Chapter 7: Toxicokinetics

Toxicokinetics is the quantitative study of the movement of an exogenous chemical from its entry into the body, through its distribution to organs and tissues via the blood circulation, and to its final disposition by way of biotransformation and excretion. The basic kinetic concepts for the absorption, distribution, metabolism, and excretion of chemicals in the body system initially came from the study of drug actions or pharmacology; hence, this area of study is traditionally referred to as pharmacokinetics. Toxicokinetics represents extension of kinetic principles to the study of toxicology and encompasses applications ranging from the study of adverse drug effects to investigations on how disposition kinetics of exogenous chemicals derived from either natural or environmental sources (generally refer to as xenobiotics) govern their deleterious effects on organisms including humans.

The study of toxicokinetics relies on mathematical description or modeling of the time course of toxicant disposition in the whole organism. The classic approach to describing the kinetics of drugs is to represent the body as a system of one or more compartments, even though the compartments do not have exact correspondence to anatomical structures or physiological processes. These empirical compartmental models are almost always developed to describe the kinetics of toxicants in readily accessible body fluids (mainly blood) or excreta (eg, urine, stool, and breath). This approach is particularly suited for human studies, which typically do not afford organ or tissue data. In such applications, extravascular distribution, which does not require detail elucidation, can be represented simply by lumped compartments. An alternate and newer approach, physiologically based toxicokinetic modeling attempts to portray the body as an elaborate system of discrete tissue or organ compartments that are interconnected via the circulatory system. Physiologically based models are capable of describing a chemical’s movements in body tissues or regions of toxicological interest. It also allows a priori predictions of how changes in specific physiological processes affect the disposition kinetics of the toxicant (eg, changes in respiratory status on pulmonary absorption and exhalation of a volatile compound) and the extrapolation of the kinetic model across animal species to humans.

It should be emphasized that there is no inherent contradiction between the classic and physiological approaches. The choice of modeling approach depends on the application context, the available data, and the intended utility of the resultant model. Classic compartmental model, as will be shown, requires assumptions that limit its application. In comparison, physiological models can predict tissue concentrations; however, it requires much more data input and often the values of the required parameters cannot be estimated accurately or precisely, which introduces uncertainty in its prediction.

We begin with a description of the classic approach to toxicokinetic modeling, which offers an introduction to the basic kinetic concepts for toxicant absorption, distribution, and elimination. This will be followed by a brief review of the physiological approach to toxicokinetic modeling that is intended to illustrate the construction and application of these elaborate models. Finally, we will address the application of toxicokinetic principles to biological monitoring for exposure assessments in industrial and environmental contexts.

Ideally, quantification of xenobiotic concentration at the site of toxic insult or injury would afford the most direct information on exposure–response relationship and dynamics of response over time. Serial sampling of relevant biological tissues following dosing can be cost-prohibitive during in vivo studies in animals and is nearly impossible to perform in human exposure studies. The most accessible and simplest means of gathering information on absorption, distribution, metabolism, and elimination of a compound is to examine the time course of blood or plasma toxicant concentration over time. If one assumes that the concentration of a chemical in blood or plasma is in some describable dynamic equilibrium with its concentrations in tissues, then changes in plasma toxicant concentration should reflect changes in tissue toxicant concentrations and relatively simple kinetic models can adequately describe the behavior of that toxicant in the body system.

Classic toxicokinetic models typically consist of a central compartment representing blood and tissues that the toxicant has ready access and equilibration is achieved almost immediately following its introduction, along with one or more peripheral compartments that represent tissues in slow equilibration with the toxicant in blood (Fig. 7-1). Once introduced into the central compartment, the toxicant distributes between central and peripheral compartments. Elimination of the toxicant, through biotransformation and/or excretion, is usually assumed to occur from the central compartment, which should comprise the rapidly perfused visceral organs capable of eliminating the toxicant (eg, kidneys, lungs, and liver). The obvious advantage of compartmental toxicokinetic models is that they do not require information on tissue physiology or anatomic structure. These models are useful in predicting the toxicant concentrations in blood at different doses or exposure levels, in establishing the time course of accumulation of the toxicant, either in its parent form or as biotransformed products during continuous or episodic exposures, in defining concentration–response (vs dose–response) relationships, and in guiding the choice of effective dose and design of dosing regimen in animal toxicity studies (Rowland and Tozer, 2011).

One-Compartment Model

The most straightforward toxicokinetic assessment entails quantification of the blood or more commonly plasma concentrations of a toxicant at several time points after a bolus intravenous (iv) injection.

Often, the data obtained fall on a straight line when they are plotted as the logarithm of plasma concentration versus time; the kinetics of the toxicant is said to conform to a one-compartment model (Fig. 7-2). Mathematically, this means that the decline in plasma concentration over time profile follows a simple exponential pattern as represented by the following mathematical expressions:

or its logarithmic transform

where C is the plasma toxicant concentration at time t after injection, C₀ is the plasma concentration achieved immediately after injection, and k_el is the exponential constant or elimination rate constant with dimensions of reciprocal time (eg, minute^–1 or hour^–1). The constant 2.303 in Equation (7-2) is needed to convert natural logarithm into base-10 logarithm. It can be seen from Equation (7-2) that the elimination rate constant can be determined from the slope of the log C versus time plot (ie, k_el = –2.303 · slope).

The elimination rate constant k_el represents the overall elimination of the toxicant, which includes biotransformation, exhalation, and/or excretion pathways. When elimination of a toxicant from the body occurs in an exponential fashion, it signifies a first-order process, that is, the rate of elimination at any time is proportional to the amount of toxicant remaining in the body (ie, body load) at that time. This means that following an iv bolus injection, the absolute rate of elimination (eg, milligrams of toxicant eliminated per minute) continually changes over time. Shortly after introduction of the dose, the rate of toxicant elimination will be at the highest. As elimination proceeds and body load of the toxicant is reduced, the elimination rate will decline in step. As a corollary, it also means that at multiple levels of the toxicant dose, the absolute rate of elimination at corresponding times will be proportionately more rapid at the higher doses. This mode of elimination offers an obvious advantage for the organism to deal with increasing exposure to a toxicant. First-order kinetics occur at toxicant concentrations that are not sufficiently high to saturate either metabolic or transport processes.

In view of the nature of first-order kinetics, k_el is said to represent a constant fractional rate of elimination. Thus, if the fractional elimination rate is constant, for example, 0.3 hour^–1, the percentage of dose or plasma concentration remaining in the body (C/C₀ · 100) and the percentage of the dose or concentration eliminated from the body after 1 hour, that is, 1 – (C/C₀ · 100), are 74% and 26%, respectively, regardless of the dose administered (Table 7-1). The reason why the amount remaining at 1 hour is slightly more than 70%, or the amount eliminated is less than 30%, is because the amount in the body declined continually over the 1-hour period and thus the actual amount eliminated is less than anticipated based on the starting amount in the body. Again, this illustrates the fact that under first-order kinetics, the actual elimination rate declines with the depletion in body load, but the percentage eliminated over a given period of time is the same regardless of dose, that is, the fractional rate of elimination of the toxicant remains constant over time after iv injection or any acute exposure. Because a constant percentage of toxicant present in the body is eliminated over a given time period regardless of dose or the starting concentration, it is more intuitive and convenient to refer to an elimination half-life (T_1/2), that is, the time it takes for the original blood or plasma concentration to fall by 50% or to eliminate 50% of the original body load. By substituting C/C₀ = 0.5 into Equation (7-1), we obtain the following relationship between T_1/2 and k_el:

where 0.693 is the natural logarithm of 2. Simple calculations reveals that it would take about 4 half-lives for >90% (exactly 93.8%) of the dose to be eliminated, and about 7 half-lives for >99% (exactly 99.2%) elimination. Thus, given the elimination T_1/2 of a toxicant, the length of time it takes for near-complete washout of a toxicant after discontinuation of its exposure can easily be estimated. As will be seen in next section, the concept of T_1/2 is also applicable to toxicants that exhibit multiexponential kinetics.

We can infer from the monoexponential decline of blood or plasma concentration that the toxicant equilibrates very rapidly between blood and the various tissues relative to the rate of elimination, such that extravascular equilibration is achieved nearly instantaneously and maintained thereafter. Depiction of the body system by a one-compartment model does not mean that the concentration of the toxicant is the same throughout the body, but it does assume that the changes that occur in the plasma concentration reflect proportional changes in tissue toxicant concentrations (Fig. 7-2 upper, right panel). In other words, toxicant concentrations in tissues are expected to decline with the same elimination rate constant or T_1/2 as in plasma; tissue and plasma concentrations should decline in parallel.

Two-Compartment Model

After rapid iv administration of some toxicants, the semilogarithmic plot of plasma concentration versus time does not yield a straight line but a curve that implies more than one dispositional phase (Fig. 7-2). In these instances, it takes some time for the toxicant to be taken up into certain tissue groupings, and to then reach an equilibration with the concentration in plasma; hence, a multicompartmental model is needed for the description of its kinetics in the body (Fig. 7-1). The concept of tissue groupings with distinct uptake and equilibration rates of toxicant becomes apparent when we consider the factors that govern the uptake of a lipid-soluble, organic toxicant. Table 7-2 presents data on the volume and blood perfusion rate of various organs and tissues in a standard size human. From these data and assuming reasonable partitioning ratios of a typical lipid-soluble, organic compound in the various tissue types, we can estimate the uptake equilibration half times of the toxicant in each organ or tissue region during constant, continuous exposure. The results suggest that the tissues can be grouped into rapid-equilibrating visceral organs, moderately slow-equilibrating lean body tissues (mainly skeletal muscle), and very slow-equilibrating body fat; these groupings give rise to three distinct uptake phases, that is, half times of <2 minutes for the rapid-equilibrating tissues, several tens of minutes for the moderately slow-equilibrating lean body tissues, and hours for the very slow-equilibrating body fat. By inference, three distinct phases of washout should also be evident following a brief exposure to the toxicant, such as after a bolus iv injection. The relative prominence of these distributional phases will vary depending on the average lipid solubility of the toxicant in each tissue grouping and any other sequestration and export mechanisms of a toxicant in particular tissues (eg, tight binding to tissue proteins, active influx into or efflux out of the tissue cell types), as well as the competing influence of elimination from the visceral organs. For example, very rapid metabolism or excretion at the visceral organs would limit distribution into the slow or very slow tissue groupings. Also, there are times when equilibration rates of a toxicant into visceral organs overlaps with lean body tissues, such that the distribution kinetics of a toxicant into these two tissue groupings become indistinct with respect to the exponential decline of plasma concentration, in which case two instead of three tissue groupings may be observed. The concept of tissue groupings with respect to uptake or washout kinetics serves to justify the seemingly simplistic, yet pragmatic, mathematical description of extravascular distribution by the classic two- or three-compartment models.

Plasma concentration–time profile of a toxicant that exhibits multicompartmental kinetics can be characterized by multiexponential equations. For example, a two-compartment model can be represented by the following biexponential equation:

where A and B are coefficients in units of toxicant concentration, and α and β are the respective exponential constants for the initial and terminal phases in units of reciprocal time. The initial (α) phase is often referred to as the distribution phase, and terminal (β) phase as the postdistribution or elimination phase. The lower, middle panel of Fig. 7-2 shows a graphical resolution of the two exponential phases from the plasma concentration–time curve. It should be noted that the α constant is the slope of the residual log-linear plot and not the initial slope of the decline in the observed plasma toxicant concentration, that is, the initial rate of decline in plasma concentration approximates, but is not exactly equal, the α rate constant in Equation (7-4).

