Ultrasonic wave propagation in viscoelastic cortical bone plate coupled with fluids: a spectral finite element study

REFERENCES

• Andrianov I , Bolshakov V , Danishevs'kyy V , Weichert D . 2008. Higher-order asymptotic homogenization and wave propagation in periodic composite materials. Proc R Soc. A464:1181–1201.
   Google Scholar
• Barkmann R , Kantorovich E , Singal C , Hans D , Genant HK , Heller M , Gluer CC . 2000. A new method for quantitative ultrasound measurements at multiple skeletal sites. J Clin Densitom. 3:1–7.
   PubMed Web of Science ®Google Scholar
• Baron C , Naili S . 2008. Elastic wave propagation in a fluid-loaded anisotropic waveguide with laterally varying properties. C R Mec. 336:722–730.
   Web of Science ®Google Scholar
• Baron C , Naili S . 2010. Propagation of elastic waves in a fluid-loaded anisotropic functionally graded waveguide: application to ultrasound characterization. J Acoust Soc Am. 127(3):1307–1317.
   PubMed Web of Science ®Google Scholar
• Baron C , Talmant M , Laugier P . 2007. Effect of porosity on effective diagonal stiffness coefficients (c ii) and anisotropy of cortical bone at 1 MHz: a finite difference time domain study. J Acoust Soc Am. 122:1810–1817.
   PubMed Web of Science ®Google Scholar
• Bathe KJ . 1996. Finite element procedure. Englewood Cliffs, NJ: Prentice Hall.
   Google Scholar
• Bossy E , Talmant M , Laugier P . 2002. Effect of bone cortical thickness on velocity measurements using ultrasonic axial transmission: a 2D simulation study. J Acoust Soc Am. 112:297–307.
   PubMed Web of Science ®Google Scholar
• Bossy E , Talmant M , Laugier P . 2004. Three-dimensional simulations of ultrasonic axial transmission velocity measurement on cortical bone models. J Acoust Soc Am. 115:2314–2324.
   PubMed Web of Science ®Google Scholar
• Bousson V , Meunier A , Bergot C , Vicaut E , Rocha M , Morais M , Laval-Jeantet A , Laredo J . 2001. Distribution of intracortical porosity in human midfemoral cortex by age and gender. J Bone Miner Res. 16:1308–11317.
   PubMed Web of Science ®Google Scholar
• Bryant J , David T , Gaskell P , King S , Lond G . 1989. Rheology of bovine marrow. Proc Inst Mech Eng. 203:771–775.
   Google Scholar
• Carcione J . 2001. Wave fields in real media: wave propagation in anisotropic, anelastic and porous media. The Netherlands: Elsevier.
   Google Scholar
• COMSOL Multiphysics . 2008. User's Guide. www.comsol.com.
   Google Scholar
• Davies B , Martin B . 1979. Numerical inversion of the Laplace transform: a survey and comparison of methods. J Comput Phys. 33(1):1–32.
   Web of Science ®Google Scholar
• Desceliers C , Soize C , Grimal Q , Haiat G , Naili S . 2008. A time-domain method to solve transient elastic wave propagation in a multilayer medium with a hybrid spectral-finite element space approximation. Wave Motion. 45(4):383–399.
   Web of Science ®Google Scholar
• Desceliers C , Soize C , Grimal Q , Talmant M , Naili S . 2009. Identification of an anisotropic elasticity tensor for an elastic layer using transient wave propagation in a fluid-solid multilayer: model with uncertainties and experiments. J Acoust Soc Am. 125(4):2027–2034.
   PubMed Web of Science ®Google Scholar
• Dong NX , Guo EX . 2004. The dependence of transverse isotropic elasticity of human femoral cortical bone on porosity. J Biomech. 37(8):1281–1287.
   PubMed Web of Science ®Google Scholar
• Givoli D . 2004. High-order local non-reflecting boundary conditions: a review. Wave Motion. 39(4):319–326.
   Web of Science ®Google Scholar
• Gopalakrishnan S , Chakraborty R , Roy Mahapatra D . 2008. Spectral finite element method. London: Springer-Verlag.
   Google Scholar
• Grimal Q , Naili S . 2006. A theoretical analysis in the time-domain of wave reflection on a bone plate. J Sound Vib. 298:12–29.
   Web of Science ®Google Scholar
• Haïat G , Naili S , Grimal Q , Talmant M , Desceliers C , Soize C . 2009. Influence of a gradient of material properties on ultrasonic wave propagation in cortical bone: application to axial transmission. J Acoust Soc Am. 125(6):4043–4052.
   PubMed Web of Science ®Google Scholar
• Han X , Liu GR , Lam KY . 2001. Transient waves in plates of functionally graded materials. Int J Numer Methods Eng. 52(8):851–865.
   Web of Science ®Google Scholar
• Han X , Liu GR , Xi ZC , Lam KY . 2001. Transient waves in a functionally graded cylinder. Int J Solids Struct. 38(17):3021–3037.
   Web of Science ®Google Scholar
• Hans D , Srivastav SK , Singal C , Barkmann R , Njeh CF , Kantorovich E , Gluer CC , Genant HK . 1999. Does combining the results from multiple bone sites measured by a new quantitative ultrasound device improve discrimination of hip fracture? J Bone Miner Res. 14(4):644–651.
   PubMed Web of Science ®Google Scholar
• Kampanis NA , Dougalis VA , Ekaterinaris JA , editors. 2008. Effective computational methods for wave propagation. New York: Chapman & Hall/CRC.
