3 Rebecca A. Clewell and Harvey J. Clewell III The intent of this chapter is to provide a general overview of the concepts and methods associated with characterizing the absorption, distribution, metabolism, and elimination of toxic chemicals in the body. The concepts described in this chapter are key elements for understanding the mode of action for the toxicity of a chemical as well as for estimating the risks associated with exposures to the chemical. This chapter explains: TK is the quantitative study of factors that control the time course for absorption, distribution, metabolism, and excretion (ADME) of toxic compounds within the body. The time course of drugs, on the other hand, has traditionally been referred to as pharmacokinetics (PK). Similarly, the effect of a drug or toxic compound in the target tissue for its effect has been referred to as pharmacodynamics (PD) and toxicodynamics (TD). This practice, of course, ignores the wisdom of Paracelsus: “Only the dose differentiates a poison and a remedy.” To avoid this false distinction, the terms biokinetic and biodynamic have sometimes been used. In this chapter these alternative terms will be used interchangeably. Biokinetic models provide sets of equations that simulate the time courses of compounds and their metabolites in various tissues throughout the body. The interest in biokinetics in pharmacology and toxicology arose from the need to relate internal concentrations of active compounds at their target sites to the doses of the compound administered to an animal or human subject. The reason for this interest is a fundamental tenet in pharmacology and toxicology—that both beneficial and adverse responses to compounds are related to the free concentrations of active compounds reaching target tissues, rather than the amount of compound at the site of absorption. The relationship between tissue dose and administered dose can be complex, especially at high doses, with repeated daily dosing, or when metabolism or toxicity at routes of entry alter uptake processes for various routes of exposure. Biokinetic models of all kinds are primarily tools to assess internal dosimetry in target tissues for a wide range of exposure situations. Environmental chemicals cover a wide range of physicochemical properties from lipophilic (“fat loving”) to hydrophilic (“water loving”), highly volatile to nonvolatile, soluble to insoluble, and highly reactive to inert. These physiochemical properties determine whether the compounds are taken up into the body by various routes (inhalation, oral absorption, dermal absorption, etc.), whether they will be subject to metabolic activation or deactivation and whether they will be quickly or slowly cleared from the body. As a result, it is difficult to predict their TK behavior. Nevertheless, some general statements can be made. For chemicals in the environment, the principal routes of exposure are ingestion, inhalation, and dermal contact. In general, environmental chemicals are well absorbed from either the gastrointestinal (GI) tract or the alveoli in the lung. Important exceptions to this rule include metals and insoluble particulates, which are often poorly bioavailable. The skin, on the other hand, is designed to serve as a barrier, and the bioavailability of chemicals is typically much lower by this route. Experimental studies in animals by artificial means such as intravenous or intraperitoneal dosing must be carefully evaluated, considering the differences in the concentration profiles for a chemical administered internally rather than by a physiologically relevant route. Once absorbed, most environmental compounds are distributed throughout the body in the blood and are rapidly taken up into the various organs and tissues. Importantly, physiological “barriers” such as the placenta and the blood–brain barrier are often ineffective at restricting the movement of environmental contaminants. The same types of enzymes that metabolize endogenous chemicals and drugs are also capable of metabolizing environmental compounds. These include “Phase 1” enzymes, such as the cytochrome P450 oxidases (cyps) and esterases, as well as “Phase 2” enzymes that conjugate chemicals with glutathione, glucuronic acid or sulfate, making them more water soluble and more readily excreted in the urine. While metabolism often serves to detoxify an active compound, some metabolism, particularly by cyps and glutathione conjugation, can make a chemical more toxic. The primary routes of elimination are exhalation (for volatile chemicals), urinary excretion (for water-soluble compounds), and fecal elimination. Elimination may be either passive (e.g., glomerular filtration of free chemical in the blood) or active (e.g., biliary or renal secretion). In the 1930s, Teorell provided a set of equations for uptake, distribution, and elimination of drugs from the body. These equations are rightly regarded as providing the first physiological model for drug distribution. However, computational methods were not available to solve the sets of equations at that time. Exact mathematical solutions for distribution of compounds in the body could only be obtained for simplified models in which the body was reduced to a small number of compartments that did not correspond directly with specific physiological compartments. Over the next 30 years, modeling of drugs focused on these simpler descriptions with exact solutions rather than on developing models more concordant with the structure and content of the biological system itself. These approaches are sometimes referred to as “data-based” compartmental modeling since the work generally took the form of a detailed collection of time-course blood/excreta concentrations at various doses. Time-course curves were analyzed by assuming particular model structures and estimating a small number of model parameters by curve fitting. In the earliest of these models, all processes for metabolism, distribution, and elimination were treated as first-order rates (i.e., rates changed in direct proportion to the concentration of the chemical species). In the 1960s and early 1970s concerns were raised about the ability of data-based compartmental modeling to account for (i) the saturation of elimination pathways and (ii) the possibility that blood flow, rather than metabolic capacity of an organ, might limit the clearance of a chemical. Saturation of elimination led to models that were not first-order, making it difficult to derive exact solutions to the sets of equations, while blood flow–limited metabolism in an organ meant that the removal rate constant from a central compartment could not increase indefinitely as the metabolic capacity increased. Scientists trained in chemical engineering and computational methods developed more complicated, physiologically based pharmacokinetic (PBPK) models for chemotherapeutic compounds. Many of these compounds are highly toxic and have therapeutic efficacy by being slightly more toxic to rapidly growing cells (i.e., cancer cells) than to normal tissues. The more complete physiological structure of the models allowed the investigators to determine the impact of different dosing scenarios to maximize efficacy in the tumor while minimizing toxicity to other tissues. These seminal contributions showed the ease with which realistic descriptions of physiology and relevant pathways of metabolism could be incorporated into PBPK models and paved the way for their more extensive use for both pharmaceutical and environmental compounds. Today, there are three major types of computation models used for the analysis of biokinetic data: noncompartmental analysis (NCA), classical compartmental models similar to those described earlier, and PBPK models. NCA is widely used in the pharmaceutical industry for the analysis of single-dose PK data and PK data generated during safety studies. NCA, which involves calculating parameters such as volume of distribution (Vss), clearance (CL), area under the plasma concentration curve (AUC), and peak plasma concentration (Cmax), based solely on experimental data (i.e., these calculations are model-independent), is a convenient way