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1 Medical Instrumentation Research Laboratory, School of Engineering, Oxford Brookes University, Headington, Oxford OX3 0BP; and 2 Nuffield Department of Anaesthetics, Radcliffe Infirmary, Oxford OX2 6HE, United Kingdom
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ABSTRACT |
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 TOP
 ABSTRACT
 INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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This study measured transit time (TT) and
attenuation of sound transmitted through six pairs of excised pig
lungs. Single-frequency sounds (50-600 Hz) were applied to
the tracheal lumen, and the transmitted signals were monitored on the
tracheal and lung surface using microphones. The effect of varying
intrapulmonary pressure (Pip) between 5 and 25 cmH2O on TT
and sound attenuation was studied using both air and helium (He) to
inflate the lungs. From 50 to ~200 Hz, TT decreased from 4.5 ms at 50 Hz to 1 ms at 200 Hz (at 25 cmH2O). Between ~200 and 600 Hz, TT was relatively constant (1.1 ms at upper and 1.5 ms at lower
sites). Gas density had very little effect on TT (air-to-He ratio of
~1.2 at upper sites and ~1 at lower sites at 25 cmH2O).
Pip had marked effects (depending on gas and site) on TT between 50 and
200 Hz but no effect at higher frequencies. Attenuation was frequency
dependent between 50 and 600 Hz, varying between 
10 and 35 dB with
air and 2 and 28 dB with He. Pip also had strong influence on
attenuation, with a maximum sensitivity of 1.14 (air) and 0.64 dB/cmH2O (He) at 200 Hz. At 25 cmH2O and 200 Hz, attenuation with air was about three times higher than with He.
This suggests that sound transmission through lungs may not be
dominated by parenchyma but by the airways. The linear relationship
between increasing Pip and increasing attenuation, which was found to
be between 50 and ~100 Hz, was inverted above ~100 Hz. We suggest
that this change is due to the transition of the parenchymal model from
open to closed cell. These results indicate that acoustic propagation
characteristics are a function of the density of the transmission media
and, hence, may be used to locate collapsed lung tissue noninvasively.
transit time; acoustic attenuation; density dependence
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INTRODUCTION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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ACOUSTIC TRANSMISSION THROUGH the lungs can be measured by introducing sound into the airway and recording the output signals on the lung surface or chest wall. The ratio of the sound injected to that received on the surface gives the transfer function (TF). Two types of information can be obtained from the TF, namely the amplitude and phase response, which are both functions of frequency. The phase can be used to calculate the time delay between the input and output signal, which is a function of sound speed through the respiratory system. The sound speed is a function of the density of the transmission media and, hence, may vary with lung pathology. Therefore, the investigation of the acoustic transmission may provide a noninvasive means for localizing lung pathology.
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METHODS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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Apparatus
A sinusoidal signal from a signal generator (Black Star Jupiter 500) was fed into a custom-built 100-W power amplifier that was connected to a 24-cm-diameter loudspeaker in an acoustically damped enclosure (Mackenzie Studio 7). The signal was varied from 50 to 600 Hz in 50-Hz steps. The electrical power supplied to the loudspeaker was kept constant at 6 W root mean square (RMS) for all frequencies. A rigid tube that was 150 cm in length and 2.5 cm in diameter was connected directly to a plate over the front of the loudspeaker to allow sound to be coupled into the trachea of the excised lungs. The apparatus and lungs could be filled with helium or air as required. Pressure within the lungs and tubing was varied by immersing the gas vent tube in water to known depths. A manometer was linked to the system to monitor pressures. The pressures on the front and back sides of the loudspeaker cone were equalized to prevent displacement of the cone. A tapered adapter and a cable tie were used to connect the tube to the trachea. Five identical electric microphones (33-1052, Realistic, Tandy; with a flat frequency response between 30 and 10 kHz) were used for sound detection. One was fitted with a custom-made flexible plastic housing and was used on the trachea; the remaining four microphones were placed in small, bell-shaped assemblies with a 3-cm-diameter contact area and 1-cm air cavity depth. The microphones were attached to the lung parenchymal surface at four locations, as shown in Fig. 1, by using four elastic Velcro strips. The output signals from the microphones were connected to custom-made amplifier-filter units. Each unit consisted of three parts: 1) a first-stage amplifier with a gain of 10, 2) an eighth-order Butterworth low-pass filter with a cutoff frequency of 1 kHz and 160 dB/decade roll-off and unity gain, and 3) a second-stage amplifier with a gain of 10. The low-pass filter served as an antialiasing filter and also eliminated higher frequency environmental noise. The amplified and filtered analog signals were digitized by using a 12-bit analog-to-digital converter (MetraByte, DASH16) at a 8,333-Hz sampling frequency in 1,024 sample blocks, which represent a recording segment of 122.88 ms. The digitized signals were passed through a digital high-pass filter with a cutoff frequency of 20 Hz. The high-pass filter is used to eliminate possible mechanical noise during the measurement. Single-frequency stepping was done automatically by a digital-to-analog converter (MetraByte, DASH16) with feedback to a frequency counter (MetraByte, DASH16) for calibration. All data acquisition and analyses were controlled by software written in C++ on an IBM PC-compatible 486DX33.
