Mathematical exposure modeling

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Mathematical exposure modeling is an indirect method of determining exposure, particularly for human exposure to environmental contaminants. It is useful when direct measurement of pollutant concentration is not feasible because direct measurement sometimes requires skilled professionals and complex, expensive laboratory equipment. The ability to make inferences in the absence of direct measurements, makes exposure modeling a powerful tool for predicting exposures by exploring hypothetical situations. It allows researchers to ask "what if" questions about exposure scenarios.

Exposure assessment is a branch of environmental science and occupational hygiene that focuses on the processes that take place at the interface between the environment containing the contaminant(s) of interest and the organism(s) being considered. These are the final steps in the path to release an environmental contaminant, through transport to its effect in a biological system. It tries to measure how much of a contaminant can be absorbed by an exposed target organism, in what form, at what rate and how much of the absorbed amount is actually available to produce a biological effect. Although the same general concepts apply to other organisms, the overwhelming majority of applications of exposure assessment are concerned with human health, making it an important tool in public health.

Pollution introduction of contaminants into the natural environment that cause adverse change

Pollution is the introduction of contaminants into the natural environment that cause adverse change. Pollution can take the form of chemical substances or energy, such as noise, heat or light. Pollutants, the components of pollution, can be either foreign substances/energies or naturally occurring contaminants. Pollution is often classed as point source or nonpoint source pollution. In 2015, pollution killed 9 million people in the world.

Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system can be divided and allocated to different sources of uncertainty in its inputs. A related practice is uncertainty analysis, which has a greater focus on uncertainty quantification and propagation of uncertainty; ideally, uncertainty and sensitivity analysis should be run in tandem.

Modeling indoor air

Mathematical modeling is commonly used to determine human exposure to indoor air pollution. Studies have shown that humans spend about 90% of their time indoors, and contaminant levels may be as high or higher inside than outside, due to the presence of multiple indoor contaminant sources, in combination with poor ventilation. Indoor air modeling requires information on a number of parameters including the air exchange rate, deposition rate, source emission rate, and physical volume of the indoor setting. Indoor environments can basically be thought of as closed systems, so models describing them are usually based on the "mass balance" equation. It is also assumed that a pollutant emitted into an indoor environment instantly spreads uniformly throughout the system, so that the concentration is the same at any point in space at any point in time. Mathematically, the total pollutant mass emitted inside a chamber during time T can be expressed as

A mass balance, also called a material balance, is an application of conservation of mass to the analysis of physical systems. By accounting for material entering and leaving a system, mass flows can be identified which might have been unknown, or difficult to measure without this technique. The exact conservation law used in the analysis of the system depends on the context of the problem, but all revolve around mass conservation, i.e., that matter cannot disappear or be created spontaneously.

Gsource(T) =
where
Gsource(T) = total mass contributed by the source over time T (e.g., mg)
g(t) = emission flow rate as a function of time t (e.g., mg/min)

The total mass lost during time T can be expressed as

Qlost(T) =
where
Qlost(T) = total mass lost from the chamber over time T (e.g., mg)
x(t) = concentration of pollutant in the air exiting the chamber (e.g., mg/m3)
w = flow rate of air exiting the chamber (e.g., m3/min)

Following the principle of the "mass balance" equation, the total mass in the chamber at time T, is the difference between the two equations above, mass generated during time T minus mass lost during time T. This value may also be calculated from the equation

Total mass inside the chamber at time T = vx(T)

Modeling human exposure to air pollution

There are two critical pieces of information that are needed to calculate human exposure. These include data on 1) the whereabouts of the individual or individuals being exposed and 2) the concentration of the pollutants in the different locations. This can be expressed mathematically as the sum of the products of time spent by a person in those different locations by the time-averaged air pollutant concentrations occurring in those locations.

Air pollutant concentrations

Air pollutant concentrations, as measured or as calculated by air pollution dispersion modeling, must often be converted or corrected to be expressed as required by the regulations issued by various governmental agencies. Regulations that define and limit the concentration of pollutants in the ambient air or in gaseous emissions to the ambient air are issued by various national and state environmental protection and occupational health and safety agencies.

Ep = CpiTpi
where
Tpi is the time spent by person p in microenvironment i, and Cpi is the concentration of the air pollutant that person p experiences in microenvironment i, Ep is the integrated exposure for person p and m is the number of different microenvironments.

As mentioned above, knowing the whereabouts of the individual or individuals, is very important when trying to determine air pollution exposure. In the absence of data obtained from direct observation, human activity pattern data may be used. This data can be found in several reports conducted by the U.S. Environmental Protection Agency. The data was collected through the National Human Activity Pattern Survey (NHAPS), and contains a representative cross-section of 24-hour daily activity patterns. This data can be used to create inhalation exposure models which can serve as useful public health tools for epidemiology, education, intervention, risk assessment, and creation of air quality guidelines.

United States Environmental Protection Agency Agency of the U.S. Federal Government

The Environmental Protection Agency (EPA) is an independent agency of the United States federal government for environmental protection. President Richard Nixon proposed the establishment of EPA on July 9, 1970 and it began operation on December 2, 1970, after Nixon signed an executive order. The order establishing the EPA was ratified by committee hearings in the House and Senate. The agency is led by its Administrator, who is appointed by the President and approved by Congress. The current Administrator is former Deputy Administrator Andrew R. Wheeler, who had been acting administrator since July 2018. The EPA is not a Cabinet department, but the Administrator is normally given cabinet rank.

Epidemiology is the study and analysis of the distribution and determinants of health and disease conditions in defined populations.

Broadly speaking, a risk assessment is the combined effort of 1. identifying and analyzing potential (future) events that may negatively impact individuals, assets, and/or the environment ; and 2. making judgments "on the tolerability of the risk on the basis of a risk analysis" while considering influencing factors. Put in simpler terms, a risk assessment analyzes what can go wrong, how likely it is to happen, what the potential consequences are, and how tolerable the identified risk is. As part of this process, the resulting determination of risk may be expressed in a quantitative or qualitative fashion. The risk assessment is an inherent part of an overall risk management strategy, which attempts to, after a risk assessment, "introduce control measures to eliminate or reduce" any potential risk-related consequences.

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References

Ott, W.R., Steinemann, A.C., Wallace, L.A.. Exposure Analysis. CRC Press (2007)

The Inside Story: A Guide to Indoor Air Quality. U.S. EPA (2009)

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