[IEEE Proceedings of the Twenty Third National Radio Science Conference (NRSC'2006) - Menouf, Egypt (2006.03.14-2006.03.16)] Proceedings of the Twenty Third National Radio Science Conference (NRSC'2006) - A New Ultrasound Phased Array Technique for Treat Liver Cancer Using Hyperthermia

_The 23d National Radio Science Conference (NRSC 2006) ThekiLz2 National March 14-16, 2006 Kg I~ Faculty of Electronic Engineering, Menoufiya University, Egypt. A New Ultrasound Phased Array Technique for Treat Liver Cancer Using Hyperthermia Mazhar Tayel ,Nour Ismail, Ashraf Talaat. Elec.,Eng.,Dept*, Faculty of engineering, Alexandria University, Alexandria Egypt. Abstract-A method is presented for calculation of the ultrasonic from NXN ultrasound phased array transducers to treat cancer in liver using hyperthermia treatment The analysis uses the bioheat transfer equation with tissue properties to get the temperature distribution. The synthesize method consists of simultaneously focusing of the ultrasound beam at different points uniformly distributed along the tumor periphery. It is demonstrates that by combining the multiple focusing features with the Esoudo inverse method and the new field phasing concept, typical undesired hot spots can be eliminated Temperature distribution associated with two methods will be simulated and discussed. I. Introduction Scanned focused ultrasound has been used as a hyperthermia treatment method since 1975 1 1 , and it is receiving increased interest as the heating method for deep-seated tumors [2]. Results from two-dimensional calculations, [3], and from in vivo and in vitro experiments [2] show that uniform temperature distributions can be obtained inside the treatment volume with a steep falloff outside the scanned volume. However, a very little quantitative information is available conceming the effect of the important parameters of a scanned focused ultrasound hyperthermia treatment, such as scanning pattern and speed, transducer choice, blood perfusion pattern and flow rate. Some information about scanning speed has been reported from in vivo and in vitro experiments [4], [5]. Nevertheless, no systematic parametric study has been done on the effect of scanning speed on the temperature fluctuations present during scanned focused ultrasound hyperthermia treatments, These temperature fluctuations, primarily present along the scanning path, can significantly affect the thermal dose delivered to the tissue [5]. An efficient field calculation method has been developed which is well suited to the determination of the field from CW rectangular transducers. II. Analytical Methods The method developed as a part of this study provides the field for an acoustic source. This can be divided into rectangular elements, surrounded by a plane rigid baffle. The sound pressure amplitude po at a point is given by jOs r where the integration is over the complete radiating surfaces p is the density of the medium, c is the phase velocity of the sound waves, ii is the velocity amplitude of the piston, X is the wavelength, k is the wave number, a is the attenuation coefficient, and r is the distance between the field point and an elemental area of the piston. This integral has been evaluated by using Huygen's principle and summing the contribution from incremental areas representing the radiating surface [61], [7], [81. In this stutdy, the source was divided into a number of rectangular elements that are too large to be represented as point sources but small enough that simplifying assumptions applied as delineated below. The total pressure p0. at a point in the field is then the sum of the pressure contributed from each element,i.e., pozz., uE(a+i )CdA (2) The 23rd National Radio Sci'ence Conference (NRSC 2006)dI]{si15 ~~~~~~March14-16, 2006 K9 2 Faculty of Electronic Engineering, Menoufiya University, Egypt. Where N is the number of elements of total area, AA = height(Ah) * width(AW), and un is the complex surface velocity for element n. The complex surface velocity u,n is the same for all elements, when a uniformly excited rectangular source is considered. For nonuniform excitations, e.g., a phased array source, u, is used to represent the local phase and magnitude of the velocity. The