TY - JOUR
AU - Sleeth, Darrah, K
AB - Abstract Based on experiments conducted in low wind speed and calm air environments, the current International Organization for Standardization (ISO) and European Committee for Standardization (CEN) convention modeling human aerosol inhalability (i.e. aspiration efficiency) may not be valid when wind speeds are less than 0.5 ms−1. Additionally, the convention is based primarily on mouth breathing data and aerosols with aerodynamic diameters smaller than 100 µm. Since the convention's development, experimental inhalation data at wind speeds lower than 0.5 ms−1 for nose, mouth, and oronasal breathing have been generated for aerosols in a wider range of sizes (1.5–135 µm). These data were gathered and modeled with the intention of providing a simple convention recommendation for inhalability in low wind speed (>0 to <0.5 ms−1) and calm air (~0 ms−1) conditions to the ISO Technical Committee (TC) 146, Subcommittee 2, Working Group (WG) 1 (‘Particle Size-Selective Sampling and Analysis'), as it relates to standard ISO 7708, and to CEN TC 137/WG 3, as it relates to standard EN 481. This paper presents several equations as possibilities, all relating aspiration efficiency to aerodynamic diameter. The equation AE=1+0.000019dae2−0.009788dae stands out as a possible new convention. This polynomial model balances simplicity and fit while addressing the weakness of the current convention. aspiration efficiency, calm air, inhalability, inhalable dust Introduction Aerosol is a broad term that refers to any organic or inorganic colloid of solid or liquid particles suspended in air (Baron, 2010). Generated by both natural and anthropogenic sources (Calvo et al., 2013), aerosols can include dusts, fumes, fogs, steam, air, fibers, mists, and smoke (American Industrial Hygiene Association (AIHA), 2011). They vary in composition, size, and origin. Human exposure to aerosols is ubiquitous, occurring in workplaces and homes, through hobbies, and generally from air pollution. While aerosol exposure can occur through dermal absorption, the most common route of exposure is inhalation through the nose and/or mouth (Vincent, 2005). The health effects of aerosol exposure via inhalation are influenced by the delivered dose, toxicity (Brown, 2005), particle size, and site of deposition (American Conference of Governmental Industrial Hygienists (ACGIH), 2017). Exposure to insoluble aerosols through inhalation is associated with adverse health effects such as respiratory diseases (e.g. rhinitis, laryngitis, bronchitis, asthma, and chronic airway obstruction; Vincent, 2007). In addition, soluble aerosols, such as manganese, nickel, chromium, lead, and cadmium, can be transferred from the respiratory tract into systemic circulation and cause damage to various organs and body systems (Vincent, 2007). Bioaerosols, which include viruses, bacteria, mold, endotoxins, enzymes, pollen, mycotoxins, plant fibers, and spores have been associated with contagious infectious diseases, respiratory diseases, acute toxic effects, allergies, and cancer (Douwes et al., 2003). Some aerosols, particularly those that are carcinogenic, highly toxic, or water soluble, can pose a health-risk wherever they are deposited in the body (Vincent, 2005). Not all aerosols present in the air are inhaled. Aerosol inhalability is influenced by particle size, wind speed, breathing method (whether through the nose, mouth, or both), breathing rate, inhaled volume per breath, body size, and air movement around the body (ISO, 1995). Since only aerosols that reach the respiratory tract pose a health threat via inhalation (Vincent et al., 1990), understanding what humans inhale under different conditions is an integral part of occupational hazard characterization. The term inhalable fraction is used by several organizations to define the fraction of total airborne particles inhaled through the mouth and nose into the respiratory tract [efficiency levels out at 50% for ~50–100 µm particles; European Committee for Standardization (CEN), 1992; International Organization for Standardization (ISO), 1995; AIHA, 2011; ACGIH, 2017]. Size-selective sampling conventions have been developed to model the inhalable, thoracic, and respirable fractions (CEN, 1992; ISO, 1995). These conventions describe the sampling efficiency for ideal samplers based on the aerodynamic diameter of the airborne particles (ISO, 1995). Conventions cannot precisely predict what fraction of aerosols are inhaled by each individual (since many variables are involved) but instead serve as a standard for how aerosols with different aerodynamic diameters should be collected (Lidén and Harper, 2006). Size-selective sampling in occupational environments, accompanied by knowledge of aerosol toxicological and physical properties, can provide approximate measures of airborne health hazards (Kennedy and Hinds, 2002). The current ISO convention for the inhalable fraction is based on studies performed in the late 1970s and early 1980s by Ogden and Birkett (1977), Vincent and Armbruster (1981), Armbruster and Breuer (1982), and Vincent and Mark (1982; CEN, 1992; ISO, 1995). First adopted by the ACGIH in 1985, it was later adopted by the CEN as EN 481 in 1992 and by ISO as ISO 7708 in 1995. The current ISO inhalable convention is given by equation (1), which is graphed in Fig. 1. Although there are some minor differences between ISO 7708 and EN 481, the convention for the inhalable fraction is the same in both standards (CEN, 1992; ISO, 1995). Figure 1. Open in new tabDownload slide Graphical representation of the current ISO/CEN convention for aspiration efficiency in moving air and the Aitken et al. equation, a suggested convention for aspiration efficiency in calm air. Figure 1. Open in new tabDownload slide Graphical representation of the current ISO/CEN convention for aspiration efficiency in moving air and the Aitken et al. equation, a suggested convention for aspiration efficiency in calm air. AE=0.5[1+exp(−0.06dae)] (1) Here, inhalability (AE), also called aspiration efficiency, is expressed as a fraction between 0 and 1 and is a function of particle aerodynamic diameter (dae) in micrometers (µm). The studies on which the current convention is based were performed with life-sized mannequins, wind tunnels, well-characterized test aerosols (i.e. with small particle size geometric standard deviation), particles smaller than 100 µm, and at moderate wind speeds (~0.75–4 ms−1; Ogden and Birkett, 1977; Armbruster and Breuer, 1982; Vincent and Mark, 1982; Vincent et al., 1990). ISO 7708 indicates that equation (1) is designed to be the target sampling curve for devices collecting the inhalable fraction when wind speeds are <4 ms−1 (ISO, 1995). The standard also includes an adjustment to equation (1) that can be made when wind speeds are in the range 4–9 ms−1(Vincent et al., 1990). Beyond 9 ms−1, however, the convention