A multiscale poromicromechanical approach to wave propagation and attenuation in bone

Ultrasonics

Volumn 54, Issue 5, 2014, Pages 1251-1269

  Morin, Claire ^a   Hellmich, Christian ^a  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

Bone; Fast and slow waves; Lacunar porosity; Poro micromechanics; Vascular porosity

Indexed keywords

DISPERSIONS; ELASTICITY; FLUID DYNAMICS; NONINVASIVE MEDICAL PROCEDURES; POROSITY; POROUS MATERIALS; TISSUE; WAVE PROPAGATION;

ACOUSTICAL SIGNALS; ATTENUATION LENGTHS; DISPERSION RELATIONS; FAST AND SLOW WAVE; MOMENTUM AND MASS BALANCE; NON-INVASIVE ASSESSMENTS; PORO-MICROMECHANICS; VASCULAR POROSITY;

BONE;

ANIMAL; ARTICLE; BIOMECHANICS; BONE; ECHOGRAPHY; FAST AND SLOW WAVES; HUMAN; LACUNAR POROSITY; PORO-MICROMECHANICS; POROSITY; THEORETICAL MODEL; VASCULAR POROSITY; VASCULARIZATION;

BONE; FAST AND SLOW WAVES; LACUNAR POROSITY; PORO-MICROMECHANICS; VASCULAR POROSITY;

ANIMALS; BIOMECHANICAL PHENOMENA; BONE AND BONES; HUMANS; MODELS, THEORETICAL; POROSITY;

EID: 84897917298     PISSN: 0041624X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ultras.2013.12.005     Document Type: Article

References (70)

