On the Importance of Exposure Variability to the Doses of Volatile Organic Compounds
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《毒物学科学杂志》
Department of Environmental Sciences and Engineering and Department of Biostatistics, School of Public Health, University of North Carolina, Chapel Hill, North Carolina 27599–7431
ABSTRACT
The connection between occupational exposure to volatile organic compounds (VOCs) and the resulting internal doses is complicated by variability in air levels from day to day and by nonlinear kinetics of metabolism. We investigated long-term liver doses of VOCs and their metabolites using a physiologically based toxicokinetic model, to which 10,000 random 8-h exposures were inputted. Three carcinogenic VOCs were studied (i.e., benzene, perchloroethylene, and acrylonitrile); these compounds are all bioactivated in the liver and represent a wide range of an important toxicokinetic parameter . For each VOC, simulations were performed using mean air concentrations (μX) between 0.0003 and 1 mg/l (which covers both linear and saturated metabolism) and using coefficients of variation of exposure (CVX) between 0.23 and 2.18 (which includes most occupational settings). Two long-term measures of internal dose were examined, i.e., the area under the liver concentration-time curve (AUCL) and the area under the metabolic rate-time curve (AURC). Interestingly, both AUCL and AURC were linear functions of cumulative exposure (CE, mg·h/l air) even when metabolism was saturated and CVX was large. Yet, at a given CE, both AUCL and AURC were affected by CVX, with the magnitude of the effect increasing with (i.e., perchloroethylene < benzene < acrylonitrile). Nonetheless, the effects of CVX were typically only a few percent and should be of little consequence unless a VOC has large values of , μX,and CVX. We conclude that CE should be a sufficient predictor of the dose of either the parent chemical (VOC) or its metabolite in the liver, even when metabolism is nonlinear. We also observed that AUCL and AURC were sensitive to changes in values of model parameters in the high-variability scenarios, suggesting that (when CVX is large) the population variability of AUCL and AURC can be quite large at a fixed CE.
Key Words: volatile organic compounds; benzene; perchloroethylene; acrylonitrile; variation of exposure.
INTRODUCTION
Persons are exposed to toxic substances in the air of their communities, their homes, and their workplaces. Among these locations, levels tend to be greatest in the workplace where chemicals are produced or used in concentrated form. If exposures are of sufficient intensity and duration, critical tissues are damaged and workers suffer adverse health effects. Here, we are interested in the relationship between airborne exposure and the dose of a contaminant accumulated by a worker over many years. Thus, we only consider chronic effects of exposure and not acute, allergenic, or reproductive effects, where the timing as well as the magnitude of exposures can be important.
As a worker breathes a contaminant at a given air level (mg/l), he or she takes up some portion of the chemical in the lungs. The uptake is related to the breathing rate (l/h) and the retention, a dimensionless quantity that depends upon the physical and chemical properties of the contaminant (gaseous or particulate, solubility, particle size, etc.). Thus, during a brief period of time, uptake = (air level) x (breathing rate) x retention, with units of mg/h. Once the contaminant is cleared from the lungs, it can be distributed to tissues and eliminated by a host of excretory and metabolic processes. The difference between input and output gives rise to an internal mass, or burden (mg), of the substance at a particular time. From mass-balance considerations, the rate at which the burden changes during a brief period is
where the elimination rate has units of h–1. By integrating the burden over time, the internal dose can be derived, where , with units of mg·h. The internal dose can be defined more conventionally as the area under the tissue concentration-time curve, i.e., , with units of mg·h/l. Since the internal dose ultimately determines the extent of tissue damage, our ability to relate workers' exposures to the corresponding AUC values is fundamental to understanding and preventing occupational diseases.
The connection between exposure and AUC is complicated by the intermittent nature of the occupational regimen, where workers tend to be exposed for 8 h per day, and by the profound variability in air levels occurring from one workday to another. Occupational exposures typically vary 15-fold from day to day within workers (median value), and variation greater than 70-fold is observed in about a fourth of occupational groups (Kromhout et al., 1993). Given such great variability, it is reasonable to ponder whether day-to-day fluctuations in air levels might alter the relationship between exposure and internal dose. If air levels vary greatly from day to day (about some mean value), would the AUC differ from that observed when the air level is the same (mean) value each day This subject has
Logically, exposure variability can affect the relationship between exposure and internal dose only if two conditions are met (Rappaport, 1991). First, the contaminant must be eliminated from the body sufficiently rapidly so as not to accumulate from week to week. This is because substances that accumulate (notably insoluble dusts, heavy metals, and lipophilic organic compounds) achieve burdens much greater than the mass taken up in a single day and thereby are reasonably invariant to daily fluctuations in air levels. For such contaminants, cumulative exposure (CE), i.e., the product of the mean exposure and time (with units of mg·h/l), should be a valid predictor of the long-term internal dose (AUC). Second, the contaminant must be either taken up by, or eliminated from, the body by a nonlinear process over the relevant range of exposure. This condition is necessary because linear kinetics would maintain a strict proportionality between AUC and CE even when the contaminant is rapidly absorbed and eliminated (a restatement of ‘Haber's Law’) (Cox, 1995; Olson and Cumming, 1981; Rappaport, 1991).
Volatile organic compounds (VOCs) are rapidly eliminated via nonlinear (saturable) metabolism. Since many VOCs have been associated with chronic health effects, the purpose of this investigation is to explore the influence of exposure variability upon the internal doses of these compounds and their metabolites. Points will be illustrated with three chemicals that are known or suspected human carcinogens, namely, benzene (Hayes et al., 1997; Savitz and Andrews, 1996, 1997; Snyder, 2002), perchloroethylene (Lash and Parker, 2001), and acrylonitrile (Collins and Strother, 1999; Kirman et al., 2000). These substances were chosen because they are biotransformed in the liver by phase-I metabolism and possess an important toxicokinetic parameter (, to be defined) that ranges in value from low (perchloroethylene), to moderate (benzene), to high (acrylonitrile). The carcinogenicity of all three compounds is likely due to the action of one or more reactive metabolites. The sites of tumor formation include the hematopoietic system (benzene), liver and kidney (perchloroethylene), and the brain (acrylonitrile).
In what follows, we will couple a random time series of simulated air levels, representing the variability in occupational exposure over many years, with a physiologically based toxicokinetic model, representing the disposition of VOCs and metabolite production in the body. Such toxicokinetic models provide the means to relate external exposure to internal levels and, thus, are well suited for evaluating the doses of VOCs and their metabolites following prolonged periods of occupational exposure.
MATERIALS AND METHODS
Toxicokinetic model. Figure 1 displays a physiologically based toxicokinetic model that is widely accepted as a reasonable depiction of mammalian absorption and elimination of VOCs (Andersen, 1981a; Droz and Guillemin, 1983; Ramsey and Andersen, 1984). The input to the model is the contaminant, at air concentration X (mg/l), inhaled into a central (lungs/blood) compartment at the alveolar ventilation rate QAlv (l/h). The contaminant is absorbed into the arterial blood according to its blood-air partition coefficient (B). Once inside the body, the chemical is transported at the rate of the cardiac output QCar (l/h) via the arterial blood at concentration CArt (mg/l). The chemical is distributed to parallel tissue groups, consisting of the liver (L, the only metabolizing tissue), the rapidly perfused tissues (RPT, mainly the central organs), the slowly perfused tissues (SPT, mainly muscles and skin), and the fat (F), at rates defined by the perfusion rates (QL for the liver, etc., l/h). The tissue groups are all assumed to be homogenous well-mixed volumes. Transfer of the chemical from the arterial blood to each tissue group is governed by the tissue-blood partition coefficient (L, etc.) and volume (VL, etc., l); the concentration is designated as CL (mg/l) for the liver, etc. The chemical is cleared from the body either passively, by exhalation at rate (mg/h), or by metabolism in the liver to metabolite M at rate RM (mg/h). For benzene, perchloroethylene, and acrylonitrile, note that M would represent the initial epoxide produced by cytochrome P450 metabolism, namely, benzene oxide, perchloroethylene epoxide, and cyanoethylene oxide, respectively.
