1. Introduction
Breast cancer has become the most common cancer in the world that harm women’s health. According to the cancer statistics of China in 2022 [
1], breast cancer accounts for 19.54% of the cancer incidence of Chinese women, ranking first in cancer incidence. Mastectomy or partial mastectomy combined with radiotherapy, chemotherapy, hormone therapy, and other medical techniques are the main treatment methods for breast cancer. Hyperthermia [
2,
3] has attracted much attention in the treatment of breast cancer, prostate cancer, liver cancer, skin cancer, etc. Considerable attention has been paid to several thermal techniques (extreme cold or heat), including cryoablation [
4], radiofrequency ablation (RFA) [
5], interstitial laser therapy (ILT) [
6], and high-intensity focused ultrasound (HIFU) [
7], which apply thermal ablation to eliminate a malignant tumor and its margins. Ongoing phase II clinical trials are evaluating the efficacy of cryoablation for low-risk breast cancer (Luminal A) as an alternative to breast surgery; however, the drawback is that there is limited control (>1.5 cm
3) over the size of the ablation zone near the metal probe. ILT and RFA are minimally invasive percutaneous technologies that destroy preclinical tumors through intense heat generated by focusing (>55 °C). In addition, RFA electrodes remains an ongoing challenge in penetrating hard fibrous tissue and controlling treatment thermal power. For larger breast tumors (>2 cm
3), HIFU is challenging. Among the various thermal technologies, focused microwave hyperthermia therapy (FMHT) has emerged as a promising technique for breast cancer treatment. The advantages of FMHT are reduction of scarring, better preservation of healthy tissue, rapid postoperative recovery, and less medical costs. The results of clinical trials combining FMHT and radiotherapy demonstrated significantly improvement in the treatment of superficial breast cancer and chest wall recurrence.
The purpose of FMHT is to raise the temperature of the breast tumors over 42 °C for 60 min and to maintain healthy tissue at a safe temperature (<40 °C). In the last two decades, several phased array applicators have been reported for non-invasive microwave hyperthermia of breast cancer, operating in the ISM band (Industrial, Scientific, and Medical) [
8] or other frequencies [
9,
10]. The ISM band includes 0.434 GHz [
11], 0.915 GHz [
8,
12], and 2.45 GHz [
13]. At present, there are few pieces of research on multi-resonance phased array applicators [
14,
15], while there are many designs of multi-band antennas [
16,
17] for FMHT of breast cancer. The multi-resonance phased array application adjusts the frequency of treatment according to the depth and volume of the tumor for better treatment results. The amplitudes and phases of treatment antennas in the phased array applicator were optimized using the hyperthermia treatment planning (HTP) process for targeting malignant tissues and ensuring the safety of healthy tissue.
HTP optimization methods optimize excitations of phased arrays based on SAR to optimize the energy distribution of tumor tissue and healthy tissue [
18]. The common HTP optimization method is time reversal (TR) technology [
8,
11]. However, the energy loss in the propagation process of microwaves affects the optimization effect of TR, resulting in the shift of focus and unexpected hotspots in healthy tissues and other treatment problems. In recent years, global optimization algorithms are involved to optimize HTP for breast cancer, including the Nelder–Mead simplex (NMS) algorithm [
12], pattern search (PS) [
19], particle swarm optimization (PSO) [
9,
14], and genetic algorithm (GA) [
20]. The particle swarm optimization (PSO) algorithm and differential evolution (DE) algorithm had been applied to optimize HTP for head and neck tumors [
21]. The treatment indicators such as hotspot to target quotient (HTQ) [
21,
22], average power absorption ratio (aPA), and tumor coverage 50% (TC
50) are used as the objective function of the optimization algorithm to improve tumor treatment outcomes. The mean SAR deposited in the tumor was also utilized as the objective function of the HTP optimization method in previous studies [
22,
23]. At present, single objective genetic algorithm (SOGA) and multi-objective genetic algorithm (MOGA), as HTP optimization algorithm, optimizes the excitations of an 18-element phased array applicator at 0.434 GHz for the treatment of large-sized breast tumors [
20]. The results show that MOGA can reduce the excess hot spots of healthy tissue and the channel power in HTP. However, the convergence rate is slow and the focusing effect needs to be further improved.
