Ultrasonic detection of bubbles with doppler flow transducers

Ultrasonic detection of bubbles with doppler flow transducers R. Y. NISHI

Doppler blood-flow transducers have been used to detect gas bubbles in the circulatory system during hyperbaric decompression. This paper describes briefly the theoretical acoustic scattering properties of bubbles and then describes various experimental procedures which have been used to determine the properties of these flow transducers. The capabilities and limitations of the transducers for the detection of bubbles were investigated by studying the scattering from both solid objects and air bubbles moving through the acoustic field. In vivo experiments indicate that it would be difficult to obtain any correlation between the output of these transducers and bubble size.

Introduction Doppler blood-flow transducers have been used to detect gas bubbles in the circulatory system during hyperbaric decompression.1-4 These transducers consist of two piezoelectric elements mounted at some angle to the direction of the blood flow. A continuous signal is transmitted by one element and reflected back to the other element bv narticles in the blood. Since these particles are in motion,Sthe frequency of the reflected signal differs from that of the transmitted signal, the difference, Af, being proportional to the velocity of the particles:

2fvcosa Af=--c

(11

where f is the frequency of the transmitted wave, u is the particle velocity, OLis the angle between the incident wave and the flow, and c is the velocity of sound in the fluid. Normally, the scatterers in the blood are the blood cells. A gas bubble, if present in the blood, is a highly efficient scatterer compared to the blood cells. Hence the bubble produces an increased signal output from the transducers which can be easily distinguished from the background flow signal. FL Y. Nishi is at the Defence and Civil Institute of Environmental Medicine (formerly Defence Research Establishment, Toronto) Ontario, Canada. Paper received 20 July 1971.

ULTRASONICS.

JULY 1972

This paper describes various experimental procedures which have been used to determine the capabilities and limitations of doppler-flow transducers for the detection of bubbles, and to find out whether quantitative information, for example, the size of the bubble, could be obtained from the output of the transducers. Experiments were conducted on both air bubbles and solid objects moving through the transducer field. Theory If an ultrasonic wave propagating through a liquid encounters a gas bubble, the periodically varying pressure from the incident wave produces a forced vibration of the gas inside the bubble, leading to a scattering and absorption of the incident wave. At the resonant frequency of the bubble, the scattering and absorption are at a maximum. Even at other frequencies, a bubble acts as a good reflector of sound because of the large acoustic impedance mismatch between the gas and liquid. The resonant frequency

of a pulsating bubble is given by 5

where R. is the equilibrium radius of the bubble, PO is the static pressure in the liquid, u is the surface tension of the

173

liquid, y is the ratio of the specific heats of the gas, p is the density of the liquid, and E is a parameter varying from one to y dependent on heat conduction in the gas. This equation does not givef, as an explicit function of R,, since E is a function of both frequency and radius:

e= (l+bi)[lt~(~~~~::~~~~~~~)](3)

where

sinh (2@R0) + sin (2@R0)

1

cash (2GRn) - cos (2@R0)

#RO

Fth= 2$Ro

sinh(2$Ro)

- sin (2$Ro)

3(y- 1) + cosh(2@Ro) - cos (2r$Ro)

pg is the density of the gas, C is the heat capacity of the gas, and K is the thermal con Buctivity coefficient of the gas. If the bubble is very small (radius less than 1 pm), the compression and expansion of the gas in the bubble is isothermal (E = y) and the resonant frequency is given by 6 Fig. 1 Resonant frequency versus bubble radius for an air bubble in blood: 1 - 1 -atm; 2 - 4 atm; 3 - 7 atm; 4 - 10 atm

(4)

For large bubbles (radius greater than 100 pm) the pulsation of the bubble is adiabatic (E = l), the surface tension term is negligible and the resonant frequency can be obtain; ed from

s=&

0

()

3YRr-J X p

(5)

