Vol. 88, Issue 4, 1457-1466, April 2000
SPECIAL COMMUNICATION
A new nasal acoustic reflection technique to estimate pharyngeal
cross-sectional area during sleep
J.
Huang1,
N.
Itai1,
T.
Hoshiba1,
T.
Fukunaga2,
K.
Yamanouchi1,
H.
Toga1,
K.
Takahashi1, and
N.
Ohya1
1 Division of Respiratory Diseases, Department
of Internal Medicine, and 2 Department of
Clinical Pathology, Kanazawa Medical University, Ishikawa 920-0293, Japan
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ABSTRACT |
The conventional acoustic
reflection technique in which acoustic waves are launched through the
mouth cannot be applied during sleep, nor can it be applied to the
nasopharynx, which is the major site of occlusion in patients with
obstructive sleep apnea syndrome. We propose a new
technique of nasal acoustic reflection to measure pharyngeal
cross-sectional areas including the nasopharynx. The acoustic waves are
introduced simultaneously to both nostrils during spontaneous nasal
breathing. A new algorithm takes into account the nasal septum with
asymmetric nasal cavities on both sides and assumes prior knowledge of
the cross-sectional area of the nasal cavities and the position of the
nasal septum. This method was tested on an airway model with a septum
and on healthy human subjects. The conventional technique gave
inaccurate measurements for pharyngeal cross-sectional areas for an
airway model with asymmetric branching, whereas the new technique
measured them almost perfectly. The oro- and hypopharyngeal
cross-sectional area measurements acquired by the new method were not
different from those obtained by the conventional method in normal
subjects. This new method can be used as a monitor of upper airway
dimensions in nocturnal polysomnography.
acoustic reflection technique; nasopharynx; sleep apnea
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INTRODUCTION |
ACOUSTIC REFLECTION TECHNIQUE has been employed to
assess the pharyngeal, tracheal, and bronchial cross-sectional areas
along the airway (2, 5, 12). This method has been used extensively, particularly for the comparative assessment of pharynx size among snorers, non-snorers, and patients with obstructive sleep apnea syndrome (3, 4, 10). It has the advantage of being noninvasive and
quick, and it also allows for continuous evaluation of the patency of
these regions. However, the technique has two major restrictions: it
cannot be used during sleep and it cannot assess the nasopharynx. In
this technique, in which acoustic waves are launched to the airway via
the mouth, subjects are requested to breathe wholly through the mouth
without wearing a nose clip. This controlled and deliberate breathing
method is required to ensure complete closure of the uvula to the
posterior wall of the nasopharynx and, thereby, to preclude
acoustic waves transmitting to the nasal pathway (15). Otherwise,
the pharyngeal cross-sectional area beyond the uvula would be distorted
by the component of the reflected waves from the nasal pathway.
Therefore, this technique has never been applied during sleep when
nasal breathing dominates.
Although this technique has also been applied to the nasal cavity by
introducing acoustic waves via one nostril (7-9), the measurement
was limited to the point of the choana, beyond which acoustic waves
separate to the nasopharynx and the opposite side of the nasal cavity,
and, hence, the pharyngeal cross-sectional area cannot be obtained for
the reason described above. The nasopharyngeal cross-sectional area
would be measured under the condition that acoustic waves enter both
nostrils simultaneously, and both nasal cavities are assumed to be
symmetric. This is because a symmetric branching and encountering of
acoustic waves in nasal cavities would measure the correct
nasopharyngeal cross-sectional area as if the septum did not exist.
However, this is generally not the case. Furthermore, the areas of both
nasal cavities temporarily change in an asymmetric way. Therefore, the
existing nasal acoustic reflection technique is not applicable to the
pharynx, including the nasopharynx.
We propose a new algorithm to overcome the difficulties described
above. After developing reflection and transmission formulas of
acoustic waves at the beginning and ending points of the nasal septum,
we combined them with the former Ware and Aki algorithm (17). Acoustic
waves were launched simultaneously to both nostrils via a nasal adapter
during spontaneous nasal breathing. The efficacy of this method was
tested by using an airway model and by application to healthy subjects.
Algorithm
Our model to infer cross-sectional areas is shown in Fig.
1, which is a cascade of equilength short
sections with constant cross-sectional area in each section. The length
of the sections, x0, is equal to one-half the
distance for acoustic waves transmitting for one sampled time interval
and is ~0.7 cm in the air in this study. The y symbols are
the acoustic admittance (reciprocal of impedance z) in each section to
be inferred by the acoustic method and can be written as
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(1)
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where
is the density of the gas, c is the velocity of sound
propagation, and A is the cross-sectional area of each section. This model is different from that of Jackson et al. (12) in the
branching portion, which includes both the nasal septum and a nasal
adapter. The formulas of the reflection and transmission of acoustic
waves at the sections without branching are the same as before, even in
the nasal cavities. Therefore, the only problems we have to formulate
are those at the beginning and ending points of the branching. The
derivation of formulas at these points are presented in the
APPENDIX.
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Fig. 1.
Model to infer cross-sectional areas by a new nasal acoustic reflection
technique, which includes a septum where acoustic waves separately
transmit and merge at the choana. y0,
ys, and ye: acoustic admittance
at the microphone (Mic) position, starting, and ending points of
septum, respectively. R, reflected wave. See text for
details.
