From SARS-CoV-2 infection to COVID-19 morbidity: an in silico projection of virion flow rates to the lower airway via nasopharyngeal fluid boluses*

Background: While the nasopharynx is initially the dominant upper airway infection site for SARS-CoV-2, the physiologic mechanism launching the infection at the lower airway is still not well-understood. Based on the rapidity of infection progression to the lungs, it has been hypothesized that the nasopharynx may be acting as the primary seeding zone for subsequent contamination of the lower airway via aspiration of virus-laden boluses of nasopharyngeal fluids. Methodology: To examine the plausibility of the aspiration-driven mechanism, we have computationally tracked the inhalation process in three anatomic airway reconstructions and have quantified the nasopharyngeal liquid volume transmitted to the lower airspace during each aspiration. Results: Extending the numerical trends on aspiration volume to earlier records on aspiration frequencies indicates a total aspirated nasopharyngeal liquid volume of 0.3 – 0.76 ml/day. Subsequently, for mean sputum viral load, our modeling projects that the number of virions reaching the lower airway will range over 2.1×10 – 5.3×10/day; for peak viral load, the corresponding number hovers between 7.1×10 – 1.8×10. Conclusions: The virion transmission findings fill in a key piece of the mechanistic puzzle on the systemic progression of SARSCoV-2, and subjectively point to health conditions like dysphagia, with proclivity to increased aspiration, as some of the potential underlying risk factors for aggressive lung infections.


Introduction
Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the causative agent for coronavirus disease 2019 (COVID- 19), has been linked (1,2) to a remarkable pattern of relatively high infectivity in ciliated epithelial cells along the nasal passage lining in the upper airway, moderate infectivity in cells lining the throat and bronchia, and relatively low infectivity in lung cells. Such viral trends are governed by the abundance of angiotensin-con-verting enzyme 2 (ACE2), a single-pass type I membrane protein that is exploited by viral spike protein binding as a gateway for cellular entry. ACE2 is abundant on ciliated epithelial cells, but is highly expressed in only a smaller subset of the alveolar cells in the lower airway (3) . These findings (1,2) are nonetheless for in vitro samples; virus-laden droplets deposited along the anterior nasal airway might not be so effective at launching an infection despite the presence of ciliated cells, as the thicker mucus layer there provides some level of protection against viral invasion and infection (4) . Hence, the nasopharynx, which is the region in the upper airway posterior to the septum and comprising the superior portion of the pharynx, has been postulated to be a dominant initial infection site for SARS-CoV-2 (1,5) . The efficacy of nasopharyngeal swabs over oropharyngeal swabs for accurate detection (6) of COVID-positive cases supports the hypothesis.
Based on the brisk pace at which lower airway infections ensue following the emergence of initial symptoms, it has been conjectured (1) that the nasopharynx (marked in Figure 1, see Panels (a)-(i)) acts as the seeding zone for subsequent spread of the disease to the lungs via lower airway aspiration of virus-laden boluses of nasopharyngeal fluids.
While the above hypothesized mechanism is superficially plausible, the key unanswered question is whether the rate of virion flow from the initial site of infection to the lower airway could be sufficiently high to account for a rapid onset of secondary infections at the lungs. In this report, we have combined earlier data on aspiration trends (7,8 ) with virological assessments of sputum in hospitalized COVID (9) patients and our computational findings on the physical flow variables in anatomically realistic airway domains -to quantify bolus-borne virion transmission rates from the nasopharynx into the lower airway.

Frequency and quantification of pharyngeal aspiration
Aspiration (i.e., accidental suction of fluid and cells into the lungs) of upper airway secretions acts as a major carrier of pathogens to the lower airway, and the phenomenon, fortunately enough, has been studied in great detail over the last few decades. As reported in the late-1990s (7) , aspirated pharyngeal liquid volume during sleep ranges from 0.011 ml to 0.129 ml, measured through tracking mildly-radioactive tracers after the subjects wake up. Further inspection of the published data indicates that the maximum data-point in the reported range is a statistical outlier. Including the maximum-reported volume in the analysis, the mean aspirated volume comes out to be 0.0345 ml and the median is 0.0215 ml. Excluding the outlier, the mean volume revises to 0.021 ml and the median volume adjusts to 0.020 ml.
That study (7) was based on a total of 10 normal subjects.
While evaluating swallowing mechanisms, it has been further reported (8) that for 5-ml bolus volumes, aspirations happen during 13% of swallows; and for 10-ml bolus volumes, aspirations happen during 11% of swallows. Boluses smaller than 10 ml are associated with silent aspiration (25) and presumably are the major sources of pathogen-carriers to the deep lungs, and with averaging the reported data for 5-ml and 10-ml volumes, 12% of the swallowing actions should result in aspiration.
Finally, earlier findings (26) suggest that a typical person swallows 500 -700 times during a day and 24 times during sleep (assuming a standard eight-hour sleep cycle). These numbers thus indicate that a subject will aspirate approximately 12% of 500 -700 times, i.e. 60 -84 times during the day, and 12% of 24 times, i.e., approximately 3 times during sleep.

