemical constants associated with the different routes are available. Extrapolation between species can also be facilitated by using physiological models to predict the delivered dose in the species of interest. In those cases in which all of the relevant model parameters cannot be measured directly in humans, however, these must be obtained by scaling the corresponding values in animals. This approach to interspecies extrapolation is of most use when the dose- response curves for animals and humans are comparable when expressed in tees of delivered dose. ACKNOWLEDGM ENTS We thank Dr. Richard Reitz for kindly providing the data shown in Figure 10, and for helpful comments on the original draft of this article. REFERENCES Adolph, E. F. 1949. Quantitative relations in the physiological constitutions of mammals. Science 109:579-585. Albert, R., A. Sellakumar, S. Laskin, M. Kuschner, N. Nelson, and C. Snyder. 1982. Gaseous formaldehyde and hydrogen chloride induction of nasal cancer in the rat. J. Nat. Cancer Inst. 68:597-603.

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PK Data in Carcinogenic Risk Assessment 467 APPENDIX: THE MULTISTAGE MODEL AND TIME-DEPENDENT DOSING Under the multistage model, the probability of a tumor occurring by . . . ~ time t Is given by: where H(t) = f O f ok P(t) = 1 —expE—H(t)l, . . (A-1) fo2 II Ai~t~dul . . . duk (A-2) i=1 denotes the cumulative hazard function and Lift) is the transition intensity function for stage i = 1, . . . k (Crump and Howe, 1984~. To accom- modate exposure to a particular xenobiotic, the intensity functions are often assumed to be linearly related to the dose date at time t, with mitt) = al + bidets, (A-3) where (ai, bi > 04. For constant exposure data = d, this reduces to the usual form of the multistage model with: tk k H(t) = II (ai + bid) k! id (A-4) To explore the effects of time-dependent dosing under the multistage model, consider the simplest case in which only the rth stage is dose dependent. Because bi = 0 for i ~ r, we have: H(t) = aLt) + beta do, where (A-S) ante = tweak= iai~lk!, bate = (brlar~aft), and do = ELd(Urk)] = To dLu~wfu; r, k— r + 1, t~du. (A-6) Here, Mu; r, k—r + 1, t) represents the marginal density of Urk, the rth order statistic in a sample of size k from the uniform distribution on to, tl. This density is given by: ur-"t—u~k-~ (A-7) (O < u < t), with B(, ~ denoting the beta function (see Murdoch and Krewski, 1987, for further details). It follows from Equation A-S that do represents that fixed dose which, if given continuously from time O to

468 DAN ~ EL KREWSK! ET AL. time t, would produce the same cumulative hazard at time t as the variable dosing regimen date. It follows from Equation A-6 that the use of a constant time-weighted average dose d, = Orb dfu~dult (A-8) will be valid when k = 1, because Mu; 1, 1, t) = 1/t for O < u < t. When k > 1, however, the use of do in place of d, does not in general lead to the same cumulative hazard at time t as that which accrues under the variable dosing regimen data. When only one stage is dose dependent, it follows from Equation A-S that the excess risk is proportional to d i. Because this function is a weighted average of the values of dfu) over O < u < t, the ratio R of the excess risk under variable dosing as compared with that based on a constant average dose is at most the maximum value of the density Mu; r, k—r + 1, tJ divided by its average value lit. This ratio can be written as: R = ~ ~ leak ~ '(!<k—)~)k-! ~ k (A-9) Thus, the excess risk under variable dosing is at most k times the risk under constant dosing.

PART V111 Perspectives