Three key events occur during an inhalation exposure, which depend on the density and dimensions of EMPs, and relate the estimated dose to health outcomes. First, during inhalation of EMPs, the inertia of inhaled EMPs may prevent transport of all airborne EMPs into the oral and nasal cavities. The inertial effects are different for spherical particles and EMPs and thus, so is their inhalability or inhaled fraction. Second, the transport and deposition of EMPs in the airways of the respiratory tract are directly related to their geometry (dimensions) and aerodynamic behavior (i.e., the particle geometry interacting with the airflow which is dictated by ventilation rate and anatomy). Volumetric flow is different in each major area of the respiratory tract with bulk flow dominating in the upper respiratory tract (URT) and the tracheobronchial (TB), and is also influenced by breathing mode (i.e., nasal or oral breathing). Impaction and interception dominate in these regions. Other external forces due to gravity, electrostatic charges, and diffusion also dictate the transport and deposition in the airways. These forces are different for EMPs and spherical particles and so will be their deposition pattern and amount deposited on airway surfaces. In addition, the net hydrodynamic viscous resistance force between the EMPs and air influences the position and orientation of EMPs in the airflow and thus transport and deposition. Consequently, the deposited dose of particles and EMPs are different even when particle mass and airborne concentration are the same. Finally, clearance of the deposited spherical particles and EMPs are different particularly in the lower respiratory tract (LRT). The retained dose in both the TB and PU regions is influenced by the shape and dimensions of deposited insoluble particles. For example, the increased dimensions (length and diameters) of EMPs may influence their dissolution rate or their ability to translocate into the interstitial space, and may also alter the capability of alveolar macrophages to engulf and remove EMPs from the lungs. These three independent events (inhalation, deposition and clearance) act collectively to formulate the fate of inhaled particles and EMPs and thus their potential health impact upon inhalation. Thus, more inclusive sizing criteria as a function of key parameters of EMPs characteristics are necessary to distinguish toxic versus non-toxic doses of EMPs and other high-aspect ratio particles (Vincent, 2005; Dement et al., 2015).

Inhalability of particles is defined as the fraction of EMP being inhaled, which depends on their ability to reach and enter the URT (Fig. 1). Inhalation creates a directed mass flow of airborne particles in the vicinity of facial region toward the nasal or oral openings. Particle momentum increases and reaches inhaled air velocity as they approach the URT. When approaching the URT, large particles with high inertia may not be able to follow the flow streamlines as they turn to enter the nasal airways. These particles are deposited on the neighboring surfaces such as the face and will escape entry to the respiratory tract. The fraction that overcomes the inertia and enter the URT is the inhaled fraction of particle. Correction for particle inhalability is required for accurate sampling and assessment of internal dose of airborne particles.

The majority of studies on particle inhalability under different environmental conditions (corresponding to high, low, and no wind speed) are conducted under controlled laboratory conditions and often with manikins in wind tunnels (Armbruster and Breuer, 1982; Hinds and Tatyan, 1998; Kennedy and Hinds, 2002; Ogden and Birkett, 1977; Vincent and Mark, 1982; Aitken et al., 1999; Breyess and Swift, 1990; Hsu and Swift, 1999). Modeling studies using computational fluid dynamics (CFD) have been performed to develop predictive models for particle inhalability (Anthony and Flynn, 2006). While there is an extensive database on the inhalability of (spherical) particles, there are no experimental or modeling studies on non-spherical particles and EMPs. Such studies are needed to refine extant particle and fiber models given the potential enhanced toxic effect of EMPs due to their shape. Distinct differences in geometry are expected to produce a significant difference in inhalability profile between particles and EMPs.

A hybrid approach is adopted to develop a model to predict the inhalability of EMPs. The database on particle inhalability as noted above was used to develop semi-empirical relationships between inhalability and parameters on which it depended. The majority of existing studies related inhalability to particle diameter. However, inhalability is better described in terms of particle inertia represented by the non-dimensional parameter Stokes number (the ratio of kinetic energy of particles to the work done on particles to bring them to a complete halt), which is the dominant parameter dictating entrance into the URT. To extend to EMPs, particle Stokes number was replaced by that for EMPs in the inhalability component of MPPD for spherical particles. Consequently, particle diameter was replaced with an equivalent impaction diameter (Yu et al., 1986) to obtain a semi-empirical relationship for inhalability as a function of its inertia. Equivalent diameter for each deposition mechanism (e.g., impaction) is the diameter of an equivalent sphere which results in the same amount of deposition as EMPs. The model was subsequently used to predict the inhaled fraction for different size EMPs and different breathing modes (nasal or oral) of inhalation.

