# Modality of human expired aerosol size distributions

Author links open overlay panel

### Highlights

► We investigate the role of human expired aerosols in disease transmission. ► Three droplet size distribution modes were identified during speech and coughing. ► We present the number of droplets and volume of aerosol material for each mode. ► Results provide insight into expired aerosol generation process.

## Keywords

Human expired aerosol
B.L.O. tri-modal model
Size distribution
Modality
Bronchiolar
Laryngeal

## 1.Introduction

The need to obtain a comprehensive understanding of human expired aerosols across the entire range of droplet sizes has become an increasingly urgent issue over the past decade. Much of the focus in infection control in the past has been on maintaining a safe distance from infected subjects. This was based on an assumption that infection would require exposure to droplet transmission in which pathogen laden respiratory droplets are deposited directly on mucosal surfaces of the respiratory tract. Although a maximum distance for droplet transmission cannot readily be defined, a safe distance of 1 m was often assumed, based on simulations with specific organisms and epidemiological studies (Dick et al., 1987, Feigin et al., 1982). But even droplets as large as 30 μm can remain suspended in the air for extended periods (Cole & Cook, 1998), and airborne transmission has been unambiguously documented for Varicella (Leclair et al., 1980, Sawyer et al., 1994) and Measles (Chen et al., 1989, Ehresmann et al., 1995).

There is also mounting evidence that the 1 m rule should be questioned for a range of other diseases. Wong et al. (2004) found that proximity to an infected patient was associated with SARS transmission, with transmission appearing to occur over distances up to and well beyond 1 m so that transmission through small aerosols could not be ruled out. Airborne transmission can result from the dissemination of airborne droplets within the respirable size range (D50=4 μm) containing respiratory pathogens that remain viable and potentially infectious over time and distance (Siegel et al., 2007). Such droplets can be dispersed by air currents and may infect susceptible individuals who have had no direct contact with an infected person. Fabian et al. (2008) detected viral RNA in aerosols emitted from subjects infected with influenza A and B during tidal breathing suggesting that the fine particles emitted during tidal breathing may be an infection risk. Fennelly et al. (2004) identified Mycobacterium tuberculosis colonies on plates collecting respiratory aerosol droplets from TB subjects in the droplet size range 0.65–0.1 μm implying that breath aerosol could be capable of transporting this organism in viable form from infected subjects. Atkinson & Wein (2008) stated that “the rarity of close, unprotected and horizontally-directed sneezes—coupled with the evidence of significant aerosol and contact transmission for rhinovirus and our comparison of hazard rates for rhinovirus and influenza—lead them to suspect that aerosol transmission is the dominant mode of transmission for influenza”.

With this increasing emphasis on the question of airborne transmission, the need to understand the mechanisms of aerosol generation as well as the sites of origin within the respiratory tract and the proximity of those sites to regions of active infection is very evident. Previous studies, which have looked at this question, arrived at a variety of conclusions. Nicas et al. (2005) reviewed and compared the results of the particle size studies for coughing and sneezing by Duguid (1946), Loudon and Roberts, 1967a, Loudon and Roberts, 1967b and Papineni & Rosenthal (1997) and found substantial differences. It appears that the results of Papineni and Rosenthal suffered from insufficient measurement size range leading to an underestimate of the numbers of larger droplets. The work of Duguid applied a potentially incorrect evaporation correction and was not reported in enough detail for an appropriate adjustment to be retrospectively applied to the reported data. Duguid combined the data produced by different techniques without explaining or justifying the approach used to do so.

A further difficulty common to virtually all reports of expired droplet size distributions is the lack of a consistent rigorous approach to size distribution data presentation. Instead the data may be presented in tabulated form using arbitrary size classifications, which do not facilitate rigorous analysis and comparison. The need for a comprehensive understanding of human expired aerosol size distributions requires the adoption of a more rigorous approach to data collection and reporting. Such standards have already been established over many years by the aerosol research community.

In an effort to address each of the issues discussed above, investigations of the expired droplets were conducted using the Expired Droplet Investigation System (EDIS) (Morawska et al., 2009), applying two separate measurement techniques to cover the entire size range from 0.5 μm to 1 mm; the Aerodynamic Particle Sizer (APS, 0.5≤d≤20 μm and Droplet Deposition Analysis (DDA, 20≤d≤2000 μm).

