# Recognition of Biological Tissue Denaturation Based on Improved Multiscale Permutation Entropy and GK Fuzzy Clustering

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theory

#### 2.1. MPE

#### 2.2. IMPE

#### 2.3. GK Fuzzy Clustering

_{i}(I = 1,2,⋯,c) is the ${i}^{th}$ cluster center, n is the sample number, ${\mu}_{ij}$ indicating the membership degree of the ${j}^{th}$ element belonging to the ${i}^{th}$ class, which satisfy the following:

- (1)
- Initializing the number of clustering c, fuzzy index θ, and the membership matrix U to satisfy Formula (12).
- (2)
- Updating the cluster center v
_{i}by Formula (13). - (3)
- Calculating the covariance matrix of the ${i}^{th}$ cluster center F
_{i}.

_{i}from covariance matrix F

_{i}, then calculating the square inner product norm ${D}_{ij}^{2}$; updating the membership matrix $U$ according to Formula (11); stopping the calculation if it satisfies $\Vert {U}^{\left(L+1\right)}-{U}^{\left(L\right)}\Vert <\eta $, otherwise, increasing iterations until the condition is met. Where, ${U}^{\left(L\right)}$ is the membership matrix of L iterations, termination error η > 0.

## 3. Results

#### 3.1. Simulation with White Gaussian Noise (WGN)

#### 3.2. Analysis of Ultrasonic Scattered Echo Signals

#### 3.3. Discussions

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Hill, C.R.; Haar, G.T. Review article: High intensity focused ultrasound—Potential for cancer treatment. Br. J. Radiol.
**1995**, 68, 1296–1303. [Google Scholar] [CrossRef] - Kennedy, J.E. High intensity focused ultrasound: Surgery of the future? Br. J. Radiol.
**2003**, 76, 590–599. [Google Scholar] [CrossRef] [PubMed] - Bailey, M.R.; Khokhlova, V.A.; Sapozhnikov, O.; Kargl, S.G.; Crum, L.A. Physical mechanisms of the therapeutic effect of ultrasound. Acoust. Phys.
**2003**, 49, 369–388. [Google Scholar] [CrossRef] - Rove, K.O.; Sullivan, K.F.; Crawford, E.D. High-intensity Focused Ultrasound: Ready for Primetime. Urol. Clin. N. Am.
**2010**, 37, 27–35. [Google Scholar] [CrossRef] [PubMed] - Cranston, D. A review of high intensity focused ultrasound in relation to the treatment of renal tumours and other malignancies. Ultrason. Sonochem.
**2015**, 27, 654–658. [Google Scholar] [CrossRef] - Kim, Y.-S.; Bae, D.-S.; Park, M.J.; Viitala, A.; Keserci, B.; Rhim, H.; Lim, H.K. Techniques to expand patient selection for MRI-guided high-intensity focused ultrasound ablation of uterine fibroids. AJR. Am. J. Roentgenol.
**2014**, 202, 443–451. [Google Scholar] [CrossRef] - Filipowska, J.; Łoziński, T. Magnetic Resonance-Guided High-Intensity Focused Ultrasound (MR-HIFU) in Treatment of Symptomatic Uterine Myomas. Pol. J. Radiol.
**2014**, 79, 439–443. [Google Scholar] [PubMed] [Green Version] - Wood, B.J.; Yanof, J.; Frenkel, V.; Viswanathan, A.; Dromi, S.; Oh, K.; Kruecker, J.; Bauer, C.; Seip, R.; Kam, A.; et al. CT and ultrasound guided stereotactic high intensity focused ultrasound (HIFU). AIP Conf. Proc.
**2006**, 829, 122–126. [Google Scholar] - Weiss, N.; Sosna, J.; Goldberg, S.N.; Azhari, H. Non-invasive temperature monitoring and hyperthermic injury onset detection using X-ray CT during HIFU thermal treatment in ex vivo fatty tissue. Int. J. Hyperther.
**2014**, 30, 119–125. [Google Scholar] [CrossRef] - Ballard, J.R.; Casper, A.J.; Ebbini, E.S. Monitoring and guidance of HIFU beams with dual-mode ultrasound arrays. In Proceedings of the 2009 Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Minneapolis, MN, USA, 3–6 September 2009; pp. 137–140. [Google Scholar]
- Wen, Q.; Wan, S.; Liu, Z.; Xu, S.; Wang, H.; Yang, B. B-ultrasound Image Registration of HIFU Monitoring Based on Ultrasonic Speckle. Sci. Technol. Rev.
**2010**, 28, 59–63. [Google Scholar] - Zhang, S.; Yang, W.; Yang, R.; Ye, B.; Chen, L.; Ma, W.; Chen, Y. Noninvasive temperature monitoring in a wide range based on textures of ultrasound images. In International Workshop on Medical Imaging and Virtual Reality; Springer: Berlin/Heidelberg, Germany, 2006; pp. 100–107. [Google Scholar]
- Poušek, L.; Jelínek, M.; Storkova, B.; Novak, P. Noninvasive temperature monitoring using ultrasound tissue characterization method. In Proceedings of the 28th International Conference on Information Technology Interfaces, Cavtat, Croatia, 19–22 June 2006; pp. 219–224. [Google Scholar]
- Parker, K.J. Ultrasonic attenuation and absorption in liver tissue. Ultrasound Med. Biol.
