IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 38. NO. 7, JULY 1991

A Spherical-Section Ultrasound Phased Array Applicator for Deep Localized Hyperthermia Emad S . Ebbini, Member, IEEE, and Charles A. Cain, Fellow, IEEE

Abstract-Computer simulation shows that a new ultrasound phased-array with nonplanar geometry has considerable potential as an applicator for deep localized hyperthermia. The array provides precise control over the heating pattern in three dimensions. The array elements form a rectangular lattice on a section of a sphere. Therefore, the array has a natural focus at its geometric center when all its elements are driven in phase. When compared to a planar array with similar dimensions, the spherical-section array provides higher focal intensity gain which is useful for deep penetration and heat localization. Furthermore, the relative grating-lobe level (with respect to the focus) is lower for scanned foci synthesized with this array (compared to a planar array with equal center-to-center spacing and number of elements). This could be the key to the realization of phased-array applicator systems with a realistic number of elements. The spherical-section array is simulated as a spot-scanning applicator and, using the pseudo-inverse pattern synthesis method, to directly synthesize heating patterns overlaying the tumor geometry. A combination of the above two methods can be used to achieve the desired heating pattern in the rapidly varying tumor environment.

I. INTRODUCTION ASED ARRAYS show increasing promise as versatile applicators for deep localized hyperthermia cancer therapy [ 11-[3]. Their ability to focus and steer ultrasonic energy in the treatment volume without physically moving the applicator assembly gives phased arrays a unique advantage over mechanically scanned applicators. Furthermore, phased arrays can be used to directly synthesize useful heating patterns tailored to the tumor geometry [2]-[4]. Direct synthesis of heating patterns can also be achieved with complex lens structures [5]. However, lens-focused transducers lack the flexibility of phased arrays in adapting to changes in the heating requirements, e.g., due to temporal and spatial variations in blood perfusion. Direct synthesis of heating patterns is advantageous in reducing the spatial-peak temporal-peak intensity required to produce the desired time-average heating pattern. This might be necessary to avoid certain nonlinear phenomena associated with high intensity ultrasound,

p"

Manuscript received June 4, 1990; revised October I , 1990. This work was supported in part by grant CA44124 from the National Institutes of Health, an Award from Hitachi Central Research Laboratory. Hitachi Ltd.. Tokyo, Japan, and Grant ECS870001 from the National Center for Supercomputing Applications (NCSA) at the University of Illinois. The authors are with the Department of Electrical Engineering and Computer Science, The University of Michigan, Ann Arbor, MI 48109. IEEE Log Number 9100502.

e.g., intensity saturation [ 6 ] , [7]. Simulation results presented in [7] for spherically focused transducers with Gaussian beam profiles indicate that nonlinear propagation can enhance the power deposition in the treatment volume. This is due to the fact that nonlinear wave propagation is associated with the generation of higher order harmonics which have higher absorption coefficients. The enhancement in power deposition depends on several factors, e.g., absorption coefficient, initial cross section of the wavefront, focal depth, etc. It should be noted, however, that this enhancement in power deposition can be achieved at certain focal intensity levels. The opposite effect can occur when much higher focal intensity levels are attempted. In such cases, higher order harmonics will be absorbed in the intervening tissue before reaching the focus (intensity saturation). At any rate, the general conclusion of the simulation study performed in [7] is that there exist optimal focal intensity levels at which nonlinear wave propagation can be used to enhance the power deposition in the tumor volume. Therefore, direct synthesis of multiple-focus field pattern can be useful not only to avoid intensity saturation, but also to enhance the power deposition in the tumor by operating at the optimal focal intensity level. An important consideration determining the choice of an applicator system for deep localized hyperthermia is the intensity gain. This is a measure of the ratio of the focal intensity (spatial-peak intensity) to the average intensity at the applicator surface. The intensity gain of a focused beam should be high enough to ensure sufficient power deposition in the target volume (in the focal region) while the tissues proximal and distal to the focus are subjected to lower intensity resulting in localized heating in the tumor volume [8]. Recent implementations of applicator systems for deep localized hyperthermia have taken this factor into account in one way or another. For example, the scanned focussed multiple-transducer system used at the University of Arizona utilizes four focused transducers that can be geometrically focused at a small volume deep into the body [9]. As another example, the Helios system currently being investigated at Mallinckrodt Institute of Radiology utilizes 30 focused transducers distributed in four rings on a spherical surface [lo]. In both of these systems the transducer assembly is mounted on a gantry which can be mechanically scanned with several degrees of freedom. Multiple-transducer applicators provide the necessary intensity gain for deep penetration.