It should be noted that distribution into and out of the tissues and elimination of the toxicant are ongoing at all times, that is, elimination does occur during the “distribution” phase, and distribution between compartments is still ongoing during the “elimination” phase. As illustrated in Fig. 7-3, the dynamics of a multicompartmental system is such that the governing factor, that is, be it intercompartmental distribution or elimination, for each of the phases depends on the relative magnitude of the rate constants for intercompartmental exchange and the elimination process. In the usual case, that of rapid distribution and relatively slow elimination (left panel of Fig. 7-3), the initial rapid phase indeed reflects extravascular distribution, and the later, slow phase reflects elimination after a dynamic equilibration between tissue and blood is attained. There are cases where distribution into some tissue group is much slower than elimination. Then, the initial phase could largely reflect elimination, and the later phase is controlled by the slow redistribution of the toxicant from the tissues associated with the peripheral compartment to the central compartment, where it is eliminated (ie, washout in the terminal phase is rate-limited by redistribution from the peripheral compartment). The aminoglycoside antibiotic gentamicin is a case in point (Schentag and Jusko, 1977). Following an iv injection of gentamicin in patients with normal renal function, serum gentamicin concentration exhibits biphasic kinetics. Serum concentration of gentamicin initially falls very quickly with a half-life of around 2 hours reflecting rapid excretion by the kidneys; a slow terminal phase does not emerge until serum concentration has fallen to less than 10% of initial concentration. The terminal half-life of serum gentamicin is in the range of 4 to 7 days. This protracted terminal half-life reflects the slow turnover of gentamicin sequestered in the kidneys. In fact, repeated administration of gentamicin leads to accumulation of gentamicin in the kidneys, which is a risk factor for its nephrotoxicity. Because of the interplay of distribution and elimination kinetics, it has been recommended that multiphasic disposition should be simply described as consisting of early and late or rapid and slow phases; mechanistic labels of distribution and elimination should be applied with some caution. Lastly, the initial phase may last for only a few minutes or for hours. Whether multiphasic kinetics becomes apparent depends to some extent on how often and when the early blood samples are obtained, and on the relative difference in the exponential rate constants between the early and later phases. If the early phase of decline in toxicant concentration is considerably more rapid than the later phase or phases, the timing of blood sampling becomes critical in the ability to resolving two or more phases of washout.

Sometimes three or even 4 exponential terms are needed to fit a curve to the plot of log C versus time. Such compounds are viewed as displaying characteristics of three- or four-compartment open models. The principles underlying such models are the same as those applied to the two-compartment open model, but the mathematics is more complex and beyond the scope of this chapter.

Apparent Volume of Distribution

For a one-compartment model, a toxicant is assumed to equilibrate between plasma and tissues immediately following its entry into the systemic circulation. Thus, a consistent relationship should exist between plasma concentration and the amount of toxicant in each tissue and, by extension, to the entire amount in the body or body burden. The apparent volume of distribution (V_d) is defined as the proportionality constant that relates the total amount of the toxicant in the body to its concentration in plasma, and typically has units of liters or liters per kilogram of body weight (Rowland and Tozer, 2011). V_d is the apparent fluid space into which an amount of toxicant is distributed in the body to result in a given plasma concentration. As an illustration, envision the body as a tank containing an unknown volume (L) of well-mixed water. If a known amount (mg) of dye is placed into the water, the volume of that water can be calculated indirectly by determining the dye concentration (mg/L) that resulted after the dye has fully dispersed, that is, by dividing the amount of dye added to the tank by the resultant concentration of the dye in water. Analogously, the apparent volume of distribution of a toxicant in the body is determined after iv bolus administration, and is mathematically defined as the quotient of the amount of toxicant in the body and its plasma concentration. V_d is calculated as

where Dose_iv is the iv dose or known amount of toxicant in the body at time zero, β is the elimination rate constant, and Display Formula$AUC0∞$ is the area under the toxicant concentration versus time curve from time zero to infinity. Display Formula$AUC0∞$ is estimated by numerical methods, the most common one being the trapezoidal rule (Gibaldi and Perrier, 1982). The product, β · Display Formula$AUC0∞$, in unit of concentration, is the theoretical concentration of toxicant in plasma if dynamic equilibration were achievable immediately after introduction of the toxicant into the systemic circulation. For a 1-compartment model, immediate equilibration of the toxicant between plasma and tissues after an acute exposure does hold true, in which case V_d can be calculated by a simpler and more intuitive equation

where C₀ is the concentration of toxicant in plasma at time zero. C₀ is determined by extrapolating the plasma disappearance curve after iv injection to the zero time point (Fig. 7-2, upper, middle panel).

For the more complex multicompartmental models, V_d is calculated according to Equation (7-5) that involves the computation of area under the toxicant concentration–time curve. Moreover, the concept of an overall apparent volume of distribution is strictly applicable to the terminal exponential phase when equilibration of the toxicant between plasma and all tissue sites are attained. This has led some investigators to refer to the apparent volumes of distribution calculated by Equation (7-5) as V_β (for a two-compartment model) or V_z (for a general multicompartmental model); the subscript designation refers to the terminal exponential phase (Gibaldi and Perrier, 1982). It should also be noted that when Equation (7-6) is applied to the situation of a multicompartmental model, the resultant volume is the apparent volume of the central compartment, often times referred to as V_c. By definition, V_c is the proportionality constant that relates the total amount of the toxicant in the central compartment to its concentration in plasma. It has limited utility, for example, it can be used to calculate an iv dose of the toxicant to target an initial plasma concentration.

V_d is appropriately called the apparent volume of distribution because it does not correspond to any real anatomical volumes. The magnitude of the V_d term is toxicant-specific and represents the extent of distribution of toxicant out of plasma and into extravascular sites (Table 7-3). Equation (7-7) provides a more intuitive interpretation of an apparent volume of distribution:

where V_p is the plasma volume and the Σ represents the summation of the apparent volume of each tissue region (t,i) as represented by the product of P_t,i (ie, partition ratio or tissue-to-plasma concentration ratio at dynamic equilibrium) and V_t,i (ie, anatomical volume of tissue). At one extreme, a toxicant that predominantly remains in the vasculature will have a low V_d that approximates the volume of blood or plasma, that is, the minimum V_d for any toxicant is the plasma volume. For toxicants that distribute extensively into extravascular tissues, V_d exceeds physiological fluid spaces, such as plasma or blood volume, interstitial fluid, or extracellular fluid. A toxicant that is highly sequestered in tissues (ie, high P_t,i) can have a volume of distribution larger than average body size (>1 L/kg). The mechanisms of tissue sequestration include partitioning of a toxicant into tissue fat, high-affinity binding to tissue proteins, trapping in specialized organelles (eg, pH trapping of amine compounds in acidic lysozomes), and concentrative uptake by active transporters. In fact, the equation below is an alternate form of Equation (7-7), which features the interplay of binding to plasma and tissue proteins in determining the partitioning of a toxicant in that only free or unbound drug can freely diffuse across membrane and cellular barriers.

where f_up is the unbound fraction of toxicant in plasma and f_ut,i is the effective unbound fraction in a tissue region. Here, P_t,i is governed by the ratio f_up / f_ut,i. Thus, a toxicant that has high affinity for plasma proteins (eg, albumin and/or α₁-acid glycoprotein) relative to tissue proteins has a restricted distribution volume; for example, the anticoagulant warfarin with a plasma-bound fraction of 0.995 or an f_up of 0.005 (Table 7-3). On the contrary, a toxicant that has a high affinity for tissue proteins and lesser affinity for plasma proteins can have a very high V_d. For example, the tricyclic antidepressant nortriptyline has a good affinity for plasma proteins with a bound fraction of 0.92 or an f_up of 0.08; however, binding of nortriptyline to tissues constituents is so much higher such that it has a V_d of 18 times the body weight in adult humans.

In addition to its value as a parameter to indicate the extent of extravascular distribution of a toxicant, V_d also has practical utility. Once the V_d for a toxicant is known, it can be used to estimate the amount of toxicant remaining in the body at any time when the plasma concentration at that time is known, that is,

where X_B is the amount of toxicant in the body or body burden, and C is the plasma concentration at a time after equilibration between tissue and plasma had been achieved.

Clearance

Toxicants are cleared from the body via various routes, for example, excretion by the kidneys into urine or via bile into the intestine ending in feces, biotransformation by the liver, or exhalation by the lungs. Clearance is an important toxicokinetic parameter that relates the rate of toxicant elimination from the whole body in relation to plasma concentration (Wilkinson, 1987). Although terminal T_1/2 is reflective of the rate of removal of a toxicant from plasma or blood, as was explained earlier, it is also subject to the influence of distributional processes, especially for toxicants exhibiting multicompartmental kinetics. Clearance, on the contrary, is a parameter that solely represents the rate of toxicant elimination; it is not influenced by extravascular distribution.

A formal definition of total body clearance is the ratio of overall elimination rate of a toxicant divided by plasma concentration at any time after an acute exposure or during repetitive or continuous exposure (ie, elimination rate/C); in effect, clearance expresses the overall efficiency of the elimination mechanisms. Because this measure of elimination efficiency is in reference to blood or plasma toxicant concentration, it is also named blood or plasma clearance. High values of clearance indicate efficient and generally rapid removal, whereas low clearance values indicate slow and less efficient removal of a toxicant from the body. By definition, clearance has the units of flow (eg, mL/min or L/h). In the classic compartmental context, clearance is portrayed as the apparent volume containing the toxicant that is cleared per unit of time. After iv bolus administration, total body clearance (Cl) is calculated by

Clearance can also be calculated if the volume of distribution and elimination rate constants are known within the context of a compartmental model; that is, Cl = V_d · k_el for a 1-compartment model and Cl = V_b · β for a 2-compartment model. It should be noted that the preceding relationship is a mathematical derivation and does not imply that clearance is dependent on the distribution volume (see later section for further commenting). A clearance of 100 mL/min can be visualized as having 100 mL of blood or plasma completely cleared of toxicant in each minute during circulation.

