**2. Design of experiments**

## **2.1. Image‐based reconstruction of nasal airway model**

First, building anatomically accurate airway models is crucial for the assessment of the health outcomes of inhalation therapies. **Figure 1** illustrates the procedures of the translation from medical images into a high-quality computational mesh or *in vitro* casts of the nose-pharynx. To reconstruct the 3-D nasal airway model, MRI scans (512 × 512 pixel resolution) of a healthy 53-year-old male were used. The multislice MRI images were segmented using MIMICS (Materialise, Ann Arbor, MI) to convert the raw image data into a set of cross-sectional contours that define the solid geometry (**Figure 1a**). A surface geometry was reconstructed based on these contours in Gambit (Ansys, Inc.). This surface geometry as shown in **Figure 1b** was subsequently imported into ANSYS ICEM (Ansys, Inc.) for meshing. In general, unless for extremely high-quality image data, a solid model that is directly reconstructed from medical images cannot be used for computational meshing due to the artifacts and resolution limits inherent in current imaging techniques. Considering the high complexity of the nasal airway structure, an unstructured mesh was generated with fine boy-fitted cells in the near-wall region (**Figure 1c**). This nasal geometry has been reconstructed with minimal surface smoothing and was intended to accurately represent the nasal anatomy of human adults. More details of image-based model development can be viewed in a recent video article from our group [33]. This model was also manufactured into hollow casts for *in vitro* studies using 3-D prototyping techniques (**Figure 1d**).

**Figure 1.** Procedures of translating medical images into computational mesh and *in vitro* casts. First, MRI scans were segmented to reconstruct the airway surface model. Second, high-quality computational mesh was generated with fine near-wall cells. Hollow *in vitro* cast replicas were also fabricated using 3-D printing technique and were used for experimental deposition studies. In order to study deposition distributions, the nasal cavity was divided into different regions: vestibule-valve region (VV), turbinate region (TR), nasopharynx (NP), and olfactory region (OL) that was at the very top of the nasal cavity (yellow color in middle panel).

## **2.2. Computational fluid‐particle transport models**

### *2.2.1. Airflow and particle dynamics*

Depending on breathing activities, multiple flow regimes, such as laminar, transitional, or fully turbulent, can exist in the human respiratory tract. The two-order turbulence models have been shown to adequately capture the main flow features and particle transport if a fine body-fitted mesh is used near the wall [34]. In particular, the low Reynolds number (LRN) *k‐ω* model has been widely adopted in computational studies of respiratory flows. It has been validated in many studies to be able to accurately predict the particle transport and deposition in the oral airway [35, 36], nasal cavity [8], and lungs [37, 38]. Moreover, the LRN *k‐ω* model was demonstrated to accurately predict the flow regime transition when the turbulent viscosity approaches zero [39]. Governing equations for the turbulent kinetic energy (*k*) and dissipation rate (*ω*) can be found in Wilcox [39].

Transport of monodisperse aerosols was solved using the discrete Lagrangian tracking algorithm through the integration of the particle dynamic equation. Spherical shape was assumed for each particle. The particle diameters range from 0.2 to 5 μm, which have very low Stokes numbers (*Stk* = *ρpdp* 2 *UCc*/18*μDh* << 1), with *ρp* being the density of the particles (1.0 g/ cm3 ), *U* being the fluid velocity, *Cc* being the Cunningham slip factor [40], and *Dh* being the nostril effective diameter. The governing equation of Lagrangian tracking is

$$\frac{d\mathbf{v}\_i}{dt} = \frac{f}{\tau\_p C\_c} (\mathbf{u}\_i - \mathbf{v}\_i) + \mathbf{g}\_i (1 - \alpha) + f\_{i, \text{Reonian}} + f\_{i, \text{light}} + f\_{i, \text{electric}} \tag{1}$$

where *ui* is the airflow velocity, *vi* is the particle speed, *f* is the drag coefficient, and *τp* = *ρp dp* 2 /18*μ* is the particle characteristic time to respond to flow variations. The drag coefficient *f* was based on the equation of Morsi and Alexander [41]. Gravity and Saffman lift force were also included for particles >1 μm [42]. Brownian motion effects were included for submicron particles [35]. It was assumed that particle motion had no effect on the flow field, i.e., a oneway coupling between fluid and aerosols in light of the dilute concentration of pharmaceutical aerosols. The impact of the anisotropic flow fluctuations near the wall was also included by applying an anisotropic turbulence model as described by Matida et al. [43]:

$$\ln \nu\_n' = f\_\nu \mathbb{E} \sqrt{2k \ / \ 3} \quad \text{and} \quad f\_\nu = l - \exp(-0.002 \,\text{y}^+) \tag{2}$$

In the above equation, *fv* is a damping component normal to the airway wall and *ξ* is a random number generated by the Gaussian probability density function.