to understand, tabulate, and compare the PK properties of compounds. However, NCA results cannot be used to extrapolate to other exposure conditions. Classical compartmental models can be used to perform simulations (e.g., use data generated from one exposure condition to simulate a different exposure condition). For example, a compartmental model parameterized with data from a single exposure can be used to predict the expected behavior for repeated exposure, assuming there is no change in the TK of the chemical over the period of the exposure. Standard software packages often provide flexible tools for developing one-, two-, and three-compartmental models from time-course plasma concentrations, and provide statistical tools for discriminating between models. However, the parameters and compartments in compartmental models have no physiological meaning and provide no basis for extrapolating from the conditions of the experimental data used to develop the model (e.g., to a different exposure route or a different species). PBPK models differ from classical compartmental models in that they include specific compartments for tissues involved in exposure, toxicity, biotransformation, and clearance processes. Tissues are connected by blood flow and compartments and blood flows are described using physiologically meaningful parameters. Figure 3.1 illustrates the structure of a simple PBPK model for a volatile, lipophilic compound—styrene. As with compartmental models, PBPK models can be used to simulate a variety of conditions. However, because PBPK models utilize realistic parameters for tissue volumes and kinetic processes, they can be used for extrapolation across doses, exposure routes, and even species. PBPK modeling has been used to great effect for interspecies extrapolation, both among animal models and for predicting human kinetics based on animal data. The mechanistic basis of PBPK models allows for applications such as understanding species differences in target tissue chemical exposure, determining if results from different experimental designs are consistent, and exploring possible mechanisms responsible for unexpected or unusual data. These attributes have led to widespread development of PBPK models in recent years. Figure 3.1 Diagram of a physiologically based pharmacokinetic (PBPK) model for styrene. In this description, groups of tissues are defined with respect to their volumes, blood flows (Q), and partition coefficients for the chemical. The uptake of vapor is determined by the alveolar ventilation (QALV), cardiac output (QT), blood:air partition coefficient, and the concentration gradient between arterial and venous pulmonary blood (CART and CVEN). Metabolism is described in the liver with a saturable pathway defined by a maximum velocity (Vmax) and affinity (Km). The mathematical description assumes equilibration between arterial blood and alveolar air as well as between each of the tissues and the venous blood exiting from that tissue. Source: Adapted from Ramsey and Andersen (1984). PBPK models have many advantages over the more empirical descriptions of chemical kinetics (NCA, classical compartmental model), perhaps the most important of which is their greater predictive power. Since known physiological parameters are used, a different species can be modeled by simply replacing the appropriate constants with those for the species of interest or by allometric scaling (scaling proportional to body weight raised to an empirically determined power). Similarly, the behavior for a different route of administration can be determined by adding equations that describe the nature of the new input function. Another important benefit is the reduced need for extensive experiments with new compounds. Since measured physical-chemical and biochemical parameters are used, the behavior for new compounds can quickly be estimated by determining the appropriate constants for key processes, such as metabolism. The process of selecting the most informative experimental data is also facilitated by a predictive PBPK model. Fundamentally, physiologically based models provide a conceptual framework for employing the scientific method: hypotheses can be described in terms of biological processes, quantitative predictions can be made on the basis of the mathematical description, and the model (hypothesis) can be revised on the basis of comparison with targeted experimental data. The trade-off for the greater predictive capability of physiologically based models is the requirement for an increased number of parameters and equations compared to the more empirical models. However, values for many parameters, particularly physiological parameters, are readily available in the literature. Furthermore, many in vitro techniques have been developed for rapid determination of compound-specific parameters, such as those describing tissue partitioning and metabolism. An important advantage of PBPK models is that they provide a biologically meaningful quantitative framework wherein in vitro data can be more effectively utilized to predict in vivo TK. There is even a prospect that predictive PBPK models can be developed based almost entirely on data obtained from in vitro studies and quantitative structure–activity relationship (QSAR) modeling, eliminating the need for the use of animals in TK analyses. This effort to eliminate the need for animal-based kinetic studies through the use of PBPK models, QSAR modeling, and in vitro data collection is generally referred to as “in vitro to in vivo extrapolation,” or IVIVE. PBPK models are often developed in support of chemical risk assessments. A properly validated PBPK model can be used to perform the high- to low-dose, dose-route, and interspecies extrapolations that are necessary for estimating human risk from toxicology studies in laboratory animals (e.g., in vivo hazard studies). PBPK models are also used for examining the effects of changing physiology on target tissue dosimetry, as in the case of early life exposure where rapid organ growth and development of important metabolic enzymes affect chemical kinetics. Target tissue dosimetry provided by PBPK modeling is also an essential component in models of chemical-induced tissue effects (PD), such as acetylcholinesterase inhibition. The rate of change in mass of chemical per unit of time (dA/dt) for a kinetic process is described in terms of concentration (C) rather than amount (A), since the free concentration of a chemical is the driving force for its kinetics. The “order” of the process refers to the power to which concentration is raised in the kinetic equation. The qualities of zero-, first-, and second-order rates are described here. Figure 3.2 Zero-order reaction. Figure 3.3 First-order reaction. An example of a second-order biokinetic process is the conjugation of a chemical with glutathione, which depends on both the concentration of the chemical and the concentration of glutathione. Under typical physiological conditions the concentration of glutathione is relatively large (several millimolar), such that the effect of the conjugation reaction on its concentration is negligible. The rate is then referred to as “pseudo-first order,” since it is approximately proportional to the concentration of the chemical alone (dA/dt = k2 × C1 × C2 × V ≈ k1 × C2 × V, where k1 = k2 × C1). However, if the conjugation reaction results in a decrease in the concentration of glutathione, the true second-order rate equation must be used. where Vmax (the enzyme capacity) is the maximum rate (amount per time); and Km (the enzyme affinity) is the concentration (amount per volume) at which the rate is half Vmax. Figure 3.4 Capacity-limited reaction. Classical compartmental modeling is largely an empirical exercise, where data on the time course of the chemical of interest in blood (and perhaps other tissues) are collected. Based on the behavior of the data, a mathematical model is selected, which possesses a sufficient number of compartments (and therefore parameters) to describe the data. The compartments do not generally correspond to identifiable physiological entities but rather are abstract concepts