Response-Surface Analysis of Exposure-Duration Relationships: The Effects of Hyperthermia on Embryonic Development of the Rat in Vitro

G. L. Kimmel*,1, P. L. Williams{dagger}, T. W. Claggett{ddagger} and C. A. Kimmel*

* National Center for Environmental Assessment, Office of Research and Development, U.S. Environmental Protection Agency, Washington, D.C. 20460; {dagger} Department of Biostatistics, Harvard School of Public Health, Boston, Massachusetts 02115; and {ddagger} Pathology Associates, International, Frederick, Maryland 21701

Received March 14, 2002; accepted June 25, 2002


    ABSTRACT
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
In developing exposure standards, an assumption is often made in the case of less-than-lifetime exposures that the probability of response depends on the cumulative exposure, i.e., the product of exposure concentration and duration. Over the last two decades, the general applicability of this assumption, referred to as Haber’s Law, has begun to be questioned. This study examined the interaction of exposure concentration and duration on embryonic development during a portion of organogenesis. Embryos were exposed in whole embryo culture to various temperature-duration combinations and evaluated for alterations in development 24 h later. The specific purpose of the study was to assess whether the developmental responses followed Haber’s Law, or whether an additional component of exposure was needed to model the relationship. The current study demonstrated that the response of the developing embryo to hyperthermia, with rare exception, was dependent on an additional component of exposure beyond the cumulative exposure. For the vast majority of the parameters measured in this study, the probability of an effect was greater at higher temperatures for short durations than at lower temperatures for long durations, given the same cumulative exposure. Thus, Haber’s Law did not adequately describe the results of our study.

Key Words: Haber’s Law; hyperthermia; whole embryo culture; developmental toxicity; risk assessment; rat; dose-rate; dose-duration; heat shock.


    INTRODUCTION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
In developing exposure standards, regulatory agencies often assume a continuous lifetime exposure, even though it is recognized that intermittent, limited-duration exposures are more generally the rule. In cases where the standard is intended to account for less-than-lifetime exposures, a number of approaches have been developed for establishing short-duration exposure limits (Jarabek, 1995Go; Kimmel, 1995Go). Each approach addresses specific exposure scenarios that are of interest to a specific regulatory body. The exposure periods vary from minutes to days, and the health endpoints of concern vary from irritation and occupational impairment to death. However, a common feature of most of these approaches is the assumption that the probability of response depends on the cumulative exposure, i.e., the product of exposure concentration and duration. The concept of a constant relationship between concentration and duration is generally referred to as Haber’s Law and is used in extrapolating to inhalation exposures that are not covered by the experimental data. The reliability of this approach in estimating the effects of a particular exposure at various concentrations and durations is relatively undefined. However, recent reviews of this area have begun to question its general applicability over wide ranges of concentration and duration (Eastern Research Group, 1998Go; Pierano et al., 1995Go).

In order to study the interaction of exposure concentration (or level) and duration, rat embryos were exposed in whole embryo culture to increased temperature and evaluated for alterations of development 24 h later. The use of hyperthermia and whole embryo culture was chosen for several reasons. First, our laboratory has substantial experience in studying the effects of hyperthermia on development. Exposure of gestation day (GD) 10 rat embryos to elevated temperatures, either in utero or in whole embryo culture, results in altered development of many growth and morphological parameters (Cuff et al., 1993Go; Kimmel et al., 1993aGo,bGo). From the whole embryo culture studies, it was noted that the pattern of response of virtually all of the evaluated parameters was defined by both the temperature level and duration of exposure (Kimmel et al., 1993bGo). Second, heat is a physical agent that is not influenced by metabolic factors, that can be carefully controlled in whole embryo culture, and that affects development following brief exposures. Finally, embryos in culture are exposed individually rather than via the dam, which decreases the need to account for intralitter correlation of responses (Williams et al., 1996Go). All of these factors simplify modeling the response to exposure of a biological entity (the embryo), which is constantly changing as development proceeds.