Results obtained using the above methods are being published by the authors in separate manuscripts (Johnson and Morawska, 2009, Morawska et al., 2009), however the relationship between the measurements had not been examined in detail and no attempt had been made to combine the measurements to form a coherent view of the overall expired aerosol size distribution. The current paper integrates the APS and DDA based measurement results for speech and coughing aerosols to produce comprehensive size distributions for both types of expired aerosol. The modality of the size distributions is examined and its significance is discussed in terms of human expired aerosol research, epidemiological modeling, infection control and breath condensate analysis research.

## 2.Methods

Aerosol size distribution measurements were conducted using an Aerodynamic Particle Sizer APS and Droplet Deposition Analysis (DDA) in the EDIS. The EDIS is described in detail in a previous publication by the authors (Morawska et al., 2009), however the schematic diagram of the system from that publication is reproduced in Fig. 1. It is a small wind tunnel 0.5 m in diameter, into which a subject can comfortably insert their head. The wind tunnel includes a series of interchangeable, interlocking transparent modules. HEPA filtered air is propelled past the subject at a very low, controlled velocity. This particle free air carries the aerosol droplets emitted by the subject to instrument sampling inlets positioned at a set distance downwind. The EDIS operates at slightly higher than ambient pressure, ensuring that no ambient aerosol contaminates the sample. The average background EDIS airflow temperature and relative humidity during the measurements were 27±1 °C and 59±7%, respectively. The average expired aerosol sample temperature and relative humidity during the measurements were 28±1 °C and 90±7%, respectively.

The APS measures the aerodynamic diameter of particles in the diameter range 0.5–20 μm, and detects particles as small as 0.3 μm. The total inlet flow rate drawn by the instrument is 5 L min−1, which includes a 4 L min−1 sheath flow and a 1 L min−1 sample flow. The detection and sizing process in the APS takes less than 5 μs, however the time required for delivering the particles to the detection area is limited by the air velocity in, and length of the sample probe and delivery tube. The sample probe used with the APS in the EDIS consists of a 0.28 m length of copper tubing with an internal diameter of 0.0163 m. The probe tube enters the EDIS perpendicular to the direction of airflow, and is curved at its end through an angle of 90° (radius of curvature 0.08 m), so that the probes’ mouth faces upwind toward the volunteer. The delay between the sample entering the probe mouth and particle detection and sizing is around 0.7 s, which was sufficient for most droplets in the instrument size range to dry to their equilibrium size before measurement (Morawska et al., 2009).

The DDA measurements involved conducting stain size and droplet distribution measurements using discrete sampling points occupied by glass slides. The DDA measurements were conducted with the ducting open to ambient air at both ends and without the use of the EDIS airflow system. Although this exposes the deposition slides to ambient aerosol, repeated testing clearly showed that when an oral rinse containing a food dye was used by the volunteers, all recorded droplets were found to contain the dye. The lack of ambient aerosol contamination of the slides is explained by the fact that the DDA technique is insensitive at sizes smaller than 20 μm and the ambient aerosol concentration was relatively small at the sizes detectable by the DDA method. The slides were laid out in a sampling grid encompassing the lower inner surface of a section of the sampling duct. The droplet stains, remaining on the glass slides after droplets settled there, were measured and classified according to size and the number of droplets of each size per unit slide surface area was calculated at each slide location.

The resulting droplet-deposition-density data points were interpolated radially and longitudinally over the interior cylindrical duct surface within the sampling grid. The resulting continuous droplet deposition field was then integrated over the grid area to obtain the total droplet concentration for each size class. The droplet number size distribution values were divided by the log of the droplet size class interval to obtain the number size distribution as dN/d Log D. This was then divided by the total volume of air exhaled to obtain the number concentration size distribution d Cn/d Log D. The total volume of air exhaled was estimated using the sampling duration and the average adult tidal volume ventilation rate (Sidebotham et al., 2007) (“minute ventilation”) of 7.5 Lpm.