with meaning only in terms of a particular calculation. In a one-compartmental model, all of the compound in the tissues is assumed to be in equilibrium with the blood. If there is evidence of a storage depot for the chemical (e.g., the fat for a lipophilic compound), a second compartment can be added to the model and rate constants for transport between the central and deep compartments can be estimated from the data. Using a one-compartment description, the change in serum concentration (Cs, mg/l) resulting from a given dose rate (D, mg/kg/day) is: where Vd = apparent volume of distribution (fraction of body weight; l/kg); and k = rate constant for elimination (day−1) = 0.693/t1/2 where 0.693 is the natural logarithm of 2, the factor by which the concentration changes over one half-life. For one-compartment kinetics, the concentration of a compound at steady state (Css) is related to the daily intake (D) by the clearance of the compound, which in turn is related to the half-life (t1/2) and volume of distribution (Vd). At steady state, Therefore, to convert a blood concentration to an intake rate, both the half-life and the volume of distribution must be experimentally determined. The kidney removes chemicals from circulating blood by filtration. The liver removes chemicals from the circulating blood by metabolism. With each of these organs, we can describe the function of the organ in terms of “clearances.” In this usage, clearance is a volumetric flow of blood (for instance, liters/hour) from which all chemical is removed. All clearances are expressed as liters/hour or as an equivalent flow term. For any particular compartment we can speak of clearance by several different processes, including: For the kidney, urinary clearance (Clurine) is estimated by the ratio of the total amount of chemical excreted in the urine over a given time interval divided by the blood concentration and duration of collection. Thus, urinary clearance becomes the volumetric flow of blood from which the chemical would have to be completely removed to account for the observed excretion into the urine. Another useful concept is extraction, that is, the proportion of blood flow from which all chemical is removed during a single pass through the organ. From the example with the kidney, extraction can be related to clearance and blood flow to the kidney (Qkidney). A great deal of work and analysis has been conducted to describe the removal of drugs and toxicants by metabolism in the liver in relation to extraction and clearance. The major relationships are similar to those for the kidney. For the case where extraction is due to metabolism, the clearance at low substrate concentrations is readily expressed in relation to liver blood flow (Qliver) and the kinetic parameters for metabolism, Vmax and Km. As with the kidney, the interpretation for liver clearance is the volumetric flow of blood from which the chemical would have to be completely removed to account for the extraction. In a PBPK model the parameters in this equation correspond to measurable biological and biochemical entities. Qliver is the actual liver blood flow (l/h), Vmax is the maximum capacity of the metabolizing enzyme (l/h), and Km is the affinity (mg/l). Both of the kinetic parameters can be estimated directly by in vitro experiments. In deriving these parameters from compartmental PK models, we can also talk about clearance of compounds from the central compartment by the liver metabolism, although the parameters no longer correspond to their biological or biochemical counterparts. A one-compartmental model with metabolic elimination in the liver is expressed in terms of the amount in the compartment (A1), the volume of distribution (Vd,1), and the concentration in the compartment (C1). The mass balance equation for the change in amount in the compartment can be written in several equivalent forms. In the last formulation, the loss of chemical from the system over time is liver clearance multiplied by the concentration in the central compartment. If there are other organs that are involved in removal, that is, in filtration by the kidney or in exhalation by the lungs, the equation is simply altered to account for the sum of all the clearances. By far, most of the metabolism of a compound occurs in the liver. In the standard description of clearance of a drug compound from blood by liver metabolism, binding in the blood is assumed to be linear and the fraction unbound (fub), which is assumed to be the fraction available for metabolism, is simply multiplied by the intrinsic hepatic clearance, Clint, leading to a straightforward relationship: In this relationship, the maximal hepatic clearance, even with a low fraction unbound, is total tissue blood flow, QL. That is, all of a compound in the blood, whether bound or free, becomes available for clearance as long as the intrinsic clearance is sufficiently large. Note that in this description the fraction unbound is not a function of the clearance. If the uptake of a compound into the metabolizing tissue is limited by the rate of dissociation of the compound from binding proteins in the blood or the rate of uptake into the tissue (referred to as restrictive clearance), the simple formula given earlier may overestimate its clearance. In the limit, the clearance for an irreversibly bound chemical would be: On the other hand, if dissociation and hepatocellular uptake are fast compared to the rate of clearance, the limiting behavior (nonrestrictive clearance) is given by: Most modeling of environmental chemicals typically assumes that the clearance is nonrestrictive; that is, all of the compound in the blood entering the liver is assumed to be available for metabolism. In the case of oral exposure, the concentration of a chemical is determined by the ratio of the dose rate (mg/kg/day) to the sum of all clearances. For a chemical that is cleared by hepatic metabolism and urinary excretion, the resulting equation would be: In this equation, the term GFR × fub represents the renal excretion of unbound parent compound in blood by glomerular filtration, where GFR is the glomerular filtration rate, which is about 6.7 l/h in human adults, and fub is the fraction of the drug in the blood that is unbound (free). The second term in the denominator is hepatic clearance, where QL is liver blood flow (typically on the order of 90 l/h in adults) and Clint is the intrinsic metabolic clearance for first-order conditions of metabolism in the liver at low concentrations. The basic approach to PBPK model development is illustrated in Figure 3.5. The process of model development begins with the identification of the chemical exposure and toxic effect of concern, as well as the species and target tissue in which the toxic effect is observed. Literature evaluation involves the integration of available information about (i) the mechanism of toxicity, (ii) the pathways of chemical metabolism, (iii) the nature of the toxic chemical species (i.e., whether the parent chemical, a stable metabolite, or a reactive intermediate produced during metabolism is responsible for the toxicity), (iv) the processes involved in absorption, transport, and excretion, (v) the tissue partitioning and binding characteristics of the chemical and its metabolites, and (vi) the physiological parameters (i.e., tissue weights and blood flow rates) for the species of concern (i.e., the experimental species and the human). Using this information, the investigator develops a PBPK model that expresses mathematically a conception of the animal/chemical system. In the spirit of the scientific method, model building is an iterative process. The literature includes many examples of successful PBPK models for a wide variety of compounds that provide a wealth of insight into various aspects of the PBPK modeling process. These published models should be consulted for further detail on the approach for applying the PBPK methodology in specific cases. This chapter will discuss general considerations in model development, validation, and application. Figure 3.5 PBPK modeling approach. In the model, the various time-dependent chemical transport and