Apparatus and method for acoustic heat generation and hyperthermia

An ultrasound hyperthermia applicator suitable for medical hyperthermia treatment, and method for using the same, includes two ultrasound sources producing focused ultrasound beams of frequencies f.sub.0 and f.sub.1. An aiming device directs the two ultrasound beams so that they cross each other confocally at the target. A controller activates the two ultrasound sources so that the target is simultaneously irradiated by the two focused ultrasound beams. The two ultrasound sources provide acoustic energy sufficient to cause significant intermodulation products to be produced at the target due to the interaction of the two ultrasound beams. The intermodulation products are absorbed by the target to enhance heating of the target. In preferred embodiments the ultrasound sources include pair of signal generator for producing gated ultrasound output signals driving single crystal ultrasound transducers. In other embodiments the ultrasound sources include a pair of phased array ultrasound transducers for generating two steerable ultrasound beams. An aiming device is provided for electronically steering and focusing the two ultrasound beams so that they cross each other confocally at the target. Further embodiments employ pluralities of transducers, arrays, or both.

BACKGROUND OF THE INVENTION 
This invention relates to a method for generating localized heat within 
materials and biological tissue by the means of intersecting beams of 
ultrasound. 
High frequency acoustic waves, or ultrasound, may be used to remotely heat 
industrial or biological materials. There has been strong evidence in 
research and clinical laboratories that focused ultrasound for cancer 
hyperthermia will become a useful mode of treating cancer patients, in 
addition to the surgical, radiological and chemotherapeutic methods that 
are available now. In the treatment of tumors in cancer hyperthermia, 
focused ultrasound heats the tumor to a temperature of approximately 
43.degree. C. while the adjacent healthy tissue is kept at a lower 
temperature closer to normal body temperature (37.degree. C.). The 
elevated temperature in the tumor disrupts the tumor growth and eventually 
kills it. This allows the cancer to potentially be treated without 
surgery, without ionizing radiation, or without chemotherapy. 
Conventional focused ultrasound for heating is employed by using either a 
scanned ultrasound transducer or with a phased array. The scanned 
transducer uses a lens, much like an optical magnifying glass focuses 
sunlight, while the phased array uses electronic delays among the array 
elements to achieve focusing. A burst of sound is then emitted which 
converges at the focus to provide localized high intensity acoustic 
energy. Some of the high intensity acoustic energy is absorbed by the 
tissue at the focus and is dissipated as concentrated focal heat. The rest 
of the energy travels through the focus and is slowly dissipated into the 
surrounding tissues as distributed heat. 
Biomedical hyperthermia applicators using a plurality of sound sources to 
heat larger, distributed volumes, have also been investigated. These 
investigations have relied upon linear thermal superposition of the 
plurality of sound sources to heat the target tissues. Nonlinear effects 
of sound propagation through animal tissue and materials have also been 
studied for a single sound source. 
The nonlinear mixing, or intermodulation, of sound waves has been known in 
oceanographic acoustics. Oceanographic acoustic applications have used 
both the linear (superposition) and nonlinear (intermodulation) effects of 
intersecting sound beams. Nonlinear acoustic sonars, known as 
oceanographic parametric sonars, deliberately promote the generation of a 
difference frequency to enhance sonar beamforming and long range sound 
propagation. The generated difference frequency is usually 30 to 60 dB 
below the level of the primary frequencies. A second product of nonlinear 
mixing is the sum frequency, which is generated by the intermodulation 
process at 10 to 40 dB below the level of the primary frequencies, 
indicating that the conversion from primary to sum frequency is a 
significantly more efficient process than the conversion of a primary to a 
difference frequency. Since higher frequencies are subject to higher 
absorption coefficients in water they generate more heat than the primary 
frequencies as they propagate, but propagate shorter distances than the 
primary frequencies. In oceanographic sonar applications, heat generation 
via sound absorption is generally an undesirable result of nonlinear 
intermodulation. 
SUMMARY OF THE INVENTION 
Little or no use has been made of the sum frequency in hyperthermia 
applications. However, the sum frequency component of nonlinear mixing, as 
well as the harmonics created by high intensity sound waves, are useful 
for enhanced heating of localized areas. The present invention provides a 
hyperthermia apparatus and method which exploits the nonlinear propagation 
properties of sound, and the nonlinear mixing of sound, to enhance heating 
of the target. The invention is particularly useful for hyperthermia 
treatment of deep seated biological tissues. The invention is also suited 
for heating in materials processing. 
