Drinking Water and Health, Volume 8 Pharmacokinetics in Risk Assessment (1987) / Chapter Skim
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III. Generalizations and Extrapolations
III. Generalizations and Extrapolations
Pages 63-182
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From page 63... ...
PART 111 Generalizations and Extrapolations
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Perhaps no single factor is more dominant in constraining animal design than body size. Size-induced patterns have been identified for all aspects of animal design and function from structural dimensions, to life history characteristics, to pharmacokinetics.
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Further, changes in size result in shifts in optimal or preferred frequencies of use. It is becoming increasingly apparent that there are a suite of body size-dependent physical laws that dictate many features of animal design.
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Lungs with alveoli and pulmonary capillaries, and circulatory systems with capillaries and red cells, are prominent examples of structures that are necessary only as a price for large body size. Interestingly, in all cases the surface areas of the above-named structures vary with body mass exponents (b)
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and, therefore, the efficiency of locomotion are strongly body size dependent. There is an energetic cost associated with small body size, the source of which could be the obligate scaling of muscle contraction times.
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Hill's speculation was that all physiological events are likely entrained to the same body size-dependent clock. Thus, critical biological times, such as gestation period or time for growth to maturity, as well as other temporally linked biological events, may all be constant if compared per unit of physiological time.
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There are at least two consequences of the regularity of physiological time that have direct bearing on pharmacokinetics and risk assessment. 1o2 1o1 _ 10° In ~ ° 10 ' [L' 10 2 10-3 10 Brood Cat ,~O myth\ _ _ 10-5 .001 .01 1 00 1 000 1 00000 .1 1 10 BODY MASS (kg)
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. These include strictly physiological times (muscle contraction)
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of O2: Respiratory Cycle Lifespan: Gestation P-rl^~ 233 M~00 65 M-O 05 Respiratory Cycle: Heart Cycle 4.5 M 1 1 1 1 1 1 1 0.001 0.01 0.1 1 10 100 1000 10000 BODY MASS (k9) FIGURE 4 Ratios of any two physiological times are nearly constant, varying little from shrew to elephant.
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Like other rate functions, those involving the biochemistry of drug metabolism are inseparably bound to physiological but not chronological time. Uptake, processing, and excretion of drugs all transpire at rates that are generally directly proportional to one another and with body mass exponents characteristicofphysiologicaltime,b ~ 1/4 (Boxenbaum, 1982;Calder, 1984; Dedrick et al., 1970; Weiss et al., 19771.
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Thus, while absolute rates of clearance varied by nearly 1,000-fold, they did so in an identifiable pattern. If those data are normalized for size and physiological time scaling, clearance can be expressed per unit of body mass per unit of physiological time (Figure 51.
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Perhaps physiological time can form the bases of comparison for risk assessment across species. The exponentially expanding pharmacokinetic data base may be outgrowing useful paradigms for interpretation.
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FIGURE 6 One method of comparing animals from diverse taxonomic groups may be on a single continuum of physiological time. Here LD50 values for fenvalerate are plotted as a function of one measure of time, namely, the time required to metabolize one body mass equivalent of O2.
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It may prove to be of significant value in understanding interspecific pharmacokinetics. It is not proposed as a substitute for direct measurements; however, cross-species comparisons should be made by normalizing for physiological time first, assuming it is the "default value." If differences persist, those can be fairly attributed to species differences.
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As an extension of this concept, we propose that species extrapolations may best be made as a function of physiological time (rather than dose or some other aspect of chronological time)
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1981. Body size, physiological time, and longevity of homeotherrnic animals.
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Anatomical parameters, such as organ size and blood flow rates, are usually constant and well-established; if not, they can often be estimated directly or by allometry (see S
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Alternatively, the metabolic clearance rate can be related to the unbound drug concentration bv the free intrinsic clearance rate (CL'i°' — f u CLiUnt) Account can also be taken that metabolism often involves more than one pathway, so that the overall intrinsic clearance in any system represents the sum of the individual processes (Equation 31: ion V i- ~ Kmi + f ES]
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From page 82... ...
