Effect of variations in tissue-level ductility on human vertebral strength

Although the ductility of bone tissue is a unique element of bone quality and varies with age and across the population, the extent to which and mechanisms by which typical population-variations in tissue-level ductility can alter whole-bone strength remains unclear. To provide insight, we conducted a finite element analysis parameter study of whole-vertebral (monotonic) compressive strength on six human L1 vertebrae. Each model was generated from micro-CT scans, capturing the trabecular micro-architecture in detail, and included a non-linear constitutive model for the bone tissue that allowed for plastic yielding, different strengths in tension and compression, large deformations, and, uniquely, localized damage once a specified limit in tissue-level ultimate strain was exceeded. Those strain limits were based on reported (mean ± SD) values from cadaver experiments (8.8 ± 3.7% strain for trabecular tissue and 2.2 ± 0.9% for cortical tissue). In the parameter study, the strain limits were varied by ±1 SD from their mean values, for a combination of nine analyses per specimen; bounding values of zero and unlimited post-yield strain were also modeled. The main outcomes from the finite element analysis were the vertebral compressive strength and the amount of failed (yielded or damaged) tissue at the overall structure-level failure. Compared to a reference case of using the mean values of ultimate strain, we found that varying both trabecular and cortical tissue ultimate strains by ±1 SD changed the computed vertebral strength by (mean ± SD) ±6.9 ± 1.1% on average. Mechanistically, that modest effect arose because the proportion of yielded tissue (without damage) was 0.9 ± 0.3% of all the bone tissue across the nine cases and the proportion of damaged tissue (i.e. tissue exceeding the prescribed tissue-level ultimate strain) was 0.2 ± 0.1%. If the types of variations in tissue-level ductility investigated here accurately represent real typical variations in the population, the consistency of our results across specimens and the modest effect size together suggest that typical variations in tissue-level ductility only have a modest impact on vertebral compressive strength, in large part because so few trabeculae are damaged at the load capacity of the bone.