Focused ultrasound split-foci control using spherical-confocal-split array with dual frequency of fundamental and harmonic superimposition

Abstract

A spherical-confocal-split array with dual frequency of fundamental and harmonic superimposition includes: array elements which are spherically confocal, whose quantity is an even number, wherein a half of the array elements operate with a lower frequency, and the other half of the array elements operate with a higher frequency; both the lower frequency and the higher frequency are MHz high-frequencies; each of the array elements corresponds to a frequency drive; array element beams don't superimpose outside the focal region; each of the array elements is connected to a channel amplifier (3) through corresponding impedance matching (2); and a multi-channel waveform controller (4) is connected to the channel amplifier (3) for controlling amplitudes and phases of all channels. The dual-frequency spherical sectorial split array is able to generate split multi-foci of the focal plane with the dual frequencies; and control strong interference of transient cavitation clouds at the adjacent foci.

Claims

1. A method of focused ultrasound split-foci control using spherical-confocal-split array with dual frequency of fundamental and harmonic superimposition, which is based on a dual-frequency confocal superimposed focused ultrasonic spherical splitting array, comprising steps of: using spherical sector array elements or spherical rectangle array elements as array elements which are spherically confocal; controlling the array elements to emit dual frequencies at chosen phases for generating focal plane split multi-foci which extend a size of a radial focal region, so as to have a larger focal region than with a single-focus; wherein under dual frequency of second-harmonic superimposition, a sound pressure at the radial focal region is controlled to be higher than a cavitation threshold; wherein a method for controlling amplitude phases of the array elements comprises steps of: defining an array element width as w, defining an array element height as h, and defining an array element area as A; setting an origin of an xyz coordinate at a top point of a spherical cap with a wave beam direction along a z-axis; reckoning a sound pressure p.sub.m of an m-th array element with Reyleigh-Sommerfeld integral, which is calculated with an equation obtained by superimposing N rectangles: $\begin{array}{cc}{p}_m=\frac{j\mathrm{ck}}{2}{u}_m\underset{n=1}{\overset{N}{.Math.}}\frac{F_{n}A}{R_n}{e}^{-\left(+jk\right)R_n}\sin c\frac{{\mathrm{kx}}_{\mathrm{sn}}w}{2R}\sin c\frac{{\mathrm{ky}}_{\mathrm{sn}}h}{2R}.& \left(1\right)\end{array}$ (1) wherein each array element m is divided into N squares with same projected areas, then sound pressures at all points of a focal plane are calculated by the equation (1); wherein in the equation (1), P.sub.m (x, y, z) is a complex sound pressure, j={square root over (1)}, and C are respectively a media density and a sound velocity, k=/c is a wave number, u.sub.m is a surface particle velocity of the m-th array element, which is used as an array element driving signal; wherein parameter calculation are as follows: parameters are: $\begin{array}{cc}{R}_n=\sqrt{{\left(z-z_n\right)}^2+{\left(y-y_n\right)}^2+{\left(x-x_n\right)}^2}& \left(2\right)\\ R=\sqrt{z^2+{\left(y-y_n\right)}^2+{\left(x-x_n\right)}^2}& \left(3\right)\\ R_{\mathrm{PP}}^2=R_{\mathrm{SP}}^2-\left(x_n^2+y_n^2\right)& \left(4\right)\\ R_n=R+\frac{1}{R}\left(R_{\mathrm{SP}}^2-{\mathrm{zR}}_{\mathrm{SP}}+z\right)R_{\mathrm{PP}}-\frac{x_n^2+y_n^2}{2})& \left(5\right)\\ x_{\mathrm{sn}}=x-\frac{z-R_{\mathrm{SP}}}{R_{\mathrm{PP}}}{x}_n& \left(6\right)\\ y_{\mathrm{sn}}=y-\frac{z-R_{\mathrm{SP}}}{R_{\mathrm{PP}}}{y}_n.& \left(7\right)\end{array}$

