Pharmacokinetic models describe the absorption, distribution, metabolism, and elimination of a chemical in an organism. Depending on the complexity of a pharmacokinetic model and the available data upon which it is based, the model can be used to predict the concentration of a parent chemical and metabolite(s) in various tissues, organs, cells, and subcellular compartments given any particular exposure pattern over time. Because target organ doses are more relevant to toxicity than the amount of exposure at a particular exterior boundary, pharmacokinetic models may be useful for assessing human health risk from exposure to a chemical or mixture of chemicals with shared metabolic pathways.
In keeping with the committee charge, this chapter discusses key scientific issues regarding approaches for pharmacokinetic modeling of trichloroethylene based on existing metabolic information and uses of pharmacokinetic modeling results for trichloroethylene risk assessment. Discussion of approaches to pharmacokinetic modeling of trichloroethylene focuses on (1) the relative strengths and weaknesses of different model structures and parameterization, including the tradeoff between model complexity (and hence completeness) and uncertainty, and (2) the evaluation of model uncertainties. Discussion of the uses of pharmacokinetic modeling results for risk assessment of trichloroethylene focuses on (1) dose metrics for developing human equivalent doses, route-to-route extrapolation, and use in biologically based dose-response modeling; and (2) uncertainties associated with pharmacokinetic-based dose metrics and consideration of nonpharmacokinetic-based scaling approaches.
This chapter does not include an exhaustive review of the literature on
pharmacokinetic models for trichloroethylene. The pharmacokinetic models used in the U.S. Environmental Protection Agency (EPA 2001b) draft health risk assessment of trichloroethylene, several of the pharmacokinetic models published since that assessment, and a model later commissioned by EPA and the U.S. Air Force (USAF) to deal with some problems of the earlier health risk assessment are the focus of this chapter.
OVERVIEW OF PHARMACOKINETIC MODELS
Pharmacokinetic models mathematically describe the absorption, distribution, metabolism, and elimination of a chemical in an organism as a function of time. Similar descriptions for metabolites also can be incorporated into pharmacokinetic models for the parent compound. Pharmacokinetic models typically include compartments that represent specific organs and tissues as well as lumped tissue compartments and are represented by using systems of differential equations. Whether a specific tissue compartment is included in a pharmacokinetic model depends on how involved that tissue is in disposing of the compound (e.g., portals of entry or excretion, sites of metabolism, targets of toxicity) and on its utility as a biomarker of exposure or response. Pharmacokinetic model development is an iterative process; the mathematical model is used to simulate data and the simulated data are compared with real data to refine the mathematical model. “All models are wrong, but some models are useful” (attributed to G. Box [Kokko 2005]). There will never be a comprehensive model that perfectly describes all the exposure and response relationships for any chemical in laboratory animals or humans, but some models may be adequate for predicting useful internal dose metrics, and some models may provide better predictions than others.
Physiologically based pharmacokinetic (PBPK) models define model parameters in terms of directly interpretable anatomic, physiologic, or biochemical quantities. In a basic PBPK model, the tissue compartments are linked by blood flow and have associated physical volumes and partition coefficients that describe the relative degree to which a given chemical (e.g., trichloroethylene) is soluble in each of those tissues versus blood. Although the fundamental mathematical forms of pharmacokinetic and PBPK models with the same compartments may be identical, parameterization in terms of measurable physiologic quantities introduces several advantages (Gibaldi and Perrier 1982). For example, blood flow rates are well characterized in many species, providing a simple and rational method for adjusting a PBPK model to extrapolate across species (e.g., from laboratory animals to humans). Moreover, direct measurements can be independently obtained for some PBPK parameters, rather than relying solely on the results of dosing experiments.
The complexity of a pharmacokinetic model depends on the availability of data, the certainty and confidence in the scientific understanding of the processes described by the model, and the intended use of the model. In general, one begins with the simplest model that describes the data and adds complexity to the structure based on experimental data, lack of model fit to the data, and lack of model applicability to a specific end point of interest. For example, if one is interested only in evaluating the concentration of the parent compound in blood and other tissues over time, the model structure can be very simple. Disappearance of the parent chemical may be described by a “whole-body” metabolism rate and details on different metabolic pathways are not necessary. Pharmacokinetic models are powerful tools that can be used to identify data gaps and research needs. As mechanistic hypotheses are developed, modifications to the model may be necessary to describe a more appropriate dose metric. For example, if one is interested in looking at the effects of a putative toxic metabolite on a specific organ (e.g., kidney), the model structure will likely be more complex.
