IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-24, NO. 2, MARCH 1977
107
A New Noninvasive Technique for Cardiac Pressure Measurement: Resonant Scattering of Ultrasound from Bubbles WILLIAM M. FAIRBANK, JR., AND MARLAN
Abstract-We suggest and analyze a new technique for making noninvasive cardiac measurements. The technique involves measurement of the spectrum of ultrasound scattered from small bubbles injected into the circulatory system as they pass through the heart. We show that the resonant frequency observed in these spectra will vary as the cardiac pressure changes. Thus the variations of the resonance can be calibrated to give the pressure excursions in a cardiac chamber. Preliminary bench tests of the method are described which show the predicted shift with pressure of the resonance frequency of bubbles in water.
SCULLY
0.
experimental tests with this apparatus. We have been able to see shifts of the resonant frequency of air bubbles in a tank of water as the pressure is periodically varied, simulating the heart. The further improvements needed to make a practical instrument are discussed. II. THEORY OF RESONANT SCATTERING BY GAS BUBBLES IN A LIQUID
To a first approximation the spherically symmetric volume pulsations of a gas bubble of radius Ro under the influence of I. INTRODUCTION a sinusoidal external pressure P exp (jcot) are described by the THE measurement of pressure in the different chambers of equation of motion for a mass on a spring the heart is important inasmuch as it provides vital information concerning the health and well-being of the organ. m2i + bb + kv = - P exp (j&ct). (1) Currently these measurements are made by catheterization, which involves inserting a pressure sensing instrument into the Here v is the change in the bubble volume from the equilibappropriate chambers of the heart. This technique, while rium volume, VO = 4 0rR3. The generalized mass, m2 = currently clinical practice, is nontrivial at best and occasionally P2 /4nRo, corresponds to the mass of the surrounding fluid of involves complications. We report here a possible new tech- density P2 which is moved. The spring constant k is approxinique for sensing the pressure in all four chambers of the heart mately the adiabatic stiffness of the gas in the bubble noninvasively. The technique involves injection of a small kad Po / Vo = 3'Po /47R3. (2) number of tiny air bubbles into the circulatory system, which carries them into the heart. By scattering of ultrasound off In (2), y is the ratio of the specific heats, CpI/Cv for the gas, these bubbles, their resonant frequency is determined in the and PO is the static external pressure. If the tosses represented by the constant b are not too large, various chambers at systole and at diastole. The observed shifts in the resonant frequency are then calibrated to give the the resonant frequency of the bubble system is given by pressure excursions. To this end we have investigated theofm = (l/2X7) (k/M2)"12 = (3hyPo/p2)' /2/2irRo. (3) retically and experimentally the pressure dependence of sound scattered from small gas bubbles. The present work provides This is the expression originally derived by Minnaert [1]. substantial encouragement for pursuing these researches in For small bubbles corrections must be made for increases in this important arena of medical physics. the gas pressure inside the bubble due to the surface tension a The organization of the paper is as follows. In Section II, and for departures from the adiabatic equation of state. The we briefly review the theory of scattering of sound by gas correct expression for the resonant frequency fo, bubbles. We show that the resonant frequency of the bubbles fo =fm(gla) X2, (4) is nearly proportional to pressure. In Section III, the instrumentation we have constructed to make these measurements is is derived in the review by Devin [2]. The correction factor a described. In Section IV, we present the results of preliminary describes the departure of the bubble stiffness from adiabatic stiffness. It varies from 1.4 in the isothermal limit for small *. nor"I_ . * Manuscript received June 13, 1975; revised October 6, 1975. This bubbles to l.U in the adiabatic limit for large bubbles. The 'I--
work was supported in part by the General Research Committee of the University of Arizona, and in part by the National Heart and Lung Divi-
sion of the National Institutes of Health. W. M. Fairbank, Jr., was with the Department of Physics and the Optical Sciences Center, University of Arizona, Tucson, AZ 85721.
He is now with the Department of Physics, Colorado State University, Fort Collins, CO 80523. M. 0. Scully is with the Department of Physics and the Optical Sciences Center, University of Arizona, Tucson, AZ 85721.
1 1 1
,
I'
I
Is
I
11
.
I-
It
s
11
12
surface tension factor g is given by
Since g and a are approximately constant, the resonant fqncy o a bubble ariew tesu as
frequency of a bubble varies with pressure as fo p0o1/2 /Ro.