is not considered valid because the limits of the data would be exceeded. At the time the convention was set, it was believed that it was applicable to all wind speeds 0–4 ms−1. It was not until new data were collected in calm air chambers (e.g. Aitken et al., 1999), which showed substantially higher aspiration efficiency in these near-zero wind speeds, that this assumption was challenged. This is a problem because wind speeds in occupational environments are consistently quite low, for example, Baldwin and Maynard (1998) found the mean wind speed from 55 work areas to be 0.3 ms−1. The convention has additional weaknesses. The standard indicates that equation (1) should not be applied when sampling for aerosols larger than 100 µm. At the time the convention was written, there was no experimental information beyond 100 µm on which a firm recommendation could be made (Vincent, 2007), although some mathematical estimates were attempted (Lidén and Kenny, 1994). In addition to the aforementioned issues, the current convention has another weakness in that aspiration efficiency begins leveling out around 40 µm (where aspiration efficiency is ~0.55 or ~55%). At an aerodynamic diameter of 100 µm, aspiration efficiency is ~50%. The equation has an asymptote at an efficiency of 0.5 (50%) and, if the equation were extrapolated to larger particle sizes, inhalability would never reach 0. This would appear to be unrealistic; at some point, an airborne particle will be too large to be inhaled. Another recent criticism of the convention is that it is based only on mouth breathing experiments, whereas people typically breathe through their nose, mouth, or both. In response to the weaknesses of the current ISO/CEN convention, further data on the inhalability of aerosols at low wind speeds (>0 and <0.5 ms−1) and calm air (~0 ms−1) have been produced for nose and mouth breathing at multiple breathing rates for a range of particle sizes (see review article by Lidén and Harper, 2006). Sleeth and Vincent contributed further to the body of existing work with a study on aspiration efficiency at low wind speeds (~0.1–0.4 ms−1; Sleeth and Vincent, 2011). They proposed a linear equation based on nose, mouth, and oronasal breathing to represent inhalability at low wind speeds (~0.1 ms−1). A linear equation seemed appropriate because, instead of leveling out like the current convention, there is a downward trend. Their equation was not statistically different from an equation proposed by Aitken et al., which was based only on mouth breathing at an inhalation rate of 20 l min−1 and modeled inhalability in calm air (~0 ms−1) (Aitken et al., 1999). The Aitken equation is given by equation (2), which is also graphed in Fig. 1: AE=1−0.0038dae (2) In addition to mannequin and human studies, computational fluid dynamics (CFD) have been used to model human inhalability. Using CFD, Anthony and Anderson investigated aspiration efficiencies for nose and mouth breathing (Anthony and Anderson, 2013; Anderson and Anthony, 2014). They also suggested a linear equation for aspiration efficiency based on nose and mouth breathing at different breathing rates and wind speeds less than 0.5 ms−1 as given by equation (3) (Anthony and Anderson, 2015): AE=1−0.00785dae (3) Besides linear equations, logistic (Menache et al., 1995; Brown, 2005), polynomial (Kennedy and Hinds, 2002), and other models have also been suggested. With the availability of such data, an empirical model applicable at low wind speeds and in calm air can be developed. ISO Technical Committee (TC) 146, Subcommittee 2, Working Group (WG) 1 (‘Particle Size-Selective Sampling and Analysis') is currently discussing a revision of ISO 7708. The related CEN TC 137, WG 3 is also involved in this revision so that both standards can be simultaneously revised. The objective is to revise these standards to include a sampling convention for the inhalable fraction as a function of aerodynamic diameter applicable for wind speeds lower than 0.5 ms−1. The new sampling convention should be based on nose, mouth, and oronasal breathing data and also include experimental aspiration efficiencies for aerosols larger than 100 µm. Like the current convention, the new equation should retain the characteristic of having aspiration efficiency to be 1 (or 100%) when particle aerodynamic size is 0 µm but, unlike the current convention, it is anticipated that aspiration efficiency will not level out at 0.5 (50%) but will get close to or reach 0 aspiration at some point. Therefore, the aim of this study is to establish a single empirical equation to describe particle inhalability for low wind speed and calm air conditions that is applicable in occupational environments. This will be accomplished by compiling data from previous research and fitting various equations to the data, which will then be analyzed and discussed. Methods Development of a new convention began with the identification of studies that contain data on aspiration efficiency in calm air (~0 ms−1) and/or at low wind speeds (<0.5 ms−1). Studies were identified by the following sources: (i) recommendations by ISO WG members and (ii) through targeted literature searches in Google Scholar. Keyword searches included ‘inhalation AND low wind speed', ‘inhalation AND calm air', and ‘computational fluid dynamics AND inhalation AND low wind speed'. Each search produced thousands of results; therefore, only the first 10 pages of each search were investigated. If a paper found using a database search matched inclusion criterion, it was submitted to ISO WG members for consideration. There may be other documents with relevant data that were not picked up in these searches (e.g. government reports); however, data from studies that were not peer reviewed were excluded. Data were included only when the aerodynamic particle size of the test aerosol(s) and the experimental aspiration efficiency were provided at a given wind speed. Data for wind speeds >0.5 ms−1 were excluded. For studies performed in moving air (i.e. wind speed >0 ms−1), data were included only if orientation averaged (i.e. aspiration efficiency was determined for different orientations with respect to the air flow direction). Data collected from a ‘facing-the-wind' orientation are likely to overestimate the average aspiration efficiency of a worker who moves about (Kennedy and Hinds, 2002). Data were included from mannequin, human (in vivo), and CFD studies. Data from nose breathing, mouth breathing, and oronasal breathing experiments were all included, as well as data from all breathing rates. Only data on adult aspiration were included. Lastly, many studies found through targeted searches were about sampler efficiency and deposition and, thus, were not of interest to the current study. All data that matched the abovementioned criteria were compiled into one database. A scatterplot was generated to visually analyze the data. Separate