Phase Compensation Technique for Effective Heat Focusing in Microwave Hyperthermia Systems

: In this paper, effective electromagnetic (EM) focusing achieved with a phase compensation technique for microwave hyperthermia systems is proposed. To treat tumor cells positioned deep inside a human female breast, EM energy must be properly focused on the target area. A circular antenna array for microwave hyperthermia allows EM energy to concentrate on a speciﬁc target inside the breast tumor. Depending on the cancerous cell conditions in the breast, the input phases of each antenna are calculated for single and multiple tumor cell locations. In the case of multifocal breast cancer, sub-array beam focusing via the phase compensation technique is presented to enhance the ability of EM energy to concentrate on multiple targets while minimizing damage to normal cells. To demonstrate the thermal treatment effects on single and multiple tumor locations, the accumulation of the speciﬁc absorption rate (SAR) parameter and temperature changes were veriﬁed using both simulated and experimental results.


Introduction
Breast cancer treatments have been investigated throughout the past decade, and thermal treatments for breast cancer using microwaves are being rapidly developed to reduce the dangerous side effects associated with conventional methods [1]. Primary breast cancer treatments include surgical operations, radiotherapy, chemotherapy, and hyperthermia. Among these, microwave hyperthermia is an effective treatment that uses a beneficial heating effect. Because cancerous tissues are highly vascularized, and it is harder to remove excess heat from them than from healthy tissues, thermal damages are sensitive to the cancer [2]. A non-invasive microwave hyperthermia system for cancer treatment is reliable, cost effective, and painless compared with surgical operations. Furthermore, hyperthermia has a synergistic effect when used in combination with radiation oncology or chemotherapy [3][4][5][6]. In hyperthermic systems, tumor cells are damaged under the temperature range of 43-47 • C, while normal cells are not damaged [7]. Non-invasive microwave hyperthermia employing an antenna array is a reliable treatment method that can achieve effective breast tumor necrosis [8]. In this procedure, electromagnetic (EM) energy is radiated from array elements and concentrated on the tumor region, where heating is applied for treatment [9][10][11].
Microwave hyperthermia for deep-seated tumors inside the human breast should be designed so that EM energy can be transferred well into the interior of the body. The human body is composed of various dielectric tissues that make it difficult to provide a suitable EM energy concentration because of dielectric losses [12]. One of the challenges of this treatment method is to design microwave hyperthermia systems that, while focusing the EM energy into the human body, heat only malignant tissues, without overheating normal tissues [13]. Mathematically, accurate EM energy focusing methods are essential for optimal accumulation. Many techniques, such as the time reversal method, specific absorption rate

The Antenna Array System for Microwave Hyperthermia Treatment
The antenna array configurations for breast cancer treatments are determined by the type, aperture size, and polarization characteristics of the designed single antenna. The prototype of the tapered slot antenna (TSA) and circular array configuration presented in this paper were proposed in our previous paper [25], which aimed to use the above elements in microwave imaging and hyperthermia systems. To verify the antenna performances, a 3D simulation of a cylindrical breast phantom was performed and the SAR and temperature results were presented in 2D planes. An antenna for delivering microwaves to a deepseated tumor should be designed to induce strong constructive interference of the E-field. Therefore, an antenna array is used to deliver EM energy to tumor cells located deep inside the breast phantom. Each antenna is arranged vertically to be efficiently organized around the small female breast phantom and for effective E-field synthesis [16,21].