The biological significance of total body clearance is better appreciated when it is recognized that it is the sum of clearances by individual eliminating organs (ie, organ clearances):

where Cl_r depicts renal, Cl_h hepatic, and Cl_p pulmonary clearance. Each organ clearance is in turn determined by blood perfusion flow through the organ (i) and the fraction of toxicant in the arterial inflow that is irreversibly removed, that is, the extraction fraction (E_i). Various organ clearance models have been developed to provide quantitative description of clearance that is related to blood perfusion flow (Q_i), free fraction in blood (f_ub), and intrinsic clearance (Cl_int,i) (Wilkinson, 1987). For example, for hepatic clearance (Cl_h), if the delivery of the toxicant to its intracellular site of removal is rate-limited by liver blood flow (Q_h) and the toxicant is assumed to have equal, ready access to all the hepatocytes within the liver (ie, the so-called well-stirred model):

where Cl_int,h is the hepatic intrinsic clearance that embodies a combination of factors that determine the access of the toxicant to the enzymatic sites (eg, plasma protein binding and sinusoidal membrane transport) and the biochemical efficiency of the metabolizing enzymes (eg, V_max/K_M for an enzyme obeying Michaelis kinetics). Cl_int,h would also embody canalicular transport activity if the toxicant is subject to biliary excretion. Equation (7-12) dictates that hepatic clearance of a toxicant from the blood is bounded by either liver blood flow or intrinsic clearance (ie, f_ub · Cl_int,h). Note that when f_ub · Cl_int,h is very much higher than Q_h, E_h approaches unity (ie, near-complete extraction during each passage of toxicant through the hepatic sinusoid or high extraction) and Cl_h approaches Q_h. Put in another way, hepatic clearance cannot exceed the hepatic blood flow rate even if the intrinsic rate of metabolism in the liver is more rapid than the rate of hepatic blood flow because the rate of overall hepatic clearance is limited by the delivery of the toxicant to the metabolic enzymes in the liver via the blood. At the other extreme, when f_ub · Cl_int,h is very much lower than Q_h, E_h becomes quite small (ie, low extraction) and Cl_h nearly equals f_ub · Cl_int,h. In this instance, the intrinsic clearance is relatively inefficient; hence, alteration in liver blood flow would have little, if any, influence on liver clearance of the toxicant. Thus, the concept of clearance is grounded in the physiological and biochemical mechanisms of an eliminating organ.

Relationship of Elimination Half-Life to Clearance and Volume

Elimination half-life (T_1/2) is probably the most easily understood toxicokinetic concept and is an important parameter as it measures the persistence of a toxicant following discontinuation of exposure. As will be seen in a later section, elimination half-life also governs the rate of accumulation of a toxicant in the body during continuous or repetitive exposure. Elimination half-life is dependent on both volume of distribution and clearance. T_1/2 can be calculated from V_d and Cl:

The above relationship among T_1/2, V_d, and Cl is another illustration that care should be exercised in interpretation of data when relying upon T_1/2 as the sole representation of elimination of a chemical in toxicokinetic studies, since T_1/2 is influenced by both the volume of distribution for the toxicant and the rate by which the toxicant is cleared from the blood. For a fixed V_d, T_1/2 decreases as Cl increases because the chemical is being removed from this fixed volume faster as clearance increases (Fig. 7-4). Conversely, as V_d increases, T_1/2 increases for a fixed Cl since the volume of fluid that must be cleared of chemical increases but the efficiency of clearance does not.

Absorption and Bioavailability

For most chemicals in toxicology, exposure occurs mostly via extravascular routes (eg, inhalation, dermal, or oral), and absorption into the systemic circulation is often incomplete. The extent of absorption of a toxicant can be experimentally determined by comparing the plasma toxicant concentration after iv and extravascular dosing. Because iv dosing assures full (100%) delivery of the dose into the systemic circulation, the AUC ratio should equal the fraction of extravascular dose absorbed and reaches the systemic circulation in its intact form, and is called bioavailability (F). In acute toxicokinetic studies, bioavailability can be determined by using different iv and non-iv doses according to the following equation, provided that the toxicant does not display dose-dependent or saturable kinetics.

where AUC_non-iv, AUC_iv, Dose_non-iv, and Dose_iv are the respective area under the plasma concentration versus time curves and doses for non-iv and iv administration. Bioavailabilities for various chemicals range in value between 0 and 1. Complete availability of chemical to the systematic circulation is demonstrated by F = 1. When F < 1, less than 100% of the dose is able to reach the systemic circulation. Because the concept of bioavailability is judged by how much of the dose reaches the systemic circulation, it is often referred to as systemic availability. Systemic availability is determined by how well a toxicant is absorbed from its site of application and any intervening processes that could remove or inactivate the toxicant between its point of entry and the systemic circulation. Specifically, systemic availability of an orally administered toxicant is governed by its absorption at the gastrointestinal barrier, metabolism within the intestinal mucosa, and metabolism and biliary excretion during its first transit through the liver. Metabolic inactivation and excretion of the toxicant at the intestinal mucosa and the liver prior to its entry into the systemic circulation is called presystemic extraction or first-pass effect. The following equation accounts for the action of absorption and sequential first-pass extraction at the intestinal mucosa and the liver as determinants of the bioavailability of a toxicant taken orally:

where f_g is the fraction of the applied dose that is released and absorbed across the mucosal barrier along the entire length of the gut, E_m is the extent of loss due to metabolism within the gastrointestinal mucosa, and E_h is the loss due to metabolism or biliary excretion during first-pass through the liver. Note that E_h in this equation is same as the hepatic extraction E_h defined in Equation (7-12), which refers to hepatic extraction of a toxicant during recirculation. This means that low oral bioavailability of a chemical can be attributed to multiple factors. The chemical may be absorbed to a limited extent because of low aqueous solubility preventing its effective dissolution in the gastrointestinal fluid or low permeability across the brush-border membrane of the intestinal mucosa. Extensive degradation by metabolic enzymes residing at the intestinal mucosa and the liver may also minimize entry of the chemical in its intact form into the systemic circulation.

The rate of absorption of a toxicant via an extravascular route of entry is another critical determinant of outcome, particularly in acute exposure situations. As shown in Fig. 7-5, slowing the absorption rate of a toxicant, while maintaining the same extent of absorption or bioavailability, leads to a delay in time to peak plasma concentration (T_p) and a decrease in the maximum concentration (C_max) (compare case 2 to case 1). The converse is true; accelerating absorption shortens T_p and increases C_max. The dependence of T_p and C_max on absorption rate has obvious implication in the speed of onset and maximum toxic effects following exposure to a chemical. Case 3 in Fig. 7-5 illustrates the peculiar situation when the absorption rate is so much slower than the elimination rate (eg, k_a << k_el for a one-compartment model). The terminal rate of decline in plasma concentration reflects the absorption rate constant, instead of the elimination rate constant; that is, the washout of toxicant is rate-limited by slow absorption until the applied dose is completely absorbed or removed, beyond which time the toxicant remaining in the body will be cleared according the elimination rate-constant. This means that continual absorption of a chemical can affect the persistence of toxic effect following an acute exposure, and that it is important to institute decontamination procedure quickly after overdose or accidental exposure to a toxicant. This is especially a consideration in occupational exposure via dermal absorption following skin contact with permeable industrial chemicals.

Metabolite Kinetics

The toxicity of a chemical is in some cases attributed to its biotransformation product(s). Hence, the formation and subsequent disposition kinetics of a toxic metabolite is at times of interest. In biological monitoring, urinary excretion of a signature metabolite often serves as a surrogate measure of exposure to the parent compound (see later section). As expected, the plasma concentration of a metabolite rises as the parent drug is transformed into the metabolite. Once formed, the metabolite is subject to further metabolism to a nontoxic byproduct or undergoes excretion via the kidneys or bile; hence at some point in time, the plasma metabolite concentration peaks and falls thereafter. Fig. 7-6 illustrates the plasma concentration–time course of a primary metabolite in relation to its parent compound under contrasting scenarios. The left panel shows the case when the elimination rate constant of the metabolite is much greater than the overall elimination rate constant of the parent compound (ie, k_m >> k_p). The terminal decline of the metabolite parallels that of the parent compound; the metabolite is cleared as quickly as it is formed or its washout is rate-limited by conversion from the parent compound. The right panel shows the opposite case when the elimination rate constant of the metabolite is much lower than the overall elimination rate constant of the parent compound (ie, k_m << k_p). The slower terminal decline of the metabolite compared to the parent compound simply reflects a longer elimination half-life of the metabolite. It should also be noted that the Display Formula$AUC0∞$ of the metabolite relative to the parent compound is dependent on the partial clearance of the parent drug to the metabolite and clearance of the derived metabolite. A biologically active metabolite assumes toxicological significance when it is the major metabolic product and is cleared much less efficiently than the parent compound.

Saturation Toxicokinetics

As already mentioned, the distribution and elimination of most chemicals occurs by first-order processes. Under first-order elimination kinetics, the elimination rate constant, apparent volume of distribution, clearance, and half-life are expected not to change with increasing or decreasing dose (ie, dose independent). As a result, a semilogarithmic display of plasma concentration versus time over a range of doses shows a set of parallel plots. Furthermore, plasma concentration at a given time or the Display Formula$AUC0∞$ is strictly proportional to dose; for example, a 2-fold change in dose results in an exact 2-fold change in plasma concentration at a given time after dosing or Display Formula$AUC0∞$. However, for some toxicants, as the dose of a toxicant increases, its volume of distribution and/or clearance may change, as shown in Fig. 7-7. This is generally referred to as nonlinear or dose-dependent kinetics. Biotransformation, active transport processes, and protein binding have finite capacities and can be saturated. For instance, most metabolic enzymes operate in accordance to Michaelis–Menten kinetics (Gibaldi and Perrier, 1982). As the dose is escalated and concentration of a toxicant at the site of metabolism approaches or exceeds the K_M (substrate concentration at one-half V_max, the maximum metabolic capacity), the increase in rate of metabolism becomes less than proportional to the dose and eventually approaches a maximum at exceedingly high doses. The transition from first-order to saturation kinetics is important in toxicology because it can lead to prolonged persistence of a compound in the body after an acute exposure and excessive accumulation during repeated exposures. Some of the salient characteristics of nonlinear kinetics include the following: (1) the decline in the concentrations of the chemical in the body is not exponential; (2) Display Formula$AUC0∞$ is not proportional to the dose; (3) V_d, Cl, k_el (or β), or T_1/2 change with increasing dose; (4) the composition of excretory products changes quantitatively or qualitatively with the dose; and (5) dose–response curves show an abruptly steeper change in response to an increasing dose, starting at the dose at which saturation effects become evident.

Inhaled methanol provides an example of a chemical whose metabolic clearance changes from first-order kinetics at low level exposures to zero-order kinetics at near toxic levels (Burbacher et al., 2004). Fig. 7-8 shows predicted blood methanol concentration–time profiles in female monkeys followed a 2-hour controlled exposure in an inhalation chamber at 2 levels of methanol vapor, 1200 and 4800 ppm. Blood methanol kinetics at 1200 ppm exposure follows typical first-order kinetics. At 4800 ppm, methanol metabolism is fully saturated, such that the initial decline in blood methanol following the 2-hour exposure occurs at a constant rate (ie, a fixed decrease in concentration per unit time independent of blood concentration), rather than a constant fractional rate. As a result, a rectilinear plot of blood methanol concentration versus time yields an initial linear decline, whereas a convex curve is observed in the semilogarithmic plot (compare left and right panels of Fig. 7-8). In time, methanol metabolism converts to first-order kinetics when blood methanol concentration falls below K_M (ie, the Michaelis constant for the dehydrogenase enzyme), at which time blood methanol shows an exponential decline in the rectilinear plot and a linear decline in the semilogarithmic plot. Moreover, Fig. 7-8 shows the greater than proportionate increase (ie, >4-fold) in C_max and Display Formula$AUC0∞$ as the methanol vapor concentration is raised from 1200 to 4800 ppm. It should be noted that a constant T_1/2 or k_el does not exist during the saturation regimen; it varies depending upon the saturating methanol dose.