In one aspect of the invention an ultrasound hyperthermia applicator, and 
method for using the same, includes at least two ultrasound sources 
producing focused ultrasound beams of frequencies f.sub.0 and f.sub.1. The 
two ultrasound beams are aimed so that they cross each other and are 
focused at the same spot on the target, i.e., they are confocused at the 
target. A controller activates the two ultrasound sources so that the 
target is simultaneously irradiated by the two focused ultrasound beams. 
The two ultrasound sources provide acoustic energy sufficient to cause 
significant intermodulation products to be produced at the target due to 
the interaction of the two ultrasound beams. The intermodulation products 
are absorbed by the target to enhance heating of the target. 
In preferred embodiments frequency f.sub.0 is substantially the same as 
frequency f.sub.1. The target is a tissue mass located within the human 
body, and frequencies f.sub.0 and f.sub.1 are chosen for useful 
penetration to the target tissue. Preferably, the target is a tissue mass 
located within the cranium. 
In other preferred embodiments the ultrasound sources include signal 
generators for producing gated ultrasound output signals at frequencies 
f.sub.0 and f.sub.1 in response to an input control signal generated by a 
controller. A power amplifier is coupled to the output of each signal 
generator, and an ultrasound transducer is coupled to the output of each 
power amplifier to convert each amplified ultrasound signal into a focused 
ultrasound beam. Each ultrasound transducer includes an acoustic lens for 
focusing its corresponding ultrasound beam at the target. Aiming means are 
provided for fixing the ultrasound transducers relative to each other so 
that the ultrasound beams cross each other at a predetermined angle. 
In yet another preferred embodiment frequency f.sub.0 is substantially the 
same as frequency f.sub.1 and the ultrasound sources include a signal 
generator for producing a gated ultrasound signal at frequency f.sub.0 in 
response to an input control signal generated by a controller. A power 
amplifier is coupled to the output of the signal generator, and a power 
splitter is coupled to the output of the amplifier for dividing the 
amplified gated ultrasound signal between two ultrasound transducers. 
In still another preferred embodiment the ultrasound sources include at 
least a pair of phased array ultrasound transducers coupled to 
corresponding ultrasound scanners for generating two steerable ultrasound 
beams. Aiming means are provided for electronically steering and focusing 
the two ultrasound beams so that they cross each other confocally at the 
target. 
In still another preferred embodiment, a plurality of focused ultrasound 
sources, directed in a confocal manner, are each driven by a continuous 
wave (CW) signal, or a pulsed wave (PW) signal, or a modulated signal, 
which is centered about f.sub.0, f.sub.1 or f.sub.n for an n-source 
configuration. Center frequencies f.sub.0, f.sub.1, . . . , f.sub.n can be 
substantially the same. The modulation can be in the form of amplitude 
modulation (AM), frequency modulation (FM) such as in an FM-sweep, or 
`chirp`, or in the form of a pseudo-random modulation. 
Thus, the invention described herein achieves efficient delivery and 
conversion of acoustic energy to enhance heating of a hyperthermia target 
by producing intermodulation products at the target, or confocal region, 
which are easily absorbed by the target to produce heat. This invention 
improves upon focused ultrasound hyperthermia techniques by deliberately 
exploiting the nonlinear propagation of sound at high intensities to 
enhance heating. The nonlinear interaction, which generates additional 
heat, does so only within the confines of the confocal region. The 
invention can advantageously be used to efficiently heat deep seated 
biological tissue targets without excessively heating surrounding tissues 
since the acoustic energy is delivered to the target in the form of 
relatively low frequency acoustic energy, which is not easily absorbed by 
the surrounding tissues. Further, the invention delivers the acoustic 
energy to the target in a plurality of crossed ultrasound beams focused at 
the target which advantageously minimizes the acoustic intensity in the 
surrounding tissues, and maximizes the acoustic intensity at the target.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
Referring to FIG. 1, a preferred embodiment of a hyperthermia applicator 10 
for heating biological tissue includes a hyperthermia controller 11 and 
two ultrasonic transducers 14 and 16 for emitting ultrasound energy which 
is acoustically coupled to a target body 12 to heat a localized region of 
tissue 18 deep within the target body. Transducer 14 and transducer 16 
each produce a focused beam of acoustic energy 20 and 22, respectively, at 
or near the same frequency. The ultrasound frequency range typically 
employed for heating biological tissue is from about 50 kHz to over 5 MHz. 
