Click for next page ( 352


The National Academies | 500 Fifth St. N.W. | Washington, D.C. 20001
Copyright © National Academy of Sciences. All rights reserved.
Terms of Use and Privacy Statement



Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.

OCR for page 351
PART Vl Applications of Mathematical Modeling

OCR for page 351

OCR for page 351
Hazard Assessment Using an Integrated Physiologically Based Dosimetry Modeling Appproach: Ozone Frederick ]. Miller, John H. Overton, Jr., Elaine D. Smolko, Richard C. Graham, and Daniel B. Menze! INTRODUCTION In examining the possible role of pharmacokinetics and pharmacody- namics in risk assessment, the underlying philosophy of the legislative mandate through which the risk assessment is applied must be kept in mind. For example, the ability of the Food and Drug Administration to invoke the Delaney Clause to regulate a substance is different from the risk assessments required for the Environmental Protection Agency's Na- tional Ambient Air Quality Standards (NAAQSs). The kind and level of information that is available can vary greatly. Reevaluation of the NAAQSs for ozone (03) focuses on whether or not the value of the standard should be changed by as little as 20%, while many carcinogenic risk assessments are trying to establish the level of risk to within one to two orders of magnitude. In any case, the uncertainties identified in risk assessments help to establish areas in which additional research would be useful. The intent of this paper is to broaden the awareness that pharmacoki- netics and mathematical dosimetry models are useful tools in risk assess- ments of noncarcinogenic as well as carcinogenic effects. While examples The research described in this paper has been reviewed by the Health Effects Research Lab- oratory, U.S. Environmental Protection Agency, and approved for publication. Approval does not signify that the contents necessarily reflect the views and policies of the Agency nor does mention of trade names or commercial products constitute endorsement or recommendation for use. 353

OCR for page 351
354 FREDERICK J. MILLER et al. Of modeling applications have been predominantly related to carcinogen- esis, health effects such as emphysema and fibrosis are not to be ignored. This is particularly true for oxidant gases. For example, several animal studies in different species show that long-term exposure to nitrogen diox- ide produces emphysema (renters et al., 1973; Hyde et al., 1978; Riddick et al., 1968), and O3 causes pulmonary fibrosis (Fujinaka et al., 19851. Moreover, subchronic exposures at relatively low levels of these gases have been shown to lead to cellular changes (Barry et al., 1985; Chang et al., 1986) that are indicative of a structural remodeling of the lung. The impetus is clear that man must be protected from such effects. But to use the animal toxicological data more quantitatively in setting appro- priate NAAQSs for these gases, extrapolation modeling is required. In this volume the need to incorporate pharmacodynamics in the mod- eling process has been discussed. Thus far, most risk assessments have assumed a priori that an equivalency of response exists between animals and man. As one proceeds from the molecular level or biochemical event toward injury at the tissue or organ level, that assumption becomes less tenable because of possible species differences in repair processes, levels of antioxidant enzymes, etc. The dose, if it is sufficiently high, can produce damage anywhere from the molecular to the organ level. On the other hand, various host defense systems can interact, and if the damage is not sufficiently severe, they can yield recovery. If the delivered dose over- whelms these defense systems, various disease states can result. Defense systems might conceivably play a role in the etiology of lung disease. All of this is a dynamic situation. Figure 1 (based on Figure 1-1 of NRC, 1983) summarizes an overview of the research, risk assessment, and risk management processes and their interrelationships that lead to the recommendation of a NAAQS. This paper focuses on the phases of the processes outlined by the dashed rectangle. Here, the area of pharmacokinetics offers great potential for improved risk assessments, particularly when these assessments are re- quired to be more quantitative in nature. The development of dosimetry models that can provide a description of the uptake and distribution of chemical compounds throughout the body and the availability of toxico- logical data that can be used to establish dose-response relationships are integral to these efforts. The incorporation of laboratory and field obser- vations of adverse health effects, hazard information, and extrapolation methods to yield dose-response assessments is critical to the risk assess- ment process. The combining of these phases can be facilitated by the integrated physiologically based dosimetry modeling approach, illustrated schematically in Figure 2. The major components of the approach are the critical toxicity reference (CTR) system (Smolko et al., in press) and the physiologically based

