2. Breast model and propagation analysis

#### 2.1. Electromagnetic property of the breast

organization structures as fatty, fibroglandular, and malignant tissues. However, the electromagnetic analysis including the antennas, supporting structure, and environment must be accurately carried out because measuring error, noise, and modeling error significantly affect the image reconstruction. Moreover, since the calculation load is enormous, it is unsuitable for mass examination. UWB radar cannot reconstruct the organization structure accurately [6]. However, since it is tolerant to measuring error and noise in comparison with tomography, it is easy to manufacture. Furthermore, since the calculation load is small, it is suitable for mass

We have developed multistatic UWB radar for early breast cancer detection. Our equipment features multistatic microwave imaging via space time (MS-MIST) algorithm, which extends the MIST algorithm to multistatic UWB radar [5] and a conformal array, which fixes the breast to the inner shape of a sensor via suction [7]. Through numerical simulations and experiments with phantoms, MS-MIST was confirmed to have high resolution with low artifacts. In addition, our sensor requires neither placement of the breast in a tank filled with a coupling liquid nor measurement of the breast shape. The proposed system has low failure rate of inspection in comparison with the already developed UWB radar [6] because the sensor with suction and fixation restrains the patient from moving and breathing during the scan. Moreover, the inspection time is short because the number of antennas is reduced by MS-MIST with high resolution and low artifact. Hence, it results in small size and low cost. First, we describe the clinical equipment developed and demonstrate the imaging results, including numerical and

The clinical test results demonstrate that the system can detect cancer that has a clear boundary and is isolated from the fibroglandular tissue. However, if the boundary is irregular or if the tumor is buried under the fibroglandular tissue, the system is unable to correctly reconstruct the shape of the tumor [6]. Therefore, we are currently working on the development of

In order to achieve accurate image reconstruction, it is necessary to obtain diverse observation data. Several methods can be employed to obtain diverse observation data. More observation data can be obtained by increasing the number of antennas; however, the scale of the apparatus increases and the computational cost becomes substantial. Furthermore, the signal-to-noise ratio (SNR) is degraded by increasing the size, which degrades the image reconstruction. A method using multiple frequencies has been proposed [12]. In general, biological tissue is a medium with frequency dependence, and its behavior is modeled using the Debye approximation with several parameters. Consequently, the number of unknown parameters increases

The multiple-polarization method has been examined as a means to obtain a variety of observation data. The impact of polarization on image reconstruction was evaluated in Ref. [13], and it was concluded that the effectiveness was limited. However, the physical considerations related to antenna arrangement have not yet been investigated. Second, we review a compact-sized imaging sensor using multipolarization. We use the distorted Born iterative method (DBIM)

with the number of frequencies; thus, the reconstruction becomes difficult.

described in Ref. [12] to solve the inverse scattering problem.

examination.

46 New Perspectives in Breast Imaging

clinical experiments.

microwave tomography [8–11].

The breast cancer detection based on microwave imaging relies on large differences in the electromagnetic properties between normal and malignant tissues. In quantitative microwave imaging, considering the biological tissues as dielectrics, the dielectric properties are reconstructed according to the differences in the complex permittivity, defined by Eq. (1):

$$
\varepsilon^\* = \varepsilon\_r + j \frac{\sigma}{\omega \varepsilon\_0} \tag{1}
$$

where ε<sup>r</sup> is the relative permittivity, σ is the conductivity of examined object, ε<sup>0</sup> is the freespace permittivity, and ω is the angular frequency.

The electromagnetic properties of breast tissue in different frequency ranges have been studied. Gabriel et al. conducted a major review of measured dielectric properties on healthy human tissues for frequencies between 10 Hz and 100 GHz [14]. In the study, the basic and well-known Debye model in Eq. (2) is introduced:

$$
\varepsilon^\*(\omega) = \varepsilon\_{\circ} + \frac{\varepsilon\_{\circ} - \varepsilon\_{\circ}}{1 + j\omega\tau} \tag{2}
$$

This equation is extended to the Cole-Cole expression to model the structure and composition of biological tissues, defined in Eq. (3):

$$
\varepsilon^\*(\omega) = \varepsilon\_\circ + \frac{\Delta\varepsilon}{1 + j\omega\tau} + \frac{\sigma\_s}{j\omega\varepsilon\_0} \tag{3}
$$

where ε<sup>∞</sup> is the static frequency permittivity constants, and σ<sup>s</sup> is the static conductivity. The magnitude of dispersion is Δε = ε<sup>s</sup> � ε∞. The relaxation time constant τ is assumed to be spatially invariant and usually considered to be in the range of 15–17 ps.

Furthermore, female breast tissues have been studied with focus on breast tumor detection. Ex vivo measurements of fresh human malignant and normal breast tissues have been performed by several groups. Lazebnik et al. reported the most comprehensive examination of the dielectric properties of normal, benign, and malignant breast tissues [3].

#### 2.2. Electromagnetic analysis

Microwave mammography consists of multiple antennas placed around the breast as shown in Figure 1. An antenna is selected, and subsequently, a microwave signal is transmitted. At this time, the signals received by other antennas are collected. The transmitting antennas are sequentially selected to obtain the received data. We reconstruct the image using a set of received data. In tomography, this physical phenomenon is modeled using a computer. Since the electric constant distribution of the image area is unknown, it is initialized with an appropriate value and repeatedly updated using Newton's method. It is necessary to obtain the electromagnetic field distribution of the image area to apply the Newton's method.

Several methods can be used to solve the electromagnetic problem, including the method of moment (MoM), finite element (FEM), and finite-difference time-domain (FDTD) [15]. It is a very difficult task to prepare the original program using these methods.

In recent years, many commercial electromagnetic field analysis simulators have been developed and widely used for antenna design, electromagnetic compatibility analysis, etc. Commercial simulators are well debugged, and various methods for modeling with high accuracy are adopted. Many simulators have functions to link with external software. We linked

Figure 1. Breast screening by microwave imaging.

MATLAB with simulators such as FEMTET, MW-S, and HFSS, analyzed the electromagnetic field with a simulator, and reconstructed the image using the MATLAB program. If the modeling error is disregarded, electromagnetic field analysis using the FDTD method or MoM is possible.