During the course of the campaign, slightly different respiratory maneuver protocols were adopted for the DDA measurements and the APS measurements. This difference was necessary because the DDA measurements focus on a region of the size distribution where although droplet mass is large, the numbers of droplets may be extremely small, necessitating long sampling times in order to acquire a statistically significant number of droplets in each size class. In contrast to the situation for DDA, droplets in the APS range are relatively plentiful. For cough emission sampling using DDA, the volunteers were asked to cough 50 times in each test. This large number of coughs necessitated that the volunteers be permitted to drink water whenever they wished during the test to prevent drying out of the upper respiratory tract and to maintain comfort. This is thought to have had little effect for the larger droplet sizes targeted by DDA because large droplets exhibit much slower evaporative diameter shrinkage. However dilution of the natural respiratory tract lining fluid by water will certainly reduce the potential size of the droplet nuclei measured by the APS, so no such fluid intake could be permitted during the APS measurements. The larger droplet number concentrations in the APS droplet size range readily accommodated a reduced sampling time, so to maintain volunteer comfort and a productive cough, the test duration for coughing was reduced to 30 s in the APS measurements. The volunteers were asked to cough naturally by their own estimation, and as many times as they could without significant discomfort, within the 30 s period.

All volunteers were recruited via a broadcast email invitation with a small financial reward. The volunteers were university students and postgraduate research students, all of whom were under 35 years of age. People who were experiencing illness, who had recently experienced respiratory problems, or who felt they were likely to experience discomfort in confined spaces were excluded. The pool of volunteers consisted of fifteen individuals. The APS measurements included all fifteen volunteers (nine females and six males). The DDA group included eight volunteers (six females and two males). This variation in the size and makeup of the groups tested is not ideal but the combination of these two data sets was considered suitable for the purposes of exploring the modality of the size distribution and for deriving a basic model of the size distribution and generation process.

### 2.1.Combining the size distributions

Composite size distributions were produced by combining the APS and DDA droplet number size distribution data sets after transformation onto a common scaling d Cn/d Log D. Here Cn denotes the concentration expressed in cm−3 and D is the particle diameter expressed in μm.

In constructing the size distribution segments for the two different measurement techniques, average particle detection frequencies for each diameter class were calculated using all available measurements across all volunteers. The number count data for individual measurements was typically very low, so that a zero particle count was frequently recorded in many of the larger size classes. Therefore in order to obtain a more nearly normal probability distribution, a square root transformation was applied to the data prior to calculating means and determining confidence intervals. Hence, except where otherwise stated, all count data manipulations including averaging and calculation of 95% confidence intervals have been performed using square root transformed data. All results are presented on the original scale through the subsequent application of an inverse transformation (squaring the result).

The resulting size distributions are considered to be representative for this group of healthy volunteers. They are not intended to be predictive of emissions for a single healthy volunteer because inter-volunteer and within-volunteer variability is very large, typically of the order of measured concentration itself or greater.

### 2.2.Overview of corrections to the measurements

In order to correctly represent the size distribution at the point of origin (the volunteer's mouth) the size distribution data obtained with both measurement techniques require corrections. These corrections are described below.

#### 2.2.1.APS data corrections

Due to their small size and the time delay between emission and measurement, droplets measured by the APS evaporate to equilibrium before sizing (Morawska et al., 2009). To estimate the initial size of the aerosol at the mouth, the aerosol detected by the APS was assumed to have evaporated to an equilibrium diameter of Deq=EF×D0 where D0 is the initial droplet size, and EF is the diameter evaporative shrinkage factor. Some degree of variation in the value of the EF with relative humidity is expected due to the presence of hygroscopic salts such as NaCl in the respiratory fluid, however for the current study we have used a value of 0.5 as adopted by Nicas et al. (2005). This value is now supported by an experimental study by Holmgren et al. (2011). The size distribution and the BLO model, which we develop here, can be adjusted using a more accurate value of this EF should it become available.

The APS data also require correction of the aerosol number concentration in order to account for sample dilution by entrained air. Average APS sample dilution factors (DF), relating the concentration in the sample to that at the source (which was taken to be the volunteers' upper respiratory tract), were calculated for speech and coughing. These were based on continuous measurements of the water vapor concentration in the aerosol sample and in the EDIS airflow, taking into account the fixed water vapor concentration in the respiratory tract according to the method described by Morawska et al. (2009).

The manufacturer claims in their specifications for the APS that the concentration accuracy is ±10%, however it should be noted that the counting efficiency of the APS may decrease with particle size for diameters smaller than 9 μm (Armendariz & Leith, 2002). We do not attempt to correct the data for losses in the sampling system or for nonlinearity in the response of the APS. Such correction would of course alter the size distributions and potentially the mode locations to a small extent.

