Current risk assessment
procedures are typically based on overall daily exposure levels,
and tend to emphasize effects resulting from continuous exposures
over a lifetime. This basis is widely recognized to be an oversimplification.
There has been an increasing realization that exposures are more
likely to be experienced as episodes (i.e., bursts or spikes,
or intermittent exposures) of varying levels. As scientists delve
further into the subject, they are discovering that Haber's rule
(which can also be referred to as Haber's law) has limitations
in its applicability. Haber's rule describes the relationship
between exposure concentration and duration (i.e., concentration
multiplied by duration). Haber's rule is widely recognized in
toxicology for its application in risk assessment.
The complexities
of exposure effects on toxic responses require consideration
of the entire exposure profile, including the timing, duration,
and intermittent nature of exposures reflecting realistic scenarios
encountered in practical settings. The proper metric for exposure
may be highly dependent on the pharmacokinetic properties of
the chemical or exposure in question. The toxic effects considered
in models must be carefully chosen to reflect the sensitive endpoints
based on the exposure characteristics.
Models have been
developed which begin to address the effect of duration of exposure
in addition to exposure levels; however, some of these models
do not incorporate mechanistic information. In addition, only
limited work has been done on developing efficient designs for
studying dose-rate effects, and these designs tend to be simplistic.
Vegetation effects
research and controlled laboratory studies of human volunteers
indicate that higher ozone hourly average concentrations elicit
a greater effect on hour-by-hour physiologic response than lower
hourly average ozone values. The weighting of the higher values
compared to mid and lower hourly average ozone concentrations
results in a nonlinear response for both human health (Adams,
2003; Adams, 2006; Hazucha et al., 1992; Hazucha and Lefohn,
2007; Lefohn, Hazucha, Shadwick, and Adams, 2010) and vegetation
(Musselman et al., 1983; Hogsett et al., 1985; Musselman et al.,
2006; Heath et al., 2009). The nonlinear response observed for
human health clinical studies and vegetation experiments involving
ozone exposures is important for assessing the validity of applying
Haber's rule (also referred to as Haber's law). Haber's rule
states that, for a given poisonous gas, C × t = k, where
C is the concentration of the gas (mass per unit volume), t is
the amount of time necessary to produce a given toxic effect,
and k is a constant, depending on both the gas and the effect.
Haber's rule, as commonly understood in inhalation toxicology,
states: C×T=constant, meaning that identical products of
concentration of an agent in air (C) and duration of exposure
(T), the CT product, should yield an identical biological
response.
The formula was
originally developed in the early 1900s by the German physical
chemist Fritz Haber (1868 -1934) to characterize the acute toxicity
of chemicals used in gas warfare. For example, the rule states
that doubling the concentration will halve the time for a given
toxic effect to occur. Haber's rule is an approximation and Haber
himself acknowledged that it was not always applicable (https://en.wikipedia.org/wiki/Haber%27s_rule).
The greater importance of concentration compared to exposure
duration for ozone human health and vegetation experiments illustrates
the limitations of applying Haber's rule. Specifically, when
concentration is more important than the time required to elicit
an adverse effect, Haber's rule will not be applicable when attempting
to determine a cumulative exposure.
As indicated in
the peer-reviewed literature, as well as the EPA reviews of the
literature since 1986 (US EPA, 2020), Haber's rule is not applicable
for ozone exposures. The US EPA (2020) has utilized for many
years the W126 exposure
index for assessing the risk associated with ozone exposures
to vegetation, as well as proposing the exposure metric as a
federal standard to protect vegetation. The W126 metric is a cumulative, concentration-weighted
index specifically designed for assessing vegetation damage,
which research has shown is more accurately predicted when higher
hourly average concentrations are provided greater weight than
lower concentrations (Lee et al., 2022). The index uses an "S"-shaped
(sigmoid) weighting curve to account for the non-linear biological
response of plants to varying ozone levels. The W126 index was developed to provide a more
biologically meaningful characterization of ozone exposure effects
on plants that explicitly accounts for the importance of the
higher hourly average concentrations (but still includes consideration
of the mid- and lower-level hourly average concentrations). The
C x t model of Haber's rule does not adequately capture the biological
characterication described in the W126
index.