Fig.1 shows the resonant frequency calculated from equa tion (2) for an air bubble in a liquid such as blood (u = 60 dyn cm-l) at 1,4,7, and 10 atm (sea level, 100, 200 and 300 ft depths respectively). For a given bubble size, the resonant frequency increases with pressure and the influence of the surface tension term becomes less. The scattering cross-section

of a bubble of radius u is 6

47ra2 Qs =

(1 -

(6)

*;/*y + s2

where 6 is a damping term representing contributions from radiation, viscosity, and heat conduction.5*7 Fig.2 shows the scattering cross-sections for an air bubble in blood (viscosity = 0.03 dyn s cmm2) at tern rature T = 37”C, and in water (viscosity = 0.01 dyn s cm- F) at temperature T = 2O”C, for an incident plane wave of frequency 5 MHz.* Bubble radius

[pm1

Fig.2 Scattering cross-section versus bubble radius for air bubbles in blood (b) and in water (w) at 5 MHz

174

Because of the higher viscosity of blood, the scattering cross-section of a resonant bubble in blood is reduced considerably by comparison with its value in water. The actual resonant size differs from that calculated from fo, the driving frequency, because of the damping terms. As

ULTRASONICS.

JULY 1972

reflected frequencies of the beam, and the amplitude depends upon the characteristics of the reflecting object. Moving-wire

Tronscutoneous

Fig.3

Configuration

of doppler blood-flow

transducers

To motor

k 0

ji

Wire

@

Tronscutaneous transducer

Fig.4

Experimental

arrangement

0

for moving-wire

/ t\ rlcl I 0

@I Cuff-type transducer

In order to determine how the output amplitude of the transducers varied with the velocity and size of the reflecting object, the transducers were calibrated by means of wires moving through the ultrasound field. Experiments involving air bubbles rising or spheres falling in still water were not used since their velocities were determined by their size. The use of wires, on the other hand, allowed full control of both velocity and size. Wires ranging in diameter from 0.0045-0.084 cm were used. Each wire was mounted across a weighted rectangular frame which was pulled up and down between two guide rails in water by a cord attached to an arm on a variable speed motor. The transducers were placed so that the wire passed through the beam while travelling at its maximum velocity (Fig.4). Maximum velocities from 3-28 cm s-l were used. The output of the transducers was recorded on an fm magnetic tape recorder at 60 in s-l and played back at 1 7/8 in s-l onto a chart recorder. Fig.5 shows an example of the waveform obtained on the chart recorder. From this representation, both frequency and amplitude could be determined. Fig.6 shows the peak amplitude of the transcutaneous unit as a function of wire velocity. For this particular unit, the amplitude, which should be independent of velocity, decreased rapidly below 6 cm s-l (Af’ 400 Hz).

experiment

the static pressure is increased, the damping terms have less influence on the resonant scattering cross-section. Below the resonant bubble size, the scattering cross-section decreases rapidly and hence it is unlikely that bubbles much smaller than the resonant size can be detected by the doppler blood-flow transducers. Experimental

experiment

procedure

Transducers In the present study, two types of doppler blood-flow transducers have been evaluated. The first type is a hinged cuff made of plastics which can be surgically implanted around a large blood-vessel in an animal 9 (Fig.3). The electrical leads are brought out through the skin and attached to the electronics package. The angle between the transmitted beam and the flow axis is 60 degrees. The operating frequency is 5 MHz. The output can be fed into a telemetry module and received on a standard fm receiver (88- 108 MHz) or can be received directly by leads if the animal is restrained from moving.