(6)
108
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, MARCH 1977
We include the RO factor here since the bubble will shrink as the static pressure increases slowly according to the isothermal equation of state P VO = const. (7) or (8) Ro (xcip 113 Thus the resonant frequency for volume pulsations varies with
pressure as
fo a;p06 (9) For small bubbles the pressure P inside the bubble in (7) is (P0 + 2a/R0). When we make this correction and include slight changes of g and a with pressure, we find
f 0pg.73 (10) for bubbles 10 pm in diameter. For 5-Mm bubbles the exponent is 0.67. It is this shift of the resonant frequency with pressure which forms the basis of the pressure measurement method proposed in this paper. It is important in order to measure small pressure changes that the resonance be reasonably sharp. The scattering cross section is given by [3]
4irR2
I(f )2 - 112 +62' MO
11
It has a full width at half maximum, Af, of
Af = = 1/Q. The damping constant
(12)
5 = 0.144. We get approximately the same total result for bubbles 5 to 40 um in diameter, although the individual contributions vary. The resonance for these bubbles will have a Q of 7, which is not particularly large but is good enough to make reasonably accurate measurements. The absorption cross section has the same shape as the scattering cross section but is larger by a factor of (6/6rad), which is about a factor of 10 for small air bubbles in water [3]. Therefore, shifts in the absorption spectrum could also be used to make pressure measurements. The above theory of volume pulsations has been confirmed by various experiments on air bubbles in water from 20 gm to 2 cm in diameter (0.3-300-kHz resonant frequencies) [2], [3]. Thus we expect the theory will also be valid for the slightly smaller bubbles desired for the cardiac pressure measurements. Actually the volume pulsation mode is not the only type of resonant oscillation of a bubble. Various oscillations of surface shape are possible in which the surface tension a supplies the stiffness. The resonant frequencies are [4], [5]
fn [(n2 - l) (n + 2)T/pR3 ] 1/2/r
(16)
where n = 2, 3, 4, For isolated bubbles the scattered sound from surface modes is negligible compared to scattering from the volume mode. However, experimental evidence indicates that surface modes scatter comparable amounts of sound when there is dust on the bubble surface [6]. Perhaps the asymmetry supplied by the dust particles is necessary for efficient excitation of surface modes [7]. From (16) and (7), the surface mode resonant frequencies vary with pressure as (17) fn cR 3/2 p '/2
If we correct (7) for surface tension effects, =Sth +6rad + bvis =bl/km2 (13) (P0 + 2a/RO)V =const., (18) results from thermal, radiative, and viscous losses during the (1 7) becomes oscillations. fn apO.43 The thermal damping constant Sth at resonance is zero in the (19) adiabatic and in the isothermal extremes, but is maximum in for a bubble. Although the change with pressure between [2]. For air bubbles in water the maximum value is is not 10-Mm-diam as large in this case as for the volume pulsation, it can 0.12 for bubbles with a resonant frequency of about 230 kHz. still be used for pressure measurements. The radiation damping is The damping for surface oscillations has not been calculated. Strasberg states that the thermal damping should be smaller R , 6rad (14) than for the volume mode and that viscosity may be the only C2 important source of damping [4]. In fact, the "anomalous" where c2 is the speed of sound in the liquid. Near resonance surface modes in Exner and Hampe's measurements had about the radiation damping for air bubbles in water is 1.36 X 10-2 half the damping of the volume pulsations for a given resonant for bubbles of all sizes. The viscous damping is calculated frequency [6]. to be Thus the shift with pressure for surface modes is smaller but the resonances may be sharper. Hence just as accurate pres= 4M , (15) sure measurements could be made with surface modes as with WR2 P2 volume pulsations. M where is the viscosity. This is expected to be important only III. DESCRIPTION OF THE PRESSURE MEASUREMENT for small bubbles or for liquids of very high viscosity. TECHNIQUE Let us calculate, for example, the damping for a 10-pm air The experimental method is straightforward. In the fluid of bubble (RO = 5 Mm) in water with a resonant frequency of To = 600 kHz. We find that the thermal, radiative, and viscous interest we create uniformly sized bubbles of a suitable gas contributions are, respectively, 0.088, 0.014 and 0.042. Thus (e.g., nitrogen or an inert gas) which all have the same resonant
FAIRBANK AND SCULLY: CARDIAC PRESSURE MEASUREMENT
109
the shift of the scattering peak can be seen on the signal averager screen. From this the pressure excursion can be calculated. Upon realizing practical application, this apparatus could be incorporated into conventional echocardiography instruments. The same pulse is used in both, and the A or B mode display could be used to set the timing of the gate. In fact, the gate could be set electronically to follow the movement of the walls of the heart in the echocardiogram. I
l
S_ISMPLE |
|SIGNAL
Q
Fig. 1. Apparatus for measuring pressure by resonant scattering of ultrasound. The solid line indicates the path of the signaL The dashed lines indicate connections for triggering.
