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.