635

Sector-vortex scanning for hyperthermia with a

large square ultrasound phased array apertureLiyong Wu, Duo Chen, Xiaozheng Zeng, Khawar Khurshid and Robert J.McGough, IEEE member

Abstract- Planar ultrasound (US) phased arrays withsquare element are easier to fabricate and model than otherconcave shaped phased arrays. Combined with phasesderived for single spot focusing, the sector-vortex phasescheme can be applied to the square planar array to gener-ate a vortex shaped pressure field that can be controlled bythe mode number M. Increasing the mode number M alsoincreases the diameter of the annular focus. The locationof the annular focus can be moved along the axis or offaxis by steering the single spot focus. The weight of thephase for single spot focusing can control the axial length ofthe sector-vortex pattern. Superposing the SAR of multiplemodes can heat large tumors with diameters up to 5 cmby broadening the temperature distribution.

I. INTRODUCTION

Cain and Umemura [1], [6] proposed a rotating phasescheme ( = MO) for a concave sector-vortex ultra-sound phased array applicator. This strategy generatesa controllable ring-shaped pattern in the focal plane. Inthis approach, the total pressure field is approximated byan Mth-order Bessel function and the size of the focus(or the radius of the main lobe) in the focal plane iscontrolled by the mode number M. The sector-vortexarray contains a small number of trapezoidal elements,and compared to square planar phased array structurespopulated with square elements, the sector-vortex arrayis relatively challenging to build and calibrate. Althoughthe focal spot size in the focal plane is adjustable withthe sector-vortex array, the location of the focus is fixedand the size of the focus along the center axis is alsonot adjustable.A large ultrasound phased array with 500 square

elements was recently reported in [4]. With new PZTfabrication technology and circuit designs [2], the num-ber of the elements in an ultrasound therapy arraycould grow very large (-1,000 or even more) and thedriving electronics system could become much morecompact. The implementation of large phased arrays forhyperthermia could offer flexible control of the focuswith a large scan angle while eliminating the formationof grating lobes. Furthermore, 2D planar arrays withsquare elements are readily available for thermal therapyapplications.A new phasing scheme directly synthesizes a con-

trollable focus for 2D planar square ultrasound arrays

with square elements or circular elements. The shape

of the focus generated by the large arrays approximates

that generated by a concave sector-vortex array. In

addition, the focus can be steered off the axis and/or

along the axis. The phasing scheme is evaluated with a

prototype ultrasound phased array applicator consisting

of 73 x 73 square elements, which generates a broad

focus in the target tumor region. Computer simulations

of the ultrasound pressure fields generated by this array

are calculated with the fast near-field method (FNM),

and the resulting temperature distribution is computed

with the bio-heat transfer equation (BHTE). Simulation

results show that the combination of several modes can

heat large tumors (with radius of 5 cm) with a broad,

uniform temperature distribution.

PHASING SCHEME

The ultrasound phase array is square planar array withN x N square elements. The square element has an edge

length a and the gap between two elements is represented

by b. The elements are arranged on the grid points shown

in Fig. 1. Each element with index (i, J) is driven by a

sinusoidal signal with the phase for each channel(FM)given by

oij = Mij- akdfj (1)

for i = 1, 2, ***, N and j = 1, 2, ***, N, where (i, j) isthe index of the element, bijis the phase of the drivensignal, Oij is the angle of the element center shown in

636

Fig. 1, M is the mode number, k is the wavenumberin water, a is the coefficient for focusing, dfj is thedistance from the element center to the focal point (dfj=j(x xf)2 + (Yij Yf )2 + Z2), (Xij, yij) is the co-

ordinate of the (i, j) element center, and (x f, yf, zf) isthe coordinate of the focal point. The first term (modeterm) of Eq. 1 shows that the phase on each elementrepeats lM times per rotation around the center point ofthe array [ 1], [6].

