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How to diagnose the bone fatigue damage at early stages is one of the hot research subjects in bone evaluation field. In this study, the propagation characteristics of ultrasonic guide wave in a long bone under different elastic moduli are analyzed using theoretical calculation and simulation methods. First, theoretical solutions of guided wave in a long bone are calculated. Then, a finite difference time-domain (FDTD) numerical method of simulating the propagation of guide wave in a long bone is presented. The simulation results are in good agreement with the theoretical values. And, the relationship between elastic modulus and the propagation characteristics, including group velocity, central frequency and attenuation, is discussed. The results show that group velocity and central frequency increase with the increase of elastic modulus. However, attenuation decreases with the increase of elastic modulus. Those results demonstrate that the propagation of guide wave can reflect the variation of elastic modulus of long bone, which provides a theoretical basis for evaluating the early stages of fatigue damage in long bone.
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Keywords:
- ultrasonic guide waves /
- long bone fatigue /
- elastic modulus /
- finite difference time-domain (FDTD)
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[2] Akkus O, Rimnac C M 2001 J. Biomech. 34 757
[3] Zioupos P, Casinos A 1998 J. Biomech. 31825
[4] Magnusson H I, Ahlborg H G, Karlsson C, Nyquist F, Karlsson M K 2003 Am. J. Sports Med. 31 596
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[7] Deng M X, Pei J F 2010 Sci. China Ser. G-Phys. Mech. Astron. 53 1286
[8] Pruell C, Kim J Y, Qu J, Jacobs L J 2009 Smart Mater. Struct. 18 035003
[9] Bossy E, Talmant M, Laugier P 2002 J. Acoust. Soc. Am. 112 297
[10] Lee K I, Yoon S W 2004 J. Acoust. Soc. Am. 115 3210
[11] Moilanen P, Talmant M, Bousson Valerie, Nicholson P H F, Cheng S L, Timonen J, Laugier P 2007 J. Acoust. Soc. Am. 122 1818
[12] Bertram A A 1990 Acoustic Fields and Waves in Solids (Second Edition) (Florida: Krieger Publishing Company) pp86-97
[13] Gazis D C 1959 J. Acoust. Soc. Am. 31 568
[14] Ta D A, Wang W Q 2009 Ultrasound Med. Biol. 35 641
[15] Ta D A, Liu Z Q, He P F 2003 Acta Meteriae Compositae Sinica 20 130 (in Chinese) [他得安, 刘镇清, 贺鹏飞2003 复合材料学报 20 130]
[16] Luo G M, Kaufman J J, Chiabrera A, Bianco B, Kinney J H, Haupt D, Ryaby J T, Siffert R S 1999 Ultrasound Med. Biol. 25 5
[17] Chen Z Q, Liu M H, Lan C H, Chen W, Tang L, Luo Z Q, Yan B R, Lü J H, Hu X W 2009 Chin. Phys. B 18 3484
[18] Wang S Y, Liu S B, Le W J L 2010 Chin. Phys. B 19 084101
[19] Tang W, Yan Y B, Li Q L, Wu Z S 2004 Acta Phys. Sin. 53 4173 (in Chinese) [汤炜, 闫玉波, 李清亮, 吴振森 2004 物理学报 53 4173]
[20] Zhang Y Q, Ge D B 2009 Acta Phys. Sin. 58 4573 (in Chinese) [张玉强, 葛德彪 2009 物理学报 58 4573]
[21] Deniel G, Tobias L, Jürg D 2004 J. Acoust. Soc. Am. 116 3284
[22] Wang G, Wen J H, Han X Y, Zhao H G 2003 Acta Phys. Sin. 52 1943 (in Chinese) [王刚, 温激鸿, 韩小云, 赵宏刚 2003 物理学报 52 1943]
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[1] Lee T C, O'Brien F J, Taylor D 2000 Int. J. Fatigue 22 847
[2] Akkus O, Rimnac C M 2001 J. Biomech. 34 757
[3] Zioupos P, Casinos A 1998 J. Biomech. 31825
[4] Magnusson H I, Ahlborg H G, Karlsson C, Nyquist F, Karlsson M K 2003 Am. J. Sports Med. 31 596
[5] Pidaparti R M, Vogt A 2001 J. Biomed. Mater. Res. 59 282
[6] Haddock S M, Yeh O C, Mummaneni P V, Rosenberg W S, Keaveny T M 2004 J. Biomech. 37 181
[7] Deng M X, Pei J F 2010 Sci. China Ser. G-Phys. Mech. Astron. 53 1286
[8] Pruell C, Kim J Y, Qu J, Jacobs L J 2009 Smart Mater. Struct. 18 035003
[9] Bossy E, Talmant M, Laugier P 2002 J. Acoust. Soc. Am. 112 297
[10] Lee K I, Yoon S W 2004 J. Acoust. Soc. Am. 115 3210
[11] Moilanen P, Talmant M, Bousson Valerie, Nicholson P H F, Cheng S L, Timonen J, Laugier P 2007 J. Acoust. Soc. Am. 122 1818
[12] Bertram A A 1990 Acoustic Fields and Waves in Solids (Second Edition) (Florida: Krieger Publishing Company) pp86-97
[13] Gazis D C 1959 J. Acoust. Soc. Am. 31 568
[14] Ta D A, Wang W Q 2009 Ultrasound Med. Biol. 35 641
[15] Ta D A, Liu Z Q, He P F 2003 Acta Meteriae Compositae Sinica 20 130 (in Chinese) [他得安, 刘镇清, 贺鹏飞2003 复合材料学报 20 130]
[16] Luo G M, Kaufman J J, Chiabrera A, Bianco B, Kinney J H, Haupt D, Ryaby J T, Siffert R S 1999 Ultrasound Med. Biol. 25 5
[17] Chen Z Q, Liu M H, Lan C H, Chen W, Tang L, Luo Z Q, Yan B R, Lü J H, Hu X W 2009 Chin. Phys. B 18 3484
[18] Wang S Y, Liu S B, Le W J L 2010 Chin. Phys. B 19 084101
[19] Tang W, Yan Y B, Li Q L, Wu Z S 2004 Acta Phys. Sin. 53 4173 (in Chinese) [汤炜, 闫玉波, 李清亮, 吴振森 2004 物理学报 53 4173]
[20] Zhang Y Q, Ge D B 2009 Acta Phys. Sin. 58 4573 (in Chinese) [张玉强, 葛德彪 2009 物理学报 58 4573]
[21] Deniel G, Tobias L, Jürg D 2004 J. Acoust. Soc. Am. 116 3284
[22] Wang G, Wen J H, Han X Y, Zhao H G 2003 Acta Phys. Sin. 52 1943 (in Chinese) [王刚, 温激鸿, 韩小云, 赵宏刚 2003 物理学报 52 1943]
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