5. A near-field radar imaging system for bimodal applications

In the last two sections, some aspects of mammography, digital tomosynthesis, and microwave imaging were reviewed. The idea of a bimodal system that takes advantage of the strengths of both systems and can potentially compensate some of the drawbacks of each modality makes sense in the case of NRI and DBT. Among the number of other different combinations that has been tested in the last few years, NRI and MRI, optical imaging and DBT, and NRI and ultrasound can be listed. In the first case, the interference of the magnetic fields with the metallic part of the microwave imaging system impeded the simultaneous implementation of the NRI and MRI sensors [86], but in the other two cases, important results such as access to the map of vessels around tumors via the optical modality [87] and detection of very small inclusion [88], down to 1.2 mm, were reported. One of the pragmatic ways by which NRI can be added as a complementary system to the DBT is to design and build a compact NRI system that conforms to the geometry of the DBT and can scan the breast in a co-registered fashion using mechanical motion. This idea is illustrated schematically in Figure 3: (1) to conform to the DBT's shape, the NRI system was designed to fit into the compression paddle, (2) to be as compact as possible, a set of antipodal Vivaldi antennas (AVAs) were used as the transducer array, (3) to enable mechanical motion, a two-dimensional motion stage was implemented. In the succeeding subsections, the various parts of the system are described in more details.

#### 5.1. Antipodal Vivaldi antennas (AVAs)

Vivaldi antennas are planar, compact in size, and easy to manufacture [91]. These qualities make Vivaldi antenna a good candidate for use in an add-on NRI system, particularly due to

Figure 3. The designed NRI mechatronic system (left) that fits into the compression paddle of the DBT (right). In this manner, first the DBT and then the NRI system scans the breast.

that a number of these antennas can fit into a small space [89]. On the other hand, Vivaldi antennas are limited in bandwidth since they require a balun to convert the micro-strip into a strip-line. One solution to remove this obstacle is to employ antipodal vivaldi antenna (AVAs) that have direct feeding micro-strip lines while maintaining the advantages of Vivaldi antennas. To further reduce the size of the AVAs and improve the coupling of electromagnetic waves going into the breast tissue, they can be designed to operate in a liquid of high dielectric constant. The use of a matching liquid can cut each dimension of the antenna by a factor of 1= ffiffiffiffi εr <sup>p</sup> , with <sup>ε</sup><sup>r</sup> being the liquid relative permittivity. Such a technique, however, asks for a supportive substrate that also has a high dielectric constant. This imposes an extra condition on the selection of the coupling liquid that will be discussed later. In the case of AVAs of the proposed system, a 2 mm ceramic layer (T-Ceram, E-37) with a relative permittivity of 37 was utilized for each antenna. Figure 4 shows the design parameters of an AVA alongside with a photo of a pair of fabricated AVAs. The exponential curves ya, yt, and yf shown in the figure are given by the following Eq. [90]:

$$y\_k = \pm \left( A\_k e^{p\_k(x - B\_k)} + \mathbb{C}\_k \right) \tag{1}$$

where

5. A near-field radar imaging system for bimodal applications

5.1. Antipodal Vivaldi antennas (AVAs)

24 New Perspectives in Breast Imaging

manner, first the DBT and then the NRI system scans the breast.

In the last two sections, some aspects of mammography, digital tomosynthesis, and microwave imaging were reviewed. The idea of a bimodal system that takes advantage of the strengths of both systems and can potentially compensate some of the drawbacks of each modality makes sense in the case of NRI and DBT. Among the number of other different combinations that has been tested in the last few years, NRI and MRI, optical imaging and DBT, and NRI and ultrasound can be listed. In the first case, the interference of the magnetic fields with the metallic part of the microwave imaging system impeded the simultaneous implementation of the NRI and MRI sensors [86], but in the other two cases, important results such as access to the map of vessels around tumors via the optical modality [87] and detection of very small inclusion [88], down to 1.2 mm, were reported. One of the pragmatic ways by which NRI can be added as a complementary system to the DBT is to design and build a compact NRI system that conforms to the geometry of the DBT and can scan the breast in a co-registered fashion using mechanical motion. This idea is illustrated schematically in Figure 3: (1) to conform to the DBT's shape, the NRI system was designed to fit into the compression paddle, (2) to be as compact as possible, a set of antipodal Vivaldi antennas (AVAs) were used as the transducer array, (3) to enable mechanical motion, a two-dimensional motion stage was implemented. In the succeeding subsections, the various parts of the system are described in more details.