**1983**, 9, 363–369. [Google Scholar] [CrossRef] - Damianou, C.A.; Sanghvi, N.T.; Fry, F.J.; Maass-Moreno, R. Dependence of ultrasonic attenuation and absorption in dog soft tissues on temperature and thermal dose. J. Acoust. Soc. Am.
**1997**, 102, 628–634. [Google Scholar] [CrossRef] - Worthington, A.E.; Trachtenberg, J.; Sherar, M.D. Ultrasound properties of human prostate tissue during heating. Ultrasound Med. Biol.
**2002**, 28, 1311–1318. [Google Scholar] [CrossRef] - Garra, B.S. Imaging and estimation of tissue elasticity by ultrasound. Ultrasound Q.
**2007**, 23, 255–268. [Google Scholar] [CrossRef] [PubMed] - Pichardo, S.; Sin, V.W.; Hynynen, K. Multi-frequency characterization of the speed of sound and attenuation coefficient for longitudinal transmission of freshly excised human skulls. Phys. Med. Biol.
**2010**, 56, 219. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Furness, G.; Reilly, M.P.; Kuchi, S. An evaluation of ultrasound imaging for identification of lumbar intervertebral level. Anaesthesia
**2015**, 57, 277–280. [Google Scholar] [CrossRef] [PubMed] - Shishitani, T.; Yoshizawa, S.; Umemura, S. Change in acoustic impedance and sound speed of HIFU-exposed chicken breast muscle. In Proceedings of the 2010 IEEE International Ultrasonics Symposium, San Diego, CA, USA, 11–14 October 2010; pp. 1384–1387. [Google Scholar]
- Mobasheri, S.; Behnam, H.; Rangraz, P.; Tavakkoli, J. Radio frequency ultrasound time series signal analysis to evaluate high-intensity focused ultrasound lesion formation status in tissue. J. Med. Signals Sens.
**2016**, 6, 91. [Google Scholar] [CrossRef] [PubMed] - Tsui, P.H.; Wan, Y.L. Effects of fatty infiltration of the liver on the Shannon entropy of ultrasound backscattered signals. Entropy
**2016**, 18, 341. [Google Scholar] [CrossRef] [Green Version] - Tsui, P.H. Ultrasound Detection of Scatterer Concentration by Weighted Entropy. Entropy
**2015**, 17, 6598–6616. [Google Scholar] [CrossRef] [Green Version] - Behnam, H.; Monfared, M.M.; Rangraz, P.; Tavakkoli, J. High-intensity focused ultrasound thermal lesion detection using entropy imaging of ultrasound radio frequency signal time series. J. Med. Ultrasound
**2018**, 26, 24. [Google Scholar] [CrossRef] [PubMed] - Montirosso, R.; Riccardi, B.; Molteni, E.; Borgatti, R.; Reni, G. Infant’s emotional variability associated to interactive stressful situation: A novel analysis approach with Sample Entropy and Lempel-Ziv Complexity. Infant Behav. Dev.
**2010**, 33, 346–356. [Google Scholar] [CrossRef] [PubMed] - Acharya, U.R.; Raghavendra, U.; Fujita, H.; Hagiwara, Y.; Koh, J.E.; Hong, T.J.; Sudarshan, V.K.; Vijayananthan, A.; Yeong, C.H.; Gudigar, A.; et al. Automated characterization of fatty liver disease and cirrhosis using curvelet transform and entropy features extracted from ultrasound images. Comput. Biol. Med.
**2016**, 79, 250–258. [Google Scholar] [CrossRef] [PubMed] - Bandt, C.; Pompe, B. Permutation entropy: A natural complexity measure for time series. Phys. Rev. Lett.
**2002**, 88, 174102. [Google Scholar] [CrossRef] - Yan, S.-Q.; Zhang, H.; Liu, B.; Tang, H.; Qian, S.-Y. Identification of denatured and normal biological tissues based on compressed sensing and refined composite multi-scale fuzzy entropy during high intensity focused ultrasound treatment. Chin. Phys. B
**2021**, 30, 028704. [Google Scholar] [CrossRef] - Liu, B.; Wang, R.; Peng, Z.; Qin, L. Identification of denatured biological tissues based on compressed sensing and improved multiscale dispersion entropy during HIFU treatment. Entropy
**2020**, 22, 944. [Google Scholar] [CrossRef] - Gao, Y.; Villecco, F.; Li, M.; Song, W. Multi-scale permutation entropy based on improved LMD and HMM for rolling bearing diagnosis. Entropy
**2017**, 19, 176. [Google Scholar] [CrossRef] [Green Version] - Li, Y.; Li, Y.; Chen, X.; Yu, J. A novel feature extraction method for ship-radiated noise based on variational mode decomposition and multi-scale permutation entropy. Entropy
**2017**, 19, 342. [Google Scholar] [CrossRef] [Green Version] - Liu, B.; Hu, W.P.; Zou, X.; Ding, Y.J.; Qian, S.Y. Recognition of denatured biological tissue based on variational mode decomposition and multi-scale permutation entropy. Acta Phys. Sin.
**2019**, 68, 028702. [Google Scholar] [CrossRef] - Liu, B.; Tan, W.; Zhang, X.; Peng, Z.; Cao, J. Recognition study of denatured biological tissues based on multi-scale rescaled range permutation entropy. Math. Biosci. Eng.
**2022**, 19, 102–114. [Google Scholar] [CrossRef] [PubMed] - Fadlallah, B.; Chen, B.; Keil, A.; Príncipe, J. Weighted-permutation entropy: A complexity measure for time series incorporating amplitude information. Phys. Rev. E
**2013**, 87, 022911. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Zang, W.; Wang, Z.; Jiang, D.; Liu, X.; Jiang, Z. Classification of MRI brain images using DNA genetic algorithms optimized Tsallis entropy and support vector machine. Entropy
**2018**, 20, 964. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Ilakiyaselvan, N.; Khan, A.N.; Shahina, A. Deep learning approach to detect seizure using reconstructed phase space images. J. Biomed. Res.
**2020**, 34, 240–250. [Google Scholar] [CrossRef] [PubMed] - Grassi, K.; Poisson-Caillault, É.; Bigand, A.; Lefebvre, A. Comparative Study of Clustering Approaches Applied to Spatial or Temporal Pattern Discovery. J. Mar. Sci. Eng.
**2020**, 8, 713. [Google Scholar] [CrossRef] - Seip, R.; Tavakkoli, J.; Carlson, R.; Wunderlich, A.; Sanghvi, N.; Dines, K.; Gardner, T. High-intensity focused ultrasound (HIFU) multiple lesion imaging: Comparison of detection algorithms for real-time treatment control. In Proceedings of the IEEE Ultrasonics Symposium, Munich, German, 8–11 October 2002; Volume 2, pp. 1427–1430. [Google Scholar]
- Ge, H.; Liu, X. Fault Diagnosis of Rolling Bearings Based on ALIFD Fuzzy Entropy and GK Clustering. Fail. Anal. Prev.
**2019**, 14, 71–78. [Google Scholar]

