# Differential Evolution Optimization of Microwave Focused Hyperthermia Phased Array Excitation for Targeted Breast Cancer Heating

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{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.

_{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.

^{3}and 2 cm

^{3}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 TC

_{50}), 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.

## 2. Hyperthermia Treatment Planning

#### 2.1. Process of HTP

#### 2.2. Breast Model and the Phased Array Applicator

^{3}and 2 cm

^{3}tumors. In this paper, DE, TR, PSO, and GA algorithms were used to optimize the phase and amplitude of the phased array applicator to achieve tumor targeting. The optimization is complete until the stop criterion or the maximum number of iterations is reached. The HTP optimization process is completed jointly by Matlab R2021a and HFSS. The SAR distribution obtained by EM simulation is returned to Matlab for objective function calculation to optimize the excitation of the phased array. The breast model and optimal power density were imported in COMSOL 5.3 for thermal simulation and the temperature distribution is obtained.

^{2}, as shown in Figure 1d,e. According to statistics, breast cancer is most likely to occur in the upper outer quadrant of the breast [27]. Therefore, 1 cm

^{3}and 2 cm

^{3}of the spherical tumors were located in the heterogeneous breast model at (36, 20, 120) and the general breast model at (33, 0, 120), respectively. Depending on the differences in the focusing range of different frequencies, 2 cm

^{3}tumors were treated at 0.915 GHz and 1 cm

^{3}tumors were heated at 2.45 GHz. The HTP optimization methods were used to optimize the excitation of the phased array applicator at two operating frequencies to improve the therapeutic effect of 1 cm

^{3}and 2 cm

^{3}tumors.

^{2}[20]. The temperature of the chest tissue exposed outside the applicator was also set to 37 °C. The steady-state temperature distribution was used to calculate the temperature parameters.

#### 2.3. Treatment Indicators

_{50}), where they are defined as

_{1}is the volume of the top 1% of healthy tissue with the highest SAR. HTQ is used to measure the ratio of the mean SAR value of V

_{1}to the mean SAR value of tumor. The smaller HTQ, the better the therapeutic effect. Generally, HTQ is used as the objective function of the optimization algorithms in HTP to improve the power in the tumor and reduce the residual heat in the healthy tissue. TC

_{50}is expressed as

_{50}provides the percentage of tumor volume with SAR above 50% of the maximum SAR in the breast [22]. The TC

_{50}quantifies selective power deposition inside the tumor.

_{50}and T

_{90}were used in thermal simulation to evaluate the treatment effect [21]. T

_{50}and T

_{90}represent the lowest temperature reached at 50% and 90% of the tumor volume, respectively. The damaged healthy tissue rate [28,29] is expressed as

#### 2.4. Optimization Methods of HTP

#### 2.4.1. Particle Swarm Optimization (PSO)

#### 2.4.2. Genetic Algorithm (GA)

#### 2.4.3. Differential Evolution (DE)

- 1.
- Mutation

- 2.
- Crossover

- 3.
- Selection

## 3. Simulation Results of HTP Optimization Methods

#### 3.1. EM Simulation Results Comparison

_{50}, and coverage rate of the DE algorithm have substantial performance. The treatment indicators of global optimization algorithms are significantly better than TR technology. Among all models, the DE has the best treatment indicators because it has the minimized HTQ value and the maximum aPA and TC

_{50}value. The mean HTQ of DE is 3.8% to 15.9% lower than GA, and the mean aPA of DE is 1.6% to 9.7% higher than GA. In particular, DE provides the minimum standard deviation for two breast models at two resonant frequencies. Compared with other optimization algorithms, the standard deviation of DE indicates that it has significant stability. The results illustrate that DE is better than the GA algorithm currently used in the 0.434 GHz microwave hyperthermia phased array applicator [20], and can locate the globally optimal values of all breast models at all frequencies more frequently and consistently. Hence, among the HTP optimization methods, the DE algorithm has optimal treatment accuracy and stable results.