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Here, we describe the new algorithm in a rather intuitive way: first,
by precisely depicting a generalized step of the conventional algorithm
and, next, by substituting some parts of the conventional one with
those of the new one, to look at the relationship between the two
algorithms. Suppose that an impulsive acoustic wave with unit amplitude
initially propagates to the right at the microphone position. After one
sampled time interval, 
= 2x0/c, by
observing the first reflected wave, R0, from the
first discontinuity of the cross-sectional area between
y0 and y1, we can calculate
y1 and thereby A1 from the
following equation and Eq. 1
![<IT>y</IT><SUB>1</SUB> = [(1 − <IT>r</IT><SUB>0</SUB>)/(1 + <IT>r</IT><SUB>0</SUB>)]<IT>y</IT><SUB>0</SUB>](/content/vol88/issue4/fulltext/1457/img002.gif)
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(2)
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where
r0 is the reflection coefficient at the
discontinuity, and equals R0. In the same way, from
R1 we can calculate y2 and
A2. Next, R2 contains not only
the primary wave (thick line with arrow in Fig. 1) but also the
secondary wave (thin line with arrow), which is the multiple
reflected wave at the discontinuity between y1 and
y2. Because we can calculate the secondary wave from already known parameters, y0,
y1, and y2, and by
subtracting it from R2, we can separate the
primary component in it, from which we can derive
y3.
The secondary wave in the nth reflected wave at the microphone
position, Rn, can be systematically
calculated with the known parameters y0,
y1, ... , yn, and
hence we can derive the primary wave and the next unknown admittance
yn + 1. The procedure to
calculate the secondary wave can be generalized as shown in Fig.
2. First, the incidental
(p'i1) and the reflected (p'r1) waves
at the discontinuity between yn 
1 and yn at the (n 
1)th
step, and the incidental waves (p
i3,
pi4, ... ) from each
discontinuity at the (n 2)th step are already known.
Next, the secondary waves at the first mesh point denoted by
a' in the (n 1)th step,
p'i2 and
p'r2, are calculated by
using p'r1 and
pi3 as shown in Fig.
3A. With the use of this newly
calculated p'r2 and the
known pi4, the waves at the next
mesh point b' are calculated as
p'i3 and
p'r3. Thus all the
secondary waves in the (n 1)th step are given by
successive calculation at each mesh point in the reverse direction
toward the microphone position. Third, the secondary waves at the
nth step can be obtained by the same process as the
(n 1)th step, successively calculating the mesh
points a, b, c, ... Finally, we get the
secondary wave at the microphone position and the primary wave by
subtracting it from Rn.
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Fig. 2.
Algorithm to calculate secondary wave in nth step (n)
in conventional Ware and Aki method (17). Secondary wave at microphone
position (thin line with arrow) can be obtained by successively
calculating incidental (pi) and reflected waves
(pr) at mesh points a',
b', c', ... and then a,
b, c, . . . . . Primary wave (thick line with arrow)
is given by subtracting secondary wave from reflected wave at
microphone position, Rn. See text for
details.
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Fig. 3.
Four structure types for pre- and postbranching points (A), and
starting (B), middle (C), and ending points of the
branching (D). Each mesh point in Fig. 2 (a',
b', c', ... and a, b,
c, ... ) was substituted with 1 of them in the new
algorithm. In A, for example, transmitting waves at mesh point
a', i.e.,
p'i2 and
p'r2, are calculated by
using incidental waves, pi3 and
p'r1, as follows
where
rn + 2 is the known reflection coefficient
between sections yn 2 and
yn 1. Subscript R and L, right and
left, respectively. See text for details of other structure types.
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In contrast, each mesh point has the same structure as in Fig.
3A in the Ware and Aki algorithm (17), and in the new algorithm one of four different structures of Fig. 3, A-D, should be
selected, depending on the position of the mesh point, i.e.,
prebranching or postbranching point, the starting, the middle, and the
ending point of the septum. To see how parameters inferred in each step are linked together in the new algorithm, suppose that we are inferring
for the postbranching position, the pharyngeal region, as the
nth step in Fig. 2. In the tour of the mesh points, to calculate the secondary waves the first mesh point of a'
is of the Fig. 3A type, and, therefore, the same procedure as
the Ware and Aki algorithm continues until the ending point of the
nasal septum, the choana. Then the structure type should be substituted with that of Fig. 3D. Here, at the discontinuity between
sections ye and ye + 1
(where e is ending), the backward-traveling pressure wave separately
transmits to both nasal cavities from the choana, and also the
forward-traveling wave from the left (right) nasal cavity separately
transmits to the nasopharynx and to the opposite nasal cavity. Because
these incidental waves to this mesh point (1 backward and 2 forward
waves) and the transmission and reflection coefficients at the
discontinuity are already known, the three transmitting waves to the
pharynx and both nasal cavities can be calculated (see
APPENDIX). For the next several mesh points, the Fig.
3C type structure is used in the nasal cavity. Here the waves
independently transmit in both nasal cavities, and, therefore, the Ware
and Aki algorithm can be employed in each nasal cavity. When the tour
of the mesh point reaches the starting point of the septum, the
discontinuity between sections ys 1 and ys (where s is starting), where the
Fig. 3B type structure is used, the forward-traveling pressure
wave transmits separately to both sides of the septum, and, in the same
way, the backward-traveling wave from the left (right) side of the septum transmits separately toward the microphone and to the opposite side of the septum. Because these incidental waves to this mesh point
(1 forward and 2 backward waves) and the transmission and reflection
coefficients at the discontinuity are already known, the three
transmitted waves can be calculated (see APPENDIX). After this mesh point, the tour meets the Fig. 3A type structure
until the microphone position and the Ware and Aki algorithm can be employed again. Eventually we get the secondary wave at the microphone position and the primary wave by subtracting it from
Rn to get the unknown admittance
yn + 1.