In addition to the complication of dose-dependent kinetics, there are toxicants whose clearance kinetics changes over time (ie, time-dependent kinetics). A common cause of time-dependent kinetics is autoinduction of xenobiotic metabolizing enzymes; that is, the substrate is capable of inducing its own metabolism through activation of gene transcription. The classic example of autoinduction is with the antiepileptic drug, carbamazepine. Daily administration of carbamazepine leads to a continual increase in clearance and shortening in elimination half-life over the first few weeks of therapy (Bertilsson et al., 1986).

Accumulation During Continuous or Intermittent Exposure

It stands to reason that continual or chronic exposure to a chemical leads to its cumulative intake and accumulation in the body. For a chemical that follows first-order elimination kinetics, the elimination rate increases as the body burden increases. Therefore, at a fixed level of continuous exposure, accumulation of a toxicant in the body eventually reaches a point when the intake rate of the toxicant equals its elimination rate, from thereon the body burden stays constant. This is referred to as the steady state. Fig. 7-9 illustrates the rise of toxicant concentration in plasma over time during continuous exposure and the eventual attainment of a plateau or the steady state. Steady-state concentration of a toxicant in plasma (C_ss) is related to the intake rate (R_in) and clearance of the toxicant.

For a one-compartment model, an exponential rise in plasma concentration is expected during continuous exposure and the time it takes for a toxicant to reach steady state is governed by its elimination half-life. It takes 1 half-life to reach 50%, 4 half-lives to reach 93.8%, and 7 half-lives to reach 99.2% of steady state. Time to attainment of steady state is not dependent on the intake rate of the toxicant. The left panel of Fig. 7-9 shows the same time to 50% steady state at 3 different rates of intake; on the contrary, the steady-state concentration is strictly proportional to the intake rate. The change in clearance of a toxicant often leads to a corresponding change in elimination half-life (see right panel of Fig. 7-9), in which case both the time to reach and magnitude of steady state concentration are altered. The same steady state principle applies to toxicants that exhibit multicompartmental kinetics; except that, accumulation occurs in a multiphasic fashion reflective of the multiple exponential half-lives for intercompartmental distribution and elimination. Typically, the rise in plasma concentration is relatively rapid at the beginning, being governed by the early (distribution) half-life, and becomes slower at later times when the terminal (elimination) half-life takes hold.

The concept of accumulation applies to intermittent exposure as well. Fig. 7-10 shows a typical occupational exposure scenario to volatile chemicals at the workplace over the course of a week. Whether accumulation occurs from day to day and further from week to week depends on the intervals between exposure and the elimination half-life of the chemicals involved. For a chemical with relatively short half-life compared to the interval between work shifts and the “exposure holiday” over the weekend, little accumulation is expected. In contrast, for a chemical with elimination half-life approaching or exceeding the between-shift intervals (>12–24 hours), progressive accumulation is expected over the successive workdays. Washout of the chemical may not be complete over the weekend and result in a significant carry forward of body burden into the next week. It should also be noted that the overall internal exposure as measured by the AUC over the cycle of a week is dependent on the toxicant clearance.

Conclusion

For many chemicals, blood or plasma chemical concentration versus time data can be adequately described by a one- or two-compartment, classic pharmacokinetic model when basic assumptions are made (eg, instantaneous mixing within compartments and first-order kinetics). In some instances, more sophisticated models with increased numbers of compartments will be needed to describe blood or plasma toxicokinetic data; for example, if the chemical is preferentially sequestered and turns over slowly in select tissues. The parameters of the classic compartmental models are usually estimated by statistical fitting of data to the model equations using nonlinear regression methods. A number of software packages are available for both data fitting and simulations with classic compartmental models; examples include WinNonlin (Pharsight Corp, Palo Alto, CA), SAAM II (The Epsilon Group, Charlottesville, VA), ADAPT II (University of Southern California, Los Angeles, CA), and PK Solutions (Summit Research Services, Montrose, CO).

Knowledge of toxicokinetic data and compartmental modeling are useful in deciding what dose or dosing regimen of chemical to use in the planning of toxicology studies (eg, targeting a toxic level of exposure), in choosing appropriate sampling times for biological monitoring, and in seeking an understanding of the dynamics of a toxic event (eg, what blood or plasma concentrations are achieved to produce a specific response, how accumulation of a chemical controls the onset and degree of toxicity, and the persistence of toxic effects following termination of exposure).

The primary difference between physiological compartmental models and classic compartmental models lies in the basis for assigning the rate constants that describe the toxicant’s movement into and out of the body compartments and its elimination (Andersen, 1991). In classic kinetics, the rate constants are defined by the data; thus, these models are often referred to as data-based models. In physiological models, the rate constants represent known or hypothesized biological processes, and these models are commonly referred to as physiologically based models. The concept of incorporating biological realism into the analysis of drug or xenobiotic distribution and elimination is not new. For example, one of the first physiological models was proposed by Teorell (1937). This model contained all the important determinants in xenobiotic disposition that are considered valid today. Unfortunately, the computational tools required to solve the underlying equations were not available at that time. With advances in computer technology, the software and hardware needed to implement physiological models are now well within the reach of toxicologists.

The advantages of physiologically based models compared with classic models are that (1) these models can describe the time course of distribution of toxicants to any organ or tissue, (2) they allow estimation of the effects of changing physiological parameters on tissue concentrations, (3) the same model can predict the toxicokinetics of toxicants across species by allometric scaling, and (4) complex dosing regimens and saturable processes such as metabolism and binding are easily accommodated (Gargas and Andersen, 1988). The disadvantages are that (1) much more information is needed to implement these models compared with classic models, (2) the mathematics can be difficult for many toxicologists to handle, and (3) values for parameters are often poorly defined in various species and pathophysiological states. Nevertheless, physiologically based toxicokinetic models are conceptually sound and are potentially useful tools for gaining rich insight into the kinetics of toxicants beyond what classic toxicokinetic models can provide.

Basic Model Structure

Physiological models are fundamentally complex compartmental models; it generally consists of a system of tissue or organ compartments that are interconnected by the circulatory network. If necessary, each tissue or organ compartments can further be divided into extracellular and intracellular compartments to describe movement of toxicant at the cellular level. The exact model structure, or how the compartments are organized and linked together, depends on both the toxicant and the organism being studied. For example, a physiological model describing the disposition of a toxicant in fish would require a description of the gills (Nichols et al., 1994), whereas a model for the same toxicant in mammals would require a lung compartment (Ramsey and Andersen, 1984). Model structures can also vary with the toxicants being studied. For example, a model for a nonvolatile, water-soluble chemical, which might be administered by iv injection (Fig. 7-11), has a structure different from that of a model for a volatile organic chemical for which inhalation is the likely route of exposure (Fig. 7-12). The route of administration is not the only difference between these 2 models. For example, the first model has a compartment for the intestines, because biliary excretion, fecal elimination, and enterohepatic circulation are presumed important in the disposition of this chemical. The second model has a compartment for fat because fat is an important storage organ for organics. However, the models are not completely different. Both contain a liver compartment because hepatic metabolism of each chemical is an important element of its disposition. It is important to realize that there is no generic physiological model. Models are simplifications of reality and should contain elements considered to represent the essential disposition features of a toxicant.

In view of the fact that physiological modeling requires more effort than does classic compartmental modeling, what then accounts for the popularity of this approach among toxicologists? The answer lies in the potential predictive power of physiological models. Toxicologists are constantly faced with the issue of extrapolation in risk assessments—from laboratory animals to humans, from high to low doses, from acute to chronic exposure, and from single chemicals to mixtures. Because the kinetic constants in physiological models represent measurable biological or chemical processes, the resultant physiological models have the potential for extrapolation from observed data to predicted scenarios.

One of the best illustrations of the predictive power of physiological models is their ability to extrapolate kinetic behavior from laboratory animals to humans. For example, physiological models developed for styrene and benzene correctly simulate the concentration of each chemical in the blood of both rodents and humans (Ramsey and Andersen, 1984; Travis et al., 1990). Simulations are the outcomes or results (such as a chemical’s concentration in blood or tissue) of numerically solving the model equations over a time period of concern, using a set of initial (such as level of exposure) or input conditions (such as route of exposure) and parameter values appropriate for the species (such as organ weights and blood flow). Both styrene and benzene are volatile organic chemicals; thus, the model structures for the kinetics of both chemicals in rodents and humans are identical to that shown in Fig. 7-12. However, the parameter values for rodents and humans are different. Humans have larger body weights than rodents, and thus weights of organs such as the liver are larger. Because humans are larger, they also breathe more air per unit of time than do rodents, and a human heart pumps a larger volume of blood per unit of time than does that of a rodent, although the rodent’s heart beats more times in the same period. The parameters that describe the chemical behavior of styrene and benzene, such as solubility in tissues, are similar in the rodents and human models. This is often the case because the composition of tissues in different species is similar.

For both styrene and benzene, there are experimental data for humans and rodents and the model simulations can be compared with the actual data to see how well the model has performed (Ramsey and Andersen, 1984; Andersen et al., 1984; Travis et al., 1990). The conclusion is that the same model structure is capable of describing the chemicals’ kinetics in two different species. Because the parameters underlying the model structure represent measurable biological and chemical determinants, the appropriate values for those parameters can be chosen for each species, forming the basis for successful interspecies extrapolation. Even though the same model structure is used for both rodents and humans, the simulated and the observed kinetics of both chemicals differ between rats and humans. The terminal half-life of both organics is longer in humans compared with rats. This longer half-life for humans is due to the fact that clearance rates for smaller species are faster than those for larger ones. Even though the larger species breathes more air or pumps more blood per unit of time than does the smaller species, blood flows and ventilation rates per unit of body mass are greater for the smaller species. The smaller species has more breaths per minute or heartbeats per minute than does the larger species, even though each breath or stroke volume is smaller. The faster flows per unit mass result in a more efficient delivery of a chemical to organs responsible for elimination. Thus, a smaller species can eliminate the chemical faster than a larger one can. Because the parameters in physiological models represent real, measurable values, such as blood flows and ventilation rates; the same model structure can resolve such disparate kinetic behaviors among species.

Compartments

The basic unit of the physiological model is the lumped compartment, which is often depicted as a box in a graphical scheme (Fig. 7-13). A compartment represents a definable anatomical site or tissue type in the body that acts as a unit in effecting a measurable kinetic process (Rowland, 1984, 1985). A compartment may represent a particular structure or functional portion of an organ, a segment of blood vessel with surrounding tissue, an entire discrete organ such as the liver or kidney, or a widely distributed tissue type such as fat or skin. Compartments usually consist of three individual well-mixed regions, or subcompartments, that correspond to specific physiological spaces or regions of the organ or tissue. These subcompartments are (1) the vascular space through which the compartment is perfused with blood, (2) the interstitial space that surrounds the cells, and (3) the intracellular space representing the cells in the tissue (Gerlowski and Jain, 1983).

As shown in Fig. 7-13, the toxicant enters the vascular subcompartment at a certain rate in mass per unit of time (eg, mg/h). The rate of entry is a product of the blood flow rate to the tissue (Q_t in L/h) and the concentration of the toxicant in the blood entering the tissue (C_in in mg/L). Within the compartment, the toxicant moves from the vascular space to the interstitial space at a certain net rate (Flux₁) and moves from the interstitial space to the intracellular space at a different net rate (Flux₂). Some toxicants can bind to protein components; thus, within a compartment there may be both free and bound toxicants. The toxicant leaves the vascular space at a certain venous concentration (C_out). C_out is equal to the concentration of the toxicant in the vascular space assuming a well-mixed compartment.

