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8 Toxicokinetic-toxicodynamic modeling Ronette Gehring and Deon van der Merwe
INTRODUCTION
different types of exposures (dose and duration of exposure), the ability to relate the formation of biomarkers to the exposure, and identifying explanations for interspecies differences in sensitivity to a toxicant.
The adverse effects of, as well as the biomarkers associated with, the presence of toxicants in the body, are linked to the dose of a toxicant that reaches the sites of toxic action within the body (Andersen et al., 2006). Toxicokinetic-toxicodynamic (TK-TD) models are potentially powerful and valuable tools for toxicological research and quantitative risk assessment, because they provide a means of studying the links between target tissue dose, toxic effects, and biomarkers of exposure quantitatively. These mathematical models simulate the underlying processes that lead to the time course of effects that are seen as a result of exposure to a toxicant, and the subsequent formation and disposition of biomarkers. There are two components to a TK-TD model, the toxicokinetic component (TK) and the toxicodynamic component (TD). Toxicokinetics refers to the mathematical description of how concentrations of a toxicant at the site of action change over time. Processes that contribute to the toxicokinetics of a toxicant are absorption, distribution, metabolism, and excretion. Toxicodynamics refers to the quantitative description of the effects of a toxicant on a biological system. These effects include a range of endpoints and products, ranging from the molecular level, to cells, tissues, organ systems, and life-history traits. TK-TD models link toxicokinetic and toxicodynamic processes to translate exposure to the time course of effects, including the effect on biomarkers of toxicity (Figure 8.1). Separating the toxicokinetics from the toxicodynamic processes in these models has several advantages, including the ability to assess the toxicity of
R. Gupta (Ed): Biomarkers in Toxicology. ISBN: 978-0-12-404630-6
TOXICOKINETIC MODELS Toxicokinetics refers to the disposition, including the movement and fate, of toxicants that enter the body (Riviere, 2011; Van der Merwe et al., 2012). The body can be viewed as a combination of compartments containing fluids and cellular matrices, separated from the outside world by epithelial barriers, and separated internally from each other by various types of cellular barriers. The compartments can be viewed in terms of physiologically and morphologically identifiable units, such as various fluid compartments, tissue types, and organs. They can also be viewed in terms of functionally similar units, where areas of the body that interact with a toxicant in a similar way are grouped together into a single, hypothetical compartment for mathematical modeling purposes. The three main approaches to the toxicokinetic portion of TK-TD models are classical compartmental toxicokinetic models, noncompartmental toxicokinetic models, and physiologically based toxicokinetic (PBTK) models. Each approach has different advantages and disadvantages, and the choice between the three is driven by the type and quality of available data, as well as the objectives of the modeler.
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© 2014 Elsevier Inc. All rights reserved. DOI: http://dx.doi.org/10.1016/B978-0-12-404630-6.00008-7
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FIGURE 8.1 The relationship between toxicokinetics, toxicodynamics, and biomarker response.
Toxicant disposition Toxicant disposition includes the absorption, distribution, and elimination of toxicants. Elimination can be further divided into biotransformation and excretion. Absorption is the process by which toxicants gain access to the internal tissues of the body by penetrating the epithelial barriers at the site of exposure and entering the central circulation (blood), which carries it to the rest of the body. The most important routes of absorption for toxicants are gastrointestinal, respiratory, and dermal (van der Merwe et al., 2012). Absorbed toxicants are typically distributed to all regions of the body through the blood circulation. They then penetrate other fluid and tissue compartments by crossing the capillary endothelium, and penetrating the surrounding fluids and tissues. The ease of crossing the capillary epithelium, particularly for relatively polar toxicants, depends on the availability of intercellular pathways between endothelial cells. The distribution of toxicants in the body is typically uneven, depending on the affinity of compounds for particular physicalchemical properties of tissues. Lipophilic compounds, for example, tend to distribute more to lipid-rich tissues in the body. The movement of polar compounds into some types of tissues is limited by tight junctions between cells. Protected tissues include the brain, the testes, and the placenta. Movement of polar compounds into those tissues is still possible, however, by active or facilitated transport through transmembrane transporter proteins. The presence of a range of physical-chemical conditions in various tissues and body compartments, and the variable expression of facilitated and active transport mechanisms, causes the distribution patterns of different compounds to be unique. Biotransformation, also referred to as metabolism, refers to the enzyme-assisted chemical reactions that transform xenobiotics into secondary metabolites that are suitable for excretion. The goal is to form water-soluble compounds that can be excreted through the most efficient route of excretion: the renal system. The biotransformation reactions can be divided into two types, or phases. Phase I reactions add a functional group to make the xenobiotic suitable for further modification. Phase I reactions include oxidation, hydrolysis, reduction, and acetylation. Phase II reactions refer to the conjugation of
the xenobiotic with polar molecules to create a watersoluble compound. Phase II reactions include conjugations with amino acids, glutathione, glucuronide, and sulfate. Differences in biotransformation enzymes that alter the efficiency of individuals in their ability to transform specific nonpolar xenobiotics into polar compounds exist at the interspecies and interindividual levels. The products of biotransformation, and, indirectly, the effects of biotransformation on the concentrations of precursor molecules, can serve as biomarkers of exposure. The final stage of toxicant disposition, unless the toxicant becomes sequestered within the body, is excretion. It refers to the process by which toxicants and their metabolites leave the body through excretory organs. The most important route of excretion is via the urine. To be excreted through the urine, compounds must be small enough to pass the glomerular filtration mechanism, and be polar enough to remain in the glomerular filtrate after entering the renal tubules and bladder. Other important routes of excretion, depending on the type of compound, are the respiratory system for compounds that are volatile, and the feces for compounds that are combined with bile. Minor routes of excretion include sweat, saliva, and other glandular secretions.