After modification of the input circuitry, a more uniform response with velocity was achieved as shown in Fig.7. Simultaneous measurements with a cuff-type doppler transducer, initially of 0.5 cm lm, arranged to allow the wire to pass between the two halves of the cuff, showed an amplitude response much less dependent upon velocity (Fig.8). Fig.9 shows the data from Figs 7 and 8 lotted as relative output-amplitude against Zcuat 10 cm s-P, where k = 2nf/c, and a is the radius of the wire. The output oscillates with increasing wire size, and it is impossible to obtain any useful correlation of amplitude with size. For comparison, the scattering of an incident beam of plane waves from an infinite rigid cylinder l1 was computed at a point @,e) where r is.the distance to the cylinder and 8 is the angle between the direction of the incident beam and the point of observation. Fig. 10 shows (Is/Z& as a function of ku, where Z, is the scattered intensity and Z is the incident intensity for back-scattered waves in which 0 = 180 degrees

The second type of transducer is a transcutaneous unit,1° designed to be placed on the skin over a superficial blood vessel (Fig.3) and suitable for use on man. The transducer elements are placed side by side so that the backscattered signal is measured. The operating frequency is 10 MHz. Both types of transducers yield a waveform signal in which the frequency is the difference between the incident and

ULTRASONICS.

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1972

Doppler Fig.5 type transducer,

transducer

output

for moving-wire

target kuft-

f= 5 MHz)

175

ma in the output amplitude occur at approximately same values of ka as for the infinite cylinder.

the

Fig.1 1 shows the directivity pattern of the transducersin decibels, calculated by measuring the response as a function of angle measured from the acoustic axis as the wire passed through the beam. Correction has been made for the angle between the acoustic axis and the direction of the wire movement. The transducer element size for the cuff type unit was 0.4 cm (in the direction of movement) x 0.35 cm and the distance from the transducer element to the wire along the acoustic axis was 0.78 cm. For the transcutaneous unit, the corresponding measurements were 0.3 x 0.15 cm, with the wire at 4.5 cm from the transducer element. In both cases, the wire was within the nearfield. As the beam-width is equal to ~7, where 7 is the time required to traverse the beam, it is proportional to 7Af, the I

IO

5

0

I

1

I

15

20

25

Velocity

I

30

3’ol------

[cm s-‘I

Relative output-amplitude versus velocity for wire targets Fig.6 (transcutaneous unit, f = 10 MHz). Wire diameters: 1 - 0.082 cm; 2 - 0.041 cm; 3 - 0.013 cm; 4 - 0.004 cm

1

3. 0

s

0

2.5-

2 ._ x g

I -5 ,a

0.52.070 I

I 5

0

Velocity

I I5

I

1 IO [cm s.‘]

Fig.8 Relative output-amplitude versus velocity for wire targets (cuff-type transducer, f = 5 MHz). Wire diameters: 1 - 0.025 cm; 2 - 0.017 cm; 3 - 0.050 cm; 4 - 0.0225 cm; 5 - 0.0605 cm; 6 - 0.041 cm; 7 - 0.017 cm; 8 - 0.0045 cm

L 0

I

1 5

I Velocity

I IO

I

I I5

[cm S’l

Fig.7 Relative output-amplitude versus velocity for wire targets (transcutaneous unit-modified, f = 10 MHz). Wire diameters: 1 - 0.084 cm; 2 - 0.0605 cm; 3 - 0.041 cm; 4 - 0.050 cm; 5 - 0.025 cm; 6 - 0.0225 cm; 7 - 0.017 cm; 8 - 0.0045 cm

3o) 2.5-

d

I

z 2.0E

(corresponding to the transcutaneous unit), and for B = 60 degrees (corresponding to the cuff-type transducer).

5 1.5,a a $! I,Oz

It should be noted that the theoretical results are based on a rigid non-moving infinite cylinder, whereas the experimental data was obtained with moving, finite wires. Nevertheless, the theoretical results do indicate that the output should oscillate with increasing values of ka, a prediction confirmed by the experimental data. Moreover, for the cuff-type transducer, it is seen that the maxima and mini-

176

g O.S-

/

/

,

Ik ,/

I

A\

,P’. \

\

,‘?ronscutoneous ‘d

__/

/IX d’

’

Cuff-type

I

Relative output-amplitude Fig.9 (velocity = 10 cm s..’ )

versus size &a) for wire targets

ULTRASONICS.

