NINETEENTH NATIONAL RADIO SCIE,NCE: CONFERENCE, ALEXANDRIA, March, 19-21,2002 mq

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Liver Tumor Hyperthermia lJsing An N X N Ultrasound Phased Array

*N. H. Isanail and **K. A. Abo El-Ela * Alexandria University , Faculty of Eng., Electric Eng. Dept., Alexandria , Egypt. ** Air Defense College, Egypt,

Abstract - Focusing of ultrasonic waves to conccmtrate their power at different , locations inside the liver tumor volume is investigated. The focusing lxocess c m be achieved by using an ultrasound phased a m y . In this paper, the N X N phased array is introduced to produce the specilic temperature distribution inside human liver . The pseudo-inverr;e field conjugation method 1s applicd to generate focused powcr points to deliver heat to the treated volume.

I. Introductioln

Liver is a complex chemical factory that helps human by regulating the supply of blood fuel , manufacturing many essential body proteins and regulating the balance of many hormones. Liver is highly vascular tissue that receives double blood supply fiom 1:)ortal vein and hepatic artery. Recause of liver filters blood from all parts of the body, cancer cells can lodge in liver iind develop into metastatic nodules. Cancers that begin in the gastrointestinal tract often spread to liver. Liver cancer classification is based on the cell of origin that becomes cancerous and whether the tumor resulting in benign or malignant. Cancers found in liver are either primary , arising from liver cedls, or secondary , origixting elsewhere in the body. Primary liver (cancers account up to SO (?h cf all cmcers in Africa, Southeast Asia ancl China . Secondary liver cancers are 30 times more prevalent than primary liver cancers [ I ] . Hyperthermia is a cancer treatment modality which aims the destruction of malignant tissues. This goal is achieved by increasing the tumor temperature to therapeutic levels for specific period of time [7] . Also, hyperthermia has been supportcd by recent biological and clinical research showing that elevated temperature have cytotoxic effect for tu.mors [3]. The non invasive hyperthermia using ultrasound is based on the absorption of ultrasound energy by tissue!; 141. For deep tumors , there is a need for a large number of transducers to carry out an efficient focused power at ihe treated volume. Ultrasound phased arrays are utilized to achieve this goal by feeding the array elements with different signals to get the desired specifications [5-7]. There are many types of phased arrays such as the tapered phased array [ 81 , the cylindrical section phased array [9] and the circular phased array I:lO]. In this paper an N X N ultrnsound phased array, reported by M. S. Ibbini et al.[ I I ] . will be used to treat a tumor inside human liver. In Section 11, the problem and the mathematical method uscd are depicted. Simulation and results are presented in Section 111. 'The discussion oflhe obtaincd results and conclusions are given in Section IV.

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11. Problem Description and Mathematical Formidations

For non invasive treattnents using an ullrasound phased array , it is required to compute the excitation of the array elements to produce highly localized foci inside the tumor volume without excessive heating at the surrounding normal tissues. Focusing can he achieved by driving the array elements with signals such that the individual hearns are added constructively at the desired focal points. The method used for ultrasound focusing is the pseudo-inverse field conjugation method [ 121. It depends on specifying M focal (control) points inside the tumor volume. The number of the phased array elcments is N (: N > M ). The set of driving signals is found by solving the sc:t of equations

NINETEENTH NATIONAL RADIO SCIENCE CONFERENCE, ALEXANDRIA, March, 19-21,2002

H U = P - . (1)

where U is the N X 1 matrix containing the phase and amplitude of the ultrasound beam at each element of the array. P is the M X 1 matrix containing the complex pressure at the control points. H is the M X N matrix describing the propagation of the ultrasound wave from each element of the array to each control point. The matrix element H(m,n) is given by Rayleigh - Sommerfield integral [12] , [ 131 as

e J +fm)-r ' (n) /

H(m,n)= j p c k l 2 n dS (2) s Ir(m) - r ' ( 4

where p is the density of tissue , c is the speed of ultrasound in the medium , k is the wave number, S

is the surface element and Ir(m) - r'(n)l is the distance between the nth element of the phased array and the mth control point. The solution of (1) is called the minimum norm solution [ 121 , and is given by

U = H ' ~ ( H H * ~ ) - ~ p (3) where HIT from the focus points to the array elements. H*T(HH*T)- ' The temperature distribution is obtained by solving the 3-D steady state bioheat transfer equation [ 1 11

is the conjugate transpose of the matrix H , which describes the ultrasound propagation is called the pseudo-inverse mairix of H.