The nonlinear behavior of the model shown in Figure 1 relates to liver metabolism, which obeys Michaelis-Menten kinetics at rate , where Vmax represents the maximum rate of metabolism (mg/h) and KM (mg/l) is the liver-blood concentration of the chemical at which RM = Vmax/2. If , then metabolism is pseudo-first order (linear) at rate . If , then metabolism is zero order at rate Vmax. At intermediate values of , the rate of metabolism lies between these limiting values. We also identify the dimensionless quantity , representing "the maximum concentration gradient that exists across the liver at a given blood flow" divided by KM (Andersen, 1981b). When , metabolism is not complete at low substrate concentrations, and the transition from first- to zero-order behavior is gradual. Conversely, when , metabolism is essentially complete at low substrate concentrations, and this transition between kinetic states is abrupt (Andersen, 1981b).
Model parameters and simulation. The flow rates (l/h) and tissue volumes (l) were scaled to a 70-kg human working at 50 W of exercise according to Tardif et al. (2002), i.e., QAlv = 1323, QCar = 603, QL = 96.4, QF = 36.2, QRPT = 163, QSPT = 307, VL = 1.82, VF = 13.3, VRPT = 3.50, and VSPT = 40.6. The chemical-dependent partition coefficients and biochemical constants, shown in Table 1, were compiled from (Dobrev et al., 2001; Sweeney et al., 2003; Travis et al., 1990) after scaling Vmax for a 70-kg human as Vmax=Vmaxc · 700.75, where Vmaxc is the scaling coefficient given by the authors.
Simulation involved introducing a time series of 8-h occupational exposures {Xi} into the model shown in Figure 1, where Xi (mg/l) is the air concentration during the ith 8-h workday (i = 1, ..., 10,000). We modeled Xi as a lognormal variate with true (unobservable) mean μX and variance (Rappaport, 1991); by randomly sampling from a given distribution (defined by μX and ), we simulated 10,000 occupational exposures representing about 40 years of work. Simulations were performed with μX = 0.0003, 0.001, 0.003, 0.01, 0.03, 0.1, 0.3, and 1.0 mg/l, and (for each value of μX) values of equal to 0.23, 0.62, and 2.18. These CVX values were selected to represent levels of occupational-exposure variability ranging from "very low" to "moderate" to "very high." [For reference, these CVX values correspond, respectively, to the 2nd, 41st and 84th percentiles of the cumulative distribution of geometric standard deviations reported by Kromhout et al. (1993). Note that, for the lognormal variate Xi, , where is the variance of Yi = ln(Xi), and the geometric . Since we consider only a single worker in our simulations, represents the within-person variance component from Kromhout et al.] After 10,000 simulated workdays, the cumulative exposure (mg·h/l) was calculated as , for 8 h of exposure per workday.
The toxicokinetic model employed mass-balance equations to describe the rates of change of the chemical concentration in each compartment, based largely upon relationships given by Ramsey and Andersen (1984) (see Supplementary Data). These equations were solved numerically by Euler's method, using a program written with SAS software (SAS Institute, Cary, NC) and employing a time step t of either 0.01 h (benzene and perchloroethylene) or 0.002 h (acrylonitrile), as required to maintain continuity. Following 8 h of simulated exposure at air concentration Xi, the inhaled air concentration was reduced to zero, and liver concentrations were monitored until t = 336 h to ensure complete clearance of the chemical from all tissues. The time series {Xi} produced the corresponding time series of internal doses, represented by the AUC of the parent chemical in the liver after each exposure {AUCLi} (mg·h/l), where and CLij is the liver concentration (mg/l), after the jth time step for the ith exposure. Metabolism was monitored in terms of the time series of the amount of metabolite produced from the ith exposure, referred to as the area under the metabolic rate-time curve (Andersen, 1981b), i.e., (mg), and RMij is the rate of metabolism (mg/h) after the jth time step for the ith exposure. The long-term liver dose of parent chemical after 10,000 exposures was calculated as (mg·h/l), and the corresponding long-term dose of metabolite as (mg). Even though both AUCL and AURC are long-term dose metrics, note that they are dimensionally different.
We focused our models upon the liver and metabolite doses (AUCL and AURC) even though the liver is not necessarily the target of toxicity for the VOCs investigated. Because our model only permits metabolism to take place in the liver, the liver is more sensitive to perturbations in levels of the parent compound than are the blood and other tissue groups. Thus, effects of exposure variability upon AUCL are at least as great as upon the analogous AUC values for other tissues. Likewise, AURC represents a global measure of metabolite production that should be relevant to all tissues where metabolites are ultimately distributed from the liver by the systemic circulation.
Sensitivity analysis. Additional simulations were conducted to determine the sensitivity of the two dose metrics AUCL and AURC to each of the parameters in the model. Each parameter was increased by 1% and the full simulation was repeated for 4 exposure distributions, representing a wide range of mean values (μX = 0.0003 and 0.3 mg/l) and variability (CVX = 0.23 and 2.18). While testing sensitivity to blood flow rates, mass balance was maintained by reducing QSPT, as necessary, to compensate for the 1% increase in QRPT, QL, or QF. Normalized sensitivity coefficients were estimated as the percentage change observed in AUCL or AURC divided by the 1% change in the parameter of interest (e.g., a 2% increase in AUCL or AURC would correspond to a normalized sensitivity coefficient of 2).
RESULTS
Exposure-Dose Relationships for Benzene
To illustrate the effect of exposure variability on the daily liver doses of benzene and its metabolite at a given mean exposure, values of {AUCLi} and {AURCi} are plotted versus exposure {Xi} in Figure 2 when the mean exposure μX = 0.010 mg/l (3.13 ppm) and CVX = 0.23 (very low variability) or CVX = 2.18 (very high variability). The effect of saturable metabolism is apparent when CVX = 2.18, but not when CVX = 0.23; this is due to the much greater range of benzene air levels in the high-variability scenario, relative to the mean value of 0.010 mg/l. Note that the shapes of the nonlinear relationships in Figures 2A and 2B differ when CVX = 2.18. As benzene metabolism approaches saturation, the ratio of the arterial blood concentration to the exposure concentration () increases, and a larger fraction of benzene is distributed to the fat, where it is stored pending eventual release to the systemic circulation (and the liver) during the subsequent period of zero exposure. This ultimately leads to values of AUCLi that are disproportionably greater than those observed at lower exposure levels. Thus, the relationship between AUCLi and exposure concentration exhibits concave-upwards behavior that becomes pronounced when Xi 0.05 mg/l (Fig. 2A). At the same time, saturation of benzene metabolism leads to reduced uptake and increased passive clearance of benzene. These effects combine to disproportionably reduce metabolism during periods of high benzene exposure and give rise to the concave-downwards shape of the relationship between AURCi and exposure (Fig. 2B). Accordingly, the rate of metabolite production is substantially saturated, given 8 h of exposure to benzene in the range of 0.2–0.4 mg/l (63–126 ppm).
The relationships shown in Figure 2 suggest that large variability in exposure can increase the liver dose of benzene and reduce the corresponding dose of the benzene metabolite at a given mean exposure μX. This is illustrated in Figure 3, which shows the time series of daily liver doses {AUCLi} and the corresponding long-term liver dose (AUCL) (Figs. 3A and 3B) as well as the daily metabolite doses {AURCi} and the corresponding long-term metabolite dose (AURC) (Figs. 3C and 3D), when μX = 0.010 mg/l and CVX = 0.23 (very low variability, Figs. 3A and 3C) or CVX = 2.18 (very high variability, Figs. 3B and 3D). The figures illustrate that, indeed, after 10,000 simulated workdays, AUCL and AURC (shown at the right axis) are different when CVX = 0.23 (AUCL = 3.9 g·h/l, AURC = 205 g) than when CVX = 2.18 (AUCL = 4.4 g·h/l, AURC = 185 g). Yet, the two values of AUCL and AURC only differ by 10–13%, despite the enormous differences in the variability of the two time series {AUCLi} and {AURCi} giving rise to the long-term doses.
