Shrinkage of Bone
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Shrinkage Of Bone Sidney Lees 50 Eliot Memorial Road, Newton, MA 02458-2704, USA ABSTRACT Shrinkage of bone and other mineralized Type 1 collagen tissues when the tissue is dried has been observed for a long time. It is anisotropic with respect to the orientation of the bone structure. It is linearly dependent on the inverse wet tissue density (specific volume) in the radial direction but not in the axial direction. The volume fraction of water in the tissue has also been shown to be linearly dependent on the inverse and other wet density leading to a direct relation between the shrinkage and the volume fraction of water. Shrinkage may be determined on any scale, macroscopic to microscopic but volume fraction of water is closely related to the lateral spacing of the collagen molecules, that is on the scale of nm. The linear dependence of shrinkage on volume fraction shows the generalized packing model underlies bone structure and is due to the properties of collagen molecules assembled in sheets. INTRODUCTION It is well known that many properties of Type I collagen tissues vary with the tissue density. The density of the specimen in the native state immersed in water is defined as the wet density. The dry density is the value when all the water has been extracted. It has been demonstrated recently that the lateral spacing of the collagen molecules is linearly dependent on the inverse wet density [1] corresponding to specific volume in physical chemistry. As seen in Fig. (1) the spacing, dw, for wet tissue decreases linearly, while the spacing, dd, for dry tissue increases with the inverse wet density. The structure that accommodates this situation has been described as the generalized packing model [2] since it seems to be applicable to all Type I collagen tissues whether mineralized or not. The centers of the molecules, as seen in Fig 5, are rigidly linked. The only possible displacement is a lateral shift that also reduces the spacing between the parallel planes. The dimensions of the model are based on the quasi-hexagonal model of Hulmes and Miller [3].
1.6
Lateral Spacing
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WET dw = 0.7213x + 0.8876 R2 = 0.9876
1.4 1.3 1.2
DRY dd = -0.3264x + 1.31
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R2 = 0.7452
1 0.45
0.55
0.65
0.75 Inverse Wet Density
0.85
0.95
Figure 1. Lateral Spacing of Collagen in Generalized Packing Model
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An hypothesis has been proposed to account for the dependence on the inverse wet density [1]. It is well known that mineral replaces water in mineralization. It is required by the hypothesis that the mass of the tissue remain constant, a condition that is satisfied if the replacing mineral has the same mass as the replaced water. Since the density of mineral is three times that of water, the volume of the tissue decreases. The tissue density increases because the volume decreases, not because the mineral content increases. The linear dependence is a consequence of the generalized packing model. SHRINKAGE Another pattern in collagen has been found that has not been previously reported. Bone shrinks when
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