The specific purpose of the study was to assess whether a response to hyperthermia depends solely on the multiple of temperature and duration (i.e., whether Haber’s Law applies), or whether there is an additional component of exposure needed to model the relationship. The models developed by Scharfstein and Williams (1994) were used to assess the compatibility with and/or departure of the responses to hyperthermia from Haber’s Law. Response-surface models were developed as a useful approach for evaluating the combined effect of more than one variable on a variety of responses through model-fitting and 3-dimensional graphs. Eventually, the goal is to develop models that permit extrapolation of data to untested exposure intensities and durations and apply these in the risk assessment process.


    MATERIALS AND METHODS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
The interaction of temperature and duration of exposure was studied in whole embryo culture using GD 10 embryos from Sprague-Dawley derived CD rats (Charles River, Kingston, NY). The basic methodology was identical to that reported in Kimmel et al.(1993b). Nulliparous females were housed under controlled conditions and bred with a proven male on the afternoon of proestrus, checking for sperm plugs on the following morning. The day of finding plugs was designated as GD 0.

Embryos were isolated from the dams on GD 10 and Reichert’s membrane was opened to expose the visceral yolk sac. Embryonic heart beat, yolk sac circulation, flexion, and position of the neural folds were noted as general signs of viability and developmental stage. Embryos used for culture were at or near the stage of neural fold apposition (10–12 somites in our laboratory). The only exception to the previous culture technique was that only one embryo was incubated per vial.

Embryos were equilibrated at 37°C for approximately 2 h before exposure to one of the temperature-duration combinations. Exposure to heat was carried out in a water bath (Precision 181, Cole-Palmer), maintained within a 0.5°C temperature range (e.g., 40.0°C = 40.0–40.5; 40.5°C = 40.5–41.0; etc.). A total of 432 embryos were cultured for this study. Table 1Go shows the 6 x 7 (temperature x duration) design employed in this study, and the number of embryos cultured at each temperature-duration combination. Following heat exposure, the vials were equilibrated to 37°C in a water bath and returned to the 37–38°C incubator/rotator for the remainder of the 20–22 h incubation. Preliminary studies indicated that both attaining the increased temperature and returning to 37°C after exposure were accomplished in less than 30 s.


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TABLE 1 Experimental Design: Number of Embryos Cultured at Each Temperature-Duration Combination
 
Following incubation, each embryo was evaluated without knowledge of exposure as described by Kimmel et al.(1993b). Indicators of viability included the presence and strength of the heart beat and yolk sac circulation, subjectively rated. Indicators of general growth included yolk sac diameter, crown-rump length, number of somites, and the mean morphological score (MMS). The MMS is the mean of scores for 13 individual morphological parameters: yolk sac, allantois, torsion, heart, hindbrain, midbrain, forebrain, otic system, optic system, olfactory system, maxillary process, branchial bars, and forelimb.

The effect of the hyperthermia on normal development was defined for both individual growth and morphological parameters, as well as for viability and collective measures of alteration. A nonviable embryo was any embryo without a heart beat and yolk sac circulation at the time of evaluation. If the embryo exhibited even a faint heart beat or yolk sac circulation, it was considered viable and evaluated for alterations in growth and morphology. For those embryos which were judged to be viable, a collective measure of whether the embryo was altered was developed, using the following criteria: yolk sac diameter, < 3.2 mm; crown rump length, < 2.9 mm; head length, < 1.4 mm; proboscis length, < 0.5 mm; somite number, < 19; somite integrity, either abnormal structure or segmentation. Somite number and integrity were evaluated on both sides of the embryo. An effect on either side was considered an alteration in normal development. Any one or more of these 6 criteria or a mean of the 13 morphological parameters < 2.69 could be the basis for considering an embryo altered. A collective measure of affected embryos included any embryo that was either nonviable or altered.

