An estimate of anisotropic poroelastic constants of an osteon

Biomechanics and Modeling in Mechanobiology

Volumn 7, Issue 1, 2008, Pages 13-26

  Yoon, Young June ^a   Cowin, Stephen C ^b  

^a CITY UNIVERSITY OF NEW YORK   (United States)

^b CITY COLLEGE OF NEW YORK   (United States)

Author keywords

Anisotropy; Elastic constants; Lacunae; Osteonal bone; Poroelasticity

Indexed keywords

ANISOTROPY; BONE; MATHEMATICAL MODELS; POROSITY;

LACUNAE; OSTEONAL BONE; POROELASTICITY;

ELASTIC CONSTANTS;

ARTICLE; BONE; ELASTICITY;

BONE AND BONES; ELASTICITY;

EID: 38149064563     PISSN: 16177959     EISSN: 16822978     Source Type: Journal    
DOI: 10.1007/s10237-006-0071-9     Document Type: Article

References (65)

1. Ascenzi A, Bonucci E (1967) The tensile properties of single osteons. Anat Rec 158:375-386
2. Ascenzi A, Bonucci E (1968) The compressive properties of single osteons. Anat Rec 161:377-391
3. Ascenzi A, Benvenuti A (1986) Orientation of collagen fibers at the boundary between two successive osteonic lamellae and its mechanical interpretation. J Biomech 19:455-463
4. Ascenzi A, Improta S, Portigliatti B, Carando S, Boyde A (1987) Distribution of lamellae in human femoral shafts deformed by bending with interfaces on mechanical properties. Bone 8:319-325
5. Ascenzi A, Baschieri P, Benvenuti A (1994) The torsional properties of selected single osteons. J Biomech 27:875-884
6. Ascenzi MG, Ascenzi A, Benvenuti A, Burghammer M, Panzavolta S, Bigi A (2003) Structural differences between "dark" and "bright" isolated human osteonic lamellae. J Struct Biol 141:22-33
7. Baron R (1999) Anatomy and ultrastructure of bone. In: Favus MJ (ed) Primer on the metabolic bone disease and disorder of mineral metabolism, 4th edn. Lippincott/Williams & Wilkins, Baltimore
8. Beno T, Yoon YJ, Cowin SC, Fritton S (2006) Estimation of bone permeability using accurate microstructural measurement. J Biomech 39:2378-2387
9. Biot MA (1941) General theory of three dimensional consolidation. J. Appl Phys 12:155-164
10. Biot MA(1955)Theory of elasticity and consolidation for a porous anisotropic solid. J Appl Phys 26:182-185
11. Burger EH, Veldhuijzen JP (1993) Influence of mechanical factors on bone formation, resorption, and growth in vitro. In: Hall BK (ed) Bone, vol 7. CRC Press, Boca Raton, pp 37-56
12. Carroll MM (1979) An effective stress law for anisotropic elastic deformation. J Geophys Res 84:7510-7512
13. Cheng AHD (1997) Material coefficients of anisotropic poroelasticity. Int J Rock Mech Min Sci 34:199-205
14. Chou PC, Carleone J, Hsu CM (1972) Elastic constants of layered media. J Compos Mater 6:80-93
15. Cowin SC (1999) Bone poroelasticity. J Biomech 32:217-238
16. Cowin SC (2003) A recasting of anisotropic poroelasticity in matrices of tensor components. Transp Porous Media 50: 35-56
17. Cowin SC (2004) Anisotropic poroelasticity: fabric tensor formulation. Mech Mater 36:665-677
18. Cowin SC, Mehrabadi MM (1995) Anisotropic symmetries of linear elasticity. Appl Mech Rev 48:247-285
19. Cowin SC, Moss ML (2001) Mechanosensory mechanisms in bone. In: Cowin SC (ed) Bone mechanics handbook, 2nd edn. CRC press
20. Cowin SC, Mehrabadi MM (2006) Compressible and incompressible constituents in anisotropic poroelasticity: the problem of unconfined compression of a disk. J Mech Phys Solids (available online 30 June 2006, in press)
21. Cowin SC, Doty SB (2007) Tissue Mechanics. Springer, New York
22. Cowin SC, Moss-Salentijin L, Moss ML (1991) Candidates for the mechanosensory system in bone. J Biomech Eng 113:191-197
23. Cowin SC, Weinbaum S, Zeng Y (1995) A case for bone canaliculi as the anatomical site of strain generated potentials. J Biomech 28:1281-1297
24. Cowin SC, Yang G, Mehrabadi MM (1999) Bounds on the effective anisotropic elastic constants. J Elast 57:1-24
25. Detournay E, Cheng ADH (1993) Fundamentals of poroelasticity. In: Hudson JA (ed) Compressive rock engineering: principles, practices & projects. Pergamon, Oxford, pp 113-171
26. Erickson EF, Axelrod DW, Melsen F (1994) Bone histomorphology. Raven Press, New York
27. Frost HM (1995) Introduction to a new skeletal physiology, vol. I and II. Pajoro Group, Pueblo
28. Han Y, Cowin SC, Schaffler MB, Weinbaum S (2004) Mechanotransduction and strain amplification in osteocyte cell processes. Proc Natl Acad Sci USA 101:16689-16694
29. Hashin Z, Shtrikman SA (1963) Variational approach to the theory of the elastic behavior of multiphase materials. J Mech Phys Solids 11:127
30. Hearmon RFS (1961) An introduction to applied anisotropic elasticity. Oxford University Press, Oxford
31. Iwakuma T, Nemat-Nasser S (1983) Composites with periodic microstructure. Comput Struct 16:13-19
32. Jee WSS (1988) The skeletal tissues, in cell and tissue biology. In: Weiss L (ed) A textbook of histology. Urban and Schwarzenberg,Baltimore