00 I8-9294/9 1/0700-0634$0 I .OO 0 199 I IEEE

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EBBlNl AND CAIN: APPLICATOR FOR LOCALIZED HYPERTHERMIA

Furthermore, they can compensate for the effects of inhomogeneities of the treatment volume. Phased-array applicators provide the above advantages (since they are multiple-transducer applicator systems). Phased arrays have the additional advantage of directly synthesizing heating patterns which can be optimized to achieve maximum intensity gain (a definition of intensity gain for multiple-focus field patterns is given below). The maximization of intensity gain is essential to the direct synthesis of heating patterns with minimum high intensity interference outside the target volume. This paper introduces a nonplanar phased-array as a potential applicator for deep localized hyperthermia. The array is composed of rectangular transducer elements forming a rectangular lattice on a section of a sphere and is, therefore, called the spherical-section array (SSA). The SSA has two distinct advantages as a spot-scanning applicator. First, it produces focal spots characterized by high intensity gain (useful for deep penetration) and small effective size (useful for heat localization). Secondly, the grating lobes associated with steered foci typically have intensity levels well below that of the focal spot even for arrays with center-to-center spacing over 3h ( h is the wavelength of the acoustic signal). This allows for the realization of a phased-array applicator with a realistically small number of elements. Simulation results presented below show the characteristic focus, steered focus and scanned field pattern produced by the SSA. Also the direct synthesis of multiple-focus heating patterns with and without gain maximization is discussed and illustrated with numerical simulations. 11. THE SPHERICAL-SECTION ARRAY

Array Geometry Fig. 1 shows an isometric view of the SSA. The array consists of N square elements each of width w distributed in N,. rows and N, columns ( N = N , x N , ) over a spherical section of radius R , angular opening 24clboth transversely and laterally. The contribution of the nth element of the array (located at the n,.th row and n, th column) to the complex pressure at an observation point defined by r = [x,y, z]' (the superscript t denotes the transpose) can be computed using the rectangular radiator method [ 1 11. This is most conveniently achieved by transforming the observation point r to a coordinate system centered at the nth element [2]. The total pressure produced by the array at r is the algebraic sum of the contributions of the individual array elements at that point. Array Dimensions The array simulaTed in this paper has N,. = 16 and N,. = 16, i.e., N = 256 square elements with w = 6 mm. The radius of curvature of the array was 120 mm and its angular opening was 60". The aperture of the array was nearly 120 by 120 mm. With these dimensions, the array can provide up to 460 W of power at its syrface assuming a maximum surface intensity of 5 W/cmL.

635

P I

Fig. 1 . Isometric view of the spherical-section array

111. COMPUTATION OF THE ARRAY EXCITATION VECTOR

The pseudoinverse pattern synthesis method provides a useful technique for the generation of precision heating patterns for hyperthermia [4]. The method determines the "minimum-energy " excitation vector capable of producing specified power deposition levels at a set of control points in the treatment volume. When the number of control points is smaller than the number of elements of the array, the pseudoinverse method yields the minimumnorm solution U =

H*'(HH*')-'~

(1)

wherep[ p l ( r l ) , p 2 ( r 2 ) ., * , p M ( r M )specifies ]' thecomplex pressure at the control points U , = [ U , , u 2 , * * , UN]' is the complex excitation vector (phase and amplitude distribution of the driving signals to the array elements), and the M X N matrix H is a forward propagation operator from the surface of the array to the set of control points. The matrix element H(m, n ) represents the complex pressure at the mth control point due to the nth element of the array when excited by a zero-phase unit- amplitude driving signal. The matrix H*' is the conjugate transpose of H (Adjoint). It is a backpropagation operator from the control-point space to the array surface [4]. The vectorp specifies the complex pressures at the control points. Our interest, however, is in the power deposition at these points rather than the complex pressures. Since the power deposition is a phase insensitive quantity, we are free to choose any phase values of the complex pressures at the control points. One would naturally be interested in finding the phase distribution that is optimum in some sense. We choose the phase distribution that maximizes the intensity gain at the control points, defined as G = -P*'P u*'u

which is a measure of energy concentration at the control points. Substituting for U by the minimum-norm solution