The relationships shown in Figure 3 indicate that AUCL and AURC increase linearly with workday when μX = 0.010 mg/l, regardless of the magnitude of CVX; that is, the slope for AUCL versus workday [in (mg·h/l)/d] = 39μX when CVX = 0.23, and equals 44 μX when CVX = 2.18, while the slope for AURC versus workday (in mg/d) = 2050μX when CVX = 0.23 and equals 1850 μX when CVX = 2.18. In fact, the same results were observed for both AUCL and AURC over an extremely wide range of benzene exposures representing kinetics that changed from linear (μX = 0.0003 mg/l, 0.1 ppm) to fully saturated (μX = 1.0 mg/l, 313 ppm) (results not shown). Since CE is a linear function of time, i.e., CE = μX x t for t representing exposure time in h (t = 80,000 h in our simulations), then CE must be a good predictor of the long-term internal dose of benzene (AUCL) or its metabolite (AURC), regardless of the variability in air levels from day to day (CVX). Figure 4 shows graphs of AUCL and AURC versus CE for benzene exposures when μX = 0.001 or 1.0 mg/l and CVX = 0.23 or 2.18. Clearly, linear relationships are observed in both cases with intercepts equal to zero and slopes of either AUCL/CE (Figs. 4A and 4B) or AURC/CE (Figs. 4C and 4D). (Since CE = μX · t and since AUCL = k · μX · t, then AUCL is a constant multiple of CE and k = AUCL/CE. The same argument holds for AURC). Furthermore, after 10,000 simulated workdays, AUCL and AURC are very close in value for both the low- and high-variability scenarios, indicating that exposure variability had small effects upon AUCL/CE and AURC/CE for benzene when 0.001 μX 1 mg/l.
Effects of Exposure Variability upon AUCL/CE and AURC/CE
It was illustrated in Figures 4A and 4C that, when the toxicokinetics for benzene were linear (μX = 0.001 mg/l), AUCL/CE and AURC/CE were virtually unchanged for scenarios involving either very low variability (CVX = 0.23) or very high variability (CVX = 2.18). However, when benzene metabolism was saturated (μX = 1.0 mg/l), the slopes differed marginally between scenarios; that is, AUCL/CE increased from 9.45 when CVX = 0.23 to 9.75 when CVX = 2.18 (Fig. 4B), while AURC/CE concurrently decreased from 64.6 to 52.5 l/h (Fig. 4D). The same behavior was observed for simulations involving perchloroethylene and acrylonitrile, although the magnitudes and patterns of the deviations differed (results not shown). This indicates that, at a given CE, highly variable exposure distributions can lead to marginally different internal doses (AUCL and AURC) than those of low variability.
The effects of exposure variability on the slopes AUCL/CE and AURC/CE (after 10,000 8-h workdays) are summarized in Figures 5A– 5F for benzene, perchloroethylene, and acrylonitrile when 0.0003 μX 1.0 mg/l and when CVX = 0.23, 0.62, and 2.18. For each chemical, AUCL/CE and AURC/CE are hardly affected by exposure variability when μX 0.01 mg/l, even when CVX = 2.18. However, as μx increases above 0.01 mg/l, upwards divergence of AUCL/CE was observed (Figs. 5A, 5C, and 5E) along with downwards divergence of AURC/CE (Figs. 5B, 5D, and 5F), consistent with increasing saturation of VOC metabolism. These changes occur first for CVX = 2.18 and then for CVX = 0.62 and 0.23, respectively.
The curves represented by CVX = 0.23 and 0.62 in Figure 5 are very similar, suggesting that low or moderate variation in occupational exposure has little impact upon the relationship between either AUCL/CE and μX or AURC/CE and μX. However, deviations of the high-variability curves (CVX = 2.18) from the low-variability curves (CVX = 0.23) can be large, depending on the particular VOC and on whether AUCL or AURC is being considered. Here we define the high-variability deviation for AUCL/CE as and that for AURC/CE as . These high-variability deviations (in percent) are shown in Figure 6A and Figure 6B for AUCL/CE and AURC/CE, respectively, for the three VOCs in our study. Referring first to AUCL/CE, the maximum deviations differed among the VOCs, i.e., 2% for perchloroethylene, 21% for benzene, and 570% for acrylonitrile (Fig. 6A). On the other hand, maximum deviations of the AURC/CE were very uniform across the VOCs, ranging between –29 and –31%. Note that these maximum deviations occurred at values of μX between 0.1 and 0.3 mg/l, depending upon the particular VOC. Since the mean exposures corresponding to maximum deviations were on the cusps between linear and saturable metabolism, the low-variability scenario resulted in essentially linear metabolism on all workdays; here, AUCL/CE and AURC/CE were near the baseline values observed at much lower mean exposures (see Fig. 5). On the other hand, the high-variability scenario included many days where metabolism was in the saturable range, thereby producing major deviations in AUCL/CE and AURC/CE from their near-baseline values. For example, from Figure 6A, the maximum deviation in AUCL/CE for acrylonitrile occurred when μX = 0.1 mg/l. Referring to Figure 5E, we see that, when μX = 0.1 mg/l and CVX = 0.23, AUCL/CE = 5.4, a value only marginally greater than the baseline value of 3.8 observed when μX 0.003 mg/l. Yet, when μX = 0.1 mg/l and CVX = 2.18, AUCL/CE = 36.5, a 7-fold deviation from the low-variability scenario! As μX increased above 0.1 mg/l for acrylonitrile, metabolism shifted into the saturable range, and AUCL/CE increased dramatically with μX when CVX = 0.23; this narrowed the gap in AUCL/CE between the low- and high-variability scenarios.
Effects of on AUCL/CE and AURC/CE
The deviations in AUCL/CE and AURC/CE between high-variability and low-variability scenarios increased in the following order: perchloroethylene < benzene < acrylonitrile, which matches the order of the toxicokinetic parameter identified earlier. When , the transition from first- to zero-order kinetics is abrupt, being described as ‘flip-flop’ behavior (Andersen, 1981b). As a consequence, the toxicokinetics of acrylonitrile with is much more likely to ‘flip-flop’ between kinetic states than either perchloroethylene or benzene . Since liver extraction is essentially complete for acrylonitrile at low levels of exposure, AUCL/CE tends to be much smaller at baseline than the corresponding value for perchloroethylene; e.g., when μX = 0.001 mg/l, AUCL/CE is 3.8 for acrylonitrile (Fig. 5E), compared to 53.6 for perchloroethylene (Fig. 5C). Conversely, efficient metabolism leads to a much larger AURC/CE for acrylonitrile at baseline than for perchloroethylene; e.g., when μX = 0.001 mg/l, AURC/CE is 1194 l/h for acrylonitrile (Fig. 5F), compared to 66.9 l/h for perchloroethylene (Fig. 5D). The flip-flop behavior of metabolism for acrylonitrile translates days of high exposure into days of very high liver dose (AUCLi); as noted earlier, this results in a 7-fold increase in AUCL/CE for the high-variability scenario (when μX = 0.1 mg/l) compared to the near-baseline value for the low-variability scenario. Since benzene and perchloroethylene do not exhibit flip-flop kinetics, deviations from their near-baseline values of AUCL/CE are much more modest, in the range of about 2–20% (Fig. 6A).
The picture regarding the metabolite dose was different, given maximum deviations in AURC/CE of about –30% for all three VOCs (Fig. 6B). This is because the large baseline value of AURC/CE for acrylonitrile tended to offset the abrupt reduction in daily metabolite dose (AURCi) occurring during the high-exposure days. Since benzene and perchloroethylene do not exhibit flip-flop kinetics, their reductions in AUCLi or AURCi were more modest during the high-exposure days; but these changes were offset by their smaller baseline values of AURC/CE, yielding essentially the same percent deviations as for acrylonitrile.
Sensitivity Analysis
Results of the sensitivity analyses are summarized in Figure 7 for AUCL and in Figure 8 for AURC, based upon a 1% increase in each of the toxicokinetic parameters. The sensitivities of the two dose metrics were greatly influenced by the variability of exposure (CVX) at a given mean exposure (μX). That is, long-term doses were much more sensitive to changes in model parameters when CVX = 2.18 than when CVX = 0.23. Indeed, it was common to observe normalized sensitivity coefficients greater than ±5 when CVX = 2.18, whereas coefficients rarely exceeded ±2 when CVX = 0.23. This suggests that AUCL and AURC would vary considerably across a population exposed at a given μX when exposure was highly variable under either linear (μX = 0.0003 mg/l) or saturated (μX = 0.3 mg/l) kinetics. The normalized sensitivity coefficients shown in Figures 7 and 8 indicate general sensitivity to most parameters. This probably reflects the structure of the model, where all parameters, except the partition coefficients and KM, were functions of body weight and, therefore, were highly correlated. In comparing among VOCs, the most notable difference concerns sensitivity of AUCL in the high-exposure, high-variability scenario (Fig. 7D), where deviations were negative for acrylonitrile but were positive for benzene and perchloroethylene. This probably points to the lipophobic nature of acrylonitrile (whereas the other compounds are lipophilic), because days of saturating exposure would not lead to a buildup of acrylonitrile in the fat (with subsequent release to the circulation and the liver) but rather to increased passive clearance in the exhaled air.