OCR for page 351
Establishing Dose-Response Relationships 355 RESEARCH RISK ASSESSMENT RISK MANAGEMENT l Laboratory and field observations of adverse health effects and exposures to particular agents Information on extrapolation methods for high to low dose and animal to human Haza rd Identifi. ation Dose-Response Assessment Field measurements, esti mated expose res, characterization of populations _ _ _ J Exposu re Assessment _ Risk Characterization \ + \ Development of regulatory options Evaluation of public health, economic, social, political consequences of regulatory options T | Agency l decisions and actions FIGURE 1 Major elements of risk assessment and risk management. The phases of the process that can be addressed by using an integrated physiologically based dosimetry modeling approach are contained within the dashed rectangle. Overall figure schematic is based on Figure 1-1 of NRC (1983). dosimetry (PBD) model. The CTR system is comprised of four elements: (1) searching the literature for references reporting toxicity data relevant to the toxicant being studied; (2) abstracting information from the selected references in a form appropriate for both quantitative and descriptive extraction; (3) constructing a data base that consists of bibliographic and abstracted information; and (4) compiling concentration-response data by a series of searches of the developed data base. The primary factors considered in developing PBD models are mammalian physiological pro- cesses, anatomical characteristics, physicochemical properties of the gas and of relevant biochemical constituents, and mass transport processes. PBD model predictions of dose, appropriate for species with the specific characteristics described in the literature, are combined with the concen-

OCR for page 351
356 FREDERICK J. MILLER et al. ll L _ _ _ _ _ _ _ Critical Toxicity Reference (CTR) System Search Literature Abstract Information Construct Data Base Compile Concentration- Response Data Exposure Concentration Time of Exposure - parameters specific to 9 iven I animal, weight, and sex Data Base animal, for weight, ~ anatomical, physiological, sex biochemical, and physical parameters 1 1 LO Physiolog ical Iy-Based Dosi metry (PBD) Model T predicted dose response | Dose-Response Relationship | Species Sensitivity Host Defense Repair Processes Genetics Identifv Research Gaps . _ .. .., .. _ . and Design Experiments | Estimate Hu j an Toxicity ~ r | Risk Characterization 1 FIGURE 2 A schematic of the elements of an integrated physiologically based dosimetry modeling approach to estimating human toxicity that leads to one of the components of risk characterization. The procedure diagrammed in the dashed rectangle is the proposed approach for implementing the dashed rectangle process shown in Figure 1. tration-response data that have been collated by species and endpoint. The resulting dose-response relationships can use various expressions of dose to obtain the most appropriate quantitative representation of toxicological effects. The analyses can incorporate species sensitivity information for con- sideration of such factors as host defense, repair processes, and genetics. One outcome of this approach is an estimation of human toxicity that can be used as input into the risk assessment and risk management processes.

OCR for page 351
Establishing Dose-Response Relationships 357 A second outcome is information to aid in the identification of data gaps and design of experiments. This latter outcome is particularly important because it can eventually yield new data that will be used in the iterative application of the integrated PBD model approach which will strengthen the overall risk assessment and risk management processes. The remaining sections of this paper illustrate the integrated PBD mod- eling approach (Figure 2) by applying data from the CTR system and predictions from a PBD model for O3 to construct dose-response rela- tionships. This will be done first by discussing the formulation, as well as sample simulation results, of a PBD model that predicts the uptake and distribution of absorbed O3 in the lungs of mammals. Although the focus will be on 03, the intent is primarily to illustrate the methodology and to provide an understanding of various aspects of delivered dose. The meth- ods discussed will be particularly important when some of these procedures are extended to volatile organic compounds, for which first-pass metabolic effects in the lung are a concern. Also, a brief discussion is provided of a data base management system, CTR, that has been developed to store and retrieve quantitative data in a manner useful for mathematical dosi- metry models. An application to ozone toxicological data is presented to illustrate the methodology of using mathematical dosimetry models to examine quantitative dose-response relationships. LOWER RESPIRATORY TRACT MATHEMATICAL DOSIMETRY MODELI NG In the papers presented in this volume, much attention is placed on the use of physiologically based pharmacokinetic models to provide a de- scription of dose distribution following inhalation of a chemical com- pound. To date, these models predict average levels of the chemical throughout an entire organ (or body compartment). As illustrated below, however, additional complexities are involved when the distribution of inhaled gases is evaluated within the lower respiratory tract (LRT), where dose in various lung regions can vary greatly and consequently have different health effect outcomes. Mode! Conceptualization The major factors affecting the regional uptake of O3 are morphology of the respiratory tract, the route of breathing, the depth and rate of breathing, gaseous physiocochemical properties, the physical processes governing gas transport, and the physiocochemical properties of the trach- eobronchial (TB) liquid lining and of the air-blood barrier in the pulmonary

