Vol. 94, Issue 2, 604-611, February 2003
Transpulmonary speed of sound input into the supraclavicular
space
R.
Paciej,
A.
Vyshedskiy,
J.
Shane, and
R.
Murphy
Faulkner/Brigham and Women's Hospitals, Boston,
Massachusetts 02130
 |
ABSTRACT |
The transpulmonary speed of sound
input at the mouth has been shown to vary with lung volume. To
avoid the disadvantages that exist in certain clinical situations in
inputting sound at the mouth, we input sound in the supraclavicular
space of 21 healthy volunteers to determine whether similar information
on the relationship of sound speed to lung volume could be obtained. We
measured the transit time at multiple microphones placed over the chest
wall using a 16-channel lung sound analyzer (Stethographics). There was
a tight distribution of transit times in this population of subjects.
At functional residual capacity, it was 9 ± 1 (SD) ms at the
apical sites and 13 ± 1 ms at the lung bases. The sound speed at
total lung capacity was 24 ± 2 m/s and was 22 ± 2 m/s at
residual volume (P < 0.001). In all subjects, the
speed of sound was faster at higher lung volume. This improved method
of studying the mechanism of sound transmission in the lung may help in
the development of noninvasive tools for diagnosis and monitoring of
lung diseases.
sound speed; lung parenchyma; sound recording; lung sound; noninvasive
| |
INTRODUCTION |
IN PREVIOUS WORK IN
OUR laboratory (2), we noted that transpulmonary
sound speed varied with lung volume, offering the promise of providing
information on lung tissue properties noninvasively. This work was done
by introducing sound through the mouth. If similar information on the
relationships of sound speed to lung volume could be obtained by
supraclavicular injection of sound, then a more practical method for
examining lung tissue properties could be obtained, as it provides a
number of benefits. It simplifies the procedure by avoiding the
necessity of using a mouthpiece. The need for the subject's
cooperation in keeping the glottis open is also avoided. In addition,
it simplifies interpretation of results by eliminating the
uncertainty associated with sound transmission through the bronchial
tree. Finally, it allows injection of sound with wider frequency
content, which in turn leads to a cross-correlation function with a
sharp peak in the envelope. With these thoughts in mind, we studied the
relationship of sound speed input at the supraclavicular space to lung
volume and compared the results with those found when sound was input
at the mouth.
| |
MATERIALS AND METHODS |
Twenty-one subjects were examined with a 16-channel lung sound
analyzer (Stethographics model 1602, www.stethographics.com). The
system (STG) was described in detail in Bergstresser et al. (2). In short, the STG uses electret microphones mounted
in commercially available stethoscope chest pieces to record data on a
personal computer. Fourteen microphones were incorporated into a soft
foam microphone pad. The microphone pad was positioned on a stretcher
or a plastic reclining chair positioned at a 45° angle. Subjects were
instructed to lie on the microphone pad. The microphone positions are
shown in Fig. 1. One microphone, referred
to as the reference microphone, was used to record sound inside a
speaker chamber.
View larger version (11K):
[in this window]
[in a new window]
|
Fig. 1.
Illustration of the position of the 14 microphones on the
back. One microphone was positioned inside the speaker chamber to
provide a reference. L, left; R, right.
|
|
The STG software played the prerecorded sound through the speaker
(diameter = 57 mm, resistance = 8 
, 0.5 W; Panasonic,
P10177-ND) mounted in a conical plastic chamber. A soft flexible
connector (length = 40 mm, diameter = 30 mm; part 2211E, RC
Medical, Tolland, CT) conducted sound from the speaker chamber to the
supraclavicular space. The back side of the speaker chamber was open to
the air. Tight closing of the back side diminished the speaker output. Subjects were instructed to take a deep breath and to breathe out
slowly to residual volume (RV). Neither flow nor volume of air
(VA) were measured.
Subjects.