Several statistical procedures were applied to evaluate the effects of hyperthermia. First, the effects of temperature and duration of exposure were assessed on each individual outcome in separate univariate models. For continuous outcomes (head length, crown rump length, yolk sac diameter, number of left and right somites, and proboscis length), a general linear regression model for predicting the mean response as a function of the exposure covariates was employed. For the morphological parameters that were assessed on an ordinal scale (1 = severe, 2 = moderate, 3 = normal), an ordinal logistic regression model was fit to each outcome to assess the effect of exposure covariates on the probability of response within each severity level. The MMS was treated as a continuous variable, and a linear regression model was also used for this response. The binary responses (nonviable, altered, and affected) were modeled via standard logistic regression models as described below.

A common approach for incorporating duration of exposure and temperature was utilized in all three types of models, i.e., the linear regression models for continuous outcomes, ordinal logistic regression models for ordinal outcomes of morphological severity, and standard logistic regression models for viability, altered and affected status. Ignoring duration of exposure, the usual dose-response model for a binary outcome models the probability p(d) of an adverse outcome as a function of dose level, as follows:


(1)

where F represents the link function, such as a logistic or probit link function. In the context of the hyperthermia experiments, the dose level d represents the increase in temperature over the control temperature of 37°C. Scharfstein and Williams (1994) describe how the above model can be extended to include a covariate that represents the cumulative exposure, d*t, along with an additional covariate t, which reflects the extra effect of duration after controlling for cumulative exposure:


(2)

In the current study, the duration of exposure at the control temperature was assumed to have no adverse effect on development, so the model above was modified such that the duration effect, t, would only be included for temperatures greater than 37°C:


(3)

where {delta}t = 1 if d > 37 and 0 otherwise. If Haber’s Law of equal responses for any constant cumulative exposure holds, then Model 3 can be reduced to:


(4)

In other words, the implication of Haber’s Law is that ß1 = 0. By fitting Model 3, one can conduct a statistical test of the significance of ß1 to assess whether Haber’s law is consistent with the observed data. In applying Models 3 and 4 to the hyperthermia data, a logistic link was employed.

For the ordinally scaled morphological outcomes, Models 3 and 4 were extended by estimating Pr(Y <= r | d, t) using standard ordinal logistic regression models, with r = 1, 2, or 3 for severely affected, moderately affected, and normal, respectively. This approach for incorporating duration of exposure into dose-response models can also be applied for the continuous outcomes. In this situation, the mean response is modeled as a linear function of the same covariates, as follows:


(5)

where the coefficient ß1 represents the effect of duration accounting for cumulative exposure. For example, the mean µ(d, t) might reflect the mean crown-rump length as a function of duration (t) and temperature level (d).

The results of fitting these models to the hyperthermia data are illustrated in two ways: (1) the p values for tests of significance of the effects of cumulative exposure (d*t) and duration (t) are provided from the univariate models for the growth outcomes, and for the binary outcomes of nonviable, altered, and affected embryos; and (2) 3-dimensional response-surface plots are generated that exhibit the actual or predicted response levels at combinations of duration of exposure and temperature level. The levels of temperature and duration of exposure form a horizontal plane, while the response level forms a surface over this plane.

The response-surface plot is very useful for visualizing the joint effects of temperature and duration of exposure. Their use originated in engineering applications aimed at maximizing the yield of some output, but more recently they have been applied to a variety of other contexts in both design and analysis of experimental data (Box and Draper, 1987Go). Several different types of response-surface plots are provided. The first illustrates the actual experimental means for a given response, represented as a pyramid at a coordinate determined by the duration of exposure and temperature and a height reflecting the response level (example, Fig. 1aGo). This plot gives an indication of the inherent variability in response data and of the gaps in areas where data was not collected. The second type of plot is a smoothed spline interpolation applied to the points on the response-surface plot (example, Fig. 1bGo), which filters out some of the random variability by taking weighted averages over all response points to determine the smoothed response-surface levels. Finally, there are two plots that illustrate the predicted response levels using the modeling techniques described above. Figure 2aGo illustrates the predicted response surface after enforcing Haber’s Law by applying Model 4. Figure 2bGo shows the predicted response surface using the general, or extended model given by Model 3.



