Considerations Regarding the Structure of the Mammalian Mineralized Osteoid from Viewpoint of the Generalized Packing Model

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Abstract
The relative magnitudes of mineral, organic and water contents of dense mammalian bone are calculated by a new theory based on recent findings (1) The neutron diffraction studies of mineralized tissues with different densities demonstrated an inverse relationship between wet density and the equatorial diffraction spacing of the collagen. (2) The neutron studies showed there was very little mineral within the collagen fibrils. (3) A generalized packing model for collagen has been advanced to show how the equatorial spacing can be varied depending on tissue type, water content, and mineral content. (4) The water content of collagen fibrils when calculated from the generalized packing model matches the experimentally determined values for rat tail tendon fibers, bone matrix, and fully mineralized bone. A computational model was developed based on the generalized packing model. It provides a unifying approach to explain many features of mineralized fibrous collagenous tissues. The results are presented as estimates of the mineralized collagen fibril density, the volume fraction of collagen in bone, the density of the extrafibrillar space, the fraction of the e.f. space occupied by mineral and the ratio of mineral within collagen to total mineral content, each expressed as a function of wet bone density. A useful data base, available from previous studies, related mineral, organic and water weight fractions to wet bone density, for a density range from 1.7 g/cc for deer antler to 2.7 g/cc for porpoise petrosal. A second order polynomial was found for each weight fraction component, with bone density as the input variable, with a standard deviation less than 2% of total bone weight. This permits the bone properties to be related to a single variable, the wet bone density. It is seen that compacting the collagen fibrils as well as reducing the organic component weight fraction are two important factors determining the structure of the mineralized osteoid. It was concluded that voids and pore spaces may occupy at least 5% of the bone volume.