scatterplots for nose breathing data and mouth breathing data were generated. In every scatterplot, aspiration efficiency is represented on the y-axis (dependent variable), while aerodynamic diameter (µm) is represented on the x-axis (independent variable). Variables which influence inhalability besides aerodynamic diameter, such as breathing method and aspiration rate, change with each person and are hard to account for in sampling devices. Since, from a physical point of view, aspiration efficiency is based on variables beyond aerodynamic diameter (specifically, the Stokes number and the ratios of the settling speed to the aspiration inlet air speed and to the local air speed), the models presented in this paper may not always make sense from a physics standpoint. Arguments for using an independent variable related to Stokes number in these equations may make more sense but are not as practical since using Stokes number requires knowing wind speed. Until sampling devices can be built to change how they sample for particles when wind speeds change in a workplace, using Stokes number is not practical. For this reason, it was not used in the determination of potential equations to model data. Analysis and model development were performed in Stata version 14.1 (StataCorp, College Station, TX, USA). First, a linear equation for all data was produced using ordinary least squares regression. As explained above, aerodynamic diameter of the aerosol size was set as the independent variable and aspiration efficiency as the dependent variable. An additional linear equation for all data was developed using least squares regression with a forced y-intercept of 1.0, much like the linear equations generated by others (Aitken et al., 1999; Anthony and Anderson, 2015). Forcing the intercept through 1.0 implies that for the smallest particles, aspiration efficiency is 100%. In other words, the concentration of an aerosol in the respiratory tract will be the same as the concentration in the surrounding air. Going through (0.0, 1.0) is an important characteristic of an ideal convention but requires extrapolation when small particle sizes are not included in data sets. Transformation of aerodynamic diameter during linear regression was also explored to see if fit improved. Nonlinear equations were developed using least squares regression. These included exponential decay, polynomial, and logistic options. As with other equations, all were forced through the y-axis at 1.0. The root mean squared error (RMSE), Bayesian information criterion (BIC), and Akaike information criterion (AIC) were used to compare the fit of all data models. The RMSE is on the same scale/units as aspiration efficiency. The AIC and BIC are useful only when comparing fits between different models; better fitting models have lower AIC and BIC values. For all-data models forced through the intercept y = 1.0, homoskedasticity and normality of the residuals were analyzed with a skewness/kurtosis test for normality and a Shapiro–Wilkinson test for normality. For equations built from all data, other characteristics that were examined include the particle sizes where aspiration efficiency was 0.9, 0.5, (i.e. the d50), and 0.0 (i.e. the x-intercept). Depending on the equation, extrapolation was sometimes necessary to see where aspiration efficiency equaled 0.0. The predicted aspiration efficiencies for small particles (i.e. <20 µm) were also compared as those sizes relate most to thoracic and respirable size ranges. To investigate how other variables influenced aspiration efficiency, data were also stratified, with linear equations built from nose breathing only, mouth breathing only, at-rest breathing only (6 to 10 l min−1), moderate breathing only (18 to 22 l min−1), and heavy breathing only (35 l min−1 and higher) data. Finally, an equation was developed using only moderate, mouth breathing data for the sake of comparison to the Aitken et al. equation. These equations were also forced through the intercept y = 1.0. Linear equations were chosen to model the relationship between aspiration efficiency and particle aerodynamic diameter for the stratified data because of their simplicity, ease of comparison with linear equations suggested by previous research, and interpretability. For these equations, 95% confidence intervals (CIs) for coefficients were calculated and RMSE reported. Results Nine articles had data that fit the inclusion criteria, the details of which are provided in Table 1. From these, 304 data points were extracted, including 110 nose breathing aspiration efficiency values, 136 mouth breathing, and 58 oronasal. One hundred forty-five data points were measured during at-rest breathing rates (5 to 10 l min−1), 132 at moderate breathing rates (19 to 20.8 l min−1), and 27 at heavy breathing rates (35 l min−1 or higher). The particle sizes tested ranged from 1.5 to 135 µm. Fig. 2 provides a scatterplot of all data points. Figs. 3 and 4 are scatterplots separated by nose and mouth breathing, respectively. Table 2 summarizes all equations, the details of which are provided in the following section. Table 1. Articles with data used in the development of a new convention by publication year. Authors Year Type Breathing method Breathing rate(s) l min−1 Particle sizes µm Wind speed(s) ms−1 # of data points Anthony and Anderson 2014 CFD Nose 7.5, 20 7, 22, 52, 68, 82, 100, 116 0.1, 0.2, 0.4 56 Anthony and Anderson 2012 CFD Mouth 7.5, 20.8, 50.3 7, 22, 52, 68, 82, 100, 116 0.1, 0.2, 0.4 56 Sleeth and Vincent 2011 Mannequin Mouth 6, 20 9.3–89.5 0.10, 0.24, 0.42 36 Nose 6 9.3–89.5 0.10, 0.24, 0.42 18 Oronasal 6, 20 9.3–89.5 0.10, 0.24, 0.42 36 Dai et al. 2007 Head nodel Nose 6, 9, 19 1.5, 5, 10, 15 ~0 12 Dai et al. 2006 In vivo Nose ‘At Rest' and ‘Moderate Exercise' 13, 40, 65, 80, 110, 135 ~0 12 Kennedy and Hinds 2002 Mannequin Mouth 20.8 7, 17, 22, 37, 52, 68, 82, 116 0.4 8 Aitken et al. 1999 Mannequin Mouth 6, 10, 20 6, 9, 13, 18, 26, 34, 46, 58, 74, 90 ~0 36 Hsu and Swift 1999 Mannequin Nose 8.5, 20 13, 40, 65, 80, 110, 135 ~0 12 Oronasal 35 13, 40, 65, 80, 110, 135 ~0 6 Breysse and Swift 1990 In vivo Nose 15 breaths per minute 18, 24.5, 27.5, 30.5 ~0 12 Authors Year Type Breathing method Breathing rate(s) l min−1 Particle sizes µm Wind speed(s) ms−1 # of data points Anthony and Anderson 2014 CFD Nose 7.5, 20 7, 22, 52, 68, 82, 100, 116 0.1, 0.2, 0.4 56 Anthony and Anderson 2012 CFD Mouth 7.5, 20.8, 50.3 7, 22, 52, 68, 82, 100, 116 0.1, 0.2, 0.4 56 Sleeth and Vincent 2011 Mannequin Mouth 6, 20 9.3–89.5 0.10, 0.24, 0.42 36 Nose 6 9.3–89.5 0.10, 0.24, 0.42 18 Oronasal 6, 20 9.3–89.5 0.10, 0.24, 0.42 36 Dai et al. 2007 Head nodel Nose 6, 9, 19 1.5, 5, 10, 15 ~0 12 Dai et al. 2006 In vivo Nose ‘At Rest' and ‘Moderate Exercise' 13, 40, 65, 80, 110, 135 ~0 12 Kennedy and Hinds 2002 Mannequin Mouth 20.8 7, 17, 22, 37, 52, 68, 82, 116 0.4 8 Aitken et al. 1999 Mannequin Mouth 6, 10, 20 6, 