Nanomechanics of Post-yield Deformation of Cortical Bone under Compression using Novel Synchrotron X-ray Scattering Techniques

INTRODUCTION Although bulk post-yield behavior of bone has been extensively reported in the literature, its underlying mechanism at ultrastructural level is still poorly understood. Lack of such knowledge has significantly hindered our understanding of age-related deterioration in bone quality. To address this issue, a mechanistic understanding of the post-yield behavior of bone becomes necessary. This is analogous to that if we did not understand the mechanism of dislocation motion, we would never be able to mechanistically explain the plastic behavior and all associated properties of metals. Previous studies on loaded bone specimens using synchrotron x-ray scattering techniques have shown that internal strains of the mineral and collagen phases are different and such differences vary with the increasing deformation [1, 2]. These results suggest that relative deformation (interfacial shear) between the two bone constituents may exist and vary with the post-yield deformation of bone. In this study, we used this novel and powerful methodology to investigate the interfacial behavior between the mineral and collagen phases during the post-yield deformation of bone. One advantage of this methodology is that the internal strains could be monitored in a timely manner while bone specimens are being loaded. Thus, the objective of this study was to investigate the correlation of the internal strains of the mineral and collagen phases with the bulk postyield behavior of bone as a function of applied strain. METHODS Six cylindrical cores of cortical bone (φ3×5mm) were acquired from the medial quadrant of middiaphysis of femurs of male human cadavers of middle age group (N=6, 51±2 years old). The long axis of the specimens was parallel to the longitudinal orientation of bone. A servo-hydraulic mechanical testing system (MTS Model 858) was used in this study. The experiments were performed at the 1-ID beamline of the Advanced Photon Source, Argonne National Laboratory (Figure 1). A monochromatic high-energy (E~80 keV) x-ray beam size of approximately 0.1mm×0.1mm was incident on the surface of the gage region of the test specimens (perpendicular to the sample’s load axis) to ensure the resolution of the measurements. The internal strains in both the mineral and collagen phases were determined by taking exposures in both the smalland wide-angle x-ray scattering (SAXS/WAXS) regimes. The sample thickness along the incident beam direction was 1.0-3.0mm thick, as the transmission through 3mm of bone at these energies was approximately 90%. Using area detectors and high energy X-rays associated with small θ, scattering from the load and transverse directions was collected simultaneously. A large area detector (GE a:Si) was used at a sample-detector distance of ~ 1.5 m to record the WAXS patterns, while a smaller area detector (PI CCD) was used further downstream from the sample (~4 m) to record the SAXS patterns. These detectors were operated sequentially to permit recording of full diffraction rings in both modes, with about one minute needed for both patterns. Both detectors were nominally normal to the incident X-ray beam. Reference specimens of ceria (NIST SRM674a) and silver behenate were used to respectively calibrate the WAXS and SAXS detector parameters such as distance, beam center, and detector tilts. The specimen axis was aligned with the load axis and a laser distance gage (Keyence LK-G152) was used to correct for small specimen shifts during the loading tests relative to the detectors. A progressive loading scheme (load-stress relaxation dwellunloading-creep dwell-reloading) (Figure 2) was conducted to measure the internal strains of both the mineral and collagen phases at each dwelling period to ensure enough time for the synchrotron x-ray measurements [3]. In addition to the bulk behavior of the specimens, the longitudinal (parallel to the loading direction) in situ strains in the mineral crystals and collagen fibrils were determined from the synchrotron x-ray measurements. Similarly, the load was measured using a force transducer and the stress was calculated by dividing the force by the cross section area of the specimen. The strain was measured using an extensometer by dividing the displacement by the gage length of the extensometer. RESULTS The stress-strain curve of progressive loading (Figure 2) indicated that cortical bone experienced elastic deformation until the macroscopic strain level of 1.2%. After that, the appreciable amount of plastic deformation was observed to accumulate. Before collagen fibrils and mineral crystals reached their peak strains at the macroscopic strain level of 1.2%, there were positively linear relationships between applied strain at the macroscopic level and internal strains at the nanoscale for both collagen and mineral phases (Figure 3). The peak strain of the collagen phase (0.72%) is about 2.6 times more than that of the mineral phase (0.28%). Coinciding with macroscopic yielding of bone, the internal strains of both collagen and mineral phases dropped sharply and decreased to 3550% of their peak strains (Figure 3). After the applied strain level of ~3.0%, the collagen phase had a relatively constant strain level of 0.2%, whereas the strain level of the mineral phase continued to drop to or below zero strain. DISCUSSION This study investigated nanoscopic mechanisms of bone deformation using synchrotron x-ray scattering techniques and a progressive loading scheme. The magnitude of collagen strain at the nanoscale is more than that of the mineral phase, suggesting that both mineral crystals and collagen fibrils are involved in the loading bearing process. The yielding point of bone at the macroscopic level is coincident with the moment when peak strains of collagen fibrils and mineral crystals at the nanoscale were reached. After yielding, both collagen and mineral phases appear to give up their role in individually carrying the compressive load. Nevertheless, the bulk tissue continues to bear relatively high load. Thus, one possible scenario is that the load to the tissue is carried through the interaction between the two phases by shear. For example, interfacial sliding at the mineral and collagen interface is likely one mechanism for load transmission and realization of permanent deformation for plastic strain energy dissipation in bone during the post-yield deformation.