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Protocol
Six pairs of excised pig lungs, weighing between 440 and 864 g, each with intact trachea and parenchyma but with the heart removed, were studied. Each experiment was carried out at room temperature of ~20°C and humidity of ~38%. The pressure-volume relationship for each pair of lungs was determined by inflating the lungs with air to a pressure of 30 cmH2O and then deflating gradually in steps of 500 ml. The volume of the degassed lungs was measured by water displacement. The density of the degassed lung was determined by weighing the lung parenchyma and dividing it by the measured volume. By changing the pressure applied to the airways from 0 to 25 cmH2O in steps of 5 cmH2O, different lung densities were obtained. The acoustic signals were recorded over five sites (Fig. 1): the anterior trachea, which was taken as the reference site (TR), and the top and bottom of the posterior surface of the left and right lung [left top (LT), left bottom (LB), right top (RT) and right bottom (RB)]. Data were recorded from all five sites simultaneously and repeated three times. The physical size of the lungs and the location of the microphones were measured during each pressure study. The lungs were then inflated with helium, and the study was repeated. To wash out the air that might have been trapped in the parenchyma, we inflated the lungs (with helium) and deflated them eight times before the helium study.Data Analysis
From the digitized acoustic sound samples, the coherence, transit time (TT), and attenuation were calculated with respect to TR. The acoustic signal recorded over the TR was considered as the input x(n), and the signal recorded from the other four sites (LT, LB, RT, and RB) represented an output y(n), where n is the sample number in time domain. In single-frequency analysis, the cross-correlation function (CCF) of the input and output signal (Rxy) was calculated using
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(1) |
is the time
delay. Rxy has the maximum amplitude (
1) when
is the actual time shift between the input and output signals.
Rxx and Ryy are the
autocorrelation function of x(n) and
y(n), respectively. The coherence function between the input and output signals for single frequency analysis is
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(2) |
in Eq. 1, and it is calculated by identifying the most positive peak on
the CCF curve. This is implemented by a computer program. The envelope of CCF was also observed, and the result suggests that it is a single-path propagation from TR to any one of the four parenchymal sites throughout our study. The calculated time delay displayed no
ambiguity or discontinuity over the frequencies used; thus no phase
unwrapping was applied in the study. The attenuation (in dB) is
calculated by using 20 * log
(yRMS/xRMS), where
xRMS and yRMS are the RMS
amplitude of input and output signal x(n) and y(n), respectively.
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RESULTS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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For all graphs, the line of best fit was calculated from the discrete data points by using a cubic spline interpolation curve fit.
Figure 2 shows a plot of the averaged
coherence function. The coherence function values of all the
measurements between 50 and 600 Hz were >0.7. This indicates a good
signal-to-noise ratio (8).
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Figure 3 illustrates the averaged results
from the six pairs of lungs. The coefficients of variation are within
±17%. The information for LT and RT has been averaged, and also that
for LB and RB, because they displayed similar characteristics and also
are the same distances from the TR. Figure 3,
A-D, shows the results for the TT measurement in
milliseconds, and Fig. 3, E-H, shows the
attenuation results in decibels. Four graphs for each principal
parameter (i.e., TT or attenuation) are subdivided into two groups: air
study and helium study. To highlight the difference between air and
helium study, Fig. 4 demonstrates the air-to-helium ratio for the TT and output signal amplitude at different
sites. There are five curves on each graph, which represent five
inflation pressure levels from 5 to 25 cmH2O. In addition, a pressure correlation function (PCF) is shown (solid line) in Fig. 3.
PCF is the correlation coefficient between pressures and the
corresponding values of TT or attenuation at each frequency. It has a
value of 1 to 1. The PCF is a simple means of illustrating the
pressure dependency of the results.