To account for total body mass (and volume) and total cardiac output (flow), pharmacokinetic models typically include “lumped” tissue compartments that are not relevant to describe a particular chemical. For example, brain, muscle, and skin are usually not included as discrete compartments unless those tissue concentrations are direct targets for prediction (e.g., brain concentration for predicting neurotoxicity). Instead, tissues are lumped as richly (or rapidly) and poorly (or slowly) perfused tissue groups. The richly perfused tissue group typically includes organs and tissues such as the brain, kidney, and alveolar region of the lungs, and the poorly perfused group includes tissues such as muscle and skin.
Advantages and Limitations
PBPK models hold particular promise in assessing human health risks from multiple routes of exposure to the same chemical or from exposures to related chemical mixtures, because of their ability to predict doses at the tissues where relevant toxic effects occur. Traditional metrics such as the lifetime average daily dose fail to reflect differences in metabolism and disposition by exposure route, particularly when metabolic rates are saturable or when multiple exposures occur simultaneously. Theoretically, an accurate PBPK model is ideal for characterizing human health risk from a complex exposure pattern involving chemical mixtures, multiple exposure routes, saturable binding and metabolism, and any other situation resulting in a nonlinear relationship between the exposure metric and the target organ dose.
PBPK models are difficult to develop, limited to predicting concentrations in particular tissues, and imperfectly model the processes their cre-
ators seek to describe. Compartments with different characteristics often must be grouped together to make parameterization and analysis feasible. Simplifying assumptions may be made without confirmation to establish parametric differential equations (e.g., the steady-state assumption used to derive the Michaelis-Menten equation, as per Gibaldi and Perrier , or the common assumption of flow-limited exchange). Imperfect models can still be quite useful (Morgan et al. 1990), but model predictions for species or exposure patterns other than those used to develop the model should be interpreted with caution after giving careful attention to model assumptions.
Pharmacokinetic model building is a difficult task, as for any complex inference problem (Neter et al. 1996). Specification of few compartments in a pharmacokinetic model facilitates direct and precise statistical estimation of parameters, provides quick results, and may be sufficient for many purposes. However, oversimplification may lead to a biased prediction. Because health risk assessment is concerned with prediction rather than hypothesis testing or other forms of inference, loss of precision in parameter estimates is acceptable to avoid bias in the prediction. Although specifying many compartments decreases the chance of biased prediction when parameters are estimated solely from dosing data, typical PBPK model parameterization often relies on external estimates in addition to direct fits to dosing data and therefore may not protect so strongly against bias through additional compartments. Bayesian statistical approaches may be particularly advantageous for complex pharmacokinetic systems, allowing one to formally incorporate external information and propagate uncertainties, while relying on experimental data to drive the final parameter estimates toward unbiased values (Wakefield and Rahman 2000).
Flow-Limited Versus Diffusion-Limited Exchange
Flow-limited exchange describes the situation in which a chemical is assumed to always be at dynamic equilibrium between the tissues represented by a compartment and venous blood leaving those tissues. In this situation, the exchange rate between the blood and the compartment is limited primarily by the blood flow rate to the tissues represented by that compartment. Flow-limited exchange appears to be a default assumption in many PBPK models, but it is sometimes an oversimplification (O’Flaherty 1991). In contrast, diffusion-limited exchange does not solely depend on blood flow rates and may be limited by rates of bone accretion or other processes. Tissues that exhibit diffusion-limited exchange may not be well characterized using a single compartment, in which case they are represented using many compartments connected in layers (O’Flaherty 1991), membrane diffusion models (McCarley and Bunge 2001), or other approaches. PBPK model
builders and users should carefully assess default assumptions of flow-limited exchange.
Parameterization of PBPK Models
PBPK models contain two basic parameter types: physiologic and chemical specific. Physiologic parameters describe the organism and include parameters such as body weight, blood flow (total cardiac output as well as flow to different organs and tissues), tissue and organ volumes, and respiratory rates. These parameters are usually specific to a given species and are gleaned from the literature rather than measured. Examples of references from which physiologic parameters for PBPK models are obtained include Brown et al. (1997) and Arms and Travis (1988). Allometric scaling is frequently used in PBPK models for volumes and flows when scaling from animals to humans.
As the name implies, chemical-specific parameters are unique for each chemical and include physicochemical parameters (e.g., tissue partition coefficients) and biochemical parameters (e.g., metabolic rate constants, absorption and excretion rates). Tissue partition coefficients describe the extent to which a chemical is soluble in various fluids and tissues. Ideally, partition coefficients are determined experimentally for each test article and in tissues from each species to be modeled. Partition coefficients for a “typical” tissue may be used as the partition coefficient in a lumped tissue compartment (e.g., liver tissue partition coefficient may be used for the liver and the lumped “richly perfused” tissue compartment). Partition coefficients also can be estimated indirectly by using known chemical properties. For example, Poulin and Krishnan (1996) developed algorithms to deterministically estimate tissue partition coefficients based on the lipid solubility of the chemical and the fat content of the tissue. Tissue partition coefficients also may be estimated based on structurally similar chemicals (or classes of chemicals) (Beliveau et al. 2003). It is possible for partition coefficients for a given chemical to vary with species and even gender within a species. However, in the absence of data to the contrary, it is often assumed that tissue partition coefficients are no species specific (e.g., the partition coefficient in the liver of a mouse is no different from that in a human).