Prior Knowledge of the Cross-Sectional Area in Both Nasal Cavities
and the Position of the Nasal Septum
When the inferring points are in the septum, including the starting and
the ending points, the algorithm should be modified from the one just
described above because there are two unknown admittances in this step.
First, we consider the inference of the starting point of the septum.
Before this point, the Ware and Aki algorithm (17) can be employed.
When the acoustic wave first arrives at this point, the discontinuity
between ys 1 and
ys in Fig. 1, the Ware and Aki algorithm gives the
sum of both branched areas at section s from the primary wave
component of Rs 1 (see
APPENDIX). Here, we presuppose that the area profile of the
left nasal cavity and thus ysL,
ys + 1L, ... , yeL
(where L is left) are known beforehand, as described at the end of this
section. Then we can calculate ysR by subtraction and hence AsR (where R is right).
Next, to infer the middle points in the right nasal cavity, we used the
following procedure. The incidental waves to both branches are
initially the same as shown in the APPENDIX. Then we can
calculate the primary waves as well as the secondary waves beforehand
in the left nasal cavity (dashed line with arrow in Fig. 1). Therefore,
we can get the primary waves from the discontinuities of the right
nasal cavity by subtracting not only the secondary waves but also the
primary waves in the left nasal cavity from Rs,
Rs + 1, ... , Re 1. From there we get
As + 1R, As + 2R,
... , AeR.
Finally, for the inference of the next section to the ending point of
the septum, ye + 1, we no longer know a
priori the primary wave from the left nasal cavity. Therefore, a
special procedure is needed to get the unknown admittance
ye + 1, which is presented in the
APPENDIX. This was done by obtaining an equation of the
primary wave component in Re in Fig. 1 and finding a solution for ye + 1.
The cross-sectional areas of one nasal cavity, AsL,
As + 1L, ... , AeL
were measured by the conventional nasal acoustic reflection technique
by introducing acoustic waves through one nostril, while closing one of
two passages of a nasal adapter at the starting point of branching (see
below). Because the cross-sectional area abruptly decreased at this
point of unilateral closing and because of the limitation of the
resolving power in the acoustic method, the areas determined in this
way were overestimated after the portion of abrupt change.
Consequently, the other side of the nasal cavity also was
underestimated at the corresponding regions, and thereby the estimation
of the pharyngeal cross-sectional area was impaired. Because the
overestimation ceased in approximately three sections, which are within
the region of the nasal adapter, and both nasal passages of the adapter
were made symmetric in shape, we substituted the first three sections,
AsL, As + 1L, and
As + 2L, with one-half of the corresponding cross-sectional areas measured by introducing acoustic waves through both passages.
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METHODS |
Apparatus
Because the fundamental apparatus for the acoustic reflection technique
is the same as that for the conventional one, we will limit our
explanation to a brief description of our apparatus. It consists of a
wave tube with a length of 4 m and inner diameter of 1.6 cm, a horn
driver located in its midpoint (ID60; University Sound, Buchanan, MI),
and a semiconductor pressure transducer to measure the incidental and
reflected acoustic waves (XCW-190; Kulite Semiconductor, Leonia, NJ).
The length of the tube could probably be shortened considerably if the
inference is limited up to the pharyngeal cross-sectional areas,
because the distance to the pharynx is rather short. Because there is a
great deal of dead space in the equipment, we used a bias flow to avoid
interfering with the subject's breathing. The transducer for the
acoustic waves was positioned at a distance of 25 cm from the end of
the tube and flush with the inside wall. For measurements in both the
supine position and the sitting position, we joined an additional 33-cm-long curved tube to the end of the wave tube. In the conventional acoustic reflection technique, we used a commercialized mouthpiece, which was attached to the wave tube. In the measurement of the nasal
acoustic reflection technique, we used a custom-made nasal adapter to
connect the apparatus and the subject's nostrils. The adapter consists
of three pieces, one of which was made of acrylate and was severed by a
lathe to connect to the end of the wave tube. The other two pieces were
inserted into the subject's two nostrils. The pieces were made of a
plastic test tube with a tapered tip cut off at a suitable position to
fit the subject's nostril. These pieces were screwed tightly into the
former one.
We measured 50 cross-sectional area vs. distance functions of the
airway at a rate of 3 times/s while each subject spontaneously breathed
room air through the mouth (the conventional method) or through the
nose (the new method). Impulsive acoustic waves were generated by a
computer, digital-to-analog converted (12 bits), amplified (A-G91V;
Victor, Tokyo, Japan), emitted by the horn driver, and launched into
the subject's airway. The incidental and reflected waves were
preamplified (SA-57; TEAC, Tokyo, Japan), low-pass filtered (SA-57; 5 kHz), analog-to-digital converted (12 bits, 25 kHz), and stored in the
computer. After calculating the airway impulse response, we derived the
area vs. distance function using the new algorithm or the Ware and Aki
algorithm (17).
Model Study
A model of the nose was made from a 10-cm-long tube of the same
material as that of the wave tube, in which an aluminum plate with a
thickness of 1.6 mm was inserted as a nasal septum and affixed with an
adhesive. Three nasal models were prepared. In the first model, the
plate was placed in the axis of the tube so that the cross-sectional
areas at both sides were equal, a special case of symmetric branching.