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TT Measurement
All graphs for the TT measurement (Fig. 3, A-D) displayed similar characteristics. There are clearly two separate stages in the TT distribution along the frequency axis. The first stage (stage 1) is between 50 and ~200 Hz, which has higher TT and is more dependent on inflation pressure. The TT moved to its second stage (stage 2) from ~200 Hz and up and demonstrated a flat pattern until the end of the frequency range (i.e., 600 Hz). This two-stage characteristic is illustrated further in Fig. 5A, which shows the standard deviations of the TT values, measured at five pressures, against frequency. Figure 5A also draws the comparisons between air and helium at top and bottom sites. The standard deviation plotting (SDP) of the TT can quantitatively reveal how much the TT is related to the inflation pressure, and the PCF can reveal how good this correlation is. For example, in Fig. 3B, the PCF indicates that pressure and TT are closely, linearly related between 400 and 600 Hz because its value is approximately equal to1. However, SDP (Fig.
5A) shows a TT standard deviation variation of 0.08 ms (8%
of the mean value) within this frequency range, which suggests that the
TT is relatively less dependent on the changes in pressure.
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Attenuation Measurement
Figure 3, E-H, shows the attenuation detected from the top and bottom sites using different gases. The PCF reveals the general pattern of the correlation between inflation pressure and attenuation. Similar PCFs were found at the top sites between air and helium (Fig. 3, E and F). However, there is an offset of 15 dB in attenuation between air and helium. All attenuation results started with a PCF of 0.96 at 50 Hz and reached1 at ~200 Hz. A PCF value of 0, where the linearity changed
the sign of its slope, also indicates that the attenuation is
independent of pressure at a particular frequency. In Fig. 3,
E-H, each graph has three stages divided by the
PCF. Stage 1 is between 50 and ~100 Hz where the first zero-PCF point occurs. In this stage, the slope of the linear relationship between attenuation and pressure is positive. However, this relationship is reversed in stage 2, which is between
the first zero-PCF point and the second zero-PCF point (i.e., ~570 Hz
in Fig. 3E). In stage 2 the slope becomes
negative, and the correlation is excellent (between 0.85 and 1).
The frequency that marks the end of stage 2 is determined by
gas density and site. Stage 3 is from the second zero-PCF
point to 600 Hz, which covers an unstable relationship between
attenuation and pressure. In general, the bottom two sites have higher
attenuation (~7 dB) than their corresponding top sites, and
attenuation in lung with air is higher than with helium (~15 dB). The
SDP in Fig. 5B shows a general peak (~5.8 dB for air and
~3.4 dB for helium) at ~200 Hz. Together with the PCF indication,
it suggests that there is a marked linear relationship between
attenuation and pressure in stage 2. It also shows that the
attenuation has greater dependence on pressure when the lungs are
filled with air rather than helium.
Gas Effect on TT and Attenuation
To demonstrate the effect of varying the type of gas on the TT and attenuation of acoustic transmission through excised pig lungs, the data of the air-to-helium ratio were calculated, as shown in Fig. 4. All pressure curves in the amplitude graphs (Fig. 4, B and D) tend to be <1, which means a much higher attenuation in air than in helium. Figure 4, B and D, also demonstrates that the effect of gas density on attenuation is less dependent on inflation pressure as well as frequency, compared with the TT curves in Fig. 4, A and C. Apart from gas density, the viscosity of air (18.1 µPa/s at 1 atm, 20°C) is also different from that of helium (19.4 µPa/s at 1 atm, 20°C), but the difference (+7%) is considered insignificant to sound transmission compared with the effect of density change (86%). Generally
speaking, the result suggests that gas density does affect sound
transmission through excised pig lungs, and the degree of effect is
dependent on frequency and site locations.
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DISCUSSION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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The lung parenchyma was first modeled as linked bubbles by Rice (9), and this approach has been widely adopted. Each alveolus is considered as an identical single bubble contained in tissue, which has similar mechanical properties as water. The theory of sound propagation in bubbly liquids is well developed and gives predictions in quite reasonable agreement with experiments (6). Generally, the speed and attenuation of sound through bubbly liquids are frequency dependent. Small fractions of bubbles in water can lead to much lower sound speeds (at low frequencies) than even the free-field speed of sound in air. At higher frequencies, around the bubble resonant frequency, the sound speed can become even lower and essentially zero. For still higher frequencies, the speed becomes greater than the pure water sound speed. Therefore, the bubble resonance frequency provides a good indication of which frequency region should be used to study the parenchyma. Assuming the average alveolar radius in normal human adults is ~0.15 mm, the resonant bubble frequency (the Minnaert frequency) would be ~18 kHz in isothermal conditions. Therefore, the speed of sound transmission through the parenchyma in the audible frequency range (20 Hz to ~16 kHz) should be lower than the speed of sound in air (34,000 cm/s), and it has been measured (4, 9) at 2,300-7,000 cm/s. One important limitation of this bubbly liquid parenchymal model is the assumption that no gas exchange takes place between alveoli and terminal bronchioles, which is not true with very-low-frequency sound (1). Therefore, the starting frequency for this model should be limited to ~100 Hz.