frequency [8]. We send broad-band ultrasound into the fluid and look at the spectrum of the transmitted or the scattered sound. The bubbles absorb and scatter the most ultrasound at the resonant frequency. There will be a dip in the transmission spectrum and a maximum in the scattering spectrum at the resonant frequency. When the static pressure is varied, the shift in the resonant frequency according to (9) or (10) can be seen as movement of the dip in transmission or the maximum in scattering spectrum. The apparatus used to make these pressure measurements is shown in Fig. 1. The pulse generator produces a broad-band exponential-like pulse of about 10 jis in duration. Transducer T1 transforms this pulse into a broad-band pulse of ultrasound. Transducer T2 receives direct transmitted sound or scattered sound, depending on its position. (Actually, in the final medical instrument, T1 will also be used to receive the scattered sound, as in echocardiography.) The amplified signal is fed into a gate. The signal which is scattered by the bubbles takes a different amount of time to go from T1 to T2 than a signal which scatters off the walls of the container (e.g., the walls of the heart). Thus the undesired scattering from the walls can be eliminated by properly setting the delays in the gate to pass only the signal from the bubbles into the spectrum analyzer [91. This gate also eliminates the initial voltage pulse from the receiving circuits if T1 is used as the receiver also. The picture on the signal analyzer consists of a series of spikes, one for each initial pulse generated. The height of a spike is proportional to the spectral component in the received sound at the instantaneous frequency of the sweeping filters in the spectrum analyzer. The envelope of these spikes gives the spectrum of the received signal. This envelope is obtained by sampling and holding the peak value of each spike. The envelope signal is digitized and averaged over many spectrum analyzer sweeps in a signal averager. The signal averager may be synchronized to the electrocardiogram in order to average spectra taken at one part of the heart cycle (e.g., the highest pressure) in one channel and spectra from a different part of the cycle (e.g., the lowest pressure) in another channel. Then
IV. EXPERIMENTAL TESTS The apparatus shown in Fig. 1 has been constructed and tested on bubbles in a tank containing water. We simulate the heart by cyclically applying a small pressure to the tank with a pump. The experimental successes which will be presented later in this section have been achieved in spite of three major difficulties. First, it is hard to make broad-band transducers which have a flat response over perhaps a decade in frequency, e.g., 100 kHz-l MHz (of course the final practical instrument need not be this broad-band once the bubble size is specified). Second, the large wavelengths below 300 kHz (X> 2 cm) result in low-frequency sound being diffracted in all directions. This sound can travel directly between the transducers and can swamp small scattered signals. Third, it is very difficult to make small bubbles of uniform size. The first problem has been nearly solved by using lead metaniobate for the transducer. This material has the lowest mechanical Q of piezoelectric substances. In addition, some testing has been done to find the housing for the transducer discs which provides the most mechanical damping. Since the radial modes are almost eliminated by the high damping, the thickness mode is the major source of resonances in the spectrum. The fundamental thickness mode resonance at 2.25 MHz is eliminated by filtering in the pulse generator. In this way we obtain transducers with reasonably flat response from 100 kHz to 1.5 MHz. With more care in matching of the electronic filter to the transducer resonance, we could have achieved flat response out to 2.5 or 3 MHz. The second problem of diffraction at long wavelengths cannot be beaten except by using large transducers, which is undesirable. Most of the background signal at low frequency was found to be due to a signal projected and received through the sides of the transducers. Presumably this involves excitation of the radial modes of the transducer. This problem was eliminated by placing the transducers just outside the tank in a piece of rubber tubing. The front face of the transducer is still in contact with the water, but the sides of the transducer are isolated. Then, very little low-frequency sound is transmitted directly through the air between the transducers. This will not be a problem on the final medical instrument because the same transducer will be used to send and receive. The third problem, the production of uniform small bubbles, has not been completely solved' yet. We have tried many different schemes. The difficulty is that in a fluid of high surface tension such as water, the bubbles produced by a small micropipette with an opening of a few microns are larger than 100 jgm. Our best success has been when we knock off small bubbles by vibrating the micropipette at 60-300 Hz with a
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, MARCH 1977
110
a.
*
100
150
.I
200 f(kHz)
Fig. 2. The observed shift in the resonant frequency of nitrogen bubbles about 30-40 ,um in diameter with pressure changes simulating the left ventricle. The solid and dotted curves correspond to diastole (no added pressure) and systole (0.2 atm added pressure), respectively.