#### 3.2. Thermal Simulation Results Comparison

_{50}and T

_{90}of two breast models obtained by TR, PSO, GA, and DE as the HTP optimization methods are shown in Table 3. It can be observed that DE has the highest T

_{50}and T

_{90}compared to other HTP optimization methods. Due to the low power in the tumor of PSO optimization, the treatment temperature of PSO was the lowest. Compare with TR, the DE algorithm improves from 0.72 °C to 1.82 °C of T

_{50}and 0.15 °C to 2.09 °C of T

_{90}. Therefore, the DE algorithm not only increases the effectiveness of focusing but also improves the temperature of tumor treatment. Table 4 shows the mean and standard deviation of damaged healthy tissue rate for two breast models using the four HTP optimization methods. In all cases, the average damaged healthy tissue rates of DE are the lowest among the four HTP optimization methods, and its standard deviations are the smallest. DE provided 16.13% and 9.75% fewer hotspots in 40–42 °C and 42–45 °C windows compared to GA, respectively. It should be noted that despite the low rate of healthy tissue damage at 0.915 GHz with PSO, the temperature of tumor treatment is also low.

#### 3.3. Convergence Rate of Optimization Algorithms

## 4. Influence of Objective Functions on DE Optimization

_{obj}, 1/aPA

_{obj}, and 1/TC

_{50obj}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.

_{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.

_{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.

_{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.

_{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

^{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.

_{obj}is the most suitable objective function for DE.

## 6. Conclusions

^{3}and 2 cm

^{3}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.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**The process of optimizing dual-resonant phased array applicator in HTP and two breast models. (

**a**) Flowchart of HTP employed in this work; (

**b**) Side view of a heterogeneous breast model; (

**c**) Top view of a heterogenous breast model; (

**d**) Side view of a general breast model; (

**e**) Top view of a general breast model.

**Figure 2.**Normalized SAR distribution in axial (XY) and coronal (XZ) planes of a general breast model optimized using four FMHT optimization methods.

**Figure 3.**Normalized SAR distribution in axial (XY) and coronal (XZ) planes of a heterogeneous breast model optimized using four FMHT optimization methods.

**Figure 4.**Steady-state temperature distribution in axial (XY) and coronal (XZ) planes of a general breast model treated by four FMHT optimization methods.

**Figure 5.**Steady-state temperature distribution in axial (XY) and coronal (XZ) planes of a heterogeneous breast model treated by four FMHT optimization methods.

**Figure 6.**Normalized SAR distribution in axial (XY) and coronal (XZ) planes of a general breast model optimized by each objective function used in DE.

**Figure 7.**Normalized SAR distribution in axial (XY) and coronal (XZ) planes of a heterogeneous breast model optimized by each objective function used in DE.

**Figure 8.**Steady-state temperature distribution in axial (XY) and coronal (XZ) planes of a general breast model optimized by each objective function used in DE.

**Figure 9.**Steady-state temperature distribution in axial (XY) and coronal (XZ) planes of a heterogeneous breast model optimized by each objective function used in DE.

Freq. (GHz) | Breast Tissue | Fat | Skin | Chest | Fibro Glandular | Tumor | |
---|---|---|---|---|---|---|---|

Dielectric Properties | 0.915 [8] | Conductivity (S/m) | 0.2 | 1.0 | 2.0 | 0.6 | 0.6 |

Dielectric constant | 15 | 40 | 65 | 55 | 55 | ||

2.45 [9] | Conductivity (S/m) | 0.15 | 1.0 | 2.0 | 0.5 | 0.5 | |

Dielectric constant | 15 | 40 | 65 | 45 | 45 | ||

Thermal [11] Properties | Density (kg/m^{3}) | 1069 | 1085 | 1040 | 1050 | 1050 | |

Specific heat capacity (J/kg K) | 2348 | 3391 | 3421 | 2960 | 2960 | ||

Thermal conductivity (W/m K) | 0.21 | 0.37 | 0.49 | 0.33 | 0.33 | ||

Blood perfusion rate (1/s) | 0.001 | 0.002 | 0.003 | 0.003 | 0.003 | ||

Metabolic heat generation (W/m^{3}) | 350 | 1620 | 1046 | 690 | 690 |

**Table 2.**Mean and standard deviation of treatment indicators of two breast models optimized using four HTP optimization methods.