Parameters

The most common types of parameters, or information required, in physiological models are anatomic, physiological, thermodynamic, and transport.

Anatomic

Anatomic parameters are used to describe the physical size of various compartments. The size is generally specified as a volume (milliliters or liters) because a unit density is assumed even though weights of organs and tissues are most frequently obtained experimentally. If a compartment contains subcompartments such as those in Fig. 7-13, those volumes also must be known. Volumes of compartments often can be obtained from the literature or from specific toxicokinetic experiments. For example, kidneys, liver, brain, and lungs can be weighed. Obtaining precise data for volumes of compartments representing widely distributed tissues such as fat or muscle is more difficult. If necessary, these tissues can be removed by dissection and weighed. Among the numerous sources of general information on organ and tissue volumes across species, Brown et al. (1997) is a good starting point.

Physiological

Physiological parameters encompass a wide variety of processes in biological systems. The most commonly used physiological parameters are blood flows and lung ventilation. The blood flow rate (Q_t in volume per unit time, such as mL/min or L/h) to individual compartments must be known. Additionally, information on the total blood flow rate or cardiac output (Q_c) is necessary. If inhalation is the route for exposure to the chemical or is a route of elimination, the alveolar ventilation rate (Q_p) also must be known. Blood flow rates and ventilation rates can be taken from the literature or can be obtained experimentally.

Parameters for renal excretion and hepatic metabolism are another subset of physiological parameters, and are required, if these processes are important in describing the elimination of a chemical. For example, glomerular filtration rate and renal tubular transport parameters are required to describe renal clearance. If a chemical is known to be metabolized via a saturable process, both V_max (the maximum rate of metabolism) and K_M (the concentration of chemical at one-half V_max) for each of the enzymes involved must be obtained so that elimination of the chemical by metabolism can be described in the model. In principle, these parameters can be determined from in vitro metabolism or transport studies with freshly isolated cells, cultured cells, or recombinant DNA expression systems; metabolic studies are also feasible with tissue homogenates or cellular fractions containing the metabolic enzymes (eg, microsomes for cytochrome P450 enzymes and uridine diphosphate glucuronosyltransferases). Appropriate in vitro–in vivo scaling is required (Iwatsubo et al., 1997; MacGregor et al., 2001; Miners et al., 2006). Although there have been examples of remarkable success with quantitative prediction of in vivo hepatic clearance based on in vitro metabolic data, there are also notable failures. There is still very limited experience with in vitro–in vivo scaling of renal or hepatic transporter function. Unfortunately, estimation of metabolic or transport parameters from in vivo studies is also fraught with difficulties, especially when multiple metabolic pathways and enzymes are involved in the metabolic clearance of a substrate, or when parallel and/or sequential transport processes mediate the passage of a solute across a cellular barrier. Estimation of metabolic and excretory parameters remains a challenging aspect of physiologically based toxicokinetic modeling.

Thermodynamic

Thermodynamic parameters relate the total concentration of a toxicant in a tissue (C_t) to the concentration of free toxicant in that tissue (C_f). Two important assumptions are that (1) total and free concentrations are in equilibrium with each other, and (2) only free toxicant can be exchanged between the tissue subcompartments (Lutz et al., 1980). Most often, total concentration is measured experimentally; however, it is the free concentration that is available for diffusion across membrane barriers, binding to proteins, metabolism, or carrier-mediated transport. Various mathematical expressions describe the relationship between these two entities. In the simplest situation, the toxicant is a freely diffusible water-soluble chemical that does not bind to any molecules. In this case, free concentration of the chemical is equal to the total concentration of the chemical in the tissue: C_t = C_f. The affinity of toxicants for tissues of different composition varies. The extent to which a toxicant partitions into a tissue is directly dependent on the composition of the tissue and usually independent of the concentration of the toxicant. Thus, the relationship between free and total concentration becomes one of proportionality: C_t = C_f · P_t; P_t is in effect the partition coefficient between total concentration in the tissue and freely diffusible concentration in the interstitial fluid or plasma water. Knowledge of the value of P_t permits an indirect calculation of the free concentration of toxicant in the tissue or C_f = C_t/P_t, assuming intracellular, interstitial and plasma concentrations of free drug are equal (ie, no concentrative transport across barriers in either direction). Pt is most often determined from tissue distribution studies in animals, preferably at steady state during continuous iv infusion of the toxicant. In some cases, it has been successfully estimated from in vitro binding studies with human or animal tissues or tissue fractions (Lin et al., 1982; MacGregor et al., 2001).

Table 7-4 compares the partition coefficients for a number of toxic volatile organic chemicals. The larger values for the fat-to-blood partition coefficients compared with those for other tissues suggest that these chemicals distribute into fat to a greater extent than they distribute into other tissues. This has been observed experimentally. Fat and fatty tissues, such as bone marrow, contain higher concentrations of benzene than do tissues such as liver and blood. Similarly, styrene concentrations in fatty tissue are higher than styrene concentrations in other tissues. It should be noted that lipophilic organic compounds often can bind to plasma proteins and/or blood cell constituents, in which case the observed tissue/blood partition coefficients will be a function of both the tissue and blood partition coefficient (ie, P_t/P_b). Hence, partitioning or binding to blood constituents (P_b) must be known in order to estimate the true thermodynamic partitioning coefficient for a tissue or the free toxicant concentration at equilibrium. P_b can be determined from in vitro studies of blood cells to plasma distribution and plasma protein binding of the toxicant.

A more complex relationship between the free concentration and the total concentration of a chemical in tissues is also possible. For example, the chemical may bind to saturable binding sites on tissue components. In these cases, nonlinear functions relating the free concentration in the tissue to the total concentration are necessary. Examples in which more complex binding has been used are physiological models for dioxin and tertiary-amyl methyl ether (Andersen et al., 1993; Collins et al., 1999).

Transport

Passage of a toxicant across a biological membrane may occur by passive diffusion, carrier-mediated transport involving either facilitated or active transporters, or a combination thereof (Himmelstein and Lutz, 1979). The simplest of these processes—passive diffusion is a first-order process described by Fick’s law of diffusion. Diffusion of a toxicant occurs during its passage across the blood capillary endothelium (Flux₁ in Fig. 7-13) and across cell barriers (Flux₂ in Fig. 7-13). Flux refers to the rate of transfer of a chemical across a boundary. For simple diffusion, the net flux (mg/h) from one side of a membrane to the other is governed by the barrier permeability and the toxicant concentration gradient.

The term PA is often called the permeability–area product for the membrane or cellular barrier in flow units (eg, L/h), and is a product of the barrier permeability coefficient (P in velocity units, eg, μm/h) for the toxicant and the total barrier surface area (A, in μm²). The permeability coefficient takes into account the diffusivity of the specific toxicant and the thickness of the cell membrane. C₁ and C₂ are the respective free concentrations of the toxicant in the originating and receiving compartments. Diffusional flux is enhanced when the barrier thickness is small, the barrier surface area is large, and a large concentration gradient exists. Membrane transporters offer an additional route of entry into cells, and allow more effective tissue penetration for toxicants that have limited passive permeability. Alternately, the presence of efflux transporters at epithelial or endothelial barriers can limit toxicant penetration into critical organs, even for highly permeable toxicant (eg, P-glycoprotein-mediated efflux functions as part of the blood–brain barrier). For both transporter-mediated influx and efflux processes, the kinetics is saturable and can be characterized by T_max (the maximum transport rate) and K_T (the concentration of toxicant at one-half T_max) for each of the transporters involved. In principle, kinetic parameters for passive permeability or carrier-mediated transport can be estimated from in vitro studies with tissue slices (eg, with tetraethylammonium ion; Mintun et al., 1980) or cultured cell monolayer systems. However, the predictability and applicability of such in vitro approaches for physiological modeling has not been systematically evaluated (MacGregor et al., 2001). At this time, the transport parameters have to be estimated from in vivo data, which are at times difficult and carry a significant degree of uncertainty.

There are two limiting conditions for the uptake of a toxicant into tissues: perfusion-limited and diffusion-limited. An understanding of the assumptions underlying the limiting conditions is critical because the assumptions change the way in which the model equations are written to describe the movement of a toxicant into and out of the compartment.

Perfusion-Limited Compartments

A perfusion-limited compartment, alternately referred to as blood flow-limited or simply flow-limited compartment, describes the situation when permeability across the cellular or membrane barriers (PA) for a particular toxicant is much greater than the blood flow rate to the tissue (Q_t), that is, PA₁ >> Q_t. In this case, uptake of toxicant by tissue subcompartments is limited by the rate at which the toxicant is presented to the tissue via the arterial inflow, and not by the rate at which the toxicant penetrates through the vascular endothelium, which is fairly porous in most tissues, or gains passage across the cell membranes. As a result, equilibration of a toxicant between the blood in the tissue vasculature and the interstitial subcompartment is maintained at all times, and the two subcompartments are usually lumped together as a single extracellular compartment. An important exception to this vascular-interstitial equilibrium relationship is in the brain, where the capillary endothelium with its tight junctions poses a diffusional barrier between the vascular space and the brain interstitium. Furthermore, as indicated in Fig. 7-13, the cell membrane separates the extracellular compartment from the intracellular compartment. The cell membrane is the most crucial diffusional barrier in a tissue. Nonetheless, for molecules that are very small (molecular weight < 100) or lipophilic (log P > 2), cellular permeability generally does not limit the rate at which a molecule moves across cell membranes. For these molecules, flux across the cell membrane is fast compared with the tissue perfusion rate (PA₂ >> Q_t), and the molecules rapidly distribute throughout the subcompartments. In this case, free toxicant in the intracellular compartment is always in equilibrium with the extracellular compartment, and these tissue subcompartments can be lumped as a single compartment. Such a flow-limited tissue compartment is shown in Fig. 7-14. Movement into and out of the entire tissue compartment can be described by a single equation.

where V_t is the volume of the tissue compartment, C_t is the toxicant concentration in the compartment (V_t · C equals the amount of toxicant in the compartment), V_t · dC_t/dt is the change in the amount of toxicant in the compartment with time, expressed as mass per unit of time, Q_t is blood flow to the tissue, C_in is the toxicant concentration entering the compartment, and C_out is the toxicant concentration leaving the compartment. Equations of this type are called mass-balance differential equations. Differential refers to the term dC_t/dt. Mass balance refers to the requirement that the rate of change in the amount of toxicant in a compartment (left-hand side of Equation (7-18)) equals the difference in the rate of entry via arterial inflow and the rate of departure via venous outflow (right-hand side of Equation (7-18)).

In the perfusion-limited case, the concentration of toxicant in the venous drainage from the tissue is equal to the concentration of toxicant in the tissue when the toxicant is not bound to blood constituents (ie, C_out = C_t = C_f). As was noted previously, when there is binding of toxicant to tissue constituents, C_f (or C_out) can be related to the total concentration of toxicant in the tissue through a simple linear partition coefficient, C_out = C_f = C_t/P_t. In this case, the differential equation describing the rate of change in the amount of a toxicant in a tissue becomes

In the event the toxicant does bind to blood constituents, blood partitioning coefficient needs to be recognized in the mass-balance equation.