In summary, we have devised and analyzed a noninvasive scheme for measuring cardiac pressure. We have also constructed a preliminary pressure measurement apparatus based on these arguments and tested it on air bubbles in a tank of water. The predicted shift in resonant frequency with pressure has been observed in spite of substantial experimental difficulties. We have not perfected the art of making small bubbles uniform enough to allow accurate calibrations of small pressure changes to be made. However, with improvements in this area, this device could become an important medical tool for noninvasive cardiac pressure measurements. ACKNOWLEDGMENT
speaker or a vibrator. We have produced bubbles uniform to about a factor of two (e.g., mostly between 20 and 40 jim). In this case many bubbles were produced per vibration cycle. One would not expect them to be uniform since the velocity of the micropipette through the water varies sinusoidally. More research is needed to improve the bubble uniformity, and we are presently working on several promising schemes
There are many people who have helped in this research. We are especially grateful to our capable technician, G. Bilanow, for technical assistance with the experiment. We have also had many stimulating discussions with Dr. F. A. Hopf, Dr. S. F. Jacobs, Dr. G. L. Lamb, Jr., Dr. W. E. Lamb, Jr., Dr. G. T. Moore, Dr. B. P. Phibbs, Dr. D. N. Rogovin, and Dr. J. L. Youmans at various phases of the project.
When we obtained the right conditions for making a cloud of small bubbles, we observed shifts in the scattering spectrum to higher frequency with increasing pressure, as shown in Fig. 2. Any background signal not due to the bubbles has been removed by subtracting an equal number of sweeps with no bubbles present. The peak frequency of about 160 kHz corresponds to the rough 30-40 gim visual estimate of the bubble size based on previous observations of rising bubbles with a microscope. Each time the experiment was repeated with the same vibration conditions, we obtained similar results. No significant spectral shifts were found at other frequencies. In most cases, however, we obtained broad-band scattering with no spectral changes with pressure. This is because the bubbles produced in other vibration conditions were so nonuniform as to broaden out the resonance or because there were too many larger bubbles with resonances below 100 kHz. Note that the cross section, (11), for large bubbles at a frequency far above resonance is a constant, 47rR2. At resonance the cross section is 4rrR2 /62. Since 1/6 7, a large bubble seven times the radius of a small bubble scatters as much as the small bubble does at the resonant frequency of the small bubble. This means that the resonant scattering from small bubbles competes with broad-band scattering from all largerthan-resonant sized bubbles. In most of our vibration conditions we observed a moderate number of 50-300-jum-diam bubbles. The broad-band scattering we usually obtain is probably dominated by these larger bubbles rather than the more plentiful smaller bubbles.
REFERENCES [1] M. Minnaert, Phil. Mag., vol. 26, pp. 235-248, 1933. See also
[101.
[2]
[3] [4] [5] [6] [7]
[8]
-
[9]
[10]
Morse and Feshbach, Methods of Theoretical Physics, Part II. New York: McGraw-Hill, 1953, p. 1498. C. Devin, Jr., J. Acoust. Soc. Am., vol. 31, pp. 1654-1667, Dec. 1959. The Sonar Analysis Group, Physics of Sound in the Sea. Wakefield, MA: Murray, 1945, ch. 28 (originally issued as NDRC Summary Tech. Rep., div. 6, voL 8, 1945). M. Strasberg, Acustica, vol. 4, p. 518, 1954. , J. Acoust. Soc. Am., vol. 28, pp. 20-26, Jan. 1956. M. L. Exner and W. Hampe, Acustica, voL- 3, pp. 67-72, 195 3. Since blood contains many sources of asymmetry such as cells and large molecules, we must consider the possibility that these surface modes may be the major source of scattering from air bubbles in blood. As the technique is perfected, we can determine experimentally which mode is dominant for a given size of bubbles in blood. a) In order to prevent embolism, we plan to use 5-10-mm-diam bubbles in the final medical instrument. Our calculations and measurements indicate that a bubble density of only 10-100 per cubic centimeter is required. This corresponds to a fraction of air in the blood of only 10--10-. This density is comparable to or smaller than the mass of tiny air bubbles which is believed to be created in the blood during injections of indocyanine green dye [8b] . As there were no problems resulting from these injections, we expect no complications due to embolism in our method. b) R. Gramiak, P. M. Shah and D. H. Kramer, Radiology, vol. 92, pp. 9 39-948, Apr. 1969. Note that this range gating technique will be effective in eliminating constructive and destructive interference from various tissue planes in the body. In fact, we are presently carrying out experiments involving encapsulated gases and biological microspheres (e.g., albumin), etc. These studies encourage us to expect that uniform, stable "bubbles" are possible and obtainable. The results of these researches will be reported in a later communication.