The DE algorithm is proposed in this work, in order to improve the therapeutic effect of the dual resonant phased array applicator for breast cancer microwave hyperthermia at 0.915 GHz and 2.45 GHz. The phased array applicator is used to target 1 cm3 and 2 cm3 spherical breast tumors in the upper outer quadrant of general and heterogeneous breast models. Comparison using TR, PSO, and GA with DE to demonstrate the advantages of DE in HTP for breast cancer. The extraordinary optimization performance of DE was determined by evaluating the treatment results of four HTP optimization methods, including treatment indicators (HTQ, aPA, and TC50), SAR distributions, temperature parameters, and temperature distributions. Results show that compared with PSO and GA used for FMHT of breast cancer, DE provides better-focused treatment results, improves the treatment temperature of tumors, and reduces unexpected hotspots in healthy tissues. The effect of different SAR-related objective functions in DE on tumor therapy is analyzed in this paper. Finally, it is verified that the DE algorithm with HTQ as the objective function is the optimal HTP optimization algorithm for breast cancer.
The structure of this paper is shown as follows. The introduction of the HTP process, evaluation criteria of treatment effect, and the optimization algorithms employed in this paper are demonstrated in
Section 2. The optimization results of DE, TR, PSO, and GA are reported in
Section 3, as well as the optimization results of different objective functions used in DE. The discussion and the conclusion of this work are reported in
Section 4 and
Section 5, respectively.
4. Influence of Objective Functions on DE Optimization
According to the above treatment results, the DE algorithm has better optimization ability than other optimization methods. The above optimization algorithm optimizes HTP based on HTQ as the objective function, in order to reduce HTQ and improve the energy ratio between the tumor and surrounding tissues. Since HTP optimization is based on SAR, all treatment indicators related to SAR can be used as the objective function of the optimization algorithm. Hence, HTQobj, 1/aPAobj, and 1/TC50obj were adopted as the objective functions of the DE algorithm to optimize the phased array excitation improves the tumor treatment effect. In order to select the optimal objective function of DE, EM, and thermal simulation were used to analyze the influence of different objective functions on the optimization effect of the DE algorithm.
Table 6 lists the treatment indicators of the heterogeneous breast model and the general breast model for the DE algorithm with three objective functions. The objective function HTQ
obj has the lowest HTQ in all cases, indicating the maximum energy ratio between the tumor and surrounding tissue. In all cases, the objective function 1/aPA
obj provided the highest aPA, with the aim of reducing power deposition and unnecessary hotspots in healthy tissue. Because the HTQ is low, it indicates that 1/aPA
obj also reduces the energy of the tumor. The objective function 1/TC
50obj had the largest tumor coverage indicator TC
50, but aPA and HTQ values were significantly worse than other objective functions.
Figure 6 and
Figure 7 show the normalized SAR distributions of the general and the heterogeneous breast models for each objective function used in DE, respectively. When HTQ
obj is the target function, there are no obvious redundant hot spots in the healthy tissue. Due to its low HTQ value, it indicates that the tissue energy ratio between the tumor and the surrounding tumor is large. When 1/aPA
obj was the objective function used in DE, the hotspot in healthy tissue is the least. Because the HTQ value of 1/aPA
obj is from 3.8% to 34% lower than HTQ
obj, it indicates that the tissue energy ratio between the tumor and the surrounding tumor is low. When 1/TC
50obj was taken as the objective function of DE, the proportion of tumors in the treatment range was the largest and the highest unexpected hotspot was reached. Therefore, aPA of 1/TC
50obj is 1.8% to 7.4% lower than that of HTQ
obj and the value of HTQ is 5.8% to 38.5% higher than that of HTQ
obj. In EM simulation, the objective function HTQ
obj provides the best HTP optimization using the DE algorithm for two breast models at two resonant frequencies.
The optimal treatment effect can be judged by the treatment temperature obtained by thermal simulation.
Table 7 shows the T
50 and T
90 values of two breast models obtained by each objective function used in DE. It can be seen that HTQ
obj and 1/aPA
obj provided the highest and lowest treatment temperatures (T
50 and T
90) of all the objective functions, respectively. The T
50 and T
90 of DE with HTQ
obj as the objective function are increased by 2% to 2.5% and 1.1% to 2.5% compared with other objective functions, respectively. In the optimization results of all objective functions of DE, the thermal damage to the surrounding healthy tissue was less than 5% in all cases (
Table 8). In particular, HTQ
obj objective function results showed the best protection for healthy tissue.
Steady-state temperature distribution can clearly observe the effect of breast cancer treatment.