The 21 normal subjects entered into this study were volunteers who had
no history of lung disease. Before the recording, verbal consent was
obtained from every subject. Twelve subjects were men, and nine were
women. Average age was 50 ± 23 (range 10-84) yr. The average
height was 163 ± 10 (range 140-180) cm. The average chest
circumference was 83 ± 14 (range 60-107) cm.
Input sound.
Our laboratory (2) has previously described how polyphonic
sounds can be used to yield a cross-correlation function with a sharp
peak in the envelope. We have observed that, when injected through the
mouth, sounds with broader frequency content exhibit stronger
destructive interference, presumably because higher frequency components travel further along the bronchial tree (16).
In this study, we avoided the problem posed by not knowing the point of
transfer of the sound from airways to the parenchyma by injecting the
sound into the supraclavicular space. We were looking for the broadest
meaningful frequency content of the injection sound. To investigate
sound transmission through the supraclavicular space, we injected
monophonic sounds from 50 to 800 Hz. Sounds with frequency <70 Hz and
>140 Hz were transmitted poorly. Therefore, we constructed a
polyphonic sound that contained frequencies from 70 to 140 Hz (Fig.
2). This sound was used in the remaining
studies. The sound contained 14 cycles. The cycle frequencies were
varied in the following pattern (cycles 1-14): 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, and 140 Hz. The
sound was played in a loop every 250 ms, yielding 80 transmission
"images" over 20 s of the recording.
View larger version (15K):
[in this window]
[in a new window]
|
Fig. 2.
A: the input sound contained 14 cycles. The cycle
frequencies were varied in the following pattern (cycles
1-14): 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125,
130, and 140 Hz. B: the autocorrelation of the input sound
exhibits a sharp peak in the envelope.
|
|
We tested for transmission of sound in the room. No detectable sound
was transmitted through the room (Fig.
3A). The sound input while the
subject slowly expired from vital capacity (VC) to residual volume (RV)
resulted in a strong signal at microphones on the side of the sound
injection (Fig. 3, B and C). On average, about
half of input sound acoustic energy was transmitted to the contralateral side compared with the ipsilateral side (53 ± 16% left to right, 60 ± 16% right to left). The reduction of the
sound transmitted to the contralateral side is statistically
significant (P < 0.005 in both cases).
View larger version (10K):
[in this window]
[in a new window]
|
Fig. 3.
Sound transmission through the lung. A: no
detectable sound was transmitted when the speaker played sound into the
room air near the subject. B: the sound input into the left
supraclavicular space resulted in a strong signal on the side of
injection. C: the sound input into the right supraclavicular
space also resulted in a strong signal on the side of injection.
|
|
We addressed the question of the mechanism of contralateral sound
transmission experimentally by injecting sound into a number of
structures around the chest and the neck. We found that there was no
difference in contralateral sound transmission between the case when
the microphone pad was made from a continuous sheet of foam and the
case when two separate microphone pads were applied to the back.
Application of a heavy metal object between the scapulae made no
difference on sound transmission to both ipsilateral and contralateral sides.
We input sound into each lung base posterolaterally. The sound on the
contralateral side was markedly attenuated in each case (right and
left). Minimal sound was transmitted to the microphones when input into
the 7th vertical vertebra. Minimal sound was transmitted when input
into the outside surface of the trachea. Minimal sound was transmitted
when the input was into the trapezius muscle just posterior to the
supraclavicular space. These observations are inconsistent with
contralateral sound transmission through the chest surface.
Furthermore, we have input sound into the carotid artery on the neck
(either left or right). Sound was transmitted equally well to both
ipsilateral and contralateral upper body microphones. This should not
be a surprise, because low-frequency heart murmurs (aortic murmur
particularly) are known to be well transmitted through the carotid
arteries. Recall that, in our experiments, the input sound is very
similar to the sound of murmurs (both are 70-140 Hz). These
observations, taken together, are consistent with the theory that the
sound is transmitted contralaterally via the large blood vessels and
other tissue located between the lungs. The wavelength of sound in lung
parenchyma is 24 m · s
1 · 100 Hz1 = 0.24 m or 24 cm. At that frequency, the
wavelengths in those intervening structures would be much longer
because the sound speeds in those structures are much higher than the
speed in lung parenchyma. Because the wavelengths within the
obstructions are much longer than the total dimension of the
obstructions, it should be possible for the compressional waves to
traverse them with little attenuation.
