Spectral analysis of Doppler ultrasonic decompression data K. KISMAN
Several aspects of spectral analysis of bubble transients in Doppler ultrasonic decompression data are discussed. The computation of energy density spectra, using fast Fourier transform techniques for analyzing bubble transients, is described. Spectral analysis of data from probes implanted within animals, using a conventional Fourier analyzer, provided good visual indications of bubble events and interesting changes in spectral structure. A new transient spectral analysis technique that is suitable for quantitative real-time monitoring of small decompression bubbles is described. In a feasibility study using data from an implanted probe, an increase of 900% in bubble signal/noise ratio was observed.
Respiration during hyperbaric exposure requires the breathing of high pressure inert gases which dissolve into the blood and tissues of divers. During decompression, the inert gases must evolve from solution. If the decompression is too rapid, the evolving gases may form cardiovascular and extravascular bubbles which are a fundamental characteristic of decompression sickness.’ ,’ The detection and monitoring of these in vivo bubbles is important to the study of hyperbaric physiology, to the treatment of decompression sickness, and to the provision of a relatively safe, objective indicator of decompression stress as an aid in the development of prophylactic decompression profiles. The most successful approaches, with regard to cardiovascular bubbles, have involved Doppler ultrasonic techniques.‘-’ In the Doppler ultrasonic technique, sound waves are scattered and shifted in frequency by moving scatterers such as red blood cells and bubbles. These Doppler frequency shifts which are typically in the audio range, O-10 kHz, appear in the output signal of the receiver and can be monitored aurally. The Doppler shift, A f,where
Af =
2fvcoscY c
is determined by the frequency, f,of the transmitted ultrasound, the velocity of sound in the tissue, c, and the component of velocity of the scatterer along the ultrasound beam, v cos CL K. K&man IS at the Defence and Civil Institute of Environmental Medicine, PO Box 2000, Downsview, Ontario, Canada, M3M 389. Paper received 17 August 1976.
ULTRASON
KS . MAY 1977
The Doppler technique is inherently powerful because the output is an audio signal that contains both amplitude and frequency information and is useful for bubble detection without quantitative calibration of the apparatus. Moreover, this technique can be used with surgically implanted probes in animals or transcutaneously with humans even under operational conditions. Doppler detection of bubbles is effective because bubbles are much more efficient scatterers of ultrasound than are formed elements of the blood. In fact, calculations similar to those of Nishi376 reveal that under ideal conditions one bubble with diameter greater than 5 pm has a larger theoretical scattering intensity than that from all the red blood cells in the scattering region of a typical transducer assembly. Electronic signal processing of decompression data is difficult because of the complexity of the Doppler signal, the variability of signals among individuals, and the variability of transducer orientation. Consequently, monitoring of Doppler signals is performed aurally in most experiments. Bubbles have been described as ‘chirps’, ‘squeaks’, or ‘clicks’ in the audio output and roughly quantified by grading the bubble sounds on a scale’ from 0 to 4. The ear has an extraordinary ability to discriminate the transient sounds of bubbles from the background signal but, unfortunately, such aural monitor. ing is subjective, qualitative, and not entirely reproducible. Hence the use of improved signal processing techniques such as spectral analysis is necessary for objective, quantitative and reproducible results. However, consideration of spectral analysis of decompression data has been very limited.3 97-9 In this paper, several aspects of spectral processing of Doppler ultrasonic data are considered. First, the data are classified and the type of spectrum appropriate for these data is introduced. Next, a conventional Fourier analyzer
105
is used to provide real-time spectra of Doppler data from the pulmonary artery and posterior vena cava of decompressed animals. Finally, a transient spectral analysis technique which compliments the above technique is presented and shown to provide considerable enhancement of the signal to noise ratio of bubble events.
(5) where N-l
X,(ft T) = ;
-y
xk,n eXp (- i 27$?%/N)
.