Biochemical parameters also are chemical specific and include parameters such as absorption and excretion rate constants and metabolic rate constants (e.g., first-order rate constant, k; Michaelis-Menten rate constants, Km and Vmax). Biochemical parameters may be measured or estimated based on a fit to experimental data. Allometric scaling across species is used to estimate biochemical parameters when data are not available for the species of interest.
Typical PBPK models include many unknown parameters and often highly multimodal likelihood surfaces, leading to challenging inference problems. In particular, parameter uncertainty can complicate inference. Possible strategies include deterministically fixing underdetermined parameters and restricting parameters to biologically meaningful constraints. Some of these strategies were used in a newly available model discussed below (USAF-EPA 2004a).
Alternatively, one could describe uncertainties in the form of probability distributions on unknown parameters. This leads to an approach known as Bayesian statistical inference. Bayesian statistics approaches inference for a random process by expressing uncertainty about unknown parameters as subjective probabilities. For example, the parameters could be unknown biochemical parameters.
The probability distribution describing uncertainty of the parameters before observing any data is known as the prior probability distribution. After observing data, the prior distribution is updated by using the rules of probability calculus. The updated probability distribution of the parameters is known as the posterior distribution. It contains all relevant information about the unknown parameters. From a Bayesian perspective, all statistical inference can be deduced from the posterior distribution by reporting appropriate summaries. In particular, this includes predictive inference.
In the context of parameterized physical systems, like the PBPK model, posterior inference and simulation for the unknown parameters are also described as the Monte Carlo method to solving the inverse problem (Mosegaard and Tarantola 1995). A recent discussion of this strategy appears in studies of Cornford et al. (2004), Haario et al. (2004), and Robert (2004).
Uncertainty is distinct from variability inherent to the described process. For example, PBPK models can include subject-specific parameters and describe subject-to-subject variation. This is formalized as a random effects distribution of subject-specific parameters. The variability of this distribution is inherent to the process. Even infinite data would never reduce this variability to zero.
Describing such variability takes the form of a hierarchical extension of the basic model. Let theta (θ) denote the subject-specific parameters, and let p(y | θ) denote the sampling model for the observed data, given the set of PBPK parameters θ. The model is hierarchically extended with a second layer θ ~ p(θ | μ) to describe intersubject variability, where mu (μ) represents
a set of unknown population parameters. In the context of population pharmacokinetic models, this strategy is described, for example, by Wakefield and Rahman (2000). The general framework is also known as mixed-effects modeling.
TRICHLOROETHYLENE PHARMACOKINETIC MODELS AND RISK ASSESSMENT
A number of pharmacokinetic models for trichloroethylene have been published over the last 30 years. During that time the amount of data from humans and experimental animal models increased significantly and these data improved the scientific understanding of trichloroethylene metabolism and the mode of action of trichloroethylene toxicity, which resulted in increased complexity of the pharmacokinetic models for trichloroethylene and its metabolites.
Exposure to trichloroethylene has been associated with a wide variety of adverse health effects including liver toxicity, kidney toxicity, reproductive and developmental toxicity, neurotoxicity, and immunotoxicity as well as cancer of the liver, kidney, lung, testes, and immune system (lymphoma). Trichloroethylene metabolism is complex (Lash et al. 2000a). As discussed in other chapters, specific metabolites have been causally associated with toxic or carcinogenic responses in different tissues and in different species. There are two major pathways for trichloroethylene metabolism: the oxidative (or cytochrome P-450) pathway and the glutathione-dependent pathway (see also Chapter 1). The flux through these two pathways differs in each tissue and the data suggest that the mode of action, including the putative toxic metabolite (dichloroacetic acid, trichloroacetic acid, chloral, and dichlorovinylcysteine), varies for different end points. To further complicate the picture, trichloroethylene metabolism varies in different species and the mode of action for a given end point also may vary with species (see details in other chapters). Clearly, there is considerable uncertainty and lack of consensus in the scientific community about the mode of action for different end points.
Other factors that complicate the assessment of human health risk from exposure to trichloroethylene include coexposure to other solvents, alcohol consumption, disease states that alter trichloroethylene metabolism and toxicity, interindividual variability in trichloroethylene metabolism, and age. There are also direct and indirect exposures to the putative toxic metabolites of trichloroethylene. For example, dichloroacetic acid and trichloroacetic acid are by-products of water chlorination and are often present in drinking water at very low concentrations, some individuals are directly exposed to chloral via medicinal use, and other parent compounds produce some of the same metabolites as trichloroethylene.