metabolic processes are described as a system of simultaneous differential equations. Generally, these differential equations describe the rate of change in the amount of chemical in a particular compartment (tissue, blood) over time. Integration of these differential equations gives an estimate of the amount of chemical in the tissue at any one time, which then allows the calculation of chemical concentration in the tissue using real tissue volumes. As an example, the differential equation defining the liver compartment in Figure 3.1 is shown here: where AL = the amount of chemical in the liver (mg); CArt = the concentration of chemical in the arterial blood (mg/l); CL = the concentration of chemical in the liver (mg/l); QL = the total (arterial plus portal) blood flow to the liver (l/h); PL = the liver:blood partition coefficient (concentration ratio at equilibrium); Vmax = the maximum rate of metabolism (mg/h); Km = the affinity (concentration at half-maximum rate of metabolism) (mg/l). The specific structure of a particular model is driven by the need to estimate the appropriate measure of tissue dose under the various exposure conditions of concern in both experimental animals and humans. Before the model can be used in risk assessment, it must be validated against kinetic, metabolic, and toxicity data and, in many cases, refined based on comparison with the experimental results. The model itself is frequently used to help design critical experiments to collect data needed for its own validation. Refinement of the model to incorporate additional insights gained from comparison with experimental data yields a model that can be used for quantitative extrapolation well beyond the range of experimental conditions on which it was based. There is no easy rule for determining the structure and level of complexity needed in a particular modeling application. For example, model elements such as inhalation and fat storage, which are important for a volatile, lipophilic chemical such as styrene, do not need to be considered in the case of a nonvolatile, water-soluble compound. Similarly, while kidney excretion and enterohepatic recirculation are important determinants of the kinetics for many compounds, they are not needed in the model of styrene. As another example, the simple description of inhalation uptake as a one-compartment gas exchange (Figure 3.1) may be adequate for some model applications, as in the case of modeling the systemic uptake of a lipophilic vapor like styrene. However, a more complicated description is required in the case of water-soluble vapors, to account for a “wash-in, wash-out” effect (chemical absorbed in the upper respiratory tract during inhalation can be reentrained in exhaled air during the second half of the breathing cycle). Thus, the decision of which elements to include in the model structure for a specific chemical and application entails striking a balance between two primary criteria: (1) parsimony (keeping it as simple as possible) and (2) biological plausibility (adequately describing the important determinants of the chemical kinetics). After deciding which compartments to include in the model, decisions must be made regarding the description of the chemical kinetics, that is, transfer between blood and tissues, metabolism, and so on. Chemical transfer between the blood and tissue compartments may be governed by passive diffusion (flow- or diffusion-limited) or active transport. Many published PBPK models are flow-limited; that is, they assume that the rate of tissue uptake of the chemical is limited only by the flow of the chemical to the tissue in the blood. While this assumption is generally reasonable, for some chemicals and tissues the uptake may instead be limited by other factors such as diffusion. Examples of tissues for which diffusion-limited transport has often been described include the skin, placenta, mammary glands, brain, and fat. If there is evidence that the movement of a chemical between the blood and a tissue is limited by diffusion, a two-compartment description of the tissue can be used with a “shallow” exchange compartment in communication with the blood and a diffusion-limited “deep” compartment. Some chemicals may be transported against the concentration gradient through energy-dependent processes, rather than diffusion. These processes can result in high tissue:blood ratios for the chemical concentration and are sometimes limited by the availability of transporter proteins leading to saturation of chemical transport at high doses. Such saturable processes are often well-described using Michealis–Menten–type kinetics as discussed earlier for metabolism. The liver is frequently the primary site of metabolism, though other tissues such as the kidney, placenta, lung, skin, and blood may also be important metabolism sites depending on the chemical. Metabolism may be described as occurring through a linear (first-order) pathway using a rate constant (kF : h − 1) or a saturable (Michealis–Menten) pathway with capacity Vmax (mg/h) and affinity Km (mg/l). If necessary, the PK of the resulting metabolite may also be explicitly described in the model. Metabolite kinetics are typically described when the metabolite is the chemical species causing the observed toxicity. The same considerations that drive decisions regarding the level of complexity of the PBPK model for the parent chemical must also be applied for each metabolite model. As in the case of the parent chemical, the most important consideration is the purpose of the model. If the concern is direct parent chemical toxicity and the chemical is detoxified by metabolism, then there may be no need for a description of metabolism beyond its role in parent chemical clearance. If reactive intermediates produced during the metabolism are responsible for observed toxicity, a very simple description of the metabolic pathways might be adequate. On the other hand, if one or more of the metabolites are considered to be responsible for the toxicity of a chemical, it may be necessary to provide a more complete description of the kinetics of the metabolites themselves. Other processes that may have significant impact on the chemical kinetics, and may be included in the model, are protein binding and excretion. Protein binding in the blood reduces the amount of free chemical available for distribution into the tissues or clearance via excretion. Binding within tissues may lead to dose- and time-dependent accumulation, and may need to be described as a saturable process. Clearance may occur through urinary or fecal excretion, exhaled air, or even through loss via hair (as in the case of mercury). This loss may often be successfully described using first-order clearance terms. However, more elaborate descriptions are sometimes required for chemicals that are substrates for transport proteins that transfer the chemical against a concentration gradient. Some transporters in the kidney and bile can increase the clearance of xenobiotics, while others, such as those responsible for reabsorption, may decrease clearance. Estimates of the various physiological parameters needed in PBPK models are available from a number of sources in the literature, particularly for the human, monkey, dog, rat, and mouse. Table 3.1 shows typical values of a number of physiological parameters in adult animals. Table 3.1 “Typical” Physiological Parameters for PBPK Models a Scaled allometrically: QC = QCC × BW75. b Varies significantly with activity level (range: 15–40). c Varies with activity level (range: 15–25). d Varies substantially (lower in young animals, higher in older animals). Estimates for the same physiological parameter often vary widely across sources, due both to experimental differences and to differences in the animals examined (age, strain, activity). Ventilation rates and blood flow rates are particularly sensitive to the level of activity. Data on some important tissues are relatively limited, particularly in the case of fat tissues. Many biochemical parameters may be measured directly from in vitro studies. For volatile chemicals, for example, partition coefficients may be measured