OCR for page 351
35~3 FREDERICK J. MILLER et al. region. All these factors interact in a complex way to determine dose and must be considered in developing a simulation model. The mathematical model formulation will focus on the lower respiratory tract for several reasons. Upper respiratory tract removal of inhaled gases and particles is amenable to experimental determination of deposition (Corn et al., 1976; Miller et al., 1979; Yokoyama, 1968; Yokoyama and Frank, 19721. The morphology of the upper respiratory tract is quite complex, difficult to measure, and variable between species (Schreider, 1986; Schreider and Raabe, 1981), so mathematical descriptions are dif- ficult to obtain. Further, airflow patterns are also complex (Patra et al., 1986), so proper treatment of gas transport processes is not apparent. Experimental values for upper respiratory tract uptake of the inhaled gas, however, can provide appropriate boundary conditions for mathematically modeling delivered doses to LRT regions. Aspects of LRT structure and their relationship to model compartments are illustrated in Figure 3. Briefly, anatomical descriptions of the lung are needed such as those available for man (e.g., Weibel, 1963; Yeh and Schum, 1980) and for various animals (e.g., Kliment, 1973; Schreider and Hutchens, 1980; Yeh et al. 19791. The top portion of Figure 3 shows Weibel's (1963) representation of the TB and pulmonary regions of the human lung. For mathematical modeling purposes, we conceptualize this representation into a series of right circular cylinders; and information is needed on the lengths, diameters, and radii of the TB airways. In the pulmonary region, data on the structure of the pulmonary ducts and sacs and on the number of alveoli, their surface areas, and volumes are nec- essary to apply the model description of gas transport processes. In the TB or conducting airways, a mucociliary layer protects the un- derlying ciliated, goblet, brush, and basal cells, etc., from direct insult by the inhaled gas. As can be seen in Figure 3, this layer consists of an epiphase and a hypophase. Lacking definitive data on the thickness and chemical composition of these phases in various portions of the TB region, the current model formulation combines them into one compartment. For ambient exposures to the highly reactive gases, such as 03, penetration to the bloodstream in the TB region can be ignored (see Miller et al., 1985, for details). Thus, in the TB region, model compartments correspond to the air, liquid lining layer, and underlying tissue. For highly soluble and nonreactive gases, however, a blood compartment and a description of the fate of the gas in other organs and compartments of the body probably would be needed. In the pulmonary region, the epithelium is chiefly comprised of type I and type II cells over which a very thin layer of a surfactant fluid can be found. Underlying the epithelium are the interstitium and the endothelial cells of the capillary network. Because the alveoli are arranged back to

OCR for page 351
Establishing Dose-Response Relationships 359 - TB ~ 14131 2 T BL BR B L ~ " PU LM ONARY t22|21|20|19|18|17 AS AD RBL ~ W~ s~ ~ W/~: O TRA- CHEA l- , a . . b ~ ,~ c rat I _ 1 . A C A`' _ ,, A d AIR TISSUE\ a ~ r ~ / ~ TISSUE ~ ;/ l l LIQUID LINING, l l AIR , , _____________________ ________ ~ , ______________ A,. AIR _ _ _' . HY~ An-- ' "'AS' UQUlD uea~c Use. LIQUID LINING FIGURE 3 The relationships between morphologies and their model representations. Panel a is a schematic of the branching airways of the TB and pulmonary region of man (based on Weibel, 1963). The generations are labeled from the right, beginning with the trachea. BR, BL, and TBL indicate bronchi, bronchioles, and terminal bronchioles, respectively; the respiratory bronchioles, alveolar ducts, and alveolar sacs are indicated by RBL, AD, and AS, respectively. Below the TB portion of the lung schematic are three cylindrical figures that indicate the model representation of the airways. Panel c shows a diagram of the structure of the liquid lining and tissue of the TB region (diagram based on Jeffrey and Reid, 1979). The different cells represented are basal (BC), ciliated (CC), brush (BrC), goblet (GC), and conciliated serous (NCC). Panel e illustrates the model representation of TB liquid lining and tissue compartments. Panel b is an electron micrograph of the interalveolar septa (based on Gehr et al., 1978). The air spaces (A), capillaries (C), type I cells and their nuclei (EP1 and NEP1), endothelial cells and their nuclei (EN and NEN), and interstitial space (IN) are indicated. Panel d illustrates the model represen- tation of the liquid lining, tissue, and capillaries of the pulmonary region.