#### 2.2.2.DDA data corrections

In the case of the DDA measurements, the aerosol size distribution was determined from stains left after the droplets settled onto the glass slides. The settling times depend strongly on the initial droplet size. The largest droplets have the greatest settling velocity but also undergo the slowest rates of relative diameter change due to evaporation. The settling time for droplets with diameters of 20 μm or smaller exceeds the time taken to dry to the equilibrium diameter and this equilibration time decreases rapidly with droplet size. Droplets smaller than 20 μm therefore remain airborne long enough to be dispersed by ambient air currents such that large numbers leave the deposition sampling area before settling. Therefore 20 μm was considered to be the lower limit for DDA sampling.

The process of droplet spreading results in stains, which are larger in diameter than the airborne droplets that produce them. When aqueous solution droplets settle onto a surface, they spread to an extent, which depends on the impaction velocity, the surface tension of the droplet liquid and the hydrophilic/phobic properties of the surface onto which they settle. This spreading can be represented by a spread factor (β) defined as the ratio of the resulting stain diameter to that of the original droplet during flight.

### 2.3.Calculation of volume size distributions

The volume and mass size distributions can be calculated from the number size distribution provided the geometry and density of the particles are known. For the cases considered here it is assumed that the particles are spherical and have unit density. The first of these assumptions is reasonable for respiratory aerosol particles of all sizes, whether measured as dry residue or liquid droplets, because each begins as a fluid droplet in which the geometry is determined by surface tension forces. The second assumption is also a good approximation because the composition of the dry residue particles and of the larger droplets is dominated by water and/or organic solutes of similar density, with only minor contributions from higher density components such as inorganic salts.

## 3.Results and discussion

The dependence of the expired aerosol size distribution within the APS range on the type of expiratory maneuver is illustrated in Fig. 2. We have restricted the size distribution to the APS range in order to focus on important aspects of the modality in that range. The APS measurement method is less labor intensive than the DDA approach and this facilitated the examination of a wider range of activities to highlight somewhat subtle but important effects of vocalization and coughing on the size distribution modality. As will be discussed later, these effects are important because of their implications concerning the source regions involved.

The figure shows the mean measured size distribution in the APS size range for (a) breathing, (b) speech, (c) sustained vocalization and (d) coughing. These respiratory maneuvers are defined in Table 1. Note that many young volunteers do not produce significant breath aerosol during tidal breathing, so for the purpose of illustration here, the breathing maneuver was purposely designed to enhance breath aerosol production by including deep exhalation breathing. It is also important to note that the data have not yet been corrected for dilution, which affects the overall concentration, or for evaporation, which affects the droplet size.

Table 1. Respiratory maneuvers.

Maneuver Label Description
(a) Breathing b-3-3 Inhaling a normal breath volume via the mouth over a 3 s period, followed immediately by a 3 s full, deep exhalation via the mouth over a 3 s period. Repeated for 2 min
(b) Speech c-v Alternately 10 s of voiced counting and 10 s of naturally paced breathing (2 min sample)
(a) Sustained vocalization aah-v Alternately 10 s of un-modulated vocalization (voiced “aah”) and 10 s of naturally paced breathing (2 min sample). Mouth open throughout
(b) Coughing cough Coughing at an intensity and frequency, which the volunteer felt comfortable with. In practice, for most volunteers, the resulting cough intensity can be best described as a mild throat clearing cough (30 s sample)
(c) Bypass bp The volunteer positioned their head to one side and slightly forward of the sample probe so that the expired air was not directly sampled

In order to indicate the level of the background, each graph includes the size distribution obtained for the bypass maneuver. This size distribution was obtained with the volunteers' heads positioned to one side of the sample inlet so that no aerosol from the subjects' mouths could directly enter the inlet.

Also shown are the upper and lower 95% confidence intervals for the size distribution and a smoothed representation obtained by performing a 5 point adjacent average smoothing. No confidence interval is shown for the bypass maneuvers because in those tests, few channels returned a non-zero count, and those that did, produced very low counts. The graphs also include a number of fitted lognormal curves, which will be discussed in detail in the subsequent section on modality.

Fig. 3 again presents the size distributions for the speech and cough aerosols, but this time the range has been extended to include the data obtained using the DDA method. The figure includes four graphs, a–d; where a and b, respectively, show the size distribution for speech before and after applying a series of corrections to the data; while c and d show the same for cough. The corrections account for dilution and evaporation in the APS data and droplet spreading in the DDA data. These will be discussed later.