2. A method of focused ultrasound split-foci control using spherical-confocal-split array with dual frequency of fundamental and harmonic superimposition, which is based on the spherical-confocal-split array with the dual frequency of fundamental and the harmonic superimposition, comprising steps of: using spherical ring array elements as array elements which are spherically confocal; and applying dual frequencies, and controlling a ratio of a high-frequency sound power and a low-frequency sound power, wherein the superimposition of two frequency pressures results in split foci along beam axial within confocal region, and the maximal peak intensity of split foci is larger than the sum of two frequency intensities of the high-frequency sound power and the low-frequency sound power; or applying a dual frequency of third-harmonic superimposition, and controlling the ratio of the high-frequency sound power and the low-frequency sound power; when a phase shift is 60, obtaining maximum superimposed wave positive peak values and negative peak values; wherein a method for controlling amplitude phases of the array elements comprises steps of: defining an array element width as w, defining an array element height as h, and defining an array element area as A; setting an origin of an xyz coordinate at a top point of a spherical cap with a wave beam direction along a z-axis; reckoning a sound pressure p.sub.m of an m-th array element with Reyleigh-Sommerfeld integral, which is calculated with an equation obtained by superimposing N rectangles: $\begin{array}{cc}{p}_m=\frac{j\mathrm{ck}}{2}{u}_m\underset{n=1}{\overset{N}{.Math.}}\frac{F_{n}A}{R_n}{e}^{-\left(+jk\right)R_n}\sin c\frac{{\mathrm{kx}}_{\mathrm{sn}}w}{2R}\sin c\frac{{\mathrm{ky}}_{\mathrm{sn}}h}{2R}.& \left(1\right)\end{array}$ wherein each array element m is divided into N squares with same projected areas, then sound pressures at all points of a focal plane are calculated by the equation (1); wherein in the equation (1), P.sub.m (x, y, z) is a complex sound pressure, j={square root over (1)}, and C are respectively a media density and a sound velocity, k=/c is a wave number, u.sub.m is a surface particle velocity of the m-th array element, which is used as an array element driving signal; wherein parameter calculation are as follows: parameters are: $\begin{array}{cc}{R}_n=\sqrt{{\left(z-z_n\right)}^2+{\left(y-y_n\right)}^2+{\left(x-x_n\right)}^2}& \left(2\right)\\ R=\sqrt{z^2+{\left(y-y_n\right)}^2+{\left(x-x_n\right)}^2}& \left(3\right)\\ R_{\mathrm{PP}}^2=R_{\mathrm{SP}}^2-\left(x_n^2-y_n^2\right)& \left(4\right)\\ R_n=R+\frac{1}{R}\left(R_{\mathrm{SP}}^2-{\mathrm{zR}}_{\mathrm{SP}}+z\right)R_{\mathrm{PP}}-\frac{x_n^2+y_n^2}{2})& \left(5\right)\\ x_{\mathrm{sn}}=x-\frac{z-R_{\mathrm{SP}}}{R_{\mathrm{PP}}}{x}_n& \left(6\right)\\ y_{\mathrm{sn}}=y-\frac{z-R_{\mathrm{SP}}}{R_{\mathrm{PP}}}{y}_n.& \left(7\right)\end{array}$

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1(a) is a sketch view of a dual-frequency confocal spherical sectorial split array and a system thereof; FIGS. 1(b) and 1(c) are respectively a focal plane sound intensity view and a focal plane sound intensity contour map of focal plane split foci generated by the spherical sectorial split array of FIG. 1(a).

(2) FIGS. 2(a) and 2(b) are sketch views of dual-frequency confocal spherical rectangle split arrays with different array element frequency distributions.

(3) FIG. 3 is a sketch view of a dual-frequency confocal spherical ring array.

(4) FIGS. 4(a) and 4(b) are sketch views of dual-frequency confocal spherical vortex split arrays with different array element frequency distributions.