OCR for page 351
360 FREDERICK J. MILLER et al. back, with capillaries between them, the model formulation for the air, liquid lining, tissue, and blood compartments is assumed to be symmetrical (Figure 31. A one-dimensional equation of mass transport is used to describe the dynamics of the cross-sectional average concentration. Experimental ev- idence for this approach is discussed by Overton (19871. The processes of axial convection and axial dispersion, the loss of O3 to the liquid lining, and lung expansion and contraction are taken into account. Lung expansion and contraction during the breathing cycle become important when pol- lutant uptake for minute ventilations corresponding to heavy exertion is modeled. When mass transfer in the liquid lining, tissue, and blood com- partments is modeled, the transport of ozone is related to molecular dif- fusion and chemical reaction terms. The reader is referred to Figure 2 of Overton et al. (J. H. Overton, R. C. Graham, and F. J. Miller, this volume) for explicit forms of the partial differential equations used in the model. For a detailed discussion of the model formulation and assumptions, as well as the basis for these assumptions, see Miller et al. (1985) and Overton et al. (19871. Note that when other gases are modeled, modifications of the expression for loss of the gas to airway walls may be necessary. In addition, high solubility or nonreactivity may necessitate changes in some aspects of treating gas transport in the airways. The information required to model adequately transport in the mucus or surfactant lining liquid, tissue, and blood compartments includes quan- titative biochemical data on the constituents as well as on the chemical reactions of O3 with these constituents. Currently, a pseudo-first-order reaction scheme is assumed when ozone uptake is modeled (see Miller et al., 19851. Estimates of liquid lining, tissue, and blood compartment thickness are also required. At present, this is an area in which most of the available information is from animal studies. Data for man are very limited, and assumptions about the distribution of compartment thickness must be made. Compartmental diffusion coefficients and partitition coef- ficients, such as those used in physiologically based pharmacokinetic models, are also needed. Much of the above topic is discussed in detail elsewhere (Miller et al., 1985; Overton et al., 19871. Examples of O3 Dosimetry Modeling Results Utilizing the model formulation concepts discussed above, Miller et al. (1985) examined the uptake of O3 in the LRT of man and performed various sensitivity analyses to illustrate the importance of LRT secretions on delivered dose. Their work shows that the net amount of O3 removed in the trachea can be several orders of magnitude different from the amount of O3 that penetrates to the underlying tissue. Proceeding distally from

OCR for page 351
Establishing Dose-Response Relationships 361 the trachea, this difference diminishes mainly because of the decline in the thickness of the liquid lining. Furthermore, because the gas-exchange region is lined with a very thin fluid that does not contain many constituents that react with 03, the net amount of O3 removed and the tissue dose of O3 are essentially the same. According to Miller et al. (1985), the net O3 dose curves are much less dependent on the thickness of the TB liquid lining than are the O3 tissue dose curves. Another example of sensitivity analysis demonstrating the importance of model parameters is concerned with the values of the liquid lining rate constants. Simulations show that the effect of increased chemical reactivity in the TB liquid lining is to increase the net airway doses in the TB region and to decrease the tissue dose throughout the LRT. Furthermore, tissue dose is found to be much more sensitive to the TB liquid lining reactions than is the net dose. For example, the tracheal tissue dose is predicted to decrease by about 3 orders of magnitude, and the tracheal net dose is predicted to increase by about 1 order of magnitude because of a rate constant change from 0 to twice the reference value. However, pulmonary net and tissue dose values are predicted to change by less than a factor of 2 as a result of the same change in the TB liquid lining rate constant. By contrast, changes in the pulmonary liquid lining rate constant lead to simulation results for LRT net and tissue doses that are essentially un- changed from those obtained with the reference values. These types of analyses show that to determine dose-effect relationships for various cell types or components (e.g., cilia) in the conducting airways, better quan- titative data than are presently available on TB liquid lining rate constants and thickness are desirable. On the other hand, the lower sensitivity of predicted pulmonary doses to parameter uncertainties gives a greater con- fidence in making interspecies comparisons of dose-effect relationships in this region compared with making such comparisons in the TB region. An example of interspecies dosimetric comparisons is illustrated in Figure 4, in which the solid and dashed lines are O3 dosimetry simulation data for the rats and man, respectively. Predictions for the rat lung use the Yeh et al. (1979) anatomical model in which the morphometric data are represented in a generational-type model analogous to the Weibel (1963, generational morphometric data for the human lung. Both the net and tissue doses of O3 are shown for these species. Dose is expressed in Figure 4 as micrograms of O3 per square centimeter of airway surface area per minute, standardized to a tracheal O3 value of 1 ~g/m3. In the mathematical dosimetry model the processes are linear. Thus, dose is proportional to the tracheal concentration. For example, for a tracheal concentration of 1,000 ~g/m3, the predicted airway doses are 1,000 times the plotted values; for a tracheal concentration of 1 ppm, multiply the plotted values by 1,960 (~g/m3 per ppm).