### 3.1.Modality of the composite size distributions and its physical significance

#### 3.1.1.Modality in the APS range—the B and L modes

The aerosol number size distribution shown in Fig. 2a is an example of a breath or breathing aerosol. Breath aerosols have been investigated in detail by co-authors Johnson and Morawska and shown to be dominated by a single mode in the APS size range as can also be seen in Fig. 2a. This aerosol is produced in the respiratory bronchioles in the early stages of inhalation. The resulting aerosol is drawn into the alveoli and held before exhalation. This mechanism was dubbed the bronchiolar fluid film burst (BFFB) mechanism (Johnson & Morawska, 2009) and the corresponding size distribution mode will be referred to as the BFFB mode or simply the B mode. These findings concerning the mechanism and modality have been subsequently confirmed by others (Almstrand et al., 2010), although there is some disagreement on the count median diameter (CMD) of the B mode.

The intensity of the B mode increases strongly with the depth of exhalation because deeper exhalation results in the closure of greater numbers of respiratory bronchioles. As discussed in the aforementioned publications, it is the opening of these fluid closures on the subsequent inhalation phase of breathing that produces the B mode aerosol. Furthermore, because B mode particles are generated during the inhalation phase of breathing, the CMD of the mode displays an inverse relationship to the duration of breath holding, because particles are lost from the large diameter side of the mode through gravitational settling in the alveoli while the aerosol remains in the alveoli. Hence the exhaled concentration in the B mode typically increases by a factor of 12 for healthy volunteers when the breathing pattern is changed from tidal breathing to deep exhalation breathing. When the breath holding period is increased to 10 s the CMD of the B mode decreases by 20–30%. A large variation is therefore to be expected in the B mode concentration and CMD in different respiratory maneuvers. The shift to smaller diameters also has the effect of reducing the apparent GSD of the mode when measured by the APS, because the detection efficiency of the APS begins to decline below 0.9 μm, which is approaching the lower limit of the instrument range (Armendariz & Leith, 2002).

We have represented the B mode aerosol by a single lognormal mode. The mode, represented by the dashed curve, was fitted to the smoothed b-3-3 breathing aerosol size distribution in Fig. 2a. The fitting algorithm was allowed to converge freely without fixing the count median diameter (CMD), geometric standard deviation (GSD) or concentration (Cn) associated with the mode and the single lognormal mode fit achieved an R2 value of 0.9991 with respect to the smoothed curve. The portion of the mode lying within the measurement range is indicated by the continuous dark line.

The aerosol size distribution for speaking, shown in Fig. 2b, has additional modal structure beyond the B mode due to the vocalization process. We have represented this by another lognormal mode. To generate the overall bimodal lognormal fitting the fitting algorithm was allowed to converge freely to the smoothed APS data without fixing the CMD, GSD or the Cn values of either of the two modes. The resulting bimodal lognormal mode fit achieved an R2 value of 0.9992 with respect to the smoothed APS data. The portion of the bimodal fit lying within the measurement range is indicated by the continuous dark line.

The source of the extra lognormal mode was examined further by simplifying the vocalization to remove any effect due to the mouth movements associated with speech articulation, while emphasizing the vibrations of the vocal folds in the larynx. The maneuver chosen for this was a repeating, monotone, sustained, vocalization without any mouth closures. This is denoted as aah-v in Table 1. The size distribution for aah-v is shown in Fig. 2c. The additional mode is clearly much more pronounced in this case clearly linking the appearance of the mode to the vocal fold vibrations associated with voicing. As in the previous case we have represented the vocalization aerosol by an additional lognormal mode, which we have called the laryngeal or L mode. We have avoided calling this a voice mode because as will be seen a second mode in the APS range is also produced during coughing, a process that also involves energetic activity at the larynx and this mode has a similar GSD to the L mode in vocalized maneuvers, although the CMD is smaller.

Once again, to generate the overall bimodal lognormal fitting to the aah-v data, the fitting algorithm was allowed to converge freely with the smoothed APS data without fixing the CMD, GSD or the Cn values of either of the two modes. The resulting bimodal lognormal mode fit in this case achieved an R2 value of 0.9995 with respect to the smoothed APS data. The portion of the bimodal fit lying within the measurement range is again indicated by the continuous dark line.

The size distribution of the voluntary-cough maneuver shown in Fig. 2d again shows broadening, which we attribute to an L mode but at reduced CMD. The same free fitting procedure was again used, in this case resulting in an R2 value of 0.9992.