As noted above, trichloroethylene and its metabolites have been associated with toxicity and carcinogenicity in one or more species. The targets of toxicity are not the same for all species and the mode of action for the various toxic end points is not well understood. A comprehensive pharmacokinetic model for use in human health risk assessment would incorporate all potential routes of exposure, target organs, and putative toxic metabolites. Such a model would be unrealistically complex and would require substantial effort to develop and validate. Ideally, the pharmacokinetic model would be linked to a biologically based pharmacodynamic model that describes the mode of action; the linked models would yield a pharmacokinetic-pharmacodynamic model. Because pharmacokinetic-pharmacodynamic models rarely describe all adverse effects, simpler models are developed and iteratively refined to improve their ability to predict human health risk.
The EPA (2001b) draft risk assessment for trichloroethylene included pharmacokinetic models published by Fisher (2000) and Clewell et al. (2000). Since the EPA draft risk assessment was published, EPA and USAF commissioned a work group to develop a “harmonized” pharmacokinetic model for trichloroethylene and its metabolites. The work group comprised scientists from EPA, the USAF, Toxicology Excellence for Risk Assessment (TERA), and others under contract to the USAF (USAF-EPA 2004a). The work group included Drs. Clewell and Fisher. Other investigators have published pharmacokinetic models for trichloroethylene and metabolites since the 2001 EPA draft risk assessment. Several of the models are discussed below.
Review of Several Trichloroethylene Models
Fisher (2000) reviewed selected pharmacokinetic models for trichloroethylene in mice and humans, focusing on liver cancer as the outcome of interest for risk assessment. As noted in Chapter 4, trichloroethylene causes liver cancer in mice but not in rats, and trichloroacetic acid is considered the principal metabolite responsible for trichloroethylene-induced liver cancer in mice. Fisher’s first-generation model includes a four-compartment description of trichloroethylene disposition (liver, fat, richly perfused, and slowly perfused tissue compartments), saturable oxidative metabolism of trichloroethylene, and a simple one-compartment model for trichloroacetic acid in the liver.
Fisher’s second-generation model includes six tissue compartments (a lung compartment was added as it is a target organ in mice, and a kidney compartment was added to describe urinary excretion of trichloroethylene metabolites) and a four-compartment submodel for each trichloroethylene
metabolite. The second-generation model for mice included trichloroethylene, chloral hydrate, trichloroacetic acid, dichloroacetic acid, trichloroethanol, and trichloroethanol glucuronide. In the second-generation model for humans, only trichloroethylene, trichloroacetic acid, and trichloroethanol were described. As in the first-generation models, all metabolism was assumed to occur in the liver for both species in the second-generation model. Neither Fisher model described metabolism via the glutathione pathway. The putative toxic metabolite in the kidney is formed via the glutathione pathway. Because no renal toxicity has been observed in mice, this pathway is not relevant for the mouse pharmacokinetic model. However, it may be important in human kidney toxicity.
Both Fisher models include inhalation and oral exposure to trichloroethylene. Dose metrics in the first-generation model were peak concentrations (Cmax) and area under the curve (AUC) for trichloroethylene in whole blood and trichloroacetic acid in plasma. Dose metrics in the second-generation model included Cmax and AUC for trichloroethylene and trichloroacetic acid in whole blood, trichloroethylene and metabolites in tissues, and urinary excretion of trichloroethylene and metabolites.
The Clewell et al. (2000) pharmacokinetic model structure for trichloroethylene in mice, rats, and humans is much more complex than the Fisher models and includes submodels for metabolites in the three principal target tissues for cancer identified in animal bioassays: lung for chloral, kidney for dichlorovinylcysteine, and liver for chloral, trichloroacetic acid, dichloroacetic acid, trichloroethanol, and trichloroethanol glucuronide. The model for trichloroethylene includes tracheobronchial, fat, rapidly perfused, slowly perfused, liver, and gastrointestinal tract compartments. The gastrointestinal tract is composed of the gut lumen, stomach lumen, and gut tissue; this more complex description of the gastrointestinal tract allowed a better fit to experimental data on oral absorption of trichloroethylene in a corn oil vehicle. In addition, the Clewell model links metabolism in tracheobronchial tissue to lung toxicity and metabolism in the liver to liver and kidney toxicity. Like the Fisher models, the Clewell model includes inhalation and oral exposure to trichloroethylene, but the mathematical description of oral absorption is different for the Fisher and Clewell models. The common dose metrics of Cmax and AUC for trichloroethylene and metabolites in various tissues, as well as urinary excretion, can be calculated with Clewell’s model. In addition, the Clewell model includes the ability to calculate the lifetime average daily dose for different metrics (e.g., trichloroacetic acid AUC in liver) and time above a critical concentration for a specific analyte in a specific tissue. Specific dose metrics are discussed for liver cancer (e.g., lifetime
average daily dose for trichloroacetic acid AUC and dichloroacetic acid AUC in plasma as a surrogate for liver; Cmax for trichloroacetic acid and dichloroacetic acid in liver), kidney cancer (lifetime average daily dose for production of reactive metabolites), lung cancer (e.g., lifetime average daily dose for chloral AUC and Cmax for chloral in the tracheobronchial region), and noncancer end points.