We concluded that, when input into supraclavicular space, most of the
acoustic energy is transmitted through lung parenchyma, not through the
chest surface.
Sound was injected consecutively through left and right supraclavicular
spaces. Sound input on the right was used for the right lung transit
time analyses, and that on the left was used for the left lung transit
time analyses. We did not analyze transscapular sound transmission.
During the recordings, the subjects were asked to move the shoulder on
the recording side slightly forward. This maneuver created a pit in the
supraclavicular space. The flexible connector was lightly pressed
against the skin in this pit. The pressure was adjusted to achieve the
maximum amplitude of transmitted sound. High pressure on the speaker
chamber tended to reduce transmitted sound, presumably because of
speaker damping. Care was used to hold the speaker chamber parallel to
the spine.
Simulation.
The theoretical prediction of the speed of sound in a two-phase system
is discussed in detail in the book One-dimensional Two-phase
Flow by Wallis (14). This two-phase model yields the following expression for the sound speed as a function of the volume
fraction of air in the lungs
|
(1)
|
where C is the speed of sound in the two-phase
system; 
is the fraction of air by volume, where = VA/(VA + VT), where VT is the tissue volume (7);
A = 1.293 kg/m3 is air density
(3); T = 0.998 × 103
kg/m3 is tissue density (3);
CA = 344 m/s is speed of sound in the air
(3), also see discussion of the effects of temperature and
humidity in Bergstresser et al. (2); and
CT = 1,460 m/s is speed of sound in the
tissue (3). For the purpose of simplicity, tissue density
was assumed to be spatially constant and independent of orientation
with the gravitational field.
The applicability of a two-phase system description to sound
propagation through lung parenchyma is discussed by Bergstresser et al.
(2). In short, sound propagation through lung parenchyma can be treated as a compressional wave in a homogeneous two-phase system. In other words, because the wavelength is expected to be large
compared with the alveolar dimensions, the sound transmission can be
simulated by using the assumption that the lung consists of a
homogeneous mixture of gas (humid air) and soft tissue phases.
In our laboratory's previous work (2), we were using an
approximation of Eq. 1 that can be used as long as is
>0.01 and <0.99
|
(2)
|
| |
RESULTS |
Transit time analysis.
An example of the transit time analysis through the right chest of the
polyphonic sound with frequencies of 70-140 Hz is shown in Fig.
4A. The sound recorded at the
speaker (reference) is shown on the top, and the sound
recorded at channel 6 is shown on the bottom.
With the use of the time interval between corresponding peaks of two
sounds to yield an approximation of transit time, the sound recorded
from channel 6 is delayed by 14.9 ms compared with the
reference.
View larger version (19K):
[in this window]
[in a new window]
|
Fig. 4.
Transit time analysis was performed with the use of a
cross-correlation technique with further verification by approximating
the interval between the corresponding peaks. A: the
reference sound is displayed on the top. The transmitted
sound recorded at the right lung base (channel 6) at
functional residual capacity is shown at the bottom. The
time interval between corresponding peaks of 2 sounds is 14.9 ms.
B: the result of cross-correlation of the 2 sounds shown in
A. The peak (arrow) corresponds to an arrival time
difference (transit time) of 14.9 ms.
|
|
In Fig. 4B, the transit time analysis was refined by
cross-correlating the two sounds. The cross-correlation shows a clear peak (arrow) corresponding to an arrival time difference of 14.9 ms
between the reference and channel 6. The correlation
coefficient at the peak of the cross-correlation function was 0.9.