9, 13, 18, 26, 34, 46, 58, 74, 90 ~0 36 Hsu and Swift 1999 Mannequin Nose 8.5, 20 13, 40, 65, 80, 110, 135 ~0 12 Oronasal 35 13, 40, 65, 80, 110, 135 ~0 6 Breysse and Swift 1990 In vivo Nose 15 breaths per minute 18, 24.5, 27.5, 30.5 ~0 12 Open in new tab Table 1. Articles with data used in the development of a new convention by publication year. Authors Year Type Breathing method Breathing rate(s) l min−1 Particle sizes µm Wind speed(s) ms−1 # of data points Anthony and Anderson 2014 CFD Nose 7.5, 20 7, 22, 52, 68, 82, 100, 116 0.1, 0.2, 0.4 56 Anthony and Anderson 2012 CFD Mouth 7.5, 20.8, 50.3 7, 22, 52, 68, 82, 100, 116 0.1, 0.2, 0.4 56 Sleeth and Vincent 2011 Mannequin Mouth 6, 20 9.3–89.5 0.10, 0.24, 0.42 36 Nose 6 9.3–89.5 0.10, 0.24, 0.42 18 Oronasal 6, 20 9.3–89.5 0.10, 0.24, 0.42 36 Dai et al. 2007 Head nodel Nose 6, 9, 19 1.5, 5, 10, 15 ~0 12 Dai et al. 2006 In vivo Nose ‘At Rest' and ‘Moderate Exercise' 13, 40, 65, 80, 110, 135 ~0 12 Kennedy and Hinds 2002 Mannequin Mouth 20.8 7, 17, 22, 37, 52, 68, 82, 116 0.4 8 Aitken et al. 1999 Mannequin Mouth 6, 10, 20 6, 9, 13, 18, 26, 34, 46, 58, 74, 90 ~0 36 Hsu and Swift 1999 Mannequin Nose 8.5, 20 13, 40, 65, 80, 110, 135 ~0 12 Oronasal 35 13, 40, 65, 80, 110, 135 ~0 6 Breysse and Swift 1990 In vivo Nose 15 breaths per minute 18, 24.5, 27.5, 30.5 ~0 12 Authors Year Type Breathing method Breathing rate(s) l min−1 Particle sizes µm Wind speed(s) ms−1 # of data points Anthony and Anderson 2014 CFD Nose 7.5, 20 7, 22, 52, 68, 82, 100, 116 0.1, 0.2, 0.4 56 Anthony and Anderson 2012 CFD Mouth 7.5, 20.8, 50.3 7, 22, 52, 68, 82, 100, 116 0.1, 0.2, 0.4 56 Sleeth and Vincent 2011 Mannequin Mouth 6, 20 9.3–89.5 0.10, 0.24, 0.42 36 Nose 6 9.3–89.5 0.10, 0.24, 0.42 18 Oronasal 6, 20 9.3–89.5 0.10, 0.24, 0.42 36 Dai et al. 2007 Head nodel Nose 6, 9, 19 1.5, 5, 10, 15 ~0 12 Dai et al. 2006 In vivo Nose ‘At Rest' and ‘Moderate Exercise' 13, 40, 65, 80, 110, 135 ~0 12 Kennedy and Hinds 2002 Mannequin Mouth 20.8 7, 17, 22, 37, 52, 68, 82, 116 0.4 8 Aitken et al. 1999 Mannequin Mouth 6, 10, 20 6, 9, 13, 18, 26, 34, 46, 58, 74, 90 ~0 36 Hsu and Swift 1999 Mannequin Nose 8.5, 20 13, 40, 65, 80, 110, 135 ~0 12 Oronasal 35 13, 40, 65, 80, 110, 135 ~0 6 Breysse and Swift 1990 In vivo Nose 15 breaths per minute 18, 24.5, 27.5, 30.5 ~0 12 Open in new tab Table 2. Equations modeling aspiration efficiency in calm air and low wind speed conditions. Data Equation # Function Equation dae Coefficient 95% CI RMSE AE = 0.90 AE = 0.50 AE = 0 Valid range Aitken et al. (1999) 2 Linear AE = 1 − 0.0038dae N/A N/A 26.32 µm 131.58 µm* 263.16 µm* 6–90 µm All data 4 Linear AE = 0.9003 − 0.0067dae (−0.0073, −0.0065) 0.1878 0.04 µm 59.75 µm 134.37 µm 6–135 µm All data 5 Linear AE = 1 − 0.0081dae (−0.0084, −0.0077) 0.1962 12.35 µm 61.73 µm 123.46 µm 6–135 μm All data 6 Exponential decay AE = 0.5 [1 + e(−0.0447dae)] (0.0346, 0.0549) 0.2433 4.99 µm Never Never 6–135 μm All data 7 Exponential decay AE = 0.9869dae (0.9860, 0.9880) 0.1958 7.98 µm 52.56 µm Never 6–135 μm All data 8 Polynomial AE = 1 + 0.000019dae2 − 0.009788dae (6.67 × 10^ − 6, 0.00003), (−0.0110, −0.0086) 0.1936 10.42 µm 57.50 µm 140.47 µm* 6–135 μm All data 9 Logistic AE = 2/[1 + e(0.01988*dae)] (0.0186, 0.0212) 0.19557 10.09 µm 55.26 µm Never 6–135 μm Nose breathing 11 Linear AE = 1 − 0.0089dae (−0.0094, −0.0084) 0.1919 11.24 µm 56.18 µm 112.36 µm 7–135 µm Mouth breathing 12 Linear AE = 1 − 0.0069dae (−0.0073, −0.0065) 0.1486 14.49 µm 72.46 µm 144.93 µm* 6–116 µm At rest breathing 13 Linear AE = 1 − 0.0088dae (−0.0094, −0.0083) 0.1904 11.36 µm 56.82 µm 113.64 µm 6–135 µm Moderate breathing 14 Linear AE = 1 − 0.0079dae (−0.0085, −0.0074) 0.1950 12.66 µm 63.29 µm 126.58 µm 6–135 µm Heavy breathing 15 Linear AE = 1 − 0.0063dae (−0.0072, −0.0054) 0.166 15.87 µm 79.37 µm 158.73 µm* 6–135 µm Moderate mouth breathing 16 Linear AE = 1 − 0.0068dae (−0.0074, −0.0062) 0.1495 14.71 µm 73.53 µm 147.06 µm* 6–116 µm Data Equation # Function Equation dae Coefficient 95% CI RMSE AE = 0.90 AE = 0.50 AE = 0 Valid range Aitken et al. (1999) 2 Linear AE = 1 − 0.0038dae N/A N/A 26.32 µm 131.58 µm* 263.16 µm* 6–90 µm All data 4 Linear AE = 0.9003 − 0.0067dae (−0.0073, −0.0065) 0.1878 0.04 µm 59.75 µm 134.37 µm 6–135 µm All data 5 Linear AE = 1 − 0.0081dae (−0.0084, −0.0077) 0.1962 12.35 µm 61.73 µm 123.46 µm 6–135 μm All data 6 Exponential decay AE = 0.5 [1 + e(−0.0447dae)] (0.0346, 0.0549) 0.2433 4.99 µm Never Never 6–135 μm All data 7 Exponential decay AE = 0.9869dae (0.9860, 0.9880) 0.1958 7.98 µm 52.56 µm Never 6–135 μm All data 8 Polynomial AE = 1 + 0.000019dae2 − 0.009788dae (6.67 × 10^ − 6, 0.00003), (−0.0110, −0.0086) 0.1936 10.42 µm 57.50 µm 140.47 µm* 6–135 μm All data 9 Logistic AE = 2/[1 + e(0.01988*dae)] (0.0186, 0.0212) 0.19557 10.09 µm 55.26 µm Never 6–135 μm Nose breathing 11 Linear AE = 1 − 0.0089dae (−0.0094, −0.0084) 0.1919 11.24 µm 56.18 µm 112.36 µm 7–135 µm Mouth breathing 12 Linear AE = 1 − 0.0069dae (−0.0073, −0.0065) 0.1486 14.49 µm 72.46 µm 144.93 µm* 6–116 µm At rest breathing 13 Linear AE = 1 − 0.0088dae (−0.0094, −0.0083) 0.1904 11.36 µm 56.82 µm 113.64 µm 6–135 µm Moderate breathing 14 Linear AE = 1 − 0.0079dae (−0.0085, −0.0074) 0.1950 12.66 µm 63.29 µm 126.58 µm 6–135 µm Heavy breathing 15 Linear AE = 1 − 0.0063dae (−0.0072, −0.0054) 0.166 15.87 µm 79.37 µm 158.73 µm* 6–135 µm Moderate mouth breathing 16 Linear AE = 1 − 0.0068dae (−0.0074, −0.0062) 0.1495 14.71 µm 73.53 µm 147.06 µm* 6–116 µm *Requires extrapolation. Open in new tab Table 2. Equations modeling aspiration efficiency in calm air and low wind speed conditions. Data Equation # Function Equation dae Coefficient 95% CI RMSE AE = 0.90 AE = 0.50 AE = 0 Valid range Aitken et al. (1999) 2 Linear AE = 1 − 0.0038dae N/A N/A 26.32 µm 131.58 µm* 263.16 µm* 6–90 µm All data 4 Linear AE = 0.9003 − 0.0067dae (−0.0073, −0.0065) 0.1878 0.04 µm 59.75 µm 134.37 µm 6–135 µm All data 5 Linear AE = 1 − 0.0081dae (−0.0084, −0.0077) 0.1962 12.35 µm 61.73 µm 123.46 µm 6–135 μm All data 6 Exponential decay AE = 0.5 [1 + e(−0.0447dae)] (0.0346, 0.0549) 0.2433 4.99 µm Never Never 6–135 μm All data 7 Exponential decay AE = 0.9869dae (0.9860, 0.9880) 0.1958 7.98 µm 52.56 µm Never 6–135 μm All data 8 Polynomial AE = 1 + 0.000019dae2 − 0.009788dae (6.67 × 10^ − 6, 0.00003), (−0.0110, −0.0086) 0.1936 10.42 µm 57.50 µm 140.47 µm* 6–135 μm All data 9 Logistic AE = 2/[1 + e(0.01988*dae)] (0.0186, 0.0212) 0.19557 10.09 µm 55.26 µm Never 6–135 μm Nose breathing 11 Linear AE = 1 − 0.0089dae (−0.0094, −0.0084) 0.1919 11.24 µm 56.18 µm 112.36 µm 7–135 µm Mouth breathing 12 Linear AE = 1 − 0.0069dae (−0.0073, −0.0065) 0.1486 14.49 µm 72.46 µm 144.93 µm* 6–116 µm At rest breathing 13 Linear AE = 1 − 0.0088dae (−0.0094, −0.0083) 0.1904 11.36 µm 56.82 µm 113.64 µm 6–135 µm Moderate breathing 14 Linear AE = 1 − 0.0079dae (−0.0085, −0.0074) 0.1950 12.66 µm 63.29 µm 126.58 µm 6–135 µm Heavy breathing 15 Linear AE = 1 − 0.0063dae (−0.0072, −0.0054) 0.166 15.87 µm 79.37 µm 158.73 µm* 6–135 µm Moderate mouth breathing 16 Linear AE = 1 − 0.0068dae (−0.0074, −0.0062) 0.1495 14.71 µm 73.53 µm 147.06 µm* 6–116 µm Data Equation # Function Equation dae Coefficient 95% CI RMSE AE = 0.90 AE = 0.50 AE = 0 Valid range Aitken et al. (1999) 2 Linear AE = 1 − 0.0038dae N/A N/A 26.32 µm 131.58 µm* 263.16 µm* 6–90 µm All data 4 Linear AE = 0.9003 − 0.0067dae (−0.0073, −0.0065) 0.1878 0.04 µm 59.75 µm 134.37 µm 6–135 µm All data 5 Linear AE = 1 − 0.0081dae (−0.0084, −0.0077) 0.1962 12.35 µm 61.73 µm 123.46 µm 6–135 μm All data 6 Exponential decay AE = 0.5 [1 + e(−0.0447dae)] (0.0346, 0.0549) 0.2433 4.99 µm Never Never 6–135 μm All data 7 Exponential decay AE = 0.9869dae (0.9860, 0.9880) 0.1958 7.98 µm 52.56 µm Never 6–135 μm All data 8 Polynomial AE = 1 + 0.000019dae2 − 0.009788dae (6.67 × 10^ − 6, 0.00003), (−0.0110, −0.0086) 0.1936 10.42 µm 57.50 µm 140.47 µm* 6–135 μm All data 9 Logistic AE = 2/[1 + e(0.01988*dae)] (0.0186, 0.0212) 0.19557 10.09 µm 55.26 µm Never 6–135 μm Nose breathing 11 Linear AE = 1 − 0.0089dae (−0.0094, −0.0084) 0.1919 11.24 µm 56.18 µm 112.36 µm 7–135 µm Mouth breathing 12 Linear AE = 1 − 0.0069dae (−0.0073, −0.0065) 0.1486 14.49 µm 72.46 µm 144.93 µm* 6–116 µm At rest breathing 13 Linear AE = 1 − 0.0088dae (−0.0094, −0.0083) 0.1904 11.36 µm 56.82 µm 113.64 µm 6–135 µm Moderate breathing 14 Linear AE = 1 − 0.0079dae (−0.0085, −0.0074) 0.1950 12.66 µm 63.29 µm 126.58 µm 6–135 µm Heavy breathing 15 Linear AE = 1 − 0.0063dae (−0.0072, −0.0054) 0.166 15.87 µm 79.37 µm 158.73 µm* 6–135 µm Moderate mouth breathing 16 Linear AE = 1 − 0.0068dae (−0.0074, −0.0062) 0.1495 14.71 µm 73.53 µm 147.06 µm* 6–116 µm *Requires extrapolation. Open in new tab Figure 2. Open in new tabDownload slide Scatter plot of all aspiration efficiency data points used in this study (wind speed <0.5 ms−1). Figure 2. Open in new tabDownload slide Scatter plot of all aspiration efficiency data points used in this study (wind speed <0.5 ms−1). Figure 3. Open in new tabDownload slide Scatter plot of nose breathing aspiration efficiency data when wind speeds are <0.5 ms−1. Figure 3. Open in new tabDownload slide Scatter plot of nose breathing aspiration efficiency data when wind speeds are <0.5 ms−1. Figure 4. Open in new tabDownload slide Scatter plot of mouth breathing aspiration efficiency data when wind speeds are <0.5 ms−1. Figure 4. Open in new tabDownload slide Scatter plot of mouth breathing aspiration efficiency data when wind speeds are <0.5 ms−1. All data models Linear models An equation for all data (nose/mouth/oronasal breathing, all aspiration rates, and all wind speeds <0.5 ms−1), determined through ordinary least squares regression, is presented in equation (4): AE=0.9003−0.0067dae (4) RMSE=0.1878; AIC=−151.9736; BIC=−144.5395 Equation (5) is the linear equation resulting when the intercept is forced through (0.0, 1.0). Overall equation fit drops when the intercept is forced. This trend was seen for all models forced through (0.0, 1.0). Equation (5) is represented graphically in Fig. 5. A residual versus fitted value plot of the data (not shown) suggested that the residuals were not perfectly homoscedastic. Regression of logarithmic, power, and multiplicative inverse transformations of aerodynamic diameter increased heteroskedasticity of residuals as compared to regression of the untransformed aerodynamic diameter and did not improve the overall fit to data. A square root transformation of aerodynamic diameter did not increase heteroskedasticity of the residuals but also did not decrease RMSE, AIC, or BIC. For these reasons, the untransformed aerodynamic diameter was determined to be most practical for equation (5) and for the linear models of stratified data discussed later on. When wind speed, breathing rate, and breathing method were included as additional independent variables in a regression through y = 1.0, fit did improve slightly (dae coefficient: 0.0077, RMSE: 0.1887, AIC: −147.0394, BIC: −132.1712). However, this option would be impractical as a convention option because it requires knowing multiple variables that are typically not collected when performing air sampling on workers. Figure 5. Open in new tabDownload slide Linear, polynomial, exponential decay, and logistic models for aspiration efficiency when wind speeds are <0.5 ms−1 represented graphically over a scatterplot of the data. Figure 5. Open in new tabDownload slide Linear, polynomial, exponential decay, and logistic models for aspiration efficiency when wind speeds are <0.5 ms−1 represented graphically over a scatterplot of the data. AE=1−0.0081dae (5) RMSE=0.1962; AIC=−126.4932; BIC=−122.7762 Exponential decay models Equation (6) is an exponential decay model that resembles the format of the current ISO/CEN convention and differs only by the constant [95% CI (0.0346, 0.0549)] by which the particle aerodynamic diameter is multiplied. The RMSE (0.2433) value is higher than others presented, and there is no improvement in fit when compared to the linear model. Additionally, AIC (4.4116) and BIC (8.1286) values were higher for equation (6) than equation (5). This equation has the same problem as the current ISO/CEN convention in that aspiration efficiency begins to level out at ~0.5 around 40 µm: AE=0.5[1+exp(−0.0447dae)] (6) RMS =0.2433; AIC=4.4116; BIC=8.1286 A simpler exponential decay model, which better balances fit and simplicity, was found in equation (7), represented graphically in Fig. 5: AE=0.9869dae (7) RMSE=0.19581; AIC=−127.67; BIC=−123.95 Polynomial model A second-degree polynomial forced through (0.0, 1.0) is presented in equation (8). Adding additional terms to the polynomial (i.e. dae3, dae4) slightly reduced RMSE values, although the increase in fit was not meaningful enough to include other polynomial options in these results. Equation (8) is shown in Fig. 5. AE=1+0.000019dae2−0.009788dae (8) RMSE=0.1936; AIC=−133.4127; BIC=−125.9787 Logistic model One possible logistic model is presented in equation (9). Another logistic equation similar in form to one suggested by Brown (2005) is presented by equation (10). Like the other models presented, RMSE, AIC, and BIC values were higher after the equation was constrained to go through y = 1.0. The aspiration efficiencies suggested by these equations are quite similar. For this reason, equation (9), represented graphically in Fig. 5, will be referenced when discussing the ‘logistic model' from here on: AE=2(11+e(0.0198886 (dae))) (9) RMSE=0.1958; AIC=−127.6274; BIC=−123.9104 AE=1+2.28698 1+2.28698e(0.0164755(dae)) (10) RMSE=0.1957; AIC=−126.9395; BIC=−119.5055 Stratified data Linear equations for nose breathing aspiration efficiency and mouth breathing aspiration efficiency are presented in equations (11) and (12), respectively, and graphed in Fig. 6. These do not have overlapping 95% CIs. When a linear equation was developed for only oronasal