Damage Tolerance and Toughness of Elderly Human Femora

Abstract

Observations of elastic instability of trabecular bone cores supported the analysis of cortical thickness for predicting bone fragility of the hip in people over 60 years of age. Here, we falsified the hypothesis that elastic instability causes minimal energy fracture by analyzing, with a micrometric resolution, the deformation and fracture behavior of entire femora. Femur specimens were obtained from elderly women aged between 66 -8 0 years. Microstructural images of the proximal femur were obtained under 3 -5 progressively increased loading steps and after fracture. Bone displacements, strain, load bearing and energy absorption capacity were analyzed. Elastic instability of the cortex appeared at early loading stages in regions of peak compression. No elastic instability of trabecular bone was observed. The subchondral bone displayed local crushing in compression at early loading steps and progressed to 8 -1 6 % compression before fracture. The energy absorption capacity was proportional to the displacement. Stiffness decreased to near-zero values before fracture. Three-fourth of the fracture energy (10.2 -2 0 . 2 J) was dissipated in the final 25% force increment. Fracture occurred in regions of peak tension and shear, adjacent to the location of peak compression, appearing immediately before fracture. Minimal permanent deformation was visible along the fracture surface. Elastic instability modulates the interaction between cortical and trabecular bone promoting an elastically stable fracture behavior of the femur organ, load bearing capacity, toughness, and damage tolerance. These findings will advance current methods for predicting hip fragility.

The effect of age and initial compression on the force relaxation response of the femur in elderly women

“…Furthermore, the femur's force relaxation response can be described as a function of the initial compression alone (figure 4) when the relative initial force is moderate ( F 0 / F L < 0.4). However, the early force relaxation response was variable and unrelated to the initial compression for subcritical levels of the relative initial force (figure 3 c ), possibly due to damage onset and progression occurring during, or early after, application of subcritical compressive loads [20]. Age was moderately associated with the logarithm of the characteristic time ( R 2 = 0.37) only when the analysis was restricted to a narrow range of the initial compression ( F 0 / F L = 0.23–0.43), explaining 35% of the variation of τ in the entire dataset.…”

“…The second device was a custom-made six-degree-of-freedom robot used to apply to the specimen assembly, and keep constant over time, a displacement generating a reaction force along the prescribed direction. The first device was used to extend the force relaxation profiles reported earlier [18,20] for four specimens to 12 specimens in total using an initial compression equal or above one-fourth of the estimated fracture load. The second device was used to provide additional force relaxation profiles using an initial compression below one-fourth of the estimated fracture load.…”

“…The data for the eight additional specimens reported in the present study were pooled with the data for the four specimens reported earlier [18,20]. The stretched exponential function by Sasaki and co-workers [9] was modified by replacing the elastic modulus E with the reaction force F , hence taking the form:Ffalse(tfalse)=A×e−false(t/τfalse)β;t=false[0,30false],where A is the scaling factor, β is the shape factor and τ is the characteristic time.…”