#### 3.1.2.Modality in the DDA range—the O mode

Inclusion of the uncorrected DDA data in Fig. 3a and c shows that the size distribution for speech and coughing in the DDA size range is well represented by a third lognormal mode. The single lognormal mode fitted to the smoothed version of the DDA data is represented by the dot-dash curve. The fitting algorithm was again allowed to converge freely without fixing the CMD, GSD or Cn associated with the mode and the single lognormal mode fit achieved an R2 value of 0.9992 with respect to the smoothed data.

The third mode contains all aerosol detected in the DDA range. In a separate experiment, droplets of this aerosol collected on glass slides and examined using a microscope always showed evidence of the food dye introduced to the test volunteers' saliva in an oral rinse. Hence it is clear that these larger droplets were produced exclusively in the region of the respiratory tract where saliva is present and hence between the lips and the epiglottis and is therefore referred to as the Oral or O Mode.

#### 3.1.3.The B.L.O. model for speaking and coughing in HVs

The BLO tri-modal models of the aerosol concentration size distributions for speaking and coughing are summarized by Eq. (1) in conjunction with Table 2 and the correction factors listed in Table 3.

Table 2. Model parameters for aerosols produced by healthy volunteers during speaking and coughing. DF=APS sample dilution factor. EF=APS sample evaporative diameter shrinkage factor. SF=DDA droplet spread factor.

i 1 2 3
(B mode) (L mode) (O mode)
Mean SE (%) Mean SE (%) Mean SE (%)
Speaking
Cni (cm−3) 0.015×DF 16 0.019×DF 15 0.00126 0.8
CMDi (μm) 0.807/EF 0.45 1.2/EF 8.1 217/SF 0.5
GSDi 1.30 1.3 1.66 3.1 1.795 0.5
Coughing
Cni (cm−3) 0.021×DF 9 0.033×DF 8 0.01596 0.6
CMDi (μm) 0.784/EF 0.61 0.8/EF 2.9 185/SF 0.4
GSDi 1.25 0.8 1.68 1.5 1.837 0.4

Table 3. Parameter correction factors: DF=APS sample dilution. EF=APS sample evaporative diameter shrinkage. SF=DDA droplet diameter spreading on slide surface.

Correction Speaking Coughing
DF (APS) 3.6 4.3
EF (APS) 0.5 0.5
SF (DDI) 1.5 1.5

The DF values for speech and coughing, determined by the method discussed earlier, are listed in Table 3. An evaporative diameter shrinkage factor (EF) for the APS samples is also included in the table. This is based on the publications by Nicas et al. and Holmgren et al. as described earlier. A diameter spread factor (SF) value of 1.5 was chosen to recover the original droplet sizes from the DDA stain diameters. This value was chosen to fall midway within the expected range discussed in Section 2.2.2. The fully corrected measurements and the corresponding BLO models are presented in Fig. 3b and d.

Naturally, given that only healthy adult volunteers were tested in these studies, the size distribution of the emitted aerosol and the sites of origin and mechanisms described cannot be assumed to hold for those suffering from respiratory disease.

BLO tri-modal model:(1)$\frac{\mathrm{d}\phantom{\rule{.1em}{0ex}}\text{Cn}}{\mathrm{d}\phantom{\rule{.1em}{0ex}}\mathrm{Log}\phantom{\rule{.1em}{0ex}}D}=\mathrm{ln}\left(10\right)×\sum _{i=1}^{3}\left(\frac{{\text{Cn}}_{i}}{\sqrt{2\mathrm{\pi }}\mathrm{ln}\left({\text{GSD}}_{i}\right)}\right)\mathrm{exp}\left(-\frac{{\left(\mathrm{ln}\phantom{\rule{.1em}{0ex}}D-\mathrm{ln}\phantom{\rule{.1em}{0ex}}{\text{CMD}}_{i}\right)}^{2}}{2{\left(\mathrm{ln}\phantom{\rule{.1em}{0ex}}{\text{GSD}}_{i}\right)}^{2}}\right),\phantom{\rule{1em}{0ex}}0.8\phantom{\rule{.1em}{0ex}}\mathrm{\mu }\mathrm{m}\le D\le 1000\phantom{\rule{.1em}{0ex}}\mathrm{\mu }\mathrm{m}$The three modes discussed above are also reflected in the volume size distributions and these can be readily calculated using the BLO model. Fig. 4 shows the cumulative number and volume concentration size distributions for speaking and voluntary coughing. These can be used to estimate concentrations within any sub-range of the distributions.