(5) FIG. 5 is sketch view of a system for controlling and detecting focal region cavitation mechanism enhanced by the dual-frequency confocal split array.

(6) FIG. 6 illustrates waveforms and a superimposed waveform of dual frequency of second-harmonic superimposition with inverted phases (180).

(7) FIG. 7(a) is a focal plane sound intensity map of 4 split foci generated by the dual double-frequencies with a spherical 4-sector split array under a 180 phase shift control; and FIG. 7(b) is a focal plane sound intensity contour map.

(8) FIG. 8 illustrates waveforms and a superimposed waveform of dual frequency of second-harmonic superimposition with 135 phase difference.

(9) FIG. 9(a) is a focal plane sound intensity map of 2 split foci generated by the dual frequency of second-harmonic superimposition with the spherical4-sector split array under a 135 phase shift control; and FIG. 9(b) is a focal plane sound intensity contour map.

(10) FIG. 10 illustrates axial sound intensity distribution generated by the dual frequency of second-harmonic superimposition with a spherical 2-ring array, wherein a driving power ratio between f.sub.2 and f.sub.1 is 0.4; strong interference of two frequency waves in the focal region generates about 9 axial split foci, and superimposed sound intensity peak value is about two times of the sum of these two frequency sound intensities.

(11) FIG. 11(a) illustrates axial sound intensities generated by the dual frequency of second-harmonic superimposition with the spherical 2-ring array, wherein the driving power ratio between f.sub.2 and f.sub.1 is 0.4; FIG. 11(b) is x-z sound intensity contour map, and the strong interference of two frequency waves in the focal region generates about 9 axial split foci.

(12) FIG. 12(a) illustrates waveforms and a superimposed waveform of dual frequency of third-harmonic superimposition with 60 phase difference; FIG. 12(b) illustrates waveforms and a superimposed waveform of dual frequency of third-harmonic superimposition with 0 phase difference.

(13) FIG. 13 illustrates axial sound intensity distribution generated by the dual frequency of third-harmonic superimposition with a spherical 2-ring array, wherein a driving power ratio between f.sub.2 and f.sub.1 is 0.28; strong interference of two frequency waves in the focal region generates about 13 axial split foci, and superimposed sound intensity peak value is about two times of the sum of these two frequency sound intensities.

(14) FIG. 14(a) illustrates axial sound intensities generated by the dual frequency of third-harmonic superimposition with the spherical 2-ring array, wherein the driving power ratio between f.sub.2 and f.sub.1 is 0.28; FIG. 14(b) is x-z sound intensity contour map, and the strong interference of two frequency waves in the focal region generates about 13 axial split foci.

(15) FIG. 15 illustrates focal injury experimental results in a transparent phantoms (polyacrylamide gel coined bovine albumin, BSA), caused by the dual frequency of second-harmonic superimposition with the spherical 4-sector split array under 180 and 135 phase shift control, which is obtained by videos, high-speed photography and PCD (passive cavitation detection) (see FIG. 16); wherein, (a), (b) and (c) are results of the 180 phase shift control; (a) and (b) are video images, and (c) is a high-speed photography image; (d), (e) and (f) are results of the 135 phase shift control; (d) and (e) are video images, and (f) is a high-speed photography image.

(16) FIG. 16 illustrates focal injury PCD results in the transparent phantoms (polyacrylamide gel coined bovine albumin, BSA), caused by the dual frequency of second-harmonic superimposition with the spherical 4-sector split array under 180 and 135 phase shift control, wherein after comb-like filter, a mean square value of wideband signals with harmonic filtered reflects focal region transient cavitation (inertial cavitation) energy.