Figure 5A shows the transit
time between the reference and all of the 14 chest sites in a different
subject at functional residual capacity. Circle size in the diagram is
proportional to the transit time. Numbers indicate transit time in
milliseconds. There was a progressive increase in this transit time
from the microphones on the apical sites to the microphones over the
basal sites. Transit time varied over the chest from 6.6 ms at the
apical sites to 13.9 ms at basal sites.
View larger version (15K):
[in this window]
[in a new window]
|
Fig. 5.
A: transit time between the reference
microphone and all of the 14 chest sites in 1 subject. Circle size in
the diagram is proportional to the transit time. Nos. indicate transit
time in milliseconds. B: transit time measured at functional
residual capacity as a function of the three-dimensional straight-line
distances between the reference microphone and 14 chest microphones.
The following distances between each microphone and the supraclavicular
space were used: channels 1 and 9,
17.0 cm; 2 and 10, 21.1 cm; 3 and
11, 25.6 cm; 4 and 12, 25.9 cm;
5 and 13, 30.4 cm; 6 and
14, 30.6 cm; 7 and 15, 30.4 cm. The
linear regression yielded a speed of sound of 2.4 cm/ms = 24 m/s.
|
|
Figure 5B shows the relationship between the transit time
measured at functional residual capacity and the three-dimensional straight-line distances between the reference microphone and 14 chest
microphones. Linear regression yielded a speed of sound of 2.4 cm/ms = 24 m/s.
Relationship of transit time to lung volume.
Transit time was shorter the bigger the lung volume, as illustrated in
Fig. 6. For every recording microphone,
the transit time in milliseconds is shown as a function of the
approximate percentage of VC. At all lung volumes, the transit time was
minimal at the apical sites (channels 1 and 9).
There was a strong tendency for the transit time to increase gradually
the further away the microphones were from the apices. This observation
was consistent in all subjects.
View larger version (27K):
[in this window]
[in a new window]
|
Fig. 6.
Transit time between the reference microphone and all of
the 14 chest sites in milliseconds shown as a function of approximate
percentage of the vital capacity (VC). Values are means ± SD,
averaged among 21 normal patients.
|
|
In all chest locations, the transit time varied inversely with lung
volume (Fig. 6). Filling the lungs with air from RV to VC reduced
transit time by up to 3.6 ms in some subjects. The paired two-sample
t-test indicated that the reduction of transit time is
statistically significant (P < 0.001) at all channels, except channels 7 and 15. The largest transit
time reduction occurred at central channels: channel 3 on
the right (1.4 ± 1.0 ms) and channel 11 on the left
(1.2 ± 0.8 ms).
Comparison to sound input at the mouth.
There was a tight distribution of transit times among the diverse
population of subjects (Fig. 6). The standard deviation of the
average transit time data was ~10% compared with 30% when sound was
injected through the mouth (2).
The transit time dependence on the lung volume was strongest at the
central sites and weakest at the peripheral sites, similar to the
results obtained with sound injection through the mouth. The average
decrease in the transit time from VC to RV was 0.8 ms with both methods
of sound injection.
Transit time was shorter on the left than on the right when sound was
injected through the mouth (2). Transit times did not vary
significantly between left and right channels when the sound was
injected into supraclavicular space.
Relationship of speed of sound in lung parenchyma to biometric
data.
The transit time was related to the three-dimensional straight-line
distance from the microphones to the injection point. Linear regression
was used to calculate the speed of sound for each patient, as noted in
the caption for Fig. 5B. The calculated speed of sound was
24 ± 2 (range: 28-20) m/s at VC, 23 ± 2 (range: 27-19) m/s at functional residual capacity, and 22 ± 2 (range: 28-19) m/s at RV.
Speed of sound showed little correlation with subject height (Fig.
7A; correlation coefficient = 
0.4), chest circumference (Fig.