Vivaldi antennas are planar, compact in size, and easy to manufacture [91]. These qualities make Vivaldi antenna a good candidate for use in an add-on NRI system, particularly due to

Figure 3. The designed NRI mechatronic system (left) that fits into the compression paddle of the DBT (right). In this

$$A\_k = \frac{y\_{k1} - y\_{k2}}{e^{P\_k(x\_{k1} - B\_k)} - e^{P\_k(x\_{k2} - B\_k)}}, \ \ C\_k = \frac{y\_{k1}e^{P\_k x\_{k2}} - y\_{k2}e^{P\_k x\_{k1}}}{e^{P\_k x\_{k2}} - e^{P\_k x\_{k1}}} \tag{2}$$

and k can be substituted with a, t, or f to obtain ya, yt, or yf, in order. The subscripts 1 and 2 for x denote the x-coordinate of the start point and endpoint of the curves. The constants Ai, Bi, Ci, and Pi for every equation are given in Table 1. The numerical values of the parameters for the

Figure 4. (a) Design parameters of the AVA used in the system. This transparent view of the antenna shows the curves on front (signal) and back (ground) of the antenna. (b) The fabricated antenna has a reduced size, as it can be seen when the size is compared to a person's hand. (c) The simulated results showing the magnitude of the electric field inside an ethanol model at different frequencies.


Table 1. The definitions of the parameters A, B, C, and P in the curve equations of the AVA.

fabricated antennas were W = 30, Wg = 2.06, Wa = 25.42, Wts = 0.29, Ws = 0.025, Lt = 8.40, Lts = 1.03, La = 26.54, all in millimetres, and Pt = �1.04, Pf = 0.94, Pa = 0.1 [91]. The radiation pattern of a single antenna is illustrated in Figure 4 (c) at different frequencies.

To select the coupling liquid, the dielectric relaxation of many liquids, such as [92–102], were considered. John D. et al. used multi-step techniques to approximate the average dielectric properties of the breast tissue and reported a minimum and maximum of about 26.5 and 27 for the relative permittivity in 1–3 GHz, respectively [103]. For a proper coupling of the electromagnetic waves, the average dielectric constant of the sought liquid must be between the relative permittivity of the antenna substrate (37) and that of the average breast (26.75). Based on this criterion and other conditions such as non-toxicity, non-carcinogenicity, low viscosity, and stability at room temperature, among many candidates, ethanol was selected as the matching liquid. The characterization of an array of two AVAs in ethanol can be found in [104].

#### 5.2. Radiation safety: Specific absorption rate (SAR)

To assure that the microwave radiation from the antennas was safe for human use, a specific absorption rate (SAR) analysis was conducted. The SAR determines the amount of power absorbed by the human tissue when it is exposed to the electromagnetic radiation [105]. The local SAR at a certain point inside the tissue is defined as

$$SAR\_{local}(\mathbf{r}, \omega) = \frac{\sigma(\mathbf{r}, \omega) |E(\mathbf{r}, \omega)|^2}{2\rho(\mathbf{r})} \tag{3}$$

where r is the position vector, ω is the frequency in [rad/s], σ(r, ω) is the material conductivity in [S/m], and r(r) is the mass density of the dielectric. For standardization purposes, SAR is averaged over a small sample volume as follows:

$$SAR\_{\text{average}}(\mathbf{r}, \omega) = \frac{1}{V} \int \frac{\sigma(\mathbf{r}, \omega) \left| E(\mathbf{r}, \omega) \right|^2}{\rho(\mathbf{r})} d\mathbf{r} \tag{4}$$

This power flow reveals itself in the form of temperature gradient over time, and it could cause harm if it trespasses a certain value. Federal Communications Commission (FCC) in the United States has set a threshold of 1.6 W/kg for the maximum value of SAR in a 1-gram sample of body parts [105]. In Europe, as set by The Council of the European Union (CEU), the limit is 2 W/kg in a 10-gram sample of body parts [107]. IEEE Standard 1528 presents a methodology to compute the peak SAR in the head under exposure to radio frequency radiation [108, 109]. This can also be applied in other body part calculations. HFSS ANSYS, which automatically applies IEEE standard P1528.4 to calculate the spatial average of SAR [111], was utilized to analyze the SAR of the heat that an AVA induces in a breast model placed directly underneath it. The model consisted of fat distribution data from a real healthy breast, obtained by the DBT system at the Massachusetts General Hospital (MGH). Figure 5 (a)–(c) illustrates the fat distribution in the model from different views. In lieu of importing the entire data set into the HFSS, the fat percentage values were averaged over cubes of 6 mm side to lessen the computational load. Next, the complex relative permittivity of the breast was approximated by a Cole-to-Cole model. The impact of the breast compression paddle and the ethanol container were also accounted for by using a simplified geometry of the NRI system, as shown in Figure 5 (d)–(e). In accordance with the real measurements, the power fed to the antennas

fabricated antennas were W = 30, Wg = 2.06, Wa = 25.42, Wts = 0.29, Ws = 0.025, Lt = 8.40, Lts = 1.03, La = 26.54, all in millimetres, and Pt = �1.04, Pf = 0.94, Pa = 0.1 [91]. The radiation pattern of