In contrast to the Fisher models, the Clewell models for rats, mice, and humans include the glutathione pathway of trichloroethylene metabolism. The Clewell model also includes descriptions for metabolites in relevant tissues. Chloral is formed from trichloroethylene and is further metabolized in the lung compartment. 1,2-Dichlorovinylcysteine is formed in the kidney, where it causes cytotoxicity or is further metabolized and excreted in urine. Trichloroethylene undergoes oxidative metabolism in the liver to form chloral, trichloroacetic acid, dichloroacetic acid, trichloroethanol, and trichloroethanol glucuronide. There is also a description of enterohepatic recirculation of trichloroethanol glucuronide:trichloroethanol.
After publication of EPA’s draft health risk assessment for trichloroethylene, a joint USAF-EPA (2004a) prepared a harmonized pharmacokinetic model for trichloroethylene and its metabolites in rats, mice, and humans. Before publication, a draft of the harmonized model was reviewed by a panel of expert scientists, whose comments were considered in the final harmonized model (USAF-EPA 2004b). The harmonized model includes a primary model for the parent compound (trichloroethylene), which is very similar in structure to the Clewell model, and a number of submodels for specific tissues (e.g., trancheobronchial and liver compartments) and specific metabolites (trichloroethanol, trichloroethanol glucuronide, trichloroacetic acid, dichloroacetic acid, and 1,2-dichlorovinylcysteine). The parent trichloroethylene model includes tracheobronchial, rapidly perfused, slowly perfused, fat, gastrointestinal tract (including stomach and duodenum for description of trichloroethylene absorption administered by corn oil gavage), and liver tissue compartments. The harmonized model accommodated oral (bolus and drinking water), inhalation, and intravenous routes of trichloroethylene exposure. The model also has the capability to describe fat as a diffusion-limited tissue compartment.
Like the Clewell model, the harmonized model includes metabolism to chloral in the tracheobronchial region, hepatic metabolism of trichloroethylene to trichloroacetic acid, dichloroacetic acid, trichloroethanol, and trichloroethanol glucuronide, and enterohepatic recirculation of trichloroethanol glucuronide:trichloroethanol. Unlike the Clewell model, the harmonized model includes hepatic metabolism of trichloroethylene
to 1,2-dichlorovinylcysteine and does not include a separate kidney compartment for 1,2-dichlorovinylcysteine. Instead, it is assumed that 1,2-dichlorovinylcysteine is formed in the liver and ends up in the kidney where it can result in toxicity or be further metabolized and excreted in urine as N-acetyldichlorovinylcysteine.
Dose metrics in the harmonized model include the concentration of trichloroethylene in blood and tissues, trichloroethylene AUC in blood, instantaneous concentration and AUC for chloral in the tracheobronchial region (dose metric for lung), total amount of trichloroethylene metabolized normalized to body weight (dose metric for metabolism), concentrations and AUC for trichloroacetic acid in plasma and liver (dose metric for liver cancer), concentration and AUC for trichloroethanol in blood (dose metric for noncancer end points in liver), and total production of a thioacetylating intermediate from 1,2-dichlorovinylcysteine normalized to kidney volume (dose metric for kidney cancer).
Authors of the harmonized model state that it should be useful in risk assessment for end points where the mode of action involves tissue exposure to trichloroethylene, trichloroacetic acid, and trichloroethanol; they acknowledge that other dose metrics (e.g., chloral in lung and 1,2-dichlorovinylcysteine in kidney) are highly uncertain because of a lack of adequate pharmacokinetic data.
None of the above models includes a description of dermal absorption of trichloroethylene. Because trichloroethylene is found in drinking water, there is dermal exposure to trichloroethylene when bathing. It has been shown for other volatile organic compounds in chlorinated drinking water (e.g., chloroform) that dermal absorption occurs in addition to absorption via the respiratory tract when showering (Jo et al. 1990). Poet et al. (2000) incorporated dermal exposure to trichloroethylene in rats and humans and their pharmacokinetic model for trichloroethylene included experimentally determined dermal permeability coefficients for both species. Because humans are exposed to trichloroethylene by the oral, inhalation, and dermal routes, dermal exposure should be included when assessing potential risk from trichloroethylene exposure. Additional data sets in experimental animals and humans after dermal exposure to trichloroethylene may be required.