Breast Type | Freq. (GHz) | Treatment Indicator | TR | PSO | GA | DE |
---|---|---|---|---|---|---|

General | 0.915 | HTQ | 0.79 | 0.72 ± 0.0741 | 0.52 ± 0.0098 | 0.50 ± 0.0051 |

aPA | 15.60 | 16.85 ± 1.36 | 19.66 ± 0.46 | 20.24 ± 0.15 | ||

TC_{50} | 79 | 89 ± 2.60 | 98 ± 0.64 | 98 ± 0.35 | ||

2.45 | HTQ | 1.36 | 0.81 ± 0.0503 | 0.69 ± 0.0128 | 0.58 ± 0.0062 | |

aPA | 8.98 | 13.11 ± 1.12 | 16.28 ± 0.26 | 17.86 ± 0.06 | ||

TC_{50} | 70 | 90 ± 1.89 | 96 ± 0.35 | 98 ± 0.26 | ||

Heterogenous | 0.915 | HTQ | 1.26 | 0.81 ± 0.0126 | 0.53 ± 0.0047 | 0.50 ± 0.0008 |

aPA | 12.75 | 15.62 ± 1.16 | 20.36 ± 0.02 | 21.17 ± 0.05 | ||

TC_{50} | 90 | 80 ± 3.15 | 99 ± 0.43 | 99 ± 0.24 | ||

2.45 | HTQ | 1.96 | 0.69 ± 0.0776 | 0.55 ± 0.0215 | 0.51 ± 0.0154 | |

aPA | 9.06 | 15.47 ± 0.94 | 17.95 ± 0.60 | 18.23 ± 0.37 | ||

TC_{50} | 40 | 85 ± 2.46 | 96 ± 0.69 | 96 ± 0.44 |

**Table 3.**Mean and standard deviation of T

_{50}and T

_{90}values for two breast models using HTP optimization methods.

Breast Type | Freq. (GHz) | T (°C) | TR | PSO | GA | DE |
---|---|---|---|---|---|---|

General | 0.915 | T_{50} | 42.96 | 41.56 ± 2.37 | 43.16 ± 0.66 | 43.68 ± 0.03 |

T_{90} | 41.75 | 40.39 ± 2.94 | 41.94 ± 0.97 | 42.46 ± 0.39 | ||

2.45 | T_{50} | 40.99 | 41.85 ± 1.35 | 42.03 ± 0.58 | 42.07 ± 0.32 | |

T_{90} | 39.77 | 40.59 ± 1.81 | 40.82 ± 0.69 | 41.86 ± 0.79 | ||

Heterogeneous | 0.915 | T_{50} | 42.98 | 41.24 ± 1.26 | 42.89 ± 0.47 | 43.16 ± 0.42 |

T_{90} | 41.80 | 40.02 ± 1.96 | 41.70 ± 0.92 | 41.95 ± 0.85 | ||

2.45 | T_{50} | 41.06 | 41.72 ± 1.82 | 42.32 ± 0.71 | 42.61 ± 0.54 | |

T_{90} | 39.89 | 40.50 ± 2.46 | 41.11 ± 0.96 | 41.46 ± 0.65 |

**Table 4.**Mean and standard deviation of damaged healthy tissue rate for two breast models using HTP optimization methods.

Breast Type | Freq. (GHz) | T (%) | TR | PSO | GA | DE |
---|---|---|---|---|---|---|

General | 0.915 | 40–42 °C | 1.78 | 1.78 ± 2.23 | 3.31 ± 0.87 | 2.05 ± 0.65 |

42–44 °C | 1.32 | 0.28 ± 0.58 | 0.96 ± 0.38 | 0.82 ± 0.31 | ||

2.45 | 40–42 °C | 1.59 | 1.8 ± 1.63 | 1.44 ± 0.79 | 1.23 ± 0.23 | |

42–44 °C | 1.11 | 0.99 ± 0.56 | 0.78 ± 0.26 | 0.36 ± 0.07 | ||

Heterogeneous | 0.915 | 40–42 °C | 4.02 | 1.60 ± 2.05 | 1.85 ± 0.85 | 1.78 ± 0.51 |

42–44 °C | 2.24 | 0.27 ± 0.76 | 0.43 ± 0.32 | 0.68 ± 0.19 | ||

2.45 | 40–42 °C | 1.05 | 1.29 ± 1.20 | 0.91 ± 0.64 | 0.83 ± 0.33 | |

42–44 °C | 0.72 | 0.36 ± 0.51 | 0.53 ± 0.22 | 0.22 ± 0.13 |

Breast Type | Frequency (GHz) | PSO | GA | DE |
---|---|---|---|---|

General | 0.915 | 91 | 106 | 63 |

2.45 | 113 | 134 | 80 | |

Heterogeneous | 0.915 | 85 | 115 | 76 |

2.45 | 78 | 108 | 52 |

**Table 6.**Mean and standard deviation of treatment indicators of two breast models for each objective function used in DE.