, respectively; and Q is the blood flow to the organ. This approach has been applied to studies with cytosine arabinoside, when the in vitro kinetics of deamination in a number of organs and in different species allowed good predictions of the in viva situation (Dedrick et al., 1972, 19731.
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From page 83... ...
, along with the unbound fraction, was incorporated into Equation 7, resulting in an in vitro predicted hepatic extraction ratio. Comparison of this with an experimentally determined steady-state extraction ratio in the isolated perfused rat liver showed excellent agreement (r = 0.988, p ~ 0.0011.
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84 ._ au Cal at: En 5 Ct Cal ._ Cal ~ _ O ~ c: Ct `_— ~ I ,= O ~ Cal S:: ~ ·_ Ct O ~ ·— ._ Cal Cal ~ LO Cal O Cal X — o ._ Cal ~ m o · _ _ ~ _ ;2 ~ — O m ~ o .
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85 a: o ._ so ._ ._ Cal no ~9 C)
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, each of which has the same eliminating activity, surrounding the cylinder. The relationship between intrinsic clearance and extraction is then given
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For example, an in vitro estimate of intrinsic clearance will predict a larger extraction ratio when incorporated into a sinusoidal perfusion model than if the same value is used in the venous equilibration model; the dispersion model provides an intermediate value. Moreover, the model discrepancies become larger as the intrinsic clearance increases, i.e., the greater the drug's extraction ratio.
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The various in vitro techniques and interpretative approaches for characterizing the kinetics of drug binding to plasma proteins are well-established, as are various factors that modulate such binding (Reidenberg and Erill, 1986; Tillement and Lindenlaub, 19861. A limited number of examples exist in which in vitro parameters of linear or nonlinear plasma binding has been explicitly incorporated into physiologically based pharmacokinetic models of specific compounds (Bischoff and Dedrick, 1968; Engasser et al., 1981; Igari et al., 1983; Tsuji et al., 19831.
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(10) Generally, it as assumed that distribution is perfusion limited, so that the emergent venous blood is in equilibrium with the average total concentration in the tissue (CT)
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Theoretically, the partition coefficient during the terminal phase of elimination (Kp app) is greater than the value obtained at steady state, the difference being smaller the more rapidly drug distributes into the tissue and the faster the rate of elimination (Equation 121: Kp Kp,app = 1 Az kT (12)
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m and in vitro-predicted (TIP) c tissue partition coefficients for several drugs and tissues in the rabbit.
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Moreover, interspecies differences in tissue binding do not appear to be as pronounced as those in plasma binding. Partitioning of a large number of drugs into muscle tissue of rats, rabbits, and humans is very similar (Fitchtl and Schuhmann, 19861.
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1979. Estimation of tissue-to-plasma partition coefficients used in physiological pharmacokinetic models.
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1982. In vitro and in vivo evaluation of the tissue-to-blood partition coefficient for physiological pharmacokinetic models.
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1983. Physiologically based pharmacokinetic model for p-lactam antibiotics.
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The biologically active Formosa may be the parent substance and/or one or more of its metabolites. In developing pharmacokinetic models to achieve this objective, investigators must consider a host of interrelated complex factors and events that could conceivably affect the time course of the parent substance and its biologically active metabolites at the action sites and to decide whether such factors are sufficiently important to include in the model.
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A model designed to describe the kinetics of a single dose of a substance may or may not be appropriate for the description of the kinetics of a substance entering the body by a series of repeated doses or at a continuous rate. Different Mechanisms When a substance enters the body by a series of repeated doses until a steady state is achieved, the investigator must also consider whether the incidence or magnitude of the biological response is most closely related to the maximum concentration, the average concentration, the minimum concentration, or the total dose of the biologically active form of the toxicant.
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Thus, the number of differential equations used by the investigator to describe a physiologically based pharmacokinetic model can be virtually infinite. The solution of such a model, however, would also require knowledge of the values of all of the rate constants that relate the amount of the substance and its metabolites in the various compartments to the rates of transfer into and out of each of the various compartments.