In the frequency range of 50 to 600 Hz, the sound attenuation and phase delay characteristics of the trachea have been shown previously to be frequency dependent (12). However, this frequency range for parenchymal modeling may be difficult, as there are three different stages that occur at increasing frequencies (1). In the open-cell stage, low-frequency (<20 Hz) wave propagation causes coupling between bulk parenchymal elasticity and density, and gas moves between alveoli and terminal bronchioles, i.e., the alveolar regions. In the transition stage between 20 and 200 Hz, gas still moves between alveolar regions, but it becomes difficult as higher forces are needed to overcome the increasing gas inertance with increasing frequency. As the frequency continues to increase, gas does not move between regions but compresses locally within each alveolus. It is this "closed-cell" stage that demonstrates the coupling of gas elasticity to parenchymal mass. The parenchyma can be modeled as bubbly liquid only when it reaches a closed-cell stage.
In the open-cell stage, sound speed through the parenchyma measured by Butler et al. (1) varied from 250 to 1,500 cm/s. Sound speed through parenchyma with closed-cell model behavior was 2,300-7,000 cm/s (4, 9). Although the parenchyma has been considered as a two-phase homogenous continuum in its closed-cell stage, it is still in doubt whether it acts as a dispersive medium to sound transmission because of its strong absorptive properties between 200 and 600 Hz. Therefore, the sound transmission through the parenchyma is also expected to be frequency dependent between 50 and 600 Hz.
The determination of the sound transmission path is an extremely important factor in the TF. By changing the gas density in the trachea and parenchyma, it is possible to investigate whether the transmission is dominated by the parenchyma (if there is no effect on gas-density change) or by the large airways (if there is). The assumption made when the transmission path is determined by changing gas density is that gas density has a negligible effect on sound transmission through the parenchyma but strongly affects the behavior of sound transmission through airways. This assumption is only valid for open- and closed-cell stages, where sound transmission is insensitive to gas physical properties, but not the transition stage between them. This means that, between 20 and 200 Hz, sound transmission should be sensitive to gas density (1).
Apart from the study by Rice and Rice in 1987 (11), most of the studies have shown a parenchymal-dominant transmission (4, 8, 9). Furthermore, the transmission path in the airways is frequency dependent. At lower frequencies, the large airway walls have higher compliance than inertia and the majority of the acoustic energy couples directly to the surrounding parenchyma and bypasses smaller airways. At higher frequencies, inertia is higher than compliance, and the large airway walls are acoustically more rigid and pass the acoustic energy further down to smaller airways, which are less rigid (7, 14).
Using a broadband noise sound source and CCF technique to find phase delay has proven unacceptable (7, 14), because it only provides an average of phase delay over the frequency range of the input noise. It ignores two aspects of the phase delay information: 1) it is frequency dependent (14), and 2) it exhibits ambiguities as the delay can be greater than one period of the input signal at higher frequencies (14). A single-frequency sinusoidal input signal and CCF can reveal the frequency dependence of the phase delay but can be time consuming.
In this preliminary study, we used excised pig lungs to eliminate the
effects of complex chest wall reflections and thoracic cavity resonance
on the sound transmission. Pig lungs show similar physiological
characteristics to human lungs (13). To examine the sound
transmission path, both helium and air were used to inflate the lungs.
Lung density was varied by changing the air-to-tissue ratio of the
lungs by altering airway pressure. However, increasing airway pressure
will increase lung tissue stiffness, due to the sigmoidal shape of the
lung pressure-volume curve, and increase gas stiffness by compression.
As tissue stiffness is ~1,000-fold less than gas stiffness, the
overall parenchymal stiffness will be dominated by tissue stiffness.