107
A New Noninvasive Technique for Cardiac Pressure Measurement: Resonant Scattering of Ultrasound from Bubbles WILLIAM M. FAIRBANK, JR., AND MARLAN
Abstract-We suggest and analyze a new technique for making noninvasive cardiac measurements. The technique involves measurement of the spectrum of ultrasound scattered from small bubbles injected into the circulatory system as they pass through the heart. We show that the resonant frequency observed in these spectra will vary as the cardiac pressure changes. Thus the variations of the resonance can be calibrated to give the pressure excursions in a cardiac chamber. Preliminary bench tests of the method are described which show the predicted shift with pressure of the resonance frequency of bubbles in water.
SCULLY
0.
experimental tests with this apparatus. We have been able to see shifts of the resonant frequency of air bubbles in a tank of water as the pressure is periodically varied, simulating the heart. The further improvements needed to make a practical instrument are discussed. II. THEORY OF RESONANT SCATTERING BY GAS BUBBLES IN A LIQUID
To a first approximation the spherically symmetric volume pulsations of a gas bubble of radius Ro under the influence of I. INTRODUCTION a sinusoidal external pressure P exp (jcot) are described by the THE measurement of pressure in the different chambers of equation of motion for a mass on a spring the heart is important inasmuch as it provides vital information concerning the health and well-being of the organ. m2i + bb + kv = - P exp (j&ct). (1) Currently these measurements are made by catheterization, which involves inserting a pressure sensing instrument into the Here v is the change in the bubble volume from the equilibappropriate chambers of the heart. This technique, while rium volume, VO = 4 0rR3. The generalized mass, m2 = currently clinical practice, is nontrivial at best and occasionally P2 /4nRo, corresponds to the mass of the surrounding fluid of involves complications. We report here a possible new tech- density P2 which is moved. The spring constant k is approxinique for sensing the pressure in all four chambers of the heart mately the adiabatic stiffness of the gas in the bubble noninvasively. The technique involves injection of a small kad Po / Vo = 3'Po /47R3. (2) number of tiny air bubbles into the circulatory system, which carries them into the heart. By scattering of ultrasound off In (2), y is the ratio of the specific heats, CpI/Cv for the gas, these bubbles, their resonant frequency is determined in the and PO is the static external pressure. If the tosses represented by the constant b are not too large, various chambers at systole and at diastole. The observed shifts in the resonant frequency are then calibrated to give the the resonant frequency of the bubble system is given by pressure excursions. To this end we have investigated theofm = (l/2X7) (k/M2)"12 = (3hyPo/p2)' /2/2irRo. (3) retically and experimentally the pressure dependence of sound scattered from small gas bubbles. The present work provides This is the expression originally derived by Minnaert [1]. substantial encouragement for pursuing these researches in For small bubbles corrections must be made for increases in this important arena of medical physics. the gas pressure inside the bubble due to the surface tension a The organization of the paper is as follows. In Section II, and for departures from the adiabatic equation of state. The we briefly review the theory of scattering of sound by gas correct expression for the resonant frequency fo, bubbles. We show that the resonant frequency of the bubbles fo =fm(gla) X2, (4) is nearly proportional to pressure. In Section III, the instrumentation we have constructed to make these measurements is is derived in the review by Devin [2]. The correction factor a described. In Section IV, we present the results of preliminary describes the departure of the bubble stiffness from adiabatic stiffness. It varies from 1.4 in the isothermal limit for small *. nor"I_ . * Manuscript received June 13, 1975; revised October 6, 1975. This bubbles to l.U in the adiabatic limit for large bubbles. The 'I--
work was supported in part by the General Research Committee of the University of Arizona, and in part by the National Heart and Lung Divi-
sion of the National Institutes of Health. W. M. Fairbank, Jr., was with the Department of Physics and the Optical Sciences Center, University of Arizona, Tucson, AZ 85721.
He is now with the Department of Physics, Colorado State University, Fort Collins, CO 80523. M. 0. Scully is with the Department of Physics and the Optical Sciences Center, University of Arizona, Tucson, AZ 85721.
1 1 1
,
I'
I
Is
I
11
.
I-
It
s
11
12
surface tension factor g is given by
Since g and a are approximately constant, the resonant fqncy o a bubble ariew tesu as
frequency of a bubble varies with pressure as fo p0o1/2 /Ro.
