POSTER 2015, PRAGUE MAY 14 1

Spiral applicator array design for local microwave

hyperthermia treatment

Daniel DUFEK1

1Dept. of Electromagnetic Field, Czech Technical University in Prague, Technicka 2, 166 27 Praha, Czech Republic

daniel.dufek@fel.cvut.cz

Abstract. Microwave hyperthermia used in combinationwith chemotherapy and/or radiotherapy is very successfulmethod of cancer treatment. Hyperthermia rises sensitivityof cancer cells to primary treatment by heating them. Heatis created by energy carried to the cancer cells by electro-magnetic waves, that are produced by the applicator.

Main goal is to design and simulation of array of planarspiral applicators in the shape of a two-armed Archimedeanspiral for local microwave hyperthermia. To calculate thedistribution of temperature field in a virtual phantom usingthe finite element method. For this software COMSOL Mul-tiphysics was used.

Keywords

Microwave hyperthermia, spiral applicator array,Archimedean spiral.

1. Design of Applicator

A double arm Archimedean spiral was chosen for thedesign, because it creates homogenous electromagnetic fieldand still have small proportions. This allows practical usage.The antennas are planar and tuned to frequency 434 MHz.

The applicator shape is formed by rotating one arm by180�. As the substrate is used thin plate of low-loss di-electrics. For connection of the antenna and the generator isused a coaxial cable and a SMA connector. Parameters andshape of spiral are derivated from impedance and frequencyrequirements.

1.1. Analytical solution

Archimedean spiral is a frequency independent an-tenna. Its geometry is depends only on angle. Each armis directly proportional to angle ✓. Archimedean spiral isdescribed in polar coordinates by this equation:

r = r0✓ + r1 (1)

where r0 is the constant of proportionality, that dependson width of threads w, distance between them s, r1 is innerdiameter and ✓ is angle.

For the simulations parametric equations are used in-stead of polar coordinates because of designing in COMSOLMultiphysics.

x(t) = r0 cos(t), y(t) = r0 sin(t) (2)

Proportionality constant r0 is computed by

r0 =

s+ w

⇡

(3)

where s is the distance between the threads and w is widthof threads.

The radiuses are calculated to frequency that the an-tenna is tuned for. Frequency and the reflection coefficientare the main parameters focused on. The minimum fre-quency f

min

depends on outer radius r2 and the maximumfrequency f

min

depends on inner radius r2. The radiuses arecalculated by these equations:

f

min

=

c

2⇡r2p"

ef

(4)

f

max

=

c

2⇡r1p"

ef

(5)

where c is speed of light, r1 inner is the radius and r2

outer is the radius of athena and "

ef

is effective the permit-tivity of a medium.

Because of the antenna is on a dielectric substrate andan whole aparatus lays on a water bolus and a tissue, its tunedfrequency is influenced by permittivities of these mediums.This parameter is represented by effective permittivity, thatis compound by average of permittivities of mediums.

"

ef

=

"

sub

+ "

tiss

+ "

water

3

(6)

where "

sub

is the permittivity of substrate, "tiss

is the per-mittivity of the tissue and "

water

is the permittivity of water.

2 D. DUFEK, SPIRAL APPLICATOR ARRAY DESIGN FOR LOCAL MICROWAVE HYPERTHERMIA TREATMENT

the length of relative circuit of the spiral have to besame as the wave length the antenna is tuned on.

� =

c

f

p"

ef

(7)

With wave length � it is easy to compound the outerradius r2.

r2 =

�

2⇡

(8)

From the knowledge of radiuses, it is possible to cal-culate the strip width w and the distance between stripss. Number of the threads N is optional. Because of bet-ter distribution of electromagnetic field and kind of largeouter radius r2 it has been chosen to create 3 threads of theArchimedean spiral.

s =

r2 � r1

2N

� w (9)

where N is number of threads.

As was earlier mentioned, another important parameterof antenna is its reflection coefficient s11 and standing waveratio SWR. SWR is created by reflected waves that aresummed together. SWR must be smaller values than 2, thatmeans that s11 should have less value than -10 dB. Smallerthe s11 coefficient the better.

s11 =

E

�

E

+(10)

s11 =

Z

in

� Z0

Z

in

+ Z0(11)

s11[dB] = 20log(s11) (12)

where E

� is intensity of the reflected wave, E+ is in-tensity of the ongoing wave, Z

in

is the impedance of appli-cator and Z0 is impedance of the generator (Z0 = 50 ⌦)

SWR =

1 + |s11|1� |s11|

(13)

1.2. Geometry

The parameters of the applicator were optimized, thatthere is the lowest reflection coefficient s11 at the interfer-ence of the water bolus and the muscle tissue. After calcu-lation of parameters and modeling, the antenna was tunedby shortening and lengthening of the arms of spirals. Finalparameters are in next table.

proportionality constant r0 0,8

height hs 17 µ

inner radius r1 1,92 mm

outer radius r2 016,64 mm

length l 157,7 mm

strip width w 1,424 mm

distance between strips s 1,089 mm

number of threads N 3

coaxial connector inner radius rk1 0,5 mm

coaxial connector outer radius rk2 1,672 mm

Tab. 1. Parameters of spiral applicator

2. Simulation

Simulations were calculated in software COMSOLMultiphysics, that works on the finite element method. Firstwas constructed model with parameters from tab. 1 and 3.Than dielectric parameters were assigned to the parts of theapplicator (table 2).

relative

permitivity

✏r [-]

relative per-

meability µ[-]

conductivity

� [S/m]

muscle

tissue

56,865 1 0,805

water

bolus

78 1 5,5e�6

air 1 1 0

substrate 4 1 0

coaxial

cable

2,1 1 0

Tab. 2. Dielectric parameters of the materials of the applicator.

