Kinetic data for ethylbenzene from rats and humans were used to estimate KMD ranges for each species. The KMD range in rats was estimated to be from 8 to 17 mg/L venous ethylbenzene, and for humans, from 10 to 18 mg/L venous ethylbenzene. These ranges correspond to an inhalation concentration of approximately 200 ppm ethylbenzene.

Our results support the conclusion of Saghir et al. (2010), that saturation of ethylbenzene elimination occurs between 200 and 500 ppm in rodents, and with Charest-Tardif et al. (2006), that ethylbenzene exposures of between 200 and 500 ppm saturates metabolism and elimination kinetics in rats. Our results are also consistent with the data from the NTP ethylbenzene bioassay results, which showed that neoplastic lesions in the rodent cancer bioassay occurred at 750 ppm, but not at lower concentrations. However, our results contradict the NTP conclusion that the reported ethylbenzene-associated rodent tumors are human relevant. Given that the KMD range is around 200 ppm in both rats and humans, our results support the conclusion that cancer is seen only at concentrations that exceed enzymatic saturation and where saturation of clearance mechanisms is apparent in both rats and humans.

In mice, tumors have also been reported following chronic exposure to ethylbenzene. Unfortunately, the available mouse data (Charest-Tardiff et al. 2006; Fuciarelli et al. 2000) needed for proper KMD estimation was determined to be insufficient for a reliable estimation of the Michaelis constants Vmax and Km for mice. This is consistent with determinations made previously by Nong et al. (2007). The kinetic profile for ethylbenzene in mice clearly differs between 75 ppm (linear) and 750 ppm (saturated), prompting the authors who reported this phenomenon to conclude that the kinetics become saturated at an intermediate concentration not greater than 500 ppm (Charest-Tardiff et al. 2006). Based on Nong et al.’s (2007) validation of a PBPK model for ethylbenzene in mice that had used Michaelis constants derived from rat, our KMD estimate should be equally applicable for interpreting the results of toxicology and carcinogenicity studies conducted in mice and rats.

The reliance of our method on the Michaelis constants Km and Vmax is a unique strength that, combined with corroborative mechanistic information, avoids the challenges often associated with application of kinetics in dose-setting and interpretation of toxicological findings, such as those discussed by Tan et al., (2021). These constants are unassailable fundamentals of biotransformation and elimination kinetics that allow KMDs to be established without reliance on Area Under the blood Concentration curve (AUC), which can be less precise than Michaelis constants (Burgoon et al. 2022). AUC data on ethylbenzene are unavailable for derivation of the KMD for ethylbenzene in rodents generally. The use of rat data was necessary for our purposes because kinetic data from mouse are as yet insufficient to derive Michaelis constants. Nonetheless, generalizing from rat to mouse is justified for this purpose as demonstrated by Nong et al. (2007), who used rat kinetic data on ethylbenzene to develop a PB/PK that was validated to be applicable to mouse.

It is important to appreciate the conservative nature of a KMD range that is estimated by the kneedle algorithm as we apply it (Burgoon et al. 2022). Because our method estimates the KMD range based on the region of the ethylbenzene exposure/blood concentration curve that approaches an asymptote, it does not utilize information from the area of the curve at which the rate of change in slope begins to increase. In other words, because our method relies on Vmax, it identifies the end of the curve, not the beginning or the mid-point of the curve. The beginning of the curve, however, may be biologically important because it indicates the range in which the relationship between exposure and blood concentration begins to change in a biologically meaningful way. Thus, it could be argued that either the beginning of the curve or the mid-point of the curve more accurately reflects a biologically meaningful KMD range than the end of the curve, and thus, that our method is overly conservative.

With this conservatism in mind, it is clear that our KMD estimate supports the argument that all cancers, tumors, and potential pre-neoplastic lesions identified in the NTP carcinogenicity study of ethylbenzene in rodent occur secondary to kinetic changes that occur in the range of 200 ppm inhalation exposure. Mechanistic factors underlying the tumorigenic activity of ethylbenzene have been investigated following inhalation exposure of F344 rats and B6C3F1 mice at 75 and 750 ppm for 6 h per day, 5 days per week, for 1 or 4 weeks (Stott et al. 2003). Exposure to the nontumorigenic concentration—75 ppm—produced few changes in organ weights, mixed function oxygenase activity, glucuronosyl transferase activities, S-phase DNA synthesis, apoptosis, α2u-globulin deposition, or histopathology. The effects differed between males and females but were generally confined to the 750 ppm exposure level. The results indicate that exposure to high, but not low, levels of ethylbenzene by inhalation can cause changes in rat kidneys characterized by acceleration of chronic progressive nephropathy (CPN) in males and females and α2u-globulin deposition in males, and mouse liver and lungs consistent with a nongenotoxic mode of tumorigenic action that is dependent on cell proliferation and alterations in the dynamics of various cell populations in target tissues (Ashby et al. 1994; Stott et al. 2003). Exacerbation of rat-specific CPN has been shown to lack a human counterpart (Hard et al. 2009) and thus, increases in the incidence of CPN-related and α2u-globulin-related renal tumors induced by ethylbenzene should not be used for human risk assessment as neither mode of action has qualitative relevance to humans.