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The time required to approach a virtual steady state depends largely on the secondorder rate constant for the formation of the complex and the equilibrium constant of the complex. Since the average residence time of blood within capillaries is probably in the range of 1 to 10 s in most organs, one can be reasonably assured that virtual steady-state values can be assumed when either the unbound concentration or the 1 IKa values for reversible binding are greater than 1o-s M
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From page 100... ...
Since a membrane is usually considered to be lipoidal in character, the value of D is usually considered to be proportional to the partition of the substance between the cell membrane and water, which is frequently estimated from the partitioning of the substance between oil and water. When the substance is a weak acid or a weak base, it is usually assumed that only the neutral form of the substance is able to pass through semipermeable membranes and that the concentration of the neutral form can be estimated from the total concentration of the unbound substance by means of the Henderson-Hasselbalch equation.
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CU2, (2b) where V2 is the apparent volume of distribution of the unbound substance in compartment 2.
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simply assume that the substance in the capillaries of an organ distribute instantaneously to all compartments within the organ, that metabolism within the cell is diffusion independent, and that the approach to virtual steady states in all organs is limited solely by blood flow rates. They describe the approach to a virtual steady state of the entire organ by a very simple differential equation.
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Ci (3) where Vi is the actual volume of the organ, Ci is the amount of a substance in the organ at any given time divided by the volume of the organ, Qi is the blood flow rate through the organ, VmaX(i' and Km(i, are MichaelisMenten parameters, and CLint(i)
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, the equations would have to be modified. Non l i near Ki netics a nd Lost Concepts When the concentration of substances approach or exceed the Km values of enzymes or transport systems or the 1/Ka values of binding sites in blood or tissues, the meanings of such terms as organ clearances, organ availabilities, organ extraction ratios, volumes of distribution, total body clearances, and biological half-life become obscure.
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and is the link between the differential equations used in general physiologically based pharrnacokinetic models and the equations used in the physiologically based linear compartment pharrnacokinetic models. Physiologically Based Linear Compartmental Pharmacokinetic Models In these models investigators simply assume that all elimination processes that occur in organs approach virtual steady states rapidly.
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From page 106... ...
attain virtual steady states by the time that the first blood sample is taken thus will be reasonably valid for most substances. Calculation of Other Compartmental Mode' Parameters The rate constants for the other compartments in the model can also be derived with the same parameters that are required for the solution of the simple physiologically based pharmacokinetic models.
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LINEAR PHARMACOKINETIC SYSTEMS Even though all processes that govern the pharmacokinetics of substances in organs do not always follow first-order kinetics, physiologically based pharmacokinetic models of first-order systems provide insights of relationships that are not always obvious. From these relationships, the investigator can identify parameters that are useful in comparing data for consistency and in making inferences and extrapolations that would be difficult, if not impossible, to obtain from direct experimentation.
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From page 108... ...
Investigators interested in biologically relevant concentrations thus should focus attention on the factors that govern the concentration of the unbound substances at action sites rather than on factors that govern the total concentration of the substance in organs containing the action sites. Classification of Organs; Routes of Administration Although the concept of AUC values have usually been restricted to the concentration of substances in arterial blood, the concept can be used to estimate AUC values of substances in blood within capillaries of various organs and within the total organ.
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Some organs, such as the intestinal mucosa, the liver, and the skin, can be either first,\\\\\\\\\\\\ _ ~ First Pass Organs .__ ~ 1 ~ 1 1 Nonfirst Pass Organs Site of Administration Venous Blood and Nonelimination Organs Lung and Other Elimination Organs _ . , ~ , ~ I Arterial Blood Kidney and Other ation organs Slowly Equilibrated Organs I Rapidly Equilibrated I Organs FIGURE 2 Relationships among sites of administration, first-pass organs, and non-f~rst-pass organs in physiologically based models.
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Thus, alterations of reversible binding to tissues other than the blood usually do not affect the average concentration of unbound substance in blood. Indeed, they do so only when the organ clearance is nonlinear and the changes in tissue binding result in oscillations in the concentration that affect any of the organ clearances.
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From page 111... ...