The total numbers and volume or mass of particles within the individual modes can be resolved by integrating the B, L and O modes individually. The number and mass concentrations, for the three modes, corrected according to Table 3, and determined from the area under the number and volume size distribution modes are summarized in Table 4. The droplets have been assumed to be spherical and to have a density of 1 g cm−3 for the reasons discussed earlier.

Table 4. Number and mass concentrations associated with the three modes. The first value in each cell is the concentration within the measurement range. The second value in italics is the concentration obtained if the mode is extrapolated beyond the measured range in both directions. The corrections in Table 3 have been applied to the parameters in Table 2 to produce these values.

i 1 2 3 Sum
(B mode) (L mode) (O mode) (B+L+O)
Speaking
Cni (cm−3) 0.069/0.069 0.085/0.086 0.001/0.001 0.16/0.16
CMDi (μm) 1.6 2.5 145 N/A
Cmi (μg m−3) 0.21/0.21 2.2/2.2 7500/9300 7500/9300
MMDi (μm) 2 5.4 404 N/A
Coughing
Cni (cm−3) 0.087/0.087 0.12/0.13 0.016/0.016 0.22/0.24
CMDi (μm) 1.6 1.7 123 N/A
Cmi (μg m−3) 0.22/0.22 1.09/1.09 69,000/83,000 69,000/83,000
MMDi (μm) 1.8 3.8 374 N/A

Assuming spherical droplets with the density of water.

In determining the volume of droplet material associated with each mode, the likely existence of larger droplets outside the measurement range should be considered. The existence of such droplets can be inferred by extrapolation of the fitted mode beyond the measured range. Nevertheless droplet production at sizes exceeding 1 mm is likely to be a rare event and there are physical limitations on the amount of fluid, which can be expelled from the mouth in individual drops. Physically the lognormal mode must be truncated at a limit not much larger than a few millimeters because although larger drops of fluid or catarrh can be expelled from the throat, the process of producing these large globules differs somewhat from a normal cough. Nevertheless the experimental range and the extrapolated values are both included in the table for comparison.

### 3.2.Comparison with other published data

Fig. 5a shows the number size distributions obtained in the current study for speaking compared with those based on the results of studies by Duguid (1946), Loudon and Roberts, 1967a, Loudon and Roberts, 1967b and Papineni & Rosenthal (1997). Also shown are recent results obtained for tidal breathing in a study by Almstrand et al. (2010) using an optical particle counter. That study confirmed our earlier finding that the BFFB (Johnson & Morawska, 2009) mechanism is responsible for aerosol formed during breathing.

Papineni and Rosenthal reported detailed concentration data for speech for only one volunteer (in graphical form) and this volunteer was the lowest emitter for speech (though highest for cough) of 5 volunteers tested, emitting less than one quarter of the concentration reported for the other volunteers.

Note that the data of Papineni and Rosenthal, and those of Almstrand are not corrected for evaporation and such a correction would shift them to larger values. Note also that both Amstrand et al. and Papineni and Rosenthal obtained their results using optical particle counters (OPCs). The accuracy of this method depends strongly on the optical properties of the aerosol droplets and these instruments are typically calibrated using standard polystyrene latex spheres, which have different optical properties and structures to respiratory aerosol where the particles may be multiphase mixture of different species. It has previously been shown that the sizing accuracy of the OPC technique can be in error by up to a factor of 2 if the device is not calibrated for the specific aerosol being measured (Liu and Daum, 2000, Pinnick et al., 2000).

Duguid reported size distribution data (presumably for a single volunteer) as average numbers of droplets registered in each size class when speaking 100 words by counting loudly. For the purposes of the current comparison a conversion of Duguid's particle count data to concentration was achieved by assuming that counting occurred at a rate of 2 words per second and the total volume of air exhaled was then estimated as 625 mL based on an average adult tidal volume ventilation rate (Sidebotham et al., 2007) of 7.5 Lpm.

Louden and Roberts reported the overall total number of droplets in size classes for a total of three volunteers during talking where each volunteer counted loudly from 1 to 100 twice. For the purposes of the current comparison a conversion of Louden and Roberts droplet count data to concentration was performed by again assuming that speech occurred at a rate of two words per second so that counting occurred at a rate of approximately one number per second (e.g. the number “twenty seven” is counted as two words). The total time was therefore assumed to be 600 s and the total volume of air exhaled was then estimated as 75 L based on an average adult tidal volume ventilation rate (Sidebotham et al., 2007) of 7.5 Lpm.