0 Wg

yi(x) AB C P

<sup>2</sup>ðePa La �1<sup>Þ</sup> Wt <sup>+</sup> Wts � Wts

To select the coupling liquid, the dielectric relaxation of many liquids, such as [92–102], were considered. John D. et al. used multi-step techniques to approximate the average dielectric properties of the breast tissue and reported a minimum and maximum of about 26.5 and 27 for the relative permittivity in 1–3 GHz, respectively [103]. For a proper coupling of the electromagnetic waves, the average dielectric constant of the sought liquid must be between the relative permittivity of the antenna substrate (37) and that of the average breast (26.75). Based on this criterion and other conditions such as non-toxicity, non-carcinogenicity, low viscosity, and stability at room temperature, among many candidates, ethanol was selected as the matching

To assure that the microwave radiation from the antennas was safe for human use, a specific absorption rate (SAR) analysis was conducted. The SAR determines the amount of power absorbed by the human tissue when it is exposed to the electromagnetic radiation [105]. The

SARlocalðr, <sup>ω</sup>Þ ¼ <sup>σ</sup>ðr, <sup>ω</sup>ÞjEðr,ωÞj<sup>2</sup>

where r is the position vector, ω is the frequency in [rad/s], σ(r, ω) is the material conductivity in [S/m], and r(r) is the mass density of the dielectric. For standardization purposes, SAR is

V

This power flow reveals itself in the form of temperature gradient over time, and it could cause harm if it trespasses a certain value. Federal Communications Commission (FCC) in the United States has set a threshold of 1.6 W/kg for the maximum value of SAR in a 1-gram sample of body parts [105]. In Europe, as set by The Council of the European Union (CEU), the limit is 2 W/kg in a 10-gram sample of body parts [107]. IEEE Standard 1528 presents a methodology to compute the peak SAR in the head under exposure to radio frequency radiation [108, 109].

<sup>ð</sup> <sup>σ</sup>ðr, <sup>ω</sup>ÞjEðr,ωÞj<sup>2</sup>

SARaverageðr, <sup>ω</sup>Þ ¼ <sup>1</sup>

<sup>2</sup>ρðr<sup>Þ</sup> (3)

<sup>2</sup> � At Pt

<sup>2</sup> � Af Pf

<sup>2</sup> � Af Pa

<sup>ρ</sup>ðr<sup>Þ</sup> <sup>d</sup><sup>r</sup> (4)

liquid. The characterization of an array of two AVAs in ethanol can be found in [104].

a single antenna is illustrated in Figure 4 (c) at different frequencies.

Table 1. The definitions of the parameters A, B, C, and P in the curve equations of the AVA.

yf Af Wt + Wts Wts

yt Wts�Wg

26 New Perspectives in Breast Imaging

ya WtsþWa

<sup>2</sup>ðePt Lt �1<sup>Þ</sup>

5.2. Radiation safety: Specific absorption rate (SAR)

local SAR at a certain point inside the tissue is defined as

averaged over a small sample volume as follows:

Figure 5. The fat distribution map of a real healthy breast used to compute the complex dielectric constant [106], and its associated model. The map as viewed from (a) top, (b) side, (c) front. The approximated model in a voxel grid of cubes of 6-mm sides, from (d) front and (e) perspective view.

Figure 6. The SAR study results of one antenna radiating towards the breast model: (a) 1-gram sample at 1 GHz, (b) 10-gram sample at 1 GHz, (c) 1-gram sample at 2.5 GHz, (d) 10-gram sample at 2.5 GHz. The maximum value of the SAR occurs at 1 GHz in the 1-gram sample model and is much less than the threshold value set by the FCC.

was set to 0 dBm (1 mW). The results for both 1- and 10-gram sample SAR models at two dissimilar frequencies in the operational bandwidth of the system, 1–3 GHz, are shown in Figure 6. As observed, the peak SAR values are clearly below the CEU and FCC thresholds, by at least three orders of magnitude, in all cases. This suggests that the radiation from the transducer array, even with an array of sixteen antennas, is safe for human use.

### 6. The mechatronic system: Motion stage and data acquisition

#### 6.1. The hardware

As mentioned earlier, to illuminate the entire breast volume under compression, the antennas needed to be moved in a pre-determined trajectory. To accomplish this, a belt-driven mechanical setup was implemented based on the open-source 3D printer, MAKERBOT Replicator. Two motors were used, one for each axis of motion, to enable the planar motion. One of the motors (Y-axis) was fixed to the walls of the container, and the other one (X-axis) was mounted on a carriage that itself moved as the first motor shaft rotated. The dimensions and other geometric properties of the box containing all the mechanical parts were majorly restrained by the compression paddle of General Electric DBT system that was available at the MGH. Given these requirements, two acrylic boxes were built, one on the bottom, serving as the matching liquid container, and one on the top, holding the motion stage assembly in place. Two Big Easy Drivers, powered by a 12 V/5 A power supply, and an Arduino Uno were used to actuate and control the motors. For the bottom box to safely contain the coupling liquid, all of its interior edges were sealed with a silicon-based sealant (General Electric), which was specifically formulated for plastics. Moreover, a lid attached to the top box via hinges was used to constrain ethanol's evaporation. The various parts of the system are shown in Figure 7.