Thus, the modes of action that likely lead to tumorigenic effects in rodents are operative at exposure levels that exceed the KMD range, but not at exposures below the KMD range. Consistent with numerous other examples of dose-dependent changes in mechanisms of toxicity (e.g., Slikker et al. 2004), a phenomenon so common it would appear to be the rule rather than the exception, this strongly suggests that effects observed following exposure to ethylbenzene concentrations above its KMD range would not be relevant for assessing cancer hazards in rodents or in humans exposed to concentrations below the KMD, since rodents and humans have similar KMD ranges. Such effects would include in rats: renal tubule adenoma and adenoma/carcinoma combined and renal tubule hyperplasia in male rats, renal tubule adenoma and hyperplasia in males and females, nephropathy in males and females, and interstitial cell adenoma in male testis (NTP 1999). In mice, these include: alveolar/bronchiolar adenoma and alveolar/bronchiolar adenoma or carcinoma (combined), alveolar epithelial metaplasia in males, hepatocellular adenoma and adenoma/carcinoma (combined) in females, syncytial alteration of hepatocytes, hepatocellular hypertrophy and hepatocyte necrosis in males, hyperplasia of the pituitary gland pars distalis and incidence of thyroid gland follicular cell hyperplasia in males and in females.

It has been argued that evidence of alveolar carcinoma was observed in mice at concentrations lower than those required to produce liver and kidney tumors. However, the incidence of frank alveolar carcinoma was not observed at any level of exposure in mice, and combined adenoma/carcinoma incidence was statistically elevated only at 750 ppm, but not at 250 ppm or 50 ppm exposure in studies conducted by the U.S. National Toxicology Program (NTP 1999). Furthermore, the alveolar precursor lesions alleged by NTP to be observable at lower concentrations are dependent on mouse-lung-specific metabolism of ethylbenzene (discussed in Nong et al. 2007). As with styrene (Cruzan et al. 2002), the higher conversion of ethylbenzene to CYP2E1 metabolites in mouse lung are likely responsible for changes observed in mouse lung at exposures below 200 ppm, but these do not appear to correspond with neoplasia or tumors at higher concentrations. Such pulmonary effects in mice are highly unlikely to be relevant to humans since the pulmonary activity of CYP2E1 in mice is approximately 20-fold higher than in mouse liver, and 23 and 600 times higher in mouse versus rats and human lung microsomes. In addition, the human relevance of the mouse lung adenomas is questionable (Cohen et al. 2020).

Despite this evidence, Huff et al., (2010), assert that cancers associated with ethylbenzene exposure in the rodent cancer bioassay are human relevant, even though it is clear from the data in the NTP report on inhalation exposure to ethylbenzene that neoplastic lesions were only seen in the group exposed to the highest concentration of 750 ppm, but not at 250 ppm or below (National Toxicology Program 1999). In contrast, Saghir et al. (2010) argued that these neoplastic lesions are consistent with high exposure levels of ethylbenzene leading to metabolic saturation. Scientists from the NTP countered that there are no high dose phenomena because they detected “[s]ignificant dose response trends”, and that the saturation argument is insufficient as they would “not expect to see much increase in tumor incidence in the top exposure [750 ppm] compared to the mid-level exposure [250 ppm], because both exposures are in the ‘saturation zone.”

Huff et al.’s (2010) reliance on “trend significance” has been termed abusive statistics (Wood et al. 2014) and must be avoided. Among the many problems with this method, it treats estimates of population effects at each concentration point as being both precise and accurate, which does not comport with good statistical practice, especially regarding fundamentals of sampling theory. Obtaining a precise, accurate reproduction of the population incidence rate for neoplastic lesions would be highly unlikely based on group sizes of 50 animals, especially when that rate is likely very small. A simple simulation using a beta-binomial distribution clearly demonstrates this point.

NTP argues that if carcinogenic transformation were dependent on saturation of elimination kinetics, tumor incidence would be similar at 250 ppm and 750 ppm rather than markedly increased at 750 ppm relative to 250 ppm, since both concentrations are within the “saturation zone” (Huff et al. 2010). That argument, however, betrays a misunderstanding of Michaelis–Menten kinetics with respect not only to saturation but also to its relationship to the mode of carcinogenic action. The issue is akin to the classic calculus problem of over-filling a bathtub, where overtopping the walls of the bathtub will cause real and significant problems, analogous to induction of a carcinogenic mode of action. A bathtub will drain at a constant rate whenever water flows into the tub at a rate equal to or greater than the drain capacity; this is analogous to saturation of elimination pathways in an animal. If the drain capacity is 200 mL/min and you are filling the bathtub at 250 mL/min, then every minute, the tub accumulates 50 mL. Let’s also assume your bathtub walls are such that it can handle 5 L/day. If you fill the bathtub for 15 min each day, then at 250 mL/min, you will never overtop the bathtub. But, at 750 mL/min you will overfill the bathtub each and every day by 3.25 L. Biologically speaking, the walls of the bathtub are the threshold required for the carcinogenic mode of action—in other words, you need to overtop the bathtub in order to activate that mode of action. So, even though the bathtub is saturated at 200 mL/min and cannot drain faster than that, it is the walls of the bathtub and the time and rate of the water (dose) inputs that determine whether there will be any damage—not saturation of the drain capacity, i.e., elimination pathways, per se. Therefore, the argument put forth by Huff et al. (2010) is fallacious prima facie—it is a form of confusing necessity and sufficiency, also known as the fallacy of the converse.