# Formation of Thermal Lesions in Tissue and Its Optimal Control during HIFU Scanning Therapy

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Theory and Methods

#### 2.1. Description of Acoustic Fields and Temperature Fields

#### 2.2. Parameters for Evaluating the Treatment Effect

#### 2.3. Optimal Control for Formation of Thermal Lesions

#### 2.4. Simulation Methods and Relevant Conditions

## 3. Results and Discussion

#### 3.1. Influence of Neighboring Treatment Spots on the Temperature Elevation

^{6}W/m

^{2}are basically confined to a circular area with a radius of 1 mm in the center of the focal region. When HIFU scanning therapy is performed, the fixed or optimized acoustic intensity shifts geometrically along the path shown in Figure 1 on the focal plane.

#### 3.2. Influence of Neighboring Treatment Spots on the Formation of Thermal Lesions

#### 3.3. Influence of the Heating Time and Acoustic Intensity on Thermal Lesions

#### 3.4. Optimal Control for the Formation of Thermal Lesions

^{2}larger than that under an optimized heating time. When ${f}_{b}$ = 0.7 and ${f}_{a}$ = 0.5 or ${f}_{b}$ = 0.8 and ${f}_{a}$ = 0.6, the value of ${S}_{pT}^{2}$ is over 100, which implies a poor temperature uniformity during the treatment process. The deviation area of thermal lesions (${S}_{D}$) can be calculated according to Equation (9) in Table 4, and its minimum is 4.2339 mm

^{2}at ${f}_{b}$ = 0.8 and ${f}_{a}$ = 0.4, which are regarded as the best optimization cases for the heating time. Compared with the data in Table 3 at an approximate total heating time (1.4${t}_{s}$), the values of ${m}_{pT}$ and ${S}_{pT}^{2}$ after optimization are reduced by 1.86 °C and 2.6921, respectively, and ${S}_{AT}$ increases by 4.913 mm

^{2}, but ${S}_{AH}$ only increases slightly (0.9439 mm

^{2}). In the case of the approximate ${S}_{AT}$ values (1.6${t}_{s})$ in Figure 4, ${t}_{T}$, ${m}_{pT}$ and ${S}_{pT}^{2}$ after optimization are reduced by 18.4 s, 4.064 °C and 6.7136, respectively; after all, compared with the case of the fixed heating time 1.8${t}_{s}$, the value of ${S}_{D}$ almost remains unchanged, but ${t}_{T}$,${m}_{pT}$ and ${S}_{pT}^{2}$ are reduced by 17.4%, 13.3% and 45%, respectively. In Table 5, when ${f}_{b}$ = 0.9 and ${f}_{a}$ = 0.5, the value of ${S}_{D}$ reaches rock bottom (4.4562 mm

^{2}), which is regard as the best optimization case for the acoustic intensity. Compared with the case of a fixed acoustic intensity 1.4${I}_{s}$ in Table 3, the value of ${S}_{AT}$ in the optimization case is basically the same, and the value of ${m}_{pT}$ decreases by 4.3 °C, but ${S}_{pT}^{2}$ increases by 44.515. Obviously, compared with the cases with a fixed acoustic intensity, the scheme of the optimized acoustic intensity provides the same total heating time, and can reduce the temperature elevation of the treatment region, but it also results in a greater reduction in the temperature uniformity. In comparison, the optimized heating time is conducive to reducing the temperature elevation and improving the temperature uniformity of the treatment region, while the optimized acoustic intensity can save more treatment time and produce larger tissue lesions.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Comparison of the temperature elevation on treatment spots. (

**a**) No. 1; (

**b**) No. 5; (

**c**) No. 13; (

**d**) No. 19.

**Figure 4.**Thermal lesions on the focal plane at different times during high intensity focused ultrasound (HIFU) scanning therapy (${t}_{n}$ = ${t}_{s}$ ). (