(17) FIG. 17 illustrates focal injury experimental results in the transparent phantoms (polyacrylamide gel coined bovine albumin, BSA), caused by the dual frequency of second-harmonic superimposition with the spherical 2-ring split array, wherein (a) is video results generated by the dual frequency of second-harmonic superimposition with 135 phase shift control and the driving power ratio between f.sub.2 and f.sub.1 is APf.sub.2/APf.sub.1=0.371; and illustrates the dual frequency of third-harmonic superimposition with same structural parameters of the spherical 2-ring array and the driving power ratio between f.sub.2 and f.sub.1 is APf.sub.2/APf.sub.1=0.28; (b) is results of 0 phase shift control; and (c) is 60 shift phase control

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

(18) Referring to FIGS. 1(a)-5, the present invention provides a spherical-confocal-split array with dual frequency of fundamental and harmonic superimposition, comprising: array elements which are spherically confocal, whose quantity is an even number (2-12), wherein a half of the array elements operate with a lower frequency, and the other half of the array elements operate with a higher frequency; both the lower frequency and the higher frequency are MHz high-frequencies (1 MHz-10 MHz); each of the array elements corresponds to a frequency drive; each of array element beams only superimposes inside a focal region instead of outside the focal region; each of the array elements is connected to a channel amplifier 3 through corresponding impedance matching 2; and a multi-channel waveform controller 4 is connected to the channel amplifier 3 for controlling amplitudes and phases of all channels.

(19) The array elements, which are spherically confocal, may be a spherical sector array 1 (shown in FIG. 1(a)), a spherical rectangle array 5 or 6 (shown in FIGS. 2(a) and 2(b)), a spherical ring array 7 (shown in FIG. 3), or a spherical vortex array 8 or 9 (shown in FIGS. 4(a) and 4(b)).

(20) A method for controlling amplitude phases of the array elements comprises steps of:

(21) defining an array element width as w, defining an array element height as h, and defining an array element area as A; setting an origin of an xyz coordinate at a top point of a spherical cap with a wave beam direction along a z-axis; reckoning a spherical rectangle sound pressure p.sub.m of an m-th array element by:

(22) $\begin{array}{cc}{p}_m=\frac{j\mathrm{ck}}{2}{u}_m\underset{n=1}{\overset{N}{.Math.}}\frac{F_{n}A}{R_n}{e}^{-\left(+jk\right)R_n}\sin c\frac{{\mathrm{kx}}_{\mathrm{sn}}w}{2R}\sin c\frac{{\mathrm{ky}}_{\mathrm{sn}}h}{2R}.& \left(1\right)\end{array}$

(23) wherein each array element m is divided into N sufficiently small squares with same projected areas, then sound pressures at all points of a focal plane are calculated by the equation (1);

(24) wherein in the equation (1), P.sub.m (x, y, z) is a complex sound pressure, j={square root over (1)}, and C are respectively a media density and a sound velocity, k=/c is a wave number, u.sub.m is a surface particle velocity of the m-th array element, which is used as an array element driving signal; wherein parameter calculation are as follows:

(25) parameters are:

(26) $\begin{array}{cc}{R}_n=\sqrt{{\left(z-z_n\right)}^2+{\left(y-y_n\right)}^2+{\left(x-x_n\right)}^2}& \left(2\right)\\ R=\sqrt{z^2+{\left(y-y_n\right)}^2+{\left(x-x_n\right)}^2}& \left(3\right)\\ R_{\mathrm{PP}}^2=R_{\mathrm{SP}}^2-\left(x_n^2+y_n^2\right)& \left(4\right)\\ R_n=R+\frac{1}{R}\left(R_{\mathrm{SP}}^2-{\mathrm{zR}}_{\mathrm{SP}}+z\right)R_{\mathrm{PP}}-\frac{x_n^2+y_n^2}{2})& \left(5\right)\\ x_{\mathrm{sn}}=x-\frac{z-R_{\mathrm{SP}}}{R_{\mathrm{PP}}}{x}_n& \left(6\right)\\ y_{\mathrm{sn}}=y-\frac{z-R_{\mathrm{SP}}}{R_{\mathrm{PP}}}{y}_n.& \left(7\right)\end{array}$

(27) The focused ultrasound split-foci control using spherical-confocal-split array with dual frequency of fundamental and harmonic superimposition is specifically described as follows.

