Bayesian modeling of exposure and airflow using two-zone models

A generic approach to estimate airborne concentrations of substances released by indoor spray processes using a deterministic 2-box model

Sprays are used both in workplace and consumer settings. Although spraying has advantages, such as uniform distribution of substances on surfaces in a highly efficient manner, it is often associated with a high inhalation burden. For an adequate risk assessment, this exposure has to be reliably quantified. Exposure models of varying complexity are available, which are applicable to spray applications. However, a need for improvement has been identified. In this contribution, a simple 2-box approach is suggested for the assessment of the time-weighted averaged exposure concentration (TWA) using a minimum of input data. At the moment, the model is restricted to binary spray liquids composed of a non-volatile fraction and volatile solvents. The model output can be refined by introducing correction factors based on the classification and categorization of two key parameters, the droplet size class and the vapor pressure class of the solvent, or by using a data set of experimentally determined airborne release fractions related to the used spray equipment. A comparison of model results with measured data collected at real workplaces showed that this simple model based on readily available input parameters is very useful for screening purposes. The generic 2-box spray model without refinement overestimates the measurements of the considered scenarios in approximately 50% of the cases by more than a factor of 100. The generic 2-box model performs better for room spraying than for surface spraying, as the airborne fraction in the latter case is clearly overestimated. This conservatism of the prediction was significantly reduced when correction factors or experimentally determined airborne release fractions were used in addition to the generic input parameters. The resulting predictions still overestimate the exposure (ratio tool estimate to measured TWA > 10) or they are accurate (ratio 0.5-10). If the available information on boundary conditions (application type, equipment) does not justify the usage of airborne release fraction, room spraying should be used resulting in the highest exposure estimate. The model scope may be extended to (semi)volatile substances. However, acceptance may be compromised by the limited availability of measured data for this group of substances and thus may have limited potency to evaluate the model prediction.

New dose-response model and SARS-CoV-2 quanta emission rates for calculating the long-range airborne infection risk

Predictive models for airborne infection risk have been extensively used during the pandemic, but there is yet still no consensus on a common approach, which may create misinterpretation of results among public health experts and engineers designing building ventilation. In this study we applied the latest data on viral load, aerosol droplet sizes and removal mechanisms to improve the Wells Riley model by introducing the following novelties i) a new model to calculate the total volume of respiratory fluid exhaled per unit time ii) developing a novel viral dose-based generation rate model for dehydrated droplets after expiration iii) deriving a novel quanta-RNA relationship for various strains of SARS-CoV-2 iv) proposing a method to account for the incomplete mixing conditions. These new approaches considerably changed previous estimates and allowed to determine more accurate average quanta emission rates including omicron variant. These quanta values for the original strain of 0.13 and 3.8 quanta/h for breathing and speaking and the virus variant multipliers may be used for simple hand calculations of probability of infection or with developed model operating with six size ranges of aerosol droplets to calculate the effect of ventilation and other removal mechanisms. The model developed is made available as an open-source tool.

A New Model Algorithm for Estimating the Inhalation Exposure Resulting from the Spraying of (Semi)-Volatile Binary Liquid Mixtures (SprayEva)