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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING. VOL. 38, NO. 1. JULY 1991

in (I), we obtain

where Q,(r) is the power deposition pattern associated with the Zth field pattern given by [ 121 (3)

P ( d P* (4 Qi(4

The problem is to choose the phases of the complex pressures at the control points such that G is maximized. An iterative algorithm for solving this problem is given in [ 2 ] . However, a suboptimal direct solution can be obtained by observing that the vectorp which maximizes (3) is the eigenvector p corresponding to the largest eigenvalue of HH*‘ (the largest singular value of H ). Since the amplitude distribution of the elements o f p does not necessarily correspond to the specified power deposition at the control points, we choose the elements of the vector p such that

where the I pm1’s are the specified amplitudes of complex pressure at the control points. The new vector of complex pressures at the control points is used to determine the excitation vector with enhanced gain according to ( 2 ) . This technique provides a fast direct method for maximizing the intensity gain. It should be noted that the maximum achievable intensity gain G,,, is fully determined by the spatial distribution of the control points and is proportional to the largest singular value of the propagation operator H . Therefore, it is possible to determine how “close” G given by (3) gets to the optimal value G,,, for a given choice of complex elements of p. Based on simulation results from different array structures and different synthesized patterns, this method typically results in significant increase in the intensity gain. IV. HEATING PATTERNGENERATION Electronic scanning is achieved by sequentially switching the array excitation vector to produce one of a series of predetermined field patterns. The spatio-temporal average of the scalar sum of the power deposition patterns of the individual focal points produces the desired timeaverage power deposition pattern throughout the treatment volume. This approach applies for both single-focus scanning and multiple-focus scanning. The main difference between multiple-focus scanning and single-focus scanning is that the “snapshot” at one time instant of the multiple-focus field pattern has more than one focal spot. Assume that there exist Nf field patterns each containing nf focal points (nf = 1 for single-focus scanning). The Nf field patterns are periodically scanned with a scan period smaller than the thermal time constants of the tissues in the treatment region. Assuming equal dwell times at each of the field patterns, the time-average power deposition in the treatment volume is given by 1

Q,, (r) = ~f

NJ

Q/(@

(5)

=

Q!

p 9

Po c

(6)

where Q! is the absorption coefficient, p ( r ) is the complex pressure, and po and c are the density and the speed of sound of the medium, respectively. The total power dissipated inside the tumor volume is approximated by n f x N/

PI =

r=l

Q,V,

(7)

where Q, is the power deposition at the ith focal point, and V, is the effective volume of the ith focal spot (in terms of its 3-dB dimensions). Simulation results show that the effective size of the focal spot remains essentially constant for a wide range of scan trajectories in the near field of the array, i.e., V, = Vf for all focal points in the scan trajectory. Assuming equal power deposition at each focal point, PI can be written as

Pt

=

nf

X

NfVfQf

(8)

where Qf is the power deposition level at each focal point. Typically, PI is estimated to achieve and sustain a specified level of hyperthermia inside a tumor with specified volume [13]. This defines the power deposition level at the focal points in the scanned field

(9) The basic difference between single-focus scanning and multiple-focus scanning is in the spatial-peak pulse-average intensity, ZSPPA, level needed to achieve the same power deposition level at a focal (control) point. This can be shown easily by finding an expression for the ZsppA needed to achieve a certain power deposition level in the tumor. The power deposition at the focus is given by 2Q!zSPPA

Q f = p . Nf Substituting for Qf in (91, one obtains ISPPA

p, 2anf Vf

=-

(10)

which shows that the use of multiple-focus field patterns reduces the spatial-peak pulse-average intensity level required to achieve a specified power deposition level in the tumor. This can be advantageous in avoiding certain nonlinear phenomena associated with high intensity ultrasound, e.g., intensity saturation. V. SIMULATION RESULTS The array described in Section I1 above was simulated at a frequency of 500 kHz. The array was assumed to radiate into a homogeneous lossy medium in which the