(6)
n=O Theoretical
considerations
The Doppler signal obtained during decompression is generally very complex. There is a background signal due mainly to scattering from red blood cells flowing through the vessel of interest, from movement of the vessel walls and from moving extravascular tissues. Intravascular aggregates involving platelets, erythrocytes or lipids may result from the interaction of bubbles with blood and tissue following a decompression insult. Individual aggregates have a much smaller scattering intensity than individual bubbles of comparable size, but large numbers of aggregates can contribute significantly to the background signal.’ Bubbles flowing through the acoustic field of the transducer appear as transients on a time scale (typically about 10 ms) determined by the size of the transducer’s field and by the velocities of the bubbles. Consequently, the Doppler signal may be subdivided and classified as a background signal which is a nonstationary random process and the bubble events which are transient, nonstationary random processes. The most promising approach toward processing the Doppler signal involves spectral analysis because this can make full use of the amplitude, frequency and signal duration information in the signal. However, conventional spectral analysis techniques apply ___ only_ to stationary data. To analyze a bubble transient process Tb such that bk@)l
f
o
for
= 0
[Xk(t)]
of duration
0 =G t < Tb
otherwise
(1)
one may define an energy spectral density function” JkCf)>
J/c(f) = 2~?[IXk(f)121 =
(2)
0
f
O
0
A smooth spectral estimate Ek(f) may be obtained by averaging the results from 4 separate time windows, each of duration T4 :
Rhonary artery data. The pulmonary artery appears to be the best site for transcutaneous ultrasonic monitoring of human divers, because of its accessibility and the fact that the entire venous system drains through this vessel. However, the signal from this site is obscured by noise because of considerable tissue motion and pulsatile blood flow near the heart so that bubbles are difficult to distinguish aurally. For animals with a cuff probe implanted around the pulmonary artery, the situation is similar, but the bubble signal/noise ratio is much greater. Doppler data obtained from an ultrasonic cuff probe implanted around the pulmonary artery of a miniature pig were made available on magnetic tape for analysis (data and techniques have been published previously by Guillerm et a14). The pig was compressed in two min to a simulated depth of 90 m, kept at this depth for three min, and decompressed back to the surface in 2.5 min. The unfiltered Doppler data were analyzed with a Hewlett Packard 545 1B Fourier analyzer which was programmed to calculate indi-
ULTRASONICS.
MAY 1977
integrate the spectral components that result from bubbles and from the low frequency background sources. The integrated bubble signal relative to the integrated background signal provides a measure of the quantity of bubbles present. Integration of time-domain Doppler data for semiquantitative analysis has been reported by Guillerm et a1.4
a
i 0 5 400
I.cJ
0:5
I.5
2.0
25
Doppler data obtained from an ultrasonic cuff probe implanted around the posterior vena cava of a rabbit were made available on magnetic tape for analysis (data and techniques have been published previously by Nishi and Livingstone3). The rabbit was compressed in 5 min to a simulated depth of 122 m, kept at this depth for 45 min, and decompressed at a rate determined by the number of bubble events detected aurally.
b
B P b
Posterior vena cava data. Doppler signals from the posterior vena cava are much easier to interpret than those from the pulmonary artery because they are less affected by heart motion. This feature combined with the fact that a considerable amount of venous blood flows through the posterior vena cava make this vessel a good site for monitoring animals with implanted transducers.
3OO-
zoo-
Energy density spectra of the rabbit data are shown in Fig. 2. In this case, these are individual spectra having a sample record time of 102 ms.
100
0 0.5
0
1.0
1.5
20
Frequency fkHz1 Fig. 1 Averaged energy densitv spectra of Doppler data from the pulmonary artery of a miniature pig, a-obtained prior to the dive;
b-obtained
Blood flow provided the main contribution to the energy density in the decompression data that did not contain bubble transients, Fig. 2a. The low frequency signal from other sources was small in this case.
30 min post-dive
vidual and averaged spectral densities and which provided real time displays of the spectra on an oscilloscope for visual monitoring. Averaged energy density spectra of the pulmonary artery data are shown in Fig. 1. They were obtained by averaging 100 samples of duration 25.6 ms spaced 220 ms apart (using the maximum processing speed capability of the Fourier analyzer). A typical spectrum, Fig. 1a, of data obtained before the dive illustrates that virtually all of the spectral energy occurred at frequencies below 1 kHz. Even when the scale was increased by a factor of 100, little energy was observed above 1 kHz. Soon after the decompression and for more than one hour thereafter, significant changes were observed in the spectra, Fig. 1b. Energy levels comparable to the low frequency background levels were distributed over the range 1-7 kHz. Before the dive, the high frequency background signal (above 1 kHz) from red blood cells was very small compared to the low frequency background signal from sources such as moving tissues and is not observable in Fig. la. Following the dive, the presence of large numbers of bubbles with high scattering power greatly increased the high frequency signal. Hence, with the low frequency energy as a reference, the occurrence of comparable high frequency energy components provided a reproducible, real-time visual presentation of bubble events that supplemented aural detection. Furthermore, with additional digital processing, the spectral results are amenable to some degree of quantification. One may
ULTRASONICS.