Development of anatomically realistic computational fluid mechanics models
Allometric relationships (27) show that the minute inhalation is approximately 14.5 -20.0 L/min for a 65-kg adult male and 8.8 -22.4 L/min for a 65-kg adult female, both for gentle steady breathing. For simplicity, as a stand-in for gentle inhalation (28)(29)(30)(31)(32) , this study simulates an airflow of 15 L/min; the process can be modeled using viscous-laminar steady state flow physics schemes. We additionally noted that subjects with proclivity to apnea are also prone to higher levels of aspiration (33) and for them, the inhaled air often disrupts into high-speed turbulent regimes. To account for such flow conditions, we have simulated a higher breathing rate of 55 L/min. Subsequently, the reconstructed geometries were exported as STL (stereolithography) files to ICEM-CFD 2019 R3 (ANSYS Inc., Canonsburg, PA, USA) and therein were spatially meshed into minute volume elements. As per established mesh refinement protocols (34)(35)(36) and other more recent reports (37,38) , each computational grid in this study contains more than 4 million unstructured, graded tetrahedral elements (namely 4.54 million in Subject 1, 4.89 million in Subject 2, and 4.05 million in Subject 3).

Simulating inhalation
Inhaled transport was studied through computational fluid Model as the sub-grid scale model (42) . Each LES computation kg/m.s was used as the dynamic viscosity of air.
The following boundary conditions were enforced in the flow simulations: zero velocity (no slip) at the internal airway walls, i.e., at the tissues and cartilages enclosing the airway; zero pressure at nostril openings, which acted as the pressure-inlet zones; and negative pressure at the airflow outlet at the base of the nasopharynx, which acted as the pressure-outlet zone. Review Figure 1 for the relative locations of the anatomic regions. With the assumption of axial symmetry in the airway conduit and no slip boundary condition at the walls, integrating the Navier-Stokes equation for momentum conservation results (43)(44)(45)(46) in: Q = -[πR 4 /(8μ)](dp/dz). Here, Q is the instantaneous aspirated volume, R is the hydraulic radius (cross-section of conduit divided by the perimeter at the nasopharyngeal base), μ is the sputum viscosity (quantified at 4.59 poise = 0.459 Pa.sec (47) for mucopurulent medium), and dp/dz is the spatial rate of pressure gradient in the streamwise direction. To adapt the formulation to the present problem, we have post-processed the simulations to extract the averaged wall pressure at the nasopharynx (pn).
We have also extracted the averaged pressure at the outlet (po), located 0.02 m (streamwise ΔZ, to ensure full flow development in the simulations) below the nasopharyngeal base. With ΔP = po -pn, the gradient rate dp/dz can therefore be approximated to simply ΔP / ΔZ.

Data on viral loading
SARS-CoV-2 is a single-stranded RNA virus (i.e., comprising single-stranded genomes made of ribonucleic acid), and the virological assessments (9) performed through PCR (polymerase chain reaction) with reverse transcription (RT-PCR) on the sputum (collected via nasopharyngeal swabs) of hospitalized COVID-19 patients indicate a mean viral load of ν avg = 7×10 6 RNA copies/ml of oral fluid. The peak load was ν peak = 2.35×10 9 copies/ml.

Computational prediction of nasopharyngeal bolus volume
With inhalation simulated at 15 L/min: for Subject 1, ΔP was -0.82 Pa; for Subject 2, ΔP was -2.33 Pa (for contour maps, see  quencing studies (52) , and also through our earlier computational findings (5) that merged fluid dynamics-based tracking of inhaled transport with the related virologic assessments). Thus, it stands to reason that a dose 10 4 -10 7 times higher (considering gentle inhalation in the host) will suffice to seed a second infection site within the same host, particularly given the relatively high levels of ACE2 expression in a subset of alveolar cells (3) .

Role of boundary layer separation in generation of aspirates
We believe that the results of our CFD modeling also point to a role for the nasopharynx specifically in seeding infections to the lungs. The wall pressure differences between the anterior nasal sites (e.g., the turbinates, the olfactory cleft) and the airway outlet in the test subjects are found to be of approximately the same order of magnitude as that between the nasopharynx and the outlet (which was -1.2 Pa, averaged over the test subjects).
For example, in Subject 3, the pressure difference was -1.15 Pa between the left middle turbinate and the outlet, -2.59 Pa between the outlet and the left olfactory roof, -2.90 Pa between the outlet and the right middle turbinate, and -2.85 Pa between the outlet and the right olfactory roof. However, quite critically, the nasopharyngeal bolus generation (and consequently, the aspiration) is predominantly triggered by the mechanistic process of shear-induced (53,54) flow separation. Boundary layer separation (or flow separation) entails the detachment of walladhering fluids owing to adverse pressure gradient imposed on the boundary layers by the outer potential flow (55) . This happens when the outer flow abruptly alters its mean direction, e.g., at the ~90° bend of the nasopharynx. Thus, the role of the nasopharynx in generation of virus-laden boluses of mucosal fluid is presumably due both to the pressure differential (a necessary but not sufficient condition) and the unique geometry of the region.

