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A quantitative technique for assessing nasal airway impairment
A quantitative technique for assessing nasal airzoay impairment Donald Chapel
W. Warren, Hill,
D.D.S., Ph.D.*
N. C.
The controversy concerning the effects of impaired nasal respiration on dentofacial development stems largely from the lack of a reliable method to assess airway impairment. The purpose of this study was to develop and validate a quantitative technique to estimate nasal airway dimensions so that normal and impaired nasorespiratory function could be defined. The method involves a modification of the theoretical hydraulic principle and utilizes the following equation to estimate cross-sectional area of the nose (N,): ‘/2 (where
d = density
of air).
Pressure drop (AP) across the nose is measured simultaneously with airflow (\i) through the nose during breathing, using appropriate transducers and a PDP 11134 computer. An analog model of the upper airway was used to determine the discharge coefficient (k) and estimate measurement error. Model studies demonstrate a measurement error of less than 5% for nasal cross-sectional areas of 0.02 to 1.2 cm*. Studies involving eighteen adult subjects and twenty-six children 8 to 11 years of age revealed mean smallest cross-sectional nasal areas of 0.62 cm2 -c 0.17 and 0.43 cm2 f 0.076, respectively. The results indicate that the technique should enable clinicians to (1) estimate size of the airway during breathing, (2) distinguish between normal and impaired nasal respiratory function, and (3) determine quantitatively the effects of surgical and/or orthodontic treatment for improving nasal respiration.
Key words:
Nasal airway impairment,
airway assessment, nasal breathing,
assessment of nasal airway
T
here is substantial disagreement among clinicians concerning the significance of impaired nasal respiration. I-’ This controversy is due in great part to our inability to evaluate nasal airway impairment quantitatively. Clearly, an understanding of upper airway respiratory function is of vital interest to clinicians in a variety of disciplines. The diagnosis of nasal obstruction is often based on clinical impressions, and yet this description may determine the course of treatment. Often an aggressive approach to correct this suspected condition is pursued.Y-‘5 Suggested remedies include surgery for the removal of adenoids with or without tonsils, turbinectomy, and correction of septal deviation. More conservative approaches include rapid maxillary expansion, the application of medications, or special dietary regimens. Since surgery entails some risk, the reasons for selecting such treatment should be based on solid, tangible considerations. Assessment of structures and the
This study was supported in part by Grants DE06061, DE06957, DE02668, and RR05333 from the National Institute of Dental Research. *Kenan Professor and Chairman, Dental Ecology, Dental Research Center, University of North Carolina at Chapel Hill.
306
PI n
P2
Fig. 1. The hydrokinetic equation estimates the smallest cross-sectional area or constriction in an airway. The two parameters necessary for measurement are pressure drop across the constriction (AP) and airflow through the constriction (i/).
way they function should be performed in a quantitative way, and diagnosis should be based on reproducible data. Orthodontists frequently diagnose nasal airway impairment from radiographs. I’, I7 This practice has been criticized because radiographs are two-dimensional superimpositions of shadows of structures and do not provide a true indication of airway patency. In fact, such radiographic artifacts caused by superimposition of shadows may lead to grossly misleading conclusions.
Volume 86 h’umbrr 4
IO:10
“MOUTH” “OROPHARVNX”
.25Diom
All Measurements
in MM
Fig.
2. Diagrammatic
representation
of the model.
Differential Pressure Transducer
Variable Nasopharyngeal Isthmus
Fig.
3. Method
of measuring
The purpose of the present study is to demonstrate a useful, noninvasive technique for determining clinically significant nasal obstruction. The technique is based upon hydrokinetic principles using instruments capable of accurately measuring respiratory parameters.
the discharge
coefficient
DESCRIPTION
k
OF TECHNIQUE
The method involves a modification of the theoretical hydraulic principle and assumes that the smallest cross-sectional area of a structure can be determined if the differential pressure across the structure is mea-
308
Am. J. Orthod. Ocrober 1984
Wurren
7.0
-
6.0
-
Y
5.0
I 0
I’ IO
I1 20
11 30
‘1 40
I’ 50
11 60
11 70
I 90
I
I 90
I
I 100
I’
1’ 110
120
AREA ( mm2 1 Fig. 4. Relationship between constriction sectional area, its average value (0.65)
size and coefficient is used as a constant.
Table I. Calculation of coefficient k Nasal area (cm’)
A 1.204
B 0.761
C 0.171
D 0.024
Pressure (dyneslcm’)
294 294 333 215 147 176 166 147 1411 705 735 940 1205 1029 793 1381
= Rate of airflow/k
Flow (cclsec)
so slightly
with cross-
k
655 662 698 555 273 297 273 285 185 128 135 149 22 20 18 24 Mean k =
2 (Differential Density
k varies
Table II. Calculated size of nasal cross-sectional area when using k as a constant value
0.71 0.72 0.71 0.70 0.66 0.66 0.62 0.69 0.65 0.63 0.66 0.64 0.60 0.61 0.59 0.61 0.65
sured simultaneously with rate of airflow through it (Fig. 1). This method has been used in speech research by my associates and me since 1961 .18-20Its reliability has been verified in a number of laboratories.21-“‘3 The equation Area
k. Since
pressure) of air
‘+ I
where k = 0.65 and density of air = 0.001 gm/cm”, involves two parameters associated with nasal breathing, namely, airway pressure and airflow. Simultaneous measurement of these two parameters provides the information necessary for application of the theoretical equation. Since even in the simplest cases, an equation cannot be developed which accounts for all the details of turbulent, nonuniform, and rotational airflow, the derivation
Actual
size (cm2)
A 1.204
B 0.761
C 0.171
D 0.024
Calculated
size (cm’)
1.315 1.329 1.317 1.320 0.777 0.771 0.730 0.81 I 0.170 0.166 0.171 0.168 0.023 0.022 0.022 0.023
Error (c-m’)
to.111 +0.125 +0.113 +0.116 +O.Olh +0.010 -0.031 t 0.050 -~o.ool -0.005 0.0 -- 0.003 -0.001 - 0.002 - 0.002 -0.001
was adapted to a fictitious average steady motion. The theoretical equation, therefore, neglects several fundamental considerations and is only an approximation of actual flow conditions in the nose and nasopharynx; that is, airflow is actually somewhat unsteady, nonuniform, and rotational. The estimated size of the nasal cross-sectional area will differ from the theoretical area because of these factors. Hence, to obtain the estimated area from this “rational approximation, ” a correction factor k must be introduced. The quadratic nature of the equation accounts for resistance and turbulence, and the discharge coefficient accounts for nonuniformity of flow. It is impossible to measure this constant k directly, so a simple model was used instead. Models are the only way to derive a k (constant), and other laboratories cited in the text support this approach. Their published
Volume 86 Number 4
Nasal
TRANSDUCER
TRANSDUCER
PRESSURE AMPLIFIER
airway
impairment
COMPUTER
. PRESSURE
r-l
TERMINAL
Fig. 5. Diagrammatic croprocessor is now
representation of mask and available for computing size.