JULY

1972

6.0

8=60degrees

0

2

4

6

8 ko

IO

1

I

12

14

16

Scattering intensity of plane waves from an infinite rigidFig.10 cylinder versus size (kal at 60 degrees and 180 degrees from the direction

of the incident

wave

Water-filfed container OFig.12

z

Apparatus for generating bubbles

3

9: c

-lOOscilloscope camero

x

z

c Z$s” umt

oz -2o-

Transcutaneous

30’

6

1

I

-5

-10

Angle Fig.1 1

I

0 5 [degrees]

L

I

I

Pulse generator

IO

Transducer exciter

Response of transducers as a function of angle

number of cycles N occurring in the waveform. Since N is independent of velocity or size of the reflecting object, it provides a convenient method for distinguishing between doppler return signals and random transients which may be caused, for example, by movement transmitted to the transducer. Camera

Bubble experiments In vitro experiments with air bubbles in water flowing through plastics tubing were conducted using the apparatus shown in Fig.12. The cuff transducer was placed around a section of the plastics tubing and immersed in water for acoustic coupling to the flow inside the tube. Bubbles were generated by forcing air into the flow through a small orifice. Larger bubbles were eliminated at a vertical Tjunction where they rose upward because of their buoyancy, while the smaller bubbles were carried downward by the flow into the transducer. The flow velocity was maintained at approximately 60 cm s-l. To determine the relation between the size of the bubble and the amplitude of the received signal, the bubble and

ULTRASONICS.

JULY

1972

yz-fillei

Fig.13

Apparatus

for photographing

bubbles and transducer

output

its corresponding output waveform from the transducer were photographed. The experimental arrangement for photography is shown in Fig.1 3. Tripping the shutter of the oscilloscope camera initiated the sweep on the oscilloscope, thus recording the waveform of any bubble passing through the transducer during the sweep. Simultaneously, the shutter initiated another trigger unit providing a delayed

177

output which fired a light source of 10 PS flash duration when the bubble was in the field of view of a second camera. This second camera was focussed on the axis of a section of glass tubing immediately below the transducer, the glass tubing being immersed in a tank of water with plane walls to minimize distortion and magnification of the bubble. Although very little control could be achieved on the size of the bubble or its position as it passed through the transducer’s field, a substantial body of useful data was obtained. Bubble sizes measured varied from 100-600 pm in diameter. Because of the extremely shallow depth of field at the magnification used (6x), small bubbles not in the focal plane could not be photographed. Some of the results are shown in Fig.14. A trend to higher amplitudes with increasing bubble size is indicated. Larger bubbles tended to overload the electronic system. The theoretical scattering intensity 8 at 60 degrees from the direction of the incident beam of 5 MHz for bubbles in this size range is shown in Fig.1 5. These calculations indicate that it should be possible to obtain some correlation between the amplitude and bubble size.

Fig.16

Transducer

output

for bubbles in rabbit blood flow

For comparison, the theoretical scattering intensity from a rigid sphere is also shown in Fig. 15. As in the case of the wire, the oscillatory nature of the scattering intensity makes it impossible to obtain any correlation between size and amplitude if solid spheres are used in place of bubbles. No allowance has been made in these calculations for the motion of the bubbles or spheres through the acoustic field. Such motion for rigid spheres has been shown to affect the scattering intensity significantly.12~13 Theoretical calculations indicate that bubbles formed during decompression are of the order of 1 pm in radius.14 If bubbles in this size range can be generated in vitro and their size measured accurately, it should be possible to obtain good correlation between amplitude and size as long as the bubbles are larger than the resonant size for the operating frequency of the transducers. If resonant bubbles are present, for instance,in a liquid such as water, it would not be possible to determine the size from amplitude alone.