7B; correlation coefficient = 0.0), and age (Fig.
7C; correlation coefficient = 0.2).
View larger version (11K):
[in this window]
[in a new window]
|
Fig. 7.
Relationship of the speed of sound in lung parenchyma to
biometric data. Speeds of sound as a function of height (correlation
coefficient = 0.4; A), chest circumference
(correlation coefficient = 0.0; B), and age
(correlation coefficient = 0.2; C) are shown.
|
|
Comparison between experimental and theoretically predicted speed
of sound.
The theoretically predicted speed of sound in a homogeneous two-phase
system is shown in Fig. 8 as a function
of the in the lungs. The minimum speed of sound (~24 m/s) occurs
when air occupies one-half of the lung volume. In the theoretical case when only air is present, = 1, the speed of sound increases to
344 m/s. When no air is present, = 0, the speed of sound increases to 1,460 m/s.
View larger version (13K):
[in this window]
[in a new window]
|
Fig. 8.
The speed of sound in a two-phase system as predicted by
Eq. 1 is shown as a function of the volume fraction of air
in the lungs. The experimental data are superimposed on the theoretical
curve. The leftmost data point corresponds to a lung
residual volume (RV) that was assumed to be 1 liter. The
rightmost data point corresponds to a VC that was assumed to
be 5.5 liters. Volume of air in conducting airways was assumed constant
at 0.15 liters. Volume of air in the lung parenchyma (VA)
was calculated by subtracting volume of air in conducting airways from
lung volume. The tissue volume (VT) was assumed to be 0.8 liters at RV (15), linearly increasing to 1.7 liters at VC
(13). These assumptions yielded fraction of air by volume
in the lung parenchyma of 0.52 at RV and 0.76 at VC. Values are
means ± SD.
|
|
To show the limiting values at = 0 and = 1, Eq. 1 was used to calculate the theoretical curve in Fig. 8. The
simplified expression, Eq. 2, diverges at both limits, i.e.,
at < 0.01 and > 0.99. It should be pointed out,
however, that, except for values of very close to those limiting
values of 0 and 1, the numerical results of the two expressions are
nearly indistinguishable. In particular, the portion of the curve with
volume fractions of air that are experimentally accessible, the
theoretical values calculated from the two expressions are virtually
identical. Also, for volume fractions of air, > 0.01, the
calculated sound speeds are essentially independent of the acoustical
properties of the tissue. The reason for this is clear: for the
propagation of a compressional wave through lung parenchyma, it is the
air that is compressed, not the tissue (2).
The experimental data from the normal subjects are superimposed on the
theoretical curve. The leftmost data point corresponds to a
lung RV that was assumed to be 1 liter. The rightmost data point corresponds to a VC that was assumed to be 5.5 liters.
VA in conducting airways was assumed constant at 0.15 liters. VA in the lung parenchyma was calculated by
subtracting VA in conducting airways from lung volume. The
VT was assumed to be 0.8 liters at RV (15),
linearly increasing to 1.7 liters at VC (13). These
assumptions yielded in the lung parenchyma of 0.52 at RV and 0.76 at VC. This range of is close to that measured in dogs,
0.51-0.93 (1, 4).
| |
DISCUSSION |
Clinicians use alterations in the conduction of sound
through the chest to obtain information on lung tissue properties.
Whispered pectriloquy, the technique of examining the transmission of
speech through the chest, is helpful in detection of conditions such as
pneumonia and pleural effusions. We have been interested in obtaining
more quantifiable information on sound conduction. As noted, we
recently reported a method for studying transpulmonary sound speed and
showed that it is varied as a function of lung volume. In this present
study, we show that the sound speed varies with lung volume in the same
way as it does when the sound is input in the mouth. Furthermore, we
show that sound input in the supraclavicular space travels rather
uniformly in normal subjects. As sound input in the supraclavicular
space requires little patient cooperation and, as mentioned, avoids the
problem of knowing precisely where sound leaves the airways to enter
the parenchyma, the technique provides a promise of yielding
information on tissue properties noninvasively. This could have
application as an aid in diagnosis and in monitoring conditions that
alter lung properties such as pneumonia and congestive heart failure.