When these principles are applied to physiologically based pharmacokinetic models, it follows that during a dosage interval under steady-state conditions, the maximum and minimum concentrations of unbound substance in arterial blood will be between the maximum and minimum concentrations of unbound substance in any non-first-pass, nonelimination organ. The maximum concentration of unbound substance in such organs will be between the maximum concentration and the AUC/; value of the unbound substance in arterial blood, and the minimum concentration of unbound substance in such organs will be between the minimum concentration and the AUC/~ value of unbound substance in arterial blood.
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Non-First-Pass, Elimination Organs According to the well-stirred model, the concentration of a substance In blood within the capillaries of an elimination organ is assumed to be the same as the concentration of the substance in venous blood leaving the organ. Thus, under steady-state conditions, the concentration of the substance in blood within the capillaries can be estimated from the arterial
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Others have suggested models that provide estimates between the well-stirred model and the parallel tube model. In the parallel tube model the average concentration of the substance in blood within the capillaries EC`av']
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As with non-first-pass, nonelimination organs, the steady-state concentration of the substance in blood within the capillaries of the organ and in venous blood leaving the organ is the same as that entering the organ. Thus, all of the conclusions that were valid for non-first-pass, nonelimination organs are also valid for first-pass, nonelimination organs, after the input concentration has been modified.
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— CL (10) CL is the total body clearance, which includes the clearance by the lung which in turn depends on the intrinsic clearances of exhalation and metabolism, Fpre is the fraction of the dose entering the body that enters the lung, and Fit is the availability of the substance in lung.
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Location of Organs of Elimination The effects of different routes of administration on the steady-state concentration of the substance in first-pass organs depends on which organs contribute to the total body clearance of the substance. If the substance were eliminated from the body by only one organ in the body, the steadystate concentration of the substance in that organ would be independent of the route of administration, even though the organ may be a first-pass organ after one route of administration but a non-first-pass organ by another.
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. It follows, therefore, that when the apparent total body clearance, as measured by the dose/A UC value, is considerably smaller than the slowest blood flow rates through any organ of elimination, the value of all elimination organs is virtually 1.0 and the elimination of the substance is flow independent.
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From page 118... ...
In Equation 12, the terms ho FS FSrg fUICLS are those that govern the steady-state concentration of unbound parent substance within the organ. The steady-state rate of formation of the metabolite can be expressed by the steady-state concentration of the unbound substance and the intrinsic clearances of the enzymes that catalyze the formation of the metabolite.
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From page 119... ...
If toxic, reactive metabolites never leave the cells in which they were formed, then the direct toxic effects would be restricted to those cells containing the enzymes that catalyzed their formation. Alterations in the activities of the enzymes that catalyze the formation of the metabolite in cells of different organs thus may alter the relative toxicities in different target organs and would be unpredictable from pharmacokinetic studies solely of the parent substance.
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Unknown Biologically Active Forms It is important to realize that when the biologically active Formosa is not known, only the dose-dependent effects on the rate and extent of absorption can be unequivocably related to the incidence and intensity of toxicities. It is frequently impossible to decide whether the response will be directly proportional to dose, greater than proportional to dose, or less than proportional to dose when increasing doses result in the approach to saturation of various enzymes and active transport systems.
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From page 121... ...
t Ss. ,,,,,,,,,,,,,,,,, SS., Steady state level of diffusible form when CL by other mechanisms is zero.
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From page 122... ...
Whatever the actual kinetics may be, the assumption that the rate of absorption would be directly proportional to the total amount of material suspended in the dosage form will not always be valid. Because the rate of absorption of substances across thin membranes is usually directly proportional to the oil/water partition ratios, it might be assumed that this would also be true for thick membranes, such as the skin.
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From page 123... ...
The rate of absorption through thick membranes, however, is seldom limited by the blood flow rate through the membrane. Under conditions ire which this would likely occur, the substance simply diffuses more deeply into the membrane and enters capillaries in the deeper regions of the membrane.
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From page 124... ...