Fig. 2 gives the inhaled fraction EMPs in humans and rats as a function of calculated equivalent impaction diameter (d_ei) using the MPPD model, v. 3.04 (ARA, Inc, 2015). Calculation of a d_ei relies on the premise that an equivalent sphere diameter is used to predict inhaled and deposited fractions of EMPs. At an equivalent impaction diameter, both spherical particles and EMPs would have the same inertia, which is represented by the Stokes number. Yu et al. (1986) derived expressions for impaction diameter by equating the Stokes number of particles and EMPs. (1)deidf=(ρρ0C¯)1/2β1.3 where d_f is the EMP minor diameter, β is the EMP aspect ratio, c¯ is the orientation effect, and ρ and ρ₀ are the EMP density and unit density, respectively. Predicted inhalation fractions (IFs) were in good agreement with reported measurements of impaction diameter (Burke and Esmen, 1978; Khan, 1982).

Predictions were based on ventilation rates associated with a light activity pattern, which was 20 m³/d in humans and 0.62 m³/d in rats and simulating calm wind conditions. The inhaled fractions in humans were calculated for oral and nasal breathing modes. Inhaled fraction decreased with increasing EMP size. All EMPs were inhalable in humans for d_ei under 10 μm. Inhalability decreased for larger-diameter EMPs and more significantly for nasal breathing than for oral breathing. EMPs of length longer than 20 μm did not enter the nasal passages and were not inhaled, in contrast to oral breathing, where EMPs as long as 1 μm were still inhalable (inhaled fraction around 10%). Rats are obligate nasal breathers and thus the results in Fig. 1 represent nasal breathing for that species. Inhalability in rats was much lower than for humans because of smaller nasal geometry and significantly lower ventilation rates. EMPs as small as 0.1 μm in minor diameter were partially inhalable (about 98%). Inhalability drops much faster with increased particle size in rats than in humans. About 90% of EMPs are inhalable at d_ei of 1 μm but only about 10% at 10 μm d_ei. Lower number or mass of EMPs entering the respiratory tract of rats compared to that of humans, emphasizes the need for equivalent and not equal exposure scenarios to inflict similar biological outcomes. The difference in inhalability increases significantly for coarse aerosols. Thus, differences in inhalability in humans and rats must be taken into account in extrapolation of dose and response data from rodent inhalation studies to humans. Rat-to-human data extrapolation will be irrelevant regardless of exposure concentration when inhalability in rats drops to zero.

Inhaled fraction of a theoretical EMP aerosol was calculated and plotted against the minor diameter to examine the effect of shape and dimensions on inhalability. EMPs had volume-equivalent spherical diameters (d_ev) of 10 μm and 100 μm with different physical dimensions, which varied from a long and thin to short and thick until reaching spherical geometry (Fig. 3A). Using calm wind conditions, a typical tidal volume of 625 cm³, a breathing frequency of 12 breaths per minute (BPM), and a functional residual capacity (FRC) of 3300 cm³ via nasal breathing for the simulations, the predicted inhaled fraction of 100 μm d_ev EMPs was considerably lower than that of the 10 μm d_ev EMPs (Fig. 3B). Inhalability also decreased as the shape of EMPs changed, i.e., as they became shorter and thicker. Particle geometry was spherical when the diameter of EMPs was the same as the equivalent volume diameter (i.e., 10 μm and 100 μm). One notable conclusion from this result is that EMPs are more inhalable than spherical particles of the same volume or mass and hence more available in the respiratory tract for deposition. Thus, based on geometry alone, longer EMPs have a higher inhalability than shorter EMPs. However, only a fraction of all inhaled particles deposit in the respiratory tract, and it is the deposited dose of inhaled particles that is generally considered to be more closely associated with potential health outcomes.