The spraying of liquid multicomponent mixtures is common in many professional and industrial settings. Typical examples are cleaning agents, additives, coatings, and biocidal products. In all of these examples, hazardous substances can be released in the form of aerosols or vapours. For occupational and consumer risk assessment in regulatory contexts, it is therefore important to know the exposure which results from the amount of chemicals in the surrounding air. In this research, a mechanistic mass balance model has been developed that covers the spraying of (semi)-volatile substances, taking into account combined exposure to spray mist, evaporation from droplets, and evaporation from surfaces as well as the nonideal behaviour of components in liquids and backpressure effects. For wall-spraying scenarios, an impaction module has been developed that quantifies the amount of overspray and the amount of material that lands on the wall. Mechanistically, the model is based on the assumption that continuous spraying can be approximated by a number of sequentially released spray pulses, each characterized by a certain droplet size, where the total aerosol exposure is obtained by summation over all release pulses. The corresponding system of differential equations is solved numerically using an extended Euler algorithm that is based on a discretisation of time and space. Since workers typically apply the product continuously, the treated area and the corresponding evaporating surface area grows over time. Time-dependent concentration gradients within the sprayed liquid films that may result from different volatilities of the components are therefore addressed by the proposed model. A worked example is presented to illustrate the calculated exposure for a scenario where aqueous solutions of H2O2 are sprayed onto surfaces as a biocidal product. The results reveal that exposure to H2O2 aerosol reaches relevant concentrations only during the spraying phase. Evaporation from sprayed surfaces takes place over much longer time periods, where backpressure effects caused by large emission sources can influence the shape of the concentration time curves significantly. The influence of the activity coefficients is not so pronounced. To test the plausibility of the developed model algorithm, a comparison of model estimates of SprayExpo, SprayEva, and ConsExpo with measured data is performed. Although the comparison is based on a limited number (N = 19) of measurement data, the results are nevertheless regarded as supportive and acceptable for the plausibility and predictive power of SprayEva.

COVID-19 Exposure Assessment Tool (CEAT): Exposure quantification based on ventilation, infection prevalence, group characteristics, and behavior

The coronavirus disease 2019 (COVID-19) Exposure Assessment Tool (CEAT) allows users to compare respiratory relative risk to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) for various scenarios, providing understanding of how combinations of protective measures affect risk. CEAT incorporates mechanistic, stochastic, and epidemiological factors including the (i) emission rate of virus, (ii) viral aerosol degradation and removal, (iii) duration of activity/exposure, (iv) inhalation rates, (v) ventilation rates (indoors/outdoors), (vi) volume of indoor space, (vii) filtration, (viii) mask use and effectiveness, (ix) distance between people (taking into account both near-field and far-field effects of proximity), (x) group size, (xi) current infection rates by variant, (xii) prevalence of infection and immunity in the community, (xiii) vaccination rates, and (xiv) implementation of COVID-19 testing procedures. CEAT applied to published studies of COVID-19 transmission events demonstrates the model's accuracy. We also show how health and safety professionals at NASA Ames Research Center used CEAT to manage potential risks posed by SARS-CoV-2 exposures.

Exposure Prioritization (Ex Priori): A Screening-Level High-Throughput Chemical Prioritization Tool

To estimate potential chemical risk, tools are needed to prioritize potential exposures for chemicals with minimal data. Consumer product exposures are a key pathway, and variability in consumer use patterns is an important factor. We designed Ex Priori, a flexible dashboard-type screening-level exposure model, to rapidly visualize exposure rankings from consumer product use. Ex Priori is Excel-based. Currently, it is parameterized for seven routes of exposure for 1108 chemicals present in 228 consumer product types. It includes toxicokinetics considerations to estimate body burden. It includes a simple framework for rapid modeling of broad changes in consumer use patterns by product category. Ex Priori rapidly models changes in consumer user patterns during the COVID-19 pandemic and instantly shows resulting changes in chemical exposure rankings by body burden. Sensitivity analysis indicates that the model is sensitive to the air emissions rate of chemicals from products. Ex Priori's simple dashboard facilitates dynamic exploration of the effects of varying consumer product use patterns on prioritization of chemicals based on potential exposures. Ex Priori can be a useful modeling and visualization tool to both novice and experienced exposure modelers and complement more computationally intensive population-based exposure models.