If the relationship,
C x T, is not applicable for a specific chemical, risk assessments
utilizing Haber's rule may provide inaccurate estimates for the
specific chemical. The inappropriateness of the assumption of
the validity of Haber's rule can result in either overestimates
or underestimates of risk, with the latter being more likely
when extrapolation is toward periods of shorter duration. Because
of its simplicity, in spite of the serious limitations of Haber's
rule, the rule continues to be applied. Miller et al. (2000)
suggest that, while many toxicologists have used Haber's rule
to analyze their experimental data (whether their chemicals,
biological endpoints, and exposure scenarios were suitable candidates
for applying the rule), it is time to move beyond the simple
relationship expressed by Haber's rule and adopt the use of more
sophisticated models.
While Haber's rule
may remain relevant in toxicology for setting exposure guidelines,
risk assessment, and developing emergency guidelines, its limitations
should be seriously discussed and qualified because the rule
does not apply to all substances or exposure scenarios.
References
Adams, W.C. 2003. Comparison of chamber and face mask 6.6-hour
exposure to 0.08 ppm ozone via square-wave and triangular profiles
on pulmonary responses. Inhalation Toxicology 15: 265-281. https://doi.org/10.1080/08958370304505.
Adams, W.C. 2006. Comparison of chamber 6.6-h exposures
to 0.04 - 0.08 ppm ozone via square-wave and triangular profiles
on pulmonary responses. Inhalation Toxicology 18, 127-136. https://doi.org/10.1080/08958370500306107.
Hazucha, M.J, Folinsbee, L.J., Seal E. 1992. Effects of
steady-state and variable ozone concentration profiles on pulmonary
function. Am Rev Respir Dis 146: 1487-1493. https://doi.org/10.1164/ajrccm/146.6.1487.
Hazucha, M., Lefohn, A.S. 2007. Nonlinearity in Human Health
Response to Ozone: Experimental Laboratory Considerations Atmospheric
Environment. 41: 4559-4570. https://doi.org/10.1016/j.atmosenv.2007.03.052.
Heath, R.L., Lefohn, A.S., Musselman R.C. 2009. Temporal
processes that contribute to nonlinearity in vegetation responses
to ozone exposure and dose. Atmos Environ 43: 2919-2928.
Hogsett, W.E., Tingey, D.T., Holman, S.R. 1985. A programmable
exposure control system for determination of the effects of pollutant
exposure regimes on plant growth. Atmos Environ 19: 1135-1145.
Lee, E.H., Andersen, C.P., Beedlow, P.A., Tingey, D.T.,
Koike, S., Dubois, J.-J., Kaylor, S.D., Novak, K., Rice, R.B.,
Neufeld, H.S., Herrick, J.D. 2022. Ozone exposure-response relationships
parametrized for sixteen tree species with varying sensitivity
in the United States, Atmospheric Environment (2022), doi: https://doi.org/10.1016/j.atmosenv.2022.119191.
Lefohn, A.S., Hazucha, M.J., Shadwick, D., Adams, W.C.
2010. An alternative form and level of the human health ozone
standard. Inhalation Toxicology 22:999-1011. https://doi.org/10.3109/08958378.2010.505253.
Miller, F.J., Schlosser, P.M., Janszen, D.B. 2000. Haber's
rule: a special case in a family of curves relating concentration
and duration of exposure to a fixed level of response for a given
endpoint. Toxicology 149 (1): 21-34.
Musselman, R.C., Oshima, R.J., Gallavan, R.E. 1983. Significance
of pollutant concentration distribution in the response of 'red
kidney' beans to ozone. J Am Soc Hortic Sci 108: 347-351.
Musselman, R.C., Lefohn, A.S., Massman ,W.J., Heath, R.L.
2006. A critical review and analysis of the use of exposure-
and flux-based ozone indices for predicting vegetation effects.
Atmos Environ 40(10): 1869-1888.
U.S. EPA. 2020. Integrated Science Assessment of Ozone
and Related Photochemical Oxidants. EPA/600/R-20/012. April.
Research Triangle Park, NC: Environmental Protection Agency.