Transducers 14 and 16 have focusing lenses, 15 and 17 respectively, which 
in turn are coupled to the target body by coupling means 19 known in the 
art. The transducers are oriented against the body 12 so that the focused 
beams 20 and 22 cross each other at their respective foci 24, 26 and 
within the localized volume of tissue 18 which represents a system 
confocal region F. 
The intersection and consequent nonlinear interaction of intersecting waves 
promotes the generation of sum-frequencies by intermodulation especially 
in the interaction (confocal) region, and this in turn accentuates the 
generation of heat. Focused intersecting beams having coincident foci 
increase the acoustic intensity at the confocal region over otherwise 
unfocused intersecting beams. Higher intensities at the confocal region 
promote nonlinear acoustic effects and lead to greater temperature rise. 
Outside the confocal region where the acoustic intensity is significantly 
less, nonlinear effects are reduced and hence less heat is deposited. By 
limiting the intersection, and hence interaction, of two or more sound 
beams to a certain volume, heat generation due to nonlinear interaction is 
accentuated within the region, and minimized outside the region. More 
energy deposition in a confocal region by nonlinear interaction means more 
heat in the confocal region and less acoustic energy which continues past 
the confocal region to be absorbed in healthy tissue elsewhere. 
Hyperthermia controller 11 includes a microprocessor 30 which communicates 
with a user interface 32, such as a keyboard and display, and generates 
timing and control signals to simultaneously activate a pair of ultrasound 
signal generators 34 and 36. Signal generator 34 produces a pulsed 
ultrasound signal at a frequency f.sub.0, gated on and off by the 
microprocessor 30, which is amplified by amplifier 38. The output of 
amplifier 38 drives ultrasound transducer 16 through an impedance 
matching, or tuning network, 40. Similarly, signal generator 36 produces a 
pulsed ultrasound signal at a frequency f.sub.1, gated on and off by the 
microprocessor 30, which is amplified by amplifier 42. The output of 
amplifier 42 drives ultrasound transducer 14 through an impedance 
matching, or tuning network, 44. Ultrasound frequencies f.sub.0 and 
f.sub.1 are typically the same, or near each other. 
Referring to FIG. 2, an alternative preferred embodiment of a hyperthermia 
applicator 10' includes a hyperthermia controller 11' having a power 
splitter 50 for driving the ultrasound transducers 14 and 16 at the same 
ultrasound frequency. In this embodiment, signal generator 34 produces a 
pulsed ultrasound signal at frequency f.sub.0, gated on and off by 
microprocessor 30, which is amplified by amplifier 38 to drive the input 
to the power splitter 50. Power splitter 50 divides the power of the 
amplified ultrasound signal and applies it equally to each transducer 14 
and 16 through its respective tuning network 44 and 40. 
Each transducer 14 and 16 (FIG. 1 or FIG. 2) includes an acoustic lens 
portion 15 and 17, respectively, for focusing the resulting ultrasound 
beam deep within the target 12. The lens portion of each ultrasound 
transducer is acoustically coupled to the target body 12 by providing 
fluid or acoustic gel (not shown) in the gap 19 which forms between each 
transducer and the target body. Alternatively, the entire target 
body/transducer interface may be immersed in fluid to aid acoustic 
coupling. 
Transducer 14 is arranged so that the main acoustic beam 20 generated by 
the transducer has its focus 24 located at the desired focal region F of 
tissue target 18. Similarly, transducer 16 is arranged to have the focus 
26 of its main acoustic beam 22 coincident with focus 24 of acoustic beam 
20. The transducers 14 and 16 are further arranged so that the center of 
acoustic beam 20 is offset from the center of acoustic beam 22 by an angle 
.theta.. Angle .theta. is typically any angle other than 0.degree. and 
180.degree.. 
Referring to FIG. 3, another alternative preferred embodiment of a 
hyperthermia applicator 10" includes a hyperthermia controller 11" having 
two phased array scanners 300 and 302 for driving respective phased array 
ultrasound transducers 304 and 306. Each ultrasound phased array 
transducer 304 and 306 includes a plurality of individually driven 
transducer elements for producing an electronically steered and focused 
ultrasound beam 308 and 310, respectively. The ultrasound signals required 
to steer and focus the ultrasound beams are produced by each of the 
corresponding phased array scanners in a manner well understood by those 
skilled in the art. Microprocessor 30 coordinates the operation of the two 
phased array scanners 300 and 302 to form beams 308 and 310. 
