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The acoustic energy distribution of high intensity focused ultrasound (HIFU) is influenced by the attenuation and the dispersion of the biological tissue. In this paper we modify the KZK equation according to the fractional wave equation, in order to accurately describe the sound field of HIFU. The theoretical and experimental studies of frequency dependences of attenuation and sound speed examine the validity of the fractional wave equation. Furthermore, the numerical simulation of HIFU field is performed using the modified KZK equation. The results demonstrate that the introduction of the fractional derivative equation could solve the problems of the attenuation and sound dispersion, leading to the accuracy improvement of HIFU therapy.
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Keywords:
- fractional derivative /
- attenuation /
- dispersion /
- HIFU
[1] Li J L, Liu X Y, Zhang D, Gong X F 2006 Acta Phys. Sin. 55 2809 (in Chinese) [李俊伦, 刘晓宙, 章东, 龚秀芬 2006 物理学报 55 2809]
[2] Xue H F, Liu X Y, Gong X F, Zhang D 2005 Acta Phys. Sin. 54 5233 (in Chinese) [薛洪惠, 刘晓宙, 龚秀芬, 章东 2005 物理学报 55 5233]
[3] Yu J, Zhang D, Liu X Y, Gong X F, Song F X 2007 Acta Phys. Sin. 56 5909 (in Chinese) [于洁, 章东, 刘晓宙, 龚秀芬, 宋富先 2007 物理学报 56 5909]
[4] Lu M Z, Wan M X, Shi Y, Song Y C 2002 Acta Phys. Sin. 51 928 (in Chinese) [陆明珠, 万明习, 施雨, 宋延淳 2002 物理学报 51 928]
[5] Qian S Y, Wang H Z 2000 Physics 29 686 (in Chinese) [钱盛友, 王鸿樟 2000 物理 29 686]
[6] Throff S, Chaussy C, Vallancien G, Wieland W, Kiel H J, Duc A L, Desgrandchamps F, Rosette J J M C H, Gelet A 2003 Journal of Endourology 17 673
[7] Kennedy J E, Wu F, Ter Haar G R, Gleeson F V, Philips R R, Middleton M R, Cranston D 2004 Ultrasonics 42 931
[8] Wu F, Wang Z B, Chen W Z, Zou J Z, Bai J, Zhu H, Li K Q, Xie F L, Jin C B, Su H B, Gao G W 2004 Ultrasound Med. Biol. 30 245
[9] Gianfelice D, Khiat A, Boulanger Y, Amara M, Belblidia A 2003 J. Vasc. Interv Radiol 14 1275
[10] Chen W, Holm S 2004 J. Acoust. Soc. Am. 115 1424
[11] Wismer M 2006 J. Acoust. Soc. Am. 120 3493
[12] Baglegy R L, Torvik P J 1983 J. Rheol. 27 201
[13] Deffieux T, Montaldo G, Tanter M, Fink M 2009 IEEE Trans. Med. Imaging 28 313
[14] Szabo T, Wu J 2000 J. Acoust. Soc. Am. 107 2437
[15] Lewandowski R, Chorãyczewski B 2010 Computers and Structures 88 1
[16] Szabo T 1994 J. Acoust. Soc. Am. 96 491
[17] Chen W, Holm S 2003 J. Acoust. Soc. Am. 114 2570
[18] Kelly J F, McGough R J 2009 J. Acoust. Soc. Am. 126 2072
[19] Wells P N T 1977 Ultrasonics 15 231
[20] Bamber J C, Fry M J, Hill C R, Dunn F 1977 Ultrasound in Medicine & Biology 3 15
[21] Cheng J C 2003 Acoustic principle (Beijing: Sience Press) p567 (in Chinese) [程建春 2003 声学原理 (北京: 科学出版社) 第576页]
[22] O'Donnell M, Jaynes E T 1981 J. Acoust. Soc. Am. 69 696
[23] He P, Zheng J 2001 Ultrasonics 39 27
[24] Wismer M 2006 J. Acoust. Soc. Am. 120 3493
[25] Kashcheeva S S, Sapozhnikov O A, Khokhlova V A, Averkiou M A, Crum L A 2000 Acoustical Physics 46 170
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[1] Li J L, Liu X Y, Zhang D, Gong X F 2006 Acta Phys. Sin. 55 2809 (in Chinese) [李俊伦, 刘晓宙, 章东, 龚秀芬 2006 物理学报 55 2809]
[2] Xue H F, Liu X Y, Gong X F, Zhang D 2005 Acta Phys. Sin. 54 5233 (in Chinese) [薛洪惠, 刘晓宙, 龚秀芬, 章东 2005 物理学报 55 5233]
[3] Yu J, Zhang D, Liu X Y, Gong X F, Song F X 2007 Acta Phys. Sin. 56 5909 (in Chinese) [于洁, 章东, 刘晓宙, 龚秀芬, 宋富先 2007 物理学报 56 5909]
[4] Lu M Z, Wan M X, Shi Y, Song Y C 2002 Acta Phys. Sin. 51 928 (in Chinese) [陆明珠, 万明习, 施雨, 宋延淳 2002 物理学报 51 928]
[5] Qian S Y, Wang H Z 2000 Physics 29 686 (in Chinese) [钱盛友, 王鸿樟 2000 物理 29 686]
[6] Throff S, Chaussy C, Vallancien G, Wieland W, Kiel H J, Duc A L, Desgrandchamps F, Rosette J J M C H, Gelet A 2003 Journal of Endourology 17 673
[7] Kennedy J E, Wu F, Ter Haar G R, Gleeson F V, Philips R R, Middleton M R, Cranston D 2004 Ultrasonics 42 931
[8] Wu F, Wang Z B, Chen W Z, Zou J Z, Bai J, Zhu H, Li K Q, Xie F L, Jin C B, Su H B, Gao G W 2004 Ultrasound Med. Biol. 30 245
[9] Gianfelice D, Khiat A, Boulanger Y, Amara M, Belblidia A 2003 J. Vasc. Interv Radiol 14 1275
[10] Chen W, Holm S 2004 J. Acoust. Soc. Am. 115 1424
[11] Wismer M 2006 J. Acoust. Soc. Am. 120 3493
[12] Baglegy R L, Torvik P J 1983 J. Rheol. 27 201
[13] Deffieux T, Montaldo G, Tanter M, Fink M 2009 IEEE Trans. Med. Imaging 28 313
[14] Szabo T, Wu J 2000 J. Acoust. Soc. Am. 107 2437
[15] Lewandowski R, Chorãyczewski B 2010 Computers and Structures 88 1
[16] Szabo T 1994 J. Acoust. Soc. Am. 96 491
[17] Chen W, Holm S 2003 J. Acoust. Soc. Am. 114 2570
[18] Kelly J F, McGough R J 2009 J. Acoust. Soc. Am. 126 2072
[19] Wells P N T 1977 Ultrasonics 15 231
[20] Bamber J C, Fry M J, Hill C R, Dunn F 1977 Ultrasound in Medicine & Biology 3 15
[21] Cheng J C 2003 Acoustic principle (Beijing: Sience Press) p567 (in Chinese) [程建春 2003 声学原理 (北京: 科学出版社) 第576页]
[22] O'Donnell M, Jaynes E T 1981 J. Acoust. Soc. Am. 69 696
[23] He P, Zheng J 2001 Ultrasonics 39 27
[24] Wismer M 2006 J. Acoust. Soc. Am. 120 3493
[25] Kashcheeva S S, Sapozhnikov O A, Khokhlova V A, Averkiou M A, Crum L A 2000 Acoustical Physics 46 170
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