V 2 T + Q / K + W b cb(G - T ) / K = O (4) '

where K is the thermal conductivity, T = T(x,y,z) is the temperature , W, is the blood perfhion rate, & is the arterial blood temperature , cb is the specific heat of blood and Q = alP I 1 p c is the power

deposition . a is the tissue attenuation coefficient.

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111. Simulation and Results

Liver is a spongy reddish brown gland that lies just below the diaphragm as shown in figure 1. An N X N square ultrasound phased array is placed at the front of liver as shown in figure 1. The simulated model is assumed as shown in figure 2. There is a bolus layer between the phased array and skin for cooling . Skin , fat and muscle thickness are 4mm ,2.1 cm and 1.5 cm, respectively. A tumor of radius 2cm and height of lcm is assumed to be located at z = 6 cm inside the liver layer of 4cm thickness as shown in figure 2. Four foci points inside the tumor volume were selected and the temperature distributions due to different values of N are evaluated . The calculations started with small values of N till reaching the sharp focusing at the required points . The required focusing is obtained at N = 20 as shown in figure 3 . But the 20 X 20 phased array area equals 8cm X 8cm ( the area of one transducer = 4 mm X 4 mm at an operating frequency of 500 KHz ) . This dimension let the radiated ultrasound wave suffer from a reflection from ribs around the liver . To overcome this problem , N =I5 is chosen 40 produce a heating pattern close to that obtained by N = 20 but it forms an area of 6cm X 6cm . Figure 4 shows the temperature distributions for N= 15 . In addition , the temperature distributions at 0.5 cm below and above the tumor border are obtained as shown in figures 5, 6. The densities, speed of ultrasound and the attenuation coefficients of skin , fat , muscle, liver and tumor are given by [ 141.

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NINETEENTH NATIONAL RADIO SCIENCE CONFERENCE, ALEXANDRIA, March, L9-21,2002

IV. Discussion and Conclusions

The numerical simulations is devoted to investigate the temperature distributions inside a tumor volume located inside human liver. It is found that the increase in the number of the phased array elements to N = 15 produced sharp focal spots at specified locations. Also, the maximum temperature values reached to 43 ’ C . While the temperature values are dropped to 38.5 ’ c at 0.5 cm above and below the tumor border. It is noticed that the dimension of the 15 X 15 phased array is about 6 cm X 6 cm which is suitable to be placed on a region facing liver and the ultrasound beam is far enough from the ribs. Also, it is recommended to f i l l stomach with water to avoid the ultrasound reflection from empty stomach.

In conclusion , this paper showed the ability of an N X N ultrasound phased array to produce localized heating patterns within the therapeutic temperature values to treat liver tumors. This kind of treatment may increase the success rate of liver cancer treatment and avoid the using of surgical operations.

References

[l] htp://www. liver .ca / English / index.html , The Canadian Liver Foundation ,2001. [2] P.Lele, Effect of Ultrasound on Solid Mammalian Tissues and Tumors in vivo in Ultrasound ,

[3] P. Lele, Physical Aspects and Clinical Studies with Ultrasonic Hyperthermia, in Hyperthermia

[4] R. Jain , Bioheat Transfer : Mathematical Models of Thermal Systems , in Hyperthermia

[5] C. J. Diederich and K. Hynynen, “ The Feasibility of Using Electrically Focused Ultrasound

M. Rapacholi , M. Grandolfo and A. Rindi Ed., New York, Plenum Publishing Corp., 1987.

in Cancer Therapy, F. Storm Ed., Boston, MA:G.K. Hall Medical Publishers, 1983.

in Cancer Therapy , F. Storm Ed., Boston, MA:G.K. Hall Medical Publishers, 1983.