central point of the element n is denoted by (xn,yn) to simplify the analysis as follows. Additionally, a second coordinate system is defined as ( x, yo) for the element at the origin as shown in Figure (1 ). Using these relations in (2) yields j Ah/2 Aw/2 -(a+jk)r Po -dxoJ Jdyo (3) n=1 -Ah/2-Aw/2 r Where R - z +(x-x,-xo) +(yy-Yn YO) (4) To find an expression for the pressure that is easily evaluated numerically, suitable approximations and their regions of applicability are defined. By choosing Ah and AW to be small, the distance to the field point is much greater than the dimensions of the source and the Fraunhofer approximation can be applied. To simplify the application of the Fraunhofer approximation, we define the intermediate variables xn =x-xt and y' = y-y nThe Fraunhofer approximation requires that the distance from the origin of the element to the point of interest in the field R =Z+XX )2 +(y _Yn )2 (5) R= jz2 + X2 +Yn2 to be large compared to xo and yo, i.e. R > xo, yo Thus, the exponential term in (3) can be expressed as follows = exp[-(a + jk).J7+ (xn -XO) + (yn - Yo) 3 -exp[-(a + jk). R2-2x, x0-2yy +xO2 +yO2] (6) Using the first two terms of a binomial expansion of the radical on the right side of (6) yields 2 2 e-(a+jk)r = exp (-(a + jk).[r- Xn Xo Yn Yo + + (7) If (kxo 2/2R + kyo2 /2R) is small compared to f7 and a «Rk,the omission of these terms produces a negligible phase error and gives the expression The 23rdNational Radio Science Conference (NRSC 2006) The 23"'Nationl March 14-16,2006 LK9 3I Y Faculty of Electronic Engineering, Menoufiya University, Egypt. e-(a+jk)r = exp{-(a+ jk).[R XnXO° YO°]} (8) R R Using this equation, assuming I/r = 1 /R, and substituting into (3) give li Aw/2 AhI2yJpC= -(a+jk)R i exp[(a +jk)Xn ]dxO J exp[( + jk) ]dyo (9) A n=1 R -Awf2 R -Ah/2 R The assumption that eCaxX/IR =_ for Aw/2> xo > - Aw/2 and the equivalent condition for yo are used to reduce the two integrals in (9) to Fourier transform expressions which upon evaluation yield [9]. j1xAA Un(+kkxn,AW kYnAh'p _ jZM , n,e-(a+jk)fimC r ll Yt(0Po 2 n=1R % sC.2R 2R (10) Simulations were performed using the three-dimensional bioheat transfer equation kV T-Wcb(T- Tb) + Qp-(= ) Where k is the thermal conductivity in the tissue in (W/m/°C), T is the tissue temperature (°C), W is the blood perfusion rat- ( kg/m3/s), Cb is the corresponding tissue specific heat (J/kg/ °C), T, is the arterial blood temperature (37°C), Qp is the local power deposition (W/m3), p is the density of the tissue (kg/r3). Boundary conditions of 37°C on all of outer surfaces, the parameter of tissues are as in Table (1), and the model under test as shown in Figure (2) . The liver tumor at Z=12 cm from the transducer surface, The foci points are selected as (X-2cm,Y=±lcm at Z=12 cm). Using the NXN=20X20 elements rectangular phased array transducer, with an area 9X9 cm2 the operation frequency is 50OKhz. Solving (11) numerically in the rectangular coordinates by using the fimite difference method to get the results, shown in figures 3and 4. From figures 3and 4 it is found that the temperature reaches to 45 C° which is suitable to treat the tumor at the exact position. When the temperature is calculated at the level 6cm ,it is found that the temperature value reduced to 41 C0 to keep the surrounding tissue in healthy condition. III. Optimization The number of elements A planer NXN square elements array applicator of an effective surface area 9X9 cm2 is assumed for all simulation. A series of simulations will be conducted to determine a largest element size and hence, the minimum number of array elements that results the minimum grating lobe level. Based on this simulations the elements were considered to have 1.5 X with an operating frequency 500 KHz and N=20. In what follows, a control source refers to continuous line or surface in the focal plane ( at location of the desired field ) that is given an assumed amplitude and phase for the purpose of computing the desired driving signal (amplitude and phase )for all array elements . This is accomplished via back propagation from the control source to the array surface using the field conjugation method [1 0],[ 11]. A control point is a discrete point given assumed complex amplitude