breathing points, the dae coefficient was 0.0090. Since it was similar to the nose breathing equation, it is not discussed further. Figure 6. Open in new tabDownload slide Graphical representation of nose and mouth breathing linear equations when wind speeds are <0.5 ms−1. Figure 6. Open in new tabDownload slide Graphical representation of nose and mouth breathing linear equations when wind speeds are <0.5 ms−1. AEnose=1−0.0089dae (11) RMSE=0.1919; 95% CI: −0.0094, −0.0084 AEmouth=1−0.0069dae (12) RMSE=0.14959; 95% CI: −0.0073, −0.0065 Aspiration efficiency for at-rest breathing, moderate breathing, and heavy breathing are presented in equations (13), (14), and (15), respectively, which are all graphed in Fig. 7. The 95% CIs for the at-rest and moderate breathing coefficients do overlap slightly, while heavy and moderate breathing do not overlap. Figure 7. Open in new tabDownload slide Graphical representation of at-rest, moderate, and heavy breathing equations when wind speeds are <0.5 ms−1. Figure 7. Open in new tabDownload slide Graphical representation of at-rest, moderate, and heavy breathing equations when wind speeds are <0.5 ms−1. AEat~-rest=1−0.0088dae (13) RMSE=0.1904; 95% CI: −0.0094, −0.0083 AEmod=1−0.0079dae (14) RMSE=0.1950; 95% CI:−0.0085, −0.0074 AEheavy=1−0.0063dae (15) RMSE=0.1660; 95% CI: −0.0072, −0.0054 To be most comparable to the Aitken et al. equation, a linear equation should only be based on mouth breathing at an aspiration rate near 20 l min−1 (moderate breathing), which is shown in equation (16). AEmouth/mod=1−0.0068dae (16) RMSE=0.1495; 95% CI: −0.0074, −0.0062 Discussion One of the main criticisms of the current ISO/CEN convention is that its developers assumed that low wind speed/calm air environments were no different than higher wind speed conditions. It was assumed that mouth breathing data were sufficient to describe aerosol inhalability. To address these two shortcomings and accomplish the study goal, equations (4)–(10) included nose, mouth, and oronasal breathing data from low wind speed/calm air conditions. This study also sought to develop a new convention that dealt with other weaknesses of the current convention while maintaining simplicity. Specifically, aspiration efficiencies for aerosols larger than 100 µm were included where available and equations where aspiration efficiency approaches/reaches 0 were developed. For all data, the models with the lowest RMSE, AIC, and BIC values that address these concerns are equations (5) (linear), (7) (simple exponential decay), (8) (polynomial), and (9) (logistic). Equation (5), the linear model forced through y = 1.0, is similar in form to models suggested by previous researchers (Aitken et al., 1999; Sleeth and Vincent, 2011; Anthony and Anderson, 2015), with a coefficient similar to the Anthony and Anderson equation. Equation (5) is easily interpreted as a practical sampling convention—an increase in dae leads to a decrease in aspiration efficiency. This interpretability is something that may be lost in equations (7)–(9). Equation (5) predicts that aspiration efficiency will be 0 for aerosols ~124 µm in size and larger. For comparison, the largest aerosols included in this study were 135 µm, for which the experimental data were ~0 (Hsu and Swift, 1999; Dai et al., 2006). Future investigations should be targeted at investigating whether or not 124 µm is an appropriate aerodynamic diameter for sampler efficiency to reach 0. In comparison to the Aitken et al. equation, that line is about half as steep as equation (5), implying that a sampler built to match the Aitken et al. equation may sample larger particles at a higher efficiency as compared to a sampler built to match equation (5). However, this difference is not surprising, because a wider range of particle sizes, wind speeds, aspiration rates, breathing methods, and experimental methods were used to generate equation (5). The simple exponential decay model [equation (7)] will never reach an aspiration efficiency of 0 (even if extrapolated beyond the limits of the data), although it gets very close. At 100 µm, the aspiration efficiency predicted by equation (7) is ~27% and would be ~7% at 200 µm (if extrapolated). It suggests that particles larger than 100 µm should be sampled at greater efficiencies than what equations (5) and (8) suggest. Similar to the simple exponential decay model is the logistic model [equation (9)]. The RMSE values of equations (9) and (7) are remarkably close (RMSE: 0.195833 versus 0.195816). The slight differences between the models are perhaps most important at small aerosol sizes (0–10 µm) because of the influence the inhalable convention has on both the thoracic and respirable sampling conventions. At 4 and 10 µm, the exponential decay model suggests aspiration efficiencies of 0.949 and 0.876 and the logistic model suggests aspiration efficiencies of 0.960 and 0.901. In both equations (8) and (9), aspiration efficiencies are higher for these particle sizes (4 and 10 µm) than they are for the current ISO/CEN convention. The polynomial model forced through the intercept y = 1.0 [equation (8)] had the lowest RMSE, AIC, and BIC of the all-data models. Hsu and Swift also found a polynomial model to be a good fit for their data, though they used the natural log of aerodynamic diameter (Hsu and Swift, 1999). Equation (8) suggests aspiration efficiency reaches 0 when aerodynamic diameter is ~140.5 µm, just beyond the upper limit of the data (135 µm). Since no data points included in this investigation were for aerosols as large as ~140.5 µm it is difficult to say if a sampling cutoff here is appropriate. A sampler built to meet aspiration efficiencies suggested by equation (8) would capture a higher concentration of particles larger than 100 µm than equation (5) but less than equations (7) and (9). For smaller particles (<20 µm), equation (8) predicts higher aspiration efficiencies than equations (7) and (9). The current inhalable fraction definition says that the 50% cut point is 100 µm. This definition would change from a mathematical standpoint when considering low wind speed/calm air situations for the four equations discussed here. Aspiration efficiency is 50% (d50) for equations (5) (linear), (7) (simple decay), (8) (polynomial), and (9) (logistic) when aerodynamic diameters are ~62, ~53, ~58, and ~55 µm, respectively. In this way, a change in the inhalable convention for low wind speed/calm air conditions may, in turn, affect the thoracic and respirable convention definitions under these conditions since these fractions are currently based on the inhalable fraction. A simple solution to this potential problem is the possibility of separating out the respirable and thoracic fractions as standalone conventions such that they would no longer be mathematically dependent on the inhalable convention. When linear equations for nose and mouth breathing were determined