Regarding perturbations to the parameters that influence metabolic clearance, i.e., Vmax, KM, and QL, AUCL was consistently more sensitive for benzene and acrylonitrile (high-affinity substrates) than for perchloroethylene (low-affinity substrate) (see Fig. 7). This suggests that factors affecting blood flow to the liver (such as exercise rate) and those influencing metabolism (such as genetic polymorphisms as well as enzyme induction and inhibition) would affect liver doses of benzene and acrylonitrile to a much greater extent than they would for the dose of perchloroethylene, particularly in situations where exposure is highly variable from day to day.
DISCUSSION
Recognition that the dose of a substance ultimately determines its toxicity has been attributed to Paracelsus in work published more than 400 years ago (Gallo, 2001). Since then, the fields of toxicology and epidemiology have embraced the dose-response relationship as fundamental to the understanding of risks of diseases caused by chemical exposures. Unfortunately, our ability to estimate long-term doses from occupational exposures has been hampered by the variability in levels within and between persons in a given population and by the lack of historical measurements of exposure. In the face of large variability and few measurements, the ability to accurately quantify dose-response relationships is sadly limited. If exposure databases are to improve for future investigations, we must adopt sampling strategies that place a premium upon longitudinal exposure data collected according to sound statistical principles (Rappaport, 1991; Rappaport et al., 1995). A strong motivation for such a change would be to accept by default the premise that CE is the principal determinant of the long-term internal dose
The purpose of this paper has been to evaluate the premise that CE is a sufficient predictor of the internal doses of benzene, perchloroethylene, and acrylonitrile, three carcinogenic VOCs that are cleared in part by saturable metabolism over a wide range of toxicokinetic behaviors (as reflected by differing values of ). We observed in all cases that both the long-term liver dose (AUCL) and the long-term metabolite dose (AURC) were essentially linear functions of CE over about 40 simulated years of occupational exposure, even when daily-dose increments (AUCLi and AURCi) were saturated (e.g., see Fig. 4). Thus, despite the enormous range of daily exposures that can be observed in the workplace, the straight-line slope representing AUCL/CE or AURC/CE after several years is essentially fixed for an individual worker at a given mean exposure (μX).
Despite the linear relationship between AUCL or AURC and CE for an individual worker, the corresponding relationship across a population could well be nonlinear if some workers have mean air levels in the saturable range. For example, in a population of workers heavily exposed to the three VOCs investigated here, we would anticipate a concave-downwards shape in the exposure-biomarker relationship across the population for any biomarker located ‘downstream’ from the initial metabolic step (see Fig. 2B). Indeed, such shapes have been reported for protein adducts and urinary metabolites of benzene (both downstream biomarkers) (Rappaport et al., 2002a,b; Waidyanatha et al., 2004), as well as for the mortality-CE curve for lymphohematopoietic cancers among benzene-exposed workers (Hayes et al., 1996).
Our results indicate that individual workers who experience the same CE could nonetheless have different long-term internal doses (AUCL or AURC) if their individual levels of exposure variability (values of CVX) differed greatly. The magnitude of such deviations would depend upon the particular dose metric. Since most VOCs are metabolized to toxic products, the more important effect of exposure variability concerns its relation to the internal metabolite dose (AURC). Here, our results indicate that differences in AURC/CE (arising from different values of CVX across the population) should be small for VOCs, with maximum deviations in the range of about –30% as observed for benzene, perchloroethylene, and acrylonitrile (Fig. 6B). We conclude that assignment of metabolite doses to VOCs, based solely on CE, should not compromise estimation of exposure-response relationships. This conclusion is at odds with the observation of Collins et al. that the number of ‘peak’ exposures to benzene (greater than 100 ppm) was a better predictor of lymphohematopoietic cancers than was CE, and could point to the large uncertainties in estimation of individual CEs mentioned by the authors (Collins et al., 2003). Another recent study found no evidence that the risk of lymphohematopoietic cancers was influenced by peak exposures (Glass et al., 2003).
Turning now to the liver dose of a VOC per se, our results indicate that AUCL/CE can differ by several hundred percent between high- and low-variability scenarios, but only when μX and CVX are large and when . If not all three of these conditions are met, then deviations of AUCL/CE should only be a few percent (see Fig. 6A for acrylonitrile when μX 0.003 mg/l or CVX 0.62 and for benzene and perchloroethylene at all values of μX). Yet there could well be situations where such a nexus of three independent factors could occur. For example, if a worker was exposed to acrylonitrile in intermittent outdoor operations, giving rise to a large (Kromhout et al., 1993), at a mean exposure level μX = 0.008 mg/l, we would anticipate a deviation in AUCL/CE of about 100% from that of a coworker having the same μX but low-to-moderate exposure variability (see Fig. 6A). This mean air concentration (μX = 0.008 mg/l) is about twice the 2004 Threshold Limit Value (2 ppm =4.3 mg/m3) (ACGIH, 2004) and, thus, would be unacceptable by current norms. However, exposures of this magnitude could easily escape detection in the developed world, where workplace air monitoring is sporadic at best, and could be commonplace in much of the developing world. Thus, we recommend that VOCs be screened to identify chemicals with , where exposure variability might lead to significant deviations in the long-term liver dose of parent chemical at a given CE. Of 16 VOCs reviewed in our perusal of the recent toxicokinetics literature, 5 chemicals had estimated values of .
Sensitivity analyses indicated that AUCL and AURC were both sensitive to small changes in the toxicokinetic parameters when CVX was large (see Figs. 7 and 8). This suggests that populations of workers exposed to a given mean exposure could have quite different long-term liver and metabolite doses of VOCs when exposure variability is great, due to differences in toxicokinetic parameters among individuals. Since physiologically-based toxicokinetic models rarely consider exposure variability, which is often quite large for VOCs in occupational and environmental settings (Rappaport and Kupper, 2004), our results indicate that such simulations probably underestimate the true sensitivity of model predictions to variability in model parameters across a population.
Finally, it is worth reiterating the sentiments of Clewell et al. that physiologically based toxicokinetic models offer powerful tools for investigating complex exposure-dose-response relationships in living organisms (Clewell et al., 2002). While most such applications have focused upon interspecies extrapolations and modes of toxic action, our analyses suggest that such models also offer logical avenues for elucidating the particular effects of exposure variability upon these complex relationships.
APPENDIX
Equations Describing the Disposition of an Inhaled Volatile Organic Compound in the Body
Following Ramsey and Andersen (1984), assuming a steady-state rate (mg h–1) between alveolar air and alveolar blood, the following mass-balance equation holds (for abbreviations refer to Figure 1 in the text):
(A1)
Using (A1) and solving for CArt, we obtain
(A2)
And, from the mass-balance equation
where the subscript g refers to the gth tissue group (richly perfused, slowly perfused, fat or liver). For g = 1, ..., 4, the concentration of chemical in the mixed venous blood is
(A3)
For the gth nonmetabolizing tissue group (richly-perfused, slowly-perfused, or fat), the rate of change (mg h–1) in the amount Ag (= VgCg) of chemical is
(A4)
Finally, the metabolism of the chemical is assumed to take place exclusively in the liver according to Michaelis-Menten kinetics. The mass-balance equation determining the rate of change in chemical concentration in the liver is
(A5)
ACKNOWLEDGMENTS
The authors appreciate the helpful discussions and suggestions of David Kim, Robert Spear, Rogelio Tornero-Velez, Jesper Kristiansen, Douglas Taylor, and Brent Johnson. This work was supported by grant MTH0311 from the American Chemistry Council and by Center Grant P30ES10126 from the National Institute for Environmental Health Sciences.