The sound speed through the parenchyma (cp) is
given by cp = (Bp/
p)1/2, where
Bp is the composite parenchymal stiffness, and
p is the composite parenchymal density. Thus, whereas
increasing pressure will decrease p, it might also
decrease Bp, especially at the extremes of the
pressures used. Changes in sound speed through the parenchyma cannot,
therefore, be wholly attributed to changes in parenchymal density.
The TT is the sum of the time for the sound traveling through
airways and the time to travel through the parenchyma. The averaged length of the extraparenchymal airway was 12 cm. The averaged chord
(straight line) distance from the point at which the primary bronchus
connected to the parenchyma to the top two sites (i.e., LT and RT) and
the bottom two sites (i.e., LB and RB) was 6 and 18.5 cm, respectively,
at 25-cmH2O pressure. Assuming that sound speed through the
large airways is approximately the same as free-field sound speed
(
340 m/s) and sound speed through the parenchyma is 35 m/s
(9), then the time for sound traveling through airways will be 0.35 ms and that for sound traveling through the parenchyma will be 1.71 ms for LT and RT and 5.29 ms for LB and RB. Therefore, the
maximum TT should be 2.06 ms for LT and RT and 5.64 ms for LB and RB.
On the other hand, if we assume that sound travels through purely and
within smaller airways in the parenchyma, the minimum TT can be
calculated as 0.53 ms for LT and RT and 0.9 ms for LB and RB.
This theoretical range sets bounds to the possible values of TT that
one would expect to measure, and the averaged values for stage
2 (as shown in Table 1) are covered
under this range. However, before applying these theoretical bounds,
two essential assumptions should be made: 1) sound
propagation through the parenchyma is not in the open-cell model, which
results in a much lower sound speed (2.5-15 m/s) (1),
and 2) smaller airways do not reduce the sound speed greatly
(11). If either of the above assumptions were incorrect, a
longer TT would be obtained, which may explain why the TTs in
stage 1 are higher than expected. The values of acoustic
attenuation in this study, which ranged from 0 to 35 dB, also agreed
with those of several previous investigators (3, 8, 16).
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In the following sections, we discuss in detail the effects of different parameters of acoustic transmission on the resultant TT and attenuation.
Frequency Dependency
TT. Frequency played a major role in both TT and attenuation determination. As shown in RESULTS, different stages of TT and attenuation behaviors were divided by frequency. In Fig. 3, A-D, averaged TT in stage 1 is about three times higher than that in stage 2. This may be because, in the lower frequency range (stage 1), sound is traveling through more parenchyma than airways, compared with in the higher frequency range (stage 2). As stated above, the significant airway wall compliance at lower frequency coupled the majority of the acoustic energy to the surrounding parenchyma; thus stage 1 represents a parenchyma-dominated acoustic transmission stage. Stage 2 is a result of more energy traveling further down the airways due to the significant wall mass and represents an airway-dominated stage. As the speed of sound through airway is much faster than through parenchyma, stage 2 has smaller TT than stage 1. TT gradually reduces as the frequency increases, which means the ratio of the airways to the parenchymal path is increasing, and, up to a certain frequency (~200 Hz), the ratio becomes constant and results in a frequency-independent TT at a higher frequency range.
One possible explanation for this constant TT at stage 2 could be that sound propagates at lower speeds in smaller airways and this speed is linearly related (slope < 0) to the increase of the airway-to-parenchymal path ratio. Theoretically, from 200 Hz and up, with a minimum airway radius of 0.016 cm, the sound speed through the airway is reduced to 70% of its free-field speed (i.e., 240 m/s) (2). Taking into account the decreased speed in smaller airways, the calculated TT still fell between the theoretical bounds described in the preceding paragraph. However, the decreasing airway radius, experimentally measured from 0.48 to 0.016 cm, would cause the airway wall inertia to decrease by 0.2% but induce a 1,500-fold increase in compliance (2). Although it is suggested that the loading effect of the airway wall inertance will be higher as one moves further down the bronchial tree (16), this effect is relatively small compared with the largely increasing airway wall compliance. It leads to the conclusion that all acoustic energy is coupled to the surrounding parenchyma in smaller airways, and most energy may be radiated to its surroundings before reaching the terminal bronchiole. The exact site for the energy transfer to take place has not been determined, but it should be a strong function of frequency (in kHz range), where the wavelength is comparable to the size of the airway. Therefore, we suggest that, in frequencies between ~200 and 600 Hz, sound transmission through the excised pig lungs has reached a constant airway-to-parenchymal path ratio, or the change in this ratio is compensated by the change in sound speed in the airway. Most of the TTs found at 50 