catheter
placement.
A small,
inexpensive
mi-
_.-_ tlmTFEnrI*L
996 7z6.m
-89
.-.-_
%i’462~
t.Ji446!i44
FLOU
Fig. 6. Hard copy of data generated during breathing. Subject has a normal airway. Top line shows pressure drop across the nasal airway (AP); second line shows mask pressure (Pz); third line shows oral pressure (P,); and bottom line shows nasal airflow (i/). Numbers at top line represent cursor points for measurement, Data are reported out at top right in the following order: flow (i/), pres,, pres*, diff pres (AP), and computed area. Areas ranged from 46.28 to 46.98 cm*.
309
310
Wurren
Fig. 7. Hard copy of data generated from subject smaller and not compatible with nasal breathing.
data demonstrate its validity. The fact that the model is nonanatomic is really not important at the low airflow rates of breathing. The point is that this is an accepted procedure to generate a discharge coefficient since a human subject cannot be used for this type of measurement. The model of the upper respiratory tract is illustrated in Fig. 2. Dimensions, such as oral cavity and nasal pathway length, were approximated from cephalometric measurements of normal adults. Structures that could not be approximated from x-ray measurements, such as cross-sectional area of the mouth and nose, were constructed so as to offer resistance to airflow comparable to known values in normal persons. The nasopharyngeal isthmus was designed so that its dimensions could be varied to simulate varying degrees of adenoid hypertrophy. Similarly, the nasal chamber was designed so that its resistance to airflow could be modified. The technique used is shown in Fig. 3 and has been described previously.“” Differential pressure between the “nasopharynx” and the outside of the ’ ‘nose ” was transmitted directly to a differential pres-
with choanal atresia. Constriction size is considerably Subject is predominantly a mouth breather.
sure transducer by two catheters. The catheters were plugged at their tips but were open at the sides for measurement of static pressures. A water manometer was used to calibrate pressure. Airflow was measured by a heated pneumotachograph connected to the “nose” and calibrated with a rotameter. An air cylinder supplied the flow necessary to simulate the aerodynamics of breathing. Data acquisition and analysis were accomplished with a PDP 11134 computer. However, a small, inexpensive microprocessor is now available for this purpose. * RESULTS
OF MODEL
STUDIES
A series of sixteen experiments was carried out on the model at four different cross-sectional areas. Table I reveals the calculated k for the equation. A mean k of 0.65 was used on the basis of these data. Fig. 4 illustrates how k varies with cross-sectional area. Table II *Pal
II, Micro
Tronics
Corp.,
Cmboro.
N. C.
Volume 86 Numhrr 4
Nusal ainvay impairment
III. Smallest nasal cross-sectional areas: Normal adults
Table
Subject
2 3
6 8 10 II 12 13 14 15 16 17 18
Area
(cm*)
0.68 0.43 0.66 0.35 0.39 0.87 0.61 0.47 0.63 0.61 0.87 0.93 0.45 0.58 0.55 0.78 0.52 0.78 Mean 0.62 SD 0.17
reveals the measurement error when a mean value fork is used. HUMAN
STUDIES
The technique was then used on forty-four normal subjects. Eighteen subjects were 15 years of age and older, and twenty-six subjects were 8 to 11 years of age. All subjects were examined by an otolaryngologist and were found to have clinically normal nasal airways. Fig. 5 illustrates mask and catheter placement. The nasal pressure drop was measured with a differential pressure transducer connected to two catheters, as in the model study. The first catheter was positioned in the subject’s oropharynx as far posteriorly as could be tolerated, and the second catheter was placed within a nasal mask in front of the nose. Nasal airflow was measured with a heated pneumotachograph connected to the well-adapted nasal mask. Each subject was asked to inhale as normally as possible through the mouth, close the lips, and then exhale through the nose. The resulting pressure and airflow patterns were transmitted to the computer and analyzed and recorded on hard copy almost simultaneously. Figs. 6 and 7 illustrate hard-copy records of two subjects, one with a normal airway and the other with choanal atresia. The latter subject is for illustration only. The data from eighteen normal adult subjects are shown in Table III. A mean cross-sectional area of 0.62 cm’ i 0. I7 was found. Areas ranged from a minimum of 0.35 cm’ to a maximum of 0.93 cm”. Montgomery
311
IV. Smallest nasal cross-sectional areas: Children aged 8 to 11 years
Table
Subject
2 3 5 6
8 9 10 11 12 13 14 I.5 16 17 18 19 20 21 22 23 24 25 26
Area
(cm’)
0.45 0.36 0.60 0.37 0.31 0.54 0.35 0.44 0.49 0.33 0.32 0.52 0.47 0.34 0.41 0.34 0.50 0.42 0.34 0.42 0.43 0.44 0.49 0.49 0.45 0.42 Mean 0.43 SD 0.08
and associates,“” using computed tomography to study the nasal airway in cadavers, observed an average smallest cross-sectional area of approximately 1.2 cm’. Although their study is probably not representative of living subjects, the dimensional differences between findings appear to be quite reasonable. Data from twenty-six normal 8- to 1 I-year-olds are shown in Table IV. A mean of 0.43 cm” +- 0.08 was observed, with a range of 0.31 cm” to 0.60 cm2. The 33% smaller mean area in children reflects the fact that nasal growth has not been completed. The limited data presented on normal adults and children serve only as an example of how airway dimensions can be quantified, and this small sample should not be considered as representative of the cross-sectional dimensions of the normal nose. The important point is that this technique is a significant improvement over nasal airway resistance measurements since it uses an equation that more realistically fits actual flow conditions.‘fiP28 Nasal airway resistance measurements must be made at a specific rate of airflow, since a laminar flow equation is used under turbulent flow conditions.