Local Scale Exposure and Fate of Engineered Nanomaterials

Nanotechnology is a growing megatrend in industrial production and innovations. Many applications utilize engineered nanomaterials (ENMs) that are potentially released into the atmospheric environment, e.g., via direct stack emissions from production facilities. Limited information exists on adverse effects such ENM releases may have on human health and the environment. Previous exposure modeling approaches have focused on large regional compartments, into which the released ENMs are evenly mixed. However, due to the localization of the ENM release and removal processes, potentially higher airborne concentrations and deposition fluxes are obtained around the production facilities. Therefore, we compare the ENM concentrations from a dispersion model to those from the uniformly mixed compartment approach. For realistic release scenarios, we based the modeling on the case study measurement data from two TiO2 nanomaterial handling facilities. In addition, we calculated the distances, at which 50% of the ENMs are deposited, serving as a physically relevant metric to separate the local scale from the regional scale, thus indicating the size of the high exposure and risk region near the facility. As a result, we suggest a local scale compartment to be implemented in the multicompartment nanomaterial exposure models. We also present a computational tool for local exposure assessment that could be included to regulatory guidance and existing risk governance networks.

Covid-19 Exposure Assessment Tool (CEAT): Easy-to-use tool to quantify exposure based on airflow, group behavior, and infection prevalence in the community

The COVID-19 Exposure Assessment Tool (CEAT) allows users to compare respiratory relative risk to SARS-CoV-2 for various scenarios, providing understanding of how combinations of protective measures affect exposure, dose, and risk. CEAT incorporates mechanistic, stochastic and epidemiological factors including the: 1) emission rate of virus, 2) viral aerosol degradation and removal, 3) duration of activity/exposure, 4) inhalation rates, 5) ventilation rates (indoors/outdoors), 6) volume of indoor space, 7) filtration, 8) mask use and effectiveness, 9) distance between people, 10) group size, 11) current infection rates by variant, 12) prevalence of infection and immunity in the community, 13) vaccination rates of the community, and 14) implementation of COVID-19 testing procedures. Demonstration of CEAT, from published studies of COVID-19 transmission events, shows the model accurately predicts transmission. We also show how health and safety professionals at NASA Ames Research Center used CEAT to manage potential risks posed by SARS-CoV-2 exposures. Given its accuracy and flexibility, the wide use of CEAT will have a long lasting beneficial impact in managing both the current COVID-19 pandemic as well as a variety of other scenarios.

Estimating Inhalation Exposure Resulting from Evaporation of Volatile Multicomponent Mixtures Using Different Modelling Approaches

In many professional and industrial settings, liquid multicomponent mixtures are used as solvents, additives, coatings, biocidal products, etc. Since, in all of these examples, hazardous liquids can evaporate in the form of vapours, for risk assessments it is important to know the amount of chemicals in the surrounding air. Although several models are available in legal contexts, the current implementations seem to be unable to correctly simulate concentration changes that actually occur in volatile mixtures and in particular in thin films. In this research, the estimation of evaporation rates is based on models that take into account non-ideal behaviour of components in liquids and backpressure effects as well. The corresponding system of differential equations is solved numerically using an extended Euler algorithm that is based on a discretisation of time and space. Regarding air dispersion of volatile components, the model builds upon one-box and two-box mass balance models, because there is some evidence that these models, when selected and applied appropriately, can predict occupational exposures with sufficient precision. That way, numerical solutions for a wide variety of exposure scenarios with instantaneous and continuous/intermittent application, even considering “moving worker situations”, can be obtained. A number of example calculations have been carried out on scenarios where binary aqueous solutions of hydrogen peroxide or glutaraldehyde are applied as a biocidal product to surfaces by wiping. The results reveal that backpressure effects caused by large emission sources as well as deviations from liquid-phase ideality can influence the shape of the concentration time curves significantly. The results also provide some evidence that near-/far-field models should be used to avoid underestimation of exposure in large rooms when small/medium areas are applied. However, the near-field/far-field model should not be used to estimate peak exposure assuming instantaneous application, because then the models tend to overestimate peak exposure significantly. Although the example calculations are restricted to aqueous binary mixtures, the proposed approach is general and can be used for arbitrary liquid multicomponent mixtures, as long as backpressure effects and liquid-phase non-idealities are addressed adequately.