using a relatively simple in vitro technique known as vial equilibration. Partition coefficients for nonvolatile compounds are not as easily measured in vitro; however, and are therefore often estimated by comparing tissue:blood levels from in vivo studies. Metabolism parameters can be obtained from parent chemical disappearance (or metabolite formation) curves in cell suspensions, tissue homogenates, or microsomal fractions. Determination of urinary metabolites after in vivo exposure can also be useful for estimating metabolism parameters in some cases. In many cases, important parameter values needed for a PBPK model may not be available in the literature. In such cases it is necessary to measure them in new experiments, to estimate them by QSAR techniques, or to identify them by optimizing the fit of the model to an informative data set. The process of adjusting a subset of the model’s kinetic parameters to achieve the best agreement of the model simulation with measured tissue chemical concentrations is called “fitting” the model. An example of a case where fitting the model to kinetic data is the only practical approach for parameter estimation is the attempt to describe enterohepatic recirculation; that is, when a compound or its metabolite is transferred into the bile and subsequently reabsorbed from the intestine. Because enterohepatic recirculation is the result of several kinetic processes in the liver, bile, and GI tract, there is no system for measuring the process in vitro. As a result, model parameters for enterohepatic recirculation are generally determined by fitting the model to in vivo kinetic data. Even in cases where initial estimates of a particular parameter value can be obtained from other sources, it may be still desirable to refine the estimate by fitting in vivo data with the model. Of course, being able to uniquely identify parameters from a kinetic data set rests on two key assumptions: (1) the kinetic behavior of the compound under the conditions in which the data was collected is informative regarding the parameters being estimated, and (2) other parameters in the model that could influence the observed kinetics have been determined by other means and are held fixed or otherwise constrained during the estimation process. Typically, a PBPK model used in risk assessment applications will include compartments for any tissues in which toxicity has been observed with a given compound (i.e., target tissues). The description of the target tissue may in some cases need to be fairly complicated, including features such as in situ metabolism, binding, and PD processes (e.g., upregulation of metabolizing enzymes) in order to provide a realistic measure of biologically effective tissue exposure. A fundamental issue in determining the nature of the target tissue description required is identifying the active form of the compound. A compound may produce an effect directly through its interaction with tissue constituents or indirectly through a metabolite. Liver toxicity, in particular, is often caused by metabolism of the parent compound to reactive (short-lived) metabolites. Circulating metabolites may also lead to adverse effects in nonmetabolizing tissues. The specific nature of the relationship between tissue exposure and response depends on the mechanism, or mode of action, involved. Rapidly reversible effects may result primarily from acute compound concentrations in the tissue, while longer-term effects may depend on both the concentration and duration of the exposure. In fact, the appropriate measure of tissue exposure for one toxic effect of a compound may even be different from the appropriate measure for another of its effects. For example, the mitogenic effect of a compound may depend on the prolonged maintenance of a relatively high concentration sufficient to occupy a receptor in the target tissue, while cytoxicity may result from transient, high rates of metabolism occurring shortly after dosing. In such a case, PBPK modeling of the concentration time course in the target tissue for different dosing routes or regimens might be necessary. For developmental toxicity, windows of susceptibility must also be considered. That is, the fetus may be more susceptible to chemical toxicity during specific times in gestation that are associated with important developmental events (e.g., implantation, neural tube closure). Thus, the evaluation of the various modes of action for the beneficial and toxic effects of a compound is the most important step in a PK analysis and a principal determinant of the structure and level of detail that will be required in the PBPK model. As described in the previous sections, the process of developing a PBPK model begins by determining the essential structure of the model based on the information available on the compound’s toxicity, mechanism of action, and PK properties. The results of this step can usually be summarized by an initial model diagram, such as that depicted in Figure 3.1. In fact, a well-constructed model diagram, together with a table of the input parameter values and their definitions, is all that an accomplished modeler should need in order to recreate the mathematical equations defining a PBPK model. In general, there should be a one-to-one correspondence of the boxes in the diagram to the mass balance equations (or steady-state approximations) in the model. Similarly, the arrows in the diagram correspond to the transport or metabolism processes in the model. Each of the arrows connecting the boxes in the diagram should correspond to one of the terms in the mass balance equations for both of the compartments it connects, with the direction of the arrow pointing from the compartment in which the term is negative to the compartment in which it is positive. Arrows only connected to a single compartment, which represent uptake and excretion processes, are interpreted similarly. The previous sections have focused on the process of designing the PBPK model structure needed for a particular application. At this point the model consists of a number of mathematical equations—differential equations describing the mass balance for each of the compartments and algebraic equations describing other relationships between model variables. The next step in model development is the coding of the mathematical form of the model into a form which can be executed on a computer. There are many options available for performing this process, ranging from programming languages such as Fortran, C, and MatLab to more user-friendly simulation software packages such as AcslX and Berkeley Madonna. Model evaluation considers the ability of the model to predict the chemical’s kinetic behavior under conditions that test the principal aspects of the underlying model structure. This is generally performed by running the model and attempting to predict measured tissue concentrations from data sets that were not used for model development. Goodness of fit, or correspondence between the model-predicted concentrations and measured concentrations, can be evaluated visually (subjective evaluation) or quantitatively through the use of automated algorithms that are available in most simulation software packages. While quantitative tests of goodness of fit may often be a useful aspect of the evaluation process, the more important consideration may be the ability of the model to provide an accurate prediction of the general behavior of the data in the intended application. Thus, if the model shows some deviation from measured concentrations, yet can consistently reproduce the trend of the data (biphasic clearance, saturation of metabolism, etc.) there will be greater confidence in the suitability of the model structure than a model that fits a portion of the data flawlessly. Indeed, the demand that the PBPK model fit a variety of data with a consistent set of parameters limits its ability to provide an optimal fit to a specific set of experimental data. For example, a PBPK model of a compound with saturable metabolism is required to reproduce both the high- and low-concentration behaviors, which appear qualitatively different, using the