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FIG. 1. (a) Observed proportions of total affected embryos for individual temperature-duration combinations. (b) Smoothed spline interpolation of the observed proportions of total affected embryos applied to a response-surface plot.

 


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FIG. 2. The predicted probability of total affected embryos using Haber’s Law, (a) Model 4, or applying the extended model, (b) Model 3, shown as response-surface plots.

 

    RESULTS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Combined Effects
The effects of the temperature-duration combinations on general embryonic development are shown in Table 2Go. The percent of affected (nonviable and/or altered) embryos in the control group (37–38°C) ranged from 0–31%. Temperature-related and duration-related effects were observed in all of the exposed groups. Even at 40°C, the lowest temperature level above control, the percent affected increased after 60 min of exposure and possibly as soon as 30 min of exposure. At 40.5°C and 41.0°C, consistent exposure-related effects were observed by 15 min, and at 41.5°C and 42.0°C, by 5 min. Figure 1aGo shows the actual experimental means of percent affected embryos, and Figure 1bGo shows a response surface plot of a smoothed spline interpolation of these data. The results demonstrate an overall pattern of a temperature/duration-related increase in the percent of affected embryos.


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TABLE 2 Percent of Affected Embryos at Each Temperature-Duration Combination
 
Hyperthermia clearly affects viability, but a temperature-duration effect is not obvious except at higher temperatures and longer exposures (Table 3Go). There was no increase in death after 5 min of exposure at any of the temperatures. Likewise, the small increases in death at 40.0°C (10–20 min) did not appear to be duration-related. Indications of an effect on viability could be seen at higher durations, but these were not clearly temperature-duration-related until 42.0°C for 20 min, 41.0–41.5°C for 30–45 min, or 40.5°C for 60 min. The percentage of altered viable embryos made up a larger proportion of the affected embryos than the nonviable embryos at almost every temperature-duration combination (Table 4Go). As little as 5 min exposure at 41.5–42.0°C altered normal growth and development. At lower temperatures (40–41°C), the exposure duration required to see an effect was increased, although not dramatically.


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TABLE 3 Percent of Nonviable Embryos at Each Temperature-Duration Combination
 

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TABLE 4 Percent of Altered Embryos among Those Viable at Each Temperature-Duration Combination
 
The predicted probability of affected embryos by using Haber’s Law (Model 4) or by applying the extended model (Model 3) are shown as response-surface plots in Figures 2a and 2bGo, respectively. If Haber’s Law holds, there would be a constant response for any d*t multiple, leading to the symmetrical response surface seen in Figure 2aGo. However, it is obvious from the response-surface plot of the extended model (Fig. 2bGo) that the surface is skewed, with the probability of an effect being greater at high temperatures for short durations than at lower temperatures for longer durations, given the same temperature-duration multiple. Response-surface plots for nonviability and malformed embryos under the extended model exhibited a similar skewed response to the varying temperature-duration combinations (plots not shown). It should be noted that for the extended model of affected embryos (Fig. 2bGo), the surface goes below the background at the lower temperatures. This is due to the fact that there were no data points collected between 37 and 40°C, so the overall surface shape in this area is imposed by trends in the data at the higher temperatures.

Summarizing the combined effects, the model that best fits the proportion of animals showing some effect includes a parameter that is in addition to the constant multiple of temperature and duration. This also appears to be the case for nonviable and altered embryos. Moreover, when the multiple of temperature and duration is held constant, short exposures to higher temperatures result in a greater proportion of affected embryos than longer exposures to lower temperatures.