for the same purpose. The rotating field conjugation method (RFCM) described in this paper can be considered as a modification of field conjugation method (FCM) described in [11]. This modified version consists of substituting the spatially continuous control source (i.e., annular ring, elliptically shape ................etc),by an appropriate number of control point sources uniformly spaced over the periphery of-the profille to be synthesized .For example, to synthesize an annular pattern of radius R and M points sources are distributed over a periphery of circle of radius R as opposed to assume a spatially continuous radiating ring source in the focal plane . An illustration of the array and the distribution of control point he 23rdNational Radio Science Conference (NRSC 2006) The 235;' National March 14-16, 2006 [ IK9|4J ~.!X Faculty of Electronic Engineering, Menoufiya University, Egypt. sources is shown in figure ( 5-a ) The procedure is similar to that used to determine the necessary number of points needed to scan a desired trajectory. In fact, an appropriate number of control point source can be determined by simply dividing the length of the desired trajectory (i.e., 2 ;z R for annular ring).This procedure results in M discrete neighboring focal regions that can be brought closer to each other by increasing the number of control sources if desired. As will be shown, this distribution of assumed sources will allow more control over the synthesized pattem (i.e., elimination of some types of hot spots). To achieve that , the assumed control sources are excited by time harmonic function of the form e9I,e1 2, em) , where 0 is an arbitrary phase to be determined , the index m is used to refer to source m (m=l,2 ,....M ),and M is the total number of control sources(i.e., M=2 ;r R/l1.5k for an annular ring of radius R). The time dependency ei 0)' of the harmonic excitation is dropped for simplicity . The angles 01, 02,. 0M can then be determined as those that make the resulting ultrasonic field as same a desired value at a given location. For our application , it is desired to directly deposit the ultrasonic energy around the periphery of small tumors and to eliminate the associated hot spot or spots along the axis of symmetry. As illustrated in figure (S.b), the pressure field produced at an arbitrary point (0,0,z) along the primary axis is given by p(O,O,z) = Xei eJim Irm (12) m=l With R2m= z2+R2 cos20m+ R2sin20m =z2+R2 (13) Where K =2 7r / A is the propagation constant in the medium and R is the radius of the tumor model(ring to be synthesized). Equation (13) shows that rm is independent ofm and, hence, the summation becomes jkjz +R M P(O,O, z) = ejo (14) The phase delay 9m can be determined as 27c OM = M~~ (15)M A similar calculation for the case of elliptical power deposition leads to the expression given by [12]. In this case, 2 22n a b 2q(6 O m2;r 7r a -b cos 2m M A a2+ b2 + z2 (16) Where il is the wavelength, a and b are the parameters of the ellipse of equation (x2/a2+y2/b2) =1, and m,, is the angle between the vector pointing to the source m and X-axis as illustrated in figure (5-c). Applying equation (13) by using Z=12cm,R=l lmm,and M=2dR/1.5A,,frequency f=500KHz,and using (14) to find the p(O,O,z), then solving (11) to get the temperature distribution in the layered medium. The results are shown in figure (6). IV. Conclusion The present work shows,in the case of using 20X20 applicators, it is noticed that the temperature reach to 45 C° in the tumor location (four foci) which can treat the liver tumor at the depth 12cm.If the level z=6cm is taken with the same applicators, notice thtthae temperature reach to 41 C0 which doesn't cause any affect in the surrounding tumor tissue. By using the (FRCM) method, we can reduce or optimize the number of elements to 15 instead of using all applicators, but from figure (6.a) it can be noticed that the temperature reaches to 41 C0 in the tumor level and reaches to 39 C0 in the z=6cm level at 500 KHz .By increasing the transducers excitation, the temnperature reaches to 45 C0 in the tumor volume that can treat it. The 23"d National Radio Science Conference (NRSC 2006) March 14-16, 2006 | K9~ Faculty of Electronic Engineering, Menoufiya University, Egypt. References Ii IP. P. Lelel, "Hyperthermia by ultrasound," in Proc. Symp. Cancer nerapy by Hyperthermia and Rudiation. Washington, DC, pp.168-178. 