(28) 1) For the spherical sector array 1: the quantity of the array elements is an even number (2-12), the dual frequencies are MHz high-frequencies (1 MHz-10 MHz); frequencies of all the array elements are shown in FIG. 1(a), wherein the array elements with different frequencies are arranged alternatively, or f.sub.2 array elements are arranged on one side (left side) and f.sub.1 array elements are arranged on the other side; f.sub.2/f.sub.1=n, n=2,3 . . . integer.

(29) Referring to FIG. 1(a), 6 array elements are provided. With dual frequencies and phase control, the 6 array elements provide 6 split foci on the focal plane. Therefore, radial distribution of multi-focus is expanded, so as to be 8 times than single-focus during treatment.

(30) Generally, a focal region sound pressure negative peak value is set to be higher than a cavitation threshold, which can be concluded from FIG. 1(b) which illustrates calculation simulation of the equation (1). Under a dual frequency of second-harmonic superimposition condition, if adjacent array elements are inversely controlled, then peak points of adjacent foci on the focal plane inversely vibrate, and the distance between the adjacent foci is one wavelength of fundamental frequency; if cavitation clouds are located at these two foci, a positive peak cavitation is closed (collapsed) at one focus, and a negative peak is maximally expanded, wherein wideband signals launched by cavitation whose previous vibration period is closed (collapsed) will reach such maximum cavitation, so a thermal absorption efficiency is highest, which is a cavitation strong interference.

(31) Effects of ultrasonic cavitation, especially transient cavitation (or inertial cavitation), enable a thermal ablation to be at least 6 times higher than the one without cavitation. The present invention takes full advantage of such ultrasonic cavitation mechanism for providing high-efficiency precise treatment. Firstly, the present invention provides simultaneous superimposition of confocal dual-frequency ultrasound in the focal region, wherein the dual frequencies are both MHz high-frequencies with an integral-multiple relationship, such as 1 MHz and 2 MHz, or 1 MHz and 3 MHz. The dual-frequency is suitable for a continuous wave or a pulse wave with a string length of more than 10 wave numbers. Dual-frequency wave superposition in the focal region will lower the cavitation threshold, wherein the cavitation threshold is lower than that of a low-frequency wave, while the transient cavitation and cavitation thermal absorption are strengthened. Referring to the dual frequency of second-harmonic superimposition in FIG. 6, each low-frequency periodic wave peak superposition increases, and the negative peak value also increases. Meanwhile, velocity is faster and increase of the negative peak will generate more cavitation. Spherical array elements are able to provide confocal control. Each of the array elements only superimposes inside the focal region instead of outside the focal region. Therefore, array element transducers with compact distribution of spherical sector, rectangle, ring and vortex array elements are used. With a single frequency, the spherical sector array will generate separated annular array multi-foci, and each array element corresponds to one focus, namely the split focus and the split array. Focal region volume expansion is equal with such multi-foci and multi-foci generated by a phased array comprising 128 or 256 array elements, but only by controlling the phases of a few spherical sector arrays, the focal region volume will be expanded by the split foci.

(32) 2) For the spherical rectangle array 5 or 6: referring to FIGS. 2(a) and 2(b), all characteristics and control thereof are the same as that of the spherical sector array.

(33) 3) For the spherical ring array 7: referring to FIG. 3, the quantity of the array elements is 2; under a certain ratio of sound power amplitudes of the dual frequencies, a plurality of the split foci are generated along the acoustic axis in the focal region; and dual-frequency superimposed sound intensity peak value is nearly two times of a sum of these two frequency sound intensities, which indicates strong interference of dual-frequency sonic wave.