MAY 1977
2
I 74 I Lo s 0 5a 0 5 B
k I5
I
2
3
4
5
6
7
0
9
4
b
Frequency CkHzl Fig. 2 Individual energy density spectra of Doppler data obtained during decompression from the posterior vena oava of a rabbit, a-illustrating the background signal; b-illustrating bubble signals
107
sample record times are made comparable to the duration of bubble transients; and the sample records are contiguous (ie no loss of data between sample records).
Signal duraton Sample record durotlon
Fig. 3
Filter response of the transient
spectral analysis technique
When bubble transients appeared, they dominated the spectra as shown in Fig. 2b where the energy density is approximately 100 times greater than that of Fig. 2a. Because the velocity distributions of the blood flow and bubbles are similar, the spectral energy profiles of Figs 2a and 2b largely overlap. However, the spectral structure in these figures is different and the bubble spectrum has components of energy at higher frequencies. This is observed because the blood flow signal is caused by scattering from a large ensemble of scatterers whereas the bubble signal is caused by scattering from a small number of bubbles which are detectable individually. Individual bubbles at the high velocity end of the velocity distribution can add detectable high frequency components to the signal. Digital analysis of spectra like those in Figs 2a and 2b to compute physical parameters may help in the indirect estimation of the sizes of decompression bubbles. Three parameters that could easily be measured in cases where the bubbles are clearly distinguishable are the intensity of the bubble signals relative to that of blood flow, the velocities of the bubbles relative to the velocity distribution of blood flow, and the rate of occurrence of bubble events. Important information concerning the formation of blood aggregates may be obtained by analyzing background spectra like that in Fig. 2a. Differences in background spectra following dives compared to those prior to the dives have been reported3 as likely due to the presence of blood aggregates. This indicates that spectral studies combined with hematological studies may establish a technique for transcutaneous monitoring of blood composition. Transient spectral analysis For cases such as human noninvasive monitoring of decompression bubbles where it is important to detect the presence of bubbles as early as possible, real-time post-processing of the energy spectra is necessary to increase the bubble signal to noise ratio. To this end, a new technique has been devised entitled transient spectral analysis. The first stage of this technique involves the computation of energy density spectra whose parameters are determined not by statistical accuracy or resolution requirements, but by the properties of the bubble transients. The frequency range of analysis is made larger than normally required in order to include all the spectral energy of the transients; the
108
The second stage in transient spectral analysis involves the comparison of energy density spectra to compute new spectra. If the sample records are contiguous one may make use of the widely different time scales of processes that determine the duration of Doppler signals to enhance bubble detection. These processes include: a-the heart beat which normally has a priod of 0.3 to 1 s; b-moving tissues which provide signals of widely varying duration and c- the passage of bubbles which occurs in approximately 10 ms. An algorithm has been devised to process the energy density spectra into new transient spectra with a view to producing a signal duration filter and optimum threshold counting of bubble transients, Consider the components W,,, of the kth transient spectrum ,Wk(f) Thich is obtainned from the energy density spectra Jk(f), Jk_r(f) and Jk+ I(f) (each having m components): wk, I
=
w;,
1
>
=
2n (11)
z
-
1 =‘2n-1
W,,,
where
W&l =
Pas
b?dk,n
-Jh+l,n)/&k+l,n
L2&k,,
-:k-1,,,16k-I
+ (1 -
a)Ak+l)j
(12)
wk;n =
pos
n zz 11,2,3 ,.... I =
1,2,3 ,....,
POS@)
Q3
=
= 0,
,n + c1 -@k-l)]
,m
cl31
(14)
2m
(15) Q>O Q
Several aspects of spectral analysis of bubble transients in Doppler ultrasonic decompression data are discussed. The computation of energy density spectra, using fast Fourier transform techniques for analyzing bubble transients, is described. Spectral analysis of data from probes implanted within animals, using a conventional Fourier analyzer, provided good visual indications of bubble events and interesting changes in spectral structure. A new transient spectral analysis technique that is suitable for quantitative real-time monitoring of small decompression bubbles is described. In a feasibility study using data from an implanted probe, an increase of 900% in bubble signal/noise ratio was observed.