Albanese et al. (2002) published a series of models that included different descriptions of the adipose compartment. These models include a stan-
dard perfusion-limited compartmental model for adipose, a diffusion-limited model, and a hybrid model with an axial-dispersion model for adipose tissue. However, as noted by the expert reviewers of the harmonized model, it may not be necessary to move away from a diffusion-limited adipose tissue compartment if the model fit to experimental data is not improved (USAF-EPA 2004b). The Albanese paper shows only model simulations of trichloroethylene concentrations in adipose tissue and no comparisons with experimental data.
Simmons et al. (2002) published a pharmacokinetic model for trichloroethylene in Long-Evans rats that focused on evaluating the neurotoxicity of trichloroethylene. This five-compartment pharmacokinetic model included brain, fat, slowly perfused tissue, rapidly perfused tissue, and liver. Partition coefficients for trichloroethylene in blood, fat, muscle, brain, and liver were determined for the Long-Evans rats. Male rats were exposed to trichloroethylene by inhalation, and blood and tissues were analyzed for trichloroethylene concentrations over time. Gas-uptake studies were conducted and the model was used to optimize Vmax based on a fit of model simulations for trichloroethylene concentrations in the chamber. The model was then used to simulate blood, liver, brain, and adipose tissue concentrations of trichloroethylene and was compared with observed concentrations of trichloroethylene in those tissues during exposure to trichloroethylene vapors (200-4,000 parts per million). As noted in Chapter 6, trichloroethylene neurotoxicity is attributed to peak trichloroethylene concentrations in brain. This model provides a reasonable fit to the experimental data. If a pharmacokinetic model is to be used to estimate neurotoxicity in humans exposed to trichloroethylene, including a brain compartment is necessary.
Keys 2003 Model
Fisher and colleagues continue to refine earlier versions of their trichloroethylene pharmacokinetic models. An expanded model was published in 2003 (Keys et al. 2003). This model included compartments for lung, heart, brain, kidney, slowly perfused tissue, fat (diffusion limited), rapidly perfused tissue, spleen, gastrointestinal tract, and liver (deep and shallow compartments). The model accommodated oral, inhalation, and intra-arterial exposure and provided for exhalation and metabolism of trichloroethylene. The pharmacokinetics of trichloroethylene in male Sprague-Dawley rats was characterized during and after inhalation exposure to trichloroethylene and after oral or intra-arterial administration of trichloroethylene. Trichloroethylene concentrations in blood and tissues were determined.
Trichloroethylene metabolites were neither measured nor modeled. As noted above for the Simmons model, including a brain compartment is advisable if one is to use a pharmacokinetic model to assess neurotoxicity risk from trichloroethylene exposure.
Keys 2004 Model
Dichloroacetic acid is formed ex vivo from trichloroacetic acid (Merdink et al. 1998); hence, the validity of data from early studies in which dichloroacetic acid was measured in animals and people exposed to trichloroethylene has been questioned. The harmonized model has a very simple dichloroacetic acid submodel, in part due to the questioned validity of experimental data on the concentration of dichloroacetic acid in blood and tissues after trichloroethylene exposure. As noted above, there is direct exposure to dichloroacetic acid in drinking water and dichloroacetic acid pharmacokinetics have been studied (Curry et al. 1985, 1991; Gonzalez-Leon et al. 1997, 1999; Saghir and Schultz 2002; Schultz et al. 2002). A pharmacokinetic model of dichloroacetic acid was developed that includes a description of the ability of dichloroacetic acid to inhibit its own metabolism by suicide inhibition of glutathione S-transferase zeta (Keys et al. 2004). Studies were done in animals exposed to dichloroacetic acid as a parent compound rather than as a metabolite of trichloroethylene, which bypasses questions related to ex vivo production of dichloroacetic acid from trichloroacetic acid. Addition of this dichloroacetic acid submodel to the harmonized model will be useful only if experimental data with a high degree of accuracy for blood and tissue dichloroacetic acid concentrations are available.
PBPK-based human equivalent doses offer a sensible biologically based approach to adjusting for differences across species but may not improve accuracy if an incorrect dose metric is used. For example, AUC for the target organ concentration as a function of time is a reasonable metric in theory, assuming that the effective damage to the target organ is cumulative and occurs at a rate proportional to the target organ concentration. However, other metrics can be proposed that are just as reasonable, such as the AUC for the log of the target organ concentration. If the toxicologic process leading to tissue damage occurs at a rate proportional to the log concentration, the AUC log concentration would likely be a better measure of exposure. Tissue repair or other compensating mechanisms could suggest alternative metrics, such as an AUC for target organ concentrations exceeding a certain threshold. In practice, it is difficult to know the best metric without
experiments designed to compare the predictive ability of different metrics or without understanding the mechanisms of toxicity in detail.