(6)
108
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, MARCH 1977
We include the RO factor here since the bubble will shrink as the static pressure increases slowly according to the isothermal equation of state P VO = const. (7) or (8) Ro (xcip 113 Thus the resonant frequency for volume pulsations varies with
pressure as
fo a;p06 (9) For small bubbles the pressure P inside the bubble in (7) is (P0 + 2a/R0). When we make this correction and include slight changes of g and a with pressure, we find
f 0pg.73 (10) for bubbles 10 pm in diameter. For 5-Mm bubbles the exponent is 0.67. It is this shift of the resonant frequency with pressure which forms the basis of the pressure measurement method proposed in this paper. It is important in order to measure small pressure changes that the resonance be reasonably sharp. The scattering cross section is given by [3]
4irR2
I(f )2 - 112 +62' MO
11
It has a full width at half maximum, Af, of
Af = = 1/Q. The damping constant
(12)
5 = 0.144. We get approximately the same total result for bubbles 5 to 40 um in diameter, although the individual contributions vary. The resonance for these bubbles will have a Q of 7, which is not particularly large but is good enough to make reasonably accurate measurements. The absorption cross section has the same shape as the scattering cross section but is larger by a factor of (6/6rad), which is about a factor of 10 for small air bubbles in water [3]. Therefore, shifts in the absorption spectrum could also be used to make pressure measurements. The above theory of volume pulsations has been confirmed by various experiments on air bubbles in water from 20 gm to 2 cm in diameter (0.3-300-kHz resonant frequencies) [2], [3]. Thus we expect the theory will also be valid for the slightly smaller bubbles desired for the cardiac pressure measurements. Actually the volume pulsation mode is not the only type of resonant oscillation of a bubble. Various oscillations of surface shape are possible in which the surface tension a supplies the stiffness. The resonant frequencies are [4], [5]
fn [(n2 - l) (n + 2)T/pR3 ] 1/2/r
(16)
where n = 2, 3, 4, For isolated bubbles the scattered sound from surface modes is negligible compared to scattering from the volume mode. However, experimental evidence indicates that surface modes scatter comparable amounts of sound when there is dust on the bubble surface [6]. Perhaps the asymmetry supplied by the dust particles is necessary for efficient excitation of surface modes [7]. From (16) and (7), the surface mode resonant frequencies vary with pressure as (17) fn cR 3/2 p '/2
If we correct (7) for surface tension effects, =Sth +6rad + bvis =bl/km2 (13) (P0 + 2a/RO)V =const., (18) results from thermal, radiative, and viscous losses during the (1 7) becomes oscillations. fn apO.43 The thermal damping constant Sth at resonance is zero in the (19) adiabatic and in the isothermal extremes, but is maximum in for a bubble. Although the change with pressure between [2]. For air bubbles in water the maximum value is is not 10-Mm-diam as large in this case as for the volume pulsation, it can 0.12 for bubbles with a resonant frequency of about 230 kHz. still be used for pressure measurements. The radiation damping is The damping for surface oscillations has not been calculated. Strasberg states that the thermal damping should be smaller R , 6rad (14) than for the volume mode and that viscosity may be the only C2 important source of damping [4]. In fact, the "anomalous" where c2 is the speed of sound in the liquid. Near resonance surface modes in Exner and Hampe's measurements had about the radiation damping for air bubbles in water is 1.36 X 10-2 half the damping of the volume pulsations for a given resonant for bubbles of all sizes. The viscous damping is calculated frequency [6]. to be Thus the shift with pressure for surface modes is smaller but the resonances may be sharper. Hence just as accurate pres= 4M , (15) sure measurements could be made with surface modes as with WR2 P2 volume pulsations. M where is the viscosity. This is expected to be important only III. DESCRIPTION OF THE PRESSURE MEASUREMENT for small bubbles or for liquids of very high viscosity. TECHNIQUE Let us calculate, for example, the damping for a 10-pm air The experimental method is straightforward. In the fluid of bubble (RO = 5 Mm) in water with a resonant frequency of To = 600 kHz. We find that the thermal, radiative, and viscous interest we create uniformly sized bubbles of a suitable gas contributions are, respectively, 0.088, 0.014 and 0.042. Thus (e.g., nitrogen or an inert gas) which all have the same resonant
FAIRBANK AND SCULLY: CARDIAC PRESSURE MEASUREMENT
109
the shift of the scattering peak can be seen on the signal averager screen. From this the pressure excursion can be calculated. Upon realizing practical application, this apparatus could be incorporated into conventional echocardiography instruments. The same pulse is used in both, and the A or B mode display could be used to set the timing of the gate. In fact, the gate could be set electronically to follow the movement of the walls of the heart in the echocardiogram. I
l
S_ISMPLE |
|SIGNAL
Q
Fig. 1. Apparatus for measuring pressure by resonant scattering of ultrasound. The solid line indicates the path of the signaL The dashed lines indicate connections for triggering.