Cross-sectional area measurement involves a quadratic equation which assumes turbulent airflow. Theoretically, the area measurement in contrast to nasal resistance measurements can be made at any point in the breathing cycle and at any rate of airflow. For example, a person might have a nasal resistance of 2.0 cm H,O/LI set at 0.3 Lisec flow, 2.5 cm HzOIL/sec at 0.4 Lisec flew, and 3.5 cm H,O/L/sec at 0.5 Lisec flow. Area measurements provide the same value at any flow rate. This new approach considers the nasal airway to be a tube with a cross-sectional area, and the equation estimates its smallest constriction. This is especially important in breathing since the size of a constriction has a geometric effect on airway resistance and the work of breathing. The more impaired an airway is, in terms of obstruction, the smaller the cross-sectional area will be. This parameter can be measured pre- and postoperatively in cases of nasal surgery, maxillary osteotomies, and maxillary expansion, and an assessment of the effects of treatment can be made in a more reliable way. One disadvantage is that the technique does mt provide any information on where the minimum area actually is. Although additional validating studies will be performed, the results to date are very encouraging. A similar technique has been used previously in speech research, and its validity has been substantiated in a number of studies.‘XP”” Subsequent studies in our laboratory should allow us to determine the dimensions of an adequate nasal airway in terms of the smallest cross-sectional area as well as define nasal airway impairment in more quantitative terms. In addition, a more definitive assessment of the effects of surgical and/or orthodontic treatment on airway impairment seems possible. REFERENCES 1. Morrison WW: The interrelationship between nasal obstruction and oral deformities. INI J ORTHOD 17: 453-458, 1931. 2. Ricketts RM: Respiratory obstruction syndrome. AM J OR~HOD 54: 495-507, 1968. 3. Linder-Aronson S: Adenoids: Their effect on mode of breathing and nasal airflow and their relationship to characteristics of the facial skeleton and the dentition. Acta Otolaryngol Suppl 265: l-132. 1979. 4. Linder-Aronson S: Effects of adenoidectomy on the dentition and facial skeleton over a period of five years. Trans Eur Orthod Sot, pp. 177-186, 1973. 5. Quinn GW: Airway interference and its effect upon the growth and development of the face, jaws, dentition and associated parts. NC Dent J 60: 28.31, 1978. 6. Leech HL: A clinical analysis of orofacial morphology and behavior of 500 patients attending an upper respiratory research clinic. Dent Pratt Dent Ret 9: 57-68, 1958. 7. Watson RM, Warren DW, Fischer ND: Nasal resistance,
8.
9. IO. Il. 12. 13. 14. 15.
16.
17.
18.
19.
20.
21. 22.
23. 24. 25.
26.
27.
28.
skeletal classification and mouthbreathing in orthodontic patients. AM J ORTHOD 54: 367-379, 1968. Vig PS, Sarver DM, Hall DJ, Warren DW: Quantitative evaluation of nasal airflow in relation to facial morphology. A\r J O~~HOD 79: 263.271, 1981. Quinn GW: Are dentofacial deformities a preventable disease’.’ NC Dent J 61: 5-6, 1978. Schulhof RJ: Consideration of airway in orthodontics. J Clin Orthod 12: 440-444, 1978. Rubin RM: Facial deformity: a preventable disease’? Angle Orthod 49: 98-103. 1979. Rubin RM: Mode of respiration and facial growth. A~I J ORIHOD 78: 505-510, 1980. Ricketts RM: On early treatment. Part I. J.C.O. Interviews. J Clin Orthod 13: 23-38, 1979. Jennes ML: Corrective nasal surgery in children. Arch Otolaryngol 79: 145-151, 1963. Reid JM, Dalston JA: The indications for tonsillectomy and adenoidectomy. Otolaryngol Clin North Am, pp 339-344. 1970. Holmberg H, Linder-Aronson S: Cephalometric radiographs as a means of evaluating the capacity of the nasal pharyngeal airway. A\I J ORTHOD 76: 479-490, 1979. Warren DW: Velopharyngeal orifice size and upper pharyngeal pressure-tlow patterns in normal speech. Plast Reconstr Surg 33: 148-161, 1964. Warren DW: Velopharyngeal orifice size and upper pharyngeal pressure-flow patterns in cleft palate speech: a preliminary study. Plast Reconstr Surg 34: 15-26, 1964. Warren DW: The determination of velopharyngeal incompetency by aerodynamic and acoustical techniques. Clin Plastic Surg, pp. 299-304. 1975. Warren DW: Aerodynamic studies of upper airway: implications for growth, breathing and speech. In McNamara JA (editor): Nasorespiratory function and craniofacial growth. Ann Arbor. 1979, University of Michigan, pp. 41-86. Lubker JC: Velopharyngeal orifice area: a replication of analog experimentation. J Speech Hear Res 12: 218-222. 1969. Smith BE, Weinberg B: Prediction of velophxyngeal orifice area: a re-examination of model experimentation. Cleft Palate J 17: 277-282. 1980. Smith BE. Weinberg B: Modeled velopharyngeal orifice area prediction. Cleft Palate J 19: 177-180, 1982. Warren DW, Lehman MD, Hinton VA: An analog study of upper airway breathing. Al~l J ORTHOD (in press). Montgomery WM, Vig PS, Staab EU, Matteson SR: Computed tomography: a three-dimensional study of the nasal airway. Ahl J ORTHOD 76: 363-375, 1979. Watson R. Warren DW, Fischer ND: Nasal resistance and mouth hreathing in children and young adults. AM J OKrFioD 54: 367. 379, 1968. Warren DW, Duany LF, Fischer ND: Nasal pathway resistance in normal and cleft lip and palate subjects. Cleft Palate J 6: 134.140. 1969. Hershey HG, Stewart BL, Warren DW: Changes in nasal airway resistance associated with rapid maxillary expansion. AM J OIUH~D
69: 274.284,
Rq~rir~ t rcqur.,~\
,o.