separately, the slopes of the lines were different. The nose breathing slope [equation (10)] was steeper than the slope of the mouth breathing equation [equation (11)], indicating that mouth breathing aspiration efficiencies are generally higher than nose breathing. The slope of equation (5) (linear; all data) was between these two. Due to the higher aspiration efficiencies suggested by mouth breathing data, it would seem that a convention based on mouth breathing alone would be more protective of worker health (i.e. larger particles would be captured with greater efficiency and, therefore, less risk of exposure underestimation). However, the need for a convention representative of different breathing methods requires that nose and mouth data both are included. As would be expected, there appears to be a dose–response relationship related to the aspiration rate, whereby higher aspiration rates resulted in higher aspiration efficiencies. Equation (13), based on heavy breathing, resulted in the least steep slope (i.e. higher predicted aspiration efficiencies than moderate or light breathing). Differences among equations (11)–(15) show how variables besides aerodynamic diameter can influence aspiration efficiency and how complicated having one convention to represent all conditions can be. An alternative approach to the all-data models would be to have a sampling convention based only on specific parameters (i.e. a specific breathing rate, breathing method, and wind speed), although this introduces many of the same issues of the current convention. For example, when Brown (2005) developed a logistic function for oral inhalation, it was based on Stokes number and an assumed wind speed of 0.3 ms−1. The Aitken et al. (1999) equation is based only on moderate, mouth breathing aspiration efficiency data in calm air. Following the Aitken et al. equation as a guide, equation (16) is based only on moderate, mouth breathing data (although no specific wind speed was chosen). The coefficient is higher than that suggested by Aitken et al. (0.0038 versus 0.0068), which could be due to the different study designs from which data came. One strength of this study is that the data come from different studies, so aspiration efficiency was determined for a wide range of particle sizes, wind speeds, and breathing rates. This may also be a weakness, however, because methods used in each study to gather data were different (i.e. some studies used mannequins, some CFD, and others in vivo) and this has the potential to introduce biases. In addition to different methods of determining aspiration efficiency, different studies determined aerosol aerodynamic diameter and/or the reference concentration differently, which also could introduce biases. The reference concentration is particularly important as it directly affects the calculation of sampling efficiency and may result in large biases. Previous studies have used isokinetic sampling (Sleeth and Vincent, 2011), pseudo-isokinetic sampling (Aitken et al., 1999), or sedimentation cups (Breysse and Swift, 1990; Hsu and Swift, 1999; Dai et al., 2006) to determine the reference concentration. Unfortunately, it is not possible to determine the magnitude of these differences in the current work, but additional research would be useful to compare these various techniques. Unfortunately, only nine studies produced data that fit the inclusion criteria. However, it is best to keep in mind that, because of the many influential factors, one equation could not necessarily guide the production of a sampler capable of collecting aerosols in a way that is truly representative of an individual's exposure. Therefore, development of sampling conventions requires compromises be made. One of these compromises is that sampling conventions are typically based on an “average” case, which does not account for possible “worst-case” scenarios, for which the convention could underestimate exposure. With this understanding, equation (8) is suggested as a possible inhalable fraction convention recommendation for low wind/calm air environments. The polynomial model has the lowest RMSE, AIC, and BIC values of the equations fitted for all the data and forced through (0.0, 1.0). In this model, aspiration efficiency does eventually reach 0 (when extrapolated just beyond the data) and includes data for mouth, nose, and oronasal breathing. A bias map was also generated comparing equation (8) to the current ISO/CEN convention to investigate the possible magnitude of change based on using the new convention. As shown in Fig. 8, for a range of mass median aerodynamic diameters (MMAD; 1–100 µm) and geometric standard deviations (GSD; 2.0–4.0), the maximum bias (~56%) occurs for the largest particle sizes, with bias less than ~25% for all particle size distributions (and all GSDs) with MMAD less than ~75 µm. If a cutoff of ~140.5 µm is found to be inappropriate, then equation (9) would be an alternative. Equations (8) and (9) are graphed alongside the current ISO/CEN convention and Aitken et al. equation in Fig. 9. Figure 8. Open in new tabDownload slide Bias map comparing the polynomial model [equation (8)] to the current ISO/CEN convention for a range of possible particle size distributions. Figure 8. Open in new tabDownload slide Bias map comparing the polynomial model [equation (8)] to the current ISO/CEN convention for a range of possible particle size distributions. Figure 9. Open in new tabDownload slide Comparison of proposed calm air and low wind speed polynomial and logistic conventions to the current ISO/CEN convention (moving air) and the Aitken et al. equation (proposed calm air convention). Figure 9. Open in new tabDownload slide Comparison of proposed calm air and low wind speed polynomial and logistic conventions to the current ISO/CEN convention (moving air) and the Aitken et al. equation (proposed calm air convention). Conclusions The current ISO/CEN convention for the inhalable fraction did not address differences in particle inhalability for low wind/calm air conditions. To address this gap, data were gathered from nine studies and used to develop linear, exponential decay, polynomial, and logistic models representing aspiration efficiency under these conditions. The influence of different variables, such as aspiration rate and breathing method, on linear models was also investigated. Several empirical equations are presented in this paper, which could possibly be used as a low wind speed/calm air convention representative of the inhalable fraction. The polynomial model stands out because it had the lowest RMSE, AIC, and BIC values while meeting the requirements of going through (0.0, 1.0), getting aspiration efficiency closer to 0.0 with larger aerosols than the current convention, and including both mouth and nose data. Research is needed to determine if a cutoff of ~140.5 µm is appropriate and if the sampling convention for the thoracic