1. J. Carcione Wave Fields in Real Media: Wave Propagation in Anisotropic, Anelastic and Porous Media 2001 Elsevier
2. J. Frenkel On the theory of seismic and seismoelectric phenomena in a moist soil J. Phys. 8 4 1944 230 241
3. M. Biot Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range J. Acoust. Soc. Am. 28 2 1956 168 178
4. M. Biot Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range J. Acoust. Soc. Am. 28 2 1956 179 191
5. R. Lakes, H. Yoon, and J. Katz Slow compressional wave propagation in wet human and bovine cortical bone Science 220 1983 513 515
6. E. Hughes, T. Leighton, G. Petley, P. White, and R. Chivers Estimation of critical and viscous frequencies for Biot theory in cancellous bone Ultrasonics 41 2003 365 368
7. A. Hosokawa, and T. Otani Ultrasonic wave propagation in bovine cancellous bone J. Acoust. Soc. Am. 101 1 1997 558 562
8. A. Hosokawa, and T. Otani Acoustic anisotropy in bovine cancellous bone J. Acoust. Soc. Am. 103 5 1998 2718 2722
9. J. Berryman Confirmation of Biot's theory Appl. Phys. Lett. 37 4 1980 382 384
10. O. Coussy Mechanics of Porous Media 1995 John Wiley & Sons
11. C. Hellmich, and F.-J. Ulm Microporodynamics of bones: prediction of the Frenkel-Biot slow compressional wave J. Eng. Mech. 131 9 2005 918 927
12. A. Fritsch, C. Hellmich, and L. Dormieux Ductile sliding between mineral crystals followed by rupture of collagen crosslinks: experimentally supported micromechanical explanation of bone strength J. Theoret. Biol. 260 2 2009 230 252
13. J. Vuong, and C. Hellmich Bone fibrillogenesis and mineralization: quantitative analysis and implications for tissue elasticity J. Theoret. Biol. 287 2011 115 130
14. J. Buckwalter, M. Glimcher, R. Cooper, and R. Recker Bone biology, part I: structure, blood supply, cells, matrix, and mineralization J. Bone Joint Surg. 77-A 8 1995 1256 1275
15. L. Dormieux, D. Kondo, and F.-J. Ulm Microporomechanics 2006 John Wiley & Sons
16. A. Zaoui Continuum micromechanics: survey J. Eng. Mech 128 2002 808 816
17. W. Drugan, and J. Willis A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites J. Mech. Phys. Solids 44 4 1996 497 524
18. C. Kohlhauser, and C. Hellmich Ultrasonic contact pulse transmission for elastic wave velocity and stiffness determination: influence of specimen geometry and porosity Eng. Struct. 47 2013 115 133
19. O. Coussy Poromechanics 2004 John Wiley & Sons
20. M. Viceconti, and A. Seireg A generalized procedure for predicting bone mass regulation by mechanical strain Calc. Tiss. Int. 47 5 1990 296 301
21. J. Salençon Handbook of Continuum Mechanics 2001 Springer
22. R. McCarthy, L. Jeffcott, and R. McCartney Ultrasound speed in equine cortical bone: effects of orientation, density, porosity and temperature J. Biomech. 23 11 1990 1139 1143
23. K. Tai, G. Pelled, D. Sheyn, A. Bershteyn, L. Han, I. Kallai, Y. Zilberman, C. Ortiz, and D. Gazit Nanobiomechanics of repair bone regenerated by genetically modified mesenchymal stem cells Tiss. Eng. A 14 10 2008 1709 1720
24. G. Li, J.T. Bronk, K.-N. An, and P.J. Kelly Permeability of cortical bone of canine tibiae Microvascul. Res. 34 3 1987 302 310
25. M. Johnson Behavior of fluid in stressed bone and cellular stimulation Calc. Tiss. Int. 36 S1 1984 72 76
26. S. Rouhana, M. Johnson, D. Chakkalakal, R. Haper, Permeability of the osteocyte lacuno-canalicular compact bone, in: Joint ASME-ASCE Conference on Biomechanics Symposium AMD, 1981, pp. 169-172.
27. R. Dillaman, R. Roer, and D. Gay Fluid movement in bone: theoretical and empirical J. Biomech. 24 1991 163 171
28. E. Malachanne, D. Dureisseix, P. Canadas, and F. Jourdan Experimental and numerical identification of cortical bone permeability J. Biomech. 41 2008 721 725
29. S.S. Kohles, J.B. Roberts, M.L. Upton, C.G. Wilson, L.J. Bonassar, and A.L. Schlichting Direct perfusion measurements of cancellous bone anisotropic permeability J. Biomech. 34 9 2001 1197 1202
30. J.-L. Auriault, C. Boutin, and C. Geindreau Homogenization of Coupled Phenomena in Heterogenous Media 2009 John Wiley & Sons
31. J. Gardinier, C. Townend, K. Jen, Q. Wu, R. Duncan, and L. Wang In situ permeability measurement of the mammalian lacunar-canalicular system Bone 46 4 2010 1075 1081
32. Y. Qin, W. Lin, and C. Rubin The pathway of bone fluid flow as defined by in vivo intramedullary pressure and streaming potential measurements Ann. Biomed. Eng. 30 2002 693 702
33. C. Hellmich, D. Celundova, and F.-J. Ulm Multiporoelasticity of hierarchically structured materials: micromechanical foundations and application to bone J. Eng. Mech. 135 5 2009 382 394
34. J. Katz, and K. Ukraincik On the anisotropic elastic properties of hydroxyapatite J. Biomech. 4 3 1971 221 227
35. C. Morin, C. Hellmich, and P. Henits Fibrillar structure and elasticity of hydrating collagen: a quantitative multiscale approach J. Theoret. Biol. 317 2013 384 393
36. S. Cusack, and A. Miller Determination of the elastic constants of collagen by Brillouin light scattering J. Mol. Biol. 135 1 1979 39 51
37. S. Lees, P. Cleary, J. Heeley, and E. Gariepy Distribution of sonic plesio-velocity in a compact bone sample J. Acoust. Soc. Am. 66 3 1979 641 646
38. S. Lees, J. Heeley, and P. Cleary A study of some properties of a sample of bovine cortical bone using ultrasound Calc. Tiss. Int. 29 1979 107 117
