Study and application of a mathematical model for the provisional assessment of areas and nasal resistance, obtained using acoustic rhinometry and active anterior rhinomanometry.

Abstract

Nasal resistance (NR) depends on the geometrical features and tortuosity of the nasal airway and on the air flow. Knowing the longitudinal distribution of cross-sectional areas (CSAs) in the nasal cavity (which can be obtained using acoustic rhinometry) and the laminar nasal resistance (obtainable by processing the rhinomanometric results), it is possible to calculate, utilizing a mathematical model elaborated on the basis of fluid dynamics, the differential nasal resistance (NRdiff) and the cumulative nasal resistance (NRcum), thus localizing the position at which the highest resistance is concentrated and the related longitudinal distribution. Using a mathematical model, we integrated the sigmoid curves DeltaP/Q of rhinomanometry with the cross-sectional areas obtained using acoustic rhinometry, thus obtaining the normal distribution of differential and cumulative nasal resistances. Afterwards, we empirically reduced the cross-sectional areas corresponding to the head, body, tail and the whole inferior turbinate, recalculating the differential and cumulative nasal resistance distribution curves. The results show that reduction of up to 50% of cross-sectional areas does not substantially affect the resistivity role of the nasal valve, while greater reductions move the highest resistivity point to an area at the junction of the body and the head of the inferior turbinate. The study of the differential nasal resistance trend curves as a function of the reduction of cross-sectional areas shows that the resistance variation of the body and the whole inferior turbinate prevail with reductions of up to 40%, while the variation of cross-sectional areas of the body bordering the inferior turbinate head is predominant with higher reductions. The cross-sectional areas of the nasal airway cavity with highest resistivity are mainly located in an anterior position, where the differential nasal resistances are higher, but there are substantial variations produced by reducing the cross-sectional area of the posterior nasal airway. A similar model can produce provisional values for the results obtainable with functional nasal surgery.