Appendix A
Body Region Hazard Analysis
INTRODUCTION
The purpose of this appendix is to summarize the BRHA (body region hazard analysis) model showing its rigorous basis and highlighting areas where additional articulation of the current model or model development might be useful. The discussion is intended to support not only the practical evaluation of protective suits but also the analysis of the efficacy of using MeS (methyl salicylate) as a simulant. This discussion relies heavily on the excellent presentations to the committee by Army personnel (Fedele, 1996; Fedele and Nelson, 1995).
CONCEPTS
The practical goal of the BRHA is to convert the information derived from a multidimensional experimental testing plan into a concise measure of the relative protection value provided by a given candidate protective ensemble. The basic idea is to convert measurements of exposures at 20 different body locations into a single measure that accounts or the variability of both chemical exposure and relative sensitivity at each body location.
The BRHA analysis provides two distinct modeling opportunities. The first, already in practice, is reducing the MIST data to a concise measure of the protective performance of the suit. The second is to examine the model derivation from first principles, thereby exposing key physical properties and approximations that enter into, and allow reduction of, the governing equations, in order to assess the efficacy
of using MeS as a simulant. The model could thus define experiments that should be conducted.
The essential mathematical starting point for the BRHA is the probability distribution for response to an exposure level. It is evidently well accepted that this is the normal function of the log of the exposure. Equation 1 summarizes this information in terms of s, the normal equivalent deviate, n, the natural log of the population response geometrical standard deviation, M, the exposure, and M_{50}, the exposure value at which half the population shows a physical reaction.
The BRHA applies this concept to each body region j. To do so, the terms of Equation 1 are rewritten as Mj, the exposure in region j, and M_{50j}, the specific exposure for each body region j that alone causes the mean response. Two additional concepts are A_{j}, the surface area of the body region j, and ε_{j}, the transport efficiency in region j. The parameter e_{j} accounts for the transport from skin deposits or absorbed agents to physiologically active sites or, in the parlance of Equation 1, M = Σε_{j}M_{j}.
Regional sensitivities have been measured, but an experimental determination of the transport efficiencies has not been made yet. The transport efficiency can be eliminated from the mathematical analysis by exploiting the behavior of the response probability distribution. Because at s = 0, half of the individuals will show a response, Equation 1 shows that this occurs when M = M_{50}. Therefore, e_{j} = M_{50}/M_{50j} when local body region exposures are used in Equation 1. This also allows Equation 1 to be rewritten as Equation 2, which accounts for the 20 different body locations:
The use of Equation 2 in the BRHA is facilitated by relating M_{j} to the vapor exposure. Far from saturation, exposure is the integral of the rate of delivery over time. This is shown in Equation 3, where C_{o} is the external vapor concentration, t is the time, v_{j} is the absorption velocity, and A_{j} is the surface area:
Equation 3 allows Equation 2 to be rewritten as:
An exposure index C_{o}T can therefore be calculated as the point where half of the individuals in a population will respond s = 0, which provides Equation 5 for the median response exposure:
The BRHA compares exposures under protected and unprotected (bare skin) circumstances. These exposures can be written as Equations 6 and 7, respectively:
Critical dosages taken from studies in the literature result in an effective amount of absorption M_{50j} when the exposure is to bare skin at various body regions. This is a useful standard and can be defined by substituting M_{50j} for M_{bj} and C_{E}T_{50j} for C_{O}T in Equation 7. This is shown in Equation 8:
Equation 8 and Equation 7 combined show that M_{bj}/M_{50j}= C_{o}T/C_{E}T_{50j}.
The BRHA seeks to account for M_{pj} by using the empirically determined relationships between M_{bj} and C_{E}T_{50j}. To do so, it is convenient to define the local body region protection factor, P_{fj}= M_{bj}/M_{pj}. This allows Equation (5) to be rewritten in terms of the experimentally determined protection factors
P_{fj}= M_{bj}/M_{pj} and their effects as summarized by C_{E}T_{50j}. The result is shown as Equation 9, which provides the mean challenge level for individuals using protective systems relative to dosages that influence individuals through unprotected bare skin:
In using Equation 9, the values of C_{E}T_{50j} are obtained from referenced toxicity studies involving human exposure to liquid VX (Sim, 1962). The application of these notions is slightly different for local and systemic analysis.
