*2.3.2. Multisectional nasal cast*

the alternating current (AC) field, the AC potential is computed by solving the conservation

In the above equation, *σ* is the electrical conductivity and *ω* is the alternating frequency (Hz). Considering that the equations for both DC and AC fields are linear, the total electric field can

where *n* is the nondimensional charge number and *e* is the elementary charge (*e* = 1.6 × 10−19 C). *E*DC and *E*AC are the intensity of the DC and AC electric fields, respectively, which

To solve the concomitant flow‐electric‐particle multiphysics involved in each of the cases considered, ANSYS Fluent (Canonsburg, PA) and COMSOL (Burlington, MA) were employed to simulate the airflow, electric field, and particle tracing. User‐supplied functions (UDFs) in the language of Fortran ad C were developed for the calculation of mass flux to the wall, initial particle profile, Brownian force [45], near‐wall velocity interpolation [36], and anisotropic turbulence effect [43]. Body‐fitted computational mesh was generated to resolve the large gradients of flow velocities near the airway surface. Local mesh refinement was made consid‐ ering the complex anatomy of the nasal cavity. A grid independence study was performed by evaluating various grid densities, such as 0.4, 0.8, 1.2, and 2.2 million computational cells. The variation in predicted deposition fraction was 1% or less when changing the grid density from 1.2 to 2.4 million. Therefore, the computational mesh of 1.2 million cells was implemented for

The *in vitro* test platform for intranasal delivery of charged particles has four components: a particle charging apparatus (**Figure 2a**), a three‐dimensional replica of a normal human nasal

( ) ; [] *j t E U E real Ve DC AC*

*j V* (4)

*fi electrophoretic* , = = + *neE ne E E* ( *DC AC* ) (5)

w

= -Ñ = - Ñ % (6)

( <sup>0</sup> ) 0 *<sup>r</sup>* -Ñ × + Ñ =

s we e

The electric force as a function of the electric field can be expressed as

The symbol means that the AC potential is a complex variable.

be obtained by superposing the DC and AC fields.

of electric currents [44]:

94 Advanced Technology for Delivering Therapeutics

are calculated as follows:

*2.2.3. Numerical methods*

all subsequent simulations.

*2.3.1. In vitro test platform*

**2.3. Experimental setup and materials**

A multisectional nasal replica was prepared that allows quantitative measurement of regional deposition as well as direct visualization of deposition distributions. After developing the nasal airway geometry model as listed in 2.1, Magics (Materialise, Ann Arbor, MI) was utilized to create the nasal cast wall with a constant layer of 4 mm. The nasal replica was divided into several parts: the nasal vestibule and valve, turbinate, and nasopharynx, as shown in **Figure 1b**. Step-shaped grooves were created at the ends of each replica section for proper sealing and easy assembly. To visualize deposition distributions within the nasal cavity, the nasal replica was cut open along the top ridge of the right nasal passage to disclose the septum and turbinate in the right nose. In order to characterize the olfactory doses, the section representing the olfactory mucosa was separated from the other region. An in-house 3-D printer with a resolution of 16 μm (0.0006 in) (Stratasys Objet30 Pro, Northville, MI) was utilized to fabricate the nasal casts using polypropylene (Veroclear, Northville, MI) that has a clear color and allows for a smooth surface.

## *2.3.3. Experimental procedures*

Dry powders of 30 μm in size (matte black powder coat paint) were selected in this study for their easy availability and excellent charging properties. and easy ava. The modification made to the powder coating system integrated a charging reservoir (a 2-L bottle) to the nozzle of the charging gun (**Figure 2a**). An additional metal wire was added to extend the charging rod to the reservoir exit, with the wire's length being parallel with the direction of the flow of solid particles. A high voltage supply (Spectracoat coating system), which has an adjustable potential output of 0–100 kV, was connected to the rod. The solid particles were distributed out of a 4-mm-diameter nozzle and subsequently distributed into a multisectional nasal cast replica. Three copper-plated electrodes (A, B, C) were attached to the top of the nose replica, and one copper-plated electrode (D) was attached to the bottom of the replica. Charged dry powders were distributed from the powder coat gun for 20 seconds per trial. For the normal delivery, particles were administered into one nostril and exited through the nasopharynx (**Figure 2b**, upper panel). In contrast, for the bi-directional delivery, the bottom of the pharynx was blocked to simulate the uplifted soft palate, while particles were administered into one nostril and exited through the other (**Figure 2b**, lower panel). A vacuum pump (Robinair 3 CFM, Warren, MI) was connected to the exit of the nasal replica in each test case to simulate the respiration. An in-line flow meter (Omega, FL-510, Stamford, CT) was used to monitor the volumetric flow rate.

## *2.3.4. Statistical analysis*

The variable of interest in this study was the ratio of the olfactory dosage to the vestibuleturbinate dosage (i.e., olfactory-nasal dosage ratio). Results were represented as the main ± standard deviation (SD), with SD being calculated from five trials for each scenario. Statistical analysis software Minitab (State College, PA) was applied to analyze the deposition data. Tukey's method and analysis of variance (ANOVA) were implemented to assess the data variances. The difference was considered statistically significant if the *p*-value was <0.05.
