Nasopharyngealometric apparatus and method

This invention relates to an acoustic pulse response system for determining the shape of the nasopharyngeal cavity in a subject by introducing an acoustic impulse through a wave tube into the respective nasal cavities of the subject. The acoustic signals and acoustic reflections thereof with respect to each one of said nasal cavities with both open and closed velums are detected by a microphone located in a wall of the tube, the microphone generating electrical signals proportional to both the impulse and acoustic reflections. The length of the nasal septum is determined, and the value of the area-distance function of the nasopharyngeal cavity is computed from the electrical signals and the length of the nasal septum.

The present invention relates to determination of the shape of 
nasopharyngeal cavities, and more particularly to the determination of 
such shape using acoustic, broadspectrum response measurements. 
The nasal passage, formed primarily of the nasal cavities and the 
contiguous nasopharynx, serves as the primary airway for children and 
adults, and is the obligate air-way in neonates. Because there are 
clinical conditions that significantly alter the shape of the nasopharynx 
(e.g., adenoiditis, oral-facial anomalies) a determination of its shape 
can provide important and clinically useful information. During speech, 
the production of nasal consonants requires an appropriate acoustic 
balance between the nasal and oral cavities which can become comprised 
with velopharyngeal inadequacy. Given the importance of nasal airway 
obstruction and proper assessment of velopharyngeal function during 
speech, several methods of evaluating nasal and nasopharyngeal patency 
have been developed recently including rhinomanometry and nasometry. 
Rhinomanometry by measurement of the pressure drop across the nasal cavity 
and airflow through the nose provides an estimate of resistance as the 
ratio of pressure divided by flow. This technique, however, is prone to 
several sources of artifacts, requires some level of patient cooperation 
and in up to 20% of children studied, reliable data cannot be obtained. 
Nasometry involves the measurement of the sound (via microphones) 
transmitted through each nostril and the oral cavity during phonation. The 
sound from each nostril, separated by a plate which rests on the upper 
lip, is compared to the acoustic energy transmitted through the oral 
cavity and results in a "nasalance" score. It has been shown, however, 
that there is little correlation between nasalance scores and nasal 
cross-sectional areas. 
A more serious disadvantage of these techniques is that the pressure drop 
across, and the energy transmitted through the nasal airway is almost 
entirely dominated by that portion of the passageway where the 
cross-sectional area is a minimum, i.e., the liminal valve, which is just 
posterior to the alar rim. Thus, measurements of nasal resistance or 
nasalance are predominately measures of liminal valve cross-sectional area 
and are relatively insensitive to the shape of other sections of a nasal 
cavity or to the shape of the nasopharynx. 
A more recently developed technique, acoustic rhinometry, provides a 
non-invasive estimate of the geometry of the nasal cavity from an acoustic 
pulse response measurement. This technique does not have the above 
limitations and has been shown to be able to map the cross-sectional area 
of the nasal cavity. It is known that it is possible to estimate the shape 
of a cavity expressed as its cross-sectional area as a function of 
distance, x, from its inlet. The relationship between the area and 
distance is called the area-distance function, and is denoted by A(x). 
A(x) is typically computed using the standard method described in detail 
by Jackson, A. C., J. P. Butler, E. J. Millet, F. G. Hoppin, Jr., and S. 
V. Dawson, Airway geometry by analysis of acoustic pulse response 
measurements. J. Appl. Physiol. 43:523-536, 1977(18) and incorporated 
herein by reference. 
The idea of estimating the shape of a cavity from a measurement of its 
acoustic pulse response was first suggested by Sondhi and Gopinath, 
Determination of vocal tract shape from impulse response at the lips, J. 
Acoust. Soc. Am. 49:1867-1873, 1971, primarily for use in the oral cavity. 
Very rapid estimates (e.g. once every 55 ms) of the shape of the cavity, 
expressed as its A(x), is then computed from the acoustic pulse response 
(APR) which is determined using a short duration pressure pulse applied to 
the inlet of the cavity and its reflections from that cavity. The APR 
technique has since been used by several investigators to measure the A(x) 
in excised dog lungs, tracheostomized dogs, human oral cavities, human 
upper airways, human tracheas, and human nasal cavities. Reviews of this 
method have recently been published in Hoffstein, V. and J. J. Fredberg, 
The acoustic reflection technique for non-invasive assessment of upper 
airway area. Eur. Respir. J. 4:602-611, 1991; and Marshall I., M. Rogers, 
and G. Drummond. Acoustic reflectometry for airway measurements. 