33. Jee WSS (1999) Structure and function of bone tissue. In: Bronner F, Worrell RV (eds) Orthopaedics, principles of basic and clinical science. CRC Press, Boca Raton
34. Kelvin, Lord [W. Thompson] (1856) Elements of a mathematical theory of elasticity. Phil Trans R Soc 166:481-498
35. Manfredini P, Cocchetti G, Maier G, Redaelli A, Montevecchi FM (1999) Poroelastic finite element analysis of a bone specimen under cyclic loading. J Biomech 32:135-144
36. Marotti G, Muglia MA (1988) A scanning electron microscope study of human bony lamellae proposal for a new model of collagen lamellar organization. Arch Ital Anat Embryol 93: 163-175
37. Marotti G, Muglia MA, Palumbo C (1995) Collagen texture and osteocyte distribution in lamellar bone. Ital J Anat Embryol 100:95-102
38. Martin RB, Burr DB, Sharkey NA (1998) Skeletal tissue mechanics. Springer, New York
39. Nemat-Nasser S, Hori M (1999) Micromechanics: overall properties of heterogeneous materials, 2nd revised edn. Elsevier, Amsterdam
40. Nemat-Nasser S, Iwakuma T, Hejazi M (1982) On composites with periodic structure. Mech Mater 1:239-267
41. Nemat-Nasser S, Yu N, Hori M (1993) Bounds and estimates of overall moduli of composites with periodic microstructure. Mech Mater 15:163-181
42. Nur A, Byerlee JD (1971) An exact effective stress law for elastic deformation of rock with fluids. J Geophys Res 76:6416-6419
43. Piekarski K, Munro M (1977) Transport mechanism operating between blood supply and osteocytes in long bones. Nature 269:80-82
44. Remaggi F, Cane V, Palumbo C, Ferretti M (1998) Histomorphometric study on the osteocyte lacuno-canalicular network in animals of different species. I. Woven-fibered and parallel fibered bones. Ital J Anat Embryol 103:145-155
45. Rice JR, Cleary MP (1976) Some basic stress diffusion solutions for fluid saturated elastic media with compressible constituents. Rev Geophys Space Phys 14:227-241
46. Smit TH, Hyughe JM, Cowin SC (2002) Estimation of the poroelastic parameters of cortical bone. J Biomech 35:829-835
47. Suvorov AP, Dvorak GJ (2002) Rate form of the Eshelby and Hill tensors. Int J Solids Struct 39:5659-5678
48. Thompson M, Willis JR (1991) A reformation of the equations of anisotropic poroelasticity. J Appl Mech 58:612-616
49. Voigt W (1910) Lehrbuch der Kristallphysik, Leipzig
50. Wagermaier W, Gupta HS, Gourrier A, Burghammer M, Roschger P, Fratzl P (2006) Spiral twisting of fiber orientation inside bone lamellae. Biointerphases 1:1-5
51. Wang L, Fritton S, Cowin SC, Weinbaum S (1999) Fluid pressure relaxation depends upon osteonal microstructure: modeling of an oscillatory bending experiment. J Biomech 32:663-672
52. Wang L, Cowin SC, Weinbaum S, Fritton S (2000) Modeling tracer transport in an osteon under cyclic loading. Ann Biomed Eng 28:1200-1209
53. Weinbaum S, Cowin SC, Zeng Y (1994) A model for the excitation of osteocytes by mechanical loading-induced bone fluid shear stresses. J Biomech 27:339-360
54. Weiner S, Traub W (1992) Bone structure: from angstroms to microns. FASEB 6:879-885
55. Weiner S, Traub W, Wagner HD (1999) Lamellar bone: structurefunction relations. J Struct Biol 126:241-255
56. Williams JL, Iannotti JP, Ham A, Bleuit J, Chen JH (1994) Effects of fluid shear stress on bone cells. Biorheology 31:163-170
57. Yoon YJ, Cowin SC (2007) The estimated elastic constants for a single bone osteonal lamella. Biomech Model Mechanobiol (submitted)
58. You J, Yellowley CE, Donahue HJ, Zhang Y, Chen Q, Jacobs CR (2000) Substrate deformation levels associated with routine physical activity are less stimulatory to bone cells relative to loading-induced oscillatory fluid flow. J Biomech Eng 122:387-393
59. You L, Cowin SC, Schaffler MB, Weinbaum S (2001) A model for strain amplification in the actin cytoskeleton of osteocytes due to fluid drag on pericellular matrix. J Biomech 34:1375-1386
60. Yoon YJ, Yang G, Cowin SC (2002) Estimation of the effective transversely isotropic elastic constants of a material from known values of the material's orthotropic elastic constants. Biomech Model Mechanobiol 1:83-93
61. You L, Weinbaum S, Cowin SC, Schaffler MB (2004) Ultrastructure of the osteocytes process and its pericellular matrix. Anat Rec A Discov Mol Cell Evol Biol 278:505-513
62. Zeng Y, Cowin SC, Weinbaum S (1994) A fiber matrix model for fluid flow and streaming potentials in the canaliculi of an osteon. Ann Biomed Eng 22:280-292
63. Zhang D, Cowin SC (1994) Oscillatory bending of a poroelastic beam. J Mech Phys Solids 42:1575-1599
64. Zhang D, Cowin SC (1996) Load carrying capacity of the pore pressure in a poroelastic beam subject to oscillatory excitations. In: Selvaduri APS (ed) Mechanics of poroelastic media. Solid Mechanics and its applications Series. Wolters Kluwer Academic Publishers, Dordrecht, pp 35:273-298
65. Zhang D, Weinbaum S, Cowin SC (1998) Estimates of the peak pressure in bone pore water. J Biomech Eng 120:697-703