Similarly, for toxicants such as trichloroethylene that have several potentially toxic metabolites, it is difficult to determine which metabolite(s) contributes to any particular health effect. Current dosing experiments are suggestive but were not designed to answer either of these questions. Although PBPK modeling is well motivated and is starting to fill in some gaps in animal-to-human and cross-route extrapolation, trichloroethylene dose-response models based on PBPK modeling are best viewed as plausible, rather than superior models, among many alternatives.
This note of caution is not intended to discourage the continued development and application of PBPK models for trichloroethylene. In fact, the EPA (2001b) risk assessment for trichloroethylene presents a sophisticated and appealing application of PBPK modeling and generally presents those results in an appropriate manner. Researchers should embrace the challenges posed by multiple metabolites and the complexity of the PBPK model predictions, as they suggest a variety of useful experiments with various dose patterns to produce different target organ concentration-time profiles or different ratios of metabolites. Aggressive experimentation in this direction should yield substantial information about the mechanisms of toxicity, best target organ dose metrics, and dose-response relationships for trichloroethylene. Hack et al. (2006) discuss how Bayesian posterior inference in the PBPK model identifies parameters with a high degree of uncertainty and suggest that future kinetic studies be designed to learn about these parameters.
Hack et al. (2006) describe inference in the harmonized PBPK model (USAF-EPA 2004a), formalized under the Bayesian paradigm by reporting posterior inference. This is a natural and convenient choice for a large hierarchical model of this type (Gelman et al. 1995).
First, the model is extended to a population PBPK model by adding a random effects distribution p(θ | μ) for subject-specific PBPK parameters θ. Specifically, the population PBPK model is defined by introducing normal and log-normal random effects models p(θ | μ) for all parameters. The model is completed with conjugate hyperpriors p(μ). A distinguishing feature of the PBPK model is the physiologic interpretation of the parameters. To ensure meaningful interpretation of the implementation, Hack et al. (2006) restrict parameters to a biologically meaningful domain. This is reasonable and appropriate.
Once the model is specified, estimating the model reduces to inference about the parameters. The use of least-squares point estimators is limited
by the large number of parameters and small amounts of data. The use of least-squares estimation is reported after imposing constraints for several parameters (Hack et al. 2006). This is reasonable for an ad hoc first estimate, but it is important to follow up with a model refinement. This is implemented by Hack et al. by reporting posterior distributions on the unknown parameters. Posterior Markov chain Monte Carlo simulation was used to implement Bayesian posterior inference—again, a natural choice and almost a compulsory consequence of the other two choices (given the difficulties of frequentist estimation in this setting).
The basic idea of Markov chain Monte Carlo simulation is the following. It can be argued that under the Bayesian paradigm most inference takes the mathematical form of expectations of some function of interest with respect to the posterior distribution. For example, a point estimate for a parameter θ is reported as the expectation of θ under the posterior probability model (that is, an integral with respect to the posterior distribution). Similarly, predictive inference can be written as an expectation of the sampling model with respect to the posterior distribution on the unknown parameters. The problem is that these integrals typically are analytically intractable. Markov chain Monte Carlo simulation instead evaluates the desired posterior integrals as sample averages. The sample average is defined as an average over iterations in a computer simulation of a Markov chain that is set up so that the desired posterior distribution is the stationary distribution. Ergodic averages with respect to the simulated Markov chain serve to estimate the posterior integrals. For example, point estimates of parameters are represented as ergodic averages of these parameters over the Markov chain simulation. An important practical advantage of the outlined strategy is the ability to implement inference in nearly any probability model and the possibility to report inference on any event of interest. Markov chain Monte Carlo simulation was introduced by Gelfand and Smith (1990) as a generic tool for posterior inference. See Gilks et al. (1996) for a review.
In the context of PBPK models, the outlined strategy can be carried out as described by Hack et al. (2006). The simulation program MCSim (Bois and Maszle 1997) was used to implement Markov chain Monte Carlo posterior simulation in the extended model. Simulation-based parameter estimation with Markov chain Monte Carlo posterior simulation gives rise to an additional source of uncertainty. Ergodic averages computed from the Markov chain Monte Carlo simulation output represent the desired posterior means only asymptotically, in the limit as the number of iterations goes to infinity. Any implementation needs to include a convergence diagnostic to judge practical convergence. Hack et al. report use of the convergence diagnostic of Gelman et al. (1996). Although the reported diagnostic statistics are not perfect, the committee finds that they are adequate in light of the highly computation-intensive likelihood. The discussion of model fits and
sensitivity of Hack et al. summarizes important features of the posterior inference.