The physiological model shown in Fig. 7-12, which was developed for volatile organic chemicals such as styrene and benzene, is a good example of a model in which all the compartments are described as flow-limited. Distribution of a toxicant in all the compartments is described by using equations of the type noted above. In a flow-limited compartment, the assumption is that the concentrations of a toxicant in all parts of the tissue are in equilibrium. For this reason, the compartments are generally drawn as simple boxes (Fig. 7-12) or boxes with dashed partitioning lines that symbolize the equilibrium between the intracellular and extracellular subcompartments (Fig. 7-14). Additionally, with a flow-limited model, estimates of fluxes between subcompartments are not required to develop the mass-balance differential equation for the compartment. Given the challenges in measuring flux across the vascular endothelium and cell membrane, this is a simplifying assumption that significantly reduces the number of parameters required in the physiological model.

Diffusion-Limited Compartments

When uptake of a toxicant into a compartment is governed by its diffusion or transport across cell membrane barriers, the model is said to be diffusion-limited or barrier-limited. Diffusion-limited uptake or release occurs when the flux, or the transport of a toxicant across cell barriers, is slow compared with blood flow to the tissue. In this case, the permeability–area product is small compared with blood flow, that is, PA << Q_t. The distribution of large and/or polar molecules into tissue cells is likely to be limited by the rate at which the molecules pass through cell membranes. In contrast, entry into the interstitial space of the tissue through the leaky capillaries of the vascular space is usually rapid even for large molecules. Fig. 7-15 shows the structure of such a compartment. The toxicant concentrations in the vascular and interstitial spaces are in equilibrium and make up the extracellular subcompartment, where uptake from the incoming blood is flow-limited. The rate of toxicant uptake across the cell membrane from the extracellular space into the intracellular space is limited by membrane permeability. Two mass-balance differential equations are necessary to describe the events in these 2 subcompartments:

Q_t is blood flow, and C is the toxicant concentration in the entering blood (in), exiting blood (out), tissue extracellular space (t1), or tissue intracellular space (t2). The subscript (ti) for the PA term acknowledges the fact that PA, reflecting either passive diffusion and/or carrier-mediated processes, can differ between tissues. Both equations feature fluxes or transfers across the cell membrane that are driven by free concentration. Hence, partition coefficients are needed to convert extracellular and intracellular tissue concentration to their corresponding free concentration. C_out in Equation (7-21) is related to C_t1/(P_t1/P_b); the blood partitioning coefficient P_b is required if the toxicant binds to plasma proteins and blood cells. The physiological model in Fig. 7-11 is composed of two diffusion-limited compartments each of which contain two subcompartments—extracellular and intracellular space, and several perfusion-limited compartments.

Specialized Compartments

Lung

The inclusion of a lung compartment in a physiological model is an important consideration because inhalation is a common route of exposure to many volatile toxic chemicals. Additionally, the lung compartment serves as an instructive example of the assumptions and simplifications that can be incorporated into physiological models while maintaining the overall objective of describing processes and compartments in biologically relevant terms. For example, although lung physiology and anatomy are complex, Haggard (1924) developed a simple approximation that sufficiently describes the uptake of many volatile chemicals by the lungs. A diagram of this simplified lung compartment is shown in Fig. 7-16. The assumptions inherent in this compartment description are as follows: (1) ventilation is continuous, not cyclic; (2) conducting airways (nasal passages, larynx, trachea, bronchi, and bronchioles) function as inert tubes, carrying the vapor to the alveoli where gas exchange occurs; (3) diffusion of vapor across the alveolar epithelium and capillary walls is rapid compared with blood flow through the alveolar region; (4) all chemicals disappearing from the inspired air appears in the arterial blood (ie, there is no hold-up of chemical in the lung tissue and insignificant lung mass); and (5) vapor in the alveolar air and arterial blood within the lung compartment are in rapid equilibrium and are related by P_b/a, the blood/air partition coefficient (eg, C_alv = C_art/P_b/a). P_b/a is a thermodynamic parameter that quantifies the equilibrium partitioning of a volatile chemical between blood and air.

In the lung compartment depicted in Fig. 7-16, the rate of inhalation of a volatile chemical is controlled by the ventilation rate (Q_p) and the inhaled concentration (C_inh). The rate of exhalation of the chemical is a product of the ventilation rate and the chemical’s concentration in the alveoli (C_alv). Chemical also can enter the lung compartment via mixed venous blood returning from the heart, at a rate represented by the product of cardiac output (Q_c) and the concentration of chemical in venous blood (C_ven). Chemical leaves the lungs via the blood at a rate determined by both cardiac output and the concentration of chemical in arterial blood (C_art). Putting these four processes together, a mass-balance differential equation can be written for the rate of change in the amount of chemical in the lung compartment (L):

Because of these assumptions, during continuous exposure at steady state the rate of change in the amount of chemical in the lung compartment becomes zero (dL/dt = 0). C_alv can be replaced by C_art/P_b/a, and the differential equation can be solved for the arterial blood concentration:

This algebraic equation is incorporated into physiological models for many volatile organics. In this case, the lung is viewed as a portal of entry and not as a target organ; the concentration of a chemical delivered to other organs by the arterial blood is of primary interest. The assumptions of continuous ventilation, rapid equilibration with arterial blood, and no hold-up in the lung tissues have worked extremely well with many volatile organics, especially relatively lipophilic volatile solvents. Indeed, the use of these assumptions simplifies and speeds model calculations and may be entirely adequate for describing the toxicokinetic behavior of relatively inert vapors with low water solubility.

Inspection of the equation for calculating the arterial concentration of the inhaled organic vapor indicates that P_b/a, the blood/air partition coefficient of the chemical, becomes an important term for simulating the uptake of various volatile organics. As the value for P_b/a increases, the maximum concentration of the chemical in the blood increases. Additionally, the time to reach the steady state concentration and the time to clear the chemical also increase with increasing P_b/a. Fortunately, P_b/a is readily measured by using in vitro techniques in which a volatile chemical in air is equilibrated with blood in a closed system, such as a sealed vial (Gargas and Andersen, 1988).

Liver

The liver is almost always featured as a distinct compartment in physiological models because biotransformation is an important route of elimination for many toxicants and the liver is considered the major organ for biotransformation of xenobiotics. A simple compartmental structure for the liver is depicted in Fig. 7-17, where uptake into the liver compartment is assumed to be flow-limited. This liver compartment is similar to the general tissue compartment in Fig. 7-14, except that the liver compartment contains an additional process for metabolic elimination. Under first-order elimination, the rate of hepatic metabolism (R) by the liver can be presented as

where C_f is the free concentration of toxicant in the liver (mg/L), and Cl_l is the clearance of free toxicant within the liver (L/h). The latter parameter is conceptually the same as the intrinsic hepatic clearance term (Cl_int,h) in Equation (7-12). In the case of a single enzyme mediating the biotransformation and Michaelis–Menten kinetics are obeyed, Cl_l is related to the maximum rate of metabolism, V_max (in mg/h) and the Michaelis constant, K_M (in mg/L) (Andersen, 1981). As a result, the rate of hepatic metabolism can be expressed in terms of the Michaelis parameters.

Under nonsaturating or first-order condition (ie, C_f << K_M), Cl_l becomes equal to the ratio of V_max/K_M. Because many toxicants at high exposure levels display saturable metabolism, the above equation is often invoked for simulation of toxicant disposition across a wide range of doses.

Other, more complex expressions for metabolism also can be incorporated into physiological models. Bi-substrate second-order reactions, reactions involving the destruction of enzymes, inhibition of enzymes, or the depletion of cofactors, have been simulated using physiological models. Metabolism can be also included in other compartments in much the same way as described for the liver.

Blood

In a physiological model, the tissue compartments are linked together by the circulatory network. Figs. 7-11 and 7-12 represent different approaches toward describing the circulatory network in physiological models. In general, the arterial system delivers a chemical into various tissues. Exceptions are the liver, which receives arterial and portal blood, and the lungs, which receive mixed venous blood from the right cardiac ventricle. In the body, the venous blood supplies draining from tissue compartments eventually merge in the vena cava and heart chambers to form mixed venous blood. In Fig. 7-11, a blood compartment is created in which the input is the sum of the toxicant outflow from each compartment (Q_t · C_vt). Outflow from the blood compartment is a product of the blood concentration in the compartment and the total cardiac output (Q_c · C_bl). The mass-balance differential equation for the blood compartment in Fig. 7-11 is as follows:

where V_bl is the volume of the blood compartment; C is concentration; Q is blood flow; bl, br, ot, k, and l represent the blood, brain, other tissues, kidney, and liver compartments, respectively; and vbr, vot, vk, and vl represent the venous blood leaving the organs. Q_c is the total blood flow equal to the sum of the venous blood flows from each organ.

In contrast, the physiological model in Fig. 7-12 does not feature an explicit blood compartment. For simplicity, the blood volumes of the heart and the major blood vessels that are not within organs are assumed to be negligible. The venous concentration of a chemical returning to the lungs is simply the weighted average of the concentrations in the venous blood emerging from the tissues.

where C is concentration; Q is blood flow; l, rp, pp, and f represent the liver, richly perfused, poorly perfused, and fat tissue compartments, respectively; and vl, vrp, vpp, and vf represent the venous blood leaving the corresponding organs. Q_c is the total blood flow equal to the sum of the blood flows exiting each organ.

In the physiological model in Fig. 7-12, the blood concentration entering each tissue compartment is the arterial concentration (C_art) that was calculated above for the lung compartment (Equation (7-24)). The decision to use one formulation as opposed to another to describe blood in a physiological model depends on the role the blood plays in disposition and the type of application. If the toxicokinetics after iv injection is to be simulated or if binding to or metabolism by blood components is suspected, a separate compartment for the blood that incorporates these additional processes is required. A blood compartment is obviously needed if the model were developed to explain a set of blood concentration–time data for a toxicant. However, if blood is simply a conduit to the other compartments, as in the case for inhaled volatile organics shown in Fig. 7-12, the algebraic solution is acceptable.

Fig. 7-18 shows the application of physiological modeling in elucidating the disposition fate of methylmercury and its demethylated product, inorganic mercury following a single peroral administration in the growing adult rat (Farris et al., 1993). The model scheme presented in Panel A for both the organic and inorganic forms of mercury has the following unique features: (1) increase in compartment size due to growth over the long duration of the tissue washout experiment; (2) mercury enters the gut lumen via biliary excretion and secretory transport from gut tissue to lumen, some of which is reabsorbed; (3) uptake of methylmercury from blood into tissues, except for the brain, is assumed to be rate-limited by plasma flow because of sequestration of mercury in rat erythrocytes and its slow release; (4) uptake of methylmercury across the blood–brain barrier is rate-limited by transport; (5) uptake of inorganic mercury into all tissues, except the liver, is limited by permeability/transport; (6) mercury is transferred from skin into hair, where it is irreversibly bound; and (7) mercury in hair is either shed or ingested by the animal during grooming. The model simulations displayed in Panels B, C, and D show two prominent features of methylmercurcy disposition: (1) methylmercury is rapidly demethylated to inorganic mercury, which is slowly eliminated from the brain and the kidneys, two major sites of methylmercury toxicities; and (2) a significant portion of mercury is sequestered in hair and the ingestion of hair by the animal contributes to the remarkable persistence of mercury in the rat. This example illustrates the capability of physiological models to deal with the varied and complex disposition kinetics of toxicants from a wide range of sources under a multitude of experimental and environmental exposure scenarios.

