TABLE 1 The governing equations for numerical turbulence model
Conservation of mass (continuity) i =0
i
u x
∂
∂
Momentum (Navier-Stokes 1
+ j j = + + j
j j j
i i
i i
u p u
t Re
u u u
x x x x x
∂ ∂
∂ − ∂ ∂ ∂
∂ ∂ ∂ ∂ （∂ ∂ ）
where p is the pressure, Re is the Reynolds number, ui = Ui/Uir, xi = Xi/dir, p = P=P/ ρ Uir, Ui is the velocity vector, Uir is the outlet average velocity, dir is the narial diameter, ρ is the aerial density.
TABLE 2 Comparison of cross-sectional airway area before and after MARPE in a teenager patient Airway area (mm²)
Before MARPE
(T0) After MARPE (T1) ΔT1–T0 Percentage of change [(ΔT1–T0)/T0] × 100%
Nasal cavity
Plane Y1 287.65 335.90 48.25 16.77%
Plane Y2 307.57 308.92 1.35 0.44%
Plane Y3 316.42 319.68 3.26 1.03%
Plane Y4 260.17 270.61 10.44 4.01%
Plane Y5 200.83 220.53 19.70 9.81%
Plane Y6 186.85 210.09 23.24 12.44%
Avergae 259.92 277.62 17.71 7.42%
Pharynx
Plane Z1 528.47 489.22 -39.25 -7.43%
Plane Z2 531.95 622.78 90.83 17.08%
Plane Z3 562.75 703.59 140.85 25.03%
Plane Z4 581.69 794.50 212.81 36.58%
Plane Z5 536.18 754.17 217.99 40.66%
Plane Z6 599.22 724.17 124.95 20.85%
Plane Z7 563.42 684.76 121.33 21.54%
Average 557.67 681.88 124.22 22.04%
TABLE 3 Comparison of airflow pressure before and after MARPE.
Variable
Pressure (Pa) Percentage of change
[(ΔT1–T0)/T0] × 100%
Before MARPE (T0) After MARPE (T1) Max.
expiration Max.
inspiration Max.
expiration Max.
inspiration Max.
expiration Max.
inspiration Nasal cavity
Plane Y1 36.95 -26.42 30.18 -22.46 -18.33% -14.99%
Plane Y2 35.07 -25.17 27.19 -21.87 -22.44% -13.12%
Plane Y3 32.24 -23.39 24.91 -20.28 -22.74% -13.31%
Plane Y4 29.12 -19.61 22.22 -17.00 -23.68% -13.33%
Plane Y5 24.05 -17.01 19.49 -13.58 -18.95% -20.16%
Plane Y6 21.63 -7.97 17.67 -6.89 -18.28% -13.51%
Avergae 29.84 -19.93 23.61 -17.01 -20.74% -14.74%
Pharynx
Plane Z1 38.73 -28.79 32.06 -25.52 -17.24% -11.34%
Plane Z2 38.92 -28.52 32.30 -25.27 -17.01% -11.42%
Plane Z3 38.92 -29.38 32.24 -25.74 -17.16% -12.38%
Plane Z4 39.03 -29.06 32.38 -25.50 -17.02% -12.25%
Plane Z5 39.22 -29.22 32.48 -25.45 -17.18% -12.87%
Plane Z6 39.32 -29.24 32.54 -25.51 -17.25% -12.76%
Plane Z7 39.53 -29.04 32.86 -25.36 -16.87% -12.65%
Avergae 39.10 -29.03 32.41 -25.48 -17.11% -12.24%
TABLE 4 Comparison of airflow velocity before and after MARPE.
Variable
Velocity(m/s) ΔT1–T0
Before MARPE (T0) After MARPE (T1) Max.
expiration Max.
inspiration Max.
expiration Max.
inspiration Max.
expiration Max.
inspiration Nasal cavity
Plane Y1 1.87 1.59 1.80 1.40 -0.07 -0.20
Plane Y2 1.53 1.46 1.41 1.22 -0.12 -0.24
Plane Y3 1.48 1.53 1.34 1.36 -0.13 -0.17
Plane Y4 1.26 1.39 1.26 1.27 0.00 -0.12
Plane Y5 2.72 2.69 2.26 2.38 -0.46 -0.31
Plane Y6 3.58 2.80 3.26 3.05 -0.32 0.25
Avergae 2.07 1.91 1.89 1.78 -0.18 -0.13
Pharynx
Plane Z1 0.87 0.94 1.08 0.88 0.21 -0.06
Plane Z2 0.74 1.15 0.66 0.85 -0.08 -0.30
Plane Z3 0.69 0.55 0.37 0.46 -0.33 -0.09
Plane Z4 0.63 0.84 0.57 0.69 -0.06 -0.14
Plane Z5 0.75 0.72 0.60 0.77 -0.15 0.05
Plane Z6 0.71 0.56 0.69 0.69 -0.02 0.13
Plane Z7 0.82 0.80 0.74 0.71 -0.08 -0.09
Avergae 0.75 0.80 0.67 0.72 -0.07 -0.07