Hz exceeded the upper limits of the theoretical bounds (varying between 2.19 and 9.79 ms). Referring to the open- and closed-cell modeling described above, Butler et al. (1) suggested that the open-cell approximation of acoustic transmission through parenchyma is valid at least up to 100 Hz. This suggests that the acoustic behavior that we have observed from 50 to 100 Hz may have been caused by a compressional wave originating from parenchymal stiffness coupling to parenchymal density (open cell) rather than the coupling between gas stiffness and parenchymal density that Rice (9) suggested for the higher frequency region (closed cell). Butler et al. (1) showed the sound speed in the open-cell stage ranged from 2.5 to 15 m/s as the applied pressure ranged from 2 to 20 cmH2O, which may explain why the TT in stage 1 of our study is much higher, especially at 50 Hz, and gradually decreases because of the transition from open-cell to closed-cell behavior. The SDP of the TT in Fig. 5A indicates a much higher standard deviation in stage 1, which suggests that pressure change is affecting the TT in that frequency range. However, the PCF in this frequency range shows no clear correlation of this effect. There is an alternative explanation for the long TT in stage 1. Suki et al. (12) have shown that the sound speed through an excised calf trachea was 172 ± 35 m/s for frequencies <200 Hz and from ~300 to 500 m/s for frequencies >200 Hz. This frequency pattern matched our two-stage characteristics of TT. Under 200 Hz, sound traveled at about one-half of the free-field speed, and this will double the lower limit of the theoretical bounds if it is applied to our study. Thus the TT in stage 1 may be caused by the acoustic properties of the trachea (12). Other important evidence of trachea-dominated transmission is shown in Fig. 3C. There are small variations from 150 Hz and up. There are two minima that can be located on the graph; they are at 200 ± 50 and 450 ± 50 Hz, which will reflect two maxima in their sound-speed plotting. If we assume that the parenchyma acts as a homogenous continuum in its closed-cell model between 150 and 600 Hz, any dispersion of sound transmission in this frequency range, such as the two minima found in its TT behavior, could not be due to the parenchyma but to the airways. In fact, Suki and colleagues also found two maxima in their propagation velocity curve at 339 ± 59 and 683 ± 119 Hz. These maxima are the two resonances of the airway wall properties that are caused by cartilage and tissue, respectively. The difference between the results of Suki et al. and ours in these resonant frequencies may be due to different-sized airways and different species. The reason that the two resonance frequencies were not clearly shown at LT and RT might be due to the fact that the distance to LB and RB has much longer airways involved than that to LT and RT. Therefore, three models that may contribute to the behavior of TT are discussed. Although the open-cell model certainly exists, particularly at 50 Hz, the airway-to-parenchymal ratio model is contrary to the airway-dominant model at stage 1. However, the last two models both reach the same conclusion, namely, that the sound transmission path is dominated by the airways at the higher frequency region (stage 2).Attenuation. Attenuation was a function of frequency, lung density, and gas density, which will be discussed in the following sections. A transition frequency (at zero-PCF point) that separates stage 1 and stage 2 was found at ~100 Hz, which indicates a transition from the open- to closed-cell model, as described previously.
There were two maxima in the attenuation around the same frequencies where TT had its two minima, as shown in Fig. 3, G and H. These maxima are present in both the air-filled and helium-filled lungs. This indicates that these maxima are independent of gas properties. This pattern again agrees with the attenuation data of Suki et al. (12) and suggests that it was caused by the aforementioned same two resonances of the airway wall properties. We have found that this pattern is true for each pair of lungs for all of the lungs studied. In Fig. 6, we have shown the attenuation and TT data of a medium-sized pair of lungs (weighing 661 g). The locations of the maxima occur at similar frequencies in both attenuation and TT plots. This evidence further confirms the suggestion of airway-dominated transmission path at the higher frequency region (stage 2).
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Lung Density Dependency
One of our main objectives was to determine which acoustic propagation parameter would be most affected by variations in lung density. Lung density changes with lung diseases; for example, higher density may be found in certain areas of the lung because of collapsed alveoli or excess lung water. The density of the excised pig lung was varied by the application of different inflation pressures varying from 5 to 25 cmH2O in steps of 5 cmH2O. The density of the airways will remain the same at different pressures but not that of the parenchyma. Therefore, we are able to show the relationships between lung parenchymal density and acoustic behavior by changing inflation pressures. The effects on TT and attenuation of doing this are discussed separately.TT.
