Biomedical Engineering Reference
In-Depth Information
Numerical Breast Model
Finite difference time domain (FDTD) TE z mode ( E x, E y and E z ) with spatial resolu-
tion of 0.5 mm square was used to obtain the backscatter signals. The computational
space consists of 401 cells along the direction of propagation and the direction of
electric field source arranged to form a square box. Uniaxial perfectly matched layer
(UPML) is used beyond the computational space to ensure perfect absorption at
the boundaries. Details of the update equations used for the FDTD simulation are
discussed in [ 23 ].
Permittivity for average breast medium, clutter sources and lesion target at
different frequencies is obtained through Debye model,
s
σ
ω 0 ,
( ω )
=
+
jωτ p
j
(1)
1
+
where ω
2 πf is the angular frequency, s the static permittivity, the infinite
permittivity, 0 the permittivity of free space, σ the conductivity of the medium and
T p is the relaxation constant. The nominal values used for the breast and lesion tissue
are given in Table 1 . The clutter sources of varying dielectric constants between 8.1
and 9.9 are introduced to mimic a realistic breast tissue.
The breast is modeled as a 5 cm radius cylinder with some regions containing
clutter sources as in [ 6 ]. A directed field point source transceiver and four additional
point receivers are placed at a radius of 6.5 cm away from the center at 15-degree
intervals. Figure 1 shows the configuration of simulation space. Two types of lesions,
smooth and spiculated, were used in this study to represent benign and malignant
lesions, respectively. Figure 2 shows a sample of each type of lesion.
Five hundred and forty backscatter responses from the respective environments,
each consisting of 3,201 temporal points, are obtained through numerical meth-
ods. Out of the 540 responses, 270 responses correspond to benign lesions, which
have been modeled as non-spiculated lesions and the rest are malignant lesions
which are highly spiculated. As an antenna array of nine antennae has been modeled,
nine backscatter signals are collected from each lesion realization. Total realization
number of the lesions is 30 lesions from each of the benign and malignant type.
Further details of the configuration, simulation steps and lesion characteristics are
discussed in [ 21 ].
=
Complex Harmonic Estimation
According to the geometrical theory of diffraction (GTD) [ 24 , 25 ], backscattered
signal from a number of scattering points has a pattern in frequency domain. As
described in [ 26 ], each scatterer in the view of the antenna will create a harmonic term
in the frequency-domain response of a UWB pulse. This means that the frequency
response of the backscattered signal is a combination of some complex harmonic
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