Abstract
Acoustically driven nebulized drug delivery (acoustic aerosol delivery) is the most efficient noninvasive technique for drug delivery to maxillary sinuses (MS). This method is based on the oscillation of the air plug inside the ostium to transport drug particles from the nasal cavity (NC) to the MS. The larger the wavelength of the air plug oscillation in the ostium, the greater the penetration of drug particles to the MS. However, using this technique, the maximum drug delivery efficiency achieved to date is 5%, which means 95% of the aerosolized drugs do not enter the MS and are wasted. Since the largest amplitude of the air plug oscillation occurs at its resonance frequency, to achieve an improved MS drug delivery efficiency, it is important to determine the resonance frequency of the nose–sinus combination accurately. This paper aims to investigate the impact of geometrical parameters on the resonance frequency of the nose–sinus model. Both experimental and computational acoustic models, along with the theoretical analysis, were conducted to determine the resonance frequency of an idealized nose–sinus model. The computational modeling was carried out using computational fluid dynamics (CFD) and finite element analysis (FEA), whereas in the analytical solution, the mathematical relationships developed for a conventional Helmholtz resonator were employed. A series of experiments were also conducted to measure the resonance frequency of a realistic NC–MS combination. The results demonstrated a good agreement between the experimental and CFD modeling, while the FEA and theoretical analysis showed a significant deviation from the experimental data. Also, it was shown that the resonance frequency of the idealized nose–sinus model increases by up to twofold with increasing the ostium diameter from 3 to 9 mm; however, it has an inverse relationship with the ostium length and sinus volume. It was also reported that the resonance frequency of the nose–sinus model is independent of the NC width and MS shape.
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Abbreviations
- cyl:
-
Cylindrical
- CFD:
-
Computational fluid dynamics
- CRS:
-
Chronic rhinosinusitis
- DE:
-
Deposition efficiency
- EPW:
-
Elements per wavelength
- FS:
-
Frontal sinus
- FEA:
-
Finite element analysis
- MS:
-
Maxillary sinus
- Mic:
-
Microphone
- NC:
-
Nasal cavity
- NC–MS:
-
NC and MS combination
- PSD:
-
Power spectral density
- sph:
-
Spherical
- rec:
-
Rectangular
- SS:
-
Sphenoid sinus
- TF:
-
Transfer function
- \(\alpha\) :
-
Acoustic attenuation coefficient
- \(c\) :
-
Speed of sound (m/s)
- \(C_{xy}\) :
-
Coherence function between x and y
- \(c_{\text{p}}\) :
-
Specific heat for constant pressure (J/mol K)
- \(c_{\text{v}}\) :
-
Specific heat for constant volume (J/mol K)
- \(D_{{{\text{H}},{\text{os}}}}\) :
-
Hydraulic diameter of the ostium (m)
- \(D_{\text{os}}\) :
-
Ostium diameter (m)
- f :
-
Frequency (Hz)
- \(F_{\text{r}}\) :
-
Resonance frequency (Hz)
- \(\gamma\) :
-
Specific heats ratio
- \(G_{xy}\) :
-
Cross-power spectral density between input and response (\({\text{Pa}}^{2} / {\text{Hz}}\))
- \(G_{xx}\) :
-
Power spectral density of input (\({\text{Pa}}^{2} / {\text{Hz}}\))
- \(G_{yy}\) :
-
Power spectral density of response (\({\text{Pa}}^{2} / {\text{Hz}}\))
- \(\kappa\) :
-
Thermal conductivity (W/m K)
- \(\lambda\) :
-
Wavelength (m)
- \(\lambda_{i}\) :
-
Characteristic velocity (m/s)
- \(L_{s}\) :
-
Ostium length (m)
- \(L_{\text{eq}}\) :
-
Equivalent length of the ostium (m)
- \(\mu\) :
-
Dynamic viscosity (kg/m s)
- \(\mu_{0}\) :
-
The reference value of density (kg/m s)
- \(\nu\) :
-
Kinetic viscosity (\({\text{m}}^{2} / {\text{s}}\))
- \(\omega\) :
-
Angular frequency (Hz)
- \(P\) :
-
Pressure (Pa)
- \(p_{0}\) :
-
Gauge pressure (Pa)
- \(p_{i}\) :
-
Pressure amplitude (Pa)
- \(Q\) :
-
Quality factor
- \(\rho\) :
-
Fluid density (\({\text{kg/m}}^{3}\))
- S :
-
Effective temperature (K)
- \(S_{0}\) :
-
Ostium cross-sectional area (m2)
- \(T\) :
-
Temperature (K)
- \(T_{xy}\) :
-
Transfer function estimate
- U :
-
Velocity (m/s)
- V MS :
-
Maxillary sinus volume (mL)
- w in :
-
Incident sound power at inlet
- w t :
-
Transmitted sound power at outlet
- W NC :
-
Nasal cavity width (mm)
- \(\zeta\) :
-
Damping ratio
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Acknowledgements
Financial support for the project has been provided by the Australian Government Research Training Program (RTP), and the Beacon of Enlightenment PhD Scholarship provided by the University of Adelaide. The authors would like to acknowledge the support of the School of Mechanical Engineering, Phoenix High Performance Computing (HPC), and the workshop at the University of Adelaide.
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Pourmehran, O., Arjomandi, M., Cazzolato, B. et al. The impact of geometrical parameters on acoustically driven drug delivery to maxillary sinuses. Biomech Model Mechanobiol 19, 557–575 (2020). https://doi.org/10.1007/s10237-019-01230-5
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DOI: https://doi.org/10.1007/s10237-019-01230-5