Particle Resuspension Dynamics in the Infant Near-Floor Microenvironment

Carpet dust contains microbial and chemical material that can impact early childhood health. Infants may be exposed to greater quantities of resuspended dust, given their close proximity to floor surfaces. Chamber experiments with a robotic infant were integrated with a material balance model to provide new fundamental insights into the size-dependency of infant crawling-induced particle resuspension and exposure. The robotic infant was exposed to resuspended particle concentrations from 10⁵ to 10⁶ m^-3 in the near-floor (NF) microzone during crawling, with concentrations generally decreasing following vacuum cleaning of the carpets. A pronounced vertical variation in particle concentrations was observed between the NF microzone and bulk air. Resuspension fractions for crawling are similar to those for adult walking, with values ranging from 10^-6 to 10^-1 and increasing with particle size. Meaningful amounts of dust are resuspended during crawling, with emission rates of 0.1 to 2 × 10⁴ μg h^-1. Size-resolved inhalation intake fractions ranged from 5 to 8 × 10³ inhaled particles per million resuspended particles, demonstrating that a significant fraction of resuspended particles can be inhaled. A new exposure metric, the dust-to-breathing zone transport efficiency, was introduced to characterize the overall probability of a settled particle being resuspended and delivered to the respiratory airways. Values ranged from less than 0.1 to over 200 inhaled particles per million settled particles, increased with particle size, and varied by over 2 orders of magnitude among 12 carpet types.

Management of Occupational Risk Prevention of Nanomaterials Manufactured in Construction Sites in the EU

Currently, nanotechnology plays a key role for technological innovation, including the construction sector. An exponential increase is expected in its application, although this has been hampered by the current degree of uncertainty regarding the potential effects of nanomaterials on both human health and the environment. The accidents, illnesses, and disease related to the use of nanoproducts in the construction sector are difficult to identify. For this purpose, this work analyzes in depth the products included in recognized inventories and the safety data sheets of these construction products. Based on this analysis, a review of the recommendations on the use of manufactured nanomaterials at construction sites is performed. Finally, a protocol is proposed with the aim of it serving as a tool for technicians in decision-making management at construction sites related to the use of manufactured nanomaterials. This proposed protocol should be an adaptive and flexible tool while the manufactured nanomaterials-based work continues to be considered as an "emerging risk," despite the expectation that the protocol will be useful for the development of new laws and recommendations for occupational risk prevention management.

Bayesian State Space Modeling of Physical Processes in Industrial Hygiene

Exposure assessment models are deterministic models derived from physical-chemical laws. In real workplace settings, chemical concentration measurements can be noisy and indirectly measured. In addition, inference on important parameters such as generation and ventilation rates are usually of interest since they are difficult to obtain. In this article, we outline a flexible Bayesian framework for parameter inference and exposure prediction. In particular, we devise Bayesian state space models by discretizing the differential equation models and incorporating information from observed measurements and expert prior knowledge. At each time point, a new measurement is available that contains some noise, so using the physical model and the available measurements, we try to obtain a more accurate state estimate, which can be called filtering. We consider Monte Carlo sampling methods for parameter estimation and inference under nonlinear and non-Gaussian assumptions. The performance of the different methods is studied on computer-simulated and controlled laboratory-generated data. We consider some commonly used exposure models representing different physical hypotheses. Supplementary materials for this article are available online.

Modeling of High Nanoparticle Exposure in an Indoor Industrial Scenario with a One-Box Model