Conclusions

The second section provides an introduction to the simpler elements of physiological models and the important assumptions that underlie model structures. For more detailed aspects of physiological modeling, the readers can consult several in-depth and well-annotated reviews on physiologically based toxicokinetic models (Clewell and Anderson, 1994, 1996; O’Flaherty, 1998; Krishnan and Anderson, 2001; Krishnan et al., 2002; Andersen, 2003). Computer softwares are available for numerically integrating the system of differential equations that form the models. Investigators have successfully used Advanced Continuous Simulation Language (Pharsight Corp, Palo Alto, CA), Simulation Control Program (Simulation Resources, Inc, Berrien Springs, MI), MATLAB (The MathWorks, Inc, Natick, MA), and SAS software applications to name a few. Choice of software depends on prior experience, familiarity with the computer language used, and cost of the software package.

The field of physiological modeling continues to evolve as toxicologists and pharmacologists develop increasingly more sophisticated applications. Three-dimensional visualizations of xenobiotic transport in fish and vapor transport in the rodent nose, physiological models of a parent chemical linked in series with one or more active metabolites, models describing biochemical interactions among xenobiotics, and more biologically realistic descriptions of tissues previously viewed as simple lumped compartments are just a few of the more sophisticated applications. Finally, physiologically based toxicokinetic models are now being linked to biologically based toxicodynamic models to simulate the entire exposure → dose → response paradigm that is basic to the science of toxicology.

This final section considers some of the basic toxicokinetic principles and methods underlying the practice of biological monitoring, which over the past several decades has become an important tool for assessment of environmental health risk, first in occupational exposure and more recently in general population exposure. Biological monitoring or biomonitoring is defined as the systematic sampling of body fluids, and at times body tissue, for the purpose of estimating an individual’s internal dose from exposure to chemicals in the workplace or assessing the range of internal exposure within a select population to environmental pollutants (Manno and Viau, 2010; Paustenbach and Galbraith, 2006). The advantages of biomonitoring over traditional environmental monitoring, such as ambient or personal air sampling or dermal dosimetry, include the accounting of other unanticipated routes of exposure, individual differences in toxicant absorption and disposition, and critical personal or lifestyle variables, such as body size and composition, workload that affects pulmonary ventilation, or cigarette smoking that could affect the metabolic status of an individual. Linking environmental exposure or dose to measurements of concentration of the parent chemical or its metabolite(s) in a biological sample is essentially an exercise in toxicokinetics.

Biomonitoring Reference

Although biomonitoring provides a measure of internal exposure, in the final analysis the data obtained must be relatable to a probable degree of health risk. Hence, for each chemical of concern a reference value must be established that corresponds to a threshold limit, below which a reasonable assurance of safety exist and above which significant risk to the exposed individual or population becomes likely.

In the occupational setting, the concept of Biological Exposure Index (BEI) has been established by the American Conference of Governmental Industrial Hygienists (ACGIH) since early 1980s. BEI for a given chemical exposure represented “… the level of the determinant most likely to be observed in the specimens collected from a worker with an internal dose equivalent to that arising solely from inhalation exposure at the TLV” (Morgan, 1997). Threshold limit values (TLVs) are the reference values recommended by ACGIH for airborne chemical concentrations in the workplace, below which nearly all workers may be exposed repeatedly over a working lifetime without known adverse health effects. BEIs for various industrial chemicals have been established through controlled exposure studies in a laboratory setting and/or simultaneous ambient exposure and biological sampling in the workplace. BEIs have also been estimated through the use of physiologically based modeling and simulations (Leung, 1992). The modeling approach is particularly attractive as it can readily simulate a wide variety of exposure condition, along with the ability to vary personal variables such as the level of physical exertion in a hypothetical worker. The impact of interindividual variability in physiological parameters on the BEI can also be evaluated using physiological models coupled with Monte Carlo simulations (Thomas et al., 1996).

A similar referencing concept, referred to as the Biomonitoring Equivalents (BEs) approach, has also been proposed in population environmental exposure context. For BEs, available toxicokinetic data are used to convert an existing exposure guidance value (eg, reference doses or concentrations—RfDs or RfCs, minimal risk levels—MRLs, tolerable daily intakes—TDIs, or a unit cancer risk—UCR) into an equivalent concentration in a biological sample (Hays and Aylward, 2009). As in the case of BEIs, the conversion can be accomplished using classic or physiological models (Hays et al., 2007).

It should be noted that in both settings, the measurement of parent chemical and/or its metabolite in a chosen biological matrix serves as a biomarker for exposure, which in turn allows for health risk assessment based on generally accepted environmental exposure–risk data. It remains to be seen whether at some future time evidence providing a direct link between biological monitoring of internal dose and health risk will become available in both the occupational and general environmental settings.

Monitoring Strategy

The design of an optimal sampling strategy for biomonitoring is guided by three key considerations: (1) sampling matrix or site that includes blood, urine, exhaled breath, saliva, or hair; (2) choice of the determinant(s) (ie, parent compound and/or metabolites); and (3) sampling time relative to the exposure routine, especially when exposure is intermittent. In addition, normalization procedures have been proposed for some matrices to account for variation in individual physiological condition at the time of sampling. These issues are, in many cases, interrelated.

Decision on sampling time relative to the exposure pattern would be a straightforward matter if exposure was continuous and constant, in which case blood, urine, or other samples can be collected at any time after steady state is reached, that is, after 4 elimination half-lives have elapsed since the start of exposure. In reality, exposure is often episodic or intermittent, and in occupational setting exposure is dictated by the work shift.

Specific sampling times are recommended by ACGIH for each BEI. The commonly designated times include the end of shift, prior to start of a workday, the end of the last shift of the workweek, and the morning after returning from the weekend. The end-of-shift is a reasonable time to assess daily peak exposure for workplace chemicals that have reasonably short elimination half-lives (<6 hours) such that carryover from day to day is not significant (see Fig. 7-10). For chemicals that have elimination half-lives in the order of 12 to 24 hours (or longer), the end of the last shift of the week would be a better measure of peak exposure (see the 24-hour T_1/2 example in Fig. 7-10). For chemicals that have multiphasic washout kinetics (ie, kinetics conforming to a multicompartmental model), timing of sample collection relative to the end of exposure in the immediate after-shift period is critical when the early disposition half-life of the parent compound prevails and could be very short (eg, in the order of minutes). This renders the end-of-shift sampling imprecise because of the high degree of measurement variability, such is the case with blood or breath toluene samples taken at the end-of-shift (Morgan, 1997). One solution is to collect the sample just before the worker returns to the next shift on the day following or after a weekend, by which time washout kinetics has reached the terminal phase with an acceptably long half-life, so as to provide a more reproducible index. Finally, repeat sampling over days or weeks are often needed to firmly establish a representative exposure pattern in individual or groups of workers.

Systematically timed sampling is hardly feasible in a community population exposure study, where sampling is typically random, and exposure comes from diffuse sources and may not occur with any definable regularity. The only approach to overcome such shortcoming is to obtain samples at different times of a day to provide diurnal coverage, which introduces obvious logistical and cost challenges in a population surveillance program.

The choice of determinant or biomarker and the sampling matrix are interrelated. Monitoring of parent compound in blood or urine is preferred, particularly if toxicology of the chemical is attributed to the parent entity. In those instances where a metabolite is solely responsible for or contribute to the adverse effects of exposure, monitoring of the active metabolite, along with the parent compound, would be a logical approach. Inactive metabolite(s) is(are) often times monitored as a surrogate marker in place of the parent toxicant due to its relative abundance, ease of analysis, and desirable toxicokinetic properties. For many chemicals, urinary excretion is not a principal route of elimination. At the same time, polar metabolites are often removed by renal excretion; hence, metabolites are present at high concentrations in urine. For example, hippuric acid (glycine conjugate of the major oxidation metabolite of toluene, benzoic acid) in urine is an accepted BEI for toluene exposure. For chemicals that have inherently short elimination half-life or effectively short washout half-life due to a prominent distribution phase, metabolite(s) with longer elimination half-life may be a more suitable biomarker (ie, being less sensitive to sampling time variation). It should, however, be noted that metabolite levels are governed by both its formation kinetics from parent chemical and its own elimination kinetics; hence, individual differences in metabolite elimination represents an additional sources of variability for metabolite monitoring. Hence, the kinetic advantage of metabolite monitoring is not predictable and must be assessed on a case-by-case basis.

It is not often appreciated that the observed level of a determinant for a chemical exposure is a function not only of current exposure, but also what happened some time before (Droz et al., 1991). This is particular so when exposure is continuous or the interval between intermittent exposures is on the order of the chemical’s elimination half-life (eg, an elimination T_1/2 of 24 hours or longer when exposure reoccurs on a daily basis). In other words, the elimination half-life of a biomarker or index compound dictates how far back in exposure history it reports. For example, exposure to the degreaser solvent, trichloroethylene results in urinary excretion of trichloroethanol (TCE) and trichloroacetic acid (TCA). The elimination T_1/2 of TCE is known to be 3 to 5 hours, whereas that of TCA ranges from 48 to 96 hours. Measuring these 2 metabolites in urine allows one to estimate the exposure of a worker to trichloroethylene during the current work shift with TEC and in the preceding workweek with TCA (Lowry, 1987). A corollary to this principle is the fact that short half-life biomarkers reflect more of the within day or day-to-day fluctuation in exposure, whereas daily fluctuation in exposure is dampened with long half-life biomarkers. Although the former cases may be viewed as undesirable because of variability in the measurement, it offers a better reflection of the oscillation in internal dose and particularly the transient peak exposures. The latter cases provide a less variable, time-averaged measure of exposure.

In addition to the above consideration of determinant abundance, the choice of sampling matrix is driven by ease of sampling and reliability in respect to inter- and intraindividual variations. The advantages and disadvantages for each of the common biological matrices are considered below.

Blood

Blood concentration of determinant(s) is the most representative biological sample, because it should be in equilibrium with all tissue concentrations in the postdistribution phase (Fig. 7-2, right panels). This consideration extends to the relationship of blood concentration to other biological fluids (eg, urine and saliva); as such, concentration of determinant in all other biological fluids (eg, urine and saliva) indirectly reflects the concentration in blood. The major drawbacks of blood sampling are its invasive nature, subject acceptance, and the need for qualified medical personnel to perform blood draw. For environmental pollutants that are sequestered in adipose tissue, fat-soluble fraction of blood has been proposed as a more practical substitute for adipose tissue sampling (Paustenbach and Galbraith, 2006).

Urine

Ease in collection is often cited as a major advantage of sampling urine for biomonitoring; unfortunately, it belies the kinetic complexity involved in the analysis of urinary biomarker data. As mentioned earlier, monitoring of parent compound in urine only applies to a few chemicals that are excreted in significant amounts in urine; in most cases, metabolite(s) are measured in urine. Hence, the elimination kinetics of the marker metabolite need to be taken into account in data interpretation.