NOTES
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ABSTRACT
The connection between occupational exposure to volatile organic compounds (VOCs) and the resulting internal doses is complicated by variability in air levels from day to day and by nonlinear kinetics of metabolism. We investigated long-term liver doses of VOCs and their metabolites using a physiologically based toxicokinetic model, to which 10,000 random 8-h exposures were inputted. Three carcinogenic VOCs were studied (i.e., benzene, perchloroethylene, and acrylonitrile); these compounds are all bioactivated in the liver and represent a wide range of an important toxicokinetic parameter . For each VOC, simulations were performed using mean air concentrations (μX) between 0.0003 and 1 mg/l (which covers both linear and saturated metabolism) and using coefficients of variation of exposure (CVX) between 0.23 and 2.18 (which includes most occupational settings). Two long-term measures of internal dose were examined, i.e., the area under the liver concentration-time curve (AUCL) and the area under the metabolic rate-time curve (AURC). Interestingly, both AUCL and AURC were linear functions of cumulative exposure (CE, mg·h/l air) even when metabolism was saturated and CVX was large. Yet, at a given CE, both AUCL and AURC were affected by CVX, with the magnitude of the effect increasing with (i.e., perchloroethylene < benzene < acrylonitrile). Nonetheless, the effects of CVX were typically only a few percent and should be of little consequence unless a VOC has large values of , μX,and CVX. We conclude that CE should be a sufficient predictor of the dose of either the parent chemical (VOC) or its metabolite in the liver, even when metabolism is nonlinear. We also observed that AUCL and AURC were sensitive to changes in values of model parameters in the high-variability scenarios, suggesting that (when CVX is large) the population variability of AUCL and AURC can be quite large at a fixed CE.
Key Words: volatile organic compounds; benzene; perchloroethylene; acrylonitrile; variation of exposure.
INTRODUCTION
Persons are exposed to toxic substances in the air of their communities, their homes, and their workplaces. Among these locations, levels tend to be greatest in the workplace where chemicals are produced or used in concentrated form. If exposures are of sufficient intensity and duration, critical tissues are damaged and workers suffer adverse health effects. Here, we are interested in the relationship between airborne exposure and the dose of a contaminant accumulated by a worker over many years. Thus, we only consider chronic effects of exposure and not acute, allergenic, or reproductive effects, where the timing as well as the magnitude of exposures can be important.
As a worker breathes a contaminant at a given air level (mg/l), he or she takes up some portion of the chemical in the lungs. The uptake is related to the breathing rate (l/h) and the retention, a dimensionless quantity that depends upon the physical and chemical properties of the contaminant (gaseous or particulate, solubility, particle size, etc.). Thus, during a brief period of time, uptake = (air level) x (breathing rate) x retention, with units of mg/h. Once the contaminant is cleared from the lungs, it can be distributed to tissues and eliminated by a host of excretory and metabolic processes. The difference between input and output gives rise to an internal mass, or burden (mg), of the substance at a particular time. From mass-balance considerations, the rate at which the burden changes during a brief period is
where the elimination rate has units of h–1. By integrating the burden over time, the internal dose can be derived, where , with units of mg·h. The internal dose can be defined more conventionally as the area under the tissue concentration-time curve, i.e., , with units of mg·h/l. Since the internal dose ultimately determines the extent of tissue damage, our ability to relate workers' exposures to the corresponding AUC values is fundamental to understanding and preventing occupational diseases.
The connection between exposure and AUC is complicated by the intermittent nature of the occupational regimen, where workers tend to be exposed for 8 h per day, and by the profound variability in air levels occurring from one workday to another. Occupational exposures typically vary 15-fold from day to day within workers (median value), and variation greater than 70-fold is observed in about a fourth of occupational groups (Kromhout et al., 1993). Given such great variability, it is reasonable to ponder whether day-to-day fluctuations in air levels might alter the relationship between exposure and internal dose. If air levels vary greatly from day to day (about some mean value), would the AUC differ from that observed when the air level is the same (mean) value each day This subject has
Logically, exposure variability can affect the relationship between exposure and internal dose only if two conditions are met (Rappaport, 1991). First, the contaminant must be eliminated from the body sufficiently rapidly so as not to accumulate from week to week. This is because substances that accumulate (notably insoluble dusts, heavy metals, and lipophilic organic compounds) achieve burdens much greater than the mass taken up in a single day and thereby are reasonably invariant to daily fluctuations in air levels. For such contaminants, cumulative exposure (CE), i.e., the product of the mean exposure and time (with units of mg·h/l), should be a valid predictor of the long-term internal dose (AUC). Second, the contaminant must be either taken up by, or eliminated from, the body by a nonlinear process over the relevant range of exposure. This condition is necessary because linear kinetics would maintain a strict proportionality between AUC and CE even when the contaminant is rapidly absorbed and eliminated (a restatement of ‘Haber's Law’) (Cox, 1995; Olson and Cumming, 1981; Rappaport, 1991).
Volatile organic compounds (VOCs) are rapidly eliminated via nonlinear (saturable) metabolism. Since many VOCs have been associated with chronic health effects, the purpose of this investigation is to explore the influence of exposure variability upon the internal doses of these compounds and their metabolites. Points will be illustrated with three chemicals that are known or suspected human carcinogens, namely, benzene (Hayes et al., 1997; Savitz and Andrews, 1996, 1997; Snyder, 2002), perchloroethylene (Lash and Parker, 2001), and acrylonitrile (Collins and Strother, 1999; Kirman et al., 2000). These substances were chosen because they are biotransformed in the liver by phase-I metabolism and possess an important toxicokinetic parameter (, to be defined) that ranges in value from low (perchloroethylene), to moderate (benzene), to high (acrylonitrile). The carcinogenicity of all three compounds is likely due to the action of one or more reactive metabolites. The sites of tumor formation include the hematopoietic system (benzene), liver and kidney (perchloroethylene), and the brain (acrylonitrile).
In what follows, we will couple a random time series of simulated air levels, representing the variability in occupational exposure over many years, with a physiologically based toxicokinetic model, representing the disposition of VOCs and metabolite production in the body. Such toxicokinetic models provide the means to relate external exposure to internal levels and, thus, are well suited for evaluating the doses of VOCs and their metabolites following prolonged periods of occupational exposure.
MATERIALS AND METHODS
Toxicokinetic model. Figure 1 displays a physiologically based toxicokinetic model that is widely accepted as a reasonable depiction of mammalian absorption and elimination of VOCs (Andersen, 1981a; Droz and Guillemin, 1983; Ramsey and Andersen, 1984). The input to the model is the contaminant, at air concentration X (mg/l), inhaled into a central (lungs/blood) compartment at the alveolar ventilation rate QAlv (l/h). The contaminant is absorbed into the arterial blood according to its blood-air partition coefficient (B). Once inside the body, the chemical is transported at the rate of the cardiac output QCar (l/h) via the arterial blood at concentration CArt (mg/l). The chemical is distributed to parallel tissue groups, consisting of the liver (L, the only metabolizing tissue), the rapidly perfused tissues (RPT, mainly the central organs), the slowly perfused tissues (SPT, mainly muscles and skin), and the fat (F), at rates defined by the perfusion rates (QL for the liver, etc., l/h). The tissue groups are all assumed to be homogenous well-mixed volumes. Transfer of the chemical from the arterial blood to each tissue group is governed by the tissue-blood partition coefficient (L, etc.) and volume (VL, etc., l); the concentration is designated as CL (mg/l) for the liver, etc. The chemical is cleared from the body either passively, by exhalation at rate (mg/h), or by metabolism in the liver to metabolite M at rate RM (mg/h). For benzene, perchloroethylene, and acrylonitrile, note that M would represent the initial epoxide produced by cytochrome P450 metabolism, namely, benzene oxide, perchloroethylene epoxide, and cyanoethylene oxide, respectively.
