Prediction of transport, deposition, and resultant immune response of nasal spray vaccine droplets using a CFPD-HCD model in a 6-year-old upper airway geometry to potentially prevent COVID-19

Abstract

This study focuses on the transport, deposition, and triggered immune response of intranasal vaccine droplets to the angiotensin-converting-enzyme-2-rich region, i.e., the olfactory region (OR), in the nasal cavity of a 6-year-old female to possibly prevent corona virus disease 19 (COVID-19). To investigate how administration strategy can influence nasal vaccine efficiency, a validated multi-scale model, i.e., computational fluid-particle dynamics (CFPD) and host-cell dynamics (HCD) model, was employed. Droplet deposition fraction, size change, residence time, and the area percentage of OR covered by the vaccine droplets, and triggered immune system response were predicted with different spray cone angles, initial droplet velocities, and compositions. Numerical results indicate that droplet initial velocity and composition have negligible influences on the vaccine delivery efficiency to OR. In contrast, the spray cone angle can significantly impact the vaccine delivery efficiency. The triggered immunity was not significantly influenced by the administration investigated in this study due to the low percentage of OR area covered by the droplets. To enhance the effectiveness of the intranasal vaccine to prevent COVID-19 infection, it is necessary to optimize the vaccine formulation and administration strategy so that the vaccine droplets can cover more epithelial cells in OR to minimize the number of available receptors for SARS-CoV-2.

Nomenclature

A_d

droplet surface area (m²)

C_m

correction factor for Fuchs-Knudsen number

c_p

specific heat of humid air (J/(kg·K))

c_p,d

specific heat of droplet (J/(kg·K))

D_w

water mass diffusivity (m²/s)

d_d

droplet diameter (m)

d_d,i

droplet initial diameter (m)

d_d,f

droplet final diameter (m)

E₀

initial number of epithelial cells

${\overrightarrow{F}}^{\text{BM}}$

Brownian motion induced force (N)

${\overrightarrow{F}}^{\text{D}}$

drag force (N)

${\overrightarrow{F}}^{\text{G}}$

gravity (N)

${\overrightarrow{F}}^{\text{L}}$

Saffman lift force (N)

$\overrightarrow{g}$

gravitational acceleration (m/s²)

H_lat

latent heat (J/kg)

K_w

Kelvin effect factor

Kn

Knudsen number

k

turbulence kinetic energy (J/kg)

k_c

thermal conductivity (W/(m·K))

k_c,t

turbulent thermal conductivity (W/ (m·K))

k_hc

modified thermal conductivity (W/(m²·K))

k_mc

mass transfer coefficient (m/s)

M_w

water molecular weight (kmol/kg)

m_d

droplet mass (kg)

N

number of fragments between max and min temperature

Nu

Nusselt number

P_eq

equilibrium vapor pressure (Pa)

P_sat

saturation vapor pressure (Pa)

Pr

Prandtl number

R

gas constant (J/(mol·K))

Re_d

droplet Reynolds number

r_d

droplet radius (m)

$S_{\text{w}}^{\text{m}}$

mass source term (kg/(m³·s))

Sc

Schmidt number

Sh

Sherwood number

T

humid airflow temperature (K)

T_d

droplet temperature (K)

t

time (s)

$\overrightarrow{u}$

flow velocity (m/s)

${\overrightarrow{u}}_{\text{d}}$

droplet velocity (m/s)

V

breathing velocity (m/s)

V_d,i

droplet initial velocity (m/s)

${\overline{V}}_{\text{w}}$

water molar volume (m³/kmol)

y_w,surf

water mass fraction at droplet surface

y_w,∞

water mass fraction in humid air mixture

Greek symbols

α_m

mass accommodation factor

λ

gas mixture mean free path (m)

μ

viscosity of humid air (kg/(m·s))

μ_t

turbulent viscosity of humid air (kg/(m·s))

μ_d,surf

viscosity of humid air at droplet surface (kg/(m·s))

ρ

density of humid airflow (kg/m³)

ρw

density of water (kg/m³)

σ

droplet surface tension (N/m)

τ

breathing cycle time (s)

Φ_exp

experimental values of reported immune response

Φ_HCD

computational values obtained for immune response

ω

specific rate of turbulence kinetic energy dissipation (J/(kg·s))

Acronyms

λ-C

λ-carrageenan

ACE-2

angiotensin-converting enzyme 2

CFPD

computational fluid-particle dynamics

COVID-19

corona virus disease 2019

DF

deposition fraction

G

generation

GG

gellan gum

HCD

host-cell dynamics

IgA

immunoglobulin A

IgG

immunoglobulin G

MRI

magnetic resonance imaging

NK

natural killer cells

ODEs

ordinary differential equations

OR

olfactory region

PBS

phosphate-buffered saline

RH

relative humidity

RMSE

root mean squared error

S

spike protein

SARS-CoV-2

severe acute respiratory syndrome corona virus 2

SST

shear stress transport

TB

tracheobronchial

UDFs

user-defined functions

VC

vaccine coverage

VT₀

initial viral titer

Author contributions

Conceptualization, H.H., Y.F.; methodology, H.H., Y.F., X.C.; calibration and validation, H.H.; geometry preparation, E.K., C.F., Y.F., H.H.; simulations, H.H.; data curation, H.H.; data analysis, H.H.; writing, original draft, H.H.; writing, review and editing, H.H., E.K., X.C., Y.F.

Declaration of competing interest

The authors have no competing interests to declare that are relevant to the content of this article.