Fig 1.
Defining the physiological domain.
(a) A demonstrative cartoon of the human respiratory system, encompassing the upper respiratory tract (URT; comprising nasal cavity, pharynx, larynx), the mouth, and the lower respiratory tract (LRT; comprising regions downwind from trachea onward), extending till the deep lungs. The visual is adopted with a perpetual license agreement from the Getty Images®. (b) Sample computed tomography (CT) imaging-based reconstruction of an adult human airway. It serves as a three-dimensional anatomically realistic equivalent of the cartoon in panel (a), with regions included till generation 3 (tertiary bronchi) of the tracheobronchial tree. For confirmation, note that there are 8 distal outlets (see panels (b)-(d)), implying = 8, where Gn = 3 is the generation number, considering two-way bifurcation for each bronchial tube at every transition [24]. The domain within the red box is isolated for the numerical experiments on inhaled downwind transport of microdroplets generated from the URT. The isolated region is additionally shown in panel (c) for an isometric view with anatomical demarcations and in panel (d) for the front coronal view. The symbol g signifies the gravity direction in the numerical simulations and the subsequent analytical framework, with x, y, and z defining the spatial orientation of the test cavity. Panel (b) additionally highlights the geometric length scale.
Fig 2.
Assessing the numerical sensitivity.
Panel (a) marks the location of the demonstrated unstructured tetrahedral meshes spatially refined with the following cell counts (in million): (b) 0.5, (c) 1.0, (d) 1.5, (e) 2.0, (f) 2.5, (g) 3.0. Panel (h) highlights the four layers of pentahedral cells used for near-wall refinement. Panels (i)-(k) present the computed flow and particulate transport variables across the six mesh resolutions: (i) resistance to inhaled airflow, (j) area-weighted average airflow velocity
at the outlet faces, and (k) deposition (or, penetration) rate η (%) in bronchial pathways for select particle sizes of 1, 5, 10, and 20 μm. The circle sizes to the right of panel (k) represent the number of tracked particulates in each simulation, scaled proportionally: red = 597, orange = 831, ocher = 1208, green = 1459, dark green = 1622, and blue = 1954 tracked particulates per size. In each case, the tracked particle count is equal the number of mesh facets (faces) on the inlet surface, directly proportional to the spatial resolution of the respective mesh. Panel (l), with its length scale included at the bottom, shows a magnified top view of the inlet surface for the mesh in (f), consisting of 400 quadrilateral facets and 1222 triangular facets.
Fig 3.
Transmission trend for particulates inhaled from outside and navigating the complete anterior airway.
(a) isolates the penetration rate through the bronchiolar outlets with the tracked particulates moving into the deeper lung regions; (b) η represents the cumulative deposition percentages at the primary, secondary, and tertiary bronchi, together with the penetration rate through the bronchiolar outlets into the deeper lung region. The reader may find it insightful to compare the trend reported here with Fig 5a,e on the navigation trend for particulates generated within the URT (and still airborne at the larynx). In the latter scenario, the larger particulates (e.g., ones
) exhibit much greater efficiency at penetrating to the lower airway.
Fig 4.
Defining the analytical domain, with representative numerical visuals.
(a) Laryngotracheal region upwind from the primary bronchi used to develop a simulation-informed reduced-order analytical model (S-ROAM) for bronchial transmission. AA′ marks the larynx upwind face and BB′ marks the downwind face of the distal tracheal cavity; see labels in Fig 1d. The cross-sectional areas of the cavity at AA′ and BB′ are 108.61 mm2 and 123.03 mm2, respectively. The corresponding hydraulic diameters are 11.03 mm and 12.20 mm, respectively. The linear spatial distance between the two faces is approximately 115.84 mm, at angle θ1 = 23.77° to the vertical (direction of gravity in the numerical simulations). Panel (b) highlights the location and orientation of the planar cross-section shown in panel (c) and also previously as the location of the mesh visuals in Fig 2. The vortex strengths and positions for the S-ROAM are extracted from the simulated data mapping this two-dimensional plane; the plane cuts through the entire cavity of panel (a). θ2 = 33.94° is the assumed angle in S-ROAM, at which microdroplets enter the AA′ inlet face and is governed by the anatomical shape of the cavity upwind from AA′ (marked by the dashed black traces; also see Fig 1). (d) 30 randomly selected representative velocity streamlines extracted from the numerically simulated inhaled airflow field. (e) Simulated trajectory of a representative 10- particulate. The geometric centroid of the inlet face, marked by the solid circle, was chosen as the particulate’s position at tracking time t = 0.
