Are mineralized tissues open crystal foams reinforced by crosslinked collagen? Some energy arguments.

Which of the elementary components (hydroxyapatite (HA) crystals, collagen, non-collagenous organic matter, water) do significantly contribute to the ultrastructural elastic stiffness magnitude and anisotropy of mineralized tissues; and how, i.e. through which shapes and assemblages (which micromechanical morphology)? We suggest answers to these questions by analyzing stiffness-volume fraction relationships of wet and dry tissue specimens in the framework of strain energy considerations. Radial stiffness values of both isotropic and anisotropic tissues are found to depend linearly to quadratically on only the mineral volume fraction. This suggests the isotropic contribution of HA to the ultrastructural stiffness. An energy-based analysis of the difference between the axial and radial stiffness values of anisotropic, collagen-rich tissues allows us to assess the collagen elasticity contribution, which is found to depend linearly on the extra-collagenous mineral concentration. These results suggest that collagen and hydroxyapatite are the elementary components governing the ultrastructural elastic stiffness magnitude and anisotropy of bone and mineralized tendons. The elastic stiffness of water and non-collagenous organic matter does not play a significant role. As for the morphological issue, we suggest that mineralized tissues are isotropic open crystal foams; and that these foams are reinforced unidirectionally by collagen molecules which are mechanically activated through tight links between these molecules and HA-crystals. The HA crystals are mechanically activated through stretching and bending in long bone tissues, they are predominantly stretched in mineralized tendons, and bent in hyperpycnotic tissues.

[1]  S. Lees,et al.  Sonic velocity and attenuation in wet compact cow femur for the frequency range 5 to 100 MHz. , 1992, Ultrasound in medicine & biology.

[2]  M. Urist,et al.  Bone cell differentiation and growth factors. , 1983, Science.

[3]  S Lees,et al.  Some acoustical properties of the otic bones of a fin whale. , 1996, The Journal of the Acoustical Society of America.

[4]  S Lees,et al.  Anisotropy in hard dental tissues. , 1972, Journal of biomechanics.

[5]  André Zaoui,et al.  Structural morphology and constitutive behaviour of microheterogeneous materials , 1997 .

[6]  S Lees,et al.  Considerations regarding the structure of the mammalian mineralized osteoid from viewpoint of the generalized packing model. , 1987, Connective tissue research.

[7]  J. Black,et al.  Biological and biomechanical performance of biomaterials: Editors: P. Christel, A. Meunier and A.J.C. Lee Elsevier Science Publishers, Amsterdam, 1986, pp 550, $124 , 1987 .

[8]  S Lees,et al.  A study of some properties of mineralized turkey leg tendon. , 1992, Connective tissue research.

[9]  P. Fratzl,et al.  Bone mineralization as studied by small-angle x-ray scattering. , 1996, Connective tissue research.

[10]  R. Pidaparti,et al.  Bone mineral lies mainly outside collagen fibrils: predictions of a composite model for osteonal bone. , 1996, Journal of biomechanics.

[11]  J. Petruska,et al.  Recent studies with the electron microscope on ordered aggregates of the tropocollagen macromolecule , 1963 .

[12]  E D Pellegrino,et al.  The chemical anatomy of bone. I. A comparative study of bone composition in sixteen vertebrates. , 1969, The Journal of bone and joint surgery. American volume.

[13]  V. Ingle,et al.  The loci of mineral in turkey leg tendon as seen by atomic force microscope and electron microscopy , 1994, Calcified Tissue International.

[14]  Steve Weiner,et al.  THE MATERIAL BONE: Structure-Mechanical Function Relations , 1998 .

[15]  M. Glimcher,et al.  Isolation of calcium‐phosphate crystals of bone by non‐aqueous methods at low temperature , 1995, Journal of bone and mineral research : the official journal of the American Society for Bone and Mineral Research.

[16]  R. G. Paul,et al.  Mechanisms of maturation and ageing of collagen , 1998, Mechanisms of Ageing and Development.

[17]  A J Bailey,et al.  Collagen cross-links in mineralizing tissues: a review of their chemistry, function, and clinical relevance. , 1998, Bone.

[18]  G. I. Barenblatt.  Scaling: Self-similarity and intermediate asymptotics , 1996 .

[19]  I Sevostianov,et al.  Impact of the porous microstructure on the overall elastic properties of the osteonal cortical bone. , 2000, Journal of biomechanics.

[20]  J. Currey,et al.  The relationship between the stiffness and the mineral content of bone. , 1969, Journal of biomechanics.

[21]  Peter Zioupos,et al.  Dependence of mechanical properties on fibre angle in narwhal tusk, a highly oriented biological composite. , 1994, Journal of biomechanics.

[22]  Pierre Suquet,et al.  Continuum Micromechanics , 1997, Encyclopedia of Continuum Mechanics.

[23]  A. Miller.  Collagen: the organic matrix of bone. , 1984, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[24]  M. Ashby,et al.  Cellular solids: Structure & properties , 1988 .

[25]  J. Katz,et al.  Elastic properties of apatites , 1982 .

[26]  S Cusack,et al.  Determination of the elastic constants of collagen by Brillouin light scattering. , 1979, Journal of molecular biology.

[27]  M. Glimcher.  Recent studies of the mineral phase in bone and its possible linkage to the organic matrix by protein-bound phosphate bonds. , 1984, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[28]  F. Fedorov.  Theory of Elastic Waves in Crystals , 1968 .

[29]  M. Spector,et al.  The ultrastructure of anorganic bovine bone and selected synthetic hyroxyapatites used as bone graft substitute materials. , 2002, Biomaterials.

[30]  S Lees,et al.  Studies of compact hard tissues and collagen by means of Brillouin light scattering. , 1990, Connective tissue research.

[31]  R. Lakes,et al.  Ultrasonic wave propagation and attenuation in wet bone. , 1986, Journal of biomedical engineering.

[32]  P. Hauschka,et al.  Nucleation and inhibition of hydroxyapatite formation by mineralized tissue proteins. , 1996, The Biochemical journal.

[33]  J. White,et al.  Phonons and the elastic moduli of collagen and muscle , 1977, Nature.

[34]  H. Mook,et al.  Comparison of dosage‐dependent effects of β‐aminopropionitrile, sodium fluoride, and hydrocortisone on selected physical properties of cortical bone , 1994 .

[35]  S Lees,et al.  Parameters influencing the sonic velocity in compact calcified tissues of various species. , 1983, The Journal of the Acoustical Society of America.

[36]  S. Lees,et al.  Visualization of crystal-matrix structure. In situ demineralization of mineralized turkey leg tendon and bone , 1996, Calcified Tissue International.

[37]  G. Pharr,et al.  The elastic properties of trabecular and cortical bone tissues are similar: results from two microscopic measurement techniques. , 1999, Journal of biomechanics.

[38]  S. Lees,et al.  The role of collagen in the elastic properties of calcified tissues. , 1977, Journal of biomechanics.

[39]  F H Silver,et al.  Assembly of type I collagen: fusion of fibril subunits and the influence of fibril diameter on mechanical properties. , 2000, Matrix biology : journal of the International Society for Matrix Biology.

[40]  Peter Zioupos,et al.  The effect of porous microstructure on the anisotropy of bone-like tissue: a counterexample. , 2001, Journal of biomechanics.