#### 6.2. The software

LABVIEW was used as the main programming tool for data acquisition, mechanical motion control, and synchronization between the two. PNA-X (N5242), a programmable network analyzer by Keysight, was used for data acquisition and LABVIEW Interface for Arduino (LIFA) was installed on the workstation (Windows 10) to enable the connection between Aruino and LABVIEW. Using the Stepper Motor Library of LIFA, the motors were configured to have a default speed of 2000 steps/sec in each section of the motion path. The collected data was the two-port s-parameters of the AVAs, which included the phase and magnitude information; and it was recorded on a folder that was shared between the operating system of the PNA-X and the workstation computer. For simplicity, in the first imaging experiments, instead of using triggers to time different events in the acquisition process, a short delay, was utilized after the command was sent to the PNA-X to ascertain that the data collection at each point of the path was complete before moving to the next position. The value of the delay was determined approximately with trial and error. As displayed in Figure 8, at any time during the motion on the default path, only one motor is active.

Near-Field Radar Microwave Imaging as an Add-on Modality to Mammography http://dx.doi.org/10.5772/intechopen.69726 29

was set to 0 dBm (1 mW). The results for both 1- and 10-gram sample SAR models at two dissimilar frequencies in the operational bandwidth of the system, 1–3 GHz, are shown in Figure 6. As observed, the peak SAR values are clearly below the CEU and FCC thresholds, by at least three orders of magnitude, in all cases. This suggests that the radiation from the

As mentioned earlier, to illuminate the entire breast volume under compression, the antennas needed to be moved in a pre-determined trajectory. To accomplish this, a belt-driven mechanical setup was implemented based on the open-source 3D printer, MAKERBOT Replicator. Two motors were used, one for each axis of motion, to enable the planar motion. One of the motors (Y-axis) was fixed to the walls of the container, and the other one (X-axis) was mounted on a carriage that itself moved as the first motor shaft rotated. The dimensions and other geometric properties of the box containing all the mechanical parts were majorly restrained by the compression paddle of General Electric DBT system that was available at the MGH. Given these requirements, two acrylic boxes were built, one on the bottom, serving as the matching liquid container, and one on the top, holding the motion stage assembly in place. Two Big Easy Drivers, powered by a 12 V/5 A power supply, and an Arduino Uno were used to actuate and control the motors. For the bottom box to safely contain the coupling liquid, all of its interior edges were sealed with a silicon-based sealant (General Electric), which was specifically formulated for plastics. Moreover, a lid attached to the top box via hinges was used to constrain ethanol's evaporation. The various parts of the system are

LABVIEW was used as the main programming tool for data acquisition, mechanical motion control, and synchronization between the two. PNA-X (N5242), a programmable network analyzer by Keysight, was used for data acquisition and LABVIEW Interface for Arduino (LIFA) was installed on the workstation (Windows 10) to enable the connection between Aruino and LABVIEW. Using the Stepper Motor Library of LIFA, the motors were configured to have a default speed of 2000 steps/sec in each section of the motion path. The collected data was the two-port s-parameters of the AVAs, which included the phase and magnitude information; and it was recorded on a folder that was shared between the operating system of the PNA-X and the workstation computer. For simplicity, in the first imaging experiments, instead of using triggers to time different events in the acquisition process, a short delay, was utilized after the command was sent to the PNA-X to ascertain that the data collection at each point of the path was complete before moving to the next position. The value of the delay was determined approximately with trial and error. As displayed in Figure 8, at any time during the

transducer array, even with an array of sixteen antennas, is safe for human use.

6. The mechatronic system: Motion stage and data acquisition

6.1. The hardware

28 New Perspectives in Breast Imaging

shown in Figure 7.

6.2. The software

motion on the default path, only one motor is active.

Figure 7. Schematic diagram of the mechanical parts of the motion stage: (a) The gantry on top, responsible for moving the transducer array in two dimensions, (b) the attachment mechanism for the top and bottom boxes, (c) the antenna holder with a structure that assures cables are fixed on the end connected to the antenna, (d) the complete assemblage, including the electronics box, fitted into the DBT paddle.

Figure 8. The two-dimensional trajectory viewed from the top. The default path is set to be maze-like (with adjustable number of back-and-forth sections) so that the whole breast volume can be covered. The straight path was used in initial experiments as will be described later.