Figure 8 and
Figure 9 show the steady-state temperature distributions of the general breast model and the heterogeneous breast model using different objective functions of the DE algorithm, respectively. It is observed that when HTQ
obj is the objective function of the DE algorithm the temperature in tumors is highest and the treatment range is most similar to the tumor size for avoiding overtreatment. The temperature of the objective function 1/aPA
obj is low relative to other objective functions caused by the lower energy deposited in the tumor. The objective function ignores the therapeutic power of the tumor by reducing hot spots in healthy tissue. However, when 1/TC
50obj was used as the target function, the treatment range completely included the tumor, but the surrounding tissue was damaged. This function ignores the health of surrounding tissue for increasing tumor treatment coverage. Therefore, the DE algorithm with objective function HTQ
obj is the most effective to treat breast tumors, which can reduce the risk of damage to the healthy tissue of the patient while adequately treating tumors.
5. Discussion
The purpose of HTP is to accurately treat breast cancer with less damage to healthy tissue. A variety of optimization methods were used to optimize the phased array excitation to achieve the selective deposition of tumor energy. At present, global optimization algorithms are used to optimize phased array excitation under single-phase frequency to accurately treat tumors. According to the results of current articles on the PSO [
9] and GA [
11,
20] algorithms used in microwave hyperthermia of breast cancer, the therapeutic results need to be further improved. Moreover, the influence of objective functions on the HTP optimization algorithm was ignored [
21]. In addition, the damaged healthy tissue rate was not analyzed to verify the effectiveness of the DE algorithm in HTP [
9].
In this work, we analyzed four microwave hyperthermia optimization methods to determine the best global optimization algorithm to generate HTP for tumor therapy and reduce hotspots in healthy tissues. The phased array applicator [
15] operating at two resonant frequencies is used for treating 1 cm
3 and 2 cm
3 breast tumors in the upper outer quadrant of the general and heterogeneous breast models. Therefore, with HTQ as the objective function, the DE algorithm was used to optimize the powers and phases of the phased array applicator at 0.915 GHz and 2.45 GHz, and compared with TR technology, PSO, and GA algorithms. According to the comparison of the above data, the DE algorithm is superior to other optimization methods in hotspot reduction and limiting SAR focus targets.
The SAR-based treatment indicators and thermal results were calculated for evaluating the optimization ability of DE. DE decreased the HTQ value by 36.3% to 60% compared with TR in order to increase the power difference between tumor and healthy tissue. Compared with GA, which is the current best algorithm, DE reduced the HTQ value by 3.8% to 15.9%, the convergence rate of DE was significantly faster, and the damaged healthy tissue rate was the lowest. By verifying the EM and thermal results of three different objective functions used in DE for HTP, it can be concluded that HTQobj is the most suitable objective function for DE.
The accuracy of the dual-resonant phased array applicator in the treatment of tumors of different sizes had been reflected in our previous work [
15]. In this paper, we analyzed the optimization effect of the DE algorithm in HTP for breast cancer. However, the traditional first-order Arrhenius thermal damage equation [
28], the modified Arrhenius equation for living tissues [
32], the temperature-dependent time-delay equation [
29], and other methods are used to quantify the thermal damage of healthy tissue and tumor. Since the uncertainty of thermal characteristics will affect the absolute temperature distribution [
20], this study only discusses the relative differences of thermal indicators for the optimization algorithms commonly used in hyperthermia literature. Considering these factors, it is expected that the thermal model established can reliably predict the relative effects of different algorithms on thermal distribution. It is important to note that the applicability of this study to other phased array applicators requires rigorous validation of the respective phased array applicators and breast models. The HTP results depend on the basic radiator, phased array configuration, and treatment site.
6. Conclusions
In this paper, through the comparison of different HTP optimization methods, it is determined that the DE algorithm has the best optimization effect on breast cancer treatment, which further improves the treatment effect of dual resonance phased array applicator on 1 cm3 and 2 cm3 tumors. In particular, compared with TR technology, the DE algorithm significantly improves the treatment results of microwave hyperthermia for breast cancer. The treatment results of DE were consistently superior to TR, GA, and PSO, focusing most of the energy on the tumor and reducing hotspots in healthy tissues. By analyzing the influence of the SAR-based objective function on DE optimization, it is determined that the objective function HTQ can improve the therapeutic effect more than other objective functions used in DE. The DE algorithm with an objective function of HTQ has a good optimization effect in microwave hyperthermia of breast cancer, which can focus the most energy on the tumor while reducing hotspots in the surrounding healthy tissue.
In the future, we plan to focus on the development and application of the multi-objective differential evolution optimization algorithm to treat more real breast models and verify the optimization ability of DE for different phased array applicators.