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(b)

Fig. 2 . Intensity profile of the characteristic focus of the SSA. ( a ) z plane. (b) Focal plane.

speed of sound and attenuation are given by 1500 m / s and 1 dB/cm/MHz, respectively. Fig. 2 shows the intensity profiles of the characteristic focus of the SSA. This focus is formed at the geometric center of the array (depth 120 mm) when the driving signals have uniform phase and amplitude distribution. The intensity gain at the focus is 23.8 dB. The focal spot extends nearly 4 mm laterally and 20 mm longitudinally (6-dB dimensions). The high intensity gain of this focused beam is advantageous for deep penetration while its small size is useful for heating localization. The characteristic focus of the array provides a good indicator of its usefulness as a scanning applicator. However, electronic scanning of focused beams is typically associated with two phenomena which can seriously limit this usefulness. These factors are the reduction of the focal intensity gain and the appearance of unwanted grating lobes away from the focus (i.e., outside the target volume). A good array design minimizes the loss in intensity gain upon scanning and results in a grating-lobe level well

=

0

below that of the main focus. To examine the quality of the steered foci produced by the SSA, the array was focused at a point 120 mm deep and 20 mm off center (x = 20 mm). The resulting intensity profile is shown in Fig. 3. The dimensions of the shifted focus are (for all practical purposes) the same as those of the characteristic focus. The intensity gain at the shifted focus was 22.1 dB (i.e., intensity gain loss of 1.7 dB compared to the characteristic focus). A grating lobe can now be seen opposite to the main focus (x = -25 mm) with an intensity level of -8 dB below the main focus. The intensity gain of the shifted focus is still sufficient for deep penetration. Furthermore, for most scan path geometries, the relative power deposition due to grating lobes (with respect to that due to the foci) can be expected to be reduced in the scanned field. This can be achieved by choosing the scan trajectory that results in a minimum overlap between grating lobes. Such a choice of scan trajectory is possible because the grating-lobe phenomenon is well understood [ 11, [ 141. Therefore, the intensity level

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Fig. 3. Intensity profile of a shifted focus produced by the SSA in the z = 0 plane.

of the grating lobe (in this case - 8 dB) is not expected to produce a hot spot outside the tumor volume. This claim is supported by several thermal simulations, using the bioheat transfer equation (BHTE), of scanned field patterns generated using different phased-array geometries [ U , r21, ~ 4 1 . As an example of a scanned field pattern, the SSA was simulated to scan a 24 mm diameter circular path parallel to the aperture of the array at a depth of 105 mm from the array vertex. The scanned field pattern was generated by sequentially and periodically focusing at 20 points uniformly distributed around the circular trajectory which can be used in heating a 30 mm diameter tumor. The resulting power deposition pattern is shown in Fig. 4. The power deposition profile was calculated according to ( 5 ) with Nf = 20. The individual focal spots forming the scan trajectory can be seen in Fig. 4(a) which shows the power deposition pattern in a plane parallel to the aperture of the array at a depth of 105 mm. Fig. 4(b) shows the power deposition pattern in the z = 0 plane which shows the lateral and longitudinal distribution of the power deposition in the treatment volume. The two peaks appearing in this profile correspond to two opposing foci along the circular path. One can clearly see that the power deposition buildup in the intervening tissue between the array and the tumor is well below the power deposition level in the tumor. This is due to the high focal intensity gain provided by the SSA. This can be appreciated by comparing these results with our previous results obtained with the cylindrical-section array [l]. One can also see that the power deposition outside the tumor due to the grating lobe is insignificant ( - 10 dB below the power deposition level in the tumor). The results shown in Fig. 4 indicate that the SSA can be used as a scanning applicator which can produce highly localized heating patterns at depth. However, the focal intensity needed to produce therapeutic heating in the