**a**) 17 s; (

**b**) 35 s; (

**c**) 53 s; (

**d**) 71 s; (

**e**) 89 s; (

**f**) 107 s; (

**g**) 125 s; (

**h**) 143 s; (

**i**)149 s; (

**j**) 159 s.

**Figure 5.**Thermal lesions on the focal plane under different heating times. (

**a**) 1.2${t}_{s}$; (

**b**) 1.4${t}_{s}$; (

**c**) 1.6${t}_{s}$; (

**d**) 1.8${t}_{s}$.

**Figure 6.**Thermal lesions on the focal plane under different acoustic intensities. (

**a**) 1.2${I}_{s}$; (

**b**) 1.4${I}_{s}$; (

**c**) 1.6${I}_{s}$; (

**d**) 1.8${I}_{s}$.

**Figure 7.**Thermal lesions on the focal plane under an optimized heating time. (

**a**) ${f}_{b}$ = 0.7,${f}_{a}$ = 0.5; (

**b**) ${f}_{b}$ = 0.8, ${f}_{a}$ = 0.5; (

**c**) ${f}_{b}$ = 0.9,${f}_{a}$ = 0.5; (

**d**) ${f}_{b}$ = 0.8,${f}_{a}$ = 0.4; (

**e**) ${f}_{b}$ = 0.8,${f}_{a}$ = 0.6.

**Figure 8.**Thermal lesions on the focal plane under an optimized acoustic intensity. (

**a**)${f}_{b}$ = 0.7,${f}_{a}$ = 0.5; (

**b**)${f}_{b}$ = 0.8,${f}_{a}$ = 0.5; (

**c**)${f}_{b}$ = 0.9,${f}_{a}$ = 0.5; (

**d**)${f}_{b}$ = 0.8,${f}_{a}$ = 0.4; (

**e**)${f}_{b}$ = 0.8,${f}_{a}$ = 0.6.

Materials | Density (kg/m^{3}) | Speed of Sound (m/s) | Attenuation (Np/m/MHz) | Specific Heat (J/(kg.K)) | Thermal Conductivity (W/(m.K)) |
---|---|---|---|---|---|

Water | 1000 | 1483 | 0.025 | N/A | N/A |

Tissue | 1036 | 1551 | 3.5614 | 3560 | 0.5212 |

Treatment Spots | Neighboring Treated Spots
$({\mathit{s}}_{\mathit{N}}$$,{\mathit{t}}_{\mathit{N}})$ (mm, s) | Neighboring Untreated Spots $({\mathit{s}}_{\mathit{N}}$$,{\mathit{t}}_{\mathit{N}})$(mm, s) |
---|---|---|

No.1 | / | No. 2(2,1), No. 3($2\surd 2$,7), No. 4(2,13), No. 5($2\surd 2$,19), No. 6(2,25), No.7($2\surd 2$,31), No. 8(2,37), No. 9($2\surd 2$,43) |

No.5 | No. 4(2,1), No.1($2\surd 2$,19) | No. 6(2,1), No.15($2\surd 2$,55), No. 16(2,61), No.17($2\surd 2$,67), No. 18 (2,73), No.19($2\surd 2$,79) |

No.13 | No.12(2,1), No.3($2\surd 2$,55) | No. 14(2,1) |

No.19 | No.18(2,1), No.6 (2,73), No.5($2\surd 2$,79), No.7($2\surd 2$,67) | No. 20(2,1) |

**Table 3.**Influence of a different heating time and acoustic intensity on the parameters for evaluating the treatment effect.

${\mathit{t}}_{\mathit{n}}\mathrm{or}{\mathit{I}}_{\mathit{n}}$ | ${\mathit{t}}_{\mathit{T}}\left(\mathbf{s}\right)$ | ${\mathit{m}}_{\mathit{p}\mathit{T}}(\xb0\mathbf{C})$ | ${\mathit{S}}_{\mathit{p}\mathit{T}}^{2}$ | ${\mathit{S}}_{\mathit{A}\mathit{T}}\left({\mathbf{mm}}^{2}\right)$ | ${\mathit{S}}_{\mathit{A}\mathit{H}}\left({\mathbf{mm}}^{2}\right)$ | ${\mathit{S}}_{\mathit{D}}\left({\mathbf{mm}}^{2}\right)$ |
---|---|---|---|---|---|---|

1.2${t}_{s}$ | 174 | 37.924 | 12.4869 | 63.822 | 0.0040 | 17.182 |

1.4${t}_{s}$ | 199 | 40.576 | 16.2177 | 73.033 | 0.2360 | 8.2030 |

1.6${t}_{s}$ | 224 | 42.780 | 20.2392 | 77.086 | 0.8760 | 4.7860 |

1.8${t}_{s}$ | 249 | 44.640 | 24.6317 | 78.923 | 1.7140 | 3.7910 |

1.2${I}_{s}$ | 149 | 41.668 | 13.2639 | 72.536 | 0.2050 | 8.6690 |

1.4${I}_{s}$ | 149 | 48.644 | 18.1242 | 79.419 | 2.2623 | 3.8433 |

1.6${I}_{s}$ | 149 | 55.572 | 23.6054 | 80.852 | 5.6758 | 5.8238 |

1.8${I}_{s}$ | 149 | 62.516 | 29.8181 | 80.991 | 9.0998 | 9.1088 |

**Table 4.**Influence of different ${f}_{b}$ and ${f}_{a}$ values on the parameters for evaluating the treatment effect under an optimized heating time.