The second term in Eq. 1 focuses the acoustic energyas shown in Fig. 2. By performing these phase adjust-ments across the aperture, the wave front emitted bythe array converges to the focus specified by (xi, yi, zi)shown in Fig. 2a. The ultrasound focus can also besteered off the center axis or steered along the axis asshown in Fig. 2a, where the coefficient of the focusingterm controls the extent of the focus along the centeraxis. Thus, adjusting the a coefficients changes the shapeof the shifted wave front. When a equals one, the initialshifted wave front is spherical. The combination of thefirst and second terms in Eq. 1 therefore focuses andmodulates the pressure field distribution radiated by thephased array.

III. METHODS

A. Pressure field calculationThe 3D pressure field radiated by each element is

calculated with the fast near-field method [5]. In pressurefield calculations for a planar 2D phased array witha center-to-center element spacing that is equal to aninteger number of grid samples, changing the elementlocation is achieved by spatially shifting the source.Therefore, the pressure produced by a single elementis calculated once, and then the field generated byeach array element is spatially shifted and the complexweighting term is also adjusted as required by the mod-ulation and focusing scheme in Eq. 1. The total acousticpressure is therefore represented by the superposition ofthe individual pressure fields.

B. Patient model and thermal calculationA cross section of the tumor model is shown in Fig. 3.

The material properties used for temperature calculationsare listed in Table I. The tumor is a 4cm diametersphere that is 6.2 cm from the skin surface. For pressureand temperature calculations, the center of the tumor islocated at [0,0,6.2] cm. The thickness of the skin layeris 0.4 cm, the fat layer is 1.5 cm thick, the muscle layeris 1.5 cm thick, and the viscera layer is 7.5 cm thick.The temperature distribution is obtained from the

power distrubution input distribution using the Bio-HeatTransfer Equation (BHTE) computed with a steady-state

X I.

ite the ft

(a) Focusing the array.

/ :/a 4,

%/vc 1;k Ylv b

Centeof the I

(b) Steering the focus.

Fig. 2. Focusing and steering the converging wavefronts generatedby the phased array.

Fig. 3. A cross section of the thermal model used for temperaturecalculations. The material properties are listed in Table I. The tumoris a 4cm diameter sphere located 6.2 cm from the skin surface. Thethickness of the skin layer is 0.4cm, the fat layer thickness is 1.5cm,the muscle layer is 1.5cm thick, and the viscera layer is 7.5cm thick.

MUSCLE

FATSKIN

,,n

Mode 4 Mode 8-60

EE

20 80 140Z(mm)

200 20 80 140Z(mm)

-30

E O

30IE0E60

200 20

Depth plane-60

E

Focal plane

Fig. 4. Pressure fields calculated in the focal plane and the axial plane for three different modes. The centers of these modes are all locatedat [0,0,12] cm (with oa = 1). The top row demonstrates the pressure distribution in the axial plane, and the bottom row shows the focal plane.From left to right, each row contains the pressure for mode 4, mode 8, and mode 12.

finite difference method [7]. In order to accelerate thecalculation, successive over-relaxation is utilized in thesetemperature simulations [3]. The thermal computationalvolume is a cuboid region, where the six boundaryfaces of the cuboid region are maintained at a constanttemperature for BHTE calculations. All tissue interfacesare set to 37°C and all water interfaces are set to 39°C.The water interface represents the temperature that ismaintained by a circulating water bath.

IV. RESULTSThe excitation frequency for the planar array is 1 MHz

in all of the following simulations. The acoustic field andtemperature response are evaluated in a 3D domain withvalues of x ranging from -6 cm to 6 cm, y ranging from-6 cm to 6 cm, and z ranging from 2 cm to 20 cm.

The spacing between grid points is 0.075 cm in all threedirections.

A. Pressure field patterns

The pressure field distributions in the axial plane andfocal plane for different modes (M = 4, M = 8 and M

= 12) are shown in Fig. 4. The center of the ring focusfor each mode is selected as [0,0,12] cm, so for modes4, 8 and 12, the peak pressure occurs at approximatelyz = 12 cm. The pressure extension along the z axisin mode 8, for example, is about 4 cm, with shorterand longer extensions for modes 4 and 12, respectively.In the top view of the axial plane of these modes,the pressure distribution appears similar to that of twoextended intersecting focal spots, but the pressure alongthe z axis is zero and a gap in the pressure appears inthe center of the focal ring. In the focal plane (z = 12cm), the pressure fields in Fig. 4 are rectangular ringswith pressure peaks at the four corners, which appear

as a consequence of the symmetry of the square array.