There were some differences in the results between the two input
modalities. Calculated sound speeds were approximately one-half as fast
when the sound was input through the supraclavicular space compared
with sound input through the mouth. In the results previously reported
(2) for sound speed through the mouth, it was assumed that
the sound was transferred from the trachea to the parenchyma at the
carina. If, in fact, the sound traveled further along large airways
before switching to transmission through parenchyma, the shorter path
length to the microphone would yield a slower speed and more closely
agree with the results presented here. An advantage of the method of
sound input through the supraclavicular space for the calculation of
sound speed is that it avoids any assumption about the location of the
transition of the sound from large airways to propagation in parenchyma.
As noted, transit time was shorter on the left than on the right
when sound was injected through the mouth (2). Transit times did not vary significantly between left and right channels when
the sound was injected into supraclavicular space. A possible explanation is that, when injected through the mouth, sound is transmitted through the heart at a higher speed than through the lung.
This scenario implies that the sound jumps from the trachea to the
heart and propagates through the heart before jumping to the
parenchyma. An appropriate theoretical treatment, utilizing the fact
that the sound wavelength in the heart tissue is much longer than the
heart's dimensions, predicts a reduction in the transit time of
L/v, where L is the size of the heart
and v is the speed of sound in the lung parenchyma. An
analogous theoretical approach is described and some applications are
discussed in Ref. 12. Substitution of 0.1 m for the
size of the heart and 23 m/s for the speed of sound yields the
reduction of transit time as much as 4.3 ms. When injected into the
supraclavicular space, sound probably travels through the lung
parenchyma around the heart; therefore, no difference between left and
right transit times is observed.
The alternative explanation of the reduced transit time on the left
base when sound is injected through the mouth can be that the sound
travels longer within the airways. There is some evidence that sound
injected through the mouth enters the parenchyma directly through the
right tracheal wall that is in direct contact with the mediastinal
aspect of the right lung. Several massive vascular structures isolate
the trachea from the left lung so that the sound would presumably have
to travel further down the airways before entering the parenchyma
of the left lung (8, 17, 10).
Table 1 compares the speed of sound in
lung parenchyma obtained with a number of different sound injection
methods. Note that the results obtained by different groups of
scientists are similar. Injection through the mouth tends to yield a
faster sound speed than direct injection into lung parenchyma. In our
case, sound injection though the mouth yielded a speed of sound that was twice as high as obtained when the sound was injected into the
supraclavicular space. This effect could be an artifact of overestimation of the distance that the sound travels in the parenchyma when the sound is injected through the mouth. In other words, it is
likely that sound propagates at high speed in the large airways over
longer distances than assumed by the models before it switches to
propagation through the parenchyma.
We have found that speed of sound of 22 ± 2 to 24 ± 2 m/s
is very similar to that predicted by Eqs. 1 and 2
at fraction of air of 0.5-0.8. The close correlation between the
experimental and theoretical data and the tight distribution of speed
of sound in healthy lung may provide a noninvasive means to deduce
fraction of air in the lung from experimentally measured speed of sound.
Conclusions.
Sound injection into supraclavicular space provides a noninvasive
method of examining sound speed in lung parenchyma. This method yields
consistent and reliable results while reducing the need for patients'
cooperation. This improved method of studying the mechanism of sound
transmission in the lung may help in the development of noninvasive
tools for diagnosing and monitoring lung diseases.
| |
ACKNOWLEDGEMENTS |
Statement of financial interests: R. Murphy holds the rights to
several lung sound-related patents. R. Murphy and A. Vyshedskiy have
financial interests in Stethographics, Inc.
| |
FOOTNOTES |
Address for reprint requests and other correspondence: A. Vyshedskiy, Faulkner/Brigham and Women's Hospitals, 1153 Centre St.,
Ste. 4990, Boston, MA 02130 (E-mail:
andrey{at}stethographics.com).