scanned field might be on the order of 100 W/cm2 or more which might be objectionable under some circumstances. The focal intensity in this case is 20 times higher than the time-average intensity in the scanned field. This is due to the spatio-temporal average in ( 5 ) . This problem can be eliminated by direct synthesis of the desired heating pattern. To illustrate this, the focal points used along the scan trajectory defined above were defined as control points and the excitation vector to the SSA was computed using the pseudoinverse pattern synthesis method. The power deposition levels at the control points were assumed to be equal. The phases of the pressures at the control points were determined using the gain maximization technique. The resulting intensity profile of the synthesized pattern is shown in Fig. 5 . The spatial-peak focal intensity (at the control points) is equal to the time-average intensity since N f = 1 in ( 5 ) . The focusing of energy at the control points can be seen from Fig. 5(a) which shows the power deposition pattern in the focal plane. Fig. 5(b) shows the intensity profile in the z = 0 plane which shows that the power deposition mainly occurs in the tumor volume. Comparing Fig. 4 with Fig. 5 , one can easily conclude that both single-focus scanning and direct synthesis result in equivalent power deposition profiles near the control points. Therefore, the same value of total power dissipation inside the tumor can be achieved using either single-focus scanning or direct synthesis. This can be seen by examining (8) where nf X Nf = 20 for both methods (for scanning Nf = 20 and nf = 1 and for direct synthesis Nf = 1 and nf = 20.) The intensity profiles shown in Fig. 5 illustrates the main advantage of using the gain maximization technique. The desired pattern was obtained in the focal plane where the control points are specified. The complex pressure distribution at the control points results in eliminating any significant constructive interference outside of the focal plane. For example, if the complex pressures at the

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639

(a)

Fig. 4. Intensity profiles of a scanned field pattern (20 focal points along a 24 m m diameter circular trajectory in a plane parallel to the aperture of the array). (a) Plane containing scan trajectory. (b) := 0 plane.

control points were chosen to be in phase, an axial interference pattern forms prior to and beyond the focal plane. The intensity level of this axial interference can exceed the intensity level over the synthesized ring in the focal plane. The presence of an axial interference pattern associated with the synthesis of a ring pattern (with equiphase pressures specified at the control points) can be predicted theoretically; using Huygens' principle and a Fresnel's approximation for wave propagation, a closedform solution for the field pattern in planes beyond the focal plane can be given by [2]

where p , 4, and z are the polar coordinates with z > 0 beyond the focal plane, X is the wavelength, k = 2 w / h is the wavenumber, .l (o ) is the 0th order Bessel function of the first kind, a is the radius of the synthesized ring, p o is the pressure specified at the control points (assumed real) and M is the number of control points on the ring. This formula for the complex pressure field shows that the transverse intensity achieves its maximum value on the axis (at p = 0) when equiphasal pressures are specified at the control points. This can be seen easily in Fig. 6 which shows the intensity profiles of a directly synthesized annular ring pattern with equiphasal pressures specified at the control points. Fig. 6(a) shows the resulting field pattern in the focal plane which is in agreement with the specified field level at the control points. However, when the field outside of the focal plane is examined, a high

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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 38, NO. 7, JULY 1991

(b)

Fig. 5 . Intensity profiles of directly synthesized annular ring pattern (20 control points along a 24 mm diameter ring). The focal plane is parallel to the aperture o f the array and is located at a depth of 105 mm from its vertex. (a) Focal plane. (b) z = 0 plane.

axial interference pattern proximal and distal to the focal plane can be expected. This can be seen in Fig. 6(b) where the maximum axial interference (at depth 90 mm) is 6 dB higher than the focal intensity. Another axial interference pattern occurs distal to the focal plane with peak intensity of 4 dB higher than the focal intensity (at depth 150 mm). The focal plane pattern in Fig. 6(b) can hardly be distinguished from the low intensity interference. Clearly, a heating pattern with such high level of interference is not useful for localized heating at depth. As evident from Fig. 5(b), the gain maximization technique results in significant reduction of interference patterns everywhere outside of the target volume. Indeed, the axial intensity beyond

the focal plane is identically zero. We have shown that the phase distribution of complex pressures at the control points determined using the gain maximization technique results in complete elimination of the axial interference pattern [2]. The synthesized field pattern shown in Fig. 5 illustrates basic concepts related to the direct synthesis of multiplefocus heating patterns. However, this pattern can be of limited use when used to heat well perfused tumor where a cold spot can be expected at the center of the tumor. This can easily remedied by synthesizing a double-ring pattern as illustrated by the intensity profile shown in Fig. 7. This heating pattern was directly synthesized using 30