Classical compartmental toxicokinetic models Functions with one or more exponential terms are used to describe a toxicant’s time-concentration profile in venous blood (or any other biological matrix) for classical compartmental TK models (Equation 8.1). The number of terms depends on the number of different slopes in the time-concentration profile, which in turn is related to the number of kinetically homogenous “compartments” through which the toxicant moves in the body. Each compartment does not represent a specific body region, but is a composite of body regions through which the toxicant moves at a similar rate (Figure 8.2). Bi-exponential equations used to describe timeconcentration data typically have this form: CðtÞ 5 Ae2α 3 t 1 Be2β 3 t
ð8:1Þ
where C(t) is the xenobiotic concentration at time t, and α and β are the slopes of two disappearance phases with different rates. A and B are their intercepts with the y-axis. The exponential equations form the basis for calculating pharmacokinetic parameters, such as Vd (volume of distribution) and CL (clearance), that are related to kinetic processes. An advantage of classical pharmacokinetic models is that they can be used to accurately predict toxicant concentrations in the matrix of interest at any time following exposure. They can also be used to predict toxicant
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FIGURE 8.2
A two-compartment toxicoki-
netic model.
concentrations following different magnitudes or durations of exposure, as long as these fall within the inference range of the model (Riviere, 2011). The challenge with classical compartmental toxicokinetic models is developing and validating the best model that will give accurate predictions for a wide range of exposure scenarios. To develop these models, rich datasets of toxicant concentrations in the matrix of interest, collected at different times following different exposures, are needed. These datasets are often not available for toxicants due to the costs and ethical dilemmas of conducting such studies with compounds that will likely cause adverse effects in experimental animals and human volunteers. Another limitation of the classical compartmental approach to toxicokinetics is that the use of exponential equations to describe timeconcentration profiles assumes that all toxicokinetic processes are first-order (i.e. the rates of the toxicokinetic processes are directly proportional to the toxicant concentration). This is not necessarily true, particularly for high exposures with potential saturation of transport and metabolic processes. In such cases, the toxicokinetics are better described using equations that incorporate terms that account for the saturation (e.g. the Michaelis-Menten model). The use of classical compartmental toxicokinetic models is limited in TK-TD modeling due to these disadvantages and limitations.
Noncompartmental analysis of toxicokinetic data Toxicokinetic data can also be analyzed using noncompartmental methods (Batra, 1995). With this approach,
parameters that summarize the time versus toxicant concentration curve are calculated directly from the data without first fitting a model. These parameters are the maximum measured toxicant concentration (Cmax), time at which this maximum concentration is measured (Tmax), and the area under the timetoxicant concentration curve (AUC). The latter parameter is typically calculated using the trapezoidal rule. Cmax represents peak exposure, whereas the AUC is a measure of total exposure over time, and these values are then correlated to measured toxic effects. The advantage of this approach is that it is computationally relatively simple, but it also has several limitations. Specifically for toxicokinetic processes that are saturated and no longer first-order (i.e. their rates are no longer directly proportional to toxicant concentration), the relationship between Cmax or AUC and toxic effect becomes nonlinear, making predictions of the effects of exposures that are beyond the inference range of the model unreliable.
