ADVANCED COMPUTER MODELING FOR INTERSTITIAL

MICROWAVE HYPERTHERMIA THERAPY

Comparison of Two Numerical Methods in Computational Electromagnetics

M. F. J. Cepeda, A. Vera, L. Leija

Dpto. de Ingeniería Eléctrica, Sección Bioelectrónica, CINVESTAV-IPN, San Pedro Zacatenco, México D.F., México

E. Ávila-Navarro

Dpto. de Ciencia de Materiales, Óptica y Tecnología Electrónica. Universidad Miguel Hernández, Elche, Spain

C. Reig, E. A. Navarro

Dpto. de Ingeniería Electrónica, Universitat de València, Burjassot, Spain

Keywords: Hyperthermia, Modelling, Applicator, Cancer.

Abstract: Microwave hyperthermia therapy is a recent development in the ﬁeld of tumor ablation. Eelectromagnetic

microwave irradiation applied to the tumor tissue causes water molecules to vibrate and rotate, resulting in

tissue heating and subsequently cell death via thermal-induced protein denaturation. To effectively treat

deep-stead tumors, the interstitial antennas should produce a highly localized specific absorption rate pattern

and be efficient radiators at different generator frequencies. Numerical electromagnetic and thermal

simulations are used to optimize the antenna design and predict heating patterns. An advanced computer

modeling of a double slot antenna for interstitial hyperthermia was designed using two different numerical

methods, the Finite Element Method and a Finite-difference time-domain. The aim of this work is to

compare and analyze both numerical methods.

1 INTRODUCTION

1.1 Hyperthermia

Hyperthermia is a type of cancer treatment in which

body tissue is exposed to high temperatures. In

oncology therapeutic treatments, the cancerous cells

can be destroyed if a controlled heating is induced

with temperatures from 6ºC to 8ºC, with minimal

injury to normal tissues. Some clinical trials have

studied hyperthermia in combination with radiation

therapy and/or chemo-therapy. These studies have

focused on the treatment of many types of cancer as

sarcoma, melanoma, and cancers of the head and

neck, brain, lung, oesophagus, breast, bladder,

rectum, liver, appendix, cervix, and peritoneal

lining. These studies have shown a significant

reduction in tumour size when hyperthermia is

combined with other treatments.

1.2 Methods of Hyperthermia

Several methods of hyperthermia are currently under

study, including local, regional, and whole-body

hyperthermia.

1) Local hyperthermia is used to heat a small area,

such as a tumor. It involves creating very high

temperatures that destroy the cells that are heated.

Radio waves, microwaves, ultrasound waves, or

other forms of energy can be used to heat the area.

2) In regional hyperthermia, various approaches

may be used to heat large areas of tissue, such as a

body cavity, organ, or limb.

3) Whole-body hyperthermia is used to treat

metastatic cancer that has spread throughout the

body. This can be accomplished by several

techniques that raise the body temperature, including

the use of thermal chambers or hot water blankets.

166

Cepeda M., Vera A., Leija L., Ávila-Navarro E., Reig C. and Navarro E. (2010).

ADVANCED COMPUTER MODELING FOR INTERSTITIAL MICROWAVE HYPERTHERMIA THERAPY - Comparison of Two Numerical Methods in

Computational Electromagnetics.

In Proceedings of the Third International Conference on Biomedical Electronics and Devices, pages 166-169

DOI: 10.5220/0002711501660169

 SciTePress

1.3 Interstitial Hyperthermia

This technique allows the tumor to be heated to

higher temperatures than external techniques. Under

anesthesia, probes or needles are inserted into the

tumor. The heat source is then inserted into the

probe. For the treatment of superficial tumors the

radiation is applied through external antennas, while

internal tumors are exposed to invasive applicators.

The operating frequency is usually 2.450 GHz,

which is one of the ISM (Industrial, Scientific, and

Medical) dedicated frequencies. These techniques

employ implanted minimally invasive thin antennas

for the delivery of local thermal doses; they are

inserted through the skin, into a biocompatible

catheter, under the guidance provided with an

imaging monitoring procedure (Ito, 2002).