From Fig. 3, A-D, the PCFs at the stage
1 frequency range in all graphs are positive. This suggests that
the pressure is generally linearly related to the TT. The estimated
lung density in our study was ~0.1-0.2 g/ml, corresponding to
pressure changes from 25 to 5 cmH2O. Assuming the ambient
pressure was 1.01 × 105 N/m2 and the
specific heat ratio is 1.4 for normal air, the theoretical prediction
of sound speed in parenchyma against its density is shown in Fig.
7 (8). Therefore, for lung
density <0.5 g/ml, increasing density will result in lower sound speed
in the parenchyma. Figure 7 shows that the sound speed is ~39 m/s for
density at 0.1 g/ml and ~29 m/s for density at 0.2 g/ml. However,
increasing the lung density by lowering the pressure will also decrease
the sound propagation path through the parenchyma, and vice versa. Changing the pressure from 25 to 5 cmH2O will decrease the
parenchymal path length by ~35% (averaged value measured from the
thickness of the parenchyma) but only by 25% for the sound speed;
hence the percent change in TT is a 13% decrease (1 0.65/0.75 = 0.13). If the speed and path length change at the same
rate, the TT will remain the same.
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(3) |
Attenuation. The measured values of attenuation showed strong relationships with lung densities. The PCF clearly reveals this relationship. The PCFs in Fig. 3, E and F, show similar patterns, thus indicating similar pressure-attenuation behavior between air and helium. In stage 1, the inflation pressure is linearly related (slope < 0) to the attenuation (higher density yields lower attenuation). This relationship is changed to the opposite in stage 2, where higher pressure gives higher attenuation. Attenuation through the parenchyma has been shown previously by Wodicka et al. (16) to be a function of both lung density and path length. Increasing lung density reduces the attenuation, but the path length is decreased at the same time due to the decreased pressure, and, in doing so, it accelerates the decline of the attenuation (toward zero). According to this theory, if we assume that sound transmission through the parenchyma has a constant path for frequencies between 150 and 600 Hz, the difference in the attenuation between different densities would be increasing as the frequency increases. In fact, the attenuation gap between densities becomes closer at higher frequencies. One possible explanation is that the sound propagation path length through the parenchyma is much reduced along the frequency increase. The rate of parenchymal path length reduction is so great that it not only compensates the increase of attenuation due to lung density, but also overcomes the path extension due to the pressure. In Fig. 3, E-H, an isoattenuation point was located at which the density dependency changed over from stage 1 to stage 2 and where the attenuation is independent of lung density. The linear relationship between density and attenuation at stage 1 may represent the attenuation behavior of the parenchyma under the open-cell model, which has never been measured before. However, stage 2 at LB and RB is shortened, and it seems that the relationship between attenuation and lung density is switched again in stage 3. We do not have an explanation for this phenomenon, and it clearly needs to be studied.
By changing the lung density, we were able to study its effect on sound attenuation and TT. However, changing parenchymal density by varying inflation pressure cannot closely simulate the change in density by disease. It may introduce errors when the sound speed is calculated through the parenchyma where gas pressure is needed (9), but it is relatively small compared with tissue stiffness. Varying inflation pressure also changes the sound transmission path length through the parenchyma, and this will dramatically affect both the TT and attenuation. However, as long as it is taken into account in the analysis, changing pressure is an easy procedure to simulate lung density changes. The finding of an isoattenuation frequency is important because it can be used as a reference point for individual subjects when their lung density is studied. By measuring at two frequencies, the isoattenuation frequency and the frequency demonstrating the maximum sensitivity of attenuation against lung density, which was found to be 5.8 (SD) dB at 200 Hz (Fig. 5B, with air study), one could easily determine the abnormal changes in lung density due to diseases by using simple ratios of attenuation rather than complex modeling.Gas Density Dependency
The main objective of changing gas density is to determine the sound propagation path through excised pig lungs. It has been proven theoretically and experimentally (5, 8, 9) that sound propagation through the parenchyma is considered independent of resident gas composition, because the contribution of gas density to overall parenchymal density is negligible compared with tissue density, which is about a thousand times higher than that of the gas. However, sound propagation through airways is a strong function of airway gas density, as verified experimentally by Rice (10). There are two possible results from this study, namely that gas density does not affect TT and attenuation, which means sound transmission is parenchyma dominated, and gas density does affect TT and attenuation, which implies that sound propagation may be shared by airways as well as parenchyma.TT.