Dr. Donald Warren School of Dentistry 209H University of. North Carolina Chapel Hill. NC 27514
1976.
Volume 86 Number 4
Nasal
Derivation of the hydrokinetic equation. The basic equations used to develop the “theoretical equation” are the equation of continuity and the energy equation combined in a special form. For developing and discussing the equation, the following symbols will be used: A P Zi ZI, S V y D V
= = = = = = = = =
Area . . . . . . . . . . . . . . . . . . . . . . . . . . . ..cm’ Absolute static pressure.. . , . . . .dynes/cm’ . . . . . . . .ergs/cm” lntemal energy . . . . . Kinetic energy.. . . . . . . . . . . . .ergs/cm” Mean axial speed of fluid . . . cmisec Volume . . . . . . . . . . . . . . . . . . . . cm3 Specific weight of the fluid . . .dynes/cm” Density of air (0.001) . . . . . . . .gm/cm’ Volume rate of airflow.. . . . . . ..cm”/sec
(3)
The general energy equation states that as each mass of fluid passes from A, to AS, the increase of its total energy, kinetic plus internal, is equal to the work done on it plus the heat added to it. The work done upon the fluid due to the pressure change is (PIV, - P*V*)
(4)
Since the weight of air is negligible, the gravitational potential can be neglected. Thus, the general energy equation becomes (ZK2
+
Zi2) -
(ZK1
Zi,) = (P,V, - P,V,)
+
(5)
It is assumed in equation 5 that there is no heat transfer (adiabatic flow). Now ordinary subsonic aerodynamics is an example of incompressible flow, so v, = v,
impairment
313
eddy currents by viscosity. If Z, represents the quantity of this dissipated energy, then Ziz - Zi, = Zd
(8)
and ZK2
-
ZK1
=
(P,
-
Pz)
v
-
Since flow is actually nonuniform, netic energy may be represented by
(9)
&,
the average ki-
(10)
Consider a steady stream flowing along a channel with rigid, impervious walls, from section A, to a section A2. According to the equation of continuity for steady flow, the mass of fluid passing any section A, per unit time is constant and equal to that passing a second section A2 per unit time. Thus, A,$ = A2S2
airway
(6)
in which I/? is the energy loss due to nonuniform flow. Finally, in nearly all cases turbulent eddying flow occurs and this component has a kinetic energy of its own, in addition to that of the axial motion already present. Thus, if the average amount of this new kinetic energy be denoted by Zt* (Zt for turbulence), the complete expression is zK=z
+v+ze
(11)
By applying this equation to the sections A, and A%, the following equation is obtained ZK2
-
ZK,
=
2’
~
2’+
(Tz2
-
VIZ)
+
(zt,’
-
Zt,‘)
(12)
Now, replacing V with l/y in equation 9 and rearranging,
S2 ---~ 22
%-
2g
(PI - P2) ;
- x
(13)
where x = z, + pP,* - yrj2) + z** 212)
(14)
The term x represents the net effect of resistance, nonuniformity, and turbulence. If, between At and A2, we neglect these factors represented by x, a simplified approximate equation can be written. Thus, s22Y22=(p a 22
-p)L 2
l
Y
(15)
so that
Thus. (ZKZ
+
Zi,) -
(ZK1
+
Zi,) = (PI - P,)V
(7)
Since practically no work of compression or expansion is done and no heat is transmitted to or from the walls, the internal energy Zi cannot change from either of these causes. However, some heat is generated by wall resistance and in the continual damping out of
If we let V be the volume rate of flow, then (+/A)
= S
(17)
according to the continuity equation and A,!$ = A&
= iJ
(1%
314
Warren
Am. J Orthod. October 1984
If we now assume AZ to be very small compared to Ai so that AZ << Al, then S, >> S1, we can neglect S12 compared to Sz2. Hence,
or rearranging A2 = +g(y)]'
(21)
s22 = “(%yp,) Y = Dg
and
(22)
then (23)
BOUND
VOLUMES
AVAILABLE
TO SUBSCRIBERS
Bound volumes ofthe AMERICAN JOURNAL OFORTHODONTICS are available to subscribers (only) for the 1984 issues from the Publisher, at a cost of $42.50 ($51 .OO international) for Vol. 84 (January-June) and Vol. 85 (July-December). Shipping charges are included. Each bound volume contains a subject and author index and all advertising is removed. Copies are shipped within 30 days after publication of the last issue in the volume. The binding is durable buckram with the journal name, volume number, and year stamped in gold on the spine. Payment must accompany all orders. Contact The C. V. Mosby Company, Circulation Department, 11830 Westline Industrial Drive, St. Louis, Missouri 63146, USA; phone (800) 3254177, ext. 351. Subscriptions must be in force to qualify. Bound volumes are not available in place of a regular Journal subscription.
