Fig 1.
Integrated modelling framework for drug deposition and diffusion.
The framework begins with CFD simulation 1—which computes the airflow field and spray particle deposition. CFD simulation 2 is a separate study that creates a mucus flow field; and the analytical calculation that combines data from the first two CFD simulations.
Fig 2.
Geometries of the spray bottle, the nasal cavity and its major anatomical regions including vestibules, main passage, septum regions, olfactory regions, maxillary sinuses and nasopharynx.
Table 1.
Geometrical information of major anatomical regions.
Fig 3.
Spray drug particle size distribution used in the CFD simulation.
(a) Measured data from Dayal et al. [30] showing cumulative mass fraction, fitted using Rosin-Rammler Distribution. (b). The corresponding mass and number probability distribution function over particle size. The range of particle size released was 1 − 150μm.
Fig 4.
Airflow streamlines passing through the right chamber of the human nasal cavity.
Streamlines are coloured with velocity magnitude. a). lateral view with transparent nasal walls. b). medial view with septum removed.
Fig 5.
Particle deposition patterns coloured by particle size ranging from 1μm to 150μm.
(a). Particle deposition distribution in 3D view of the right chamber. Nasal walls were set transparent to visualise particle deposition locations. (b). Particle distribution in the unwrapped 2D view. All deposited particles were at the right cavity where the spray particles were released. There are three hot-spots of deposition caused by direct impaction. The first hot-spot mainly depicted by large droplets with size >30μm was a band-like region that across vestibule and septum (① and ②), the second one is located at the tip of the middle turbinate (③) and the third one mainly hosts small droplets with size <30μm was a more concentrated area that across vestibule and lateral cavity (④). Another deposition hot-spot for nearly 30μm particles is located around the maxillary ostia (⑤).
Fig 6.
Regional particle depositions in the vestibule and main cavity and comparisons with reported in-vitro measurements from Azimi et al. [31] and reported CFD simulation results from Rygg and Longest [21].
Fig 7.
Simulated mucus velocity distribution on the nasal cavity wall.
(a) Mucus velocity visualised on both lateral and septal sides of the left and right nasal cavities separately. (b) Mucus velocity visualised in a surface-unwrapped domain.
Fig 8.
Post-deposition particle transport over time.
The particles were coloured by deposition location.
Fig 9.
Total and regional drug absorption over drug solute radius.
Fig 10.
Total drug absorption produced from initial deposition regions, for different solute radius.
Fig 11.
Properties for dissolved drug particle diffusion through mucus gel layer.
(a) Solutes’ diffusion coefficient were calculated using Obstruction-Scaling model and plotted with typical macromolecular measured in the study of Olmsted et al. [32]. h represents human proteins, (b) Absorption functions over time predicted by Eq (11) were plotted for solute particles with an effective radius of 10nm, 50nm and 90nm.
Fig 12.
The CFD nasal cavity model contained polyhedral mesh elements.
(a) Surface mesh on the vestibule, the nasal cavity and the outlet extension. All surface areas were covered with a 10 μm thick mucus layer, but the source term for mucus injection was applied in the main nasal cavity only (coloured in blue). An extension from the nasopharynx exit was extruded with a length of 10 times its diameter to ensure fully developed flow at the outlet. (b) Refined surface mesh around the nozzle tip. (c) Cross section slice located at 60 mm away from the tip of nose showing the internal mesh. It also shows major anatomical regions including superior/middle/inferior nasal passages, superior/middle/inferior turbinates, olfactory regions and maxillary sinuses. (d) 8X zoomed view of the internal mesh containing polyhedral cells, prism layers and thin mucus layer (coloured in blue).
Fig 13.
Schematic of the mucus layer structure and dissolved drug particle diffusion through the gel layer.
The mucus model and the diffusion model were reproduced from studies of Shang et al. [25] and Erickson et al. [26].