Each phased array transducer 304 and 306 is capable of forming a focused 
beam within its respective sector 312 and 314. Thus, the two beams 308 and 
310 can be electronically steered to cross each other anywhere within the 
three-dimensional overlap 316 of sectors 312 and 314. Each beam can be 
electronically focused at the selected beam crossing site F. The two 
phased array transducers can be fixed relative to each other by attachment 
to a rigid structure 318. The beams generated by each transducer are 
electronically aimed and focused to cross each other at a plurality of 
confocal points located in 316, as a function of time. This preferred 
embodiment thus allows for a wide range of electronically selectable 
treatment sites within the target body 12. 
This invention is particularly well-suited for heating biological tissue in 
vivo for therapeutic purposes without invasive surgery, for hyperthermia 
treatment of cancerous tumors, and for ablation of target volumes of 
tissues. The utilization of this invention will be important in many 
areas, such as transmission of ultrasound at relatively low ultrasound 
frequencies through different portions of the skull but coincident within 
a treatment volume in the brain, and in treatment of tissues overlying a 
critical tissue such as bone or lung which must be spared from heating. 
The heat generation results from the transformation of acoustic waves into 
heat. Heat generation depends on the acoustic absorption coefficient of 
the medium, the acoustic intensity, and the frequency of the acoustic 
waves. Acoustic absorption and heating increases as the frequency and 
intensity of the acoustic waves increases. This invention recognizes that 
simultaneous bursts of sound from separate sources converging upon the 
same focal location will effect a linear adding of heat at the focus, as 
well as interact with each other in a nonlinear manner to produce 
mixed-frequency energy at the focus which provides extra heating at the 
focus. This extra heating means more heating at the confocal region F, 
where it is desired, and less heating elsewhere, where it is undesired. 
This invention is particularly useful in heating cranial targets without 
surgery because the primary transmit frequencies may be made low enough to 
penetrate the skull with low absorption and low scattering. Thus, 
sufficient acoustic energy would survive the passage through the skull so 
that nonlinear interaction of intersecting beams at the target would give 
rise to useful localized heat generation. 
This invention is not limited to only two transducers, or two transducer 
arrays, since the nonlinear heating effect at the tissue target 18 is 
caused by the confocal intersection of two or more beams. It will be 
apparent to those skilled in the art that almost any plurality of 
transducer sources, and associated driving circuitry, can be used to 
effect similar nonlinear results. The plurality of transducer sources can 
emit pulses which are similar in frequency content or pulses which are 
substantially different in frequency content. The frequency content of the 
pulses can include pure CW tones, or modulated bandlimited frequencies. 
The acoustic drive characteristics of the transducers can also be used to 
determine the frequency content of the pulses. For instance, overdriving a 
transducer often produces triangular wave output signals which are rich in 
harmonics of the fundamental driving frequency. It should be noted that 
the intermodulation of broadband signals which are rich in harmonics 
produce a similarly rich variety of mixing products at frequencies which 
are easily absorbed by the target to produce excess heat. 
Furthermore, while focusing the beams at the target site increases the 
acoustic intensity to enhance intermodulation at the site, unfocused beams 
may also be used if they can deliver sufficient acoustic intensity at the 
site to provide similar intermodulation results. However, acoustic power 
levels must remain below that which will cause excess heating to the 
surrounding tissues or cavitation of the tissue medium. Therefore, focused 
ultrasound beams are a more practicable means for delivering high 
intensity acoustic power to a deep seated target site than unfocused 
ultrasound beams. 
Eperimental Results 
An experiment was conducted to verify the nonlinear enhanced heating 
mechanism of this invention. FIG. 4 shows the ultrasound transducer 
geometry used for the experiment and FIG. 5 shows a block diagram of the 
experimental instrumentation. The objective of this experiment was to 
determine if the heating within the confocal (intersecting) region F of 
two focused sound beams generated heat in a nonlinear way. 
Two fixed-amplitude, fixed-focus ultrasound transducers 100 and 102, 
labeled B (Blue) and Y (Yellow) respectively, were arranged to have 
coincident foci F upon a silicone rubber 122 encapsulated thermocouple 
temperature probe 104. Ultrasound transducer B was pulsed for .tau. 