Principles, limitations, and previous work. Clin. Phys. Physiol. Meas. 
12:131-141, 1991. This method has been shown to provide reasonably 
accurate estimates of the shape of various portions of the respiratory 
system including central airways in tracheostomized dogs and in humans, 
the oral cavity, upper airways, trachea, and the nasal cavity. 
There are four fundamental assumptions made in the development of the 
equations used to compute A(x) from a measure of an acoustic response. 
These assumptions are that; 1) the waves of the impulse propagate within 
the cavity as plane waves, 2) there are no parallel pathways, 3) the walls 
of the cavity are acoustically rigid, and 4) there are negligible viscous 
acoustic losses. Considering the first assumption, it is possible to 
estimate from theoretical considerations whether acoustic waves (with a 
given frequency content) will propagate as plane waves in a cavity of 
known dimensions. Such waves will propagate in tubes with circular 
cross-section as plane waves provided that the wave length, .lambda., is 
greater than 1.86.pi. times the diameter of the tube. Wave length .lambda. 
is, as well known, c/f, where c is the wave propagation velocity (34,600 
cm/s in room air) and f is frequency. If the diameter of the wave-tube 
used in these measurements is 1.4 cm, the pressure waves with frequencies 
below 14.5 kHz will propagate as plane waves. Any portion of the signal 
that may be propagating in some higher order mode and not as a plane wave, 
can be eliminated by filtering the signal above 14.5 kHz. Lang, Clinical 
anatomy of the nose, nasal cavity and paranasal sinuses. Georg Thieme 
Verlag, Stuttgart-New York, 1989. p. 52, gives the maximum transverse 
dimension of the nasal cavity as 4.57 cm. Thus, in a tube of this diameter 
with a circular cross-section, only waves with frequencies below about 5 
kHz will propagate as plane waves. This prediction is probably quite 
erroneous with respect to a nasal cavity which typically does not have a 
circular cross-section. Non-plane wave propagation becomes very noticeable 
by the existence of rather large high frequency oscillations which result 
in instabilities in the A(x) computation. 
The validity of the second assumption, i.e., that there are no parallel 
pathways, can be established simply from anatomical considerations. For 
distances in a nasal cavity from the entrance thereof to the posterior 
margin of the nasal septum, there are no parallel pathways. Thus, the 
second assumption is relatively valid for a nasal cavity, and the acoustic 
response technique would be expected to provide reasonably accurate 
estimates of its shape. However, once past the posterior margin of the 
nasal septum, the contralateral nasal cavity and the nasopharynx represent 
parallel pathways. The second assumption thus is clearly not true for the 
nasopharynx because where the measurement is made through one nostril, the 
contralateral nasal cavity represents a parallel pathway with that nostril 
and the nasopharynx. 
The validity of the other two assumptions are much more difficult to 
determine theoretically but they can be assessed experimentally. It is 
important to note that even though these assumptions may not be strictly 
valid, their influence can be considered to be negligible if the technique 
does in fact return accurate estimates of cross-sectional areas. For 
example, since the accuracy of acoustic rhinometry has been established 
for the nasal cavity (Hilberg, O., Jackson, A. C., Swift, D. L., and O. F. 
Pedersen. Acoustic rhinometry: Evaluation of nasal cavity geometry by 
acoustic reflections. J. Appl. Physiol. 66:295-303, 1989), it can be 
assumed that even though there may be viscous losses and the wall may not 
be rigid, these factors have negligible influences on the A(x) estimate. 
Similar evidence has been provided that this technique accurately 
estimates the subglottal airways in excised and in-vivo dog lungs, casts 
of human central air-ways, as well as the supraglottal airways in humans. 
Thus, even though strict validity of these assumptions has not been 
demonstrated in these cavities, they are generally accepted as being 
generally valid. 
There has been some question as to the validity of the rigid wall 
assumption in human subglottal air-ways. To decrease the influence of wall 
compliance, the prior art has suggested using a gas mixture (80% helium 
and 20% oxygen) whose density is less, and in which the wave propagation 
velocity is about twice that in room air. As is well known, because of 
this greater propagation velocity, significantly higher frequencies can be 
used before the plane wave propagation assumption becomes invalid. At 
these higher frequencies, the cavity walls would behave dynamically more 
rigidly due to their mass, and by including these higher frequencies the 
influence of wall motion would be reduced. 
