Abstract
The wave propagation modeling in cylindrical human long wet bones with cavity is studied. The dynamic behavior of a wet long bone that has been modeled as a piezoelectric hollow cylinder of crystal class 6 is investigated. An analytical solutions for the mechanical wave propagation during a long wet bones have been obtained for the flexural vibrations. The average stresses of solid part and fluid part have been obtained. The frequency equations for poroelastic bones are obtained when the medium is subjected to certain boundary conditions. The dimensionless frequencies are calculated for poroelastic wet bones for various values for non-dimensional wave lengths. The dispersion curves of the dry bone and wet bone for the flexural mode n=2 are plotted. The numerical results obtained have been illustrated graphically.
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References
Natali AN, Meroi EA (1989) A review of the biomechanical properties of bone as a material. J Biomed Eng 11(4):266–276
Thompson GA, Young DR, Orne D (1976) In vivo determination of mechanical properties of human ulna by means of mechanical impedance tests: experimental results and improved mathematical model. Med Biol Eng 14:253–262
Doherty WP, Boville EG, Wilson EL (1974) Evaluation of the use of resonant frequencies to characterize physical properties of long bones. J Biomech 7:559–561
Jurist JM (1970) In vivo determination of the elastic response of bone-I. Method of ulnar resonant frequency determination. Phys Med Biol 15:417–426
Papathanasopoulou VA, Fotiadis DI, Foutsitzi G, Massalas CV (2002) A poroelastic bone model for internal remodeling. Int J Eng Sci 40:511–530
Fotiadis DI, Fouttsitzi G, Massalas CV (2000) Wave propagation in human long bones of arbitrary cross-section. Int J Eng Sci 38(14):1553–1591
Fotiadis DI, Foutsitzi G, Massalas CV (1999) Wave propagation modeling in human long bones. Acta Mech 137:65–81
Sebaa N, Fellah Z, Lauriks W, Depollier C (2006) Application of fractional calculus to ultrasonic wave propagation in human cancellous bone. Signal Process 86(10):2668–2677
Padilla F, Bossy E, Haiat G, Jenson F, Laugier P (2006) Numerical simulation of wave propagation in cancellous bone, ultrasonic propagation in cancellous bone. Ultrasonics 44:e239–e243
Haeat G, Padilla F, Barkmann R, Gluer CC, Laugier P (2006) Numerical simulation of the dependence of quantitative ultrasonic parameters on trabecular bone micro architecture and elastic constants. Ultrasonics 44:e289–e294
Pithious M, Lasaygues P, Chabrand P (2002) An alternative ultrasonic method for measuring the elastic properties of cortical bone. J Biomech 35:961–968
Kaczmarek M, Kubik J, Pakula M (2002) Short ultrasonic waves in cancellous bone. Ultrasonics 40:95–100
Levitsky SP, Bergman RM, Haddad J (2004) Wave propagation in a cylindrical viscous layer between two elastic shells. Int J Eng Sci 42:2079–2086
Tadeu A, Mendes PA, António J (2006) 3D elastic wave propagation modelling in the presence of 2D fluid-filled thin inclusions. Eng Anal Bound Elem 30:176–193
Paul HS, Murali VM (1992) Wave propagation in cylindrical poroelastic bone with cavity. Int J Eng Sci 30:1629–1635
Qina Q, Qua C, Ye J (2005) thermoelectroelastic solutions for surface bone remodeling under axial and transverse loads. Biomaterials 26:6798–6810
Biot MA (1962) Mechanics of deformation and acoustic propagation in porous media. J Appl Phys 33(4):1482–1498
Lang SB (1970) Ultrasonic method for measuring elastic coefficients of bone and results on fresh and dried bovini bones. IEEE Trans Biomed Eng 17:101–105
Davis CF (1970) On the mechanical properties of bone and a poroelastic theory of stresses in bone. PhD Thesis, Univ of Delaware
Ghista DN (1979) Applied Physiological Mechanics. Ellis Horwood, Chichester, pp 31–96
Salzstein RA, Pollack SR, Mak AFT, Petrov N (1987) Electromechanical potentials in cortical bone a continuum approach. J Biomech 20:261–270
Ding H, Chenbuo L (1996) General solutions for coupled equations for piezoelectric media. Int J Solids Struct 16:2283–2298
Gtizelsu N, Saha S (1981) Electro-mechanical wave propagation in long bones. J Biomech 14:9–33
Mahmoud SR (2010) Wave propagation in cylindrical poroelastic dry bones. Appl Math Inf Sci 4(2):209–226
Protopappas VC, Vavva MG, Fotiadis DI, Malizos KN (2008) Ultrasonic monitoring of bone fracture healing. IEEE Trans Ultrason Ferroelectr Freq Control 55(6):1243–1255
Vavva MG, Protopappas VC, Fotiadis DI, Malizos KN (2008) Ultrasound velocity measurements on healing bones using the external fixation pins: a two-dimensional simulation study. J Serb Soc Comput Mech 2(2):1–15
Kauffman JJ (2008) Ultrasonic guided waves in bone. IEEE Trans Ultrason Ferroelectr Freq Control 55(6):1205–1218
Moilanen P (2008) Ultrasonic guided waves in bone. IEEE Trans Ultrason Ferroelectr Freq Control 55(6):1277–1286
Vavva MG, Protopappas VC, Gergidis LN, Charalambopoulos A, Fotiadis DI, Polyzos D (2009) Velocity dispersion of guided waves propagating in a free gradient elastic plate: Application to cortical bone. J Acoust Soc Am 125(5):3414–3427
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Abd-Alla, A.M., Abo-Dahab, S.M. & Mahmoud, S.R. Wave propagation modeling in cylindrical human long wet bones with cavity. Meccanica 46, 1413–1428 (2011). https://doi.org/10.1007/s11012-010-9398-5
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DOI: https://doi.org/10.1007/s11012-010-9398-5