The Antenna for the Array Configuration
Since this paper is a part of ongoing research related to our existing work, the antenna for microwave hyperthermia used in this study was a TSA, based on our previous study [25]. The designed TSA has a small aperture size for easier application, and has been optimized to effectively deliver EM energy into the breast. The design configuration of a single antenna is presented in Figure 1a. To verify the EM effects on the 2D plane, a cylindrical shaped artificial breast phantom that takes into account the breast's fatty component (ε r = 5.14, σ = 0.137 S/m) was modelled as homogeneous medium [26]. The designed TSA was printed on an 0.8-mm-thick FR-4 substrate (ε r = 4.3, tanδ = 0.025) over an 80 mm × 40 mm area, as shown in Figure 1b [25]. The meander line was designed beneath the tapered slot of the TSA to operate at 2.45 GHz for the microwave hyperthermia treatment. In Figure 2, the simulated and measured reflection coefficients are compared. The reflection coefficient (S 11 ) was measured under the condition presented in Figure 1a, where the designed antenna is in direct contact with the phantom. For the antenna measurement and thermal experiment, a gelatin-based phantom was fabricated, and the dielectric property of performed phantom is ε r = 5.1 at 2.45 GHz [27].
Since this paper is a part of ongoing research related to our existing work, the antenna for microwave hyperthermia used in this study was a TSA, based on our previous study [25]. The designed TSA has a small aperture size for easier application, and has been optimized to effectively deliver EM energy into the breast. The design configuration of a single antenna is presented in Figure 1a. To verify the EM effects on the 2D plane, a cylindrical shaped artificial breast phantom that takes into account the breast's fatty component ( r = 5.14, σ = 0.137 S/m) was modelled as homogeneous medium [26]. The designed TSA was printed on an 0.8-mm-thick FR-4 substrate ( r = 4.3, tanδ = 0.025) over an 80 mm × 40 mm area, as shown in Figure 1b [25]. The meander line was designed beneath the tapered slot of the TSA to operate at 2.45 GHz for the microwave hyperthermia treatment. In Figure 2, the simulated and measured reflection coefficients are compared. The reflection coefficient ( 11 ) was measured under the condition presented in Figure 1a, where the designed antenna is in direct contact with the phantom. For the antenna measurement and thermal experiment, a gelatin-based phantom was fabricated, and the dielectric property of performed phantom is r = 5.1 at 2.45 GHz [27].
For effective electric field concentration in the female breast phantom, each antenna is arranged vertically. For these antennas' arrangement, the same linear polarization profile in each array antenna element is related to the effective hyperthermia treatment. In Figure 3, the E-field distribution at 2.45 GHz in the breast phantom, including in the tumor, is presented. A spherical breast tumor of radius r = 5 mm is positioned in the center of the cylindrical phantom. As shown in this figure, the polarization of the single TSA antenna is wellformed along the z-axis. A full simulation was performed with FIT-based CST Studio Suite 2019 [28].   For effective electric field concentration in the female breast phantom, each antenna is arranged vertically. For these antennas' arrangement, the same linear polarization profile in each array antenna element is related to the effective hyperthermia treatment. In Figure 3, the E-field distribution at 2.45 GHz in the breast phantom, including in the tumor, is presented. A spherical breast tumor of radius r = 5 mm is positioned in the center of the cylindrical phantom. As shown in this figure, the polarization of the single TSA antenna is well-formed along the z-axis. A full simulation was performed with FIT-based CST Studio Suite 2019 [28].

Antenna Array Configuration for Effective Electric Field Concentration
As mentioned in the previous section, the designed TSA antenna is linearly polarized along the radiation direction, and each antenna should be aligned along the surface of the cylindrical phantom for effective E-field synthesis. The number of radiators, which should be determined for the successful E-field concentration on the target area, was set at 12 due to the SAR accumulation in the breast phantom, in accordance with our previous study [25]. The array configurations for inducing microwave hyperthermia along the xz-and xy-planes are presented in Figure 4a,b, respectively. To feed the array antenna, simultaneous excitation is induced with an EM simulation tool. To apply the input power to each antenna, a discrete port is assigned to each TSA and the open boundary condition in CST is set to analyze the antennas' performances. The narrowband antennas are arranged at regular intervals for vertical linear polarization along the z-axis.

Antenna Array Configuration for Effective Electric Field Concentration
As mentioned in the previous section, the designed TSA antenna is linearly polarized along the radiation direction, and each antenna should be aligned along the surface of the cylindrical phantom for effective E-field synthesis. The number of radiators, which should be determined for the successful E-field concentration on the target area, was set at 12 due to the SAR accumulation in the breast phantom, in accordance with our previous study [25]. The array configurations for inducing microwave hyperthermia along the xz-and xy-planes are presented in Figure 4a,b, respectively. To feed the array antenna, simultaneous excitation is induced with an EM simulation tool. To apply the input power to each antenna, a discrete port is assigned to each TSA and the open boundary condition in CST is set to analyze the antennas' performances. The narrowband antennas are arranged at regular intervals for vertical linear polarization along the z-axis.