If the four assumptions listed above are valid, the prior art technique 
should provide a reasonably accurate estimate of the nasopharyngeal A(x). 
In such case, the A(x) for distances beyond the posterior septal margin 
should be identical whether measured from the right or left nostril. 
Further, A(x) should go to a value of zero when measured with the 
subject's velum closed. In all subjects, the A(x)s determined for 
distances less than the length of the nasal septum are nearly equal in a 
given nostril whether the velum is open or closed. However, for distances 
greater than or beyond the length of the nasal septum, in no subject is 
the A(x) measured in the right nostril with closed velum (A.sub.R,C (x) 
equal to the A(x) measured in the left nostril with closed velum 
(A.sub.L,C (x), or the A(x) measured in the right nostril with open velum 
(A.sub.R,O (x) equal to the A(x) measured in the left nostril with open 
velum (A.sub.L,O (x). Furthermore, for distances beyond the NSL, the 
A.sub.C (x) is less than the A.sub.O (x) in both the right and left 
measurements. However, in no subject does the closed velum A.sub. C (x) go 
to a value of zero which it should if the viscous losses and the influence 
of the contralateral nasal cavity were negligible. The conclusion then is 
that the nasopharyngeal A(x) is not accurately estimated using the prior 
art technique. 
It is therefore clear that it would be desirable to have a non-invasive, 
acoustic pulse response technique that does provide data related to the 
shape of the nasopharynx, thus permitting one to evaluate patients with 
oral-facial anomalies since such individuals frequently manifest 
significant velopharyngeal impairment. Because as noted, this APR 
technique can provide very rapid estimates of A(x), it would be applicable 
to study the dynamics of the nasopharynx during speech. Another useful 
clinical application of an acoustic nasopharyngealometric technique would 
be to estimate the degree of obstruction due to adenoiditis, inasmuch as 
surgeons and patients are becoming increasingly sensitive to adequate 
quantitative evaluation of the degree of nasopharyngeal obstruction to 
justify adenoidectomies. As earlier noted, however, because of the failure 
of one or more of the basic assumptions underlying computation of A(x) to 
hold true with respect to the combined nasal cavities and nasopharynx, 
current acoustic rhinometric techniques do not provide accurate estimates 
of the A(x) for the nasopharyngeal cavity. 
A principal object of the present invention is therefore to provide a 
noninvasive, acoustic, broad-spectrum response system that provides data 
related to the shape of the nasopharynx. Other objects of the present 
invention are to provide an acoustic nasopharyngealometric system in which 
the effects of the contralateral nasal cavity on the accurate 
determination of A(x) are substantially overcome. Other objects of the 
present invention will in part be obvious and will in part appear 
hereinafter. 
Generally, the foregoing and other objects are achieved by implementation 
of methods of compensating for the influence of the parallel nasal 
cavities in the nasal cavities on the determination of the A(x) of the 
nasopharyngeal cavity, involving the steps of introducing a broad-spectrum 
acoustic signal such as an acoustic pulse through a wave tube into a 
nasopharyngeal cavity; detecting that pulse and acoustic reflections 
thereof from the nasopharyngeal cavity at a point in the tube between the 
source of the pulse and the nasopharyngeal cavity; generating electrical 
signals proportional to both the pulse amplitude and acoustic reflections 
thereof from the nasopharyngeal cavity; processing the electrical signals, 
as by amplifying and low-pass filtering to remove frequencies above about 
14.5 kHz; determining the length of the nasal septum; and computing the 
value of A(x) for the nasopharyngeal cavity from the processed signals and 
the length of the nasal septum. 
Apparatus embodying the principles of the present invention generally 
comprise an acoustic pulse source, a wave tube connectable to a nasal 
cavity so that an input pulse from the source can be launched into the 
latter through the tube, microphonic means disposed in the tube adjacent 
the end thereof couplable to the nasal cavity for generating signals 
proportional to both the amplitude of the input pulse and acoustic 
reflections thereof from the nasal and naso-pharyngeal cavities, 
electronic means for amplifying and low-pass filtering those acoustic 
reflections, and electronic computer means for determining the A(x) of the 
nasopharyngeal cavity from the amplified, filtered signals. 
The invention accordingly comprises the apparatus possessing the 
construction, combination of elements and arrangement of parts, and the 
method comprising the several steps and the relation of one or more of 
such steps with respect to each of the others, all as exemplified in the 
following detailed disclosure, and the scope of the application of which 
will be indicated in the claims.