Transport and deposition of inhaled EMPs depend on their geometry (wall trapping) and aerodynamic properties. Several major deposition mechanisms influence the removal of airborne EMPs from the inhaled air, each corresponding to an external force and differ in relative contribution to deposition depending on the respiratory tract region as shown in Fig. 4. The main deposition mechanisms for inhaled particles and fibers include the following: interception, inertial impaction, gravitational settling, Brownian diffusion, and electrostatic charge. These mechanisms act collectively to cause a net deposition of particles throughout the respiratory tract in accordance with the regional significance of each deposition mechanism.

Interception is a significant mechanism for high-aspect ratio particles such as EMPs. Inertial impaction is the mechanism that causes partial entry of airborne particles into the head airways on inhalation. Due to their elongated geometry, EMPs also intercept the respiratory tract surfaces and deposit as they enter the LRT, at the main bronchial bifurcation, or on airway walls. When particles approach an airway bifurcation, the airflow splits and switches direction to exit through daughter branches. Heavy particles will deviate from the flow streamlines (depending on the inertia) and may collide with the walls of the carina according to their inertia. The particle’s mass influences its inertia (and since mass equals density times volume, the particle density and dimensions also play a role) – the higher the inertia, the higher the probability of deposition near the bifurcation region. Inertial impaction is significant for heavy particles when flow velocity is high (typically at the proximal region of the LRT). Gravitational settling is the result of deposition due to the force of gravity and is directly related to the mass of each individual EMPs. It is significant for particles with micrometer and larger diameters when the airflow rate in the lung has subsided in the distal portion of the LRT and there is an adequate time for particles to deposit by the force of gravity. Finally, EMPs may deposit via Brownian diffusion. Brownian diffusion is the random force on particles from collision with the surrounding air molecules. The collisions result in a net particle movement from regions of particle concentration (near the center of airways) to low concentration (at the walls). This deposition mechanism is significant for particles with sub-micrometer and smaller diameters in the deep lung where the airflow velocity is greatly diminished (i.e., at low Reynolds number defined as the ratio of inertial to viscous forces at less than unity). Particles that carry charge may deposit primarily by specific electrical forces called image forces and secondarily by space charges.

The retained dose of inhaled EMPs depends on the degree of biological clearance (mucociliary, alveolar macrophage-mediated) and physical dissolution in lung cells/fluids, which are influenced by their shape and dimensions. In the absence of mechanistic information (such as mucociliary velocity and macrophage movement), observations on particle movement from lung surfaces through tissues into the interstitium and lymph nodes were used to calculate compartment specific rate constants (ICRP, 1994) or develop empirical relationship for rate constants as a function of the mass (Yu et al., 1990a) and dimensions of the retained particles (Yu et al., 1990b). Modeling of the retained mass of EMPs should also account for their dimensions and longitudinal or traversal splitting, as derived previously for chrysotile asbestos based on available data of the mean length and diameter at consecutive post-exposure time intervals (Yu et al., 1991). Lack of mechanistic information limits the analysis of respiratory tract burden as a function of the dimensions of EMPs.

In the following example, MPPD v. 3.04 was used to predict the deposition of EMPs in LRT airways as a function of dimensions and to compare with predictions for spherical particles. Regional deposition of a theoretical EMPs aerosol predicted to deposit in the LRT of humans is shown in Fig. 5 for a sitting activity level, including a typical tidal volume of 625 cm³, breathing frequency of 12 breaths per minute (BPM), and functional residual capacity (FRC) of 3300 cm³ via nasal breathing. Inhalability of EMPs was excluded to examine unbiased deposition mechanisms in the LRT. Model predictions were made for deposition fraction plotted against EMPs diameter (d_f) and for EMPs length to diameter ratios (aspect ratio, β) of 10 and 50 in the URT (Fig. 5A), TB (Fig. 5B) and PU (Fig. 5C) regions. Deposition in the URT was by Brownian diffusion for light EMPs and inertial impaction for heavy EMPs, respectively. As seen, the deposition pattern was bell shaped. Deposition in the TB regions was also by inertial impaction and Brownian diffusion. However, filtering of EMPs by the URT affected the shape of the deposition curve in the TB region. Deposition in the PU was due to Brownian diffusion and sedimentation. However, the expected bell shape trend was further disrupted by the filtering of EMPs in the URT and TB regions. Particle filtering and cumulative effects of different deposition mechanism did not allow drawing a simple relationship between EMPs dimensions (e.g., diameter and aspect ratio) and deposition fraction in the different regions of the respiratory tract. The filtering effects were evident by the peak deposition around EMPs minor diameter of 1 μm in the TB region from URT (Fig. 5B) and peaks in the PU region around 0.01 μm and 1 μm due to EMPs deposition in the URT and TB regions. In addition, lower deposition of heavier of ultrafine EMPs were due to the filtering effects.