Fig. 4 also shows that the inner and outer diameters ofthe pressure ring increase as the mode number increases,where the outer diameter of the focal ring for mode 8 isnearly 3 x 3 cm.

With moving the focus center, the pressure field can

be steered off axis and along the center axis. Off axissteering and along axis steering can be done at the same

time, shown in Fig5, by moving the focus center from

EE

637

Mode 12

EE

80 140Z (mm)

200

E

X (mm)

J UX (mm)

60-60 -30 0 30 60

X (mm)

E

638

skin fat muscle viscera tumor

Blood Perfusion Wb(kglm3 s) 0 4.0 4.0 4.0 4.0Thermal Conductivity ,(W/m/ C) 0.21 0.16 0.42 0.55 0.56

TABLE IMATERIAL PROPERTIES FOR THE TISSUE PHANTOM MODEL IN FIG. 3. A SPECIFIC HEAT OF Cb = 4000J kgl0C FOR BLOOD IS ASSIGNED

THROUGHOUT THE PHANTOM MODEL.

E

z (mm)0

Z(mm) a= 1.25

I 0X (mm)

Fig. 5. Steering mode 4 off axis to [10, 0, 13.5] cm (with oa

[0,0,12] cm to [10,0,13.5] cm. The reference patternwithout steering is shown in the left column of Fig.4.Adjusting the coefficient a, the focus is elongated whena is less than 1 or shrunken, when a is larger than 1,shown Fig.6 with mode number 8 and the focus centerat [0,0,12] cm. The pressure field for mode 8 with a = 1is shown in the center column of Fig.4. The actual focuscenter moves close to the array when a is larger than 1,and moves away from the array when a is less than 1.

B. Temperature distribution

The 4 cm diameter tumor, shown in Fig.3, is heatedwith different modes: mode 4, mode 8 and mode 12. Thecoefficient a is set 1 for simplicity in these analysis.The focus center of mode 4 is located at [0,0,10] cm,the mode 8 center is at [0,0,10.5] cm and the focuscenter of the mode 16 is at [0, 0, 13] cm. In thesethree 3D temperature distribution, sphere mesh is the

50 80 110 140 170 200Z (mm) a 0.75

1).Fig. 6. a steering for Mode 8. The plot of a = lis shown in thecenter column of Fig. 4.

target tumor and four 2D square mesh plots are skin, fat,muscle, viscera boundary respectively. The black solidsurfaces show the isothermal surface of 42°C. The peaktemperature are 44°C in each calculation. The three di-mensional field of one mode and temperature distributionin 12 x 12 x 18cm3 region are calculated within half hour(Intel P4 2.4GHz CPU and 1GB memory).

V. DIscusSIONThe two terms in Eq. 1 with different functions work

with each other very well. For mode 0, the first termof Eq. 1 equals zero, there is no mode modulation on thefocus and the size of the focus is close to one wavelength(1.5 mm for 1MHz in water). When the mode numberis larger than zero, the pressure field in the depth planehas two peaks and there is a gap between two peaks, thepressure field in the focal plane is a rectangular ring with

639

E

N

0

Y (mm)

(a)

40

20mm

X(mm}(b)

EN

(c)

Fig. 7. Temperature distribution for Mode 12, 8 and 4 (with oa = 1).The mesh plots are the tumor model and the black solid surfaces are theisothermal surface of 42°C. The peak temperature are 440C in eachcalculation. a) Mode 12 with focus located at [0,0,12] cm, b) Mode8 with focus located at [0,0,11] cm, c) Mode 4 with focus located at[0,0,10.5] cm.

one peak at each corner, shown in Fig. 4. Because anyarray element and it's center axis symmetry element have180 degree input phase difference, the pressure fieldsgenerated by these two elements are canceled out alongthe center axis. The total pressure field generated by thearray is zero along the center axis and very low closethe center axis. The region inside of the focus with largemode number (For example: mode 12) can not be heatedwell, which is shown in Figs 4 and 7a.

