Abstract
Applicator
Model
Methods
Results
Summary
References

FDTD Analysis of the Electromagnetic Fields Produced by a Fourchannel RF
Applicator
Abstract:
A fourchannel
radiofrequency (RF) electromagnetic (EM) phased array applicator has been
designed for hyperthermia treatments of locally advanced breast cancer. Simulations of the electric field produced
inside and outside of the tank are performed by the finite difference time
domain (FDTD) method, which is an efficient approach for computating
of electromagnetic wave propagation within complex structures. In these 3D FDTD simulations, the absorbing
boundary condition (ABC) is implemented as a perfectly matched layer (PML) on
the outer surface of the computational domain. The tank is modeled with the staircase
approximation, and to reduce the numerical error introduced by the sloped
surface of the tank, a cell spacing of 2.4mm is selected in all three dimensions. The endloaded dipole antennas are modeled
by the DeyMittra technique for structures
containing perfect electric conductors (PECs), which is the result of the Yee algorithm
derived from the integral form of Faraday's Law and Ampere's Law instead of
the differential form of these expressions.
The size of the computational domain is 1m by 0.72m by 0.7m, and the
source frequency is 140MHz. Simulation results obtained with the FDTD method
demonstrate that the phased array applicator generates standing waves within
the water tank, and constructive interference ultimately produces a focus in
the center of the tank.
Applicator 3D models for EM
simulation:
Four
endloaded dipole antennas^{[}^{1]}
are mounted on a water tank such that each antenna points in the direction of
the intended target. The lexan water tank is filled
with deionized water, which is depicted in figure
1. The geometric focus is in the upper central region of the applicator. The
source frequency is 140MHz in all simulations.
Figure 1 : RF phased array applicator with 4 antennas
Methods :
The EM field inside the applicator is
simulated with the FiniteDifference TimeDomain (FDTD) method. Berenger’s perfectly matched layer (PML) is chosen as the
absorbing boundary condition (ABC)[3][5]. The
simulation grid consists of cubic FDTD cells that are 2.4mm on a side, which is about 1/100 of
the wavelength in water. The lexan tank is modeled with staircase cells and all cells
containing antennas are modeled with the DeyMittra
technique for PEC structures^{[3]}
Results :
The size of tank is 30cm(x) by 55cm(y)
by 27cm(z). The FDTD simulation results are
evaluated in deionized water, in the lexan enclosure, and in the air surrounding the
tank. Fig. 2 contains two orthogonal
2D slices of a simulated 3D electric field (E field) evaluated for the 4
antenna breast applicator depicted in Fig. 1. This result shows that the E
field at (0, 0, 3cm) is
maximized with a sinusoidal 140MHz excitation. The upper figure shows the E
field in the xy plane located at z = 3 cm
while the lower figure shows the E
field in the yz plane which is located at x = 0cm. All of the results are shown in
dB.
Fig. 2: E field evaluated
in the xy and yz planes
Figure 3a demonstrates simulated and
measured electric field values along the Z axis from about 2.5 cm above the
water surface to 14cm below the surface.
The FDTD simulation correctly predicts the locations of the measured
minimum and maximum values for the 4antenna applicator. The maximum measured and simulated values
are observed 3cm below the water surface, whereas the minimum measured and
simulated values occur 12cm below the water surface. Fig 3b and 3c also shows
a broad peak along the X and Y axes for both the measured and simulated
electric fields. In Figure 3, the
measurements confirm the overall trend of the simulated electric field in
each direction.
Fig. 3a: Measured and simulated E field evaluated
along the Z axis (X=0, Y=0)
Fig. 3b: Measured and simulated
E field evaluated along the X axis
(Y=0, Z=3cm)
Fig. 3c: Measured and
simulated E field evaluated along the Y axis
(X=0, Z=3cm)
After validating
the FDTD algorithm on this model, a plastic cup is inserted into the tank to fix
the position of breast, as shown in Fig. 1, the cup inner diameter is 10cm,
the thickness is 3mm, and the height is 12 cm. Next, a breast phantom is placed in the
center of the applicator. The breast phantom conforms to the shape of the
cup, the outer 5mm of the phantom material is modeled as mammary tissue, and
the remaining phantom material is modeled as tumor, as shown in Fig 4. All
material parameters are listed in Table 1.
Fig. 4: Breast model

Material/tissue

Permittivity

Conductivity σ (S m1)

Density
(kg m3)

Patient

Mammary

10

0.06

880

Muscle

75

0.75

1050

Malignant mammary

65

0.74

1050

Applicator

Deionized water

76.5

0.001

1000

metal

1

107

7900

Lexan

2.9

0

1190

Table 1: Material and
tissue properties for FDTD modeling^{[1],[2]}
Fig. 5 shows the
simulated E field distribution when the cup is included in the model. Fig. 6
shows the E field distribution when a breast phantom is placed into the
applicator. All results show the same yz plane
located at x = 0 and xy plane located.
Fig. 5: E field
distribution for the cup model Fig.6: E field
distribution for a phantom breast
evaluated in the xy and yz planes placed in the
applicator with an additional cup.
Summary & Future work:
Comparisons between
simulated and measured electric fields show that FDTD results successfully predict
the measured E field as demonstrated in the figures above. FDTD simulations in a breast phantom show
that this applicator can heat a tumor surrounded by a thin layer of mammary
tissue. More detailed human models, based on MR and/or CT images, will be
included in future FDTD simulation results.
References:
 W. T. Joines, Y.
Zhang, C Li, and R. L. Jirtle, “The Measured Eletrical Properties of Normal and Malignant
Human tissues from 50 to 900
MHz” Med. Phys. 21(4), 547550
(1994).
 H.
Kroeze, J. B. Van de Kamer, A. A. C. De Leeuw and J. J. W. Lagendijk. “Regional hyperthermia applicator
design using FDTD modeling”. Phys. Med. Biol. 46 No 7 19191935 (2001).
 ”Computational Electrodynamics: The
FiniteDifference TimeDomain Method”, Second edition. by A. Taflove, S. C. Hagness. Artech House (2000).
 S. M. Foroughipoul and
K. P. Esselle, “The theory of a
SingularityEnhanced FDTD Method of Diagonal Metal Edges”, IEEE
Transactions on Antennas and Propagation Vol. 51, No.2, 312321 (2003).
 J. P. Berenger,
“ThreeDimensional Perfectly Matched Layer for the Absorption of
Electromagnetic Waves”, Journal of Computational Physics 127, Article
No. 0181 363–379 (1996)

Author:
Ruihua Ding
Contact:
dingruih@msu.edu
Links:
My Group
MSU EGR
MSU