W. Warren, Hill,
D.D.S., Ph.D.*
N. C.
The controversy concerning the effects of impaired nasal respiration on dentofacial development stems largely from the lack of a reliable method to assess airway impairment. The purpose of this study was to develop and validate a quantitative technique to estimate nasal airway dimensions so that normal and impaired nasorespiratory function could be defined. The method involves a modification of the theoretical hydraulic principle and utilizes the following equation to estimate cross-sectional area of the nose (N,): ‘/2 (where
d = density
of air).
Pressure drop (AP) across the nose is measured simultaneously with airflow (\i) through the nose during breathing, using appropriate transducers and a PDP 11134 computer. An analog model of the upper airway was used to determine the discharge coefficient (k) and estimate measurement error. Model studies demonstrate a measurement error of less than 5% for nasal cross-sectional areas of 0.02 to 1.2 cm*. Studies involving eighteen adult subjects and twenty-six children 8 to 11 years of age revealed mean smallest cross-sectional nasal areas of 0.62 cm2 -c 0.17 and 0.43 cm2 f 0.076, respectively. The results indicate that the technique should enable clinicians to (1) estimate size of the airway during breathing, (2) distinguish between normal and impaired nasal respiratory function, and (3) determine quantitatively the effects of surgical and/or orthodontic treatment for improving nasal respiration.
Key words:
Nasal airway impairment,
airway assessment, nasal breathing,
assessment of nasal airway
T
here is substantial disagreement among clinicians concerning the significance of impaired nasal respiration. I-’ This controversy is due in great part to our inability to evaluate nasal airway impairment quantitatively. Clearly, an understanding of upper airway respiratory function is of vital interest to clinicians in a variety of disciplines. The diagnosis of nasal obstruction is often based on clinical impressions, and yet this description may determine the course of treatment. Often an aggressive approach to correct this suspected condition is pursued.Y-‘5 Suggested remedies include surgery for the removal of adenoids with or without tonsils, turbinectomy, and correction of septal deviation. More conservative approaches include rapid maxillary expansion, the application of medications, or special dietary regimens. Since surgery entails some risk, the reasons for selecting such treatment should be based on solid, tangible considerations. Assessment of structures and the
This study was supported in part by Grants DE06061, DE06957, DE02668, and RR05333 from the National Institute of Dental Research. *Kenan Professor and Chairman, Dental Ecology, Dental Research Center, University of North Carolina at Chapel Hill.
306
PI n
P2
Fig. 1. The hydrokinetic equation estimates the smallest cross-sectional area or constriction in an airway. The two parameters necessary for measurement are pressure drop across the constriction (AP) and airflow through the constriction (i/).
way they function should be performed in a quantitative way, and diagnosis should be based on reproducible data. Orthodontists frequently diagnose nasal airway impairment from radiographs. I’, I7 This practice has been criticized because radiographs are two-dimensional superimpositions of shadows of structures and do not provide a true indication of airway patency. In fact, such radiographic artifacts caused by superimposition of shadows may lead to grossly misleading conclusions.
Volume 86 h’umbrr 4
IO:10
“MOUTH” “OROPHARVNX”
.25Diom
All Measurements
in MM
Fig.
2. Diagrammatic
representation
of the model.
Differential Pressure Transducer
Variable Nasopharyngeal Isthmus
Fig.
3. Method
of measuring
The purpose of the present study is to demonstrate a useful, noninvasive technique for determining clinically significant nasal obstruction. The technique is based upon hydrokinetic principles using instruments capable of accurately measuring respiratory parameters.
the discharge
coefficient
DESCRIPTION
k
OF TECHNIQUE
The method involves a modification of the theoretical hydraulic principle and assumes that the smallest cross-sectional area of a structure can be determined if the differential pressure across the structure is mea-
308
Am. J. Orthod. Ocrober 1984
Wurren
7.0
-
6.0
-
Y
5.0
I 0
I’ IO
I1 20
11 30
‘1 40
I’ 50
11 60
11 70
I 90
I
I 90
I
I 100
I’
1’ 110
120
AREA ( mm2 1 Fig. 4. Relationship between constriction sectional area, its average value (0.65)
size and coefficient is used as a constant.