Mass balance models have proved to be effective tools for exposure prediction in occupational settings. However, they are still not extensively tested in real-world scenarios, or for particle number concentrations. An industrial scenario characterized by high emissions of unintentionally-generated nanoparticles (NP) was selected to assess the performance of a one-box model. Worker exposure to NPs due to thermal spraying was monitored, and two methods were used to calculate emission rates: the convolution theorem, and the cyclic steady state equation. Monitored concentrations ranged between 4.2 × 104-2.5 × 105 cm-3. Estimated emission rates were comparable with both methods: 1.4 × 1011-1.2 × 1013 min-1 (convolution) and 1.3 × 1012-1.4 × 1013 min-1 (cyclic steady state). Modeled concentrations were 1.4-6 × 104 cm-3 (convolution) and 1.7-7.1 × 104 cm-3 (cyclic steady state). Results indicated a clear underestimation of measured particle concentrations, with ratios modeled/measured between 0.2-0.7. While both model parametrizations provided similar results on average, using convolution emission rates improved performance on a case-by-case basis. Thus, using cyclic steady state emission rates would be advisable for preliminary risk assessment, while for more precise results, the convolution theorem would be a better option. Results show that one-box models may be useful tools for preliminary risk assessment in occupational settings when room air is well mixed.

The general ventilation multipliers calculated by using a standard Near-Field/Far-Field model

In conceptual exposure models, the transmission of pollutants in an imperfectly mixed room is usually described with general ventilation multipliers. This is the approach used in the Advanced REACH Tool (ART) and Stoffenmanager® exposure assessment tools. The multipliers used in these tools were reported by Cherrie (1999; http://dx.doi.org/10.1080/104732299302530 ) and Cherrie et al. (2011; http://dx.doi.org/10.1093/annhyg/mer092 ) who developed them by positing input values for a standard Near-Field/Far-Field (NF/FF) model and then calculating concentration ratios between NF and FF concentrations. This study revisited the calculations that produce the multipliers used in ART and Stoffenmanager and found that the recalculated general ventilation multipliers were up to 2.8 times (280%) higher than the values reported by Cherrie (1999) and the recalculated NF and FF multipliers for 1-hr exposure were up to 1.2 times (17%) smaller and for 8-hr exposure up to 1.7 times (41%) smaller than the values reported by Cherrie et al. (2011). Considering that Stoffenmanager and the ART are classified as higher-tier regulatory exposure assessment tools, the errors is general ventilation multipliers should not be ignored. We recommend revising the general ventilation multipliers. A better solution is to integrate the NF/FF model to Stoffenmanager and the ART.

Probabilistic risk assessment of emerging materials: case study of titanium dioxide nanoparticles

The development and use of emerging technologies such as nanomaterials can provide both benefits and risks to society. Emerging materials may promise to bring many technological advantages but may not be well characterized in terms of their production volumes, magnitude of emissions, behaviour in the environment and effects on living organisms. This uncertainty can present challenges to scientists developing these materials and persons responsible for defining and measuring their adverse impacts. Human health risk assessment is a method of identifying the intrinsic hazard of and quantifying the dose-response relationship and exposure to a chemical, to finally determine the estimation of risk. Commonly applied deterministic approaches may not sufficiently estimate and communicate the likelihood of risks from emerging technologies whose uncertainty is large. Probabilistic approaches allow for parameters in the risk assessment process to be defined by distributions instead of single deterministic values whose uncertainty could undermine the value of the assessment. A probabilistic approach was applied to the dose-response and exposure assessment of a case study involving the production of nanoparticles of titanium dioxide in seven different exposure scenarios. Only one exposure scenario showed a statistically significant level of risk. In the latter case, this involved dumping high volumes of nano-TiO₂ powders into an open vessel with no personal protection equipment. The probabilistic approach not only provided the likelihood of but also the major contributing factors to the estimated risk (e.g. emission potential).

Bayesian Modeling for Physical Processes in Industrial Hygiene Using Misaligned Workplace Data

In industrial hygiene, a worker's exposure to chemical, physical, and biological agents is increasingly being modeled using deterministic physical models that study exposures near and farther away from a contaminant source. However, predicting exposure in the workplace is challenging and simply regressing on a physical model may prove ineffective due to biases and extraneous variability. A further complication is that data from the workplace are usually misaligned. This means that not all timepoints measure concentrations near and far from the source. We recognize these challenges and outline a flexible Bayesian hierarchical framework to synthesize the physical model with the field data. We reckon that the physical model, by itself, is inadequate for enhanced inferential and predictive performance and deploy (multivariate) Gaussian processes to capture uncertainties and associations. We propose rich covariance structures for multiple outcomes using latent stochastic processes. This article has supplementary material available online.