Antenna Array Configuration for Effective Electric Field Concentration
As mentioned in the previous section, the designed TSA antenna is linearly polarized along the radiation direction, and each antenna should be aligned along the surface of the cylindrical phantom for effective E-field synthesis. The number of radiators, which should be determined for the successful E-field concentration on the target area, was set at 12 due to the SAR accumulation in the breast phantom, in accordance with our previous study [25]. The array configurations for inducing microwave hyperthermia along the xz-and xy-planes are presented in Figure 4a,b, respectively. To feed the array antenna, simultaneous excitation is induced with an EM simulation tool. To apply the input power to each antenna, a discrete port is assigned to each TSA and the open boundary condition in CST is set to analyze the antennas' performances. The narrowband antennas are arranged at regular intervals for vertical linear polarization along the z-axis.

The Specific Absorption Rate and Temperature Increase
The EM field produced by the TSA antenna array elements propagates toward the inside of the breast phantom and concentrates in the target area. The localized EM energy is used to calculated the SAR parameter, which is defined as a measure of energy absorbed per unit mass of the human body in the unit time t. The SAR is defined as the time derivative of the incremental energy (dW) absorbed by the incremental mass (dm) [29].

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The incremental mass dm can be replaced with a volume element dV for a given density of the tissue ρ. The SAR factor can also be defined for time-harmonic E-fields using the Poynting vector theorem [30]: where σ is the electrical conductivity of the tissue material and E i is the intensity of the internal E-field in volts per meter. The average SAR parameter is defined as the ratio of the total power absorption per unit mass of the exposed human body. The induced E-field interacts with the body and changes the temperature depending on the square of the magnitude of the E-field strength.
The analysis of temperature distribution as a function of the applied external E-field was conducted to broaden our study to incoporate multiphysics methods. To show the rate of temperature increase in human tissue exposed to external microwave energy, the Pennes bioheat equation is given below [31]: where ρ, C p , k, and σ are the density, heat capacity, thermal conductivity, and electric conductivity of tissue, respectively, and W b and C b are the perfusion rate and heat capacity of blood, respectively. The external E-field is an essential factor for determining the temperature increase in the exposed tissue over a certain period of time following the EM exposure of the TSA antennas' array.

Electromagnetic Focusing for Unifocal Breast Cancers
Each TSA antenna radiates with precise input phase characteristics to provide effective treatment to randomly positioned cancer cells in the breast phantom. The radius of the breast tumor for microwave hyperthermia treatment was set at 5 mm. The breast tissue properties of the fat and the tumor applied to all simulations are presented in Table 1 to verify the SAR and temperature distributions. Table 1. Dielectric and thermal properties of breast tissues at 2.45 GHz [32].

