Numerical and Machine Learning Analysis of the Parameters Affecting the Regionally Delivered Nasal Dose of Nano- and Micro-Sized Aerosolized Drugs

Abstract

The nasal epithelium is an important target for drug delivery to the nose and secondary organs such as the brain via the olfactory bulb. For both topical and brain delivery, the targeting of specific nasal regions such as the olfactory epithelium (brain) is essential, yet challenging. In this study, a numerical model was developed to predict the regional dose as mass per surface area (for an inhaled mass of 2.5 mg), which is the biologically most relevant dose metric for drug delivery in the respiratory system. The role of aerosol diameter (particle diameter: 1 nm to 30 µm) and inhalation flow rate (4, 15 and 30 L/min) in optimal drug delivery to the vestibule, nasal valve, olfactory and nasopharynx is assessed. To obtain the highest doses in the olfactory region, we suggest aerosols with a diameter of 20 µm and a medium inlet air flow rate of 15 L/min. High deposition on the olfactory epithelium was also observed for nanoparticles below 1 nm, as was high residence time (slow flow rate of 4 L/min), but the very low mass of 1 nm nanoparticles is prohibitive for most therapeutic applications. Moreover, high flow rates (30 L/min) and larger micro-aerosols lead to highest doses in the vestibule and nasal valve regions. On the other hand, the highest drug doses in the nasopharynx are observed for nano-aerosol (1 nm) and fine microparticles (1-20 µm) with a relatively weak dependence on flow rate. Furthermore, using the 45 different inhalation scenarios generated by numerical models, different machine learning models with five-fold cross-validation are trained to predict the delivered dose and avoid partial differential equation solvers for future predictions. Random forest and gradient boosting models resulted in R² scores of 0.89 and 0.96, respectively. The aerosol diameter and region of interest are the most important features affecting delivered dose, with an approximate importance of 42% and 47%, respectively.

Keywords: machine learning; nanodrug delivery; nasal drug delivery; numerical modelling; targeted drug delivery.

Figure 1

The viscosity ratio as indicator to ensure the mesh quality for LES analysis (nut/nu, where nut and nu are turbulent and molecular kinematic viscosities, respectively). (A): cross-section colored by the viscosity ratio. (B): iso-surface of the viscosity ratio of 0.1.

Figure 2

Comparison of the aerosol deposition efficiency (DE) inside the present nasal cavity and the other realistic nasal cavities reported in the literature scaled by Stokes number for unity density aerosol (d²Q) [15,34,35,36,37,38,39].

Figure 3

The velocity contours and streamlines for the nasal airflow at different flow rates of 4 (A), 15 (B), and 30 L/min (C).

Figure 3

The velocity contours and streamlines for the nasal airflow at different flow rates of 4 (A), 15 (B), and 30 L/min (C).

Figure 4

The locations of the vestibule, nasal valve, and nasopharynx are visualized in the upper panel. In four regions of the vestibule (A), nasal valve (B), the olfactory epithelium (C), and the nasopharynx (D), the corresponding delivered dose in the form of mass per square centimeter is calculated for three airflow rates of 4, 15, 30 L/min and aerosols with diameters between 1 nm and 30 µm.

Figure 5

The distribution of the data extracted from the numerical analysis is represented as boxplots (A) and histograms (B).

Figure 6

Prediction of the regionally delivered dose using the gradient boosting (A) and random forest (B) models compared to CFD-driven results (observations). Blue dots show the CFD-driven and ML-driven dose predictions and the black line is the identity line (1:1 line).

Figure 7

The flow rate, the region of interest, and the aerosol diameter are factors that affect the regional deposited dose, and the random forest and gradient boosting models are used to determine their importance in predicting the dose.

Figure 8

The anatomy of the nasal cavity with vestibule, nasal valve, olfactory, and nasopharynx is colored in the left figure. A detailed cross-section of the mesh inside the nasal cavity is shown, along with a closeup view of one of the most complex cross-sections inside the nasopharynx (right figure).