and respirable fractions at low wind speeds and calm air need to be modified as well. Funding Funding for this project was provided in part by the National Institute for Occupational Safety and Health grant #T42OH008414 and by the University of Utah Department of Family and Preventive Medicine Health Studies Fund. Disclaimer One of the authors (D.S.) was Convenor of ISO TC 146/SC 2/WG 1 at the time the project was undertaken. The authors declare no other potential conflict of interest relating to the material presented in this article. Its contents, including any opinions and/or conclusions expressed, are solely those of the authors. Acknowledgement The authors would like to thank Dr Göran Lidén for his thoughtful discussion on this topic. References American Conference of Governmental Industrial Hygienists (ACGIH) . ( 2017 ) Threshold limit values and biological exposure indices . Cincinnati, OH : American Conference of Governmental Industrial Hygienists . Google Preview WorldCat COPAC American Industrial Hygiene Association (AIHA) . ( 2011 ) The occupational environment: its evaluation, control and management . Fairfax, VA: American Industrial Hygiene Association . Google Preview WorldCat COPAC Aitken RJ , Baldwin PEJ , Beaumont GC et al. ( 1999 ) Aerosol inhalability in low air movement environments . J Aerosol Sci ; 30 : 613 – 26 . Google Scholar Crossref Search ADS WorldCat Anderson KR , Anthony TR . ( 2014 ) Computational fluid dynamics investigation of human aspiration in low velocity air: orientation effects on nose-breathing simulations . Ann Occup Hyg ; 58 : 625 – 45 . Google Scholar PubMed WorldCat Anthony TR , Anderson KR . ( 2013 ) Computational fluid dynamics investigation of human aspiration in low-velocity air: orientation effects on mouth-breathing simulations . Ann Occup Hyg ; 57 : 740 – 57 . Google Scholar PubMed WorldCat Anthony TR , Anderson KR . ( 2015 ) An empirical model of human aspiration in low-velocity air using CFD investigations . J Occup Environ Hyg ; 12 : 245 – 55 . Google Scholar Crossref Search ADS PubMed WorldCat Armbruster L , Breuer H . ( 1982 ) Investigations into defining inhalable dust . Ann Occup Hyg ; 26 : 21 – 32 . Google Scholar PubMed WorldCat Baldwin PEJ , Maynard AD . ( 1998 ) A survey of wind speeds in indoor workplaces . Ann Occup Hyg ; 42 : 303 – 13 . Google Scholar Crossref Search ADS PubMed WorldCat Baron P . ( 2010 ) Aerosol 101: generation and behavior of airborne particles (Aerosols). Centers for Disease Control and Prevention . Available at https://www.cdc.gov/niosh/topics/aerosols/pdfs/Aerosol_101.pdf. Accessed 24 September 2019. Google Preview WorldCat COPAC Breysse PN , Swift DL . ( 1990 ) Inhalability of large particles into the human nasal passage: in vivo studies in still air . Aerosol Sci Technol ; 13 : 459 – 64 . Google Scholar Crossref Search ADS WorldCat Brown JS . ( 2005 ) Particle inhalability at low wind speeds . Inhal Toxicol ; 17 : 831 – 7 . Google Scholar Crossref Search ADS PubMed WorldCat Calvo AI , Alves C , Castro A et al. ( 2013 ) Research on aerosol sources and chemical composition: past, current and emerging issues . Atmos Res ; 120–121 : 1 – 28 . Google Scholar Crossref Search ADS WorldCat European Committee for Standardization (CEN) . ( 1992 ). EN 481. Workplace atmospheres: size fraction definitions for measurement of airborne particles in the workplace . Brussels, Belgium : CEN . Google Preview WorldCat COPAC Dai Y-T , Chang C-P , Tu L-J et al. ( 2007 ) Development of a Taiwanese head model for studying occupational particle exposure . Inhal Toxicol ; 19 : 383 – 92 . Google Scholar Crossref Search ADS PubMed WorldCat Dai Y-T , Juang Y-J , Wu Y-Y et al. ( 2006 ) In vivo measurements of inhalability of ultralarge aerosol particles in calm air by humans . J Aerosol Sci ; 37 : 967 – 73 . Google Scholar Crossref Search ADS WorldCat Douwes J , Thorne P , Pearce N et al. ( 2003 ) Bioaerosol health effects and exposure assessment: progress and prospects . Ann Occup Hyg ; 47 : 187 – 200 . Google Scholar PubMed WorldCat Hsu D-J , Swift DL . ( 1999 ) The measurements of human inhalability of ulatralarge aerosols in calm air using mannikins . J Aerosol Sci ; 30 : 1331 – 43 . Google Scholar Crossref Search ADS WorldCat International Organization for Standardization (ISO) . ( 1995 ). Air quality-particle size fraction definitions for health-related sampling, ISO 7708 . Geneva, Switzerland : ISO . Google Preview WorldCat COPAC Kennedy NJ , Hinds WC . ( 2002 ) Inhalability of large solid particles . J Aerosol Sci ; 33 : 237 – 55 . Google Scholar Crossref Search ADS WorldCat Lidén G , Harper M . ( 2006 ) The need for an international sampling convention for inhalable dust in calm air . J Occup Environ Hyg ; 3 : D94 – 101 . Google Scholar Crossref Search ADS PubMed WorldCat Lidén G , Kenny L . ( 1994 ) Erros in inhalable dust sampling for particles exceeding 100 µm . Ann Occup Hyg ; 38 : 373 – 84 . WorldCat Menache M , Miller F , Raabe O . ( 1995 ) Particle inhalability curves for humans and small laboratory animals . Ann Occup Hyg ; 39 : 317 – 28 . Google Scholar Crossref Search ADS PubMed WorldCat Ogden T , Birkett J . ( 1977 ) The human head as a dust sampler . Inhaled Part ; 4 : 93 – 105 . WorldCat Sleeth DK , Vincent JH . ( 2011 ) Proposed modification to the inhalable aerosol convention applicable to realistic workplace wind speeds . Ann Occup Hyg ; 55 : 476 – 84 . Google Scholar PubMed WorldCat Vincent JH . ( 2005 ) Health-related aerosol measurement: a review of existing sampling criteria and proposals for new ones . J Environ Monit ; 7 : 1037 – 53 . Google Scholar Crossref Search ADS PubMed WorldCat Vincent JH . ( 2007 ) Aerosol sampling: science, standards, instrumentation and applications . Chichester, UK: John Wiley . Google Preview WorldCat COPAC Vincent JH , Armbruster L . ( 1981 ) On the quantitative definition of the inhalability of airborne dust . Ann Occup Hyg ; 24 : 245 – 8 . Google Scholar PubMed WorldCat Vincent JH , Mark D . ( 1982 ) Applications of blunt sampler theory to the definition and measurement of inhalable dust . Ann Occup Hyg ; 26 : 3 – 19 . Google Scholar PubMed WorldCat Vincent J , Mark D , Miller B et al. ( 1990 ) Aerosol inhalability at higher windspeeds . J Aerosol Sci ; 21 : 577 – 86 . Google Scholar Crossref Search ADS WorldCat © The Author(s) 2019. Published by Oxford University Press on behalf of the British Occupational Hygiene Society. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model)
TI - Development of an Empirical Formula for Describing Human Inhalability of Airborne Particles at Low Wind Speeds and Calm Air
JO - Annals of Work Exposures and Health (formerly Annals Of Occupational Hygiene)
DO - 10.1093/annweh/wxz074
DA - 2019-11-13
UR - https://www.deepdyve.com/lp/oxford-university-press/development-of-an-empirical-formula-for-describing-human-inhalability-r00J59HmJ8
SP - 1046
VL - 63
IS - 9
DP - DeepDyve
ER -