seconds at a frequency f.sub.B =1.5 MHz and the temperature rise at the 
thermocouple probe was measured. Then, independently, ultrasound 
transducer Y was pulsed for .tau. seconds at a frequency f.sub.Y =0.9 MHz 
and the temperature rise at the thermocouple probe was measured. The 
temperature changes for these two trials are denoted .DELTA.T.sub.B and 
.DELTA.T.sub.Y respectively. Finally, both ultrasound probes B and Y were 
simultaneously pulsed for .tau. seconds at their original frequencies and 
power levels, and the temperature rise at the thermocouple probe was 
measured, which is denoted as .DELTA.T.sub.B+Y. A dimensionless ratio 
.sigma..sub.heat indicative of the nonlinear heat generation due to the 
intersection and interaction of the two ultrasound beams at F is defined 
to be 
##EQU1## 
If the process of two sound beams interacting is a linear process, then the 
principle of superposition would hold and .sigma..sub.heat should equal 
1.0. If the process is nonlinear, then .sigma..sub.heat should be &gt;1.0, 
where the extra heat is due to sound energy transforming itself from the 
fundamental transmit frequencies for B and Y, into a spectrum of 
frequencies comprising the fundamental frequencies and mixing frequency 
products of those fundamental frequencies. 
Ultrasound transducers 100 and 102 were quartz transducers with attendant 
transducer heads (not shown) water-sealing cones (flanges) (not shown) and 
lenses 114, 116, respectively. Each transducer head-cone combination 
contained degassed water sealed into each unit by means of stretched latex 
condom. Small air bubbles were removed from the sealed unit by the use of 
a syringe which was designed to attach to a special valve on the body of 
the water-seal cone. Thus, each transducer assembly was ensured of being 
free of any air bubbles for the duration of the experiment. 
Each transducer head was mounted on a separate positioning mechanism (not 
shown). The 1.5 MHz Blue transducer was mounted on a six 
degree-of-freedom, motorized computer controlled platform (not shown), and 
was inclined to an angle .theta..sub.1 of about 54.degree. from the 
vertical axis 120. The 0.9 MHz Yellow transducer was mounted on a five 
degree-of-freedom, manually controlled platform (not shown), with the 
transducer aimed straight down along the vertical axis. Thus, the 
intermediate angle .theta..sub.1 between the transducers was 54.degree.. 
The position resolution of each platform was about 1 mm. Each transducer 
was calibrated for voltage versus radiation pressure (as measured in 
grams) using a Mettler PC 440 electronic scale. The power level chosen for 
each transducer was in the linear range based on the radiation pressure 
measurement. 
The instrumentation used for the experiment, and shown in FIG. 5, included 
a computer 200 for controlling the B and Y transducer systems. Each 
transducer system included a Wavetek Model 278 waveform generator 202 
independently controllable by the computer 200 to produce pulses of the 
desired duration at the desired frequency. The Y system waveform generator 
was set to 0.9 MHz and the B system waveform generator was set to 1.5 MHz. 
The output of each waveform generator 202 was connected to drive a power 
amplifier. In the case of the Yellow system, the output of waveform 
generator 202 drives power amplifier 204 which is an EIN RF power 
amplifier Model 3100L, which produces approximately 200W into a 50.OMEGA. 
load. In the case of the Blue system, the output of waveform generator 202 
drives another amplifier 206 which was an IFI, Inc. (Farmingdale, N.Y.) 
Model M2600, which produces approximately 130 W into a 50.OMEGA. load. The 
output of each amplifier was coupled to its respective transducer through 
a tuning network 208. 
The thermocouple probe 104 used for the experiment was constructed using a 
capacitive discharge butt weld technique to join together 0.003" (0.076 
mm) diameter chromel and constantin Teflon-coated wires. The thermocouple 
bead at the junction of the two dissimilar wires was observed under a 
microscope and found to be free of oxide and not much larger than the wire 
diameter. A thermocouple capsule 122 was formed by encapsulating the 
thermocouple in General Electric RTV-615 silicone rubber using a 5.5 cm 
diameter, 0.75 cm deep petri dish mold. This encapsulant was chosen for 
its reasonable match to the .rho.c of water (i.e., .rho.=1.02 g/cc), its 
transparency, and the relative ease with which the two encapsulant 
components are degassed after mixing, by means of a laboratory vacuum. The 
encapsulant also absorbs ultrasound to the same order of magnitude, per 
unit thickness, as certain types of human tissue. The DC resistance across 
the thermocouple leads was checked after welding, after encapsulation, and 
after the experiment to verify electrical continuity. 
The encapsulated thermocouple (hereinafter referred to as the thermocouple) 
was mounted on a block of wedge-absorber polyethylene (not shown), which 
is similar to a glass fibre wedge absorber employed in air acoustic 
anechoic chambers. The polyethylene block was then placed at the bottom of 
an 8 gallon capacity acrylic-walled tank (not shown) filled with degassed 
water, and suitably weighted to prevent floatation and thermocouple 
movement. Several other polyethylene wedge absorbers were also randomly 
placed in the tank to enhance the absorption of echoes, and to reduce the 
quantity of degassed water needed to fill the tank. 