Clinical ramifications
The findings suggest a simple aspiration-based physiological mechanism for COVID-19 etiology following initial SARS-CoV-2 infection in the nasopharynx. Such a mechanistic link may be valuable in identifying risk factors that predispose patients to progress to acute COVID-19 morbidity following SARS-CoV-2 infection. For example, a prediction that emerges readily from this proposed mechanism is that individuals with dysphagia may be at increased risk of developing COVID-19 following SARS-CoV-2 onset and may have more negative outcomes with the disease.
In this context, the reader should note that while "dysphagia" is a broad clinical condition, we are specifically using the term here to refer to situations where aspiration or microaspiration may occur with, for instance, difficulty in swallow initiation.
One condition associated with dysphagia is obstructive sleep apnea (OSA) (56)(57)(58) , with increased nocturnal aspiration (33) and risk of aspiration-induced pneumonia (59) . Based on the mechanism proposed by us for viral spread to the lungs, individuals with OSA would thus be expected to be at a higher risk for COVID-19 (or, for that matter, any progressive respiratory viral disease).
In fact, this has been reported by several different investigators (60)(61)(62)(63)(64) . One study, for example, reported an association of OSA with increased risk for hospitalization (OR 1.65; 95% CI (1.36, 2.02)) and respiratory failure (OR 1.98; 95% CI (1.65, 2.37)) owing to COVID-19, after adjusting for diabetes, hypertension, and body mass index (65) . As a practical matter, our work suggests that individuals with OSA should not suspend the use of their CPAP (continuous positive airway pressure) devices upon testing positive for SARS-CoV-2, as has been suggested by some practitioners (66) .
As the prevalence of dysphagia also increases with other factors such as increased age (67) , cancer treatment (68) , and Parkinsonism (69) , the physiological mechanism proposed here may also account for some of the documented increased risk of adverse outcomes (70)(71)(72)(73) in these groups. Any sedation outside of the hospital (e.g., from alcohol / substance use) or within the hospital (from sedating medications) might also trigger increased aspiration. Further study is required to understand the importance of dysphagia in general as a predictive factor for adverse outcomes with COVID-19.
Our findings also point to the potential risk posed by vaccine breakthrough cases. We now know that vaccines against SARS-CoV-2 do not provide sterilizing immunity -recent real-world data points to a reduction in risk of infection for vaccinated individuals that ranges from 20-50% of that of unvaccinated individuals (74) . Such a scenario is of particular concern for the current wave of vaccines that target the spike protein; work by us (75) and others (76)(77)(78)(79) suggests that the spike protein has a relatively high mutational tolerance and can readily generate immune- (with whole-genome sequencing of vaccine breakthrough cases) showed evolutionarily mediated immune evasion to be a common feature of vaccine breakthrough (52,74,76) . Critically, our work thus suggests that the current public health strategy of using vaccines to limit severe disease while ignoring breakthrough infections -particularly asymptomatic ones (81) -may underestimate the systemic threat posed by nasopharyngeal SARS-CoV-2 infections.

Study limitations
While the general fluid mechanics framework of our study is extensible to other respiratory pathogens, our results should still be interpreted as being preliminary, given that the numerical findings are based on simulated data from only three test subjects. We, however, note that there is a good agreement between the numerical predictions of aspiration frequency with earlier observational findings, which lends to the validity of the underlying computational and mathematical framework. The size of the projected viral dose also speaks to the robustness of the conclusion -it is likely that virion flow from the nasopha-rynx to the lungs occurs in large excess of the minimum dose required to seed a lung infection for many individuals, thereby precipitating a brisk aggravation of the disease symptoms.
Note that, from a clinical standpoint, we have not considered the contribution of mucociliary activity, propelling a bolus toward the oropharynx from the nasopharynx. However, while that would theoretically increase the bolus volume and the potential frequency of aspiration, it would also provide a protective mechanism after aspiration, as the bolus could be propelled up through a reflux mechanism at the trachea.
Finally, the aspirated pharyngeal liquid volumes could be significantly variable depending on other disease processes, including gastroesophageal reflux disease (GERD), which is very common in the United States (82,83) .

Conclusion
Although the nasopharynx stands out as the dominant initial infection site for SARS-CoV-2, the physiological mechanism launching the lower airway infection is still not well-understood.

Acknowledgments
The researchers accessed computing facilities at both South Dakota State University and UNC Chapel Hill, to derive the reported in silico findings.

Funding
This work was partially supported by the National Science

Ethics approval and consent to participate
No approval or consent needed.

Consent for publication
Not applicable.

Availability of data and materials
On request, all data and study protocol can be made available.

Conflict of interest
The authors declare no competing interests.