**Figure 1.**White Gaussian noise used in multiscale permutation entropy (MPE) and improved multiscale permutation entropy (IMPE) simulation.

**Figure 4.**Time-domain samples of experimental ultrasonic scattered echo: (

**a**) non-denatured tissue; (

**b**) denatured tissue.

**Figure 5.**Recognition of denatured and non-denatured tissue based on support vector machine (SVM): (

**a**) MPE-SVM; (

**b**) IMPE-SVM.

**Figure 6.**Recognition of denatured and normal issue based on Gustafson–Kessel (GK) fuzzy clustering: (

**a**) MPE-GK; (

**b**) IMPE-GK.

Entropy | Samplings | |||
---|---|---|---|---|

500 | 1000 | 3000 | 5000 | |

MPE | 0.0917 | 0.0587 | 0.0143 | 0.0119 |

IMPE | 0.0215 | 0.0103 | 0.0049 | 0.0020 |

Recognition Methods | Non-Denatured Tissue | Denatured Tissue | Recognition Rate (%) |
---|---|---|---|

MPE-SVM | 81/100 | 96/100 | 88.5 |

IMPE-SVM | 86/100 | 98/100 | 92.0 |

MPE-GK | 85/100 | 97/100 | 91.0 |

IMPE-GK | 92/100 | 99/100 | 95.5 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Peng, Z.; Zhang, X.; Cao, J.; Liu, B.
Recognition of Biological Tissue Denaturation Based on Improved Multiscale Permutation Entropy and GK Fuzzy Clustering. *Information* **2022**, *13*, 140.
https://doi.org/10.3390/info13030140

**AMA Style**

Peng Z, Zhang X, Cao J, Liu B.
Recognition of Biological Tissue Denaturation Based on Improved Multiscale Permutation Entropy and GK Fuzzy Clustering. *Information*. 2022; 13(3):140.
https://doi.org/10.3390/info13030140

**Chicago/Turabian Style**

Peng, Ziqi, Xian Zhang, Jing Cao, and Bei Liu.
2022. "Recognition of Biological Tissue Denaturation Based on Improved Multiscale Permutation Entropy and GK Fuzzy Clustering" *Information* 13, no. 3: 140.
https://doi.org/10.3390/info13030140