Modelling occupational inhalation exposure to concentration peaks of chemicals and associated health risk assessment

OBJECTIVES

The aims of this study were to estimate inhalation exposure to chemicals and the resulting acute health risks for working scenarios characterized by successive peaks of pollutant concentrations.

METHODS

A stochastic two-zone model combining a time-varying emission function and field-derived probabilistic distributed input parameter was used to predict both instantaneous and 15-min averaged pollutant concentrations during the decanting operations performed in a pathology laboratory. The location of the workers was taken into account in the model for computing probability distributions of inhalation exposures and for subsequently characterizing hazard quotients (HQ) for health risk purposes. The model was assessed by comparison with repeated individual monitoring performed on the workers during the same tasks.

RESULTS

Modelled inhalation exposure profiles revealed 15-min average concentrations of 1.7 and 208 mg m(-) (3) for formaldehyde (FA) and toluene (TOL), respectively. The individual monitoring performed showed similar average concentrations, with 1.2 and 175 mg m(-) (3) for FA and TOL. No more than three to five successive FA concentration peaks were generally sufficient in the modelling exercise to provide 15-min estimated exposures exceeding short-term exposure limits (STEL). Modelled HQ higher than unity and STEL exceedance probabilities higher than 0.5 were found for FA, whereas estimated TOL health risks were notably lower according to high exposure limits. Estimated inhalation exposure distributions frequently ranged over one order of magnitude for the two pollutants, reflecting both the natural exposure variability and the uncertainty of some of the two-zone model input parameters.

CONCLUSIONS

These findings indicate that the developed approach may be useful for modelling occupational exposures and acute health risks related to chemicals in situations involving time-varying emission sources. Modelled exposure distributions may also be used within Bayesian decision analysis frameworks for making exposure judgements and refining risk management measures.

Modelling the time profiles of organic solvent concentrations for occupational exposure assessment purposes

OBJECTIVES

Confronted by variable exposure scenarios characterized by intermittent concentration peaks, our study aimed to develop methods and determine mathematical functions reproducing organic solvent concentration profiles in order to assess health risks.

METHODS

Two similar repetitive decanting tasks using either formalin or toluene (TOL) were studied at a teaching hospital pathology laboratory. Real-time air monitoring performed in the immediate vicinity of pollutant sources over a 1-year period identified intermittent concentration peaks. In order to describe these specific exposure profiles, two different methods were used. In a first descriptive approach, concentration peaks were either assimilated to an equivalent series of rectangle functions or described by a mathematical bell-shaped function. As an alternative approach, a model based on the schedule of decanting tasks was constructed. To this end, a time-varying emission function was incorporated into three deterministic exposure models of increasing complexity (well-mixed room, two-zone, spherical turbulent diffusion) and field-derived emission parameters were estimated by fitting model outputs to measured concentration profiles.

RESULTS

Real-time measurements revealed highly variable concentration profiles, consisting of 1-8 peaks ranging from 5 to 220 s per decanting task, and average concentrations within peaks varying over 1-2 orders of magnitude. Acceptable fits were obtained by both descriptive approaches. The tested emission function seemed relevant in reproducing intermittent pollutant releases. Only advanced models (two-zone and diffusion) gave satisfying fits within assigned input parameter ranges. Average emission rate estimates varied in the range 10-47 mg min(-1) for formaldehyde and 360-1780 mg min(-1) for TOL, depending on the model tested.

CONCLUSIONS

Both descriptive approaches and deterministic models accurately reproduced the patterns of measured concentration peaks. However, only deterministic models provided an understanding of the relations between pollutant releases, air movements, and the resulting concentrations and may thus be recommended for exposure variability assessment purposes.