Arrays to Induce Deep Hyperthermia via Body Cavitation, ” IEEE Trans. on Ultrasonic, Ferroelectrics, and Frequency Control, Vo1.38, No. 3, pp. 207-219, 1991.

via Body Cavities, “ h t . J Hyperthermia, Vo1.9, No. 2, pp. 263 - 274, 1993.

Motion Compensation for ultrasonic Hyperthermia Phased Arrays: Experimental Results,” IEEE Trans. on Ultrasonic, Ferroelectrics, and Frequency Control, Vo1.41, No. 1, pp. 34-43, 1994.

[6] K. Hynynen and K. L. Davi , “Small Cylindrical Ultrasound Sources for Induction of Hyperthermia

[7] H. Wang , E. S. Ebbini , M. O’Donnell and C . A. Cain, “ Phase Aberration Correction and

[8] P. J. Benkeser , L. A. Frizzell , K. B. Ocheltree and C. A. Cain ,” A Tapered Phased Array Ultrasound Transducer for Hyperthermia Treatment, ‘‘ IEEE Trans. on Ultrasonic, Ferroeleclrics, and Frequency Control, Vo1.34, No.4, pp.446-5 13, 1987.

Ultrasound Hyperthermia Phased Array Applicator ,” IEEE Trans. on Ultrasonic , Ferroelectrics, and Frequency Control, Vo1.38, No.5, pp.5 10-520, 1991.

Treatments,” 1 7th Radio Science conference, K4 ,2000.

Applicator: Simulated Temperature Distributions Associated with Directly Synthesized Heating Patterns,”IEEE Trans. on Ultrasonic, Ferroelectrics, and Frequency Control, Vo1.37, No.6, pp.

[9] E. S . Ebbini and C. A. Cain, ” Experimental Evaluation of a Prototype cylindrical Section

[lo] N. H. Ismail , ” Heat Generated By a Circular Ultrasound Phased Array for Deep Seated Tumor

[l 11 M. S. Ibbini, E. S . Ebbini and C. A. Cain, “ N X N Square-Element Ultrasound Phased Array

491-500, 1990. [ 121 R. J. Lalonde, “ Field Conjugate Acoustic Lenses for yultrasound Hyperthermia,”IEEE Trans.on

Ultrasonic, Ferroelectrics, and Frequency Control, Vo1.40, No.5, pp.592-602, 1993. [ 131 E. S. Ebbini and C. A. Cain , ” Multiple-Focus Ultrasound Phased-Array Pattern Synthesis:

Optimal Driving - Signal Distributions for Hyperthermia,” IEEE Trans. on Ultrasonic, Ferroelectrics, and Frequency Control, Vo1.36, No.5, pp. 540-548, 1989.

Microwave Power, Vol. 15, No. 1, pp. 19-23 , 1980. [ 141 M. Stuchly and S. Stuchly ,” Dielectric properties o f biological substances- tabulated ,” J.

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NINETEENTH NATIONAL RADIO SCIENCE CONFERENCE, ALEXANDRIA, March, 19-21,2002 mj

Apex of right lung

phased array pancreas

Fig.i Over view of viscera of the thorax and abdomen

. I

Bolus NxN Phased Array

Skin ____*

Fat - , ... c ,

Muscle -

‘len

6 cm

Focus

Liver --. Tumor

Liver - Muscle ,-*

,” Fat +

Skin +

Fin2 NxNphased array located on a multi-layers medium contains liver with tumor

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NINETEENTH NATIONAL RADIO SCIENCE CONFERENCE, ALEXANDRIA, March, 19-2 1,2002 m15)

0.05

- . X(m) -0.05 -0.05

Fig.3 Temperature distributiorl inside the ttiinor volunre. N=20

0.04

Fig.4 Temperature dislributiorl inside the tunlor volume. N= 15

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NINETEENTH NATIONAL RADIO SCIENCE CONFERENCE, ALEXANDRIA, March, 19-21,2002

41

40

39 v i=

38

37 0.04

x(m) -0.04 -0.04 Y"

Fig.5 Temperature distr-ihtioii at the level of 0.5 ctii above the ttirnor border. N=IS

0.04

Fig6 Temperature dislribirtiort nt the level of 0.5 cni below the tiunor border. N = I S

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