In the second model, the plate was placed off axis so that the
cross-sectional areas at the sides were different but remained constant
along the tube, giving asymmetric branching without reflections. In the
third model, the plate was positioned centrally at the beginning and off axis at the end of the tube, giving asymmetric branching with changing cross-sectional areas. A model of the pharynx was made of
acrylate and was severed by a lathe to give a precise dimension. The
nasal and the pharyngeal models were securely joined to each other and
connected directly to the wave tube. Data from these models were
compared with data from the conventional method without branching and
those from the conventional method with branching.
Human Study
Subjects.
Five healthy male subjects were recruited from our laboratory. They
ranged in age from 25 to 47 yr and in body mass index [= weight
(kg)/height2 (m2)] from 22.5 to 27.5 (Table 1). Their pharyngeal cross-sectional areas both in the sitting and supine positions determined by the two
methods were compared. All subjects gave their informed consent to the
study protocol.
Analysis of pharyngeal cross-sectional area.
Figure 4 shows a typical example of airway
cross-sectional area vs. distance functions comparing the two methods
in one subject. After recognizing the narrowest portion in around
~7-9 cm from teeth as the fauces and that in around
~18-20 cm as the glottis in the data by the conventional method,
we defined a region between 2 cm distal to the fauces and 2 cm proximal
to the glottis as the pharyngeal segment and calculated the mean
pharyngeal cross-sectional area. The corresponding pharyngeal
cross-sectional area by the nasal method was also obtained. The
distance in the nasal pathway from the nostril to the glottis was ~3
cm longer than that from the teeth to the glottis from observation with
a bronchoscope. We corrected for the difference of the site of the
pharyngeal segment in the area vs. distance functions between the two
methods.
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Fig. 4.
Typical example comparing this (nose AR; B) and
conventional acoustic reflection technique (mouth AR;
A) in a 47-yr-old healthy male subject. Fifty cross-sectional
area vs. distance functions were depicted together in each panel.
Distances were measured from the teeth position in A and from
nostril in B. In B, only 1 side of the septum was
depicted. Differences between the teeth-glottis and the nostril-glottis
distances were adjusted. In both panels, whispering phonation, which
was small enough not to interfere with the acoustic signal, created
decreases in cross-sectional areas in positions farther than the
glottis. Pharyngeal cross-sectional areas between 2 vertical lines were
averaged and compared between the 2 methods.
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Measurement of the length of the nasal septum.
The algorithm requires a prior knowledge of the position of the ending
point of branching, the choana. We determined it by an acoustic method,
by introducing an impulsive acoustic wave to one nostril, measuring the
incidental wave and the transmitted wave to the other nostril, and
multiplying one-half of the propagation time between the two nostrils
by the speed of sound.
Protocol.
Because many prior studies reported the accuracy of the pharyngeal and
the tracheal cross-sectional areas determined by the conventional
method, we compared the data from the new method with those from the
conventional method. Data were obtained in both the sitting and the
supine positions. The jaw position was carefully observed, and efforts
were made to keep it as similar as possible in each body posture in the
two methods. To determine the cross-sectional area of one nasal cavity
earlier in the measurement with the new method, one of two pieces
inserted into the nostrils of the nasal adapter was closed with sealing
material at the starting point of the branching. After the
cross-sectional area in either nasal cavity was measured in this way,
acoustic waves were simultaneously introduced to both nostrils.
Statistical analysis.
We used a paired t-test to test differences in the data for the
conventional method and those for the new technique. The level of
statistical significance used was P < 0.05.
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RESULTS |
Model
Figure 5A shows inferred
cross-sectional area vs. distance functions for the first model, the
septum of which branches with equal cross-sectional areas (dashed
line). Comparison with the conventional algorithm (dotted line)
disclosed perfect coincidence in the pharyngeal region, showing the
validity of the new algorithm. These data also agree well with the
inferred pharyngeal areas in a model without septum (solid line), which
is the consequence of symmetric branching as described in the
APPENDIX.
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Fig. 5.
Model study with a septum (solid bar), where airway branches
symmetrically (A) and asymmetrically but with a preservation of
constant areas on both sides (B). Dotted and dashed lines are
data from conventional and new method, respectively. B: wide
part of the septum was used as a priori determined cross-sectional area
in the new method, and, therefore, dashed line shows only the narrow
part of the septum. Solid line was obtained by removing the septum from
this model and by the conventional method. Both methods obtained an
identical inference of pharyngeal cross-sectional areas for these
models.
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For the second model, in which the cross-sectional areas at the sides
of the septum are different but constant (reflectionless condition),
the two algorithms gave identical pharyngeal cross-sectional areas
(Fig. 5B). These data also agree with that in a model without septum, which confirms the theory (see APPENDIX).
In the third model with asymmetric branching, the conventional acoustic
reflection technique gave inaccurate cross-sectional areas, whereas the
new technique recovered them almost perfectly (Fig.
6).
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Fig. 6.
Model study with asymmetric branching at the septum (solid bar). Septum
was positioned in the axis of the airway at the beginning point and off
axis at the ending point. Dashed lines in B and C are
data from conventional and new method, respectively. In the new method
(C), the wide part of the septum was used as a priori
determined cross-sectional area, and, therefore, dashed line shows only
the narrow part of the septum. Solid line is the data for the symmetric
branching model (Fig. 5A). The new method (C) recovered
the pharyngeal areas with a high degree of accuracy, whereas the
conventional method did not (B).