39. S. Lees, D. Hanson, and E.A. Page Some acoustical properties of the otic bones of a fin whale J. Acoust. Soc. Am. 99 4 1995 2421 2427
40. S. Lees Ultrasonic measurements of deer antler, bovine tibia and tympanic bulla J. Biomech. 15 11 1982 867 874
41. S. Lees, J. Ahern, and M. Leonard Parameters influencing the sonic velocity in compact calcified tissues of various species J. Acoust. Soc. Am. 74 1 1983 28 33
42. S. Lees, D. Hanson, E.A. Page, and H. Mook Comparison of dosage-dependent effects of beta-aminopropionitrile, sodium fluoride, and hydrocortisone on selected physical properties of cortical bone J. Bone Min. Res. 9 9 1994 1377 1389
43. C. Hellmich, and F.-J. Ulm Are mineralized tissues open crystal foams reinforced by crosslinked collagen? - some energy arguments J. Biomech. 35 2002 1199 1212
44. C. Hellmich, F.-J. Ulm, and L. Dormieux Can the diverse elastic properties of trabecular and cortical bone be attributed to only a few tissue-independent phase properties and their interactions? - arguments from a multiscale approach Biomech. Model. Mechanobiol. 2 2004 219 238
45. A. Fritsch, and C. Hellmich 'Universal' microstructural patterns in cortical and trabecular, extracellular and extravascular bone materials: micromechanics-based prediction of anisotropic elasticity J. Theoret. Biol. 244 4 2007 597 620
46. V. Sansalone, S. Naili, V. Bousson, C. Bergot, F. Peyrin, J. Zarka, J.D. Laredo, and G. Haiat Determination of the heterogeneous anisotropic elastic properties of human femoral bone: from nanoscopic to organ scale J. Biomech. 43 10 2010 1857 1863
47. E. Hamed, E. Novitskaya, J. Li, P.-Y. Chen, I. Jasiuk, and J. McKittrick Elastic moduli of untreated, demineralized and deproteinized cortical bone: validation of a theoretical model of bone as an interpenetrating composite material Acta Biomater. 8 3 2012 1080 1092
48. L. Eberhardsteiner, C. Hellmich, and S. Scheiner Layered water in crystal interfaces as source for bone viscoelasticity: arguments from a multiscale approach Comput. Meth. Biomech. Biomed. Eng. 17 1 2014 48 63
49. K. Mizuno, M. Matsukawa, T. Otani, P. Laugier, and F. Padilla Propagation of two longitudinal waves in human cancellous bone: an in vitro study J. Acoust. Soc. Am. 125 5 2009 3460 3466
50. T. Bourbié, O. Coussy, B. Zinszner, Acoustics of Porous Media, Institut français du pétrole publications, Technip edn., 1987.
51. R. Lakes, H.S. Yoon, and J.L. Katz Ultrasonic wave propagation and attenuation in wet bone J. Biomed. Eng. 8 2 1986 143 148
52. S. Lees, and E. Page A study of some properties of mineralized turkey leg tendon Connect. Tiss. Res. 28 4 1992 263 287
53. S. Lees Mineralization of type I collagen Biophys. J. 85 2003 204 207
54. J. Gong, J. Arnold, and S. Cohn Composition of trabecular and cortical bone The Anatom. Rec. 149 1964 325 332
55. F. Hammet A biochemical study of bone growth. I. Changes in the ash, organics matter and water during growth (mus norvegicus albinus) J. Biol. Chem. 64 1925 409 428
56. C. Burns The effect of the continued ingestion of mineral acid on growth of body and bone and on the composition of bone and of the soft tissues Biochem. J. 23 5 1929 860 867
57. R. Biltz, and E. Pellegrino The chemical anatomy of bone J. Bone Joint Surg. 51-A 3 1969 456 466
58. S. Lees Considerations regarding the structure of the mammalian mineralized osteoid from viewpoint of the generalized packing model Connect. Tiss. Res. 16 4 1987 281 303
59. C. Morin, and C. Hellmich Mineralization-driven bone tissue evolution follows from fluid-to-solid phase transformations in closed thermodynamic systems J. Theoret. Biol. 335 2013 185 197
60. C. Hellmich, and F.-J. Ulm Average hydroxyapatite concentration is uniform in the extracollagenous ultrastructure of mineralized tissues: evidence at the 1-10-μm scale Biomech. Model. Mechanobiol. 2 2003 21 36
61. Y. Benveniste A new approach to the application of Mori-Tanaka's theory in composite materials Mech. Mater. 6 2 1987 147 157
62. R. Hill Continuum micro-mechanics of elastoplastic polycrystals J. Mech. Phys. Solids 13 1965 89 101
63. A. Hershey The elasticity of an isotropic aggregate of anisotropic cubic crystals J. Appl. Mech. - Trans. ASME 21 3 1954 236 240
64. R. Hill Elastic properties of reinforced solids: some theoretical principles J. Mech. Phys. Solids 11 1963 357 362
65. T. Mori, and K. Tanaka Average stress in matrix and average elastic energy of materials with misfitting inclusions Acta Metall. 21 5 1973 571 574
66. C. Hellmich, J.-F. Barthélémy, and L. Dormieux Mineral-collagen interactions in elasticity of bone ultrastructure - a continuum micromechanics approach Euro. J. Mech. A - Solids 23 2004 783 810
67. V. Levin, T. Michelitsch, and I. Sevostianov Spheroidal inhomogeneity in a transversely isotropic piezoelectric medium Arch. Appl. Mech. 70 2000 673 693
68. J. Eshelby The determination of the elastic field of an ellipsoidal inclusion, and related problems Proc. R. Soc. Lond., Ser. A 241 1957 376 396
69. A. Zaoui Structural morphology and constitutive behavior of microheterogeneous materials P. Suquet, Continuum Micromechanics 1997 Springer, Wien New York 291 347
70. Q. Grimal, G. Rus, W.J. Parnell, and P. Laugier A two-parameter model of the effective elastic tensor for cortical bone J. Biomech. 44 8 2011 1621 1625