The thermocouple was precalibrated using a cold reference ice bath. A Grass 
polygraph 210 (Model 7, Grass Instrument, Quincy, Mass.) was used to 
record the temperature of the thermocouple and was precalibrated for 
operation from 20.degree. to 60.degree. C. A small Panametrics transducer 
212 (f.sub.r =6 MHz) aimed at the confocal region was used to measure the 
ambient noise of the system during the tests by means of a Hewlett-Packard 
8553B spectrum analyzer 214. This measurement was intended to identify 
finite amplitude harmonics, stable cavitation, and unstable cavitation. 
With the thermocouple and transducers thus arranged and calibrated, a 
series of pulses were issued from each transducer to align each transducer 
focus with the thermocouple, starting with the Yellow 0.9 MHz system. When 
the two transducers were suitably arranged with foci believed to be 
coincident with the thermocouple, the experiment was ready to commence. 
The protocol for the experiment was a test involving 10 pulses for B only, 
10 pulses for Y only, and then 10 pulses for simultaneous B and Y 
transmission. The computer was programmed to give a 0.1 second duration 
pulse to simultaneously trigger the two waveform generators. The 
relatively long pulse duration, combined with the fast rise time of the 
electronics (capable of operation to at least 35 MHz) and the simultaneous 
triggering ensures overlap of the acoustic waves from the B and Y 
transducers as they travel through the confocal region, and gives adequate 
opportunity for nonlinear effects to occur. 
Discussion and Conclusions 
FIG. 6 illustrates the geometry for the 1.5 MHz B transducer. The main 
radiation axis 250 is shown emanating from the lens 114 of the transducer 
into the water (layer 1) at an angle .theta..sub.1 =54.degree. angle from 
the normal axis 252, and penetrating the silicone rubber (layer 2) at an 
angle .theta..sub.2 from the normal axis. The speed of sound propagation 
in water is c.sub.1 =1480 m/sec, and in silicone rubber is c.sub.2 =1025 
m/sec. Since c.sub.1 &gt;c.sub.2, the waves will always propagate from the 
water and into the silicone rubber. We observe this by assuming that any 
wavelength in layer 1 projects a trace wavelength at the layer 1/layer 2 
interface, and this trace wavelength must likewise match the projected 
wavelength in layer 2. This is merely Snell's law, and thus 
##EQU2## 
where, 
##EQU3## 
thus, 
##EQU4## 
The inclination angle of a small streak of cavitation bubbles embedded in 
the rubber (about 1 cm from the thermocouple, and created during focal 
alignment but not during the actual measurements) was measured at 
33.7.degree. from the normal, thereby experimentally confirming this 
result. 
The propagation of the oblique 1.5 MHz B transducer waves was modeled using 
the well known SAFARI computer code to produce a contour plot of 
transmission loss shown in FIG. 7. (see, Schmidt, H., "SAFARI: 
Seismo-Acoustic Fast Field Algorithm for Range Independent Environments. 
User's Guide.", SR 113, SACLANT ASW Research Centre, La Spezia, Italy 
(1987)). The focused 1.5 MHz B transducer was replaced in the model by a 
similarly focused line array 260 shown at the extreme left side of FIG. 7 
at a depth of about 0.03 to 0.08 meters (note the dashed lines showing the 
focusing lens 114, and the dark solid line for the line array 260). The 
silicone rubber encapsulant 122 location is shown by the two parallel 
dashed lines at 0.1117 and 0.1187 meters depth. The air-water interface 
exists at zero depth, and the remaining regions above and below the 
silicone rubber are water. The thermocouple location 104 is shown by a 
small black triangle at depth=0.1115 meters, and range=0.0817 meters. Note 
that the thermocouple is not exactly at the focus center due to the 
refraction of the silicone rubber. 
The SAFARI model creates full-wave solutions for two-dimensional linear 
acoustic wave propagation problems in layered media. In this case, the 
approximations made are that the circular-symmetry focused transducer is 
replaced by a similarly sized, 100-element focused line array 260 
(.lambda./2 spacing), and the model is 2-D (range and depth). The contours 
represent the sound field transmission loss in 6 dB increments, and 
absorption is included for both sound waves in the water, and for 
longitudinal (sound) and shear waves in the silicone rubber. The input 
file for the model is included at the top of the figure. 