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Human
Figure 7 shows a comparison of the
cross-sectional areas between the new and the conventional method in a
subject (JH), who induced asymmetric branching in the nasal
septum with unilateral decongestion. Here, as in the model study
described above, the same acoustic waves were used between the new and
the conventional methods. When the nasal cavity was almost symmetric
before decongestion, there were few differences in the pharyngeal
cross-sectional areas obtained by the two methods (Fig. 7A). On
the other hand, when the left nasal cavity was decongested and enlarged
with two sprays of 60 µg of tetrahydrozoline hydrochloride, the two
methods derived significant differences in the cross-sectional areas of
the nasal cavity and the pharynx, showing the influence of asymmetric
branching (Fig. 7B).
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Fig. 7.
Human study with an almost symmetric or asymmetric branching at the
nasal cavity in a subject (JH). A: condition when both
sides of the nasal cavity are almost symmetric. Bottom: solid
and dashed lines show cross-sectional areas of left and right side of
the nasal cavity, respectively. Abscissa shows distance from the
nostril, i.e., the negative distance represents the portion of the
nasal adapter, and the positive distance nasal cavity. Each area vs.
distance function is mean value of 50 measurements during normal nasal
breathing. Top: cross-sectional areas represented by new (solid
line) and conventional method (dashed line) were almost identical. For
cross-sectional areas in the branching portion including the nasal
cavity and the nasal adapter (between 2 vertical lines), we depicted
the sum of the cross-sectional areas of both sides at corresponding
distances. B: when the left nasal cavity is unilaterally
decongested, cross-sectional areas of both nasal cavities showed a
marked asymmetric configuration (bottom). Top:
cross-sectional areas in the nasal cavity and the pharynx were
significantly different between the 2 methods.
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Figure 8 shows a comparison of oro- and
hypopharyngeal cross-sectional areas between the new and the
conventional method in the sitting or supine position. In this
instance, the acoustic waves were introduced through the mouth in the
conventional method vs. through both nostrils in the new method. Oro-
and hypopharyngeal cross-sectional areas did not differ between the two
methods in either position and decreased in the supine position
compared with the sitting position in both methods.
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Fig. 8.
Comparison of pharyngeal cross-sectional areas between this (nose) and
the conventional (mouth) methods in healthy male subjects (mean ± SE,
n = 5). There were no differences between the 2 methods either
in the sitting or supine positions. In both methods, pharyngeal
cross-sectional area decreased in the supine position. NS, not
significant.
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Nasopharyngeal cross-sectional area.
Figure 9 shows how the nasopharyngeal
cross-sectional area is displayed by this method in a healthy subject.
When the subject switched from nasal breathing to breathing through the
mouth (Fig. 9A), the cross-sectional area immediately after the
choana markedly decreased, reflecting the closure of the soft palate
and uvula to the nasal pathway. When the subject, initially breathing
through the nose with the mouth slightly open, placed his tongue
against the soft palate, the nasopharyngeal cross-sectional area
decreased slightly because the tongue pushed up the soft palate and
narrowed the corresponding nasal pathway.
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Fig. 9.
Nasopharyngeal cross-sectional areas in a 47-yr-old male subject. Fifty
area vs. distance functions were superimposed on each panel. A:
subject breathed nasally at first and then switched to mouth breathing.
Cross-sectional areas of the nasopharynx decreased, reflecting the
velum closure to the nasal pathway. B: subject breathed nasally
with a slight opening of his mouth at first and then pushed the soft
palate with his tongue. Cross-sectional areas of the nasopharynx
decreased, while the more distant airways remained unchanged.
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DISCUSSION |
To date, the acoustic reflection technique has never been applied to
the assessment of the upper airway dimensions during sleep. Sleep apnea
or sleep-related disordered breathing only occurs during sleep.
Therefore, the new technique may provide a strong tool for extracting
information about the pathogenesis of the upper airway, which cannot be
obtained by measurements taken in a patient who is awake.
As shown by the model data, both this and the conventional methods
accurately measured the simulated pharyngeal cross-sectional areas
following the symmetrically branched septum (Fig. 5). In the case of
asymmetrically branched septum, however, only this new method correctly
recovered the pharyngeal cross-sectional areas (Fig. 6). As
demonstrated in the differences between the two methods in the human
study (Fig. 7), the conventional method will give impaired data when
acoustic waves are simultaneously introduced to both nostrils and both
nasal cavities are quite different from each other, especially in the
region near the choana.
To study the accuracy of this method, we compared the oro- and
hypopharyngeal cross-sectional areas inferred by this and the conventional methods, with acoustic waves introduced through the nose
in the former and through the mouth in the latter. The rationale of
this comparison is that these pharyngeal regions are capable of being
inferred by both methods and that the accuracy by the conventional
method in these regions has already been established by several authors
(5, 13). The pharyngeal cross-sectional areas did not vary between the
methods, as expected. Furthermore, the measurements in both methods
decreased with the postural change from the sitting to the supine
position, as reported (6). We believe that the accuracy is also
preserved in the nasopharyngeal cross-sectional areas because, if that
were not so, the accuracy of further distances, i.e., oro- and
hypopharynx, would not be preserved either. However, further studies,
including comparisons with magnetic resonance-computerized tomography,
are needed to confirm this because this pharyngeal region has not
previously been inferred by the acoustic reflection technique.
Methodological Problems
Although the new technique seems to be fairly reliable, some problems
must be considered. First, the paranasal sinuses may influence the data
because they form additional parallel pathways (branches) in the nasal
cavity. Hilberg and Pedersen (9) investigated the influence of the
maxillary sinuses on estimated nasal cross-sectional areas, which were
determined by acoustic waves introduced from one nostril. They
estimated the size of the ostium of the maxillary sinus in normal
subjects to be ~3-8 mm in diameter when the nasal cavity was
decongested by xylometazoline, and the sinus overestimated the
cross-sectional areas in the posterior part of the nasal cavity and
epipharynx. However, they also showed that the wider the ostium, the
greater the overestimation, and, when not decongested, the degree of
overestimation was rather small. We believe that the influence of this
factor on our data is minimal because, except for Fig. 7, we did not
use any decongesting agents and there were no differences in the oro-
and hypopharyngeal cross-sectional areas between this and the
conventional methods.