frequency [8]. We send broad-band ultrasound into the fluid and look at the spectrum of the transmitted or the scattered sound. The bubbles absorb and scatter the most ultrasound at the resonant frequency. There will be a dip in the transmission spectrum and a maximum in the scattering spectrum at the resonant frequency. When the static pressure is varied, the shift in the resonant frequency according to (9) or (10) can be seen as movement of the dip in transmission or the maximum in scattering spectrum. The apparatus used to make these pressure measurements is shown in Fig. 1. The pulse generator produces a broad-band exponential-like pulse of about 10 jis in duration. Transducer T1 transforms this pulse into a broad-band pulse of ultrasound. Transducer T2 receives direct transmitted sound or scattered sound, depending on its position. (Actually, in the final medical instrument, T1 will also be used to receive the scattered sound, as in echocardiography.) The amplified signal is fed into a gate. The signal which is scattered by the bubbles takes a different amount of time to go from T1 to T2 than a signal which scatters off the walls of the container (e.g., the walls of the heart). Thus the undesired scattering from the walls can be eliminated by properly setting the delays in the gate to pass only the signal from the bubbles into the spectrum analyzer [91. This gate also eliminates the initial voltage pulse from the receiving circuits if T1 is used as the receiver also. The picture on the signal analyzer consists of a series of spikes, one for each initial pulse generated. The height of a spike is proportional to the spectral component in the received sound at the instantaneous frequency of the sweeping filters in the spectrum analyzer. The envelope of these spikes gives the spectrum of the received signal. This envelope is obtained by sampling and holding the peak value of each spike. The envelope signal is digitized and averaged over many spectrum analyzer sweeps in a signal averager. The signal averager may be synchronized to the electrocardiogram in order to average spectra taken at one part of the heart cycle (e.g., the highest pressure) in one channel and spectra from a different part of the cycle (e.g., the lowest pressure) in another channel. Then
IV. EXPERIMENTAL TESTS The apparatus shown in Fig. 1 has been constructed and tested on bubbles in a tank containing water. We simulate the heart by cyclically applying a small pressure to the tank with a pump. The experimental successes which will be presented later in this section have been achieved in spite of three major difficulties. First, it is hard to make broad-band transducers which have a flat response over perhaps a decade in frequency, e.g., 100 kHz-l MHz (of course the final practical instrument need not be this broad-band once the bubble size is specified). Second, the large wavelengths below 300 kHz (X> 2 cm) result in low-frequency sound being diffracted in all directions. This sound can travel directly between the transducers and can swamp small scattered signals. Third, it is very difficult to make small bubbles of uniform size. The first problem has been nearly solved by using lead metaniobate for the transducer. This material has the lowest mechanical Q of piezoelectric substances. In addition, some testing has been done to find the housing for the transducer discs which provides the most mechanical damping. Since the radial modes are almost eliminated by the high damping, the thickness mode is the major source of resonances in the spectrum. The fundamental thickness mode resonance at 2.25 MHz is eliminated by filtering in the pulse generator. In this way we obtain transducers with reasonably flat response from 100 kHz to 1.5 MHz. With more care in matching of the electronic filter to the transducer resonance, we could have achieved flat response out to 2.5 or 3 MHz. The second problem of diffraction at long wavelengths cannot be beaten except by using large transducers, which is undesirable. Most of the background signal at low frequency was found to be due to a signal projected and received through the sides of the transducers. Presumably this involves excitation of the radial modes of the transducer. This problem was eliminated by placing the transducers just outside the tank in a piece of rubber tubing. The front face of the transducer is still in contact with the water, but the sides of the transducer are isolated. Then, very little low-frequency sound is transmitted directly through the air between the transducers. This will not be a problem on the final medical instrument because the same transducer will be used to send and receive. The third problem, the production of uniform small bubbles, has not been completely solved' yet. We have tried many different schemes. The difficulty is that in a fluid of high surface tension such as water, the bubbles produced by a small micropipette with an opening of a few microns are larger than 100 jgm. Our best success has been when we knock off small bubbles by vibrating the micropipette at 60-300 Hz with a
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, MARCH 1977
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Fig. 2. The observed shift in the resonant frequency of nitrogen bubbles about 30-40 ,um in diameter with pressure changes simulating the left ventricle. The solid and dotted curves correspond to diastole (no added pressure) and systole (0.2 atm added pressure), respectively.
