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ELASTIC PROPERTIES OF WOVEN BONE: EFFECT OF MINERAL CONTENT AND COLLAGEN FIBRILS ORIENTATION
Presentation 1623 − Topic 12. Bone remodelling and adaptation
S115
ELASTIC PROPERTIES OF WOVEN BONE: EFFECT OF MINERAL CONTENT AND COLLAGEN FIBRILS ORIENTATION J. García, J. Martínez-Reina, J. Domínguez
Department of Mechanical and Materials Engineering, University of Seville, Spain
Introduction The overall aim of this study is providing an estimation of the mechanical properties of woven bone to a model, being developed in parallel to this study, that simulates the osteogenic distraction process. With this purpose, others authors have used simpler models based in the rule of mixtures for the compounds of woven bone. This model attempts also to predict changes in elastic properties when the collagen fibrils of the tissue are reoriented along preferred directions as Su et al. suggested [1997], as well as changes in the mineral content of the tissue.
, is unknown in this tissue, so a parametric study of its influence has been done. Collagen fibrils are assumed transversely isotropic, and the matrix (initially water and then hydrated mineral) is assumed isotropic [Martinez-Reina, 2011].
Results The uniform ODF assumed for the tissue leads to a composite with isotropic elastic properties. Figure 1 shows the evolution of the Young’s modulus through mineralization, as a function of the ash fraction for the volumetric fraction of fibrils assumed. 18
Methods
ξ = 0.530 ξ = 0.580 ξ = 0.631
16 14 12 E (GPa)
The structure of woven bone can be approximated by a composite with a matrix of mineral (hydroxyapatite) and inclusions of collagen fibrils with a more or less random orientation. In a previous work the authors have proposed a method to estimate the mechanical properties of cortical bone [Martinez-Reina, 2011]. In that work, a multiscale model was used to consider the different hierarchical levels of cortical bone: fibrils, fibres and lamella. Woven bone is far more disorganized, so it has been assumed that only fibrils and no further higher level structures can be arranged. These fibrils can be internally mineralized, as in cortical bone, and externally too, thus being surrounded by a mineral matrix, forming a kind of composite whose inclusions are those mineralized collagen fibrils. Mineralization and re-orientation of fibrils have been observed in woven bone during fracture healing [Su, 1997]. Mineralization is assumed to occur in two stages: first exclusively within the fibril until its saturation with mineral takes place. In this phase, the matrix is bone marrow (with the elastic properties of water). Then, in a second stage mineral replaces water in the matrix, with fixed properties of the inclusions (fibrils). Ash fraction, , is the variable used to measure the mineral content. The elastic properties of the composite were estimated using the MoriTanaka homogenization scheme. The correction made by Ferrari [Ferrari, 1989] is included to consider the somewhat random orientation of fibrils, by means of an orientation distribution function (ODF), which is assumed uniform in the three directions of space, as a first approach. The volumetric fraction of mineralized collagen fibrils,
10 8 6 4 2 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
α
Figure 1: Evolution of isotropic elastic modulus with mineralization for typical values of .
Discussion It can be observed that the Young’s modulus is highly dependent on the mineral content, especially after the second mineralization phase begins ( >0.4). For the assumed variation of , it is evident that their influence is not relevant. Anyway, the higher is , the stiffer is the tissue, so, a greater concentration of osteoblasts is beneficial for the stiffness of the bone callus. An experimental measurement of elastic properties is needed to validate this model.
References Su et al, Connective Tissue Research, 36(3):271286, 1997 Martinez-Reina et al, Biomechanics and Modelling in Mechanobiology, 10:309-322, 2011 Ferrari et al, Mechanics of Materials, 8:67-73, 1989
ESB2012: 18th Congress of the European Society of Biomechanics
Journal of Biomechanics 45(S1)
S115
ELASTIC PROPERTIES OF WOVEN BONE: EFFECT OF MINERAL CONTENT AND COLLAGEN FIBRILS ORIENTATION J. García, J. Martínez-Reina, J. Domínguez
Department of Mechanical and Materials Engineering, University of Seville, Spain
Introduction The overall aim of this study is providing an estimation of the mechanical properties of woven bone to a model, being developed in parallel to this study, that simulates the osteogenic distraction process. With this purpose, others authors have used simpler models based in the rule of mixtures for the compounds of woven bone. This model attempts also to predict changes in elastic properties when the collagen fibrils of the tissue are reoriented along preferred directions as Su et al. suggested [1997], as well as changes in the mineral content of the tissue.
, is unknown in this tissue, so a parametric study of its influence has been done. Collagen fibrils are assumed transversely isotropic, and the matrix (initially water and then hydrated mineral) is assumed isotropic [Martinez-Reina, 2011].
Results The uniform ODF assumed for the tissue leads to a composite with isotropic elastic properties. Figure 1 shows the evolution of the Young’s modulus through mineralization, as a function of the ash fraction for the volumetric fraction of fibrils assumed. 18
Methods
ξ = 0.530 ξ = 0.580 ξ = 0.631
16 14 12 E (GPa)
The structure of woven bone can be approximated by a composite with a matrix of mineral (hydroxyapatite) and inclusions of collagen fibrils with a more or less random orientation. In a previous work the authors have proposed a method to estimate the mechanical properties of cortical bone [Martinez-Reina, 2011]. In that work, a multiscale model was used to consider the different hierarchical levels of cortical bone: fibrils, fibres and lamella. Woven bone is far more disorganized, so it has been assumed that only fibrils and no further higher level structures can be arranged. These fibrils can be internally mineralized, as in cortical bone, and externally too, thus being surrounded by a mineral matrix, forming a kind of composite whose inclusions are those mineralized collagen fibrils. Mineralization and re-orientation of fibrils have been observed in woven bone during fracture healing [Su, 1997]. Mineralization is assumed to occur in two stages: first exclusively within the fibril until its saturation with mineral takes place. In this phase, the matrix is bone marrow (with the elastic properties of water). Then, in a second stage mineral replaces water in the matrix, with fixed properties of the inclusions (fibrils). Ash fraction, , is the variable used to measure the mineral content. The elastic properties of the composite were estimated using the MoriTanaka homogenization scheme. The correction made by Ferrari [Ferrari, 1989] is included to consider the somewhat random orientation of fibrils, by means of an orientation distribution function (ODF), which is assumed uniform in the three directions of space, as a first approach. The volumetric fraction of mineralized collagen fibrils,
10 8 6 4 2 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
α
Figure 1: Evolution of isotropic elastic modulus with mineralization for typical values of .
Discussion It can be observed that the Young’s modulus is highly dependent on the mineral content, especially after the second mineralization phase begins ( >0.4). For the assumed variation of , it is evident that their influence is not relevant. Anyway, the higher is , the stiffer is the tissue, so, a greater concentration of osteoblasts is beneficial for the stiffness of the bone callus. An experimental measurement of elastic properties is needed to validate this model.
References Su et al, Connective Tissue Research, 36(3):271286, 1997 Martinez-Reina et al, Biomechanics and Modelling in Mechanobiology, 10:309-322, 2011 Ferrari et al, Mechanics of Materials, 8:67-73, 1989
ESB2012: 18th Congress of the European Society of Biomechanics
Journal of Biomechanics 45(S1)