Another source of error could arise from the accuracy of the position
and the length of the nasal septum. As shown in Fig. 1, we assumed that
the septum starts and ends at distances of an integer multiple of the
short segment from the microphone position, i.e., s and e + 1 multiple,
respectively. We obtained the septum length from the independent
measurement of the transmission time of acoustic waves between the two
nostrils and divided it by the length of the segment, 0.7 cm, to get
the integer multiple. Therefore, any error of the septum position would
be 0.35 cm at most. This magnitude of error was not considered to be
important because the resolving power of the cross-sectional area was
~3 cm in the distance axis in this study with the use of air as a
test gas. The model results demonstrated this assertion, i.e., despite
the fact that we did not adjust the length or the position of the models, the estimated data almost exactly recovered the actual measurements. To further verify this, we examined the influence of an
additional error of one integer multiple of the septum position, i.e.,
another 0.7-cm error. The difference between estimations was noticeable
but not excessive (data not shown). This confirms the above argument
that the truncation of the septum position to integer multiple does not
produce a significant influence on the estimation.
Third, we assumed in this new algorithm that both nasal cavities
communicated to the nasopharynx, although they were asymmetric. However, one or both nasal cavities can be closed or extremely narrow.
The attenuation of sound is large in this case, and the algorithm would
not work well. This problem remains to be solved.
Applications
There are many fields in which this method can be applied. First, it
can be used as a monitor of the pharyngeal and airway cross-sectional
areas in nocturnal polysomnography, detecting the site of closure of
the upper airway in patients with obstructive sleep apnea syndrome. To
this end, endoscopy and magnetic resonance imaging have been used (1,
11, 16). Because the former is too invasive to be placed in the pharynx
all night and the latter is too expensive to apply to all patients and
too noisy to allow natural sleep, these methods have not been used as a monitor and have been limited to use for research purposes. Therefore, this method can be the first for monitoring the pharyngeal and airway
dimensions during sleep.
The method can be also used as a monitor of airway choking in newborn
babies. With application in children and infants, increase of the
sampling frequency to 100 kHz may improve the resolution to 1.7 mm,
provided the scaling of the equipment and the frequency characteristics
of the microphone are adequate. It can also be a convenient method of
measuring the nasopharyngeal cross-sectional areas. To our knowledge,
this is the first method for this purpose other than well-established
imaging techniques, such as computed tomography, using X-ray or
magnetic resonance.
Future Directions
In this study, we assumed that subjects breathed through the nose
during sleep. Although this is normally true, they may breathe through
both the nose and mouth simultaneously. Because acoustic waves
introduced from both nostrils split to the hypopharynx and mouthward at
the uvula in this situation, the estimation fails for distances beyond
the nasopharynx for the reason described in the introduction. Even in
this circumstance, however, the method is valid for the nasopharyngeal
cross-sectional areas. The method could be modified to overcome this
obstacle by introducing acoustic waves not only from the nostrils but
also from the mouth and taking into account an additional branching in
the mouth.
It is not comfortable for subjects to sleep through the night using the
method described here because head and neck positions are fixed with
the equipment. The technique should be improved by a reduction in the
size of the equipment and in the nasal adapter. A two-microphone
method, rather than a single-microphone method, can reduce the size
substantially (14). A special nasal mask not requiring insertion of any
materials into the nostrils should be developed to introduce the
acoustic waves.
In this study, we presented a new acoustic reflection technique that
enabled us to assess the size and function of the pharynx during sleep.
This is also the first method using the acoustic reflection technique
to measure the nasopharynx. Long-term continuous use of this equipment
as a monitor would more extensively clarify the physiological and/or
pathophysiological condition of the upper airway.
| |
APPENDIX |
Sound Transmission at the Beginning and Ending Points of
the Septum
At the starting point of the septum, there are three waves into this
point: one forward- and two backward-traveling waves, as shown in Fig.
3B. We separately formulated these waves and then combined them
based on the principle of the superposition. First, we consider a wave
traveling to the right into the beginning of the branching as shown in
Fig. 10A (a forward
traveling wave pi). The continuity conditions of
pressure and volume flow at the boundary are as follows
|
(A1)
|
|
(A2)
|
where
pi, pr,
ptR, and ptL are the
incidental, reflected, and transmitted acoustic pressure waves to the
right and left branches, respectively. From these, the reflection
coefficient (r) and the transmission coefficient (t) at
the boundary are given as follows
|
(A3)
|
|
(A4)
|
where
ys = ysR + ysL, which corresponds to the sum of the
cross-sectional areas in the right and the left branches at section s. Equation A4 expresses that transmitted waves in both
branches are the same, i.e., the same pressure waves begin to transmit to both branches irrespective of the difference in their
cross-sectional areas.
View larger version (19K):
[in this window]
[in a new window]
|
Fig. 10.
Reflection and transmission of an incidental wave from the left
(A), a reflected wave from the right to the starting point of
the septum (B), and acoustic waves at the ending point of the
septum (C). Subscript t, transmitted. See text for details.
|
|
Hence, if there is physical similarity between the structures of both
branches, or if the cross-sectional area of each branch remained
unchanged (reflectionless condition), the waves in both branches are
identical at the same distances and behave as if they did not branch.