same parameter values. If one were independently fitting single curves with a model, different parameter values might provide better fits at each concentration, but would be relatively uninformative for extrapolation. Ideally, model performance should be evaluated against data in the species, tissues and exposure scenarios of concern to risk assessors. However, it is not always possible to collect the data needed for such evaluation, particularly in humans. Where only some aspects of the model can be evaluated, it is particularly important to assess the uncertainty associated with those aspects that are untested. For example, a model of a chemical and its metabolites that is intended for use in cross-species extrapolation to humans would preferably be verified using data in different species, including humans, for both the parent chemical and the metabolites. If only parent chemical data is available in humans, the correspondence of metabolite predictions with data in several animal species could be used as a surrogate, but this deficiency should be carefully considered when applying the model to predict human metabolism. One of the values of biologically based modeling is the ability to use in vitro data to set model parameters, such as enzyme activity and substrate binding assays, which would improve the quantitative prediction of toxicity in humans from animal experiments. Finally, it is important to remember that in addition to comparing model predictions to experimental data, model evaluation involves assessing the plausibility of the model structure and parameters and the confidence that can be placed in extrapolations performed by the model. This aspect of model evaluation is particularly important in the case of applications in risk assessment, where it is necessary to assess the uncertainty associated with risk estimates calculated with the model. The process of assessing health risks associated with human exposure to environmental chemicals inevitably relies on a number of assumptions, estimates, and rationalizations. Some of the greatest challenges in risk assessment result from the need to extrapolate from the conditions in the studies providing evidence of the toxicity of the chemical to the anticipated conditions of human exposure in the environment or workplace. For risk assessments based on animal data, the most obvious extrapolation that must be performed is from the tested animal species to humans. However, other extrapolations are also often required: from high dose to low dose, from one exposure route to another, and from one exposure time frame to another. PBPK modeling provides a powerful method for increasing the accuracy of these extrapolations. The inherent capabilities of PBPK modeling are particularly advantageous for cross-species extrapolation: physiological and biochemical parameters in the model can be changed from those for the test species to those which are appropriate for humans in order to provide a biologically meaningful animal to human extrapolation. Nonetheless, a full PBPK model may not always be necessary to support a PK risk assessment; in some cases (particularly those where human data are available) only a simple compartmental PK description is needed. Simple PK approaches have sometimes been used by regulatory agencies in cancer risk assessment. However, the first case where an agency used a full PBPK approach was in the U.S. Environmental Protection Agency’s (USEPA) revision of its inhalation cancer risk assessment for methylene chloride. In 1989, the USEPA revised the inhalation unit risk and risk-specific air concentrations for methylene chloride in its Integrated Risk Information System (IRIS) database, citing a published PBPK model for the chemical. The resulting risk estimates were lower than those obtained by the USEPA’s default approach by more than a factor of 10. That is, using the PBPK model, they determined that methylene chloride presented a substantially lower risk to humans than was predicted by the standard risk assessment calculations. Subsequently, an adaptation of the same PBPK model was used by the Occupational Safety and Health Administration in their rulemaking for a permissible exposure level (PEL) for methylene chloride. PBPK modeling has since become standard practice in risk assessment. The ultimate aim of using PK modeling in risk assessment is to provide a measure of dose (dose metric) that better represents the “biologically effective dose”; that is, the dose that causally relates to the toxic outcome. The improved dose metric can then be used in place of traditional dose metrics (such as inhaled air concentrations or absorbed dose) in an appropriate dose–response model to provide a more accurate extrapolation to the human exposure conditions of concern. Implicit in any application of PK to risk assessment is the assumption that the toxic effects in the target tissue must be related to the concentration of the active form(s) of the chemical in that tissue. Moreover, in the absence of PD differences between animal species, it is expected that similar responses will be produced at equivalent tissue exposures regardless of species, exposure route, or experimental regimen. The motivation for applying PK in risk assessment, then, is the expectation that the observed effects of a chemical will be more simply and directly related to a measure of target tissue exposure than to a measure of administered dose. The specific nature of the relationship between target tissue exposure and response depends on the chemical mechanism of toxicity, or mode of action, involved. Many short-term, rapidly reversible toxic effects, such as acute skin irritation or acute neurological effects, may result primarily from the current concentration of the chemical in the tissue. In such cases, the likelihood of toxicity from a particular exposure scenario can be conservatively estimated by the maximum concentration (Cmax) achieved in the target tissue. On the other hand, the acute toxicity of highly reactive chemicals, as well as many longer-term toxic effects such as tissue necrosis and cancer, may be cumulative in nature, depending on both the concentration and duration of the exposure. A simple metric for such cases is the AUC in the tissue, which is defined mathematically as the integral of the concentration over time. This mathematical form implicitly assumes that the effect of the chemical on the tissue is linear over both concentration and time. The use of the AUC represents an extension of “Haber’s Law,” a concept developed from observations of the effects of chemical warfare gases that toxicity is proportional to the product of the concentration and time of exposure (C × T). As stated previously, however, fetal effects will be determined by the chemical concentration and duration of exposure, as well as the gestational time period in which the exposure occurs. Another complicating factor in describing the relationship between chemical concentration and tissue response is the need to determine the toxicologically active form of the chemical. In some cases, a chemical may produce a toxic effect directly, either through its reaction with tissue constituents (e.g., ethylene oxide) or by its binding to cellular control elements (e.g., dioxin). Often, however, it is the metabolism of the chemical that leads to its toxicity. In this case, toxicity may result primarily from reactive intermediates produced during the process of metabolism (e.g., chlorovinyl epoxide produced from the metabolism of vinyl chloride (VC)) or from the toxic effects of stable metabolites (e.g., trichloroacetic acid produced from the metabolism of trichloroethylene). The selection of the dose metric, that is, the active chemical form for which tissue exposure should be determined and the nature of the measure to be used, for example, peak concentration (Cmax) or AUC, is the most important step in applying PK in risk assessment. Whether intended or not, any dose metric will be consistent with the modes of action for some chemicals, and not for others. The USEPA, in a joint effort with scientists from several other agencies, prepared a review paper