Generally speaking, the sound propagation through excised pig lungs
filled with helium is faster than those filled with air. The averaged
air-to-helium ratio for the top two sites is 1.27 (Fig. 4A)
and for the bottom two sites is 1.12 (Fig. 4C). Using Eq. 3 to form two equations for air (340 m/s) and helium
(960 m/s) to solve two unknowns, airway path and parenchymal path at LT, with the use of the same data provided in Table 1, one can find
that they are actually 12.1 and 2.38 cm, respectively, and very close
to our previously predicted values (16 and 2.04 cm). The difference in
TT between air and helium shows that the airways played an important
part in the transmission path. The TT through airways was ~41% (16 cm 
340 m/s 1.15 ms) of the overall TT for LT, and 68%
(30 cm 340 m/s 1.3 ms) for LB. Changing from air (340 m/s) to helium (960 m/s) should reduce the TT through airways
by 65%. Hence, it is expected to be 41% × 65% = 27% faster at LT
and 68% × 65% = 44% faster at LB. The 27% faster value at the top
two sites is approximately the same as what we have found from Fig.
4A, but 44% calculated for the bottom two sites is much higher than the 12% value found in Fig. 4C. A possible
hypothesis would be that the smaller speed occurred at smaller airways
toward the bottom sites.
Attenuation. As shown in Table 1, helium increased the zero-PCF point defining the upper limit of stage 1 from 78 to 104 Hz. As discussed above, gas movement between alveolar regions exists during sound propagation, and the forces required to move the gas are insignificant compared with the forces involved in vibrating the parenchymal tissue. However, when the frequency increases, gas becomes more difficult to move interregionally, because the forces required will be higher under high-frequency disturbance, and eventually the forces are only enough to compress gas locally, which forms the closed-cell model of the parenchyma. The forces required to move helium will be about one-tenth that to move air because of the lower density of helium (0.178 kg/m3) compared with air (1.293 kg/m3).
Lower attenuation in lungs filled with helium was found in all frequency ranges. The characteristics of the frequency response between air and helium are similar, apart from a ~15-dB offset between them. Under the assumption that attenuation through the parenchyma should not be changed by gas density, this 15-dB offset can only be caused by airways. We do not have data on how the airways will attenuate sound quantitatively. There is a peak at ~200 Hz in the attenuation SDP (Fig. 5B); a standard deviation of 5.8 dB was found for the air study and 3.4 dB for the helium study. It indicates a higher sensitivity of sound attenuation in air than in helium. A possible explanation for this behavior is as follows. When the sound wave passes through an airway, the airway wall will be stretched cyclically and the resident gas will be compressed cyclically. Because the impedance against gas compression is higher in air than in helium, the sensitivity of sound speed, as well as attenuation to changes in airway wall compliance (due to changes in mean airway pressure), is increased in air. The results are in contradiction with some previous investigations (5, 8, 9), which showed that gas density does not affect TT or attenuation. We draw the same conclusion as Rice (10), that sound transmission from trachea to pleura is traveling more through airways than the parenchyma. Other investigators have performed studies on human volunteers, which inevitably involves other factors that may influence sound propagation from mouth to chest, such as the interaction between the lung and chest wall (15). This may account for the differing results. In conclusion, the dependency on frequency, lung density, and gas density of TT and attenuation of sound through excised pig lungs were studied. An open-cell model of the parenchyma with interregional gas exchange explains the low sound speed found at low frequencies. Gas density may change the frequency boundary that separates the open-cell and closed-cell stages. The ratio of the airway to parenchymal transmission path is a function of frequency; a longer parenchymal path will occur at lower frequencies because of the larger airway wall compliance that favors acoustic energy coupling to surrounding parenchyma. However, longer airway paths will be found at higher frequencies because of the higher airway wall inertia, which will favor energy transfer further down to smaller airways. It also suggests that energy transfer from bronchus to alveoli may not take place at the terminal bronchiole but at smaller airways. The study suggests that sound transmission through excised pig lungs may not be dominated by the parenchyma, because gas density does affect the measured TT and attenuation. An isoattenuation point (constant attenuation at different lung densities) is located and may be used to select a reference frequency for sound-attenuation mapping of lung density.| |
ACKNOWLEDGEMENTS |
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We thank Andreas Pohlmann for support in the experiments.
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FOOTNOTES |
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Address for reprint requests and other correspondence: A. Leung, c/o S. Sehati, School of Engineering, Oxford Brookes Univ., Headington, Oxford OX3 0BP, UK (E-mail: ssehati{at}brookes.ac.uk).
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.
Received 20 April 1999; accepted in final form 21 July 2000.
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REFERENCES |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
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