User-oriented independent analysis of the toxic load model's ability to predict the effects of time-varying toxic inhalation exposures

Highlights

• The toxic load model has difficulty modeling steady exposures under 10 min.

• The toxic load model has difficulty modeling time-varying inhalation exposures.

• Some model variants predict the effects of time-varying exposures better than others.

• Data utilization is maximized by directly comparing predictions to observations.

Abstract

Toxic industrial chemicals and chemical warfare agents present an acute inhalation hazard to exposed populations. The hazardous materials consequence assessment modeling community requires toxicity models to estimate these hazards. One popular phenomenological toxicity model is the toxic load model. Although this model is only well-defined for constant-concentration exposures, several generalizations have been proposed for the case of time-varying exposures. None of them, however, were validated by experimental evidence at the time they were proposed. Accordingly, the Defense Threat Reduction Agency (DTRA) sponsored experiments to explore the effects of time-varying inhalation exposures of hydrogen cyanide (HCN) and carbon monoxide (CO) gas on rats. The experiments were designed and executed by the U.S. Army's Edgewood Chemical and Biological Center (ECBC) and the Naval Medical Research Unit Dayton (NAMRU-D) between 2012 and 2015.

We conducted an independent analysis of the toxic load model's ability to predict the ECBC/NAMRU-D experimental data using an analytical methodology oriented toward hazard prediction model users. We found that although some of the proposed extensions of the toxic load model perform better than others, all of them have difficulty reproducing the experimental data. The toxic load model also has difficulty reproducing even the constant-concentration data for HCN exposures under 10 min.

Introduction

The toxic load model, a phenomenological exposure-response model of the effects of toxic inhalation exposures, has been adopted by military and civilian hazard prediction modelers to estimate the human health impact of accidental releases of toxic industrial chemicals or intentional chemical weapon attacks (Bliss, 1940; Finney, 1947; ten Berge et al., 1986; Sommerville et al., 2006; Rusch, 2006; Hawkins et al., 2016; Lees, 2004; Sommerville et al., 2009; U.S. Army Chemical School, 2005). These chemical exposures may occur over timescales of minutes to tens of minutes or longer. The toxic load model was designed to improve upon Haber's Law, in which toxic effects depend only on the dosage, i.e., the time-integrated airborne chemical vapor concentration (usually presumed to be proportional to the total inhaled dose) (Witschi, 1999; Haber, 1924; Flury, 1921). The toxic load model attempts to account for time-dependent biological response indirectly by replacing the dosage as the measure of exposure with a quantity called the toxic load (Eq. (1)) (Ostwald and Dernoscheck, 1910; Bliss, 1940; Finney, 1947, ten Berge et al., 1986; Sommerville et al., 2006).

TL = Cⁿ × T

In Eq. (1), C is the airborne chemical vapor concentration during the exposure, T is the exposure duration, and n is a phenomenological constant called the toxic load exponent. The toxic load is assumed to have a one-to-one correspondence with a specified level of toxicological effect, K. If no effects are observed below a concentration threshold C₀, the concentration C in Eq. (1) must be replaced with (C − C₀).

Many authors assume that the relationship between the logarithm of the toxic load and the population response follows a sigmoidal relationship that can be described by a probit equation, in analogy to the usual log(dosage)–probit equation. The general form of this equation in probit space is given by the equivalent Eqs. (2), (3), (4)) (Finney, 1947; Griffiths and Megson, 1984; ten Berge et al., 1986; Hilderman et al., 1999; Sommerville et al., 2006).

Y_N = Y_P – 5 = b₀ + b₁ log₁₀(C) + b₂ log₁₀(T)

Y_N = Y_P – 5 = –m log₁₀(TL₅₀) + m log₁₀(CⁿT)

P = Φ(m log₁₀(TL/TL₅₀))

Here P is the fraction of the exposed population responding for a given toxic endpoint, Y_N is P measured on a normit scale, Y_P is P measured on a probit scale, Φ is the cumulative distribution function of the normal distribution, TL₅₀ = 10ˆ(-b₀/m) is the median effective toxic load for the given toxic endpoint, m = b₂ is the probit slope for the toxic load, and n = k₁/k₂ is the toxic load exponent in Eq. (1). Note that the normit and probit scales differ by 5 units. Eq. (3) is the probit-scale version of Eq. (4).