In summary, we have devised and analyzed a noninvasive scheme for measuring cardiac pressure. We have also constructed a preliminary pressure measurement apparatus based on these arguments and tested it on air bubbles in a tank of water. The predicted shift in resonant frequency with pressure has been observed in spite of substantial experimental difficulties. We have not perfected the art of making small bubbles uniform enough to allow accurate calibrations of small pressure changes to be made. However, with improvements in this area, this device could become an important medical tool for noninvasive cardiac pressure measurements. ACKNOWLEDGMENT
speaker or a vibrator. We have produced bubbles uniform to about a factor of two (e.g., mostly between 20 and 40 jim). In this case many bubbles were produced per vibration cycle. One would not expect them to be uniform since the velocity of the micropipette through the water varies sinusoidally. More research is needed to improve the bubble uniformity, and we are presently working on several promising schemes
There are many people who have helped in this research. We are especially grateful to our capable technician, G. Bilanow, for technical assistance with the experiment. We have also had many stimulating discussions with Dr. F. A. Hopf, Dr. S. F. Jacobs, Dr. G. L. Lamb, Jr., Dr. W. E. Lamb, Jr., Dr. G. T. Moore, Dr. B. P. Phibbs, Dr. D. N. Rogovin, and Dr. J. L. Youmans at various phases of the project.
When we obtained the right conditions for making a cloud of small bubbles, we observed shifts in the scattering spectrum to higher frequency with increasing pressure, as shown in Fig. 2. Any background signal not due to the bubbles has been removed by subtracting an equal number of sweeps with no bubbles present. The peak frequency of about 160 kHz corresponds to the rough 30-40 gim visual estimate of the bubble size based on previous observations of rising bubbles with a microscope. Each time the experiment was repeated with the same vibration conditions, we obtained similar results. No significant spectral shifts were found at other frequencies. In most cases, however, we obtained broad-band scattering with no spectral changes with pressure. This is because the bubbles produced in other vibration conditions were so nonuniform as to broaden out the resonance or because there were too many larger bubbles with resonances below 100 kHz. Note that the cross section, (11), for large bubbles at a frequency far above resonance is a constant, 47rR2. At resonance the cross section is 4rrR2 /62. Since 1/6 7, a large bubble seven times the radius of a small bubble scatters as much as the small bubble does at the resonant frequency of the small bubble. This means that the resonant scattering from small bubbles competes with broad-band scattering from all largerthan-resonant sized bubbles. In most of our vibration conditions we observed a moderate number of 50-300-jum-diam bubbles. The broad-band scattering we usually obtain is probably dominated by these larger bubbles rather than the more plentiful smaller bubbles.
REFERENCES [1] M. Minnaert, Phil. Mag., vol. 26, pp. 235-248, 1933. See also
[101.
[2]
[3] [4] [5] [6] [7]
[8]
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[9]
[10]
Morse and Feshbach, Methods of Theoretical Physics, Part II. New York: McGraw-Hill, 1953, p. 1498. C. Devin, Jr., J. Acoust. Soc. Am., vol. 31, pp. 1654-1667, Dec. 1959. The Sonar Analysis Group, Physics of Sound in the Sea. Wakefield, MA: Murray, 1945, ch. 28 (originally issued as NDRC Summary Tech. Rep., div. 6, voL 8, 1945). M. Strasberg, Acustica, vol. 4, p. 518, 1954. , J. Acoust. Soc. Am., vol. 28, pp. 20-26, Jan. 1956. M. L. Exner and W. Hampe, Acustica, voL- 3, pp. 67-72, 195 3. Since blood contains many sources of asymmetry such as cells and large molecules, we must consider the possibility that these surface modes may be the major source of scattering from air bubbles in blood. As the technique is perfected, we can determine experimentally which mode is dominant for a given size of bubbles in blood. a) In order to prevent embolism, we plan to use 5-10-mm-diam bubbles in the final medical instrument. Our calculations and measurements indicate that a bubble density of only 10-100 per cubic centimeter is required. This corresponds to a fraction of air in the blood of only 10--10-. This density is comparable to or smaller than the mass of tiny air bubbles which is believed to be created in the blood during injections of indocyanine green dye [8b] . As there were no problems resulting from these injections, we expect no complications due to embolism in our method. b) R. Gramiak, P. M. Shah and D. H. Kramer, Radiology, vol. 92, pp. 9 39-948, Apr. 1969. Note that this range gating technique will be effective in eliminating constructive and destructive interference from various tissue planes in the body. In fact, we are presently carrying out experiments involving encapsulated gases and biological microspheres (e.g., albumin), etc. These studies encourage us to expect that uniform, stable "bubbles" are possible and obtainable. The results of these researches will be reported in a later communication.