Respiration during hyperbaric exposure requires the breathing of high pressure inert gases which dissolve into the blood and tissues of divers. During decompression, the inert gases must evolve from solution. If the decompression is too rapid, the evolving gases may form cardiovascular and extravascular bubbles which are a fundamental characteristic of decompression sickness.’ ,’ The detection and monitoring of these in vivo bubbles is important to the study of hyperbaric physiology, to the treatment of decompression sickness, and to the provision of a relatively safe, objective indicator of decompression stress as an aid in the development of prophylactic decompression profiles. The most successful approaches, with regard to cardiovascular bubbles, have involved Doppler ultrasonic techniques.‘-’ In the Doppler ultrasonic technique, sound waves are scattered and shifted in frequency by moving scatterers such as red blood cells and bubbles. These Doppler frequency shifts which are typically in the audio range, O-10 kHz, appear in the output signal of the receiver and can be monitored aurally. The Doppler shift, A f,where
Af =
2fvcoscY c
is determined by the frequency, f,of the transmitted ultrasound, the velocity of sound in the tissue, c, and the component of velocity of the scatterer along the ultrasound beam, v cos CL K. K&man IS at the Defence and Civil Institute of Environmental Medicine, PO Box 2000, Downsview, Ontario, Canada, M3M 389. Paper received 17 August 1976.
ULTRASON
KS . MAY 1977
The Doppler technique is inherently powerful because the output is an audio signal that contains both amplitude and frequency information and is useful for bubble detection without quantitative calibration of the apparatus. Moreover, this technique can be used with surgically implanted probes in animals or transcutaneously with humans even under operational conditions. Doppler detection of bubbles is effective because bubbles are much more efficient scatterers of ultrasound than are formed elements of the blood. In fact, calculations similar to those of Nishi376 reveal that under ideal conditions one bubble with diameter greater than 5 pm has a larger theoretical scattering intensity than that from all the red blood cells in the scattering region of a typical transducer assembly. Electronic signal processing of decompression data is difficult because of the complexity of the Doppler signal, the variability of signals among individuals, and the variability of transducer orientation. Consequently, monitoring of Doppler signals is performed aurally in most experiments. Bubbles have been described as ‘chirps’, ‘squeaks’, or ‘clicks’ in the audio output and roughly quantified by grading the bubble sounds on a scale’ from 0 to 4. The ear has an extraordinary ability to discriminate the transient sounds of bubbles from the background signal but, unfortunately, such aural monitor. ing is subjective, qualitative, and not entirely reproducible. Hence the use of improved signal processing techniques such as spectral analysis is necessary for objective, quantitative and reproducible results. However, consideration of spectral analysis of decompression data has been very limited.3 97-9 In this paper, several aspects of spectral processing of Doppler ultrasonic data are considered. First, the data are classified and the type of spectrum appropriate for these data is introduced. Next, a conventional Fourier analyzer
105
is used to provide real-time spectra of Doppler data from the pulmonary artery and posterior vena cava of decompressed animals. Finally, a transient spectral analysis technique which compliments the above technique is presented and shown to provide considerable enhancement of the signal to noise ratio of bubble events.
(5) where N-l
X,(ft T) = ;
-y
xk,n eXp (- i 27$?%/N)
.