Table I. Calculation of coefficient k Nasal area (cm’)
A 1.204
B 0.761
C 0.171
D 0.024
Pressure (dyneslcm’)
294 294 333 215 147 176 166 147 1411 705 735 940 1205 1029 793 1381
= Rate of airflow/k
Flow (cclsec)
so slightly
with cross-
k
655 662 698 555 273 297 273 285 185 128 135 149 22 20 18 24 Mean k =
2 (Differential Density
k varies
Table II. Calculated size of nasal cross-sectional area when using k as a constant value
0.71 0.72 0.71 0.70 0.66 0.66 0.62 0.69 0.65 0.63 0.66 0.64 0.60 0.61 0.59 0.61 0.65
sured simultaneously with rate of airflow through it (Fig. 1). This method has been used in speech research by my associates and me since 1961 .18-20Its reliability has been verified in a number of laboratories.21-“‘3 The equation Area
k. Since
pressure) of air
‘+ I
where k = 0.65 and density of air = 0.001 gm/cm”, involves two parameters associated with nasal breathing, namely, airway pressure and airflow. Simultaneous measurement of these two parameters provides the information necessary for application of the theoretical equation. Since even in the simplest cases, an equation cannot be developed which accounts for all the details of turbulent, nonuniform, and rotational airflow, the derivation
Actual
size (cm2)
A 1.204
B 0.761
C 0.171
D 0.024
Calculated
size (cm’)
1.315 1.329 1.317 1.320 0.777 0.771 0.730 0.81 I 0.170 0.166 0.171 0.168 0.023 0.022 0.022 0.023
Error (c-m’)
to.111 +0.125 +0.113 +0.116 +O.Olh +0.010 -0.031 t 0.050 -~o.ool -0.005 0.0 -- 0.003 -0.001 - 0.002 - 0.002 -0.001
was adapted to a fictitious average steady motion. The theoretical equation, therefore, neglects several fundamental considerations and is only an approximation of actual flow conditions in the nose and nasopharynx; that is, airflow is actually somewhat unsteady, nonuniform, and rotational. The estimated size of the nasal cross-sectional area will differ from the theoretical area because of these factors. Hence, to obtain the estimated area from this “rational approximation, ” a correction factor k must be introduced. The quadratic nature of the equation accounts for resistance and turbulence, and the discharge coefficient accounts for nonuniformity of flow. It is impossible to measure this constant k directly, so a simple model was used instead. Models are the only way to derive a k (constant), and other laboratories cited in the text support this approach. Their published
Volume 86 Number 4
Nasal
TRANSDUCER
TRANSDUCER
PRESSURE AMPLIFIER
airway
impairment
COMPUTER
. PRESSURE
r-l
TERMINAL
Fig. 5. Diagrammatic croprocessor is now
representation of mask and available for computing size.
catheter
placement.
A small,
inexpensive
mi-
_.-_ tlmTFEnrI*L
996 7z6.m
-89
.-.-_
%i’462~
t.Ji446!i44
FLOU
Fig. 6. Hard copy of data generated during breathing. Subject has a normal airway. Top line shows pressure drop across the nasal airway (AP); second line shows mask pressure (Pz); third line shows oral pressure (P,); and bottom line shows nasal airflow (i/). Numbers at top line represent cursor points for measurement, Data are reported out at top right in the following order: flow (i/), pres,, pres*, diff pres (AP), and computed area. Areas ranged from 46.28 to 46.98 cm*.
309
310
Wurren
Fig. 7. Hard copy of data generated from subject smaller and not compatible with nasal breathing.
data demonstrate its validity. The fact that the model is nonanatomic is really not important at the low airflow rates of breathing. The point is that this is an accepted procedure to generate a discharge coefficient since a human subject cannot be used for this type of measurement. The model of the upper respiratory tract is illustrated in Fig. 2. Dimensions, such as oral cavity and nasal pathway length, were approximated from cephalometric measurements of normal adults. Structures that could not be approximated from x-ray measurements, such as cross-sectional area of the mouth and nose, were constructed so as to offer resistance to airflow comparable to known values in normal persons. The nasopharyngeal isthmus was designed so that its dimensions could be varied to simulate varying degrees of adenoid hypertrophy. Similarly, the nasal chamber was designed so that its resistance to airflow could be modified. The technique used is shown in Fig. 3 and has been described previously.“” Differential pressure between the “nasopharynx” and the outside of the ’ ‘nose ” was transmitted directly to a differential pres-
with choanal atresia. Constriction size is considerably Subject is predominantly a mouth breather.
sure transducer by two catheters. The catheters were plugged at their tips but were open at the sides for measurement of static pressures. A water manometer was used to calibrate pressure. Airflow was measured by a heated pneumotachograph connected to the “nose” and calibrated with a rotameter. An air cylinder supplied the flow necessary to simulate the aerodynamics of breathing. Data acquisition and analysis were accomplished with a PDP 11134 computer. However, a small, inexpensive microprocessor is now available for this purpose. * RESULTS
OF MODEL
STUDIES
A series of sixteen experiments was carried out on the model at four different cross-sectional areas. Table I reveals the calculated k for the equation. A mean k of 0.65 was used on the basis of these data. Fig. 4 illustrates how k varies with cross-sectional area. Table II *Pal
II, Micro
Tronics
Corp.,
Cmboro.