The nonlinear behavior of the model shown in Figure 1 relates to liver metabolism, which obeys Michaelis-Menten kinetics at rate , where Vmax represents the maximum rate of metabolism (mg/h) and KM (mg/l) is the liver-blood concentration of the chemical at which RM = Vmax/2. If , then metabolism is pseudo-first order (linear) at rate . If , then metabolism is zero order at rate Vmax. At intermediate values of , the rate of metabolism lies between these limiting values. We also identify the dimensionless quantity , representing "the maximum concentration gradient that exists across the liver at a given blood flow" divided by KM (Andersen, 1981b). When , metabolism is not complete at low substrate concentrations, and the transition from first- to zero-order behavior is gradual. Conversely, when , metabolism is essentially complete at low substrate concentrations, and this transition between kinetic states is abrupt (Andersen, 1981b).
Model parameters and simulation. The flow rates (l/h) and tissue volumes (l) were scaled to a 70-kg human working at 50 W of exercise according to Tardif et al. (2002), i.e., QAlv = 1323, QCar = 603, QL = 96.4, QF = 36.2, QRPT = 163, QSPT = 307, VL = 1.82, VF = 13.3, VRPT = 3.50, and VSPT = 40.6. The chemical-dependent partition coefficients and biochemical constants, shown in Table 1, were compiled from (Dobrev et al., 2001; Sweeney et al., 2003; Travis et al., 1990) after scaling Vmax for a 70-kg human as Vmax=Vmaxc · 700.75, where Vmaxc is the scaling coefficient given by the authors.
Simulation involved introducing a time series of 8-h occupational exposures {Xi} into the model shown in Figure 1, where Xi (mg/l) is the air concentration during the ith 8-h workday (i = 1, ..., 10,000). We modeled Xi as a lognormal variate with true (unobservable) mean μX and variance (Rappaport, 1991); by randomly sampling from a given distribution (defined by μX and ), we simulated 10,000 occupational exposures representing about 40 years of work. Simulations were performed with μX = 0.0003, 0.001, 0.003, 0.01, 0.03, 0.1, 0.3, and 1.0 mg/l, and (for each value of μX) values of equal to 0.23, 0.62, and 2.18. These CVX values were selected to represent levels of occupational-exposure variability ranging from "very low" to "moderate" to "very high." [For reference, these CVX values correspond, respectively, to the 2nd, 41st and 84th percentiles of the cumulative distribution of geometric standard deviations reported by Kromhout et al. (1993). Note that, for the lognormal variate Xi, , where is the variance of Yi = ln(Xi), and the geometric . Since we consider only a single worker in our simulations, represents the within-person variance component from Kromhout et al.] After 10,000 simulated workdays, the cumulative exposure (mg·h/l) was calculated as , for 8 h of exposure per workday.
The toxicokinetic model employed mass-balance equations to describe the rates of change of the chemical concentration in each compartment, based largely upon relationships given by Ramsey and Andersen (1984) (see Supplementary Data). These equations were solved numerically by Euler's method, using a program written with SAS software (SAS Institute, Cary, NC) and employing a time step t of either 0.01 h (benzene and perchloroethylene) or 0.002 h (acrylonitrile), as required to maintain continuity. Following 8 h of simulated exposure at air concentration Xi, the inhaled air concentration was reduced to zero, and liver concentrations were monitored until t = 336 h to ensure complete clearance of the chemical from all tissues. The time series {Xi} produced the corresponding time series of internal doses, represented by the AUC of the parent chemical in the liver after each exposure {AUCLi} (mg·h/l), where and CLij is the liver concentration (mg/l), after the jth time step for the ith exposure. Metabolism was monitored in terms of the time series of the amount of metabolite produced from the ith exposure, referred to as the area under the metabolic rate-time curve (Andersen, 1981b), i.e., (mg), and RMij is the rate of metabolism (mg/h) after the jth time step for the ith exposure. The long-term liver dose of parent chemical after 10,000 exposures was calculated as (mg·h/l), and the corresponding long-term dose of metabolite as (mg). Even though both AUCL and AURC are long-term dose metrics, note that they are dimensionally different.
We focused our models upon the liver and metabolite doses (AUCL and AURC) even though the liver is not necessarily the target of toxicity for the VOCs investigated. Because our model only permits metabolism to take place in the liver, the liver is more sensitive to perturbations in levels of the parent compound than are the blood and other tissue groups. Thus, effects of exposure variability upon AUCL are at least as great as upon the analogous AUC values for other tissues. Likewise, AURC represents a global measure of metabolite production that should be relevant to all tissues where metabolites are ultimately distributed from the liver by the systemic circulation.
Sensitivity analysis. Additional simulations were conducted to determine the sensitivity of the two dose metrics AUCL and AURC to each of the parameters in the model. Each parameter was increased by 1% and the full simulation was repeated for 4 exposure distributions, representing a wide range of mean values (μX = 0.0003 and 0.3 mg/l) and variability (CVX = 0.23 and 2.18). While testing sensitivity to blood flow rates, mass balance was maintained by reducing QSPT, as necessary, to compensate for the 1% increase in QRPT, QL, or QF. Normalized sensitivity coefficients were estimated as the percentage change observed in AUCL or AURC divided by the 1% change in the parameter of interest (e.g., a 2% increase in AUCL or AURC would correspond to a normalized sensitivity coefficient of 2).
RESULTS
Exposure-Dose Relationships for Benzene
To illustrate the effect of exposure variability on the daily liver doses of benzene and its metabolite at a given mean exposure, values of {AUCLi} and {AURCi} are plotted versus exposure {Xi} in Figure 2 when the mean exposure μX = 0.010 mg/l (3.13 ppm) and CVX = 0.23 (very low variability) or CVX = 2.18 (very high variability). The effect of saturable metabolism is apparent when CVX = 2.18, but not when CVX = 0.23; this is due to the much greater range of benzene air levels in the high-variability scenario, relative to the mean value of 0.010 mg/l. Note that the shapes of the nonlinear relationships in Figures 2A and 2B differ when CVX = 2.18. As benzene metabolism approaches saturation, the ratio of the arterial blood concentration to the exposure concentration () increases, and a larger fraction of benzene is distributed to the fat, where it is stored pending eventual release to the systemic circulation (and the liver) during the subsequent period of zero exposure. This ultimately leads to values of AUCLi that are disproportionably greater than those observed at lower exposure levels. Thus, the relationship between AUCLi and exposure concentration exhibits concave-upwards behavior that becomes pronounced when Xi 0.05 mg/l (Fig. 2A). At the same time, saturation of benzene metabolism leads to reduced uptake and increased passive clearance of benzene. These effects combine to disproportionably reduce metabolism during periods of high benzene exposure and give rise to the concave-downwards shape of the relationship between AURCi and exposure (Fig. 2B). Accordingly, the rate of metabolite production is substantially saturated, given 8 h of exposure to benzene in the range of 0.2–0.4 mg/l (63–126 ppm).
The relationships shown in Figure 2 suggest that large variability in exposure can increase the liver dose of benzene and reduce the corresponding dose of the benzene metabolite at a given mean exposure μX. This is illustrated in Figure 3, which shows the time series of daily liver doses {AUCLi} and the corresponding long-term liver dose (AUCL) (Figs. 3A and 3B) as well as the daily metabolite doses {AURCi} and the corresponding long-term metabolite dose (AURC) (Figs. 3C and 3D), when μX = 0.010 mg/l and CVX = 0.23 (very low variability, Figs. 3A and 3C) or CVX = 2.18 (very high variability, Figs. 3B and 3D). The figures illustrate that, indeed, after 10,000 simulated workdays, AUCL and AURC (shown at the right axis) are different when CVX = 0.23 (AUCL = 3.9 g·h/l, AURC = 205 g) than when CVX = 2.18 (AUCL = 4.4 g·h/l, AURC = 185 g). Yet, the two values of AUCL and AURC only differ by 10–13%, despite the enormous differences in the variability of the two time series {AUCLi} and {AURCi} giving rise to the long-term doses.