OCR for page 351
4 ~ ~ PAU ~ F. MORR ISON ET AL. except for a decade difference in ordinate scale. The first curve (a) also scales with dose by the appropriate factor of 5. This scalability arises, in spite of the presence of nonlinearities in the complete scheme, because over 95% of the volume of MTX distribution is composed of non-transport- saturating, rapidly equilibrating compartments, principally the kidney, liver, plasma, skin, and extracellular volume of the muscle. In addition, the small compartments that do exhibit nonlinear distribution, the intra- cellular spaces of the gut, spleen, and bone marrow, do not rapidly trans- port drug into their cells. Hence, several plasma half-lives in the rat (tin = 0.3 h) can pass after administration of drug in the therapeutic dose range before plasma levels fall to the point where return of the small amount of drug in these deep nonlinear compartments could influence plasma kinetics. On the other hand, if one is interested in assessing the drug delivery to the gut, spleen, and bone marrow, then nonlinear pharmacokinetics prevents dose scaling from applying. These organs exhibit two strong nonlinearities in the first few hours after drug administration: saturable uptake of MTX from plasma, and strong binding of MTX (and its poly- glutamates) to the target enzyme dihydrofolate reductase. This is exhibited in Figure 3, in which total MTX concentrations in rat bone marrow (ex- tracellular MTX + intracellular MTX) are plotted as a function of time for four doses (Dedrick et al., 19731. The bar denotes the concentration of reductase in this tissue. Note that plasma-to-marrow concentration ratios are not constant over the 140 min shown here, and thus that marrow concentration does not scale with dose. The total marrow concentration shown in Figure 3 does scale with dose at short times, but this only reflects the rapid equilibrium attained between plasma and extracellular space (the dominant transport before cell uptake becomes significant). Note also that the marrow curves of the two lower dose levels are flat at long times and lie below the reductase content bar, thereby reflecting strong nonlinear enzyme binding of the drug that enters the cells in the first few minutes of exposure. Because the tight binding prevents drug efflux from occur- ring, the mass of enzyme-bound drug reflects the cumulative result of transport into the cell. At 0.05 and 0.25 mg/kg, this mass scales with dose (0.02 versus 0.10 ~g/ml) and thus transport is linear. However, attempts at using linear transport to extrapolate from 0.25 to 2.5 mg/kg fail, an observation that is consistent with plasma levels at the higher dose exceeding a Michaelis transport constant of about 1 ~M, a value char- acteristic of the range found in a variety of cell lines (Goldman, 1969, 1971; Schilsky et al., 19811. Figure 4 shows the magnitude of this saturable transport effect by dose level as the difference between the dashed and solid lines. The solid line shows rat marrow concentrations when saturation

OCR for page 351
Methotrexate: Pharmacokinetics and Toxicity 4~9 t00 10 or 1.0 At lo he o - \ 2 S mg~g _ _ ~ _ - - _ - - - - - - - - \L- ~ 0.1 0.25 0.05 GO' 20 40 60 80 TIME, min 100 120 140 FIGURE 4 Companson of model simulation of linear and saturable transport in bone marrow at several doses. The dashed lines represent the model simulations for linear transport to the intracellular compartment of bone malTow. The solid lines represent model simulations with saturable transport. SOURCE: Dedrick et al. (1973). is operative, while the dashed line, providing a poor fit to the data (not shown), shows the result when linear transport is assumed. Hence, it can be concluded that, for sufficiently short times (e.g., <4 h in the rat), many organ regions are dose scalable, while others, for example, the gut, marrow, and spleen, are not.