0

0

I 100

I

I 330

xx) Bubble

I

500

J

rodius[pml

Fig.14 Relative output-amplitude transducer, f = 5 MHz)

N

I

400

versus bubble size (cuff-type

401

I

In vivo experiments conducted on rabbits subjected to hyperbaric decompression have shown that the transducer outputs from single bubbles, which were detected, varied greatly in amplitude. Fig. 16 shows examples of waveforms obtained from single bubbles in the inferior vena cava with a cufftype transducer of 05 cm lm. The waveforms are similar to those obtained from in vitro bubble experiments. The background waveform is due to the blood corpuscles. The output amplitude increases considerably when bubbles become more frequent, the waveform eventually deteriorating and becoming saturated. There appears to be little way of obtaining absolute values of bubble size from the output amplitude unless some reference value can be specified. Qualitatively, it might be assumed that small amplitude signals would probably indicate small bubbles, whereas large amplitude signals would indicate larger bubbles. However, this may not be true if bubbles are near the resonant size. Conclusions This paper has described experiments designed to determine whether quantitative information could be obtained from doppler blood-flow transducers. Experiments using wires as reflecting objects have shown that the output amplitude can be made independent of velocity. A correlation between output amplitude and bubble size is possible for in vitro experiments when bubble size can be measured.

Radius

1urn]

Fig.1 5 Theoretical scattering intensity as a function of size for large non-resonant bubbles and rigid spheres (f = 5 MHz, 0 = 60 degrees)

178

In vivo, the doppler blood-flow transducer is useful for detecting the presence of bubbles in the circulatory system. Only a crude estimate of size (ie small or large) is possible. Absolute values of size cannot be obtained without an in vivo reference.

ULTRASONICS.

JULY 1972

Acknowledgements

5

The author would like to express his gratitude to E. F. Stark and Dr S. D. Livingstone for their assistance in this work.

6

References 1

2

3

4

Spencer, M. P., Cambell, S. D., Sealey, J. L., Henry, F. C., Lindbergh, J. Experiments on decompression bubbles in the circulation using ultrasonic and electromagnetic flowmeters, Journal of OccupationalMedicine 11 (1969) 238 Smith, K. H., Spencer, M. P. Doppler indices of decompression sickness: Their evaluation and use, Aerospace Medicine 41 (1970) 1396 Gillis, M. F., Karagianes, M. T., Peterson, P. L. Bends: Detection of circulating gas emboli with external sensors, Science 161 (1968) 579 Gillis, M. F., Peterson, P. L., Karagianes, M. T. In vivo detection of circulatory gas emboli associated with decompression sickness using the doppler flowmeter, Nature 217 (1968) 965

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JULY 1972

10 11 12 13 14

Devin, C. Survey of thermal, radiation, and viscous damping of pulsating air bubbles in water, Journal of the Acoustical Society ofAmerica 31 (1959) 1654 Spitzer, L. Acoustic properties of gas bubbles in a liquid, Columbia University Office of Scientific Research and Development, Report 1705 NDRC 6 l-Sr20-918 CUDWR (15 July 1943) Kapustina, 0. A. Gas bubbles in a small-amplitude sound field, Soviet Physics-Acoustics 15 (1970) 427 Nishi, R. Y. The scattering and absorption of sound waves by a gas bubble in a liquid (to be published) Ward Associates La Jolla California, A-5000 series transducer, transducer exciter, demodulator and telemetry transmitter, model 1502 Parks Electronics Lab, Beaverton Oregon, transcutaneous doppler Morse, P. M., Ingard, K. U. Theoretical acoustics, (McGrawHill New York, 1968) Hickling, R., Wang, N. M. Scattering of sound by a rigid movable sphere, Journal of the Acoustical Society of America 39 (1966) 276 Tsoi, P. I. Diffraction of stationary sound waves by a moving sphere, Soviet Physics-Acoustics 16 (1971) 500 Piccard, J. Aero-emphysema and the birth of gas bubbles, Staff Meetings Mayo Clinic 16 (1941) 700

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