The relationships shown in Figure 3 indicate that AUCL and AURC increase linearly with workday when μX = 0.010 mg/l, regardless of the magnitude of CVX; that is, the slope for AUCL versus workday [in (mg·h/l)/d] = 39μX when CVX = 0.23, and equals 44 μX when CVX = 2.18, while the slope for AURC versus workday (in mg/d) = 2050μX when CVX = 0.23 and equals 1850 μX when CVX = 2.18. In fact, the same results were observed for both AUCL and AURC over an extremely wide range of benzene exposures representing kinetics that changed from linear (μX = 0.0003 mg/l, 0.1 ppm) to fully saturated (μX = 1.0 mg/l, 313 ppm) (results not shown). Since CE is a linear function of time, i.e., CE = μX x t for t representing exposure time in h (t = 80,000 h in our simulations), then CE must be a good predictor of the long-term internal dose of benzene (AUCL) or its metabolite (AURC), regardless of the variability in air levels from day to day (CVX). Figure 4 shows graphs of AUCL and AURC versus CE for benzene exposures when μX = 0.001 or 1.0 mg/l and CVX = 0.23 or 2.18. Clearly, linear relationships are observed in both cases with intercepts equal to zero and slopes of either AUCL/CE (Figs. 4A and 4B) or AURC/CE (Figs. 4C and 4D). (Since CE = μX · t and since AUCL = k · μX · t, then AUCL is a constant multiple of CE and k = AUCL/CE. The same argument holds for AURC). Furthermore, after 10,000 simulated workdays, AUCL and AURC are very close in value for both the low- and high-variability scenarios, indicating that exposure variability had small effects upon AUCL/CE and AURC/CE for benzene when 0.001 μX 1 mg/l.
Effects of Exposure Variability upon AUCL/CE and AURC/CE
It was illustrated in Figures 4A and 4C that, when the toxicokinetics for benzene were linear (μX = 0.001 mg/l), AUCL/CE and AURC/CE were virtually unchanged for scenarios involving either very low variability (CVX = 0.23) or very high variability (CVX = 2.18). However, when benzene metabolism was saturated (μX = 1.0 mg/l), the slopes differed marginally between scenarios; that is, AUCL/CE increased from 9.45 when CVX = 0.23 to 9.75 when CVX = 2.18 (Fig. 4B), while AURC/CE concurrently decreased from 64.6 to 52.5 l/h (Fig. 4D). The same behavior was observed for simulations involving perchloroethylene and acrylonitrile, although the magnitudes and patterns of the deviations differed (results not shown). This indicates that, at a given CE, highly variable exposure distributions can lead to marginally different internal doses (AUCL and AURC) than those of low variability.
The effects of exposure variability on the slopes AUCL/CE and AURC/CE (after 10,000 8-h workdays) are summarized in Figures 5A– 5F for benzene, perchloroethylene, and acrylonitrile when 0.0003 μX 1.0 mg/l and when CVX = 0.23, 0.62, and 2.18. For each chemical, AUCL/CE and AURC/CE are hardly affected by exposure variability when μX 0.01 mg/l, even when CVX = 2.18. However, as μx increases above 0.01 mg/l, upwards divergence of AUCL/CE was observed (Figs. 5A, 5C, and 5E) along with downwards divergence of AURC/CE (Figs. 5B, 5D, and 5F), consistent with increasing saturation of VOC metabolism. These changes occur first for CVX = 2.18 and then for CVX = 0.62 and 0.23, respectively.
The curves represented by CVX = 0.23 and 0.62 in Figure 5 are very similar, suggesting that low or moderate variation in occupational exposure has little impact upon the relationship between either AUCL/CE and μX or AURC/CE and μX. However, deviations of the high-variability curves (CVX = 2.18) from the low-variability curves (CVX = 0.23) can be large, depending on the particular VOC and on whether AUCL or AURC is being considered. Here we define the high-variability deviation for AUCL/CE as and that for AURC/CE as . These high-variability deviations (in percent) are shown in Figure 6A and Figure 6B for AUCL/CE and AURC/CE, respectively, for the three VOCs in our study. Referring first to AUCL/CE, the maximum deviations differed among the VOCs, i.e., 2% for perchloroethylene, 21% for benzene, and 570% for acrylonitrile (Fig. 6A). On the other hand, maximum deviations of the AURC/CE were very uniform across the VOCs, ranging between –29 and –31%. Note that these maximum deviations occurred at values of μX between 0.1 and 0.3 mg/l, depending upon the particular VOC. Since the mean exposures corresponding to maximum deviations were on the cusps between linear and saturable metabolism, the low-variability scenario resulted in essentially linear metabolism on all workdays; here, AUCL/CE and AURC/CE were near the baseline values observed at much lower mean exposures (see Fig. 5). On the other hand, the high-variability scenario included many days where metabolism was in the saturable range, thereby producing major deviations in AUCL/CE and AURC/CE from their near-baseline values. For example, from Figure 6A, the maximum deviation in AUCL/CE for acrylonitrile occurred when μX = 0.1 mg/l. Referring to Figure 5E, we see that, when μX = 0.1 mg/l and CVX = 0.23, AUCL/CE = 5.4, a value only marginally greater than the baseline value of 3.8 observed when μX 0.003 mg/l. Yet, when μX = 0.1 mg/l and CVX = 2.18, AUCL/CE = 36.5, a 7-fold deviation from the low-variability scenario! As μX increased above 0.1 mg/l for acrylonitrile, metabolism shifted into the saturable range, and AUCL/CE increased dramatically with μX when CVX = 0.23; this narrowed the gap in AUCL/CE between the low- and high-variability scenarios.
Effects of on AUCL/CE and AURC/CE
The deviations in AUCL/CE and AURC/CE between high-variability and low-variability scenarios increased in the following order: perchloroethylene < benzene < acrylonitrile, which matches the order of the toxicokinetic parameter identified earlier. When , the transition from first- to zero-order kinetics is abrupt, being described as ‘flip-flop’ behavior (Andersen, 1981b). As a consequence, the toxicokinetics of acrylonitrile with is much more likely to ‘flip-flop’ between kinetic states than either perchloroethylene or benzene . Since liver extraction is essentially complete for acrylonitrile at low levels of exposure, AUCL/CE tends to be much smaller at baseline than the corresponding value for perchloroethylene; e.g., when μX = 0.001 mg/l, AUCL/CE is 3.8 for acrylonitrile (Fig. 5E), compared to 53.6 for perchloroethylene (Fig. 5C). Conversely, efficient metabolism leads to a much larger AURC/CE for acrylonitrile at baseline than for perchloroethylene; e.g., when μX = 0.001 mg/l, AURC/CE is 1194 l/h for acrylonitrile (Fig. 5F), compared to 66.9 l/h for perchloroethylene (Fig. 5D). The flip-flop behavior of metabolism for acrylonitrile translates days of high exposure into days of very high liver dose (AUCLi); as noted earlier, this results in a 7-fold increase in AUCL/CE for the high-variability scenario (when μX = 0.1 mg/l) compared to the near-baseline value for the low-variability scenario. Since benzene and perchloroethylene do not exhibit flip-flop kinetics, deviations from their near-baseline values of AUCL/CE are much more modest, in the range of about 2–20% (Fig. 6A).
The picture regarding the metabolite dose was different, given maximum deviations in AURC/CE of about –30% for all three VOCs (Fig. 6B). This is because the large baseline value of AURC/CE for acrylonitrile tended to offset the abrupt reduction in daily metabolite dose (AURCi) occurring during the high-exposure days. Since benzene and perchloroethylene do not exhibit flip-flop kinetics, their reductions in AUCLi or AURCi were more modest during the high-exposure days; but these changes were offset by their smaller baseline values of AURC/CE, yielding essentially the same percent deviations as for acrylonitrile.
Sensitivity Analysis
Results of the sensitivity analyses are summarized in Figure 7 for AUCL and in Figure 8 for AURC, based upon a 1% increase in each of the toxicokinetic parameters. The sensitivities of the two dose metrics were greatly influenced by the variability of exposure (CVX) at a given mean exposure (μX). That is, long-term doses were much more sensitive to changes in model parameters when CVX = 2.18 than when CVX = 0.23. Indeed, it was common to observe normalized sensitivity coefficients greater than ±5 when CVX = 2.18, whereas coefficients rarely exceeded ±2 when CVX = 0.23. This suggests that AUCL and AURC would vary considerably across a population exposed at a given μX when exposure was highly variable under either linear (μX = 0.0003 mg/l) or saturated (μX = 0.3 mg/l) kinetics. The normalized sensitivity coefficients shown in Figures 7 and 8 indicate general sensitivity to most parameters. This probably reflects the structure of the model, where all parameters, except the partition coefficients and KM, were functions of body weight and, therefore, were highly correlated. In comparing among VOCs, the most notable difference concerns sensitivity of AUCL in the high-exposure, high-variability scenario (Fig. 7D), where deviations were negative for acrylonitrile but were positive for benzene and perchloroethylene. This probably points to the lipophobic nature of acrylonitrile (whereas the other compounds are lipophilic), because days of saturating exposure would not lead to a buildup of acrylonitrile in the fat (with subsequent release to the circulation and the liver) but rather to increased passive clearance in the exhaled air.
