Haber’s rule

The first principle of dose-response determination in inhalation toxicology is based on Haber s rule, which states that responses to an inhaled toxicant will be the same under conditions where C varies in complementary manner to t (Haber, 1924). For example, if C t elicits a specific magnitude of the same response that is, Ct = K, where A is a constant for the stated magnitude of response (as shown in Figure 10.2). 

This rule holds reasonably well when C or t varies within a narrow range for acute exposure to a gaseous compound (Rinehart and Hatch, 1964) and for chronic exposure to an inert particle (Henderson et al., 1991). Excursion of C or / beyond these limits will cause the assumption Ct = K to be incorrect (Adams et al., 1950, 1952 Sidorenko and Pinigin, 1976 Andersen et al., 1979 Uemitsu et al., 1985). For example, an animal may be exposed to 1000 ppm of diethyl ether for 420 min or 1400 ppm for 300 min without incurring any anesthesia. However, exposure to 420,000 ppm for lmin will surely cause anesthesia or even death of the animal. Furthermore, toxicokinetic study of fiver enzymes affected by inhalation of carbon tetrachloride (Uemitsu et al., 1985), which has a saturable metabolism in rats, showed that Ct = K does not correctly reflect the toxicity value of this compound. Therefore, the limitations of Haber s rule must be recognized when it is used in interpolation or extrapolation of inhalation toxicity data. 

In studies eondueted by Bide and Risk (2004), male CD-I strain miee were exposed whole body to GB for time periods ranging from 20 to 720 min. LC50 values for 3-12 h were progressively higher (toxicity lower) than that predieted by either Haber s rule or the Ten Berge relationship (Ten Berge et al, 1986). In studies eondueted by Anthony et al. (2004), male and female SD rats were exposed whole... 

The relationship between dose and time to response for any given chemical is a function of the physical and chemical properties of the substance and the unique toxicologic and pharmacologic properties of the individual substance. Historically, the relationship according to Haber (1924), commonly called Haber s law (NRC 1993a) or Haber s rule (i.e., C x t = k, where C = exposure concentration, t = exposure duration, and k = a constant) has been... 

A key element in the procedure of time scaling is the use of a value or values for n in the equation C" x t = k. If empirical data for exposure durations other than the AEGL-specified exposure periods are available to quantify the exposure concentration-exposure duration relationships for a health-effect endpoint, including lethality, the value of n should be derived using the method of calculation described in this section. It is believed that empirically derived values of n are scientifically more credible than a default value of n = 1 (Haber s rule) or attempting to derive an alternate value of n. 

The relationship between dose and exposure time to produce a toxic effect for any given chemical is a function of the physical and chemical properties of the substance and the unique toxicologic and pharmacologic properties of the individual substance. Historically, the relationship according to Haber (1924), commonly called Haber s law (NRC 1993) or Haber s rule (i.e., C x t = k, where C = exposure concentration, t = exposure duration, and k = a constant) has been used to relate exposure concentration and duration to a toxic effect (Rinehart and Hatch 1964). This concept states that exposure concentration and exposure duration may be reciprocally adjusted to maintain a cumulative exposure constant (k) and that this cumulative exposure constant will always reflect a specific quantitative and qualitative response. This inverse relationship of concentration and time may be valid when the toxic response to a chemical is equally dependent upon the concentration and the exposure duration. However, an assessment by ten Berge et al. (1986) of LC50 data for certain chemicals revealed chemical-specific relationships between exposure... 

The guidance values proposed refer basically to effects seen in a standard 90-day toxicity study conducted in rats. They can be used as a basis to extrapolate equivalent guidance values for toxicity studies of greater or lesser duration, using dose/exposure time extrapolation similar to Haber s rule for inhalation, which states essentially that the effective dose is directly proportional to the exposure concentration and the duration of exposure. The assessment should be done on a case-by-case basis e.g. for a 28-day study the guidance values below would be increased by a factor of three. 

FIGURE 11.3 Comparison of Haber s rule and toxic load model. If Haber s rule applies (n — 1), then tbe dose required to produce a given response is constant relative to exposure time. However, for a toxic load model with an u > 1, tbe dose required to produce a given response increases as the exposure time increases. For a toxic load model with an u < 1 (not shown), the dose required to produce a given response decreases as the exposure time increases. 

Clark (1937) further expanded Haber s rule for the action of a number of drugs ... 

So, the perfect fit of Haber s rule to the carcinogenic action of 4-DAB suggested that threshold concentration (c ) and minimum time of response (i ) were (in Clark s words) so small as not to produce a measurable error. 

The perfect fit of Haber s rule to the carcinogenic action of dieldrin in mouse liver provided no evidence of a subthreshold dose. Therefore, nongenotoxic carcinogens should not be assumed to exhibit a threshold per se rather they must be evaluated with regard to mode of action and human relevance, as discussed in Chapter 13. 

An equally good fit was found for data relating to a 1% mortality from exposure to chlorine among rats. That the toxicity of chlorine follows Haber s Rule so closely is unsurprising Haber studied chlorine closely. 

Interestingly, Miller also showed that data relating to the delayed acute toxicity in rats of the dioxin compound, HpCDD (1,2,3,4,6,7,8-heptachlorodibcnzo-p-dioxin), also followed Haber s Rule. If time to death from wasting is plotted against dose (mg kg ) the data are closely fitted by a curve of the equation ... 

However, not all dose-response curves follow Haber s rule. If the dioxin data referred to above are considered again and time is plotted on the x-axis, with dose needed to produce a 10% mortality on the y-axis, then the data are well fitted by an equation ... 

Miller FJ, Schlosser PM, Janszen DB, (2000). Haber s Rule a special case in a family of curves recording concentration and duration of exposure to a fixed level of response for a given endpoint. Toxicology, 149 21-34. 

Haber s law (or Haber s rule) was discussed at some length in Chapter 2. A recent paper by Hatch et al (2001) has extended this discussion with special reference to phosgene. The authors focused on repeated and chronic exposures and showed that adaptation occurred if exposures were not overwhelming and were repeated daily. Adaptation was shown to wane over the period of a month or so. Repeated exposure at monthly intervals was associated with the development of chronic effects. This work shows that great care is needed in predicting responses from the Ct product if exposures are repeated and that the... 

Bide and Risk (2004) studied the inhalation toxicity of sarin in mice from longer exposures to low-level concentrations in an effort to establish toxicity estimates for humans. The exposure period ranged from 20 minutes to 12 hours in their study. The LCT 50 values for 20-, 60-, 180-, 360-, and 720-minute exposures were 430, 540, 900, 1210, and 2210 mg min/m, respectively, corresponding to LC50 values 21.5, 9.0, 5.0, 3.4, and 3.1 mg/m, respectively. The authors reported their data did not fit Haber s rule... 

Peay, T.S., McKee, J., Willson, G.A., et al, 2010. Acute studies of inhaled chlorine in F344 rats suggests alternative to Haber s rule for risk extrapolations. Toxicologist 114, 216-217. 

When the LCtjo is constant with respect to t, it is said to obey Haber s rule (Haber, 1924). However, Haber s rule is more of an exeeption than a true rule. Thus, a new term, toxic load (TL), has been developed and extensively used in IH toxicology to account for time dependent toxieity. TL is... 

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