Eqs. (2), (3), (4)) show that the toxic load model has three independent parameters for a given chemical, population, route of exposure, and toxic endpoint. We use the three parameters TL₅₀, m, and n in Eq. (4). When n > 1, a short, high-intensity exposure is more toxic than a long, low-intensity exposure with the same dosage; when n < 1, the reverse is true. When n = 1, the toxic load model reduces to Haber's Law. We note that the choice of the base of the logarithms in Eqs. (2), (3), (4)) is arbitrary, but it affects the values of the toxicity parameters. We use base 10. We further note that the choice of a log–probit relationship is arbitrary, although common. The equations Cⁿ × T = constant effect, or C^α × T^β = constant effect, are alternative forms of the toxic load relationship that do not make any assumptions about the distribution of population susceptibility, as is inherent in the probit relationship. We exclusively used Eqs. (1), (2), (3), (4)) in our analysis.

The toxic load model has been shown to fit exposure-response data better than Haber's Law for certain chemicals (ten Berge et al., 1986). Most of the previous experimental work parameterizing and validating the toxic load model, however, was performed using only steady exposures of constant concentration. This type of exposure is not representative of real-world atmospheric dispersion events, in which atmospheric turbulence can lead to highly fluctuating and intermittent chemical vapor concentrations due to in-plume turbulence and turbulent plume meander, respectively (Wilson, 1995). The toxic load model must be extended in order to account for time-varying exposures, and none of the proposed extensions had been validated at the time they were proposed. This led the Defense Threat Reduction Agency (DTRA), an element of the U.S. Department of Defense, to fund a series of toxicological experiments that were designed and managed by the U.S. Army's Edgewood Chemical and Biological Center (ECBC) and executed by the Naval Medical Research Unit Dayton (NAMRU-D) (Sweeney et al., 2013, 2014, 2015, 2016). The three-year experimental campaign subjected rats to one- and two-pulse (i.e., time-varying) exposures of hydrogen cyanide (HCN) or carbon monoxide (CO) using a nose-only inhalation apparatus.

The objective of the work we report here is to independently analyze the ECBC/NAMRU-D data to assess the potential utility of the toxic load model – and its proposed extensions – to the hazard prediction modeling community. Our analysis methodology, which focuses on applying and assessing the toxic load model within a user-oriented context, differs somewhat from that of the authors of the ECBC/NAMRU-D experiments. We attempted to emulate aspects of how hazard prediction modelers perform toxic load modeling in practice. These modelers typically estimate the number of human casualties from time series of atmospheric concentrations at different locations derived from atmospheric dispersion modeling or from chemical sensor measurements. To do so, they apply a chosen extension of the toxic load model to the concentration time series data. They typically parameterize the toxic load model using data from the toxicological literature, which, as far as we aware, always have been derived from laboratory experiments that use constant-concentration exposures (other than the set of experiments we discuss in this paper). See, for example, the review of toxic load modeling by Sommerville et al. (2006). The modelers generally assume that only one set of toxic load model parameters (TL₅₀, m, and n) applies across the entire range of acute exposure durations and intensities for each chemical (Lees, 2004; U.S. Army Chemical School, 2005; Griffiths, 1991; Franks et al., 1996).

Our methodology follows a similar procedure to that described above to predict lethality for each trial in the Sweeney et al. experiments. We generated predictions for each of five proposed extensions of the toxic load model to the case of time-varying chemical vapor concentrations. We applied statistical measures of scatter and bias to determine the degree of agreement between toxic load model predictions and observations, and performed statistical tests to determine whether any disagreement between predictions and observations is within the range that is expected from small sample size errors (i.e., variability due to small numbers of rats per exposure in the laboratory experiments). We note that our analysis methodology is not designed to explain differences between model predictions and experimental observations; it merely quantifies those differences so that model users can determine how much confidence they should have in their modeling protocols.