EBBINI A N D CAIN: APPLICATOR FOR LOCALIZED HYPERTHERMIA

641

(b)

Fig. 6 . Intensity profiles of a directly synthesized annular ring pattern with equiphasal pressures at the control points. The control points are the same as Fig. 5 . (a) Focal plane. (b) := 0 plane.

control points distributed uniformly over two rings (10 points over the inner 12 mm diameter ring and 20 points over the outer 24 mm diameter ring). The gain maximization technique was used to determine the phases of the complex pressures at the control points which were assumed to produce equal power deposition. One can see that the interference patterns outside of the target volume are well below the power deposition pattern inside.

VI. DISCUSSION A N D CONCLUSION Computer simulations of a spherical-section phased array were performed to assess its value as an applicator for deep localized hyperthermia. Focused beams generated by the SSA are characterized by high focal intensity gain

(which is useful for deep penetration) and small size of the focal spot (which is useful for heating localization). Furthermore, the grating lobe intensity level was shown to be well below that of the main focus. This is quite significant considering the fact that the element to element spacing between the array elements which is 2X. The moderate grating lobe level with this large element to element spacing is mainly due the geometry of the array. The grating lobe results from the periodicity of the array elements over a uniform lattice. One way to reduce the grating lobe intensity level is to fabricate the array with nonuniform element to element spacing. When the elements of the SSA are projected on the its aperture, they form a nonuniform lattice which is responsible for the reduced grating lobe intensity level.

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(b)

Fig. 7 . Intensity profiles of a directly synthesized double-ring pattern (30 control points; 10 along the inner 12 mm diameter ring and 20 points along the outer 24 m m diameter ring). (a) Focal plane. (b) i = plane.

The properties of focused beams produced by the SSA indicate that this array is capable of producing highly localized heating pattems. This was verified by simulating the SSA in scanning a 20-point circular trajectory located at a depth of 105 mm from the vertex. The scanned field pattem shows clearly that the power deposition buildup outside the tumor is very insignificant compared to the power deposition inside the tumor. One can claim that this array can produce ‘‘surgically clean” heating patterns when used as a spot-scanning applicator. The only con-

cern with this approach is the need for high focal intensity to achieve the required therapeutic heating. This can be avoided by the direct synthesis of multiple-focus heating patterns which can be used to produce the necessary timeaverage intensities with acceptable spatial-peak pulseaverage intensities. Direct synthesis of heating patterns has another potential advantage over scanning. When the heating pattern is produced by periodically scanning a number of field patterns, the overlapping volumes of the beams add up on a

EBBINI A N D CAIN. APPLICATOR FOR LOCALIZED HYPERTHERMIA

power basis. In direct synthesis, on the other hand, the field outside the target volume is a result of constructive and destructive interference of the complex pressures of all the array elements. If the synthesis problem is formulated such that destructive interference dominates outside the target volume, then highly localized heating patterns can be achieved. This is exactly what the gain maximization technique does. The simulated intensity profiles of directly synthesized field patterns shown in this paper and elsewhere illustrate the effect of gain maximization on interference patterns outside the target volume r21, ~ 4 1 .