Growth Parameters
Table 5Go summarizes the response of 6 growth parameters as they relate to the covariates, i.e, the cumulative exposure effect (d*t), and the extra effect of duration after controlling for cumulative exposure (t). The values were obtained from fitting Model 5. With the exception of yolk sac diameter, all of the individual growth parameters were sensitive to changes in temperature and duration of exposure. The fact that both d*t and t were consistently significant (p < 0.05) indicates that Haber’s Law did not adequately describe the effects of hyperthermia on individual growth parameters. In particular, since the coefficient on the duration effect (ß1) was consistently estimated to be positive for each of the growth parameter models, this suggests that short acute exposures result in more retardation of growth parameters than do longer lower-level exposures within the same d*t multiple. Although significant effects of both exposure variables were observed, the proportion of the total variability explained by these covariates was relatively low; the R-squared values ranged from 8–11%. This implies that while both exposure covariates have a significant impact on the mean response for each growth parameter (except yolk sac diameter), there still remains considerable variability around the mean in the responses of embryos exposed to the same exposure level and duration.


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TABLE 5 Summary of Individual Growth Parameters
 
As an example of the effects of temperature and duration of exposure on the growth parameters, the effects on the mean number of right somites are shown in Figure 3Go. Figure 3aGo shows the actual means of the individual temperature-duration combinations; Figure 3bGo shows a smoothed spline interpolation of these data. Since the response is in a negative rather than a positive direction, the base coordinates are reversed from those in the previous figures to make viewing the response easier. At 37°C, the mean number of right somites varied between 22.5 and 23.7 over the various exposure durations. Reductions in somite number outside of this range were observed at 40.0°C at the 30-, 45-, and 60-min exposures. With increasing temperature, the effect was even more pronounced, and at 42.0°C the range was 18.7–21.0.



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FIG. 3. Effects of temperature and duration of exposure on the mean number of right somites as the experimental means (a) and as a smoothed spline interpolation of these data (b).

 
Morphological Parameters
As with the growth parameters, significant effects of both cumulative exposure (d*t) and the extra effect of duration (t) were observed on each of the 13 morphological parameters, with the exception of yolk sac vasculature and development of the allantois (Table 6Go). The response of the yolk sac vasculature appeared to depend solely on the cumulative exposure (i.e., Haber’s Law appeared to be appropriate for describing the effect of temperature and duration on this parameter). In contrast, there appeared to be no association between the development of the allantois and the exposure levels. For the remaining 11 morphological parameters, Haber’s Law alone did not seem to describe the responses to varying durations of increased temperature, as exhibited by the significant effect of duration of exposure (t), even after accounting for cumulative exposure (d*t). In all 11 of these models, the coefficient on duration (ß1) was estimated to be negative, indicating a higher probability of moderate or severe morphological change at short acute exposures than for longer lower-level exposures with the same d*t multiple. The exposure covariates had the greatest impact on the forebrain, otic system, olfactory system, branchial bars, and the forelimb, with a lesser impact on torsion, hindbrain, and heart.


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TABLE 6 Summary of Morphological Parameters
 
In a fashion similar to the individual morphological endpoints, both MMS and somite division exhibited a response to hyperthermia that was not accounted for by the cumulative exposure (d*t) alone (not shown). The MMS p values for effects were 0.0001 for both cumulative exposure and duration. For somite division, previously shown to be a highly responsive endpoint to hyperthermia on GD 10 (Cuff et al., 1993Go; Kimmel et al., 1993), the p values for effects were 0.0001 for cumulative exposure and 0.0072 for duration.


    DISCUSSION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
What has come to be known as Haber’s Law was originally proposed by Haber to describe the effects of mustard gas exposures of short durations and high concentrations (see Witschi, 1997Go, 1999Go). This approach assumed that equivalent multiples of concentration and duration would result in the same response. However, the approach was not intended for exposures of long durations and/or low concentrations. Nevertheless, current approaches for incorporating the concentration and duration components of exposure into risk analyses generally assume a constant relationship of C x T, irrespective of concentration or duration.