1.4 Numerical Methods

Three main techniques exist within computational

electromagnetics (CEM). The first of these, the

finite-difference time-domain (FDTD) (Yee, 1966)

uses finite difference approximations of the time and

space derivatives of Maxwell's curl. This method has

been widely used to numerically evaluate the

electromagnetic radiation patterns of antennas in

tissue (Sullivan, 1990). The method of moments

(MoM), approximates numerical solutions to

integral equations, formulated in the frequency

domain to determine an unknown current

distribution for an antenna. The finite element

method (FEM), has been extensively used in

simulations of cardiac and hepatic radiofrequency

(RF) ablation (Haemmerich, 2003). FEM models

can provide users with quick, accurate solutions to

multiple systems of differential equations and as

such, are well suited to heat transfer problems like

ablation (Bertram, 2006).

2 MATERIALS AND METHODS

2.1 Governing Equations

The frequency-dependent reflection coefficient and

specific absorption rate (SAR) pattern in tissue are

important for the performance of interstitial

antennas. The frequency-dependent reflection

coefficient, can be expressed as:

Γ f

()

= 10 ⋅ log

()

⎛

⎝

⎜

⎞

⎠

⎟

[]

(1)

where P

is the input power and P

indicates

reflected power (W). The frequency where the

reflection coefficient is minimum is commonly

referred to as the resonant frequency and should be

approximately the same as the operating frequency

of the generator used. SAR represents the amount of

time average power deposited per unit mass of tissue

(W/Kg) at any position. It can be expressed

mathematically as

SAR =

W / kg

[]

(2)

where σ is tissue conductivity (S/m), ρ is tissue

density (kg/m

) and E is the electric field vector

[V/m]. The tissue temperature increase results from

both power and time, caused by direct MW heating

(from SAR) and tissue thermal conduction. MW

heating thermal effects can be roughly described by

Pennes’ Bioheat equation (Pennes, 1948):

∇⋅ −k∇T

(

)

− T ) + Q

met

+ Q

ext

(3)

where k is the tissue thermal conductivity (W/m°K),

is the blood density (Kg/m

), C

is the blood

specific heat (J/Kg°K), ω

is the blood perfusion rate

(1/s). T

is the temperature of the blood and T is the

final temperature. Q

met

is the heat source from

metabolism and Q

ext

an external heat source.

2.2 Material Properties

The antenna is based on a 50Ω UT-085 semirigid

coaxial cable. The outer conductor is copper, in

which a two small ring slot of width is cut close to

the short-circuited distal tip of the antenna to allow

electromagnetic wave propagation into the tissue.

The inner conductor is made from silver-plated

copper wire (SPCW) and the coaxial dielectric used

is a low-loss polytetraﬂuoroethylene (PTFE).

Furthermore the antenna is encased in a PTFE

catheter to prevent adhesion of the probe to

desiccated ablated tissue. Characteristics of the

materials and tissue are listed in Tab. 1.

2.3 Applicator Design

Antenna geometry parameters were chosen based on

the effective wavelength in muscle at 2.45 GHz,

which was calculated using the equation:

[]

eff

(4)

where c is the speed of light in free space (m/s), f is

the operating frequency (2.45 GHz), and ε

= 52.729

ADVANCED COMPUTER MODELING FOR INTERSTITIAL MICROWAVE HYPERTHERMIA THERAPY -

Comparison of Two Numerical Methods in Computational Electromagnetics

167

is the relative permittivity of the tissue at the

operating frequency. Fig. 1 shows that the slot

spacing length corresponds to 0.25 λ

eff

, and 0.0125

eff

respectively, that was chose to achieve localized

power deposition near the slots of the antenna.

Table 1: Dimensions and material properties for the

materials and tissue.