There are several types of urine collection: (1) timed collection over 24 hours or several hours; (2) spot urine usually from random collection; and (3) first morning specimen (Hill et al., 1988). The timed urine collection should be performed according to the “double-void” protocol. Urine is collected after first emptying the bladder and then waiting until the next voiding. For extended collection, say over 24 hours, multiple in-between voids are collected and pooled with the final voiding at the end of the collection period. Timed urine collection affords a measure of the total amount of determinant excreted or the average excretion rate of the determinant over a defined time period. Spot urine, either from first morning sample or other times during the day, offers a measure of the urinary concentration of the determinant. The first morning sample has the advantage of being a concentrated overnight sample.

In order to appreciate the applicability and limitation of various urine collection methods in biomonitoring, a brief review of urinary excretion kinetics is in order. As was shown in the “Clearance” section, urinary excretion rate (dU_B/dt) of a biomarker or determinant is related to its concentration in blood or plasma concentration (C) by renal clearance (Cl_r).

It should be noted that dU_B/dt represents an average urinary excretion over a relatively short collection interval; C is the blood or plasma concentration at the mid-time point. The differential form of Equation (7-29) can be integrated over an extended collection period, say 24 hours, to yield a relationship between the total amount excreted in the collection period (U_B,24) and the corresponding area under the blood or plasma concentration–time curve (AUC_0-24, an integral measure of exposure).

Hence, either excretion rate or cumulative excretion over a defined collection period of a urinary biomarker is the most appropriate index secondary to blood concentration measurement. Unfortunately timed urine collection is not widely adopted because of logistical difficulties in the occupational setting and cost issue in a population surveillance system.

Urinary excretion rate is in turn related to pooled urine concentration (C_UB,Δt) and urinary flow rate (V_Δt/Δt).

Urinary concentration as measured from spot collection offers convenience and flexibility; however, it has the distinct disadvantage of being influenced by urine flow rate, which varies greatly from time to time depending on the hydration state of the individual. Several methods have been proposed to adjust for variation in urine flow rate. Urinary creatinine is most often used to normalize urinary concentration data. The following equation shows one such normalization (Garde et al., 2011).

where C_UB and C_UCr are the respective biomarker and creatinine concentration in the spot urine collection, and U_Cr,24 is the daily urinary output of creatinine. This method assumes that blood concentration of biomarker is reasonably constant throughout the day (eg, during stable, continuous exposure or for a chemical with very long elimination half-life). The daily urinary output of creatinine is assumed to be constant between individual; alternately, it can also be adjusted according to individual variables that are known to affect creatinine production: body mass, age, and sex (Boeniger et al., 1993).

An alternate, more commonly adopted normalization is to simply express the amount of biomarker in the spot urine collection per mmol of creatinine. This simple normalization is valid for spot urine collection if we assume creatinine excretion is constant throughout the day and reproducible from individual to individual, which are often not true. It is not surprising that validity of normalizing urinary biomarker to per mmol creatinine has been questioned (Boeniger et al., 1993). Other normalization methods including adjustment to a standard urine flow rate, specific gravity, or osmolality have also been proposed (Hill et al., 1988; Boeniger et al., 1993).

The performance of these various normalization procedures has not been subject to rigorous comparison. It is doubtful any of them could offer a facile solution to the inherently difficult problem posed by spot urine collection in face of the known physiological variability in diuresis and creatinine production and excretion.

Breath

Breath sampling is applicable to biomonitoring of volatile organic compounds (VOCs) including many industrial solvents. In some instances, it can be extended to volatile metabolites of nonvolatile organic chemicals. Breath sampling offers the advantages of being noninvasive and can be performed rapidly, especially when repeated sampling at short time intervals is needed.

The utility of breath sample as a biomarker rests on the assumption that during exposure, VOC in the inspired air reaches the alveoli where it undergoes equilibrium exchange with the arterial blood, which in theory is predicted by the blood/air partition coefficient in vitro (see “Specialized Compartment: Lung”). This alveolar equilibrium assumption is valid for VOCs that have blood/air partition coefficients exceeding 10 (Kelman, 1982). Likewise, in the postexposure situation, unmetabolized volatile compound in mixed venous blood comes into equilibrium exchange with alveolar air, which is exhaled and sampled. Hence, breath sampling can provide an estimate of arterial blood concentration of VOCs based on their known blood/air partition coefficients (Wallace et al., 1996). Partition coefficients for a large number of VOCs have been determined from in vitro studies; most have been validated by blood/breath ratios observed in controlled exposure studies in human subjects at ppm levels that are encountered in occupational settings. There are data to suggest that blood/breath ratio of some VOCs may increase at low ppb exposure levels typically present in the general environment (see example with benzene, Perbellini et al., 1988).

Only 350 mL of the 500 mL inspired volume (tidal volume) actually ventilate the alveoli and undergo gaseous exchange. About 150 mL of inspired air is held in the anatomical dead space between the nose or mouth and the respiratory bronchioles. As a result, expired air when collected in total is a mixture of alveolar air and dead space air. If sampling is done during exposure, the dead space air has a VOC concentration of the last inspired air. If sampling is done postexposure, the dead space air would have a near zero or background VOC concentration (Hill et al., 1988). Therefore, total breath collection is not appropriate for biomonitoring. It has been suggested that mixed expired air concentration can be normalized to alveolar concentration using the observed CO₂ concentration (Wilson, 1986). However, this proposed method of normalization has not been sufficiently validated for VOCs of environmental interest.

Alveolar concentration is best measured by collecting the last part of an expiration (about 200 mL), that is, the end-expired or end-tidal air (Wilson, 1986; Hill et al., 1988). Various devices for collection of end-expired air have been described (Wilson, 1986; Wilson and Monster, 1999). Breath holding and rebreathing techniques have also been proposed to promote equilibration of VOCs between alveolar air and blood in the pulmonary capillaries.

The major difficulty with breath as a biomonitoring matrix is achieving reproducible sampling. Success is critically dependent on strict adherence to a standardized breathing and collection protocol aimed at maintaining a consistent blood/breath ratio between occasions. It is well documented that variability is introduced when subjects breathe too quickly (hyperventilate) or breathe too slowly (hypoventilate) (Wilson, 1986; Hill et al., 1988). Physical activity or workload, which affects ventilation–perfusion of the lungs, is known to alter end-expired air concentration of some VOCs (Wilson, 1986). Finally, standardization of volume and concentration from ambient condition during measurement to body temperature, pressure and water vapor saturation (Hill et al., 1988), along with minor adjustment for contamination of dead space air in end-expired sample using CO₂ level have been proposed to improve the estimation of alveolar air concentration (Wallace et al., 1996).

Saliva

Saliva has drawn attention as a matrix for biomonitoring because of ease in its collection. Transfer of drugs and xenobiotics from blood into saliva occurs via diffusion across the salivary glands and is known to depend on the compound’s lipophilicity and ionization (Caporossi et al., 2010). Saliva contains a low concentration of proteins, mainly albumin derived from plasma and glycoproteins, which impart viscosity and protect the buccal epithelium. As a result, saliva/plasma ratio for neutral, nonprotein bound compounds is expected to be about one. Compounds that are highly bound to plasma proteins can have a saliva/plasma ratio well below one. Saliva pH is usually less than that of plasma; hence, in the absence of binding to plasma proteins, acidic compounds are predicted to have a saliva/plasma ratio less than one, whereas basic compounds could have saliva/plasma ratios greater than one due to pH trapping.

There are several ways to collect saliva. Most often whole saliva is collected, which is a complex mixture of oral fluids, including salivary gland secretions, gingival crevicular fluids, expectorated bronchial and nasal secretions, and even trace of serum and blood from oral bleeding. Whole saliva can be collected by spitting into a vial, wiping the oral cavity with a swap, or using commercially available collectors (eg, Salivette). Stimulants of salivary flow, such as citric acid and chewing gum, have been used to facilitate collection and increase the sample volume. Blood/saliva ratio could differ between stimulated and unstimulated collection condition; for example, change in saliva pH is associated with an increase in salivary flow, which may affect transfer of ionizable compounds into saliva. Direct collection of secretion from the parotid gland for therapeutic monitoring of drug level has been attempted using special collection devices.

In order to apply saliva sampling to biomonitoring, a consistent relationship between blood and saliva concentrations of the determinant is required. This has proven to be a problem for metals and industrial chemicals. For example, the use of saliva for monitoring of Hg and Pb has been investigated in a number of studies. In many instances, Hg or Pb levels in saliva were below the limit of detection, or when detected poor correlations between concentrations in saliva and those in blood were observed. Use of saliva has also been evaluated for several pesticides, polychlorinated biphenyls (PCBs), polychlorinated dibenzo-p-dioxins (PCDDs), and industrial chemicals with mixed results (Esteban and Castaño, 2009; Caporossi et al., 2010). More data will be required to assess the applicability of saliva in occupational and environmental biomonitoring.

Hair

Hair is easy to collect, transport, and store. As hair grows out of the hair follicle, it carries with it a record of past exposure that stretch over weeks to many months. In fact, a temporal exposure pattern can be reconstructed by segmental analysis of a strand of hair. As such, hair is a unique biomonitor of cumulative exposure and is best suited for environmental pollutants that have long elimination half-lives in the order of days to weeks. The main disadvantages of hair as a biological matrix are the difficulty in differentiating external and internal exposure and the variable influence of hair pigmentation and hair care. Assay of biomarkers in the typical quantity of hair collected (50–200 mg) also requires highly sensitive analytical methodologies.

Hair has been used as a matrix for human biomonitoring of exposure to methylmercury for a number of years (Esteban and Castaño, 2009). A strong correlation exists between total Hg in hair and dietary intake of methylmercury, mainly through fish consumption. A predictable relation between hair Hg and blood Hg has also been documented; hence, hair Hg is an acceptable biomarker for the internal dose of Hg from methylmercury exposure. There are also adequate data to support the use of hair measurement as an indicator for occupational and environmental Pb exposure. In contrast, conflicting data exist on the relationship between hair Cd and body burden of Cd.

Much less is known in regards to hair as a biomonitor for organic pollutants (Appenzeller and Tsatsakis, 2012). Pesticides, particularly organochlorine pesticides, are the most investigated environmental pollutants in hair. Indeed hair sampling has been used to monitor workplace exposure to pesticides, as well as PCDDs, polychlorinated dibenzofurans (PCDFs), and coplanar PCBs; however, these reports offer mostly descriptive information (eg, percent of individuals being positive for presence of test pollutants in hair samples, levels of pollutants present in the hair) and have rarely evaluated the relationship of hair pollutant concentration to environmental levels or corresponding concentrations in blood and other biological matrices. Hence, the feasibility of hair sampling for occupational and environmental biomonitoring awaits further research.

Conclusions

The toxicokinetic principles that guide the design of biological monitoring have been established through more than two decades of occupational health research and are now being extended to assessment of population health risk from exposure to environmental pollutants. With the forthcoming of the wealth of environmental biomonitoring data that have recently been collected by public health agencies, such as the U.S. Centers for Disease Control and Prevention (CDC), much more will be learned in regards to biomonitoring strategy as it is applied to surveillance of low level environmental exposure in the various community settings. Even in the occupational health sector, more research is needed to improve the existing biomonitoring methods and technologies so that they become more cost-effective and in turn widen its adoption at the workplace.