The effects of concentration-dependent changes in the reversible binding to blood components on the maximum, minimum, and average concentrations of unbound substance after a steady state is achieved during repeated administration of the substance largely depend on the influence that reversible binding of the substance to blood components has on the rate of absorption of the substance and the extraction ratios and location of the elimination organs. If saturation of the binding sites decreases the rate of absorption without having much effect on the extraction ratio of
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From page 125... ...
Thus, the effects of saturation of binding sites to blood components is unpredictable. Saturation of binding sites in tissues within the organs, however, causes greater increases than expected in the magnitude of the oscillations between the maximum and minimum concentrations of unbound substance in the blood and the organs during the dosage interval, which may be relevant to the magnitude of rapid responses initiated by reversible binding to receptor sites.
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From page 126... ...
, the changes in liver metabolites of highly extracted substances caused by changes in either the blood flow rate or the fraction of unbound drug are not accurately predicted by either the well-stirred model or the parallel tube model. Instead, the experimental availabilities are usually between the values predicted by the two models.
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From page 127... ...
. Also imagine that the intrinsic clearance of enzyme 1 was considerably greater than the hepatic blood flow rate.
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From page 128... ...
The parallel tube model also predicts that the location of enzymes that catalyze the metabolism of a metabolite affects the apparent organ availability of the metabolite, when the intrinsic clearance of the enzyme that catalyzes the metabolism of the metabolite greatly exceeds the hepatic blood flow. If enzyme 1 generates the metabolite and enzyme 3 metabolizes it (model 1)
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CLM is the total body clearance of the toxic metabolite (M,)
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From page 130... ...
CLMi is the total body clearance of the toxic metabolite (Ma)
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The increase in the steady-state concentration of the metabolite remains virtually directly proportional to the rate of infusion until the rate of infusion approaches the sum of the VmaX values of the two enzymes (see Gillette, 1986; O'Flaherty, 1986~. This follows from the definition of a steady state; i.e., the rate of elimination of the substance must equal the rate of infusion.
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The equation is not valid for multicompartment systems, and thus, iterative approaches would be needed to simulate not only the approach to steady states but also the concentration changes within a dosage interval. Nevertheless, Equation 15 may be useful for estimating a range of permissible dosage schedules in toxicity studies from in vitro estimates of Vial,,; and Km values.
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From page 133... ...
By contrast, the intensity of a toxicity caused by a metabolite of enzyme 2 may be proportional to the dose, and the dose-intensity relationship of a toxicity caused by the parent substance may be very sharp and appear to have a dose threshold. When the pharmacokinetic studies are not a part of the toxicity studies and the toxic form is unknown, such issues become clouded and risk estimators would not know which pharmacokinetic parameters should be used in their calculations.
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From page 134... ...
From comparisons of the simulations in Figures 7 and 8, it should be obvious that studies of the kinetic parameters of all processes of elimination of the substance and its biologically active metabolites are needed to predict their steady-state concentrations. Knowledge of the kinetic parameters of enzymes without knowledge of the clearance by other pathways of elimination of the parent substance is also necessary.
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From page 135... ...
If the metabolite were formed and eliminated by the same enzyme, however, a steady state could be achievable, because the parent substance and the metabolite would serve as mutual competitive inhibitors as the steady-state concentration of the substance is increased. If the metabolite were eliminated solely by the enzyme, the steady-state concentration of the metabolite can be predicted by the equation: EM]
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Integration of Equation 20 can be performed only by an iterative procedure, but it describes the approach to a virtual steady state, after which time:
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From page 137... ...
, it is noteworthy that dose-dependent depletion of cofactors for all three reactions would tend to increase the virtual steady-state concentration of the toxic form of the drug. Suicide Inhibitors Occasionally a substance is converted to a metabolite that never leaves the enzyme that catalyzes its formation and thereby causes virtual irreversible inhibition of the enzyme.
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(2 lb) Inspection of Equation 21a reveals that the approach to the new steady state should be first order and that at the new steady state the amount of active enzyme should equal koEIk.