The current study demonstrates that the response of the developing embryo to hyperthermia is dependent on an additional component of exposure duration beyond the cumulative exposure. This is true for the combined developmental effects as well as for all but three of the individual endpoints evaluated. Thus, for the vast majority of parameters measured in this study, Haber’s Law was not sufficient by itself to describe the relationship of responses to various temperature-duration combinations. Moreover, the probability of an effect was greater at higher temperatures for shorter durations than at lower temperatures for longer durations, given the same temperature-duration multiple, and this pattern of response is generally consistent across endpoints.

The temperature and duration of hyperthermia at which effects were first observed in the current study are below those levels that have been routinely used in studying the effects of hyperthermia on embryonic development. Generally, both in vivo and in vitro, exposure temperatures or core body temperatures of 42°C or higher have been employed for periods exceeding 15 min (e.g., Mirkes, 1985Go; Shiota, 1988Go; Walsh et al., 1987Go). Mirkes (1985) did report a slight effect at 41°C in vitro, but it required more than 2 h of exposure. In an in vivo study that more closely approximates the current study design, Germaine et al.(1985) maintained GD 9 rats at various core body temperatures (ranging from 40.5°C to 43.5°C) for various durations (a "spike" or from 2 min to 480 min). They observed litters with abnormal fetuses at all but the lowest core temperature (40.5°C). At 40.5°C, they did not observe an effect, even after 8 h of exposure. In the present study, effects were observed at temperatures as low as 40.0°C, following approximately 30–60 min of exposure.

Although it is not possible to directly compare our in vitro results with the in vivo study of Germaine et al.(1985), the lowest temperatures (40–41°C) used in the two studies are within the range of potential human exposures. Hyperthermia in the human can result from febrile illness, as well as from occupational and environmental conditions; and associations of hyperthermia with developmental alterations in humans have been made (Edwards et al., 1995Go; Graham et al., 1998Go). Under in vivo conditions in our laboratory, the GD 10 maternal Sprague-Dawley rat maintains a core body temperature of 37–38°C (Kimmel et al., 1993aGo). Thus, our results suggest that even at an elevation of only 2–3°C above core body temperature, the duration required to achieve an effect may be less than 60 min. This is similar to previous reports of threshold elevations of 1.5–2.5°C above the core body temperature being required for alterations in development (Edwards, 1986Go; Graham et al., 1998Go).

It should be noted that the responses observed at 37°C can be considered normal variation within the test system. Embryos that equilibrate and are maintained in culture over 22–24 h at 37°C generally develop comparable to embryos in vivo. Occasionally, even an unexposed embryo will show an observable alteration in development. Another factor that may result in an affected embryo in the 37°C group is a misclassification during the morphological evaluation. The number of embryos per group, while large by some standards, will still result in an 8–10% increase for every affected embryo. The way the model is defined, we deliberately do not take into account duration of exposure at 37°C. However, this does not imply that we assume there to be no baseline effect. Rather, we assume the baseline effect to be constant over duration of exposure for the 37°C heat level. In fitting the model, an overall average response was estimated for all of those embryos exposed to 37°C, and the response predicted by the model would be the same for all embryos in this exposure group.

The in vitro induction of hyperthermia, as used in this study, provides an ideal system for the initial modeling of the relationship of level and duration of exposure on embryonic development. Heat is a physical agent that appears to act directly on the embryo (Cuff et al., 1993Go; Kimmel et al., 1993bGo). This, coupled with the isolation of the embryo in culture, removes potential confounders such as maternal tissue layers, and metabolic and pharmacokinetic factors, that may modulate the observed response. Our previous studies have shown that embryonic development in whole embryo culture is comparable to what is observed in vivo, both in control and heat-treated embryos, at least over the 24-h period used in this study (Cuff et al., 1993Go; Kimmel et al., 1993bGo). The whole embryo culture also permits the level of the exposure to be controlled within clearly defined ranges (0.5°C in this study) for discrete periods of time. Finally, the duration of exposure required to obtain an effect is relatively short, effectively removing the influence that normal developmental changes may have on the susceptibility of a particular endpoint.