It is only under these conditions and when the acoustic waves are
simultaneously introduced to both nostrils that the nasal septum does
not affect the estimated pharyngeal cross-sectional areas by the
conventional acoustic reflection technique. In the typical case, in
which branching at the septum is asymmetric, a marked influence on the
pharyngeal area by the existing method was demonstrated (Figs. 6 and
7).
When a wave traveling to the left in the right branch (reversed
direction) comes back to the same branching point as shown in Fig.
10B (a backward-traveling wave
pRiR), the reflection (rs 1,R) and the transmission
coefficient (ts 1,R) are, in the same
way as in Eqs. A3 and A4, given as follows
![<IT>p</IT><SUP>R</SUP><SUB>rR</SUB>/<IT>p</IT><SUP>R</SUP><SUB>iR</SUB> = −<IT>r</IT><SUB>s−1,R</SUB> = [<IT>y</IT><SUB>sR</SUB> − (<IT>y</IT><SUB>sL</SUB> + <IT>y</IT><SUB>s−1</SUB>)]/(<IT>y</IT><SUB>sR</SUB> + <IT>y</IT><SUB>sL</SUB> + <IT>y</IT><SUB>s−1</SUB>)](/content/vol88/issue4/fulltext/1457/img009.gif)
|
(A5)
|
|
(A6)
|
where superscript R denotes the corresponding waves to
pRiR and the negative sign in the
reflection coefficient was introduced to represent the reversed
direction of the incidental wave and to give the correspondence to the
Ware and Aki algorithm (17). Actually, when the reflection and the
transmission coefficients for a forward-traveling wave are
ri and 1 + ri, respectively, at the ith discontinuity, those for a backward- traveling wave are ri and 1 ri in the conventional algorithm.
For a wave traveling to the left in the left branch (a
backward-traveling wave pLiL),
those coefficients are as follows
![<IT>p</IT><SUP>L</SUP><SUB>rL</SUB>/<IT>p</IT><SUP>L</SUP><SUB>iL</SUB> = −<IT>r</IT><SUB>s−1,L</SUB> = [<IT>y</IT><SUB>sL</SUB> − (<IT>y</IT><SUB>sR</SUB> + <IT>y</IT><SUB>s−1</SUB>)]/(<IT>y</IT><SUB>sL</SUB> + <IT>y</IT><SUB>sR</SUB> + <IT>y</IT><SUB>s−1</SUB>)](/content/vol88/issue4/fulltext/1457/img012.gif)
|
(A7)
|
|
(A8)
|
By the principle of superposition, the resultant waves
are the sum of those waves. Finally, the formulas for the ending point of the septum are the same as those described above and are not presented here.
An Estimation Method of
ye + 1
A procedure to infer ye + 1, the next section
to the ending point of the septum, consists of obtaining an equation of
the primary wave in Re in Fig. 1 and rearranging it
to calculate ye + 1. Two primary waves
transmitted to the ending point of the septum in both branches,
T+L and T+R, are written as follows (Fig.
10C)
|
(A9)
|
|
(A10)
|
where ti is the transmission
coefficient at the discontinuities from the microphone position to the
starting point of the septum,
tjL and
tjR are those in each nasal
cavity, and these are known parameters. Then we can write the two
reflected waves, L and R, from the discontinuity
between ye and ye + 1 as
follows
|
(A11)
|
|
(A12)
|
where
![<IT>r</IT><SUB>eL</SUB> = [ <IT>y</IT><SUB>eL</SUB> − ( <IT>y</IT><SUB>eR</SUB> + <IT>y</IT><SUB>e+1</SUB>)]/( <IT>y</IT><SUB>eL</SUB> + <IT>y</IT><SUB>eR</SUB> + <IT>y</IT><SUB>e+1</SUB>)](/content/vol88/issue4/fulltext/1457/img020.gif)
|
(A13)
|
![<IT>r</IT><SUB>eR</SUB> = [ <IT>y</IT><SUB>eR</SUB> − ( <IT>y</IT><SUB>eL</SUB> + <IT>y</IT><SUB>e+1</SUB>)]/( <IT>y</IT><SUB>eL</SUB> + <IT>y</IT><SUB>eR</SUB> + <IT>y</IT><SUB>e+1</SUB>)](/content/vol88/issue4/fulltext/1457/img021.gif)
|
(A14)
|
These
sum up to the primary wave component of Re in Fig.
1 as
|
(A15)
|
where
|
(A16)
|
|
(A17)
|
The negative sign of ti,
tjL, and
tjR denotes the corresponding
transmission coefficients for the backward-traveling waves at each
discontinuity. Rearranging Eq. A15 yields the admittance
ye + 1
|
(A18)
|
where
![&ggr; = [Prim(<IT>R</IT><SUB>e</SUB>) − <IT>T</IT><SUP>−</SUP><SUB>L</SUB><IT>T</IT><SUP>+</SUP><SUB>R</SUB> − <IT>T</IT><SUP>−</SUP><SUB>R</SUB><IT>T</IT><SUP>+</SUP><SUB>L</SUB>]/(<IT>T</IT><SUP>−</SUP><SUB>L</SUB> + <IT>T</IT><SUP>−</SUP><SUB>R</SUB>)](/content/vol88/issue4/fulltext/1457/img029.gif)
|
(A19)
|
The primary wave component in Re was
obtained by subtracting the secondary component in it, and then the
unknown admittance ye + 1 was calculated by
Eq. A18.
| |
ACKNOWLEDGEMENTS |
This work was supported by a grant for Collaborative Research from
Kanazawa Medical University (C96-9, C98-2).
| |
FOOTNOTES |
The FORTRAN source program is available. Please write to J. Huang.