on cross-species extrapolation in cancer risk assessment, which concluded that “tissues experiencing equal average concentrations of the carcinogenic moiety over a full lifetime should be presumed to have equal lifetime cancer risk.” The use of the term “carcinogenic moiety” in this statement reflects the concern that the dose metric should be representative of the active form of the chemical. For example, the use of the lifetime average daily concentration for the parent chemical might be appropriate for a directly genotoxic chemical such as ethylene oxide, which is detoxified by metabolism; however, it would not be appropriate for a chemical like VC, which requires metabolic activation to be genotoxic. In the latter case, increasing metabolism would increase the exposure to the genotoxic species but would decrease a dose metric based on parent chemical concentration. In such a case, where a reactive species produced during the metabolism of a chemical is responsible for its carcinogenicity, an appropriate cancer dose metric would be the lifetime average daily amount of metabolism in the target tissue divided by the volume of the tissue, as was used in the PK risk assessment for methylene chloride. Similar considerations apply in the case of noncancer risk assessment, except that the dose metrics are only averaged over the duration of the exposure (acute, subchronic, or chronic), not over a full lifetime. The plausibility of a given dose metric is determined primarily by two factors: (1) its consistency with available information on the mode of action (mechanism of toxicity), and (2) the consistency of its dose–response with that of the end point of concern. The first factor has been discussed earlier; the second factor refers both to evaluating the dose metric’s ability to linearize the dose–response for the associated end point within a study (internal consistency), and to its ability to demonstrate a consistent quantitative relationship of dose metrics for positive versus negative exposures, regardless of differences in exposure scenario, route, and species (external consistency). When it became evident that VC was carcinogenic both in animals and in humans, many of its uses were discontinued. The current use of VC is limited to serving as a chemical precursor in the production of such materials as polyvinyl chloride (PVC) and copolymer resins. However, VC is also produced from the biodegradation of another environmental chemical—trichloroethylene—by bacteria in the soil. Thus, past spills of trichloroethylene may lead to current or future exposures of the public to VC in drinking water or other environmental sources. The previous potency estimates for VC published by the USEPA did not quantitatively incorporate PK information on VC into the risk calculations. To provide a more accurate assessment of human risk from exposure to VC, a PBPK model was developed that describes the uptake, distribution, and metabolism of VC in mice, rats, hamsters, and humans following inhalation or oral exposure. The PBPK model was used to predict the total production of reactive metabolites from VC both in the animal bioassays and in human exposure scenarios. These measures of internal exposure were then used to predict the risk associated with lifetime exposure to VC in air or drinking water. The PK risk assessment for VC demonstrated all of the attributes of an effective dose metric. First, the form of the metric (total daily metabolism divided by the volume of the liver) was consistent with the mode of action for the end point of concern (liver tumors), which involves DNA adduct formation by a highly reactive chloroethylene epoxide produced from the metabolism of VC. Second, while the dose–response for liver tumors versus exposure concentration of VC is highly nonlinear, with a plateau at several hundred ppm, the dose–response for liver tumors versus the metabolized dose metric is essentially linear from 1 to 6000 ppm. Finally, and most impressively, when the potency of VC liver carcinogenicity was expressed in terms of the metabolized dose metric, essentially the same potency was calculated from both inhalation and oral studies in the mouse and rat, as well as from occupational inhalation exposures in the human. Thus, PBPK models can support more accurate prediction of air and water concentrations that are likely to significantly increase the risk of cancer in the human population based on animal studies by eliminating factors (species differences in metabolism) that could confound such extrapolations. Risk assessments have typically applied default factors to account for uncertainty regarding animal to human extrapolation and human variability. That is, when significant uncertainty exists in an aspect of the risk estimate, factors are applied in order to make it more conservative. These uncertainty factors are not based on data, but rather on the assumption that decreasing exposure by a factor of 10–1000 will account for the different types of uncertainty (interspecies or intraspecies differences in TK or TD) in the risk assessment process. Significant progress has been made in recent years in refining this approach beyond the use of default uncertainty factors. An important step forward in the development of approaches for incorporating chemical-specific data in risk assessment is the recent guidance from the International Programme for Chemical Safety (IPCS) addressing the data requirements for replacing default uncertainty factors with chemical-specific adjustment factors (CSAFs). The IPCS CSAF approach breaks the inter- and intraspecies uncertainty factors into TK and TD components, each of which can be replaced by a CSAF if adequate chemical-specific data are available. The TK factor for interspecies differences (AKUF) represents the ratio of the external exposures in humans and animals that would produce the identical internal (target tissue) exposures. Similarly, the TK factor for human variability (HKUF) represents the ratio of the doses in average and sensitive individuals that would produce the identical internal (target tissue) exposure. Depending on the data available for the chemical, the magnitude of the adjustment factor for TK may be calculated based on a variety of biokinetic factors, such as the clearance of the chemical or the AUC for the chemical. For example, a cross-species TK adjustment factor for boric acid has been estimated by USEPA on the basis of the ratio of glomerular filtration rates in animals and humans. PBPK models can also be used to estimate the adjustment factors for TK, as described in the example here. The calculation of a CSAF for interspecies differences in TK, AKUF, for 2-butoxyethanol provides a good example of the approach and considerations required for the IPCS methodology. In the case of 2-butoxyethanol, several PBPK models had been developed that could be used to determine the cross-species adjustment for TK. In fact, it would be difficult to determine the AKUF in this case without a PBPK model. This is because the best animal data available to support the calculation of an AKUF consist of AUCs of 2-butoxyacetic acid in the blood of rats exposed to 2-butoxyethanol by inhalation for 6 h; however, the AUCs were reported for the postexposure period only. Therefore, it was necessary to estimate the total AUC using a PBPK model, by integrating the predicted concentration of 2-butoxyacetic acid in venous blood both during and following an inhalation exposure of 6 h. Using the rodent PBPK model, Health Canada determined that the AUC during the exposure period was actually on the same order as the AUC reported for the postexposure period. Thus, use of the reported AUCs would result in a factor of two errors in estimating the AKUF. Use of the human data in the calculation of an AKUF was also problematic, because the exposures were conducted under exercising conditions. Analyses performed with the human PBPK model indicated that the uptake of the parent compound is linearly related to the ventilation rate. Therefore, the AUC value in this study was adjusted to account for working versus resting conditions using the results of the human