(34) A precise axial sound pressure equation of a sound pressure of the spherical ring array 7 along the acoustic axis is able to be obtained by Reyleigh-Sommerfeld integral, so as to obtain a precise sound pressure equation, wherein axial sound pressure equation of each ring is:

(35) $\begin{array}{cc}P\left(z\right)=\{\begin{array}{cc}j{\mathrm{ckR}}_{\mathrm{SR}}u\frac{\begin{array}{c}{e}^{-\left(+jk\right)\sqrt{{\left(z-R_{\mathrm{SR}}+\sqrt{R_{\mathrm{SR}}^2-R_2^2}\right)}^2+R_2^2}-}\\ e^{-\left(+jk\right)\sqrt{{\left(z-R_{\mathrm{SR}}+\sqrt{R_{\mathrm{SR}}^2-R_1^2}\right)}^2+R_1^2}}\end{array}}{\left(z-R_{\mathrm{SR}}\right)\left(+jk\right)}& \mathrm{if}z{R}_{\mathrm{SR}}\\ j\mathrm{cku}\left(\sqrt{R_{\mathrm{SR}}^2-R_1^2}-\sqrt{R_{\mathrm{SR}}^2-R_2^2}\right)e^{-\left(+jk\right)R_{\mathrm{SR}}}& \mathrm{if}z=R_{\mathrm{SR}}\end{array}& \left(2\right)\end{array}$

(36) wherein a wave number:

(37) $k=\frac{}{c}=\frac{2f}{c};$
is an attenuation coefficient; R.sub.SR is a radius of curvature of each ring; R.sub.1 is a radius of an inner hole of each ring, R.sub.2 is a radius of an outer ring of each ring; and u is an array element surface vibration velocity which is proportional to an array element driving sound pressure.

(38) Sound pressure calculation of two frequency rings is: firstly using the equation (2) to calculate the sound pressure of each frequency ring, and then adding to obtain axially sound pressure of the spherical ring array 7.

(39) With a certain frequency amplitude ratio, strong cavitation interference at a plurality of the foci is able to be obtained under two frequency phases.

(40) 4) For spherical vortex array 8 or 9: referring to FIGS. 4(a) and 4(b), the quantity of the array elements is an even number (4, 8 or 12); all control methods are the same as that of the spherical sector array 1; like the spherical sector array elements, split multi-foci on focal plane are generated for expanding the focal region treatment volume, and sound power ratio of the dual frequencies is adjustable for obtaining axial high sound intensity of the split foci.

(41) Driving controls of the spherical rectangle, ring and vortex arrays have a same structure as the driving control of the spherical sector array as shown in FIG. 1(a).

(42) An experimental system according to preferred embodiments of dual-frequency split focus modes of the above split arrays are shown in FIG. 5, wherein HIFU focus mode ultrasonic cavitation in transparent tissue phantom contained bovine albumin (BSA) may be estimated by a cavitation high-speed camera 15, and a PCD or ultrasound imaging device 14; a host computer 13 is responsible for controlling the split focus modes, the cavitation high-speed camera 15 and the PCD (passive cavitation detection) 14; the host computer 13 sends phase and amplitude information of a dual-frequency split focus mode to a channel power amplifying and control unit 12 which generates waveforms needed by each array element and sends to a split array transducer 10 through as array element matching network 11; the split array transducer 10 sends the split focus modes.

