Elastic properties of collagen in bone determined by measuring the Debye–Waller factor

Abstract

Force constant values for thermal vibrational motion of a collagen molecule along the helix axis in tendon, completely demineralized bone (CDB), and partially demineralized bone (PDB) were estimated by determining the Debye–Waller factor (DW factor) for the diffracted X-ray intensity from these specimens. The DW factor for nominal value of 0.286nm meridional diffraction representing a period along the helical axis of a collagen molecule was measured. As the atomic scattering factor of mineral constituents is much larger than that of collagen, it is difficult to detect the diffraction from collagen in bone specimen. Therefore, PDB was used in this study. In order to compare obtained force constant value for CDB with mechanical properties of collagen in the literature, the value was translated into Young's modulus value using the cross-sectional area of a collagen molecule. In the case of collagen in PDB, i.e., collagen with the close presence of HAp mineral particles, as the DW factor of the diffracted intensity by hydroxyapatite (HAp) was considered to be negligible compared with that of collagen, the DW factor determined was interpreted as that of collagen molecule in PDB specimen. The force constant value obtained for collagen in PDB was significantly larger than that of collagen in CDB. This result was thought to be a manifestation of the hardening of collagen matrix in bone by HAp mineral particles and the first straightforward evidence for a difference in collagen properties depending on the presence of HAp mineral particles. The method employed in this study can be utilized for detecting mechanical properties of the individual constituents of composite materials.