REFERENCES [ I ] E. Ebbini et al., “A cylindrical-section ultrasound phased-array applicator for hyperthermia cancer therapy.” lEEE Truna. Ultrcisori. Ferroc,lect. Freq. Cnntr.. vol. 35, pp. 561-572. 1988. [2] E. S . Ebbini, “Deep localized hyperthermia with ultrasound phased arrays using the pseudoinverse pattern synthesis method,” Ph.D. dissertation, Univ. Illinois. Urbana, 1L. 1990. [3] C . Cain and S . Umemura. “Concentric-ring and sector-vortex phasedarray applicators for ultrasound hyperthermia,” lEEE Truris. M i c w wave Theory Tech.. vol. MTT-34, pp. 542-551. 1986. 141 E. Ebbini and C . Cain, “Multiple-focus ultrasound phased-array pattern synthesis: Optimal driving signal distributions for hyperthermia,” lEEE Trans. Ultratisoti. Ferroe/ecr. Frcy. Co/itr..vol. 36. pp. 540-548. 1989. 151 R. Lalonde et a l . , “A complex lens system for ultrasound hyperthermia.” (Abstract only) presented at 10th Ann. Meet. North Amer. Hyperthermia Group, New Oreans. LA. 1990. [6] E. Carstensen et U / . , ”Demonstration of nonlinear acoustical effects at biomedical frequencies and intensities.” Ultrmourid Med. Biol.. vol. 6. pp. 359-368, 1980. [7] W . Swindell, “A theoretical study of nonlinear effects with focused ultrasound in tissues: An acoustic Bragg peak.” Ultrtr.sourid M r d . Biol.. vol. 11. no. I , pp. 121-130. 1985. [SI P. Lele. “Physical aspects and clinical studies with ultrasonic hyperthermia,” in Hyerrhermiu iti C u n c ~ rTherupy. F. Storm. Ed. Boston, MA: G . K . Hall Medical. 1983. 191 K . Hynenen et U / . , “A scanned, focused. multiple transducer ultrasonic system for localized hyperthermia treatments.“ f t i t . J . H J / J C ~ thermia. vol. 3 . no. I , pp. 21-35. 1987. [IO] G . Nussbaum er a l . , “Localized deep heating in soft tissue environments with a multiple overlapping beam ultrasonic hyperthermia system.“ (Abstract only). presented at 10th Ann. Meet. North Amer. Hyperthermia Group, New Oreans, LA. 1990. [ I I ] K . Ocheltree and L. Frizzell. “Sound field calculations for rectangular sources, lEEE Trutis. Ultrutisoti. Frrror/rt.t. Frry. Coritr.. vol. 36, pp. 242-248, 1989. ”

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[ 121 T . Cavvichi and W . O’Brien, Jr.. “Heat generated by ultrasound in an absorbing medium,” J . A(v)u.sr. Soc.. A r ~ e r . vol. . 76. no. 4. Oct. 1984. 1131 P. Lele, “Local Hyperthermia by ultrasound.” in Ph~,sic.trlAspect.\ ~f’Hyprrthrrmicr.G. Nassbaum. Ed. New York: AAPM, 1982. [ 141 E. Ebbini and C . Cain. “Optimization of the intensity gain of multo tiple-focus phased-array heating patterns.” f ! ! t , J . Hy/~rrthc~rt~iicr, be published.

Emad S . Ebbini (S’84-M‘90) was born in Karak. Jordan. in December 1961. He received the B.Sc. from the University of Jordan. Amman. and the M.S. and Ph.D. degrees from the University of Illinois. Urbana-Champaign. in 1985. 1987. and 1990, respectively. all in elcctrical engineering. From 1985 to 1986. he worked as a graduate assistant in the Department of Electrical Engineering at Yarmouk University (currently the Jordan University for Science and Technology), Irbid. Jordan. He is currently with the Department of Electrical Engineering and Computer Science at the University of Michigan, Ann Arbor. His current research interests are in digital signal processing and phased-array beam forming with applications to biomedical ultrasonics.

Charles A. Cain (S’65-M.71-SM.80-F.89) was born in Tampa. FL. on March 3 . 1943. He received the B.E.E. (highest honors) degree in 1965 from the University of Florida. Gainesville. the M.S.E.E. degree in 1966 from the Massachusetts Institute of Technology, Cambridge. and the Ph.D. degree in electrical engineering in 1972 from the University of Michigan. Ann Arbor. During 1965-1968, he was a member of the Technical S t a f at Bell Laboratories. Naperville. IL, where he worked in the electronic switching systems development area. During 1972-1989. he was in the Department of Electrical and Computer Engineering. University of Illinois at UrbanaChampaign, where he was a Professor of Electrical Engineering and Bioengineering and the Chairman of the Bioengineering Faculty. Since 1989. he has been in the College of Engineering. The University o f Michigan. Ann Arbor. as a Professor of Electrical Engineering and Computer Science and the Chairman of the Bioengineering Program. He has been involved in Research o n the biological effects and medical applications of microwaves and ultrasound. He is currently an Associate Editor of the lEEE T R ~ N S ACTION O N BIOMEDICAL E N G I N ~ ~and K Iis~an G editorial board member of the Iiilertiurioi?tr/ Jourmrl of Hy[Jerlherl~fitr.