Method
The sample size was two. The models included a 35-year-old male (model 1) and a 25-year-old male (model 2) who participated in the study as healthy adult volunteers. Sections with a width of 1.0 mm and a pixel size of 0.488 × 0.488 × 0.488 mm were collected and scanned using a CT instrument (SIEMENS SOMATOM Definition Edge®, Germany), and a nasal cavity and paranasal sinus 3D model was created using Mimics 23.0® (Materialize, Belgium) (Fig. 1). We checked all CT slices and natural ostium and remodeled them. Therefore, we prepared two accurate nasal cavity and paranasal sinus 3D models.
Moreover, 3-matic 15.0® (Materialize, Belgium) was used for mesh formation after the smoothing procedure. The TetGen mesh generator was used here with the boundary condition that the boundary surface must remain intact (unchanged), both at the vertices and the triangles. This means that if tetrahedron vertices (called Steiner points in Delauney terminology) are to be added by the algorithm, they are never added at the boundary surface, but only at the interior of the model. The number of surface meshes was 177448 in Model 1 and 136332 in Model 2. The number of volume meshes was 353933 in Model 1 and 285874 in Model 2. The number of nodes was 103629 in Model 1 and 82312 in Model 2. The grid convergence of these models was calculated. We confirmed that the number of volume meshes of these models were appropriate.
Fluent 17.2® (ANSYS, American) was employed for fluid analysis using the continuity equation for three-dimensional incompressible flow and the Navies–Stokes equation for the basic equations. Both models were Laminar models. The SIMPLE calculation method using the finite volume method was employed here, and the quadratic precision upwind difference method was used to discretize the convection terms.
The boundary condition was as follows:
i) the velocity is equal to zero at the nasal wall;
ii) a pressure of zero is presumed at the nostrils as the atmospheric pressure;
iii) at the trachea side, the velocity (v) is given.
In the steady solution, the iteration number was 300. In turn, in the unsteady solution, the iteration number was 20/time step and the time step width was 0.001 [s]. We used a sine function of 3 s per period as the breath airflow.
The nasal resistance value, R [Pa/(cm3/s)], was calculated by the following formula using the flow rate V [cm3/s] at the nostril when the pressure difference (ΔP) between the atmospheric pressure and the pharynx was 100 [Pa]:
R = ∆P/V,
where R is the nasal resistance [Pa/(cm3/s)], ΔP is the differential pressure between the atmospheric pressure and the pharynx [Pa], and V is the flow rate [cm3/s].
After the calculation of the resistance for each cavity, the right resistance (Rright) and left resistance (Rleft) were calculated, with the total resistance for both cavities, Rtotal, being calculated as follows:
1/Rtotal = 1/Rright + 1/Rleft.
First, we performed a simulation at the flow velocity of 1.5 (m/s) applied to the pharyngeal side in the steady solution. A pressure difference of Δ100 [Pa] is required to measure the nasal resistance value. Second, we performed a simulation in the same condition in the unsteady solution for the nasal resistance. The maximum flow velocity in Model 1 was 1.5 (m/s) on the right and 1.5 (m/s) on the left. Moreover, in Model 2, the maximum flow velocity was 3.0 (m/s) on the right and 6.0 (m/s) on the left in the unsteady solution.
Rhinometry was performed using an MPR-3100® instrument (Nihonkoden, Japanese). Nasal resistance was measured in the two subjects using active anterior rhinometry (without vasoconstriction). To rule out the effect of the nasal cycle, nasal resistance was measured right after CT.