As shown in the drawing, the apparatus of the present invention includes 
acoustic wave source transducer 20 for producing an acoustic pressure 
wave, conduit means such as wave tube 22 into one end of which an 
broad-spectrum acoustic wave from source 20 can be launched. Microphone 24 
is provided for detecting the propagation of both the original acoustic 
waves and reflections thereof in tube 22 at a location between the ends of 
tube 22, and for generating electrical signals proportional to detected 
acoustic waves. For processing those electrical signals, the apparatus 
typically includes electronic amplifier means 26 for amplifying the 
electrical signals and low-pass filter 28 connected for filtering the 
electrical signals. Means are provided for determining the length of the 
nasal septum of the subject in whom the shape of the nasopharyngeal cavity 
is to be measured. Computation means, typically in the form of electronic 
computer means 30 are provided for computing A(x) from the length of the 
nasal septum and the processed electrical signals. 
One end of wave tube 22 is typically acoustically coupled to source 20, and 
microphone 24 is preferably positioned at a point in the wall of tube 22 
adjacent the other or distal end of the tube. Signal source transducer 20, 
the source of a broad spectrum of frequencies, preferably is an electrical 
spark generator capable of producing broad-spectrum acoustic signals with 
energy at much higher frequencies that the electromechanical devices 
typically used in the prior art. Thus, the present invention allows one to 
determine whether there are differences between nasal A(x) measurements 
made with room-air (f&lt;14.5 kHz) and with gas mixtures such as He-Ox at 
considerably higher frequencies (e.g. f&lt;29 kHz). 
The method of the present invention requires initial determination of where 
the nasal cavity ends and the nasopharynx begins in each subject. To this 
end, in one embodiment, the distance to the posterior margin of the nasal 
septum, i.e. the nasal septum length (NSL), is invasively determined using 
a flexible nasopharyngofiberscope (Pentax, model PNE) that is passed into 
one nasal cavity of a subject and visual determination is made when the 
instrument tip reaches the end of the nasal septum. The 
nasopharyngo-fiberscope is marked at the margin of the nostril, withdrawn 
and the distance that it had been inserted is measured, and the 
measurement used as the NSL. As will be seen hereinafter, in another 
embodiment of the present invention, the NSL is determined non-invasively 
from analysis of the A(x)'s. 
The distal end of wave tube 22 is inserted into a nostril of the subject, 
making certain that the tube is well seated so that the juncture between 
the end of the nostril and tube presents no acoustic discontinuity. In one 
embodiment, the exterior cross-sectional configuration of at least the 
distal end of wave tube 22 is ellipsoidal (which term is to be construed 
herein to include ovals as well as ellipses) to match more closely the 
cross section configuration of human nostrils and thus, when properly 
dimensioned for the subject, minimizing distortion of the nostril when 
inserted into the latter. A circular internal cross-section configuration 
of tube 22 is preferably provided regardless of the external 
configuration. 
Source 20 is then activated to generate an acoustic signal that travels 
down the tube and into the nasal cavity. Signals proportional to pressure 
of both incident and reflected waves are generated by microphone 24, 
preferably then digitized, stored in computer 26 which then computes the 
A(x) using the standard method described in detail by Jackson, A. C., J. 
P. Butler, E. J. Millet, F. G. Hoppin, Jr., and S. V. Dawson, Airway 
geometry by analysis of acoustic pulse response measurements. J. Appl. 
Physiol. 43:523-536, 1977(18) and incorporated herein by reference. A(x) 
is measured from the resulting electrical signals derived from the 
acoustic waves detected for at least one nasal cavity, but preferably for 
both the right and left nasal cavities while the subject maintains his or 
her velum in both the open and closed position. Measurement can be taken 
alternately between the nostrils or alternatively, simultaneously in both 
nostrils. In the former case, it is preferred to minimize the distortion 
of the nostril by introduction of the wave tube. In the latter case, some 
distortion is acceptable provided that the distortion is substantially the 
same degree in each nostril. 
The method of the present invention accounts for the two parallel pathways 
of the nasal cavities, relying on knowledge of the nasal septum length 
which can be obtained, as noted above, by invasive methods. It has now 
been found that the NSL can also be determined by determining A(x) for 
both nostrils with velum closed and open. From those A(x) it is seen that 
at or near the junction of the nasal and nasopharyngeal cavities, there is 
a large and rapid increase in the A(x) in normal subjects whether measured 
in the right or left nostril. Significantly, it has also now been found 
that A(x)s for the open and closed velum diverge consistently and 
significantly from zero at the anatomical point where the hard palate ends 
and the soft palate begins, i.e. in close proximity to the posterior 
margin of the nasal septum. 