PBPK model. Note that the effect of ventilation rate on the highly soluble 2-butoxyethanol contrasts with the case of poorly soluble, lipophilic compounds, where ventilation rate has little impact on uptake. Thus, different adjustment factors would be calculated for each of these compounds, rather than using the same default adjustment factor in both cases. One of the more challenging issues that must be considered in performing a human health risk assessment is the heterogeneity among humans. This heterogeneity is produced by interindividual variations in physiology, biochemistry, and molecular biology, reflecting both genetic and environmental factors, and results in differences among individuals in the biologically effective tissue dose associated with a given environmental exposure (PK) as well as in the response to a given tissue dose (PD). This interindividual variability is not as evident in animal studies, where breeding and environmental controls limit within-study differences. Because the parameters in a PBPK model have a direct biological correspondence, they provide a useful framework for determining the impact of observed variations in physiological and biochemical factors on the population variability in dosimetry within the context of a risk assessment for a particular chemical. It is useful to consider the total variability among humans in terms of three contributing sources: (1) the variation across a population of “normal” individuals at the same age, for example, young adults; (2) the variation across the population resulting from their different ages, for example, infants or the elderly; and (3) the variation resulting from the existence of subpopulations that differ in some way from the “normal” population, for example, due to genetic polymorphisms. A fourth source of variability, health status, should also be considered, although it is frequently disregarded in environmental risk assessment. To the extent that the variation in physiological and biochemical parameters across these population dimensions can be elucidated, PBPK models can be used together with Monte Carlo methods to integrate their effects on the in vivo kinetics of a chemical exposure and predict the resulting impact on the distribution of risks (as represented by target tissue doses) across the population. There has sometimes been a tendency in risk assessments to use information on the variability of a specific parameter, such as inhalation rate or the in vitro activity of a particular enzyme, as the basis for expectations regarding the variability in dosimetry for in vivo exposures. However, whether or not the variation in a particular physiological or biochemical parameter will have a significant impact on in vivo dosimetry is a complex function of interacting factors. In particular, the structures of physiological and biochemical systems frequently involve parallel processes (e.g., blood flows, metabolic pathways, excretion processes), leading to compensation for the variation in a single factor. Moreover, physiological constraints may limit the in vivo impact of variability observed in vitro. For instance, high-affinity intrinsic clearance can result in essentially complete metabolism of all the chemical reaching the liver in the blood; under these conditions, variability in amount metabolized in vivo would be more a function of variability in liver blood flow than variability in metabolism in vitro. Thus it is often true that the whole (the in vivo variability in dosimetry) is less than the sum of its parts (the variability in each of the PK factors). The dosimetric impact of variations in physiological factors also depends on the nature of the chemical causing the toxicity, including such physicochemical properties as reactivity, lipophilicity, water solubility, and volatility. For example, variations in inhalation rate will tend to have more impact on the uptake of a water soluble chemical such as isopropanol than on a relatively water insoluble chemical such as VC. In addition, the impact of a particular factor on dosimetry also depends on the mode of action of the chemical; that is, how the chemical causes the effect of concern. Of particular importance is whether the toxicity results from exposure to the chemical itself, one of its stable, circulating metabolites, or a reactive intermediate produced during its metabolism. Another key issue is whether the toxicity results from direct reaction with tissue constituents, from binding to a receptor, or from physical (e.g., solvent) effects on the tissue. To illustrate these considerations, one can contrast the acute neurotoxicity of many solvents (a physical effect of the chemicals themselves) with their chronic hepatotoxicity (produced by products of their metabolism). The most important PK factor in the acute toxicity of volatile solvents is the blood:air partition coefficient, and increasing metabolic clearance typically decreases toxicity. In contrast, the most important PK factors in the chronic toxicity are liver blood flow and metabolism, and increasing metabolic clearance typically increases toxicity. The following example illustrates the use of PBPK modeling to investigate the impact of PK variability on risk for the case of age-dependent PK. Specifically, the question being evaluated in this example is how normal changes in PK parameters from birth, through childhood and adulthood affect the dosimetry for environmental chemical exposures. To this end, a PBPK model was developed to simulate the physiological and biochemical changes in humans associated with growth and aging. In the age-dependent model, all physiological and biochemical parameters change over time based on data from the literature. Figure 3.6 shows the results of using this age-dependent model to simulate continuous inhalation of isopropanol at air concentrations of 1 ppb, beginning at birth and continuing for 75 years. The model predicts that, for the same inhaled concentration, the blood concentrations of isopropanol and its metabolite, acetone, achieved during early life are significantly higher than those achieved during adulthood. The capacity for metabolism is reduced in the infant compared to older children and adults. Figure 3.6 Blood concentrations of isopropanol (IPA) and its metabolite acetone as a function of age for continuous inhalation exposure at 1 ppb. Source: Adapted from Clewell et al. (2004).
TOXICOKINETICS
3.1 INTRODUCTION
Absorption, Distribution, Metabolism, and Elimination
Absorption
Distribution
Metabolism
Elimination
Toxicokinetic Modeling
3.2 TOXICOKINETIC MODELING FUNDAMENTALS
Kinetic Processes
Compartmental Analysis
Clearance Modeling
Renal (Kidney) Clearance
Hepatic (Liver) Clearance
Restrictive and Nonrestrictive Hepatic Clearance
PBPK Modeling
PBPK Model Structure
PBPK Model Parameters
Species
Mouse
Rat
Monkey
Human
Ventilation
Alveolar (l/h–1 kg)a
29.0b
15.0b
15.0b
15.0b
Blood flows
Total (l/h–1 kg)a
16.5c
15.0c
15.0c
15.0c
Muscle (fraction)
0.18
0.18
0.18
0.18
Skin (fraction)
0.07
0.08
0.06
0.06
Fat (fraction)
0.03
0.06
0.05
0.05
Liver (arterial) (fraction)
0.035
0.03
0.065
0.07
Gut (portal) (fraction)
0.165
0.18
0.185
0.19
Other organs (fraction)
0.52
0.47
0.46
0.45
Tissue volumes
Body weight (kg)
0.02
0.3
4.0
80.0
Body water (fraction)
0.65
0.65
0.65
0.65
Plasma (fraction)
0.04
0.04
0.04
0.04
RBCs (fraction)
0.03
0.03
0.03
0.03
Muscle (fraction)
0.34
0.36
0.48
0.33
Skin (fraction)
0.17
0.195
0.11
0.11
Fat (fraction)
0.10d
0.07d
0.05d
0.21
Liver (fraction)
0.046
0.037
0.027
0.023
Gut tissue (fraction)
0.031
0.033
0.045
0.045
Other organs (fraction)
0.049
0.031
0.039
0.039
Intestinal lumen (fraction)
0.054
0.058
0.053
0.053
Target Tissue Considerations
Interpreting a PBPK Model Diagram
Running a PBPK Model
Evaluating a PBPK Model
3.3 APPLICATIONS OF TOXICOKINETICS
Risk Assessment
Example of Cancer Risk Assessment with a Toxicokinetic Model: Vinyl Chloride
Chemical-Specific Adjustment Factors
Example of the Calculation of a CSAF Using a PBPK Model
Interindividual Variability
Determinants of Impact
Example: Age-Dependent Variability
Stay updated, free articles. Join our Telegram channel
Full access? Get Clinical Tree