If the statistical model employed in this study is to be of general use for understanding exposure-duration relationships, it will have to be shown to be more generally applicable to chemical and other physical agents. Weller et al.(1999) have recently reported a similar pattern of response for many of the same developmental parameters in an in vivo study of ethylene oxide exposure during pregnancy in mice. In that study, high exposure levels of shorter duration had a much greater effect on fetal viability, growth, and malformations than low exposure levels at longer durations, given a constant concentration-duration multiple. Other investigators have also reported divergence from Haber’s Law for neurotoxic effects (Bushnell, 1997Go; Crofton et al., 1996Go). The responses were dependent on dose-rate, but not in a strict C x T relationship.

The development of appropriate models should more clearly define the relationship of exposure concentration and duration. Initial application of these models will require broad assumptions about the mode of action. Ultimately, as our understanding of operative modes of developmental toxicity increases, such models should permit interpolation of data to untested C x T combinations, reducing the uncertainty in assessing the data and increasing our confidence in predicting potential human risk. The current study suggests that Haber’s Law is likely to underestimate the probability of an effect when extrapolating to higher exposure levels for shorter durations and overestimate the probability at lower exposure levels for longer durations. The more restrictive Haber’s model (Model 4) underestimates the probability of an abnormal embryo by as much as 30% at the shorter exposure durations and high temperatures (e.g., 5–10 min at 42°C), while it overestimates the probability of an abnormal embryo by 20–30% at the longer durations at low temperatures (e.g., 30–60 min at 40.5–41°C). In contrast, the extended model (Model 3) provides predicted probabilities that are closer to those actually observed. This may vary depending on the relative exposure period, the endpoint being investigated, and the proximity to the target site. It should be reemphasized that Haber’s Law was originally developed to apply to a specific exposure scenario based on specific assumptions. There is no reason to expect it to fit every situation, especially when being applied to the developing embryo, which presents a constantly changing exposure target.

Current practice in risk assessment is to use Haber’s Law for duration adjustment when extrapolating from shorter to longer exposure durations, but not when adjusting from longer to shorter exposure periods. This appears to be a conservative approach based on the data from this study and those by other investigators (Bushnell, 1997Go; Weller et al., 1999Go). In general, no duration adjustment is currently made for developmental toxicity data, based on the assumption that a single, discrete exposure during a critical developmental period is all that is necessary to cause an alteration (U.S. EPA, 1991Go). However, the results of modeling in this study and that of Weller et al.(1999) show a significant effect of exposure-duration on developmental responses and suggest that continuing this practice may not be conservative enough to adequately protect against potential developmental toxicity when predicting responses from shorter to longer durations. Further efforts to describe exposure-duration relationships will foster development of more predictive models for use in risk assessment for developmental toxicity.


    ACKNOWLEDGMENTS
 
We thank Dr. M. E. Stratmeyer, Center for Devices and Radiological Health, Food and Drug Administration, Rockville, MD, for his support throughout this project; and Ms. Natalie Tudor for her technical assistance. P.L.W. acknowledges partial support for this work from Grant ES07981 from the National Institute of Environmental Health Sciences.


    NOTES
 
1 To whom correspondence should be addressed at U. S. Environmental Protection Agency (8623-D), Ariel Rios Building, 1200 Pennsylvania Ave., NW, Washington, DC 20460. Fax: (202) 565-0078. E-mail: kimmel.gary{at}epa.gov. Back

This work was supported in part by a grant from the National Institute of Environmental Health Science. The views expressed herein are those of the authors and not necessarily the views of the U.S. Environmental Protection Agency.

Portions of this data were presented at the U.S. EPA Workshop on the Relationship Between Exposure Duration and Toxicity, August 5–6, 1998, Washington, DC.


    REFERENCES
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 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
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