Measurements of the broad-spectrum acoustic pulse response are preferably 
made in both the right and left nostrils of each subject with conditions 
of open and closed velums. To close the velum, the subject is instructed 
to breath through pursed lips and not allow any air to pass through the 
nose. To maintain the velum in the open position, the subject is 
instructed to breath through the nose with the mouth closed. One can 
determine whether the subject is capable of maintaining a closed velum by 
monitoring the temperature of the air in the alar rim with thermocouples. 
It has been found that with a closed velum, the temperature does not vary 
with the respiratory cycle but remains constant and close to room 
temperature. With an open velum, the temperature varies with the 
respiratory cycle, increasing with expiration and decreasing with 
inspiration. Prior to making the measurements, it is preferred to 
administer oxymatazolene aerosol to each nostril to maximally dilate each 
nostril and thus reduce the reported time dependent variations in nasal 
geometry. From these, the AR(x) and AL(X) are computed with the 
modifications outlined hereinafter, and compared. For distances 
appropriate for the nasopharynx (i.e., for x&gt;NSL as determined from direct 
measurements with a nasopharyngo- scope), the AR(x) and AL(X) should be 
equal and they both should go to zero at an appropriate distance with the 
closed velum. 
The preferred method for accounting for the effects of the contralateral 
nasal cavity can be advantageously described employing an electrical 
analogy to analyze transmissions and reflections in the bifurcated airway, 
inasmuch as acoustic and electromagnetic plane waves obey similar wave 
equations and hence share similar properties. Acoustic waves in a hollow 
tube represent variations in pressure p(x) and longitudinal velocity u(x) 
that satisfy the differential equations 
EQU -.delta.p/.delta.x=.rho..sub.o (.delta.u/.delta.t) (1) 
EQU and 
EQU -.rho..sub.o .gamma.P.sub.o (.delta.u/.delta.x)=.delta.p/.delta.t(2) 
where 
.rho..sub.o is the ambient air density, 
P.sub.o is the equilibrium gas pressure, and 
.gamma. is the ratio of specific heat of the transmission medium at 
constant gas pressure to the specific heat at constant gas volume. 
These two equations can be combined to yield the classic acoustic wave 
equation 
EQU .delta..sup.2 p/.delta.x.sup.2 =(.rho..sub.o /.gamma.P.sub.o)(.delta..sup.2 
p/.delta.t.sup.2) (3) 
where the wave propagation velocity c.sub.a is given by 
EQU c.sub.a =(.gamma.P.sub.o /.rho..sub.o).sup.1/2 (4) 
If the wave equation (3) is solved (assuming negligible viscous losses) in 
the geometry of a closed, rigid walled tube, the tube's characteristic 
acoustic impedance, Z.sub.a (x), defined by the ratio p(x)/u(x) at any 
point, becomes 
EQU Z.sub.a (x)=.rho..sub.o c.sub.a /A(x) (5) 
where A(x) is the cross-sectional area of the tube at position x (i.e., the 
area-distance function). It is this equation that allows us to compute 
A(x) from a measure of the acoustic pulse response (APR), and it is here 
that the conditions of plane wave propagation, no parallel pathways, 
negligible viscous losses, and rigid walls are assumed. 
Transverse electromagnetic (TEM) waves propagating along a two-wire 
transmission line, if expressed in the form of transverse voltage and 
longitudinal current, obey a similar set of equations that describe the 
electromagnetic induction and displacement-current effects. Specifically, 
the voltage V(x) and current I(x) are related by 
EQU -.delta.I/.delta.x=C(.delta.V/.delta.t) (6) 
EQU and 
EQU -.delta.V/.delta.x=L(.delta.I/.delta.t) (7) 
where L and C are the inductance and capacitance per unit line length, 
respectively. 
These equations are direct extensions of Maxwell's electromagnetic 
equations. As in the acoustic case, equations (6) and (7) can be combined 
into a single second-order differential wave equation 
EQU .delta..sup.2 V/.delta.x.sup.2 =LC(.delta..sup.2 V/.delta.t.sup.2)(8) 
where the propagation velocity c is given by 
EQU c=1/(LC).sup.1/2 (9) 
and the line impedance by 
EQU Z.sub.e =.sqroot.L/C (10) 
The acoustic and electrical wave equations (4) and (8), identical in 
mathematical form, predict propagation of waves at constant velocity. The 
propagating waves need not be sinusoidal, but can take the form of 
transients of arbitrary shape, including step or impulse functions. 