Because the tumor could be off the center axis ofthe array, the shape of the tumor could be irregular orthe The peaks of the pressure field and peaks of thetemperature are not exactly in the focal plane and theyare usually shifted small distance to the array, the largermode number has the larger shift distance. In order heatthe tumor at the same location, different modes havedifferent focus center, shown in Figs. 7. From the Fig.5,this phase scheme can also move the focus around thetarget region without the shape changed. Fig.6 shows thephase scheme has the ability to control the focus sizealong the center axis. Large mode number usually has alarge extension along the center axis, which will result inhot spot outside the tumor. Adjusting the a coeffient forlarge mode number can constrain the power depositionwithin the tumor region.

With the mode number increasing, the size of the focusis enlarged, shown in Figs. 4, and the size of the over420C temperature region is also increased, shown inFigs.7. From the temperature distribution, large numbermode (Mode 12) has hollow region which is not wellheated by this mode and small number mode (Mode 4)can a small solid region very well. Combing the SARof different modes and optimizing the weight of eachmode, the over 420C temperature region could extendthe entire tumor region with 5 cm diameter withoutintervene heating problem.

VI. CONCLUSIONTwo phase terms, phase for single spot focusing,

sector-vortex phase scheme, are combined together togenerate the large and size controllable focus for the2D planar array, since the planar array is much easierto build than the concave shaped array. The large sizefocus is a good choice for thermal treatment of thelarge size tumor (diameter up to 4 or 5 cm). The focussteering property and different modes of this new phasescheme are investigated to heat the 4 cm diameter tumorwhich is about 6 cm underneath the skin. This phasescheme also offers a way to adjust the extension of focusalong the axis direction. The ultrasound pressure fieldsare calculated with fast near-field method (FNM) andthe temperature distribution is computed by solving astatic bio-heat transfer equation. Different modes havedifferent heating performance. Large number mode can

640

heat large region, but the region at the center of the focusis not well heated and intervene heating problem willappear. Small number mode can heat a small region withuniform temperature distribution. Mode number from 4to 12 and the combination of them are recommended forhyperthermia.

REFERENCES

[1] C. Cain and S. Umemura. Concentric-ring and sector vortexphased array applicators for ultrasound hyperthermia. IEEE Trans.Microwave Theory Tech., 34(5):542-551, 1986.

[2] D. Chorman and R. J. McGough. Development of prototypephased array ultrasound system for hyperthermia and targeted drugdelivery. Proceedings of the acoustics week in Cannada 2005,33(3):88-90, Sep 2005.

[3] E. S. Ebbini. Deep localized hyperthermia with ultrasound phasedarrays using the pseudoinverse pattern synthesis method. Thesisfor PHD degree in Electrical Engineering in the Graduate Collegeof UIUC, 1990.

[4] K. Hynynen, G. T. Clement, N. McDannold, N. Vykhodtseva,R. King, P. J. White, S. Vitek, and F. A. Jolesz. 500-elementultrasound phased array system for noninvasive focal surgery ofthe brain: A preliminary rabbit study with ex vivo human skulls.Magn. Reson. Med., 52(1):100-107, Jun 2004.

[5] R. J. McGough, T. V. Samulski, and J. F. Kelly. An efficientgrid sectoring method for calculations of the nearfield pressuregenerated by a circular piston. Journal of Acoustic Society ofAmerica, 115(5):1942-54, May 2004.

[6] S. Umemura and C. Cain. The sector-vortex phased array: acousticfield synthesis for hyperthermia. IEEE Trans. Ultrason. Ferroelect.Freq. Contr., 36(2):249-257, 1989.

[7] J. Wang and 0. Fujiwara. Fdtd computation of temperature rise inthe human head for portable telephones. IEEE Trans. MicrowaveTheory Tech., 47(8):1528-34, Aug 1999.