Nasal Valve Manometry by Differential Pressure Measurements

Introduction

Differential pressure refers to the difference in air pressure from one location to another within a system. Differential pressure between two points in the nose is related to a correct ventilation of the inner cavities by which infections and contaminations can be prevented [1]. The nasal area [2] is a three-dimensional region, that is, a volume delimited by well-defined borders, which can be altered by anatomical anomalies [3]. The rhinologist surgeon aims at modifying and normalizing, in shape and size, the inner nasal contour. Cottle [4] divides the interior of the nasal pyramid into 5 areas: vestibular, valve, attic, anterior and posterior parts of the turbinates and of the choanal opening. Deformations of the Cottle areas and of the related fluid-dynamical resistances can severely affect the respiratory dynamics [5]. In the present work, we analyse the fluid-dynamical effects of deformations in the nasal valve (Figure 1).

Figure 1:Description of the Cottle areas in the nose.

Differential Pressure Concepts

When describing air flow from point O in the nasal valve to point A in the nose cavity (see Figure 1) it should be noted that the pressure gradient p_A − p_o is negative, due to the depression generated by lungs. In this case we can talk about gauge pressure since point O is at atmospheric pressure. If air flow is considered laminar, non-viscous and irrotational, but not stationary, Bernoulli’s theorem for non-stationary fluid flow may be applied. In fact, under these conditions and in the limit of low velocities, air can be considered an ideal fluid. The main effect of this pressure gradient is a difference in the velocities, 𝑉𝑂 and 𝑉𝐴, of the fluid in points O and A, respectively. In fact, by writing Bernoulli’s equation for nonstationary fluid flow, we have:

where 𝑎𝑥 is the acceleration (assumed to be uniform over the path along the 𝑥-direction (going from O to A) of the fluid and x = x_A − x_O Is the (positive) distance between points O and A. When inertial effects are neglected and the velocity 𝑉_O is taken equal to zero, Formula 1 reduces to the following:

So that a constant velocity can be maintained at steady state at point A of the nasal valve (see figure 2). Let us now consider the same sector with two different sections of cross-sectional areas 𝑆_𝐴 in 𝐴 and 𝑆_𝐵 in B, as in Figure 2. We can thus rewrite Equation (2) also for point B as follows:

Figure 2:Two adjacent regions, A and C, separated by a nasal spur in B. Region C consists of two subregions, C1 and C2, with different fluiddynamical properties

(Figure 2) The differential pressure Δp_AB = ρ_B − p now be defined, according to Equation (2) and (3), as follows:

In the case shown in Figure 2, however, 𝑉_𝐵 is greater than 𝑉𝐴. In fact, point B can be considered a nasal deviation reducing the cross section in that sector, so that 𝑆_𝐴 > 𝑆_𝐵. In fact, by mass conservation

so that

Therefore, the highest is the ratio S_A/S_B the most negative is the differential pressure Δ𝑝. This differential pressure can be measured by means of the nose and sinus manometry using a two- terminal probe (see Figure 3), fit for getting the values of the pressure in points 𝐴 and 𝐵 [5]. Beyond point B, the cross section of the same sector is equal to 𝑆_𝐴, but with different flow pattern. In fact, the considered nasal valve anomaly affects air flow properties in points 𝐶₁ and 𝐶₂, as shown in Figure 2. Let us then assume that the region beyond point B is formed by two subregions of cross- sectional areas Sc1 and 𝑆𝐶₂, respectively. In this way, by proceeding as in Equation (6), for 𝐶₁ we may set:

Figure 3:Double-ended probe for differential pressure manometry.

Being the flow pattern in 𝐶1 very similar to that in B, we expect a very small value of. On the other hand, assuming that we can still apply Bernoulli’s equation in the region close to point 𝐶₂, we may write:

having set the velocity 𝑉𝐶₂ close to point 𝐶₂ equal to zero. Therefore, we can summarize these results by saying that the differential pressure between points 𝐶₁ and B is approximately equal to zero, while the differential pressure between points 𝐶₂ and 𝐵 is positive. In terms of fluid flow patterns, we may therefore say that air flow velocity in _𝐶1 is almost equal to 𝑉_𝐵, while a stagnation region is formed around point 𝐶₂.

Methods

The work was performed in accordance with the principles of the 1983 Declaration of Helsinki. The study was approved by the local board of medical ethics. Written informed consent was obtained from all participants prior to the inclusion in the study. Twenty non-smoker Caucasian subjects suffering from incomplete nasal valve sub-obstruction were enrolled [6,7]. All of them underwent nasal endoscopy. The sample was homogeneous by age, sex, and body weight (10 M, 10 F; mean age 42.64 ±13.1) (Figure 4). To carry out pressure measurements, we used the DDM-MG1 patented manometer. Technical characteristics of this digital manometer can be obtained in reference. [8,9]. The differential pressure has been measured by means of the nose and sinus manometry using a two-terminals probe (double-ended), spaced apart by 0.5cm, fit for getting the values at the same time in two close points of the nasal valve deviation, for points A-B, B-C1, B-C2 (See Figure 2). The probe was placed in these points under endoscopic guidance. Subjects were asked to breathe through the nose for four seconds slowly and deeply [9-10] while the selected nasal area was checked by video-endoscopy for the entire duration of the examination (see Figure 4). This respiration pattern is adopted to avoid turbulent flow. The manometer was connected to a computer with software for visualization and recording of pressure values. Data supporting this study is included within the article.

Figure 4:Endoscopic control and computer analysis of the manometric measurements.

Results

In Table 1 we report the average peak values of the differential pressure, expressed in mbar. Experimental data for sectors A-B, B-C1, B- C2 were gathered for both groups of patients. We obtained an average peak of the differential pressure of -0,3 mbar for sector A-B, of about 0,0 mbar for sector B-C1 and of +0,1 mbar for sector B-C2 (Table 1).

Discussion and Conclusions

Considering the experimental values for the differential pressure between points A and B (second column in Table 1), we notice that they are negative, as predicted by Equation (6). The small values of the pressure gradient allow stationary air flow without generating turbulences. As for the experimental values for the differential pressure between points B and C1 (third column in Table 1), we notice that they are almost equal to zero since the velocity profile does not vary appreciably. Finally, for the experimental values for the differential pressure between points B and C2 (fourth column in Table 1), we notice that they are positive, as predicted by Equation (8), since higher pressure in the stagnation region C2 is present. The differential pressure approach is thus useful to investigate the fluid dynamical phenomena induced by the presence of a nasal valve deviation. In this respect, we notice that the reduced size of the probe allows a pinpoint measurement localized with precision in the chosen valve area, not modifying the anatomy or the air flow pattern during measurements. In this respect, we also mention that the nose-sinus manometry allows us to detect the pressure values at the “critical points” under investigation in real time. Finally, we may notice that this method can be adopted for any point of the nasal cavity where a septum spur is present. All authors declare that they have no conflicts of interest. This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Table 1:Average peak of the differential pressure for a spur in the nasal valve area.

Conflict of Interest

No conflict of interest.

Acknowledgement

None.

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