Acoustic and electromagnetic waves can be made analogous by equating 
pressure p(x) with voltage V(x) and velocity u(x) with current I(x). Any 
reflections or transmissions that occur at the discontinuities of an 
acoustic airway system can thus be predicted or analyzed by the analogous 
events in an equivalent electrical transmission line system. 
The reflection from a voltage pulse of amplitude V.sub.1.sup.+ incident 
from a line of impedance Z.sub.1 onto a line of impedance Z.sub.2 is given 
by the expression 
EQU V.sub.1.sup.- =V.sub.1.sup.+ (Z.sub.2 -Z.sub.1)/(Z.sub.2 +Z.sub.1)=R.sub.12 
V.sub.1.sup.+ (11) 
where the superscript (+) denotes a positive traveling wave, the (-) 
superscript denotes a negative traveling wave, and the factor R.sub.12 
designates the reflection coefficient. Similarly, the amplitude of the 
pulse transmitted from line 1 onto line 2 can be expressed by 
EQU V.sub.2.sup.+ =V.sub.1.sup.+ (2Z.sub.2)/(Z.sub.2 +Z.sub.1)=T.sub.21 
V.sub.1.sup.+ (12) 
where T.sub.21 is the transmission coefficient. 
The reflection and transmission coefficients described above are also valid 
in the acoustic domain and form the basis for present methods used to 
determine the area-distance function of a single hollow airway. These 
known methods involves measuring the reflections that occur when a pulse 
in pressure is applied at the airway entrance. The subsequent reflections 
are sampled at discrete intervals, allowing the airway to be modeled as a 
sequence of short tube increments of varying cross-sectional area. The 
segmental representation of transmission lines is discussed in more detail 
hereinafter. The incremental length of the equivalent segments is 
detemined by the sampling interval and by the wave propagation velocity. 
From the measured acoustic pulse response (APR), the characteristic 
impedance, Z.sub.a (x) as a function of distance is computed. Finally, the 
area-distance function, A(x), is computed using equation (5). 
As is known, computation of the transmitted pulse amplitudes in a 
transmission line system can be made using a Thevenin equivalence model 
for describing the interaction of an incoming pulse with an impedance 
discontinuity. Assume that a voltage pulse, or by analogy, an acoustic 
pressure pulse, of amplitude V.sup.+ is incident from a line of impedance 
Z.sub.1 onto a second line of impedance Z.sub.2. At the moment of impact, 
before the occurrence of any further reflections from downstream of the 
impedance discontinuity, the effect of the second line on the first can be 
modeled as a load resistance of value Z.sub.2. Application of appropriate 
boundary conditions, in this case that the voltage and current both be 
continuous across the interface, yields the respective equations 
EQU V.sub.1.sup.- +V.sub.1.sup.+ =V.sub.2.sup.+ (13) 
EQU and 
EQU (V.sub.1.sup.- -V.sub.1.sup.+)/Z.sub.1 =V.sub.2.sup.+ /Z.sub.2(14) 
In these latter equations, the net line voltage on either side of the 
boundary consists of the sum of the positive traveling wave amplitude 
V.sup.+ and the negative traveling wave amplitude V.sup.-. Similarly, the 
net line current on either side consists of the difference between V.sup.+ 
and V.sup.- divided by the line impedance. Note that V.sup.- equals zero 
on line 2 because any reflections that might later arrive from downstream 
of the discontinuity do not effect events at the initial moment of impact 
of the V.sub.1.sup.+ pulse on the discontinuity. The above boundary 
conditions can be solved for the transmitted pulse amplitude V.sub.2.sup.+ 
associated with the event, yielding 
EQU V.sub.2.sup.+ =2V.sub.1.sup.+ [(Z.sub.2)/(Z.sub.2 +Z.sub.1)](15) 
This latter equation is identical to equation (12) and describes the 
amplitude of the voltage pulse transmitted onto line 2 from line 1. The 
reflected pulse amplitude predicted by these boundary conditions becomes 
EQU V.sub.1.sup.- =V.sub.1.sup.+ [(Z.sub.2 -Z.sub.1)/(Z.sub.2 +Z.sub.1)](16) 
which describes the usual coefficient of the pulse reflected back onto line 
1 as given by equation (11). The voltage division implied by equation (15) 
suggests that the transmitted pulse magnitude can also be determined from 
a simple Thevenin equivalent circuit. The transmitted pulse amplitude 
V.sub.2.sup.+ becomes equivalent to the voltage measured across Z.sub.2 as 
determined by simple voltage division. 