As was also explained by Nicas, Duguid greatly overestimated the adjustment required to allow for evaporation of the smaller droplets, which are most affected by evaporation in his measurements, but Duguid did not say which of his data points had been so adjusted. A correction factor of 4 was used by Duguid but a more realistic factor would be 2 according to Nicas so the mode near 10 μm in Duguid's result might be shifted considerably toward smaller diameters independently of the larger droplet component of the size distribution although the exact diameter below which this should occur cannot be discerned from the information provided in Duguid's manuscript.

Fig. 5b shows the number size distributions obtained in the current study for coughing compared with those based on the results of other studies. The data of Duguid, of Louden and Roberts and of Papineni and Rosenthal have been scaled using the average cough exhalation volume of 1400 mL reported by Zhu et al. (2006). As was pointed out by Nicas et al. (2005), Duguid's (1946) results for coughing are an order of magnitude higher than several other studies including those by Louden and Roberts. Again, the mode at 11 μm in Duguid's size distribution should be shifted to much smaller diameters to correct for Duguid's overcompensation for evaporation making the size distribution more obviously bimodal and bringing it more into line with that obtained in the current study and those of Loudon and Roberts, 1967a, Loudon and Roberts, 1967b and Papineni & Rosenthal (1997).

Again, Papineni and Rosenthal used an OPC to obtain their data and their results are therefore subject to a very significant sizing inaccuracy but the concentrations and approximate form of the size distribution is expected to be representative allowing for this unknown shift in particle size. Their results are also uncorrected for evaporation and such a correction would further increase the diameters.

#### 3.2.1.Implications and conclusions

The modality of the aerosols and the association of the modes with specific source regions, together show that the collection of aerosol samples for the purpose of assessing the concentration of substances originating from specific regions of the respiratory tract can be designed to target specific source regions. This could be achieved using size specific collection methods and by choosing respiratory maneuvers designed to emphasize specific modes. Such measurements might assess viral loadings for the purpose of investigating or modeling modes of infection transmission such as droplet spray and airborne droplet transmission. Measurements might also be performed to more effectively assess the presence and concentration of materials produced through gene expression associated with pathological changes in the lung.

Epidemiological modeling studies utilizing detailed size distribution data such as those presented here can be designed to make full use of the entire human expired aerosol volume size distribution and its associated modality for the cough and speech activity aerosols presented here. If specific viral loadings for each droplet size distribution mode (i.e. B, L and O) can be determined, these too can be included in such modeling in combination with existing models of particle deposition efficiency versus particle size in the respiratory tract.

Significant variation of viral loading with the aerosol source region is likely, because pathogens tend to colonize specific regions of the respiratory tract and because the ratio of tissue surface to respiratory tract lining fluid volume varies throughout the respiratory tract. Another important parameter to be included is the viral strain specific infectivity of different regions of the respiratory tract based on emerging knowledge of the distribution of key proteins in the cell surface required for viral attachment (Shinya et al., 2006, van Riel et al., 2007).

In principle the model parameters given in Table 2 and the corrections in Table 3 allow particle number and volume emission rate size distributions and total emission fluxes for healthy volunteers to be estimated on a mode by mode basis or across all sizes. The particle number (or mass) concentration size distributions for each mode can be reproduced by inserting the corresponding parameters for the modes into separate lognormal size distribution functions. The complete composite distribution function is then the sum of these functions. A factor equal to the average exhalation rate during the maneuver will convert such a concentration size distribution function to an emission rate size distribution function. The particle number or volume emission rate size distribution function can in turn be integrated across particle size to obtain the total number and volume production rates (fluxes) within any size range.

Hence the B.L.O. model provides an improved basis for estimating parameters needed for improving our epidemiological modeling of influenza epidemics. Droplet number and droplet volume production rates can be estimated for each aerosol size distribution mode during speech and coughing and these can then be coupled with models of transport in realistic environments. The distributions will also provide a basis for devising experiments to measure parameters for those models such as pathogen concentrations in the different respiratory fluids comprising each mode, and the inactivation rates of those pathogens in the aerosol phase.

## Acknowledgments

This work was supported by the Australian Research Council under Grant DP0558410 and a QUT IHBI ECR Grant (2009).

## References

Empty content. Please select category to preview