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SPECI ES-TO-SPECI ES EXTRAPOLATIONS It may be useful to describe categories of the various factors that govern the pharmacokinetics of substances and their biologically active metabolites according to the extent to which we believe they would contribute to differences between individuals in the human population and to differences between experimental animals and subpopulations of human beings. Extrapolations in the Absorption of Substances Some of the factors that govern the pharmacokinetics of a substance and its metabolites are dependent predominantly on the physical chemical characteristics of the substances and the physiological characteristics of animals.
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From page 140... ...
But the extent to which metabolism by intestinal flora would contribute to differences in formation of toxic metabolites also depends on the consumption of antibiotics. Extrapolations of ~nterorgan Distribution of Substances As pointed out above, most phamacokineticists who use physiologically based pharmacokinetic models assume that a substance entering an organ is distributed virtually instantaneously and that equilibration of the substance between that in blood and that within nonelimination organs is governed solely by the blood flow rate and the partition ratio between the total concentration of the substance and the total concentration in blood, i.e., R
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From page 141... ...
Indeed, some substances may have remarkably long half-lives in the body, even when the hepatic clearance approaches hepatic blood flow, because the partition ratios in many of the organs are very high. Moreover, the combination of blood flow and partition ratios can have a profound influence on the approach to steady state during repeated administration of the substance.
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From page 142... ...
SPECIES DIFFERENCES IN THE ELIMINATION OF FOREIGN COMPOUNDS To the extent that species differences in the magnitude of toxicities are due to pharmacokinetic factors, it is likely that most differences are due to factors that govern the total body clearances of substances and the formation and elimination of biologically active metabolites. Elimination by Excretion into Urine, Air, and Bile To the extent that substances are excreted unchanged from the body by processes that depend predominantly on physiological processes of animals and the physical chemical characteristics of the substance, it seems likely that allometric methods for extrapolating from one species to another provide reasonably valid results.
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From page 143... ...
Thus, Rorgan/b~ooa'' fat in blood, or blood flow rates may be largely irrelevant to discussions of the species differences in pharmacokinetic factors that contribute to species differences in the toxicities of substances that are administered repetitively to test animals during toxicity studies lasting several weeks or months. INDIVIDUALS AND STRAIN DIFFERENCES IN METABOLISM OF FOREIGN COMPOUNDS During the past three decades, it has become obvious that foreign compounds are seldom metabolized in the body by a single enzyme.
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From page 144... ...
The presence of such enzymes is frequently difficult to detect from in vivo pharmacokinetic studies, especially when the studies are interrupted before the concentrations of unbound substance have not declined to levels below the Km values of the high-affinity enzymes. SEX DIFFERENCES The amounts of many of the isozymes in various organs are under hormonal control.
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From page 145... ...
Thus, at a given dose, an inducer may cause marked alterations in the pattern of isozymes in one strain of animals but not in another. INTERORGAN DIFFERENCES IN METABOLISM Although liver is rightly considered the major organ involved in the metabolism of most foreign compounds, drug-metabolizing enzymes, including isozymes of cytochrome P-450, are also present in other organs.
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From page 146... ...
For example, smoking and consumption of certain vegetables and open-fire-broiled meat are known to alter the metabolism of many foreign compounds (Conney et al., 1980; Kappas et al., 19771. Moreover, polymorphisms are also known to exist (Kalow, 19621; those associated with the acetylation of arylamines, the hydrolysis of succinyl choline and paroxon, and the hydroxylation of debrisoquine (Smith, 1985)
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From page 147... ...
Interspecies Differences in the Metabolism of Foreign Compounds Over the past several decades there has been a plethora of studies of the metabolism of foreign compounds in various animal species. But there does not appear to be any consistent relationship that would justify the assumption that species differences can always be related by allometric methods.
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From page 148... ...
. GENERAL COMMENTS The utopian objective of a quantitative risk assessment is to be able to predict the incidence rates of toxicities in a human population that is exposed to low doses of toxicants solely from the results of a single toxicity study in a single strain of test animal subjected to relatively large doses of toxicants.
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From page 149... ...
Thus, if the action sites act independently of one another, the fraction of the total number of receptor sites that are occupied by the substance at any given concentration of unbound substance will usually follow the Law of Mass Action, i.e.: (Effect/Maximum Effect)
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From page 150... ...