A similar model can also be applied to the case where the incident line, 
one of two parallel lines with impedances Z.sub.1 and Z.sub.2 
(representing the parallel nasal cavities) feeds a third line having 
impedance Z.sub.3 (representing the pharyngeal cavity) in series with the 
first two as shown in FIG. 2. In this latter case, the Thevenin equivalent 
circuit would show a parallel combination of line impedances Z.sub.2 and 
Z.sub.3 (denoted with the character .parallel.), forming the load to 
impedance Z.sub.1 so that the magnitude of the pulses transmitted 
respectively onto lines Z.sup.2 and Z.sub.3 become 
EQU V.sub.2.sup.+ =V.sub.3.sup.+ =2V.sub.1.sup.+ [(Z.sub.2 
.parallel.Z.sub.3)/(Z.sub.2 .parallel.Z.sub.3 +Z.sub.1)] (17) 
The voltage pulses transmitted onto lines 2 and 3 have the same magnitudes 
because the lines are connected in parallel. If lines 2 and 3 have 
different impedances, the transmitted currents will have different 
magnitudes. 
This latter model also suggests that the magnitude of the pulse reflected 
back onto line 1 can be computed from 
EQU V.sub.1.sup.- =V.sub.1.sup.+ [(Z.sub.2 .parallel.Z.sub.3 -Z.sub.1)/(Z.sub.2 
.parallel.Z.sub.3 +Z.sub.1)] (18) 
where the parallel combination of Z.sub.2 and Z.sub.3 has been included in 
the reflection coefficient. The above sequence of equations can be 
inverted to provide the value of Z.sub.3 from the measured value of 
V.sub.1.sup.- if Z.sub.1 and Z.sub.2 are known. 
If impedance discontinuities exist downstream of lines 2 and 3, pulses will 
be reflected back toward the bifurcation point. The subsequent 
transmission and reflection of these pulses can also be computed using a 
Thevenin model similar to that described. In this case the magnitude of 
the pulse transmitted onto lines 1 and 2 by a pulse of amplitude 
V.sub.3.sup.- arriving from line 3, for example, can be computed from 
EQU V.sub.2.sup.- =V.sub.1.sup.- =2V.sub.3.sup.- [Z.sub.1 .parallel.Z.sub.2 
/(Z.sub.1 .parallel.Z.sub.2 +Z.sub.3)] (19) 
where the load seen by negative-traveling waves on line 3 consists of the 
parallel combination of lines 1 and 2. Similarly, the magnitude of the 
pulse further reflected back onto line 3 will be given by 
EQU V.sub.3.sup.+ =V.sub.3.sup.- [(Z.sub.1 .parallel.Z.sub.2 -Z.sub.3)/(Z.sub.1 
.parallel.Z.sub.2 +Z.sub.3) (20) 
The method has thus been extended to provide information about impedance 
changes in line 3 downstream of the bifurcation point. 
The most general case consists of a combination of multisegmented, 
bifurcated lines as shown schematically in FIG. 2 wherein paths 1 and 2 
represent two nasal passages with varying area-distance functions A.sub.1 
(x) and A.sub.2 (x), and path 3 represents the nasopharynx with area 
distance function A.sub.3 (X). When an impulse of magnitude V.sub.0 is 
launched at the open end of path 1, representing one of the nostrils, the 
Thevenin transmission algorithm, when used recursively, predicts the 
subsequent reflected pulse amplitudes observed at the excitation point. 
Conversely, inversion of the basic algorithm permits determination of the 
various segment impedances from the values of the pulse reflections 
obtained by measurements at the excitation point. Though algebraically 
intensive, the method is not complicated and is easily performed on a 
general purpose computer as a post-measurement procedure. 
The use of the Thevenin transmission algorithm to determine the impedance 
distribution of a bifurcated airway can be demonstrated by simulating the 
system of FIG. 2 electrically using the industry standard SPICE 
(Simulation Program with Integrated-Circuit Emphasis) software program. 