Properties Fat Tumor
Dielectric permittivity ε r 5.14 55 Loss tangent tan δ 0.137 0.29 Density ρ (kg/m 3 ) 920 920 Thermal conductivity σ (W/K/m) 0.42 0.42 Heat capacity C p (J/K/kg) 3000 3000 The phase delay of each antenna (ϕ n ) should be compensated to focus the E-field on the target position, thereby localizing the heat operation to a treatment area. The input phase characteristics of the TSA antenna array can be defined by compensating the phase delay caused by the different path lengths of the antennas to the target tumor. Hence, the in-phase condition of the radiated E-fields can be satisfied with an unifocal breast cancer, leading to strong constructive interference. Figure 5 presents a schematic view of the EM waves focusing on the breast phantom while the array configuration encircles the breast phantom. The phase delay of each antenna is calculated to meet the requirements for the in-phase condition of the E-field deep inside the phantom. The locations of the antennas are defined as (x n , y n ) and the cancer location in the phantom is defined as (x t1 , y t1 ). The path length from each antenna to the cancer location defined by 2D Cartesian coordinates can be defined as: where n is the current antenna number. The radius of the breast phantom is 50 mm, with the middle defined as (0,0), so with Cartesian coordinates, each path length between the radiating antenna and cancer location can be calculated and converted to the phase as follows: where k is the wave number, and λ eff is the effective wavelength in the phantom (ε r = 5.14) at 2.45 GHz. To determine the input phases of each antenna, the phase delay should be calculated accordingly: where ϕ min is the minimum phase value among the 12 path lengths. Therefore, the calculated final input phase ϕ n is the total compensating input phase to satisfy the in-phase condition on the focusing area. Thus, ϕ n of each antenna is calculated depending on the tumor position. where n is the current antenna number. The radius of the breast phantom is 50 mm, with the middle defined as (0,0), so with Cartesian coordinates, each path length between the radiating antenna and cancer location can be calculated and converted to the phase as follows: where k is the wave number, and eff is the effective wavelength in the phantom ( r = 5.14) at 2.45 GHz. To determine the input phases of each antenna, the phase delay should be calculated accordingly: where min is the minimum phase value among the 12 path lengths. Therefore, the calculated final input phase is the total compensating input phase to satisfy the in-phase condition on the focusing area. Thus, of each antenna is calculated depending on the tumor position.
To verify that the EM was focusing on the unifocal cancer, the input phases of each antenna when the tumor was positioned at (20,0) mm and (15,15) mm were calculated for the xy-plane in Table 2. These calculated input phases ( ) were aimed to enhance the constructive interference of the E-field at the focal point, which leads to a high SAR distribution on the treatment area. The maximum SAR distribution values at (20,0) mm and (15,15) mm according to the xy-planes presented in Figure 6a,b are 23.1 W/kg and 27.7 W/kg, respectively, at the focal points. To verify that the EM was focusing on the unifocal cancer, the input phases of each antenna when the tumor was positioned at (20,0) mm and (15,15) mm were calculated for the xy-plane in Table 2. These calculated input phases (ϕ n ) were aimed to enhance the constructive interference of the E-field at the focal point, which leads to a high SAR distribution on the treatment area. The maximum SAR distribution values at (20,0) mm and (15,15) mm according to the xy-planes presented in Figure 6a,b are 23.1 W/kg and 27.7 W/kg, respectively, at the focal points.

Electromagnetic Focusing for Multifocal Breast Cancer
In the case of multifocal breast cancer, time and costs can be reduced by treating multiple tumors simultaneously rather than sequentially. Unlike for a single tumor, the calculation method for the input phases ( ) for multiple targets should be modified to deliver precise EM energy deposition. In deep-seated tumors, the TSA antennas should transfer adequate energy to necrotize the tumor cells without harming the normal tissue. To enhance the thermal focusing, an exquisite phase control technique should be applied to each microwave antenna, and unwanted electric field focusing should be avoided. Thus, the multiple E-field focusing technique with a sub-array antenna configuration and phase compensation technique will be discussed.
The configuration of the E-field focused on two breast tumors with an antenna subarray is presented in Figure 7. The radii of the two breast tumors for multifocal breast cancer were set at 5 mm as well. The magnitude of the radiated E-field is decreased due to the dielectric loss component of the breast phantom. Therefore, in terms of the tumor positions, designating the antennas that are closest to the tumor cell as a sub-array ensures E-field concentration on each breast tumor. Therefore, as shown in Figure 7, sub-arrays #1 and #2 consist of antennas #1-6 and #7-#12, respectively. Tumor cells #1 and #2 are located at positions ( t1 , t1 ) and ( t2 , t2 ) in the phantom, respectively. To focus the E-field on two breast tumors at the same time, each antenna sub-array radiates the E-field onto tumor cells #1 and #2. The input phase of each antenna sub-array should be calculated separately to provide optimal focusing depending on the multiple targets. The phase delay of each antenna is calculated to meet the requirement of the in-phase condition of the Efield deep inside the phantom. Hence, the path length from each antenna sub-array to the tumor cells using 2D Cartesian coordinates can be defined as follows:

Electromagnetic Focusing for Multifocal Breast Cancer
In the case of multifocal breast cancer, time and costs can be reduced by treating multiple tumors simultaneously rather than sequentially. Unlike for a single tumor, the calculation method for the input phases (ϕ n ) for multiple targets should be modified to deliver precise EM energy deposition. In deep-seated tumors, the TSA antennas should transfer adequate energy to necrotize the tumor cells without harming the normal tissue. To enhance the thermal focusing, an exquisite phase control technique should be applied to each microwave antenna, and unwanted electric field focusing should be avoided. Thus, the multiple E-field focusing technique with a sub-array antenna configuration and phase compensation technique will be discussed.
The configuration of the E-field focused on two breast tumors with an antenna subarray is presented in Figure 7. The radii of the two breast tumors for multifocal breast cancer were set at 5 mm as well. The magnitude of the radiated E-field is decreased due to the dielectric loss component of the breast phantom. Therefore, in terms of the tumor positions, designating the antennas that are closest to the tumor cell as a sub-array ensures E-field concentration on each breast tumor. Therefore, as shown in Figure 7, sub-arrays #1 and #2 consist of antennas #1-6 and #7-#12, respectively. Tumor cells #1 and #2 are located at positions (x t1 , y t1 ) and (x t2 , y t2 ) in the phantom, respectively. To focus the E-field on two breast tumors at the same time, each antenna sub-array radiates the E-field onto tumor cells #1 and #2. The input phase of each antenna sub-array should be calculated separately to provide optimal focusing depending on the multiple targets. The phase delay of each antenna is calculated to meet the requirement of the in-phase condition of the E-field deep inside the phantom. Hence, the path length from each antenna sub-array to the tumor cells using 2D Cartesian coordinates can be defined as follows: where n 1 and n 2 are the antenna numbers of sub-arrays #1 and #2, respectively. The calculated path lengths can be converted to the phases of each sub-arrays accordingly: where k is the wave number and λ eff is the effective wavelength in the phantom (ε r = 5.14) at 2.45 GHz, and ϕ PL n1 and ϕ PL n2 are the calculated phases of antenna sub-arrays #1 and #2, respectively. To decide the input phases of each antenna, the phase delay should be calculated as follows: where ϕ min1 and ϕ min2 are the minimum phase values of the phases in sub-array #1 and #2, respectively. Therefore, the calculated final input phases ϕ n1 and ϕ n2 are the total compensating input phases to satisfy the in-phase condition of each tumor. Thus, ϕ n1 and ϕ n2 of each antenna are calculated and applied depending on the position of the tumor cells.
where k is the wave number and eff is the effective wavelength in the phantom ( r = 5.14) at 2.45 GHz, and PL 1 and PL 2 are the calculated phases of antenna subarrays #1 and #2, respectively. To decide the input phases of each antenna, the phase delay should be calculated as follows: where min1 and min2 are the minimum phase values of the phases in sub-array #1 and #2, respectively. Therefore, the calculated final input phases 1 and 2 are the total compensating input phases to satisfy the in-phase condition of each tumor. Thus,   Figure 8a. Antennas #1-#6 transmit microwaves to tumor #1, while #7-#12 transmit EM energy to tumor #2 in the simultaneous cancer treatment regimen. The calculated input phases aimed to concentrate the E-field on the two tumors in different positions. However, the SAR patterns were formed at positions away from the desired locations, and an unwanted E-field was applied to the breast phantom, as shown in Figure 8b. Although each antenna sub-array focused the electric field on different targets (tumors #1 and #2), incorrect field synthesis occurred outside of the target area due to the interactions of the E-fields passing through the tumor cells. In addition, unwanted E-field synthesis was observed due to interferences from the TSA antennas, which were facing each other. To minimize unwanted interference and provide a correct beamforming condition to the target positions, the phase compensation technique will be discussed in the next section.  Figure 8a. Antennas #1-#6 transmit microwaves to tumor #1, while #7-#12 transmit EM energy to tumor #2 in the simultaneous cancer treatment regimen. The calculated input phases aimed to concentrate the E-field on the two tumors in different positions. However, the SAR patterns were formed at positions away from the desired locations, and an unwanted E-field was applied to the breast phantom, as shown in Figure 8b. Although each antenna sub-array focused the electric field on different targets (tumors #1 and #2), incorrect field synthesis occurred outside of the target area due to the interactions of the E-fields passing through the tumor cells. In addition, unwanted E-field synthesis was observed due to interferences from the TSA antennas, which were facing each other. To minimize unwanted interference and provide a correct beamforming condition to the target positions, the phase compensation technique will be discussed in the next section.