N. C.
Volume 86 Numhrr 4
Nusal ainvay impairment
III. Smallest nasal cross-sectional areas: Normal adults
Table
Subject
2 3
6 8 10 II 12 13 14 15 16 17 18
Area
(cm*)
0.68 0.43 0.66 0.35 0.39 0.87 0.61 0.47 0.63 0.61 0.87 0.93 0.45 0.58 0.55 0.78 0.52 0.78 Mean 0.62 SD 0.17
reveals the measurement error when a mean value fork is used. HUMAN
STUDIES
The technique was then used on forty-four normal subjects. Eighteen subjects were 15 years of age and older, and twenty-six subjects were 8 to 11 years of age. All subjects were examined by an otolaryngologist and were found to have clinically normal nasal airways. Fig. 5 illustrates mask and catheter placement. The nasal pressure drop was measured with a differential pressure transducer connected to two catheters, as in the model study. The first catheter was positioned in the subject’s oropharynx as far posteriorly as could be tolerated, and the second catheter was placed within a nasal mask in front of the nose. Nasal airflow was measured with a heated pneumotachograph connected to the well-adapted nasal mask. Each subject was asked to inhale as normally as possible through the mouth, close the lips, and then exhale through the nose. The resulting pressure and airflow patterns were transmitted to the computer and analyzed and recorded on hard copy almost simultaneously. Figs. 6 and 7 illustrate hard-copy records of two subjects, one with a normal airway and the other with choanal atresia. The latter subject is for illustration only. The data from eighteen normal adult subjects are shown in Table III. A mean cross-sectional area of 0.62 cm’ i 0. I7 was found. Areas ranged from a minimum of 0.35 cm’ to a maximum of 0.93 cm”. Montgomery
311
IV. Smallest nasal cross-sectional areas: Children aged 8 to 11 years
Table
Subject
2 3 5 6
8 9 10 11 12 13 14 I.5 16 17 18 19 20 21 22 23 24 25 26
Area
(cm’)
0.45 0.36 0.60 0.37 0.31 0.54 0.35 0.44 0.49 0.33 0.32 0.52 0.47 0.34 0.41 0.34 0.50 0.42 0.34 0.42 0.43 0.44 0.49 0.49 0.45 0.42 Mean 0.43 SD 0.08
and associates,“” using computed tomography to study the nasal airway in cadavers, observed an average smallest cross-sectional area of approximately 1.2 cm’. Although their study is probably not representative of living subjects, the dimensional differences between findings appear to be quite reasonable. Data from twenty-six normal 8- to 1 I-year-olds are shown in Table IV. A mean of 0.43 cm” +- 0.08 was observed, with a range of 0.31 cm” to 0.60 cm2. The 33% smaller mean area in children reflects the fact that nasal growth has not been completed. The limited data presented on normal adults and children serve only as an example of how airway dimensions can be quantified, and this small sample should not be considered as representative of the cross-sectional dimensions of the normal nose. The important point is that this technique is a significant improvement over nasal airway resistance measurements since it uses an equation that more realistically fits actual flow conditions.‘fiP28 Nasal airway resistance measurements must be made at a specific rate of airflow, since a laminar flow equation is used under turbulent flow conditions.
Cross-sectional area measurement involves a quadratic equation which assumes turbulent airflow. Theoretically, the area measurement in contrast to nasal resistance measurements can be made at any point in the breathing cycle and at any rate of airflow. For example, a person might have a nasal resistance of 2.0 cm H,O/LI set at 0.3 Lisec flow, 2.5 cm HzOIL/sec at 0.4 Lisec flew, and 3.5 cm H,O/L/sec at 0.5 Lisec flow. Area measurements provide the same value at any flow rate. This new approach considers the nasal airway to be a tube with a cross-sectional area, and the equation estimates its smallest constriction. This is especially important in breathing since the size of a constriction has a geometric effect on airway resistance and the work of breathing. The more impaired an airway is, in terms of obstruction, the smaller the cross-sectional area will be. This parameter can be measured pre- and postoperatively in cases of nasal surgery, maxillary osteotomies, and maxillary expansion, and an assessment of the effects of treatment can be made in a more reliable way. One disadvantage is that the technique does mt provide any information on where the minimum area actually is. Although additional validating studies will be performed, the results to date are very encouraging. A similar technique has been used previously in speech research, and its validity has been substantiated in a number of studies.‘XP”” Subsequent studies in our laboratory should allow us to determine the dimensions of an adequate nasal airway in terms of the smallest cross-sectional area as well as define nasal airway impairment in more quantitative terms. In addition, a more definitive assessment of the effects of surgical and/or orthodontic treatment on airway impairment seems possible. REFERENCES 1. Morrison WW: The interrelationship between nasal obstruction and oral deformities. INI J ORTHOD 17: 453-458, 1931. 2. Ricketts RM: Respiratory obstruction syndrome. AM J OR~HOD 54: 495-507, 1968. 3. Linder-Aronson S: Adenoids: Their effect on mode of breathing and nasal airflow and their relationship to characteristics of the facial skeleton and the dentition. Acta Otolaryngol Suppl 265: l-132. 1979. 4. Linder-Aronson S: Effects of adenoidectomy on the dentition and facial skeleton over a period of five years. Trans Eur Orthod Sot, pp. 177-186, 1973. 5. Quinn GW: Airway interference and its effect upon the growth and development of the face, jaws, dentition and associated parts. NC Dent J 60: 28.31, 1978. 6. Leech HL: A clinical analysis of orofacial morphology and behavior of 500 patients attending an upper respiratory research clinic. Dent Pratt Dent Ret 9: 57-68, 1958. 7. Watson RM, Warren DW, Fischer ND: Nasal resistance,
8.
9. IO. Il. 12. 13. 14. 15.
16.
17.
18.
19.
20.
21. 22.
23. 24. 25.
26.
27.
28.