1975. [2] -, "Ultrasound: Is it the modality of choice for controlled, localized heating of deep tumors?" in Hyperthermia Oncology 1984, vol..2, Proc. 4rh Int. Symp. Hyperthermia Oncology, J Overg'aard, Ed London: Taylor and Francis, pp. 122-154. 1985. [3] K. J Parker and P. P. Lele, "The effect of blood flow on temperature distributions during localized hyperthennia," Ann. N. 1' Acad Sci.,,vol. 335, pp. 64-65, 1980. [4] K . J. Parker,. "The generation and analysis of hyperthermia by ultra-sound," Ph.D. dissertation, MIT, Cambridge, MA, 1981. [5] R.- B Roemer, W. Swindell, S . Clegg, and R. Kress, "Simulation of focused, scanned ultrasonic heating of deep-seated tumors: The effect of blood perfusion," IEEE Trans. Sonics Ultrason., vol. SU-3 1, pp. 457-466, 1984. (6]I J.- Zemanek. "Beam behavior within the nearfield of a vlhrating piston."J. Acorlsr. Soc. A'm., v o 1. '49, no. I. pp. 181-191, Jan. 1971. [7] P. R. Stepanishen, "The time-dependent force and radiation impedance on a piston in a rigid infinite planar baffle,"JT Acousr. Soc. Am., vol. 49, no. 3, pp. 841-849, Mar. 1971. [8] K. B. Ocheltree,f."Theoretical analysis of ultrasonic linear phased arrays for hyperthermic treatment," M. S.thesis, Dept Elec. and Comp, univ., of kuopio. [9] K .B. Ocheltree and L. A. Frezell 'Sound Field Calculation for Rectangular Sources' IEEE Trans. Sonics Ultrason., vol. SU-36, pp. 242-248, 1989. [10] M. Ibbini and C.cain ' a field conjugation method for direct synthesis of hyperthermia phased array hieating patterns, ' ' IEEE Trans Utrason., Ferro., Freq., contr., vol.36, no.1I pp . 3-9 , 1989. [11I M. Ebbini , E. ebbini 'A new technique based on the field conjugation method as an alternative to scaning,' in proc.1987 ultrason., sump., pp.8673-866. 1987. [12] M.ebbini,E.ebbini 'NXN square element ultrasound phased array applicator simulated temperature distribution associated with directly synthesized heating patterns' ' IEEE Trans Ultrason., Ferro., Freq., contr., vol.37, no6 pp. 491-500,F 1990. [13] R. Paul and, HI.George burkitt, 'Functtional histology a text and color atlas'Elbs, uk, 1987,ch. I15,p.p 225. _____ Tab106 .Tsuepraeer ___ Viscra 1.07*1000 3.5*1000 .55 4 The 23d National Radio Science Conference (NRSC 2006) The 23"' National March 14-16, 2006 (NK912006 SY Faculty of Electronic Engineering, Menoufiya University, Egypt. liver 1.03*1000 | 3*1000 .50 4.5 Skin (5mm) Fat (2cm) Muscle (6cm) Viscra (1.5cm) (Live Viscra (.5 mm) Fig.2. The model under test [13]. Ta Zlevel= 12e-2 m 55. T(c) 45 4O 4.5 4~5 -4.5 -4.5 - Y(Cr}) X (cm) Fig.3. The temperature distribution in the liver tissue at X=+2cm, Y=+Icm, Z=12 cm . _4~111 The 23rd National Radio Science Conference (NRSC 2006) c.j' LS NMarh 14-16, 2006 K91 7 j N&X :7 Faculty of Electronic Engineering, Menoufiya University, Egypt. eZlenwi ( s.: 44~~~~~~~~~~4 T ((I~1: | 4.C - 4.5 Y (Cn) 4 5 4.5 X(cm) Fig.4. The temperature distribution in the liver at (X"±2cm,Y=±tcm, Z=6 cm). X A.s.W +X a M~~~~~~~~~~Si' Mis ~t j s 2: AtSn4~4S#I*4b Fig.5.(a) Schematics of the NXN square elements applicators where W is the element width and D is centre to centre spacing Distribution of the assumed sources (qi,q2,. -etc) illustrates a possible alternative to assuming a spatially continuous vibrating rings .(b) An illustration of the calculation of the field produced by the annular distribution of control sources along the axis.(c) Geometry of the elliptical pattern synthesis of equation (x/a)2=(y/b)2=l. The 23d National Radio Science Conference (NRSC 2006) The 23rd>National March 14-16, 2006 ( K920 8 %4~~ Faculty of Electronic Engineering, Menouflya University, Egypt. T at level z= 12e-002 43- 42 T(C) 41 - 400 45 -45 01Y(cm) X(CM) (a) Tatlel UeM2 4$~~~~~~~~4 T(C0) 44~....... 2 A21.'~./'"',''. ,'j 4.5 rlGfI.}0.5 4.5 Hvfca}~~~~~~~~4.f ' ) ' X(tm) (b) Tat level r6e 002 41 .r... 40/ T(Cfl 39w 38 4.5~~~~~~~~~~~~~~~~~. Y(cm) X(cmn) (c) Fig.6. The temperature distribution using (FRCM) at 500 KHz. And using 15 elements applicators. (a) at z = 12 cm, (b) at z= 12 am and increasing the excitation and (c) at z= 6 cm.