The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement"
in accordance with 18 U.S.C. §1734 solely to indicate this fact.
Address for reprint requests and other correspondence: J. Huang,
Division of Respiratory Diseases, Dept. of Internal Medicine, Kanazawa
Medical Univ., 1-1 Daigaku, Uchinada-machi, Kahoku-gun,
Ishikawa-ken, 920-0293 Japan (E-mail:
huang{at}kanazawa-med.ac.jp).
Received 12 February 1998; accepted in final form 23 November
1999.
| |
REFERENCES |
1.
Abbey, NC,
Block AJ,
Green D,
Mancuso A,
and
Hellard DW.
Measurement of pharyngeal volume by digitized magnetic resonance imaging. Effect of nasal continuous positive airway pressure.
Am Rev Respir Dis
140:
717-723,
1989[Medline].
2.
Brooks, LJ,
Castile RG,
Glass GM,
Griscom NT,
Wohl MEB,
and
Fredberg JJ.
Reproducibility and accuracy of airway area by acoustic reflection.
J Appl Physiol
57:
777-787,
1984[Abstract/Free Full Text].
3.
Brooks, LJ,
and
Strohl KP.
Size and mechanical properties of the pharynx in healthy men and women.
Am Rev Respir Dis
146:
1394-1397,
1992[Web of Science][Medline].
4.
Brown, IB,
McClean PA,
Boucher R,
Zamel N,
and
Hoffstein V.
Changes in pharyngeal cross-sectional area with posture and application of continuous positive airway pressure in patients with obstructive sleep apnea.
Am Rev Respir Dis
136:
628-632,
1987[Medline].
5.
Fredberg, JJ,
Wohl MEB,
Glass GM,
and
Dorkin HL.
Airway area by acoustic reflections measured at the mouth.
J Appl Physiol
48:
749-758,
1980[Abstract/Free Full Text].
6.
Harper, RM,
and
Sauerland EK.
Sleep Apnea Syndromes. New York: Liss, 1978, p. 190.
7.
Hilberg, O,
Jackson AC,
Swift DL,
and
Pedersen OF.
Acoustic rhinometry: evaluation of nasal cavity geometry by acoustic reflection.
J Appl Physiol
66:
295-303,
1989[Abstract/Free Full Text].
8.
Hilberg, O,
Jensen FT,
and
Pedersen OF.
Nasal airway geometry: comparison between acoustic reflections and magnetic resonance scanning.
J Appl Physiol
75:
2811-2819,
1993[Abstract/Free Full Text].
9.
Hilberg, O,
and
Pedersen OF.
Acoustic rhinometry: influence of paranasal sinuses.
J Appl Physiol
80:
1589-1594,
1996[Abstract/Free Full Text].
10.
Hoffstein, V,
Wright S,
Zamel N,
and
Bradley TD.
Pharyngeal function and snoring characteristics in apneic and nonapneic snorers.
Am Rev Respir Dis
143:
1294-1299,
1991[Web of Science][Medline].
11.
Isono, S,
Tanaka A,
Sho Y,
Konno A,
and
Nishino T.
Advancement of the mandible improves velopharyngeal airway patency.
J Appl Physiol
79:
2132-2138,
1995[Abstract/Free Full Text].
12.
Jackson, AC,
Butler JP,
Millet EJ,
Hoppin FG, Jr,
and
Dawson SV.
Airway geometry by analysis of acoustic pulse response measurements.
J Appl Physiol
43:
523-536,
1977[Abstract/Free Full Text].
13.
Jackson, AC,
and
Krevans JR, Jr.
Tracheal cross-sectional areas from acoustic reflections in dogs.
J Appl Physiol
57:
351-353,
1984[Abstract/Free Full Text].
14.
Louis, B,
Glass GM,
Kresen B,
and
Fredberg JJ.
Airway area by acoustic reflection: the two microphone method.
J Biomech Eng
115:
278-285,
1993[Web of Science][Medline].
15.
Rubinstein, I,
McClean PA,
Boucher R,
Zamel N,
Fredberg JJ,
and
Hoffstein V.
Effect of mouthpiece, noseclips, and head position on airway area measured by acoustic reflections.
J Appl Physiol
63:
1469-1474,
1987[Abstract/Free Full Text].
16.
Suto, Y,
Matsuda E,
and
Inoue Y.
MRI of the pharynx in young patients with sleep disordered breathing.
Br J Radiol
69:
1000-1004,
1996[Abstract/Free Full Text].
17.
Ware, JA,
and
Aki K.
Continuous and discrete inverse-scattering problems in a stratified elastic medium. Plane waves at normal incidence.
J Acoust Soc Am
45:
911-921,
1969.
J APPL PHYSIOL 88(4):1457-1466
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TOP
ABSTRACT
INTRODUCTION
![<IT>y</IT><SUB>e + 1</SUB> = ([ <IT>y</IT><SUB>eL</SUB>(−&ggr; + <IT>T</IT><SUP>+</SUP><SUB>L</SUB> − <IT>T</IT><SUP>+</SUP><SUB>R</SUB>) + <IT>y</IT><SUB>eR</SUB>(−&ggr; − <IT>T</IT><SUP>+</SUP><SUB>L</SUB> + <IT>T</IT><SUP>+</SUP><SUB>R</SUB>)]](/content/vol88/issue4/fulltext/1457/img027.gif)