Although the mathematics required to describe other mechanisms of response would be different, the basic meanings of the dose-magnitude of response and the dose-incidence of response curves are applicable to all mechanisms of response. Many risk assessments for carcinogens are based on the multistage model, which is described by the equation: P= 1 —e-X where (23)
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From page 151... ...
Some promoters can act by releasing growth factors, but the rate or extent of release of these factors may not be directly proportional to the dose. On the other hand, the bioassay coupled with pharmacokinetic studies may not always reveal the presence of high-affinity, low-capacity enzymes that can be of predominant importance at low doses but only of trivial significance at high doses.
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From page 152... ...
In the extrapolation of the calculated values of tumors/cells in Equation 24 from high doses in animals to low doses in humans, it is important to remember that the sequence is an extrapolation from high doses to low doses for the animals in the bioassay and then an extrapolation from low doses in the experimental animals to low doses in the human population. Thus, to the extent that pharmacokinetic parameters contribute to interspecies differences in the magnitude of the response, the differences usually can be expressed by differences in the parameters of linear models.
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From page 153... ...
Indeed, the range of variability within the human population is known to vary with the foreign compound. In attempting to extrapolate estimates from animals to the mean of the human population, various investigators have pointed out that interspecies differences in many physiological processes, including cardiac output, organ sizes, blood flow rates, and basal metabolism rates, may be related to the surface area of the animals and physiological time.
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From page 154... ...
I am less hopeful that allometric methods will always provide valid interspecies extrapolations when toxic parent substances are eliminated from the body predominantly by enzymes having intrinsic clearances much less than the blood flow rates through the organs of elimination or when the toxicity is caused by metabolites of the toxicant. In such cases allometric methods may provide reasonably valid interspecies extrapolations for some toxicants, but not for others.
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From page 155... ...
Thus, in the absence of complete information concerning the mechanisms of toxicity and the pharmacokinetic and pharrnacodynamic factors that govern the manifestations of the toxicities, it is perhaps advisable to try to establish a consensus among scientists of arbitrary broad ranges of uncertainty, even though such ranges cannot be rigorously defended by science. When the mechanism of toxicity becomes known and if it can be established that intraspecies and interspecies differences in the pharrnacodynamic and pharmacokinetic factors can be predictable within narrower ranges of uncertainty for given toxicities caused by given toxicants, the arbitrary range of uncertainty can be narrowed for that toxicity and toxicant.
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From page 156... ...
1982. Sequential organ first-pass effects: Simple methods for constructing compartmental pharmacokinetic models from physiological models of drug disposition by several organs.
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From page 157... ...
1986. A physiological pharmacokinetic model for dermal absorption.
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From page 158... ...
Pp. 361-384 in Drug Metabolism: Chemical and Biological Aspects.
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From page 159... ...
Before considering the application of physiologically based pharmacokinetic modeling for performing these extrapolations, we will briefly review current practices in each of the four areas. Much of the introductory material for this paper is from H
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From page 160... ...
( 1966) , who examined the interspecies differences in toxicity of a variety of antineoplastic drugs.
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From page 161... ...
Exposure Scenario There are many other ways in which animal studies may differ from expected human exposure scenarios, chiefly relating to the frequency and duration of exposure. Examples include estimating lifetime carcinogenic risk from studies of less than lifetime duration, correlating 50% fetal doses (LDsoS)
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From page 162... ...
The volumes of the compartments and the values of the rate constants are adjusted to fit the experimental data, after which the model can be used for interpolation and limited extrapolation. Physiologically based pharmacokinetic models differ from the conventional compartmental models in that they are based to a large extent on the actual physiology of the organism (Figure 11.
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From page 163... ...
to investigate the pharmacokinetics of styrene. In this description, groups of tissues are defined with respect to their volumes, blood flows (Q)
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From page 164... ...