#### *2.2.2. Electric field and electric force*

**2. Design of experiments**

92 Advanced Technology for Delivering Therapeutics

prototyping techniques (**Figure 1d**).

very top of the nasal cavity (yellow color in middle panel).

*2.2.1. Airflow and particle dynamics*

**2.2. Computational fluid‐particle transport models**

**2.1. Image‐based reconstruction of nasal airway model**

First, building anatomically accurate airway models is crucial for the assessment of the health outcomes of inhalation therapies. **Figure 1** illustrates the procedures of the translation from medical images into a high-quality computational mesh or *in vitro* casts of the nose-pharynx. To reconstruct the 3-D nasal airway model, MRI scans (512 × 512 pixel resolution) of a healthy 53-year-old male were used. The multislice MRI images were segmented using MIMICS (Materialise, Ann Arbor, MI) to convert the raw image data into a set of cross-sectional contours that define the solid geometry (**Figure 1a**). A surface geometry was reconstructed based on these contours in Gambit (Ansys, Inc.). This surface geometry as shown in **Figure 1b** was subsequently imported into ANSYS ICEM (Ansys, Inc.) for meshing. In general, unless for extremely high-quality image data, a solid model that is directly reconstructed from medical images cannot be used for computational meshing due to the artifacts and resolution limits inherent in current imaging techniques. Considering the high complexity of the nasal airway structure, an unstructured mesh was generated with fine boy-fitted cells in the near-wall region (**Figure 1c**). This nasal geometry has been reconstructed with minimal surface smoothing and was intended to accurately represent the nasal anatomy of human adults. More details of image-based model development can be viewed in a recent video article from our group [33]. This model was also manufactured into hollow casts for *in vitro* studies using 3-D

**Figure 1.** Procedures of translating medical images into computational mesh and *in vitro* casts. First, MRI scans were segmented to reconstruct the airway surface model. Second, high-quality computational mesh was generated with fine near-wall cells. Hollow *in vitro* cast replicas were also fabricated using 3-D printing technique and were used for experimental deposition studies. In order to study deposition distributions, the nasal cavity was divided into different regions: vestibule-valve region (VV), turbinate region (TR), nasopharynx (NP), and olfactory region (OL) that was at the

Depending on breathing activities, multiple flow regimes, such as laminar, transitional, or fully turbulent, can exist in the human respiratory tract. The two-order turbulence models have been shown to adequately capture the main flow features and particle transport if a fine body-fitted For the direct current (DC) field, the electric potential, *U*DC, is attained by solving the Poisson's equation,

$$-\nabla \cdot \varepsilon\_0 \varepsilon\_r \nabla U = 0 \tag{3}$$

where *ɛ*0 and *ɛr* are the absolute (F/m) and (dimensionless) permittivity of the free space, respectively. The zero value on the right-hand side of the equation means no space charge. For the alternating current (AC) field, the AC potential is computed by solving the conservation of electric currents [44]:

$$-\nabla \cdot \left(\sigma + j\alpha \varepsilon\_0 \varepsilon\_r\right) \nabla V = 0 \tag{4}$$

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 be obtained by superposing the DC and AC fields.

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

$$f\_{i,alcrophovertic} = neE = ne(E\_{DC} + E\_{AC})\tag{5}$$

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 are calculated as follows:

$$E\_{\rm DC} = -\nabla U; \; E\_{\rm AC} = -real[\nabla \tilde{V} e^{(\rm \mu a)}] \tag{6}$$

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

#### *2.2.3. Numerical methods*

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 all subsequent simulations.

#### **2.3. Experimental setup and materials**

#### *2.3.1. In vitro test platform*

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 cavity, voltage supplies to induce electric fields, and a scale to quantify deposition. A powder coating system (Powder System Solutions, Nolensville, TN) was modified to charge the dry powders. Copper plates and DC power supplies (MPJA, Lake Park, FL) were implemented to produce external electric fields. A high-precision electronic scale (Sartorius) was utilized to quantify the deposited mass of aerosols. A microscope (AmScope B120C-E1) was used to estimate the diameter of the charged particles. Details of the sectional nasal cast preparation and experimental procedures are described below.

**Figure 2.** *In vitro* experiments to test the feasibility of electric-guided olfactory drug delivery: (a) experimental setup and (b) two delivery strategies: normal and bi-directional. In both delivery strategies, drug particles are administered into the right-side nostril. However, particles exit the airway through the trachea in the normal delivery and exit through the left nostril in the bi-directional delivery.