OCR for page 351
420 PAUL F. MORRISON ET AL. DOSE SCHEDULING We next turn our attention to the rather dramatic effects that dose scheduling has on toxic response and to the formal connection between MIX pharmacokinetics and toxic response. Up to this point, the discussion has mainly involved distributional events that occur after bolus dosage. We will now see that the time of inhibition of dihydrofolate reductase is the primary correlate with toxicity. Table 2 shows acute toxic response in terms of the lethal dose for 50% of mice (LDso) exposed to a variety of drug schedules (Zaharko, 19751. The first entry is for a bolus dose of 350 mg/kg, while the next entries correspond to divided doses of decreasing total dose, and the final entry corresponds to a 96-h infusion of a 3-mg/kg total dose. These results immediately show that response does not directly correlate with total dose. Decreasing dose by more than a factor of 100 led to an increase, rather than a substantial decrease, in toxicity. Furthermore, the area under the plasma concentration-time curve, a frequently used metric, does not cor- relate with toxic response. This can be seen in Figure 5 (Zaharko, 19751. The steep curve shows the MIX plasma concentration following the 350- mg/kg bolus dose, while the flat curve shows the concentration following the 3-mg/kg 96-h infusion. The area under the bolus curve is about 2 orders of magnitude greater than that under the infusion curve, yet toxic response is greater with infusion. The principal correlate with response is the length of time that dihy- drofolate reductase and, consequently, DNA synthesis are strongly inhib- ited. If inhibition of DNA synthesis is a good correlate, then one would expect that the onset of toxicity should be observable after the same inhibition time, regardless of dose schedule. For at least two infusion schedules, this has been observed experimentally in mouse small intestine (Zaharko et al., 19771. Figure 6 shows the recovery of DNA synthesis in mice, as measured by deoxyuridine incorporation into DNA, following an infusion of 1 fig of MTX/h for 48 h, a schedule that just barely avoids TABLE 2 Schedule Dependence of Methotrexate Toxicity in Mice - Peak plasma Individual concentration dose (mg/kg) Schedule Total dose (mg/kg) (M) Effect 350 Single dose 350 10-3 LDso 25 Twice daily 50 lO-4 LDSo 3 Every 3 h, 5 times, rest 8 h, and then 24 1o-s >Lids every 3 h, 3 times 0.5 Every 3 h, 20 times 10 lo-6 >LDso 0.8 ~g/h Infusion 96 h 3 10-8 >LDso

OCR for page 351
Methotrexate: Pharmacokinetics and Toxicity 421 1000 -~ 1 00 10 ~ O BY \ O O O \:, . ~_~ o . -2 X 1O - 8M 0.001 . 1 . I . 1 . 1 . ~ 0 20 40 60 80 100 Ti me, Or FIGURE 5 Concentration of methotrexate in mouse plasma. Open circles, single dose of 350 mg/kg i.v.; closed circles, constant infusion of 0.8 ~g/h. SOURCE: Zaharko (1975). lethal toxicity. If severe inhibition of greater than 90% is considered, DNA synthesis is inhibited relative to control for 35 h. Figure 7 shows similar data for a 10-fold higher rate of infusion (10 ~g/h) but of shorter duration (17 h). Like the previous schedule, this one is designed to just barely avoid lethal toxicity at the end of the infusion period (Table 2 of Zaharko et al., 1977~. An inhibition time virtually identical to that above was observed, a period of about 30 h. Further indication of DNA synthesis inhibition time as an appropriate measure of toxicity comes from observing the trend in lethality if, at a fixed infusion rate, infusion times are lengthened. As expected, lethality increases. For 10 fig of MTX/h, lethality jumps from 20% following a 24-h infusion to 90% following a 56-h infusion (Zaharko et al., 19771.

OCR for page 351
200 I ~ 1 o at I o L, ILL I foot fir 50 |I SEM Controk ~ SEM Controk \ 422 PAUL F. MORRISON ET AL. am_ 1 , ~ , i l - b~fus~on _ _ _ 1\ ~ -1 1 1 10 20 30 40 50 ~ 70 80 90 HOURS FIGURE 6 Incorporation of 3H into DNA of small intestine following an MTX infusion of 1 ~g/h for 48 h and an injection of [3H]thymidine (dark circle) or [3H]uridine injection (open circle). Vertical standard error bars indicate the range of the two mice used per point. At least six controls were used for each experiment. The first 10 cm of the small intestine was used from each mouse. SOURCE: Zaharko et al. (1977). Lethality correlation with total dose exists for a fixed infusion rate, but not when extended over a range of infusion rates. To predict toxic response from a given dose and schedule, the phar- macokinetic model of MIX must be coupled to the inhibition of DNA

OCR for page 351
Methotrexate: Pharmacokinetics and Toxicity 423 I ~ ~ ~ 1 ~ 290 C) ~ 1~ on C) lo he o 0 100 at 50 _ ~ SEW Control 1 /1 ~ _ \Intus~on ~ ~ - \ ~~- _ ' - - 1 610 70 110 90 10 20 30 40 50 HOURS FIGURE 7 Same as described in the legend to Figure 6, except that the MTX infusion was 10 ,ug/h for 17 h. Solid dots without vertical error bars are an identical experiment with MTX (intraperitoneal dose of 25 mg/kg) given at the start of infusion; mean of two mice; the range was not included, but it was similar to those in other experiments. SOURCE: Zaharko et al. (1977). synthesis. In the mid-1970s, this was accomplished very simply by ob- serving that recovery of DNA synthesis occurred when MTX plasma concentrations, as measured by a competitive binding assay, fell below 10-8 M (Chabner and Young, 1973~. Figure 8 shows that recovery in