   Google Scholar
• Kausel E . 2006. Fundamental solution in elastodynamics. New York: Cambridge University Press.
   Google Scholar
• Lakes R , Yoon HS , Katz JL . 1986. Ultrasonic wave propagation and attenuation in wet bones. J Biomed Eng. 8:143–148.
   PubMedGoogle Scholar
• Langton CM , Ali A , Riggs CM , Evans JA , Bonfield W . 1990. A contact method for the assessment of ultrasonic velocity and broadband attenuation in cortical and cancellous bone. Clin Phys Physiol Meas. 11:243–249.
   PubMedGoogle Scholar
• Liu G , Xi ZC . 2002. Elastic waves in anisotropic laminates. Florida: CRC Press.
   Google Scholar
• Lowet G , Van derPerre G . 1996. Ultrasound velocity measurements in long bones: measurement method and simulation of ultrasound wave propagation. J Biomech. 29:1255–1262.
   PubMed Web of Science ®Google Scholar
• Macocco K , Grimal Q , Naili S , Soize C . 2005. Probabilistic modelling of an ultrasonic setup: calculation of the dispersion on wave measurement. C R Mec. 333:565–573.
   Web of Science ®Google Scholar
• Macocco K , Grimal Q , Naili S , Soize C . 2006. Elastoacoustic model with uncertain mechanical properties for ultrasonic wave velocity prediction: application to cortical bone evaluation. J Acoust Soc Am. 119:729–740.
   PubMed Web of Science ®Google Scholar
• Marzani A . 2008. Time-transient response for ultrasonic guided waves propagating in damped cylinders. Int J Solids Struct. 45(25–26):6347–6368.
   Web of Science ®Google Scholar
• Moilanen P . 2008. Ultrasonic guided waves in bone. IEEE Trans Ultrason, Ferroelectr, Freq Control. 55(6):1277–1286.
   PubMed Web of Science ®Google Scholar
• Naili S , Vu MB , Grimal Q , Talmant M , Desceliers C , Soize C , Haïat G . 2010. Influence of viscoelastic and viscous absorption on ultrasonic wave propagation in cortical bone: application to axial transmission. J Acoust Soc Am. 127(4):2622–2634.
   PubMed Web of Science ®Google Scholar
• Nayfeh HA . 1995. Wave propagation in layered anisotropic media. The Netherlands: Elsevier.
   Google Scholar
• Nicholson P , Moilanen P , Karkkainen T , Timonen J , Cheng S . 2002. Guided ultrasonic waves in long bones: modelling, experiment and in vivo application. Physiol Meas. 23(4):755–768.
   PubMed Web of Science ®Google Scholar
• Pham TL, Moinonzio JG, Talmant M, Laugier P . 2009. Impact of a multi-frequency sequence of measurement on first arriving signal velocity on a bone plate model. IEEE Int Ultrason Symp Proc. 574–577.
   Google Scholar
• Protopappas VC , Kourtis IC , Kourtis LC , Malizos KN , Massalas CV , Fotiadisa DI . 2007. Three-dimensional finite element modeling of guided ultrasound wave propagation in intact and healing long bones. J Acoust Soc Am. 121(6):3907–3921.
   PubMed Web of Science ®Google Scholar
• Sansalone V , Naili S , Bousson V , Bergot C , Peyrin F , Zarka J , Laredo JD , Haïat G . 2010. Determination of the heterogeneous anisotropic elastic properties of human femoral bone: from nanoscopic to organ scale. J Biomech. 43:1857–1863.
   PubMed Web of Science ®Google Scholar
• Sasso M , Haïat G , Yamato Y , Naili S , Matsukawa M . 2007. Frequency dependence of ultrasonic attenuation in bovine cortical bone: an in vitro study. Ultrasound Med Biol. 33(12):1933–1942.
   PubMed Web of Science ®Google Scholar
• Sasso M , Haïat G , Yamato Y , Naili S , Matsukawa M . 2008. Dependence of ultrasonic attenuation on bone mass and microstructure in bovine cortical bone. J Biomech. 41(2):347–355.
   PubMed Web of Science ®Google Scholar
• Schanz M , Antes H . 1997. Application of ‘operational quadrature methods’ in time domain boundary element methods. Meccanica. 32:179–186.
   Web of Science ®Google Scholar
• Shuvalov A , Poncelet O , Deschamps M . 2006. Analysis of the dispersion spectrum of fluid-loaded anisotropic plates: leaky-wave branches. J Sound Vib. 296(3):494–517.
   Web of Science ®Google Scholar
• Stegman MR , Heaney RP , Travers-Gustafson D , Leist J . 1995. Cortical ultrasound velocity as an indicator of bone status. Osteoporos Int. 5(5):349–533.
   PubMed Web of Science ®Google Scholar
• Thomas C , Feik SA , Clement J . 2005. Regional variation of intracortical porosity in the midshaft of the human femur: age and sex differences. J Anat. 206:115–125.
   PubMed Web of Science ®Google Scholar
• Thompson LL , Huan R . 2000. Implementation of exact non-reflecting boundary conditions in the finite element method for the time-dependent wave equation. Comput Methods Appl Mech Eng. 187(1–2):137–159.
   Web of Science ®Google Scholar
• Virieux J . 1986. P-SV-wave propagation in heterogeneous media: velocity–stress finite-difference method. Geophysics. 51(4):889–901.
   Web of Science ®Google Scholar