Physiologically based toxicokinetic models An alternative approach to toxicokinetic modeling, which is being used more often, is the PBTK model. In PBTK models, the anatomical, physiological, chemical, and physical phenomena that contribute to the absorption, distribution, metabolism, and excretion of toxicants are transcribed into a system of differential equations so that toxicant concentrations can be predicted at the site of action (Figure 8.3). PBTK models strive to be as mechanistic as possible, although some assumptions and simplifications are inevitably necessary to make the model tractable (Frederick et al., 2002; Van der Merwe et al., 2006). PBTK models rely on a priori knowledge of
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the anatomy and physiology of the target animal/ human as well as biochemical information specific for the toxicant of interest. The accuracy of the predictions made by these models is dependent on the availability and quality of this information. An advantage of the PBTK approach is that the model can be adapted to a wide range of exposure scenarios, physiological conditions, disease states, and even interspecies differences, by adjusting the model parameter values according to the physical and mechanistic differences between systems. As long as the processes that affect the toxicokinetic in a particular system are well understood, and the differences in parameters that quantify those processes are known for different scenarios, the toxicokinetics of systems for which direct toxicokinetic data are
not available may be predictable based on a PBTK model.
TOXICODYNAMIC MODELS There are many different types of toxicodynamic models that can be incorporated into a TK-TD model, ranging from models that describe quantal (the individual either shows the response or it does not) to graded responses (gradual changes in individuals). Toxicodynamic models can also consider either lethal or sublethal effects (Ashauer et al., 2011). The quantitative description of changes in the expression of carefully selected biomarkers that are linked to sublethal toxic effects and tissue damage are typically toxicodynamic models of nonlethal, graded responses to toxicant exposure. Toxicodynamic models of graded endpoints quantitatively describe the relationship between toxicant concentration at the site of action and the degree of an individual’s response. Parameters of these models, which are typically sigmoidal doseresponse curves, include the minimum response (biomarker expression in the absence of toxicant exposure, Emin), the concentration of toxicant (EC100) that leads to maximal biomarker expression (Emax), the concentration of toxicant (EC50) that leads to biomarker expression that is 50% maximum response (E50), and the slope of the sigmoidal doseresponse curve. This slope measures the response to a change in the exposure concentration averaged over all exposed individuals. The magnitude of the differences in response between individuals in the target population does not affect the slope, but influences the variability at each concentration (Figure 8.4).
FIGURE 8.3 A simple, whole-body physiologically based toxicokinetic model.
Emax
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FIGURE 8.4 graded endpoints.
A toxicodynamic model of
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REFERENCES
CONCLUDING REMARKS AND FUTURE DIRECTIONS The heterogeneity in adverse outcomes and biomarkers between individuals in a population, and between different subpopulations, can be ascribed to either toxicokinetic variability (variability in toxicant concentrations and duration at the site of action) or toxicodynamic variability (different sensitivities to the same concentration of toxicant at the site of action, and different rates of biomarker formation), or both. A statistical model can be overlaid on the structural toxicokinetic and/or toxicodynamic models to identify correlates of variability in parameter values such as age, body weight, renal function, and hepatic function. Toxicokinetic-toxicodynamic models can play a role in making better quantitative predictions related to the detection of biomarkers, and potentially of the outcomes of toxicant exposures in individuals. Although not yet widely used in toxicology, this approach has the potential to improve our understanding of how different individuals react differently to the same toxicant exposures.
REFERENCES Andersen, M.E., Lutz, R.W., Liao, K.H., and Lutz, W.K. (2006) Dose-incidence modeling: Consequences of linking quantal measures of response to depletion of critical tissue targets. Toxicol Sci 89: 331337. Ashauer, R., Agatz, A., Albert, C. et al. (2011) Toxicokinetictoxicodynamic modeling of quantal and graded sublethal endpoints: A brief discussion of concepts. Environ Toxicol Chem 30: 25192524. Batra, V.K. (1995) Toxicokinetic/Toxicodynamic correlations: Goals, methods and limitations. Toxicol Pathol 23: 158164. Frederick, C.B., Lomax, L.G., Black, K.A. et al. (2002) Use of a hybrid computational fluid dynamics and physiologically based inhalation model for interspecies dosimetry comparisons of ester vapors. Toxicol Appl Pharmacol 183: 2340. Riviere, J.E. (2011) Comparative Pharmacokinetics: Principles, Techniques, and Applications, second ed. Iowa State University Press, Ames, IA. Van der Merwe, D., Brooks, J.D., and Gehring, R. (2006) A physiologically based pharmacokinetic model of organophosphate dermal absorption. Toxicol Sci 89: 188204. Van der Merwe, D., Gehring, R., and Buur, J. (2012) Toxicokinetics. In Veterinary Toxicology: Basic and Clinical Principles, second ed., Gupta, R.C., ed. Academic Press/Elsevier, Amsterdam, pp. 3747.