OCR for page 351
424 PAUL F. MORRISON ET AL. 175 , 150 125 2 100 a 75 50 25 - Non tumor bearing o- - -a Tumor bearing ( ) Dow : O 1~7 O_ _~>' _~ , ' 1,,,,, , O' O 10 - 8 [MTX] plasma t l I P P (350)/ ,'{50} I , I , , I , , I ,'(350},/ 11 /'i50} (A I I , / I . l (5) 10~9 FIGURE 8 Incorporation of [3H]ur~dine into DNA of mouse bone marrow as a percentage of the pretreatment rate. The indicated doses are in milligrams/kilogram, administered intraper~- toneally. SOURCE: Chabner and Young ( 1973). bone marrow was a strong function of this pseudo-threshold following bolus dosing from 5 to 350 mg/kg. Thus, the pharmacokinetic model outlined earlier only needed to be solved for the length of time that the plasma concentration remained above 10-8 M to infer toxic response. The 10-8 M value was interpreted as the free MTX concentration in equilibrium with just sufficient free reductase (about 5% of the total) to allow re- sumption of thymidylate synthesis. Since the mid-1970s, the interpretation of these observations has become much more complex. The reason for this was the discovery of significant metabolism of MTX. When only low bolus doses were considered, cy- totoxic concentrations of MTX did not exist for a sufficiently long period for significant metabolism to be detected. With the introduction of high- dose protocols, and their long infusion times, in the mid-1970s (Frei et al., 1975; Jaffe et al., 1978), metabolism became apparent, and new assays were developed for the detection of metabolites. Some of these metabolic events, particularly the polyglutamation of MTX (Balinska et al., 1982; Baugh et al., 1973; Jolivet et al., 1982;

OCR for page 351
Methotrexate: Pharmacokinetics and Toxicity 425 Momson and Allegra, 1987) were shown to create very active drug forms that cleared from the intracellular milieu of cells at rates that were far slower than the clearance of parent drug from the plasma. Hence, a ratio- nale was needed to explain just why 10-8 M plasma concentrations have been observed to correlate so well with recovery of DNA synthesis and, more importantly, to identify the conditions under which this correlation might break down and when another approach to bridging MTX phar- macokinetics to toxicity would be required. Thus, there is no theoretical reason for expecting that when the 10-8 M concentration is reached, DNA synthesis should immediately resume under all protocols. - A full rationale requires more research, but preliminary analysis indi- cates that, under single-bolus conditions (as employed in Figure 8), cells are incapable of producing truly inhibiting quantities of polyglutamates, leaving the parent drug form alone to account for inhibition and recovery of DNA synthesis as observed. Under long-term infusion or closely spaced multiple bolus conditions, however, cells have much more time to produce polyglutamates and attain inhibiting levels of these compounds. Under these circumstances, MTX pharmacokinetic models need to be expanded to include polyglutamation kinetics, and intracellular MTX polyglutamate concentrations, rather than plasma concentrations of parent compound, need to be correlated with levels of DNA synthesis. SUMMARY In summary, we have seen that (1) only about half of the parameters of the (nonmetabolizing) physiological pharmacokinetic model can be obtained from chemical invariants and interspecies scalings; (2) dose scal- ing applies to the large-volume organ regions (e.g., kidney, liver, plasma) for a few hours after injection, but never to the principal organs of toxicity, the sensitive tissues of the marrow and intestinal mucosa; and (3) toxic response is a strong function of dose scheduling, correlating neither with total drug dose nor area under the MTX-plasma concentration curve, but with the time that MTX (and polyglutamate) concentrations remain above inhibiting levels of dihydrofolate reductase. REFERENCES Balinska, M., Z. Nimec, and J. Galivan. 1982. Characteristics of methotrexate polyglu- tamate formation in cultured hepatic cells. Arch. Biochem. 216:466-476. Baugh, C. M., C. L. Krumdieck, and M. G. Nair. 1973. Polygammaglutamyl metabolites of methotrexate. Biochem. Biophys. Res. Commun. 52:27-34. Bischoff, K. B., R. L. Dedrick, D. S. Zaharko, and J. A. Longstreth. 1971. Methotrexate pharmacokinetics. J. Pharm. Sci. 60:1128-1133.