${\mathit{f}}_{\mathit{b}}$$\mathbf{and}{\mathit{f}}_{\mathit{a}}$ | ${\mathit{t}}_{\mathit{T}}\left(\mathbf{s}\right)$ | ${\mathit{m}}_{\mathit{p}\mathit{T}}(\xb0\mathbf{C})$ | ${\mathit{S}}_{\mathit{p}\mathit{T}}^{2}$ | ${\mathit{S}}_{\mathit{A}\mathit{T}}\left({\mathbf{mm}}^{2}\right)$ | ${\mathit{S}}_{\mathit{A}\mathit{H}}\left({\mathbf{mm}}^{2}\right)$ | ${\mathit{S}}_{\mathit{D}}\left({\mathbf{mm}}^{2}\right)$ |
---|---|---|---|---|---|---|

0.7,0.5 | 204 | 38.472 | 13.8263 | 77.872 | 1.2112 | 4.3392 |

0.8,0.5 | 194.2 | 37.860 | 11.8358 | 76.641 | 0.7878 | 5.1468 |

0.9,0.5 | 188.2 | 37.196 | 11.5362 | 75.838 | 0.6050 | 5.7670 |

0.8,0.4 | 205.6 | 38.716 | 13.5256 | 77.946 | 1.1799 | 4.2339 |

0.8,0.6 | 187.2 | 36.828 | 20.6404 | 74.996 | 0.7183 | 6.7223 |

**Table 5.**Influence of different ${f}_{b}$ and ${f}_{a}$ values on the parameters for evaluating the treatment effect under an optimized acoustic intensity.

${\mathit{f}}_{\mathit{b}}$$\mathbf{and}{\mathit{f}}_{\mathit{a}}$ | ${\mathit{t}}_{\mathit{T}}\left(\mathbf{s}\right)$ | ${\mathit{m}}_{\mathit{p}\mathit{T}}(\xb0\mathbf{C})$ | ${\mathit{S}}_{\mathit{p}\mathit{T}}^{2}$ | ${\mathit{S}}_{\mathit{A}\mathit{T}}\left({\mathbf{mm}}^{2}\right)$ | ${\mathit{S}}_{\mathit{A}\mathit{H}}\left({\mathbf{mm}}^{2}\right)$ | ${\mathit{S}}_{\mathit{D}}\left({\mathbf{mm}}^{2}\right)$ |
---|---|---|---|---|---|---|

0.7,0.5 | 149 | 48.3080 | 108.9916 | 80.789 | 6.1953 | 6.4063 |

0.8,0.5 | 149 | 45.6080 | 76.4708 | 80.358 | 4.3431 | 4.9851 |

0.9,0.5 | 149 | 44.3440 | 62.6392 | 79.797 | 3.2532 | 4.4562 |

0.8,0.4 | 149 | 49.1320 | 86.0464 | 80.825 | 6.1612 | 6.3362 |

0.8,0.6 | 149 | 43.7040 | 100.1212 | 79.734 | 3.6970 | 4.9630 |

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## Share and Cite

**MDPI and ACS Style**

Zou, X.; Qian, S.; Tan, Q.; Dong, H.
Formation of Thermal Lesions in Tissue and Its Optimal Control during HIFU Scanning Therapy. *Symmetry* **2020**, *12*, 1386.
https://doi.org/10.3390/sym12091386

**AMA Style**

Zou X, Qian S, Tan Q, Dong H.
Formation of Thermal Lesions in Tissue and Its Optimal Control during HIFU Scanning Therapy. *Symmetry*. 2020; 12(9):1386.
https://doi.org/10.3390/sym12091386

**Chicago/Turabian Style**

Zou, Xiao, Shengyou Qian, Qiaolai Tan, and Hu Dong.
2020. "Formation of Thermal Lesions in Tissue and Its Optimal Control during HIFU Scanning Therapy" *Symmetry* 12, no. 9: 1386.
https://doi.org/10.3390/sym12091386