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. Section 1734 solely to indicate this fact.
First published October 18, 2002;10.1152/japplphysiol.00568.2002
Received 27 June 2002; accepted in final form 13 October 2002.
| |
REFERENCES |
1.
Baile, EM,
Pare PD,
Dahlby RW,
and
Hogg JC.
Regional distribution of extravascular water and hematocrit in the lung.
J Appl Physiol
46:
937-942,
1979.
2.
Bergstresser, T,
Ofengeim D,
Vyshedskiy A,
Shane J,
and
Murphy R.
Sound transmission in the lung as a function of lung volume.
J Appl Physiol
93:
667-674,
2002.
3.
Hodgman, CD
(Editor).
CRC Handbook of Chemistry and Physics (35th ed.). Cleveland, OH: CRC, 1953.
4.
Hogg, JC,
and
Nepszy S.
Regional lung volume and pleural pressure gradient estimated from lung density in dogs.
J Appl Physiol
27:
198-203,
1969.
5.
Jahed, M,
and
Lai-Fook SJ.
Stress wave velocity measured in intact pig lungs with cross-spectral analysis.
J Appl Physiol
76:
565-571,
1994.
6.
Jahed, M,
Lai-Fook SJ,
Bhagat PK,
and
Kraman SS.
Propagation of stress waves in inflated sheep lungs.
J Appl Physiol
66:
2675-2680,
1989.
7.
Kraman, SS.
Speed of low-frequency sound through lungs of normal men.
J Appl Physiol
55:
1862-1867,
1983.
8.
Kraman, SS,
and
Bohadana AB.
Transmission to the chest of sound introduced at the mouth.
J Appl Physiol
66:
278-281,
1989.
9.
Mahagnah, M,
and
Gavriely N.
Gas density does not affect pulmonary acoustic transmission in normal men.
J Appl Physiol
78:
928-937,
1995.
10.
Pasterkamp, H,
Patel S,
and
Wodicka GR.
Asymmetry of respiratory sounds and thoracic transmission.
Med Biol Eng Comput
35:
103-106,
1997.
11.
Rice, DA.
Sound speed in pulmonary parenchyma.
J Appl Physiol
54:
304-308,
1983.
12.
Slater, JC,
and
Frank NH.
Mechanics New York: McGraw-Hill, 1949, chapt. 9, sect. 4, problem 10.
13.
Thompson RB, Ennis DB, Derbyshire JA, Arai AE, and McVeigh ER.
Respiratory resolved cine phase contrast MRI: measurements of right and
left heart cardiac output during inspiration and expiration. Proc
Intl Soc Mag Reson Med 10: 2002.
14.
Wallis, GB.
One-dimensional Two-phase Flow. New York: McGraw-Hill, 1969, p. 20-29.
15.
Whimster, WF,
and
Macfarlane AJ.
Normal lung weights in a white population.
Am Rev Respir Dis
110:
478-483,
1974.
16.
Wodicka, GR,
Aguirre A,
DeFrain PD,
and
Shannon DC.
Phase delay of pulmonary acoustic transmission from trachea to chest wall.
IEEE Trans Biomed Eng
39:
1053-1059,
1992.
17.
Wodicka, GR,
Defrain PD,
and
Kraman SS.
Bilateral asymmetry of respiratory acoustic transmission.
Med Biol Eng Comput
32:
489-494,
1994.
18.
Yen, RT,
Fung YC,
Ho HH,
and
Butterman G.
Speed of stress wave propagation in lung.
J Appl Physiol
61:
701-705,
1986.
J APPL PHYSIOL 94(2):604-611
8750-7587/03 $5.00
Copyright © 2003 the American Physiological Society
TOP
ABSTRACT
INTRODUCTION