Appendix A includes the data obtained from the thermocouple during 
performance of the experiment. Calculations summarizing the data are shown 
in Table I. These calculations show that the linear sum of the measured 
temperature increase at the thermocouple probe caused by the B and Y 
transducers operated at different times resulted in a total 12.7.degree. 
C. temperature increase. In contrast, the measured temperature increase at 
the probe caused when the B and Y transducers were operated simultaneously 
was 13.5.degree. C. Thus, simultaneous operation of the B and Y 
transducers resulted in a 0.8.degree. C. greater temperature increase for 
the same electrical input power to the transducers. This corresponds to a 
.sigma..sub.heat at of 1.065, which indicates a 6.5% heat gain of the 
system due to the nonlinear interaction of the two focused ultrasound 
beams at the thermocouple probe. 
The presence of ambient second harmonics during the B, Y, and B+Y tests 
strongly suggests the presence of nonlinear effects either from the 
acoustic drive levels themselves, or from nonlinear effects. The second 
harmonics could also be a consequence of stable cavitation, but this could 
not be confirmed due to the local oscillator spectral line of the analyzer 
interfering with the measurement of stable cavitation subharmonics. Third 
and fourth harmonics were not observed suggesting that the system could be 
driven harder, and there was no evidence of broadband impulsive noise 
suggesting that there was no unstable cavitation. Microscope inspection of 
the encapsulated thermocouple after all tests showed no evidence of 
cavitation bubbles anywhere along the thermocouple wire. 
To assess cavitation, we can estimate the acoustical intensity in 
Watts/cm.sup.2 at both the surface of the lens and at the focus for each 
of the B and Y transducers and compare them to established values for 
cavitation threshold in the literature. This is done by the following: 
##EQU5## 
B (1.5 MHz): 12.8 W (input power from calibration) Y (0.9 MHz): 1.3 W 
(input power from calibration) 
lens surface intensity: B: 12.8/30.2=0.42 W/cm.sup.2 Y: 1.3/30.2=0.043 
W/cm.sup.2 
##EQU6## 
where .lambda.=wavelength, f=focal length (101 mm), a=lens radius (31 mm) 
B (1.5 MHz): d.sub.f =0.321 cm 
Y (0.9 MHz): d.sub.f =0.535 cm 
##EQU7## 
B (1.5 MHz): A.sub.f =0.0809 cm.sup.2 Y (O.9 MHz): A.sub.f =0.2248 
cm.sup.2 
focal intensity: B: 12.8/0.0809=158 W/cm.sup.2 Y: 1.3/0.2248=5.78 
W/cm.sup.2 
These estimates for focal intensity assume no absorption in either the 
water or in the silicone rubber. To account for absorption we multiply the 
absorption-free intensity by the following (for GE RTV-615, .mu.=1.44 dB 
cm.sup.-1 MHz.sup.-1): 
Y (0.9 MHz): 
.mu..sub.0.9 =1.296 dB/cm 
.alpha..sub.0.9 =.mu..sub.0.9 /8.686=0.149 Nepers/cm 
.alpha..sub.0.9-power =2.alpha..sub.0.9 =0.298 Nepers/cm coefficient of 
transmission at normal 
incidence=0.95 
##EQU8## 
B (1.5 MHz): .mu..sub.1.5 =2.16 dB/cm 
.alpha..sub.1.5 =.mu..sub.1.5 /8.686=0.249 Nepers/cm 
.alpha..sub.1.5-power =2'.sub.1.5 =0.497 Nepers/cm coefficient of 
transmission at normal 
incidence=0.48 
##EQU9## 
These values suggest two things. First, the .DELTA.T for the Y and B 
systems were both about 6.degree. C. and yet the intensities at the focus 
were an order of magnitude different. This implies that the B system (1.5 
MHz) did not have its true focus aligned with the thermocouple, but 
instead a focal sidelobe was present. This is reasonable because the two 
transducers could not have been moved any closer to each other with the 
lenses and the 54.degree. separation angle used. Noting the focal 
displacement due to refraction in FIG. 7, it is entirely possible that the 
B system was not adequately aligned. Thus, the theoretical peak focal 
intensity is 54 W/cm.sup.2 for the 1.5 MHz system, however the actual 
intensity at the thermocouple was reduced by an order of magnitude because 
the temperature increases were about the same. If we assume that the Y 
system was properly aligned with the thermocouple, then we may assume that 
the intensity for each of the systems was about 5 W/cm.sup.2, and it is 
these intensities which are responsible for the heat generation. 