These simulations provide impulse response data, APR.sub.1 and APR.sub.2, 
arising from application of an impulse into path 1 and into path 2, 
respectively. The initial reflections of APR.sub.1 coming from segments 
Z.sub.1a through Z.sub.1d were used to compute the impedances of the 
segments in path 1. Similarly, the initial reflections of APR.sub.2 coming 
from segments Z.sub.2a through Z.sub.2d were used to compute the 
impedances of the segments in path 2. Knowledge of the impedances in paths 
1 and 2 along with the remaining reflections of APR.sub.1 or APR.sub.2 
permitted computation of the segment impedances in path 3. In this way one 
can test the ability of the program written to implement the inverse 
algorithm to reconstruct the profile of impedances along each line. For 
these simulations, the segment impedances are chosen to vary arbitrarily. 
In order to simplify and speed up the calculations, the change in 
impedance between any two adjacent segments is made small (as they are in 
the nasal and nasopharyngeal cavities), so that all transmission 
coefficients have values close to unity and all reflection coefficients 
have magnitudes of order .epsilon., where .epsilon.&lt;&lt;1. This 
simplification allows all but primary reflections to be neglected at each 
line junction, because the observed effects of second and higher order 
reflections can be shown to be of order .epsilon..sup.3 or smaller. The 
impedance change cannot generally be considered small at the bifurcation 
point, of course. Hence reflections of order two or higher that occuring 
at the bifurcating junction must generally be included in the inverse 
algorithm. Note that the assumption of small impedance changes between 
segments is not a requirement of the Thevenin transmission model and can 
be relaxed to accommodate systems with large discontinuities in impedance 
along a given path. 
Accuracy can be improved when higher order reflections are included in the 
computations which is in agreement with results reported by Marshall I. 
Impedance reconstruction methods for pulse reflectometry, Acustica. 
76:118-128, 1992. 
The present invention then includes a method of computing the area-distance 
function of the nasopharyngeal cavity including a modification that 
accounts for the parallel impedances of the two nasal cavities. This 
method relies on the separate determination of APR from both the right and 
left nasal cavities, and knowledge of the NSL. Measurements of the APR 
from the right and left nostril are made, and from these, the AR(X) and 
AL(X) are computed using the standard method. The NSL is identified and 
for distances &lt;NSL in centimeters (that is, for times less than 
t=NSL/34,600) the AR(X) and AL(X) will be used as the correct values for 
the right and left nasal cavity cross-sectional areas. Because the 
cross-sectional areas of the nasopharynx are incorrectly estimated using 
this technique, the modified technique is used to compute more correct 
values for the cross-sectional area of the nasopharynx (i.e., for 
distances &gt;NSL). 
While the present invention has been described as using acoustic pulses, 
the principles of the present invention can be implemented even more 
advantageously, in some respects, by a different technique employing 
continuous wideband noise as the input signal. In such case, acoustic wave 
source transducer 20 is selected for producing a continuous wideband 
acoustic pressure wave, typically white noise. Current devices for 
measuring the area-distance function of bodily cavities, exemplified by 
U.S. Pat. No. 4,326,416, based on the use of transient pressure waves such 
as acoustic pulses, require a time-separation of the excitation signal and 
the reflected pressure wave. Such separation necessitates the use of wave 
tubes 22, typically of 5 meters or more, that are quite unacceptable 
clinically. By using continuous wideband pressure waves, one can transmit 
and receive the respective input signals and reflections using a much 
shorter tube 22, e.g. 580 mm. Further, the use of acoustic transient 
signals exposes the system to the effects of external acoustic noise of 
any nature that will interfere with the signal measured and introduce 
errors into the area-distance function computed. 
It will be appreciated that using continuous wideband noise as the input 
signal eliminates the necessity of time-separating input and reflected 
signals. The input and reflected signals are superimposed in the acoustic 
system and the superimposed signals are preprocessed statistically to 
transform them into pseudo-time space to provide time separation, to 
eliminate the influence of external noise and to adapt the wideband noise 
generator to the characteristics of the cavity being examined. The use of 
an appropriate algorithm to further process the preprocessed signals then 
provides the desired area-distance function. Apparatus providing the 
requisite wideband signal generator and the appropriate algorithms for 
statistical processing are commercially available from SRE Electronics 
ApS, Lynge, Denmark. 
Since certain other changes may be made in the present invention without 
departing from the scope of the invention herein involved, it is intended 
that all matter contained in the above description be construed in an 
illustrative and not in a limiting sense.