An important element of variability for the reported risk assessment is the choice of dose metric. The PBPK model provides a comprehensive probabilistic description of all metabolites in all specified compartments. The Markov chain Monte Carlo implementation allows easy inference about any event of interest. In particular, for any tentative dose metric the model includes inference about variation with dose and correlation with other tentative dose metrics. Although the PBPK model cannot deliver a decision on the choice of dose metric, it can simplify the decision by describing the joint distribution of possible dose metrics. The committee recommends that the investigators consider a moderately large set of possible dose metrics, including the metrics described earlier in this chapter, and report the correlation of those metrics over different exposure and inhalation concentrations. Hack et al. (2006) include results on correlation of dose metrics and parameters and suggest that parameters that have little impact on the predicted dose metrics are less critical for risk assessment.
FINDINGS AND RECOMMENDATIONS
EPA’s use of the Fisher (2000) and Clewell et al. (2000) PBPK models for trichloroethylene in its 2001 draft risk assessment was reasonable given the available data for liver and kidney cancer. The committee supports the inclusion of multiple dose metrics including AUC, Cmax, and lifetime average daily dose, as it is not clear which is the most appropriate dose metric for a given end point.
EPA relies on the description by Bois (2000a,b) of uncertainty in the Fisher (2000) and Clewell et al. (2000) models. This includes updating uncertainties by using the paradigm of Bayesian inference and implementation by Markov chain Monte Carlo posterior simulation. Bois’ extension to population models captures an important aspect of the variability. A joint probability model for all relevant quantities (concentrations in different tissue compartments) implies a coherent description of the variability across different dose metrics.
None of the currently available PBPK models considers all possible routes of trichloroethylene exposure (e.g., dermal) or dose metrics for all adverse health effects (e.g., neurotoxicity). The harmonized model is a reasonable extension of the Fisher and Clewell models and is a step in the right direction, but the mode of action and appropriate dose metric are not clear for each end point. PBPK models do not resolve the uncertainty about the
mode of action, but they can inform experimental designs for studying the mode of action. Moreover, understanding the mode of action drives PBPK model elaboration.
Because there is potential for trichloroethylene exposure via dermal absorption, the committee recommends that future PBPK models used for trichloroethylene risk assessment include a description of dermal absorption similar to the approach of Poet et al. (2000).
The committee recommends additional studies to evaluate how well alternative dose metrics predict toxic response. The model could be used to investigate alternative study designs. For example, one could simulate liver concentrations of trichloroacetic acid in several different groups of laboratory animals that receive the same lifetime average daily dose by different dosing regimens to compare the lifetime average daily dose with an internal dose metric (that is, trichloroacetic acid concentration or AUC in liver). One group of subjects could receive intermittent high exposures to trichloroethylene and another group could receive lower daily doses; some groups may receive the same daily dose by different routes (e.g., inhalation versus drinking water). Carrying out the corresponding studies in laboratory animals would facilitate the desired comparison of alternative metrics with respect to their ability to predict the toxic end point.
The PBPK models used in the 2001 draft risk assessment focused on liver (Fisher) and kidney (Clewell) cancer. End points not addressed by currently available PBPK models include reproductive and developmental toxicity, neurotoxicity, immunotoxicity, and others.
PBPK models should be developed for other toxicity end points, such as neurotoxicity and developmental outcomes.
Simmons et al. (2002) and Keys et al. (2003) included a brain compartment in their models for trichloroethylene, which could be used to predict target organ doses relevant to neurotoxicity in future generations of PBPK models used for trichloroethylene risk assessment. The committee recognizes that there may be little or no data available to confirm model predictions for brain tissue concentrations of trichloroethylene and metabolites in humans. However, including all relevant uncertainties is key and can be
formalized under Bayesian inference and implemented with the Markov chain Monte Carlo approach used by Bois (2000a,b). Description of uncertainties in prior simulation might indicate that the approach is not practical without collecting additional data.
Fisher and others have incorporated developmental exposure in utero and via lactation in their PBPK models for perchlorate (Clewell et al. 2003a,b; Fisher et al. 2000); this approach could be applied to trichloroethylene to investigate dose metrics relevant to developmental effects of trichloroethylene exposure. See Chapter 9 for additional guidance on producing developmental PBPK models.
None of the PBPK models for trichloroethylene describes the effect of exposure to chemical mixtures that include trichloroethylene. For example, ethanol and trichloroethylene share enzymatic pathways of metabolism.
A combined PBPK model for trichloroethylene and ethanol would enable investigation of exposure to this mixture. This approach could be used for other mixtures with shared metabolic pathways or common metabolites. A similar approach could be taken to include the effect of disease states on trichloroethylene disposition (e.g., induction of CYP2E1 in diabetes).
In summary, pharmacokinetic models can be useful tools to identify data gaps and research needs to reduce uncertainty in risk assessment. More data and a better understanding of the mode of action for various end points are needed for a revised trichloroethylene pharmacokinetic model, in conjunction with appropriate pharmacodynamic models, to be useful for further understanding the risks posed by trichloroethylene.