The relationship between nasal resistance to airflow and the airspace minimal cross-sectional area

Abstract

The relationship between nasal resistance (R) and airspace minimal cross-sectional area (mCSA) remains unclear. After the introduction of acoustic rhinometry, many otolaryngologists believed that mCSA measurements would correlate with subjective perception of nasal airway obstruction (NAO), and thus could provide an objective measure of nasal patency to guide therapy. However, multiple studies reported a low correlation between mCSA and subjective nasal patency, and between mCSA and R. This apparent lack of correlation between nasal form and function has been a long-standing enigma in the field of rhinology. Here we propose that nasal resistance is described by the Bernoulli Obstruction Theory. This theory predicts two flow regimes. For mCSA>Acrit, the constriction is not too severe and there is not a tight coupling between R and mCSA. In contrast, when mCSA<Acrit, nasal resistance is dominated by the severe constriction and it is predicted to be inversely proportional to the minimal cross-sectional area (R∝mCSA(-1)). To test this hypothesis, computational fluid dynamics (CFD) simulations were run in 3-dimensional models based on computed tomography scans of 15 NAO patients pre- and post-surgery (i.e., 60 unilateral nasal cavities). Airspace cross-sectional areas were quantified perpendicular to airflow streamlines. Our computational results are consistent with the theory. Given that in most people mCSA>Acrit (estimated to be 0.37cm(2)), this theory suggests that airway constrictions are rarely an exclusive contributor to nasal resistance, which may explain the weak correlation between mCSA and subjective nasal patency.

Keywords: Acoustic rhinometry; Computational fluid dynamics (CFD); Computational streamline rhinometry; Nasal resistance; Orifice flow.

Figure 1

The concept of computational streamline rhinometry. (LEFT) Flow streamlines were calculated using computational fluid dynamics. (RIGHT) Cross-sectional areas, calculated perpendicular to flow streamlines in the anterior nose and perpendicular to the nasal floor in the posterior nose, were plotted as a function of the distance from nostrils. The distance was normalized by the streamline length (i.e., Distance = 0 corresponds to nostril; Distance = 1 corresponds to choana). The shape of seven cross-sections and their locations in the area-distance curve are illustrated.

Figure 2

Nasal cross-sectional areas were averaged among ten streamlines. (LEFT) Three-dimensional model of the nasal cavity displaying the 10 streamlines used to compute cross-sectional areas in the pre-surgery right nasal cavity of one NAO patient. (RIGHT) Cross-sectional area vs. distance from the nostril along each of the ten streamlines (black lines) and the average area-distance curve among all streamlines (red line).

Figure 3

Pre-surgery vs. post-surgery nasal cross-sectional areas in two NAO patients. (TOP PANELS) Patient A underwent septoplasty alone, which increased the minimal cross-sectional area (mCSA) in the left cavity and decreased mCSA in the right cavity. A symmetrical distribution of left-to-right mCSA was achieved post-surgery. (BOTTOM PANELS) Patient B underwent septoplasty combined with bilateral inferior turbinate reduction. An increase in the airspace cross-sectional area was observed in both nasal cavities.

Figure 4

Average minimal cross-sectional area and nasal resistance in a cohort of 15 NAO patients pre-surgery and post-surgery. The unilateral nasal cavities were assigned as most obstructed or least obstructed based on the pre-operative VAS scores. Asterisk (*) denotes statistical significance at level p < 0.05; N.S. = non-significant.

Figure 5

(A) Unilateral nasal resistance vs. minimal cross-sectional area in the entire cohort (n = 60 nasal cavities corresponding to 15 NAO patients pre- and post-surgery). A power law curve fit provided a correlation of ∣r∣ = 0.816. (B) and (C) The correlation between R and mCSA was stronger in nasal cavities with mCSA < 0.37 cm² (∣r∣ =0.921) than in nasal cavities with mCSA > 0.37 cm² (∣r∣ =0.572). (D) Fitting the CFD-derived nasal resistance with the orifice flow equation yielded a discharge coefficient C_d = 0.49 ± 0.02.

Figure 6

Illustration of how severe airway constrictions contribute disproportionately to nasal resistance. (A) Lateral view of a nasal cavity model showing uniformly spaced coronal planes (D = distance from nostrils divided by the length of septum). (B) Pressure drop in each of the eleven segments defined in panel (A). In the left cavity, most of the pressure drop occurs in the nasal vestibule (nostril to D=0) due to a severe constriction located in that segment (mCSA = 0.12 cm²). In the right cavity, the nasal vestibule was wider (mCSA = 0.66 cm²), thus the 19 Pa pressure drop was distributed more evenly throughout the nasal cavity.