Phase Compensation Technique for Multiple Focusing
As mentioned in the previous section, unwanted E-field focusing occurred due to the interactions between the sub-arrays. In circular antenna arrays, the interferences between the antennas on opposite sides are most severe. An inaccurate synthesis of the E-field inside the breast phantom can degrade the success of the hyperthermia treatment. Therefore, in this section, the phase compensation technique is applied to enhance the SAR focusing in the target points.
To minimize the number of unwanted interferences, each input phase was calculated to satisfy the in-phase condition in the target tumors, and the phase compensation technique was applied to allow destructive interference to occur between the sub-arrays, as shown in Figure 8a. In the calculated input phase of sub-array #2, the modified phase ϕ m was added to antennas #7-#12 to compensate for phase ϕ n2 in Equation (10): where ϕ * n2 is the modified phase applied to sub-array #2. The input phases depending on the different values of the modified phases are reported in Table 3, and the SAR distributions with phase compensation depending on the modified phase values are presented in Figure 9. The added modified phases ϕ m are 0 • , 60 • , 120 • , and 180 • , respectively. In Figure 9, the modified phase is insufficient for achieving destructive interference in the unwanted spot, and inaccurate E-field synthesis is still observed. However, when the modified phase ϕ m is 180 • , sub-arrays #1 and #2 are out-of-phase, so destructive interference occurs outside the cancer spots, and maximum SAR occurs at (15,10)

Phase Compensation Technique for Multiple Focusing
As mentioned in the previous section, unwanted E-field focusing occurred due to the interactions between the sub-arrays. In circular antenna arrays, the interferences between the antennas on opposite sides are most severe. An inaccurate synthesis of the E-field inside the breast phantom can degrade the success of the hyperthermia treatment. Therefore, in this section, the phase compensation technique is applied to enhance the SAR focusing in the target points.
To minimize the number of unwanted interferences, each input phase was calculated to satisfy the in-phase condition in the target tumors, and the phase compensation technique was applied to allow destructive interference to occur between the sub-arrays, as shown in Figure 8a. In the calculated input phase of sub-array #2, the modified phase m was added to antennas #7-#12 to compensate for phase 2 in Equation (10): where 2 * is the modified phase applied to sub-array #2. The input phases depending on the different values of the modified phases are reported in Table 3, and the SAR distributions with phase compensation depending on the modified phase values are presented in Figure 9. The added modified phases m are 0°, 60°, 120°, and 180°, respectively. In Figure 9, the modified phase is insufficient for achieving destructive interference in the unwanted spot, and inaccurate E-field synthesis is still observed. However, when the modified phase m is 180°, sub-arrays #1 and #2 are out-of-phase, so destructive interference occurs outside the cancer spots, and maximum SAR occurs at (15,10) mm and (−15,−10) mm, as shown in Figure 9d. In this condition, the E-fields are well concentrated on the desired positions, leading to successful thermal therapeutic effects.
To confirm the out-of-phase condition between sub-array #1 and #2, the modified phase m = 180° is applied in sub-array #2 for two other cases of tumor locations: case  To confirm the out-of-phase condition between sub-array #1 and #2, the modified phase ϕ m = 180 • is applied in sub-array #2 for two other cases of tumor locations: case 1-two tumors are at (−10, 20) mm and (15,−10) mm; case 2-two tumors are at (20,0) mm and (−15,−15) mm. The input phases for case 1 and 2 are shown in Table 4. In Figure 10a,b, the SAR distributions in accordance with the input phases in Table 4 Figure 10b, respectively. By applying the modified phase, ϕ m = 180 • in sub-array #2, the out-of-phase condition is achieved between sub-array #1 and #2 and the EM energy is well-focused in the target areas.
Appl. Sci. 2021, 11, 5972 10 of 15 phase, m = 180° in sub-array #2, the out-of-phase condition is achieved between subarray #1 and #2 and the EM energy is well-focused in the target areas.   phase, m = 180° in sub-array #2, the out-of-phase condition is achieved between subarray #1 and #2 and the EM energy is well-focused in the target areas.