The antennas in shape of double the Archimedean spi-ral are placed on a dielectric substrate and from other sideare placed the SMA connectors, that are connected to theantennas through a conductor. One arm is connected to thephase and other to the ground. The centers of the antennasare distant 43,28 mm from each other. Around the applica-tor is a phantom of air, whole applicator lays on the waterbolus and beneath it is the muscle tissue phantom, that hasassigned physics Bioheat Transfer, that simulates distribu-tion of a heat in live organism. Temperature was set to 37�C.At an interference of the tissue and water was set heat gen-erator to 20�C, that simulates cooling the tissue with waterbolus. To phantoms were assigned dielectric attributes thatcharacterize them. Generator power was set to 15 W. Thatis enough to rise the temperature in the treated area to thera-peutical value.

The coefficients of reflection S11 from each antennahave minimum at -11 dB and maximum at -15,8 dB. In thefigure 1 you can see that 8 values are range of 1 dB, thatare the side antennas and the one is 5 dB lover, the middleantenna. It is because of the interactions of electromagnetic

POSTER 2015, PRAGUE MAY 14 3

parameters [mm]

muscle tissue 60 x 220 x 220

water bolus 10 x 220 x 220

air 11,5 x 220 x 220

substrate 1,5 x 180 x 180

Tab. 3. Parameters of apparatus and phantom

waves. The antennas were tuned to the lover peak, becauseif the antennas were tuned to peak that is seen at 2.7MHzwith S11 = -20 dB, the area of antenna was small and aneffectivity was not acceptable.

Fig. 1. Computed reflection coefficient S11 for all applicators.

Because it is needed to create as large area as possiblethat is heated up to 43-45�C, the middle antenna on position(2,2) was phase shifted by ⇡/8. Without this shift, the epi-center of treated area will be heated up to 48�C, that couldirreversibly damage tissue.

The resulting area has circular platform with 4cm ra-dius and 1-2 cm in width. (figure 2 - side slice). maximumtemperature reaches 44,278�C and is located in 3 cm beneathsurface of muscle tissue phantom. It is also seen that the wa-ter bolus successfully cools the top of the tissue phantom, soit wont reach higher values than is recommended.

Fig. 2. Distribution of temperature in side slice of virtual phan-tom.

In the figure 3 is seen distribution of SAR. Maximumreaches 251,7 W/kg. Also it is seen that under middle an-

tenna is SAR lowest with maximum at 171,3 W/kg. Bothmaxima were located in 1 cm depth and in further depth de-creasing fast. Color scale was set to 1/3 with maximum at84 W/kg, that figure had more to tell.

Fig. 3. Distribution of SAR in 1 mm slice of virtual phantom.

Fig. 4. Distribution of temperature in 1 mm slice of virtual phan-tom.

2.1. Possible connections

With regulation of power distributed to antennas of ap-plicator and their phase shift, it is possible to create variousshapes of treated areas. It is one of the best benefits of ma-trix of antennas. In ideal, we want to heat only the canceroustumor, which mostly doesn’t have ideal shape, that healthytissue won’t be damaged by the procedure. Some types ofpossible connections are simulated in figure 5.

3. Conclusion

Simulations were successful and proves, that matrix ofspiral applicator in shape of double Archimedean spiral canbe used for medical treatment. As it is seen in figure 1 and

4 D. DUFEK, SPIRAL APPLICATOR ARRAY DESIGN FOR LOCAL MICROWAVE HYPERTHERMIA TREATMENT

Fig. 5. Types of possible connections.

2 this antenna design has low coefficient of reflection andsuccessfully heats tissue with no apparent dangerous spot.Also with small size of the antennas and various types ofconnection, there is possibility to create matrix with moreantennas, that will cover larger area.

For treatment there won’t be ideal flat surface of thetissue, this problem should be solved by separating antennasfrom one desk and manually apply them to the surface of thetissue. That will secure same distance from the tissue foreach antenna and it will help with optimization for reflectioncoefficient.

In Future research I will be focusing on construction ofthis design and comparing with the simulated data. One ofthe main task will be to create a suitable power generator,that will split energy to the all antennas and with impedanceat all exits 50 Ohm.

Another problem that has to be solved is cooling of thetissue. The water bolus or material used as the bolus shouldbe composed of dielectric material with low resistivity, thatthere won’t be large power loss. Also the bolus have to beable to cool the tissue as much as possible, that it won’t bedamaged.

Acknowledgements

Research described in the paper was supervised by Ing.David Vrba, Phd., FBMI CTU in Prague.

References

[1] VRBA, J. Lekarske aplikace mikrovlnne techniky CVUT, Prague 2003,ISBN 80-01-02705-8

[2] BALANIS, Constantine A. Antenna Theory: Analysis and Design. 2nded. Arizona State University, 1997, ISBN 0-471-59268-4.

[3] BALANIS, Constantine A. Advanced Engineering Electromagnetics.2nd ed. Arizona State University, 1989, ISBN 0-471-62194-3.

[4] DUONG, Lawrence Computational electromagnetics in microwave hy-perthermia McGill University Montreal, 2005.

[5] POZAR, David M. Microwave Engineering University of Mas-sachusetts at Armherst 2012, ISBN 978-0-470-63155-3

[6] SAFARIK, J., RYCHLIK, O. Paskovy aplikator pro lokalnı termoter-apii. Prague, CVUT FEL 2009.

[7] BEREZNANIN, M. Model of microwave hyperthermia treatment .Prague, FEKT VUT 2011.

About Authors. . .

Daniel Dufek was born in Prague and finished bachelors de-gree on FBME CTU in Prague. Now he studies masters pro-gram Biomedical engineering on FEE CTU in Prague.