Breast Type | Freq. (GHz) | Treatment Indicator | HTQ_{obj} | 1/aPA_{obj} | 1/TC_{50obj} |
---|---|---|---|---|---|

General | 0.915 | HTQ | 0.52 | 0.54 | 0.55 |

aPA | 21.03 | 21.18 | 20.65 | ||

TC_{50} | 98 | 98 | 99 | ||

2.45 | HTQ | 0.65 | 0.87 | 0.90 | |

aPA | 16.89 | 17.22 | 16.46 | ||

TC_{50} | 97 | 97 | 98 | ||

Heterogeneous | 0.915 | HTQ | 0.50 | 0.53 | 0.55 |

aPA | 21.19 | 21.97 | 19.63 | ||

TC_{50} | 100 | 100 | 100 | ||

2.45 | HTQ | 0.50 | 0.67 | 0.68 | |

aPA | 18.56 | 18.89 | 18.13 | ||

TC_{50} | 96 | 96 | 97 |

**Table 7.**The values of T

_{50}and T

_{90}of each objective function used in DE optimized the dual-resonant phased array excitations.

Breast Type | Frequency (GHz) | T (°C) | HTQ_{obj} | 1/aPA_{obj} | 1/TC_{50obj} |
---|---|---|---|---|---|

General | 0.915 | T_{50} | 43.70 | 42.52 | 42.98 |

T_{90} | 42.52 | 41.34 | 41.73 | ||

2.45 | T_{50} | 42.42 | 41.03 | 41.67 | |

T_{90} | 41.26 | 40.46 | 40.83 | ||

Homogeneous | 0.915 | T_{50} | 43.62 | 42.29 | 43.15 |

T_{90} | 42.86 | 41.71 | 41.90 | ||

2.45 | T_{50} | 43.21 | 42.03 | 42.66 | |

T_{90} | 42.00 | 41.23 | 41.85 |

Breast Type | Frequency (GHz) | T (%) | HTQ_{obj} | 1/aPA_{obj} | 1/TC_{50obj} |
---|---|---|---|---|---|

General | 0.915 | 40–42 °C | 1.72 | 1.52 | 3.40 |

42–44 °C | 0.60 | 0.07 | 1.01 | ||

2.45 | 40–42 °C | 1.19 | 0.70 | 1.31 | |

42–44 °C | 0.33 | 0.13 | 0.53 | ||

Homogeneous | 0.915 | 40–42 °C | 1.62 | 1.28 | 2.13 |

42–44 °C | 0.66 | 0.01 | 0.69 | ||

2.45 | 40–42 °C | 0.75 | 0.90 | 0.82 | |

42–44 °C | 0.20 | 0.36 | 0.22 |

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## Share and Cite

**MDPI and ACS Style**

Lyu, C.; Li, W.; Yang, B.
Differential Evolution Optimization of Microwave Focused Hyperthermia Phased Array Excitation for Targeted Breast Cancer Heating. *Sensors* **2023**, *23*, 3799.
https://doi.org/10.3390/s23083799

**AMA Style**

Lyu C, Li W, Yang B.
Differential Evolution Optimization of Microwave Focused Hyperthermia Phased Array Excitation for Targeted Breast Cancer Heating. *Sensors*. 2023; 23(8):3799.
https://doi.org/10.3390/s23083799

**Chicago/Turabian Style**

Lyu, Cheng, Wenxing Li, and Bin Yang.
2023. "Differential Evolution Optimization of Microwave Focused Hyperthermia Phased Array Excitation for Targeted Breast Cancer Heating" *Sensors* 23, no. 8: 3799.
https://doi.org/10.3390/s23083799