Thermal Experiment Results
To verify the thermal effects, the temperature measurement setup and block diagram of the temperature measuring system are presented in Figure 11a,b, respectively. At the boundaries of the phantom in simulation, the initial temperature was set to 0 • C for a clear comparison of the measured temperature increase. The thermal experiments consisted of four stages of radio frequency (RF) signal generation and amplification, RF energy excitation, an experiment on the fabricated phantom, an experiment on the thermal effect, and an evaluation of the effects of the temperature rise [19]. The thermal effects on tumor necrosis were verified by analyzing the effective treatment area (ETA) [8], which was regarded as a region in which the tumor satisfies the temperature increase requirement of 7-10°C.
Appl. Sci. 2021, 11, 5972 12 of 15 tumor cell positions and areas, thereby leading to effective thermal therapeutic effects. The inducing power, simulated SAR, and thermal effects achieved with the proposed TSA antenna array are summarized in Table 5.
(a) (b) Figure 11. (a) Configuration of the temperature measurement setup, and (b) block diagram of the temperature measuring system [25].
(a) (b) Figure 11. (a) Configuration of the temperature measurement setup, and (b) block diagram of the temperature measuring system [25].
To verify the heating effect on both a single tumor and on multiple tumors, the thermal measurements were conducted as follows: two for single tumor cases and one for a double tumor case. The first and second cases were conducted on a single tumor located at (0,0) mm and (20,0) mm, respectively, and the third case was conducted on two tumors located at (15,10) mm and (−15,10) mm. The phases of each antenna array were applied to the delay lines based on the calculated input phases. The thermal increase that occurred inside the cylindrical breast phantom was measured using a multi-channel thermometer with 12 probes and a data logger to manage the real time temperature data. The probe was set to detect the middle of the cylindrical phantom in the vertical axis. The simulated and measured results of the thermal effects on a single tumor cell and two tumor cells are shown in Figure 12a-f. The target positions of the tumor cells are marked with a black circle. To achieve an optimum temperature increase during a 1-h period heating, the total input powers of the array antenna were decided by the bio-heat equation supported by the CST Studio Suite [27]. The total input powers for the single tumor cells at (0,0) mm and (20,0) mm were 7.1 W and 6 W, respectively. The simulated and measured maximum temperature increases were 8.4°C and 8.3°C for the single tumor cell at (0,0) mm, and 8.5°C and 8.3°C for the single tumor cell at (20,0) mm, respectively. The target therapeutic areas of the multifocal breast cancer were at (15,10) mm and (−15,−10) mm, as shown in Figure 12e,f. To provide a heating effect on two targets simultaneously, phase compensation was applied in sub-array #2, and the input phases were controlled with delay lines. The induced total RF power was 7.1 W for 1-h treatment. The simulated and measured maximum temperature increases were 7.8°C and 7.7°C, respectively. The temperature transient distribution over time and the simulation and measurement results are shown in Figure 12a-c, where a single tumor was present at (0,0) mm and (20,0) mm, and two tumors at (10,15) mm and (−10,−15) mm. All the temperature results were postprocessed using MATLAB. As shown in Figure 13, the temperature increased gradually over time. When comparing the simulation and measurement results, the hot spots were well-formed, and the results were well-matched. Moreover, the ETAs covered the target tumor cell positions and areas, thereby leading to effective thermal therapeutic effects. The inducing power, simulated SAR, and thermal effects achieved with the proposed TSA antenna array are summarized in Table 5.

Conclusions
An antenna array that uses the phase compensation technique to effectively concentrate EM energy during microwave hyperthermia treatment for deep-seated breast cancer

Conclusions
An antenna array that uses the phase compensation technique to effectively concentrate EM energy during microwave hyperthermia treatment for deep-seated breast cancer was proposed in this paper. The thermal effect was determined based on the E-field absorbed in the therapeutic region. To deliver EM energy inside the human breast, the input phases of each antenna should be controlled based on the location of the tumor cells. Strong constructive interference in the target area can be achieved when each TSA has equal polarization characteristics. Therefore, the direction of each antenna and array configuration was optimized for effective E-field synthesis. Moreover, accurate phase control is needed on the target area to minimize thermal damage to normal cells. The input phase of each antenna in the 12-element array was calculated for single and multiple targets depending on the tumor condition in the breast phantom. For multiple targets in particular, sub-array beam focusing was applied to simultaneously provide therapeutic effects on the multifocal breast cancer. To minimize interference between the sub-arrays, the values of the modified phase for phase compensation were added to the antennas in one of the sub-arrays so that sub-arrays #1 and #2 were out-of-phase. The temperature distribution of the single tumor and multiple tumor cases were simulated and measured to verify the therapeutic performance of the proposed approach. Consequently, the proposed 12-element array system and the phase compensation technique provided enhanced therapeutic capabilities for breast cancer hyperthermia treatment.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy restrictions.