(6)
n=O Theoretical
considerations
The Doppler signal obtained during decompression is generally very complex. There is a background signal due mainly to scattering from red blood cells flowing through the vessel of interest, from movement of the vessel walls and from moving extravascular tissues. Intravascular aggregates involving platelets, erythrocytes or lipids may result from the interaction of bubbles with blood and tissue following a decompression insult. Individual aggregates have a much smaller scattering intensity than individual bubbles of comparable size, but large numbers of aggregates can contribute significantly to the background signal.’ Bubbles flowing through the acoustic field of the transducer appear as transients on a time scale (typically about 10 ms) determined by the size of the transducer’s field and by the velocities of the bubbles. Consequently, the Doppler signal may be subdivided and classified as a background signal which is a nonstationary random process and the bubble events which are transient, nonstationary random processes. The most promising approach toward processing the Doppler signal involves spectral analysis because this can make full use of the amplitude, frequency and signal duration information in the signal. However, conventional spectral analysis techniques apply ___ only_ to stationary data. To analyze a bubble transient process Tb such that bk@)l
f
o
for
= 0
[Xk(t)]
of duration
0 =G t < Tb
otherwise
(1)
one may define an energy spectral density function” JkCf)>
J/c(f) = 2~?[IXk(f)121 =
(2)
0
f
O
0
A smooth spectral estimate Ek(f) may be obtained by averaging the results from 4 separate time windows, each of duration T4 :
Rhonary artery data. The pulmonary artery appears to be the best site for transcutaneous ultrasonic monitoring of human divers, because of its accessibility and the fact that the entire venous system drains through this vessel. However, the signal from this site is obscured by noise because of considerable tissue motion and pulsatile blood flow near the heart so that bubbles are difficult to distinguish aurally. For animals with a cuff probe implanted around the pulmonary artery, the situation is similar, but the bubble signal/noise ratio is much greater. Doppler data obtained from an ultrasonic cuff probe implanted around the pulmonary artery of a miniature pig were made available on magnetic tape for analysis (data and techniques have been published previously by Guillerm et a14). The pig was compressed in two min to a simulated depth of 90 m, kept at this depth for three min, and decompressed back to the surface in 2.5 min. The unfiltered Doppler data were analyzed with a Hewlett Packard 545 1B Fourier analyzer which was programmed to calculate indi-
ULTRASONICS.
MAY 1977
integrate the spectral components that result from bubbles and from the low frequency background sources. The integrated bubble signal relative to the integrated background signal provides a measure of the quantity of bubbles present. Integration of time-domain Doppler data for semiquantitative analysis has been reported by Guillerm et a1.4
a
i 0 5 400
I.cJ
0:5
I.5
2.0
25
Doppler data obtained from an ultrasonic cuff probe implanted around the posterior vena cava of a rabbit were made available on magnetic tape for analysis (data and techniques have been published previously by Nishi and Livingstone3). The rabbit was compressed in 5 min to a simulated depth of 122 m, kept at this depth for 45 min, and decompressed at a rate determined by the number of bubble events detected aurally.
b
B P b
Posterior vena cava data. Doppler signals from the posterior vena cava are much easier to interpret than those from the pulmonary artery because they are less affected by heart motion. This feature combined with the fact that a considerable amount of venous blood flows through the posterior vena cava make this vessel a good site for monitoring animals with implanted transducers.
3OO-
zoo-
Energy density spectra of the rabbit data are shown in Fig. 2. In this case, these are individual spectra having a sample record time of 102 ms.
100
0 0.5
0
1.0
1.5
20
Frequency fkHz1 Fig. 1 Averaged energy densitv spectra of Doppler data from the pulmonary artery of a miniature pig, a-obtained prior to the dive;
b-obtained
Blood flow provided the main contribution to the energy density in the decompression data that did not contain bubble transients, Fig. 2a. The low frequency signal from other sources was small in this case.
30 min post-dive
vidual and averaged spectral densities and which provided real time displays of the spectra on an oscilloscope for visual monitoring. Averaged energy density spectra of the pulmonary artery data are shown in Fig. 1. They were obtained by averaging 100 samples of duration 25.6 ms spaced 220 ms apart (using the maximum processing speed capability of the Fourier analyzer). A typical spectrum, Fig. 1a, of data obtained before the dive illustrates that virtually all of the spectral energy occurred at frequencies below 1 kHz. Even when the scale was increased by a factor of 100, little energy was observed above 1 kHz. Soon after the decompression and for more than one hour thereafter, significant changes were observed in the spectra, Fig. 1b. Energy levels comparable to the low frequency background levels were distributed over the range 1-7 kHz. Before the dive, the high frequency background signal (above 1 kHz) from red blood cells was very small compared to the low frequency background signal from sources such as moving tissues and is not observable in Fig. la. Following the dive, the presence of large numbers of bubbles with high scattering power greatly increased the high frequency signal. Hence, with the low frequency energy as a reference, the occurrence of comparable high frequency energy components provided a reproducible, real-time visual presentation of bubble events that supplemented aural detection. Furthermore, with additional digital processing, the spectral results are amenable to some degree of quantification. One may
ULTRASONICS.