(43) According to a preferred embodiment 1, the split array is the spherical 4-sector array (see element 1, FIG. 1(a)), wherein the dual frequencies of second-harmonic superimposition are f.sub.1=1.2 MHz and f.sub.2=2.4 MHz, and frequency distribution of the array elements are f.sub.2 array elements on one side (left side) and f.sub.1 array elements on the other side (see element 5, FIG. 2(a)). FIG. 6 illustrates waveforms and a superimposed waveform of the dual frequency of second-harmonic superimposition with inverted phases (180), wherein after superposition, the positive peak value increases, and the negative peak value also increases. Meanwhile, the velocity is faster and increase of the negative peak will generate more cavitation. FIGS. 7(a) and 7(b) illustrate the sound intensity distribution of the 4 split foci generated by the adjacent array elements with opposite phases, which proves that dual frequencies of second-harmonic superimposition are also able to produce 4 split foci, while such control ensures that the focal region sound pressure is higher than the cavitation threshold. The adjacent foci on the focal plane inversely vibrate, and the distance between the adjacent foci is one wavelength of fundamental frequency; cavitation cloud strong interference at the adjacent foci is generated under a transient cavitation condition, so as to obtain efficient transient cavitation thermal conversion results. For the same spherical 4-sector array, if adjacent same frequency array elements have equal phases (0), and adjacent array elements with dual frequency of second-harmonic superimposition have a low-frequency phase difference of 135, waveforms and a superimposed waveform of dual frequency of second-harmonic superimposition with 135 phase difference is shown in FIG. 8, wherein after superimposition, the positive wave is widened while its peak value doesn't increase, and two negative peaks superimpose to provide a maximum superimposed negative peak value, which is most conducive to generating more cavitation. FIGS. 9(a) and 9(b) illustrate the sound intensity distribution of the 2 split foci whose adjacent same frequency array elements have equal phases (0), and adjacent array elements with dual frequency of second-harmonic superimposition have a phase difference of 135.

(44) According to a preferred embodiment 2, the split array is the spherical 2-ring array (see element 7, FIG. 3), wherein the dual frequencies of second-harmonic superimposition are f.sub.1=1.1 MHz and f.sub.2=2.2 MHz. As a result, there is no focal plane radially split focus, and a confocal superposition result is only focal region superimposition. With the precise axial sound pressure equation (2), axial sound pressure superimposed results are obtained, as shown in FIG. 10. Due to sufficient dual-frequency focal region coverage, strong interference is generated by two waves at the focal region, resulting in about seven split foci in the focal region superimposed results, and the distance between the adjacent foci is one wavelength of fundamental frequency. The split foci generated depend on the ratio of the high-frequency and low frequency sound power instead of the dual-frequency phases. When the ration is APf.sub.2/APf.sub.1=0.4, then strong interference is generated by two waves. At this time, the peak value of sound intensity of split foci produced by the superimposition of dual frequency is larger than the sum of two frequency intensities, and is nearly twice of the sum. The results of waveform superimposition of this dual frequency of second-harmonic superimposition are similar to those of the sector array which are shown in FIGS. 6 and 8, which means when the phase shift is 135, the negative peak superimposition is maximized and cavitation generation is best. When the phase shift is 135, the adjacent foci inversely vibrate, and cavitation cloud strong interference at the two foci is generated under a transient cavitation condition. FIGS. 11(a) and 11(b) illustrate focus sound intensity distribution of the spherical 2-ring array, wherein FIG. 11(a) illustrates the focus sound intensity distribution on the focal plane, wherein sound power control based on such array elements ensures that the focal region sound pressure is higher than the cavitation threshold during experiment; and FIG. 11(b) illustrates 7 axial split foci.

(45) According to a preferred embodiment 3, the split array is the spherical 2-ring array (see element 7, FIG. 3), wherein the dual frequencies of third-harmonic superimposition are f.sub.1=1.1 MHz and f.sub.2=3.3 MHz. When it comes to waveform superimposition, one phase superposition of the dual frequency of third-harmonic superimposition is most conducive to cavitation efficiency, wherein when a low-frequency wave phase is 60, two positive peaks encounter as well as two negative peaks, so both are maximized, which is conducive to cavitation generation and collapse, see FIG. 12(a); when the low-frequency wave phase is 0, the positive and negative peaks encounter, so peak values are minimized, see 12(b). FIG. 13 shows when the ration is APf.sub.2/APf.sub.1=0.4, then strong interference is generated by the two waves, about 13 split foci are generated due to superimposition, and the distance between the adjacent foci is a half wavelength of fundamental frequency. FIGS. 14(a) and 14(b) illustrate focus sound intensity distribution of the spherical 2-ring array with dual frequency of third-harmonic superimposition, wherein FIG. 14(a) illustrates the focus sound intensity distribution on the focal plane, wherein sound power control based on such array elements ensures that the focal region sound pressure is higher than the cavitation threshold during experiment; and FIG. 14(b) illustrates 13 axial split foci.