For local analyses, the P_{f} values for each location j are multiplied by the locationõs cutaneous mustard vapor toxicity value. The lowest vapor challenge level defines the effectiveness of the protective system. For systemic analyses, the critical whole body exposure C_{o}T_{50} is calculated from an area-weighted variant of Equation 9 with P_{fj}= 1 for all j, as shown in Equation 10:
The resulting C_{o}T_{50c} has a value of 2.45 using Sim's (1962) data for A_{j} percent and C_{E}T_{50j} represent the whole body exposure that, when uniformly applied to the 20 different locations on an unprotected person, results in the reaction.
The BRHA computes the actual challenge whole body exposure (or the whole body effective exposure discussed in the body of the report) by incorporating the location-specific, normalized exposures P_{fj} as in Equation 11:
The protective clothing is then rated with a protective actor PF as in Equation 12:
OPPORTUNITIES AND APPLICATIONS
BRHA calculations are executed in terms of a spreadsheet, which appears to be automated and systematic. Defending the logic of the BRHA model is more problematic. Perhaps the most basic question involves the normalization of exposures and the subsequent normalization of overall effects. Why is the starting point, although intuitively quite reasonable, rigorously correct? What is the physiological or transport basis for it? What are the essential approximations? Another question is the transformation of Equation 1 to Equation 2. It would be useful to articulate the rigorous logic on which these exposure ''mixing rules'' are based. Why normalize on a "spot-by-spot" basis before calculating the overall effect, for example? Why not use the actual exposures for each spot and then normalize? The weighting of
the P_{fj} in Equation 11 is intuitively reasonable, but is it rigorously correct? Again, further articulation of the model derivation would be helpful.
Thus, the conceptual approximations, assumptions, and related limitations of the model would emerge from a more systematic derivation, complete with sample calculations. But another, more global benefit would also result. Systematic development would reveal the dependence of the model parameters on the physical properties (e.g., diffusivities, adsorption and absorption constants, viscosity, vapor pressures) of the system. This would, in turn, provide a more quantitative basis for assessing the efficacy of MeS as a chemical agent simulant.
NOMENCLATURE
A_{j} |
surface area of body region j |
b |
bare skin |
C_{o} |
external vapor concentration |
C_{E}T_{50} |
critical dosage that results in an effective amount of absorption (M_{50j}) |
C_{0}T |
exposure index |
(C_{0}T_{50})_{c} |
critical whole body exposure for systemic analysis |
M |
exposure |
M_{j} |
exposure in region j |
M_{50j} |
specific exposure for each body region j that alone causes the mean response |
M_{50} |
the exposure value at which half the population shows a physical reaction |
n |
the natural log of the population response geometric mean standard deviation |
p |
protected skin |
P_{fj} |
the local body region protection factor |
PF |
rating factor for protective clothing |
s |
the normal equivalent deviate |
t |
time |
v_{j} |
absorption velocity |
REFERENCES
Fedele, P. 1996. Presentation of MIST/BRHA to the Committee on Program and Technical Review of the U.S. Army Chemical and Biological Defense Command. Aberdeen Proving Ground, Md., December 1996.
Fedele P.D., and D. Nelson. 1995. A report on the Method of Assessing Full Individual Protective System Performance Against Cutaneous Effects of Aerosol and Vapor Exposures. Aberdeen, Md.: Edgewood Research, Development and Engineering Center.
Sim, V.M. 1962. Variability of Different Intact Human Skin Sites to the Penetration of VX. Technical Report 3122. Army Chemical Center, Md: U.S. Army Chemical Research and Development Laboratories.