The second feature is that the peak focal intensities in degassed water are 
well below the estimates for unstable cavitation, and below the levels 
considered for stable cavitation. Therefore, the extra heat supplied by 
two transducers firing simultaneously cannot be attributed to either 
cavitation phenomena. 
From the thermocouple data listed in Appendix A, the thermoelectric voltage 
change for the temperature range from 20 to 26.degree. C. (for a pulse 
from either the B or the Y system) is: 
##STR1## 
The thermoelectric voltage change for the temperature range 20.degree. to 
32.degree. C. (for the simultaneous pulsing from both B and Y systems) is: 
##STR2## 
From these two we may estimate the dimensionless nonlinearity parameter 
.sigma..sub.T/C associated with the thermocouple by the same ratio used in 
finding .sigma..sub.heat. That is 
##EQU10## 
Likewise from the data in Appendix A, we note that the amplitude linearity 
for the Grass polygraph oscilloscope is 2% full-scale. Since full-scale 
for this experiment was 40.degree. C., then a 12.degree. C. temperature 
rise represents, at worst, 30% of the full-scale error, or 0.6%. The 
dimensionless nonlinearity parameter for the oscilloscope recorder is then 
1.006. We note that the parameters for both the thermocouple and for the 
oscilloscope recorder are below the .sigma..sub.heat parameter. 
Furthermore, the combined nonlinearity associated with the thermocouple 
and the recorder is the multiplication of the two, which gives 1.015. This 
is still too small to account for the .sigma..sub.heat =1.065 from the 
experimental data. 
One final comment is that the contamination of the heat transfer between 
the B, Y, and B+Y experiments. The thermocouple wire and the encapsulant 
together provide the heat conduction path for the thermocouple bead. 
During the solo trials for B, and for Y, the temperature rise was about 
6.degree. C. With both B and Y transmitting, the temperature rise was 
about 13.degree. C. Since the temperature rise was about twice as high 
during the B+Y trials as it was during the solo B, or solo Y trials, the 
heat transfer rate would likewise be twice as fast. What this empirically 
suggests is that the heat conduction during the B+Y trials was more severe 
than in the B and Y trials, and so the B+Y trial was contaminated more 
than the B or the Y. The heat transfer mechanism reduces the maximum 
temperature that either the B+Y, the B, or the Y could reach, but it 
influences the B+Y about twice as much as the B, or the Y trials. This 
means that the heat transfer mechanism actually reduces the value of 
.sigma..sub.heat. A heat transfer model could estimate the amount of the 
reduction, but for the purposes of this experiment, it is sufficient to 
note that the heat transfer comparison between the solo trials, and the 
simultaneous trials, is a source of experimental error that reduces 
.sigma..sub.heat. This is in contrast to the errors associated with the 
thermocouple and the recorder. 
The lack of unstable cavitation at the thermocouple site, the lack of 
sufficient nonlinearity in the thermocouple and in the polygraph, the 
acoustical intensities below the cavitation threshold, and 
.sigma..sub.heat &gt;1.0 strongly support the existence of nonlinear heat 
generation from confocal ultrasound transducers. 
While this invention has been particularly shown and described with 
references to preferred embodiments thereof, it will be understood by 
those skilled in the art that various changes in form and details may be 
made therein without department from the spirit and scope of the invention 
as defined by the appended claims. For instance, other means for 
generating ultrasound may be used, or the techniques described herein may 
be mixed, e.g., a single crystal transducer and a phased array transducer 
may be combined in the same hyperthermia apparatus. This invention may be 
implemented from a plurality of unfocused transducers, focused 
transducers, or electronically steered and/or focused arrays. A variety of 
waveforms may also be used to drive the plurality of sources. The sources 
may radiate the same waves, different waves, modulated waves, or radiate a 
combination of waves as a means to enhance the nonlinear interaction. 
Although this invention has been described with respect to ultrasound 
hyperthermia of biological tissue, there are other important areas which 
use ultrasound for heating which may benefit from this invention, for 
instance the materials processing industry. Furthermore, this invention 
applies to other types of waves which propagate in a medium in a nonlinear 
manner, or which may otherwise be made to interact in a nonlinear fashion. 
For example, the main discussions herein have referred to acoustic wave 
propagation, which is a longitudinal compression-rarefaction wave. There 
may be instances in material processing where the nonlinear interaction of 
transverse shear waves in solids may benefit from enhanced heating.