Comparison of EMPs deposition with that of spherical particles to evaluate the influence of EMPs dimensions on deposition in the respiratory tract were made in Fig. 6A. Deposition fractions were calculated assuming no deposition in the URT (Fig. 6B), which was a hypothetical scenario, and with deposition in the URT (Fig. 6C) to study the influence of URT filtering on subsequent LRT deposition. Three cases were studied: spherical particles of 1 μm diameter and two different EMPs, each of equivalent mass but with different aspect ratios of 10 and 50. Particle minor diameters were: 1 μm (spherical), 0.33 μm (fiber with β = 10), and 0.2 μm (fiber with β = 50). Predicted deposition fractions in the TB and PU regions are given in Fig. 6B and C for the same breathing frequency (12 BPM) and tidal volume (625 cm³) as in Fig. 5. Deposition in the LRT increased when URT deposition was excluded, and may occur with an oral breathing mode. With URT filtering, there was a smaller fraction of longer and thinner EMPs in the TB and PU regions compared to that for shorter and thicker EMPs. Deposition in the TB region was higher than that in the PU region for EPMs. In addition, deposition in the TB region increased with increasing EMP length, whereas PU deposition showed the reverse trend, partly due to the filtering by the TB region. There was not a clear pattern for TB deposition with EMP dimensions. Spherical particles deposited more in the LRT. Findings from Figs. 5 and 6 emphasizes the need for comprehensive dosimetry analyses using models over consideration of singular dimensions or aspect ratio alone to study the fate of inhaled fibers and EMP.

The findings from this example of EMPs deposition in the human respiratory tract in MPPD (v. 3.04) are compared to those in another model of a different type of elongated particles, carbon nanotubes (CNTs) (Sturm, 2015). In that model, single-walled CNTs were assumed to have a diameter of 5 nm and aspect ratios of 10, 100, or 1000. Multi-walled CNTs were assumed to have a diameter of 50 nm and the same aspect ratios as for SWCNT. Agglomeration of CNTs was not modeled. Particle density was assumed to be < 2.2 (density of graphite) since CNTs are not solid cylinders but form rolled sheets of carbon. Similar respiratory parameters for sitting (nasal breathing) conditions were used in Sturm (2015) and here, that is: tidal volume of 750 ml (vs. 625 ml here); 4.2 s/breaths (or 14.3 BPM) (vs. 12 BPM here); and FRC of 3300 ml in both studies. Predicted pulmonary (acinar) deposition of CNTs in sitting adults were ~10–25% in Sturm (2015), Figs. 4d and 6d) and ~8–10% for EMPs in this study (Fig. 6c of this article). Deposition of spherical particles (volume-equivalent diameter to the carbon nanotubes) in the pulmonary region was ~5–20% (Sturm, 2015, Fig. 6d), compared to ~10% for spherical particles with equivalent volume to EMPs (Fig. 6c of this article). Tracheobronchial deposition of spherical particles was ~2–7% in Sturm (2015), Fig. 6c and ~7% for EMPs (Fig. 6c in this article). Tracheobronchial deposition of CNTs was ~4–20% in Sturm (2015), Fig. 6c and ~5% for EMPs (Fig. 6c here). Despite the differences in the dimensions of elongated particles and the different dosimetry models used in these two analyses (Sturm, 2015 and here), the estimated deposition fractions are similar. In this article, TB deposition fractions of EMPs were higher and PU deposition fractions were lower than those of volume-equivalent spherical particles (Fig. 6B and C). In contrast, Sturm (2015) reported increased TB and PU deposition fractions of the CNTs compared to volume-equivalent spheres at nasal breathing (Fig. 6C in Sturm, 2015). The purpose of this comparison was to provide a general evaluation of these EMPs modeling results compared to another model under similar conditions. Contradictory differences in LRT predictions are likely due to differences in filtering efficiencies of the nasal passages. Thus, the dimensions of inhaled particles including EMPs are shown to influence the estimates of the total and regional deposited doses in the human respiratory tract.