MAY 1977
2
I 74 I Lo s 0 5a 0 5 B
k I5
I
2
3
4
5
6
7
0
9
4
b
Frequency CkHzl Fig. 2 Individual energy density spectra of Doppler data obtained during decompression from the posterior vena oava of a rabbit, a-illustrating the background signal; b-illustrating bubble signals
107
sample record times are made comparable to the duration of bubble transients; and the sample records are contiguous (ie no loss of data between sample records).
Signal duraton Sample record durotlon
Fig. 3
Filter response of the transient
spectral analysis technique
When bubble transients appeared, they dominated the spectra as shown in Fig. 2b where the energy density is approximately 100 times greater than that of Fig. 2a. Because the velocity distributions of the blood flow and bubbles are similar, the spectral energy profiles of Figs 2a and 2b largely overlap. However, the spectral structure in these figures is different and the bubble spectrum has components of energy at higher frequencies. This is observed because the blood flow signal is caused by scattering from a large ensemble of scatterers whereas the bubble signal is caused by scattering from a small number of bubbles which are detectable individually. Individual bubbles at the high velocity end of the velocity distribution can add detectable high frequency components to the signal. Digital analysis of spectra like those in Figs 2a and 2b to compute physical parameters may help in the indirect estimation of the sizes of decompression bubbles. Three parameters that could easily be measured in cases where the bubbles are clearly distinguishable are the intensity of the bubble signals relative to that of blood flow, the velocities of the bubbles relative to the velocity distribution of blood flow, and the rate of occurrence of bubble events. Important information concerning the formation of blood aggregates may be obtained by analyzing background spectra like that in Fig. 2a. Differences in background spectra following dives compared to those prior to the dives have been reported3 as likely due to the presence of blood aggregates. This indicates that spectral studies combined with hematological studies may establish a technique for transcutaneous monitoring of blood composition. Transient spectral analysis For cases such as human noninvasive monitoring of decompression bubbles where it is important to detect the presence of bubbles as early as possible, real-time post-processing of the energy spectra is necessary to increase the bubble signal to noise ratio. To this end, a new technique has been devised entitled transient spectral analysis. The first stage of this technique involves the computation of energy density spectra whose parameters are determined not by statistical accuracy or resolution requirements, but by the properties of the bubble transients. The frequency range of analysis is made larger than normally required in order to include all the spectral energy of the transients; the
108
The second stage in transient spectral analysis involves the comparison of energy density spectra to compute new spectra. If the sample records are contiguous one may make use of the widely different time scales of processes that determine the duration of Doppler signals to enhance bubble detection. These processes include: a-the heart beat which normally has a priod of 0.3 to 1 s; b-moving tissues which provide signals of widely varying duration and c- the passage of bubbles which occurs in approximately 10 ms. An algorithm has been devised to process the energy density spectra into new transient spectra with a view to producing a signal duration filter and optimum threshold counting of bubble transients, Consider the components W,,, of the kth transient spectrum ,Wk(f) Thich is obtainned from the energy density spectra Jk(f), Jk_r(f) and Jk+ I(f) (each having m components): wk, I
=
w;,
1
>
=
2n (11)
z
-
1 =‘2n-1
W,,,
where
W&l =
Pas
b?dk,n
-Jh+l,n)/&k+l,n
L2&k,,
-:k-1,,,16k-I
+ (1 -
a)Ak+l)j
(12)
wk;n =
pos
n zz 11,2,3 ,.... I =
1,2,3 ,....,
POS@)
Q3
=
= 0,
,n + c1 -@k-l)]
,m
cl31
(14)
2m
(15) Q>O Q