OCR for page 351
426 PAUL F. MORRISON ET AL. Breithaupt, H., and E. Kuenzlen. 1982. Pharmacokinetics of methotrexate and 7-hydroxy- methotrexate following infusions of high-dose methotrexate. Cancer Treatment Rep. 66: 1733-1741. Chabner, B. A., and R. C. Young. 1973. Threshold methotrexate concentration for in vivo inhibition of DNA synthesis in normal and tumorous target tissues. J. Clin. Invest. 52:1804-1811. Dedrick, R. L., K. B. Bischoff, and D. C. Zaharko. 1970. Interspecies correlation of plasma concentration history of methotrexate (NCS-740) Cancer Treatment Rep. 54:95- 101. Dedrick, R. L., D. S. Zaharko, and R. J. Lutz. 1973. Transport and binding of methotrexate in viva. J. Pharm. Sci. 62:882-890. Frei, E., N. Jaffe, M. H. N. Tattersall, S. Pitman, and L. Parker, 1975. New approach to cancer chemotherapy with methotrexate. N. Engl. J. Med. 292:846-851. Goldman, I. D. 1969. Transport energetics of the folic acid analogue, methotrexate, in L1210 leukemia cells. J. Biol. Chem. 244:3779-3785. Goldman, I. D. 1971. The characteristics of the membrane transport of amethopterin and the naturally occurring folates. Ann. N.Y. Acad. Sci. 186:400-422. Goldman, I. D., and L. H. Matherly. 1986. The cellular pharmacology of methotrexate. Pp. 283-308 in Membrane Transport of Antineoplastic Agents, I. D. Goldman, ed. New York: Pergamon. Jackson, R. C., and K. R. Harrap. 1973. Studies with a mathematical model of folate metabolism. Arch. Biochem. Biophys. 158:827-841. Jackson, R. C., and K. R. Harrap. 1979. Computer models of anticancer drug interaction. Pharmacol. Ther. 4:245-280. Jacobs, S. A., C. J. Derr, and D. G. Johns. 1977. Accumulation of methotrexate diglutamate in human liver during methotrexate therapy. Biochem. Pharmacol. 26:2310-2313. Jaffe, N., E. Frei, H. Watts, and D. Traggis. 1978. High-dose methotrexate in osteogenic sarcoma; a 5-year experience. Cancer Treatment Rep. 62:259-264. Jolivet, J., and B. A. Chabner. 1983. Intracellular pharmacokinetics of methotrexate poly- glutamates in human breast cancer cells. J. Clin. Invest. 72:773-778. Jolivet, J., R. L. Schilsky, B. D. Bailey, J. C. Drake, and B. A. Chabner. 1982. Synthesis, retention, and biological activity of methotrexate polyglutamates in cultured human breast cancer cell. J. Clin. Invest. 70:351-360. Kates, R. E., and T. N. Tozer. 1976. Biliary secretion of methotrexate in rats and its inhibition by probenecid. J. Pharm. Sci. 65: 1348-1352. Kennedy, D. G., R. Clarke, H. W. van den Berg, and R. F. Murphy. 1983. The kinetics of methotrexate polyglutamate formation and efflux in a human breast cancer cell line: The effect of insulin. Biochem. Pharmacol. 32:41-46. Morrison, P. F., and C. J. Allegra. 1987. The kinetics of methotrexate polyglutamation in human breast cancer cells. Arch. Biochem. Biophys. 254:597-610. Peppas, N. A., P. J. Hansen, and P. A. Buri. 1984. A theory of molecular diffusion in the intestinal mucus. Int. J. Pharm. 20:107-118. Schilsky, R. L., B. D. Bailey, and B. A. Chabner. 1981. Characteristics of membrane transport of methotrexate by cultured human breast cancer cells. Biochem. Pharmacol. 30: 1537-1542. Whitehead, V. M., M. M. Perrault, and S. Stelcner. 1975. Tissue-specific synthesis of methotrexate polyglutamates in the rat. Cancer Res. 35:2985-2990. Zaharko, D. S. 1975. The kinetics of drug action. Pp. 69-83 in Pharmacological Basis of Cancer Chemotherapy, 27th Annual Symposium on Fundamental Cancer Research 1974. Baltimore, The Williams & Wilkins Co.

OCR for page 351
Methotrexate: Pharmacokinetics and Toxicity 427 Zaharko, D. S., and R. L. Dedrick. 1984. Pharmacokinetics of methotrexate in animals and man. Pp. 97-131 in Folate Antagonists as Therapeutic Agents, Vol. 2. Pharma- cology, Experimental and Clinical Therapeutics, F. M. Sirotnak, J. J. Burchall, W. D. Ensminger, and J. A. Montgomery, eds. Orlando, Fla.: Academic Press. Zaharko, D. S., W. P. Fung, and K.-H. Yang. 1977. Relative biochemical aspects of low and high doses of methotrexate in mice. Cancer Res. 37:1602-1607.

OCR for page 351