Regarding perturbations to the parameters that influence metabolic clearance, i.e., Vmax, KM, and QL, AUCL was consistently more sensitive for benzene and acrylonitrile (high-affinity substrates) than for perchloroethylene (low-affinity substrate) (see Fig. 7). This suggests that factors affecting blood flow to the liver (such as exercise rate) and those influencing metabolism (such as genetic polymorphisms as well as enzyme induction and inhibition) would affect liver doses of benzene and acrylonitrile to a much greater extent than they would for the dose of perchloroethylene, particularly in situations where exposure is highly variable from day to day.
DISCUSSION
Recognition that the dose of a substance ultimately determines its toxicity has been attributed to Paracelsus in work published more than 400 years ago (Gallo, 2001). Since then, the fields of toxicology and epidemiology have embraced the dose-response relationship as fundamental to the understanding of risks of diseases caused by chemical exposures. Unfortunately, our ability to estimate long-term doses from occupational exposures has been hampered by the variability in levels within and between persons in a given population and by the lack of historical measurements of exposure. In the face of large variability and few measurements, the ability to accurately quantify dose-response relationships is sadly limited. If exposure databases are to improve for future investigations, we must adopt sampling strategies that place a premium upon longitudinal exposure data collected according to sound statistical principles (Rappaport, 1991; Rappaport et al., 1995). A strong motivation for such a change would be to accept by default the premise that CE is the principal determinant of the long-term internal dose
The purpose of this paper has been to evaluate the premise that CE is a sufficient predictor of the internal doses of benzene, perchloroethylene, and acrylonitrile, three carcinogenic VOCs that are cleared in part by saturable metabolism over a wide range of toxicokinetic behaviors (as reflected by differing values of ). We observed in all cases that both the long-term liver dose (AUCL) and the long-term metabolite dose (AURC) were essentially linear functions of CE over about 40 simulated years of occupational exposure, even when daily-dose increments (AUCLi and AURCi) were saturated (e.g., see Fig. 4). Thus, despite the enormous range of daily exposures that can be observed in the workplace, the straight-line slope representing AUCL/CE or AURC/CE after several years is essentially fixed for an individual worker at a given mean exposure (μX).
Despite the linear relationship between AUCL or AURC and CE for an individual worker, the corresponding relationship across a population could well be nonlinear if some workers have mean air levels in the saturable range. For example, in a population of workers heavily exposed to the three VOCs investigated here, we would anticipate a concave-downwards shape in the exposure-biomarker relationship across the population for any biomarker located ‘downstream’ from the initial metabolic step (see Fig. 2B). Indeed, such shapes have been reported for protein adducts and urinary metabolites of benzene (both downstream biomarkers) (Rappaport et al., 2002a,b; Waidyanatha et al., 2004), as well as for the mortality-CE curve for lymphohematopoietic cancers among benzene-exposed workers (Hayes et al., 1996).
Our results indicate that individual workers who experience the same CE could nonetheless have different long-term internal doses (AUCL or AURC) if their individual levels of exposure variability (values of CVX) differed greatly. The magnitude of such deviations would depend upon the particular dose metric. Since most VOCs are metabolized to toxic products, the more important effect of exposure variability concerns its relation to the internal metabolite dose (AURC). Here, our results indicate that differences in AURC/CE (arising from different values of CVX across the population) should be small for VOCs, with maximum deviations in the range of about –30% as observed for benzene, perchloroethylene, and acrylonitrile (Fig. 6B). We conclude that assignment of metabolite doses to VOCs, based solely on CE, should not compromise estimation of exposure-response relationships. This conclusion is at odds with the observation of Collins et al. that the number of ‘peak’ exposures to benzene (greater than 100 ppm) was a better predictor of lymphohematopoietic cancers than was CE, and could point to the large uncertainties in estimation of individual CEs mentioned by the authors (Collins et al., 2003). Another recent study found no evidence that the risk of lymphohematopoietic cancers was influenced by peak exposures (Glass et al., 2003).
Turning now to the liver dose of a VOC per se, our results indicate that AUCL/CE can differ by several hundred percent between high- and low-variability scenarios, but only when μX and CVX are large and when . If not all three of these conditions are met, then deviations of AUCL/CE should only be a few percent (see Fig. 6A for acrylonitrile when μX 0.003 mg/l or CVX 0.62 and for benzene and perchloroethylene at all values of μX). Yet there could well be situations where such a nexus of three independent factors could occur. For example, if a worker was exposed to acrylonitrile in intermittent outdoor operations, giving rise to a large (Kromhout et al., 1993), at a mean exposure level μX = 0.008 mg/l, we would anticipate a deviation in AUCL/CE of about 100% from that of a coworker having the same μX but low-to-moderate exposure variability (see Fig. 6A). This mean air concentration (μX = 0.008 mg/l) is about twice the 2004 Threshold Limit Value (2 ppm =4.3 mg/m3) (ACGIH, 2004) and, thus, would be unacceptable by current norms. However, exposures of this magnitude could easily escape detection in the developed world, where workplace air monitoring is sporadic at best, and could be commonplace in much of the developing world. Thus, we recommend that VOCs be screened to identify chemicals with , where exposure variability might lead to significant deviations in the long-term liver dose of parent chemical at a given CE. Of 16 VOCs reviewed in our perusal of the recent toxicokinetics literature, 5 chemicals had estimated values of .
Sensitivity analyses indicated that AUCL and AURC were both sensitive to small changes in the toxicokinetic parameters when CVX was large (see Figs. 7 and 8). This suggests that populations of workers exposed to a given mean exposure could have quite different long-term liver and metabolite doses of VOCs when exposure variability is great, due to differences in toxicokinetic parameters among individuals. Since physiologically-based toxicokinetic models rarely consider exposure variability, which is often quite large for VOCs in occupational and environmental settings (Rappaport and Kupper, 2004), our results indicate that such simulations probably underestimate the true sensitivity of model predictions to variability in model parameters across a population.
Finally, it is worth reiterating the sentiments of Clewell et al. that physiologically based toxicokinetic models offer powerful tools for investigating complex exposure-dose-response relationships in living organisms (Clewell et al., 2002). While most such applications have focused upon interspecies extrapolations and modes of toxic action, our analyses suggest that such models also offer logical avenues for elucidating the particular effects of exposure variability upon these complex relationships.
APPENDIX
Equations Describing the Disposition of an Inhaled Volatile Organic Compound in the Body
Following Ramsey and Andersen (1984), assuming a steady-state rate (mg h–1) between alveolar air and alveolar blood, the following mass-balance equation holds (for abbreviations refer to Figure 1 in the text):
(A1)
Using (A1) and solving for CArt, we obtain
(A2)
And, from the mass-balance equation
where the subscript g refers to the gth tissue group (richly perfused, slowly perfused, fat or liver). For g = 1, ..., 4, the concentration of chemical in the mixed venous blood is
(A3)
For the gth nonmetabolizing tissue group (richly-perfused, slowly-perfused, or fat), the rate of change (mg h–1) in the amount Ag (= VgCg) of chemical is
(A4)
Finally, the metabolism of the chemical is assumed to take place exclusively in the liver according to Michaelis-Menten kinetics. The mass-balance equation determining the rate of change in chemical concentration in the liver is
(A5)
ACKNOWLEDGMENTS
The authors appreciate the helpful discussions and suggestions of David Kim, Robert Spear, Rogelio Tornero-Velez, Jesper Kristiansen, Douglas Taylor, and Brent Johnson. This work was supported by grant MTH0311 from the American Chemistry Council and by Center Grant P30ES10126 from the National Institute for Environmental Health Sciences.
NOTES
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