Parameter Value

Center conductor diameter 0.51 mm

Dielectric diameter 1.68 mm

Outer conductor diameter 2.2 mm

Diameter of catheter 1.79 mm

Tissue electrical conductivity 1.7388 S/m

Tissue thermal conductivity 0.5 W/m°K

Material ε

Inner dielectric of the coaxial cable 2.03

Catheter 2.60

Tissue 52.729

2.4 Computer Model Definition

2.4.1 Finite Element Method

Effects are modeled using commercial software

package (COMSOL Multiphysics ™). The FEM

model assumes that the coaxial slot antenna is

immersed in homogeneous tissue. Fig. 1 shows the

axial schematics of each section of the antenna, and

the interior diameters. The inner and outer

conductors of the antenna were modeled using

perfect electric conductor boundary conditions and

boundaries along the z axis are set with axial

symmetry.

Figure 1: Shows the axial schematics of each section of

the antenna, and the interior diameters.

2.4.2 Finite-Difference Time-Domain

The code was originally designed for the simulation

of especially printed antennas (Ávila-Navarro, 2006)

and recently adapted for material with losses. This is

an algorithm in 3D Cartesian coordinates and full-

wave in order to obtain electromagnetic fields in the

time domain at any point in the simulated structure.

The mesh used for the spatial discretization of the

problem is configurable. By applying the Fast

Fourier Transform (FFT) the field distributions is

calculated in any plane, and therefore the SAR is

obtained.

3 RESULTS

3.1 Finite Element Method

The mesh size was generated using the mesh

parameters in Table 2. The mesh consists of 3655

triangular elements. Dense mesh zone has been

generated in the vicinity of the tip of the antenna,

where the temperature is more concentrated.

Table 2: Mesh parameters.

Maximum element size scaling factor 0.55

Element growth rate 1.25

Mesh curvature factor 0.25

Mesh curvature cutoff 0.0005

Fig. 2 shows the heat source density. The

axisymmetric model requires 220 MB memory and

11 s of CPU time for single simulation on a Intel 2.4

GHz Core 2 Duo processor and a MAC OS X

v10.5.7 operative system.

3.2 Finite-Difference Time-Domain

The simulated reflection coefficient expressed

logarithmically of the coaxial double slot antenna at

2.45 GHz was -20.04. The total number of cells is

approximately 587,000. The applicator is immersed

in a homogeneous region simulating the human

tissue. Fig. 3 shows the SAR obtained with the

FDTD code for the coaxial double slot applicator

used. The reflection coefficient calculated for the

frequency of 2.45GHz is -11.2dB.

3.3 Model Validation

To validate the performance of computer model, a

double slot antenna was constructed from UT-85

semirigid coaxial cable and a SMB connector. Fig. 4

shows the temperature distribution in a Cholesteric

BIODEVICES 2010 - International Conference on Biomedical Electronics and Devices

168

Liquid Crystals (LCR, model NPR30C5B) at 1 W.

The temperature measurement experiment setup is

described in (Cepeda – 2008).

Figure 2: The computed microwave heat source density.

4 CONCLUSIONS

We have developed two models in parallel of an

applicator for microwave hyperthermia therapy. The

first of these was using commercial software based

on FEM. For the other a specific code based on

FDTD has been developed. Nevertheless both results

are comparable. The potency of the first and

versatility of the second method allows

complementing and improving the design for a

future application. Finally, there is an increasing

need to design and evaluate applicators, which

permit to improve antennas for interstitial

hyperthermia using the Penne’s bioheat equation.

Figure 3: SAR distribution produced by FDTD.

Figure 4: A picture of the hyperthermia experiment.

Shows the color changes with the rise in temperature.

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Cepeda M: F: J, Vera A and Leija L., Microcoaxial

Double Slot Antenna for Insterstitial Hyperthermia:

Modeling and Validation”, International Conference

on Advances in Electronics and Micro-Electronics

ENICS 2008, Valencia, Spain, September, 2008, 138-

143pp. ISBN: 978-0-7695-3370-4

ADVANCED COMPUTER MODELING FOR INTERSTITIAL MICROWAVE HYPERTHERMIA THERAPY -

Comparison of Two Numerical Methods in Computational Electromagnetics

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