skeletal classification and mouthbreathing in orthodontic patients. AM J ORTHOD 54: 367-379, 1968. Vig PS, Sarver DM, Hall DJ, Warren DW: Quantitative evaluation of nasal airflow in relation to facial morphology. A\r J O~~HOD 79: 263.271, 1981. Quinn GW: Are dentofacial deformities a preventable disease’.’ NC Dent J 61: 5-6, 1978. Schulhof RJ: Consideration of airway in orthodontics. J Clin Orthod 12: 440-444, 1978. Rubin RM: Facial deformity: a preventable disease’? Angle Orthod 49: 98-103. 1979. Rubin RM: Mode of respiration and facial growth. A~I J ORIHOD 78: 505-510, 1980. Ricketts RM: On early treatment. Part I. J.C.O. Interviews. J Clin Orthod 13: 23-38, 1979. Jennes ML: Corrective nasal surgery in children. Arch Otolaryngol 79: 145-151, 1963. Reid JM, Dalston JA: The indications for tonsillectomy and adenoidectomy. Otolaryngol Clin North Am, pp 339-344. 1970. Holmberg H, Linder-Aronson S: Cephalometric radiographs as a means of evaluating the capacity of the nasal pharyngeal airway. A\I J ORTHOD 76: 479-490, 1979. Warren DW: Velopharyngeal orifice size and upper pharyngeal pressure-tlow patterns in normal speech. Plast Reconstr Surg 33: 148-161, 1964. Warren DW: Velopharyngeal orifice size and upper pharyngeal pressure-flow patterns in cleft palate speech: a preliminary study. Plast Reconstr Surg 34: 15-26, 1964. Warren DW: The determination of velopharyngeal incompetency by aerodynamic and acoustical techniques. Clin Plastic Surg, pp. 299-304. 1975. Warren DW: Aerodynamic studies of upper airway: implications for growth, breathing and speech. In McNamara JA (editor): Nasorespiratory function and craniofacial growth. Ann Arbor. 1979, University of Michigan, pp. 41-86. Lubker JC: Velopharyngeal orifice area: a replication of analog experimentation. J Speech Hear Res 12: 218-222. 1969. Smith BE, Weinberg B: Prediction of velophxyngeal orifice area: a re-examination of model experimentation. Cleft Palate J 17: 277-282. 1980. Smith BE. Weinberg B: Modeled velopharyngeal orifice area prediction. Cleft Palate J 19: 177-180, 1982. Warren DW, Lehman MD, Hinton VA: An analog study of upper airway breathing. Al~l J ORTHOD (in press). Montgomery WM, Vig PS, Staab EU, Matteson SR: Computed tomography: a three-dimensional study of the nasal airway. Ahl J ORTHOD 76: 363-375, 1979. Watson R. Warren DW, Fischer ND: Nasal resistance and mouth hreathing in children and young adults. AM J OKrFioD 54: 367. 379, 1968. Warren DW, Duany LF, Fischer ND: Nasal pathway resistance in normal and cleft lip and palate subjects. Cleft Palate J 6: 134.140. 1969. Hershey HG, Stewart BL, Warren DW: Changes in nasal airway resistance associated with rapid maxillary expansion. AM J OIUH~D
69: 274.284,
Rq~rir~ t rcqur.,~\
,o.
Dr. Donald Warren School of Dentistry 209H University of. North Carolina Chapel Hill. NC 27514
1976.
Volume 86 Number 4
Nasal
Derivation of the hydrokinetic equation. The basic equations used to develop the “theoretical equation” are the equation of continuity and the energy equation combined in a special form. For developing and discussing the equation, the following symbols will be used: A P Zi ZI, S V y D V
= = = = = = = = =
Area . . . . . . . . . . . . . . . . . . . . . . . . . . . ..cm’ Absolute static pressure.. . , . . . .dynes/cm’ . . . . . . . .ergs/cm” lntemal energy . . . . . Kinetic energy.. . . . . . . . . . . . .ergs/cm” Mean axial speed of fluid . . . cmisec Volume . . . . . . . . . . . . . . . . . . . . cm3 Specific weight of the fluid . . .dynes/cm” Density of air (0.001) . . . . . . . .gm/cm’ Volume rate of airflow.. . . . . . ..cm”/sec
(3)
The general energy equation states that as each mass of fluid passes from A, to AS, the increase of its total energy, kinetic plus internal, is equal to the work done on it plus the heat added to it. The work done upon the fluid due to the pressure change is (PIV, - P*V*)
(4)
Since the weight of air is negligible, the gravitational potential can be neglected. Thus, the general energy equation becomes (ZK2
+
Zi2) -
(ZK1
Zi,) = (P,V, - P,V,)
+
(5)
It is assumed in equation 5 that there is no heat transfer (adiabatic flow). Now ordinary subsonic aerodynamics is an example of incompressible flow, so v, = v,
impairment
313
eddy currents by viscosity. If Z, represents the quantity of this dissipated energy, then Ziz - Zi, = Zd
(8)
and ZK2
-
ZK1
=
(P,
-
Pz)
v
-
Since flow is actually nonuniform, netic energy may be represented by
(9)
&,
the average ki-
(10)
Consider a steady stream flowing along a channel with rigid, impervious walls, from section A, to a section A2. According to the equation of continuity for steady flow, the mass of fluid passing any section A, per unit time is constant and equal to that passing a second section A2 per unit time. Thus, A,$ = A2S2
airway
(6)
in which I/? is the energy loss due to nonuniform flow. Finally, in nearly all cases turbulent eddying flow occurs and this component has a kinetic energy of its own, in addition to that of the axial motion already present. Thus, if the average amount of this new kinetic energy be denoted by Zt* (Zt for turbulence), the complete expression is zK=z
+v+ze
(11)
By applying this equation to the sections A, and A%, the following equation is obtained ZK2
-
ZK,
=
2’
~
2’+
(Tz2
-
VIZ)
+
(zt,’
-
Zt,‘)
(12)
Now, replacing V with l/y in equation 9 and rearranging,
S2 ---~ 22
%-
2g
(PI - P2) ;
- x
(13)
where x = z, + pP,* - yrj2) + z** 212)
(14)
The term x represents the net effect of resistance, nonuniformity, and turbulence. If, between At and A2, we neglect these factors represented by x, a simplified approximate equation can be written. Thus, s22Y22=(p a 22
-p)L 2
l
Y
(15)
so that
Thus. (ZKZ
+
Zi,) -
(ZK1
+
Zi,) = (PI - P,)V
(7)
Since practically no work of compression or expansion is done and no heat is transmitted to or from the walls, the internal energy Zi cannot change from either of these causes. However, some heat is generated by wall resistance and in the continual damping out of
If we let V be the volume rate of flow, then (+/A)
= S
(17)
according to the continuity equation and A,!$ = A&
= iJ
(1%
314
Warren
Am. J Orthod. October 1984
If we now assume AZ to be very small compared to Ai so that AZ << Al, then S, >> S1, we can neglect S12 compared to Sz2. Hence,
or rearranging A2 = +g(y)]'
(21)
s22 = “(%yp,) Y = Dg
and
(22)
then (23)
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