The resulting set of constants together with the general physiological parameters provide a model of parent chemical behavior and rate of metabolism which can be predictive of kinetic behavior at various concentrations, for various dose routes, in a variety of species, with any number of exposure scenarios. In essence, the same approach can be used with nonvolatile xenobiotics; but at present experiments to determine solubility, tissue binding, and metabolic constants are not as easily conducted with these chemicals as they are with the gases and volatile liquids.
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From page 165... ...
We have now collected the partition coefficients and metabolic constants for all these chemicals and used these constants to construct simple, four-compartment, physiologically based models. In our laboratory, it now takes about 2 weeks to develop the metabolic and solubility constants needed to develop a physiological model for these volatile chemicals.
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From page 166... ...
By varying the input function in a physiologically based pharmacokinetic model that includes both of these metabolic pathways, the time course of Dibromomethane can be predicted for a variety of exposure routes.
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From page 167... ...
However, within reason, the number of equations does not pose any problem. It is relatively straightforward to solve the small groups of equations that describe most physiological models of xenobiotic disposition, requiring only a personal microcomputer and readily accessible software.
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From page 168... ...
As a challenge of the ability of this model to accurately predict kinetics for very different exposure scenarios, we performed short-duration, high-concentration exposures of rats to methylene chloride and bromochloromethane (Andersen et al., 1984a)
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From page 169... ...
To predict the time course of blood carboxyhemoglobin, the basic dihalomethane model was expanded to include a description of the fate of the CO produced by the oxidative pathway, including competition with oxygen for binding to hemoglobin and exhalation of unbound CO. The longer postexposure metabolism of bromochloromethane as compared with methylene chloride reflects its greater tissue solubility.
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From page 170... ...
CLEWELL Ill AND MELVIN E ANDERSEN that are much more complex than that of methylene chloride.
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From page 171... ...
Methylene chloride concentration (in milligrams per liter) in mixed venous blood (A)
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From page 172... ...
These curves can be quantitatively analyzed with a physiological model to estimate the values of the kinetic constants for metabolism. The tissue partition coefficients are determined experimentally, and physiological parameters are estimated based on a combination of literature values and laboratory experience derived from the modeling process.
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From page 173... ...
These chloroethylenes are metabolized by a single, highaffinity, saturable pathway. With the appropriate values of tissue partition coefficients and physiological parameters and assuming a single saturable pathway, it was impossible to generate a good fit to the experimental data.
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From page 174... ...
12, 8, and 5 ppm. Symbols represent the measured chamber atmosphere concentrations, and the solid lines are the best result that could be obtained from an attempt to fit all of the data with a single set of metabolic constants by using the closed-chamber model described in the legend to Figure 6.
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From page 175... ...
The conjugation pathway for the reaction of methylene chloride and glutathione regenerates glutathione, but with other volatile chemicals, such as 1,2-dichloroethane and allyl chloride, the conjugation reaction consumes glutathione. In gas-uptake
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From page 176... ...
CLEWELL Ill AND MELVIN E ANDERSEN experiments with allyl chloride, both the oxidative and the conjugative (glutathione)
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From page 177... ...
CONCLUSION The mathematical structure of physiological pharmacokinetic models is somewhat more complex than that of simpler one-, two-, or three-compartment models that have closed-form solutions. The solution of these physiological models requires numerical integration of a series of nonlinear, simultaneous differential equations.
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From page 178... ...
CLEWELL Ill AND MELVIN E
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From page 179... ...
Toxicological studies are the cornerstone of any risk analysis and provide dose-response curves on which risk analyses must be based. In contrast, pharmacokinetic models are interpretive tools to be used in conjunction with toxicity and mechanistic studies.
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From page 180... ...
In fact, in a way they introduce new uncertainties: the adequacy of the model, the accuracy of the parameters in the model, and the appropriateness of the chosen measure of effective dose. The rationale for using physiologically based pharmacokinetic models in risk assessment is that they provide a documentable, scientifically defensible means of bridging part of the gap between animal bioassays and human risk estimates.
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From page 181... ...
1979. A review of the application of physiologically based pharmacokinetic modeling.
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From page 182... ...
1986. A physiological pharmacokinetic model for dermal absorption of vapors in the rat.
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Key Terms
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