(46) According to the preferred embodiment 1, experimental results of the dual frequency of second-harmonic superimposition with the spherical 4-sector split array under 180 and 135 phase shift control are shown in FIG. 15 which illustrates two best split focus modes. In the 180 mode, a shape of the cavitation clouds strong interference at the four foci is shown in FIG. 15(c), wherein cavitation clouds at the four foci rapidly move towards the transducer in parallel, and generate effective thermal ablation as shown in FIG. 15(b). FIGS. 5(c) and 5(b) are similar, indicating effective cavitation thermal ablation. In the 135 mode, there is a large cavitation region at two foci in the focal region, and a shape of the cavitation clouds strong interference is shown in FIG. 15(f), wherein cavitation clouds at the two foci rapidly move towards the transducer in parallel, and generate effective thermal ablation as shown in FIG. 15(e). FIGS. 5(f) and 5(e) are similar, indicating effective cavitation thermal ablation. Although a total sound power of the 135 mode is lower than that of the 180 mode, namely 0.8 times, damage sizes during final 10 s are both about 10 mm10 mm11 mm, indicating that the 135 mode produces more cavitation and stronger cavitation effect. The injury experiments with 180 and 135 phase shift control are simultaneously detected by PCD, and results thereof are shown in FIG. 16. After comb-like filter, a mean square value of wideband signals with harmonic filtered reflects focal region transient cavitation (inertial cavitation) energy. Referring to FIG. 16, 135 phased inertial cavitation energy is slightly higher than 180 phased inertial cavitation energy, proving that the 135 mode produce more cavitation and stronger cavitation effect.

(47) FIG. 17(a) illustrates experimental results of the spherical 2-ring split array with the dual frequency of second-harmonic superimposition, wherein treatment parameters are: dual frequency of second-harmonic superimposition of f.sub.1=1.1 MHz and f.sub.2=2.2 MHz, 135 phase shift, a low-frequency sound power of 70 w, a high-frequency sound power of 26 w, and a treatment period of 10 s. A damage size shown is 3 mm3 mm8.7 mm, wherein because cavitation damages are caused faster at the split foci on the acoustic axis of the focal region, an overall damage shape is cylindrical, which is suitable for focus arrangement during treatment planing.

(48) With same spherical 2-ring array structural parameters, FIGS. 17(b) and 17(c) illustrate experimental results with dual frequency of third-harmonic superimposition, wherein treatment parameters are: dual frequency of third-harmonic superimposition of f.sub.1=1.1 MHz and f.sub.2=3.3 MHz, 60 and 0 phases shift, a low-frequency sound power of 70 w, a high-frequency sound power of 20 w, and a treatment period of 10 s. 0 phase shift damage is shown in FIG. 7(b), wherein a damage size is 3.6 mm3.6 mm8 mm. 60 phase shift damage is shown in FIG. 7(c), wherein a damage size is 4.4 mm4.4 mm10.8 mm. With the dual frequency of third-harmonic superimposition, although a high-frequency sound power is 6 w lower, but the damage size is larger than the one with dual frequency of second-harmonic superimposition, wherein with 0 phase shift, the dual frequency of third-harmonic superimposition damage size is 1.3 times of the dual frequency of second-harmonic superimposition damage size; with 60 phase shift, the triple-frequency damage size is 2.6 times of the dual frequency of second-harmonic superimposition damage size. High-frequency increase and closer split foci may be a reason for damage size increase. The dual frequency of third-harmonic superimposition damage size is largest with 60 phase shift because the superimposition of these two frequencies makes the superimposed positive and negative peak values maximal, thus generating more and stronger cavitation.