Fig 5.
Numerically simulated bronchial transmission trend for URT-derived particulates navigating through the redacted test geometry.
(a) represents the penetration rate through the bronchiolar outlets, calculated as
%, as a function of the tracked particulate sizes d. (b)-(d) Respective deposition percentages
,
, and
at the primary, secondary, and tertiary bronchi. They are computed as
, with
; see Table 1 caption for definitions of nj. (e) η represents the cumulative deposition percentages at the primary, secondary, and tertiary bronchi, summed with the penetration rate through the bronchiolar outlets into the deeper lung regions. The underlying solid red line is a fitted curve of the Heaviside step function form (see Eq 18), with the solid black circles showing simulation-derived η values (reported in Table 1). (f)
provides a count of virions penetrating to the bronchial space in 3 days, with a conservative estimate of 1 particulate of each test size generated during each breathing cycle. For perspective, the red line marks the infection-triggering viral load for SARS-CoV-2 [26,27]. Selected values from this plot are listed in Table 2. (g) Comparison of the numerical penetration trend with published experimental data [66]. The shaded patch marks the experimental observation domain, while the data points from the present study are represented by solid black circles.
Table 1.
Numerical transmission trend: The numerically simulated bronchial deposition and penetration data are detailed herein. Particulate sizes explored further in Table 2 (to formalize the viral transmission trends as a function of the microdroplet dimensions) are in bold font. Symbols: d = tested aerosol (or, droplet) diameter; = total number of aerosols (or, droplets) tracked for each particulate diameter; np = number of deposited particulates in the primary bronchi; ns = number of deposited particulates in the secondary bronchi; nt = number of deposited particulates in the tertiary bronchi; nd = number of particulates penetrating into the respiratory bronchioles toward the deep lungs; η = cumulative deposition (or, penetration) rate (in %) to the bronchial pathways and computed as
, with
.
Table 2.
Magnitude of viral load transmission into bronchial pathways as a function of inhaled particulate sizes: The duration in consideration is 3 days, with a conservative estimate of 1 particulate of each test size generated during each breathing cycle. The breathing cycles last 5 s [68]. Listed data is a subset of Fig 5f.
Fig 6.
Simulation-guided analytical modeling in the laryngotracheal space.
(a) Simulated vorticity contour map on a representative two-dimensional cross-section (the S-ROAM domain) running approximately midway through the cavity; see Fig 4b. The core of the dominant vortex patch is conservatively bounded in the rectangle, marked by , with its area equating the vortex patch area A used in the S-ROAM. Panels (b-h) show two sample particle pathlines (in red) against the S-ROAM streamlines (in grey), respectively for particle sizes 5, 10, 15, 20, 25, 30, and 50
. The black lines on either side of the S-ROAM domain mark the slip wall boundaries. In each case, the vortex patch
is mimicked by a set of five point vortices embedded on the two-dimensional flow field with background unidirectional flow in the β-direction. The representative particles entering near the middle of the inlet face and near the right edge of the model channel are respectively marked as
and
.
Fig 7.
Particle transport trend in the analytical case.
Comparison of the absolute deviation (, normalized with respect to the S-ROAM channel width) of the particle pathlines from the respective streamline they were embedded on at the inlet face. The deviation is measured along the α-direction (see Fig 6). Deviation curves for particles entering near the middle and the right edge of the model channel inlet are respectively marked as
and
.
Fig 8.
Interfacial interactions and morphological complexity along mucus-coated upper airway walls.
(a) Representative planar outline of the nasopharyngeal surface topology. Phase 1 = inhaled air; Phase 2 = mucus substrate. The blue arrow indicates the inhaled air flux sweeping over the mucus (in pale red). (b) Tortuosity measurement of the anatomical space using a sagittal cutting plane.
Table 3.
Potential directions for future research to address current limitations and enhance the described URT-to-LRT transmission framework.