Can deterministic mechanical size effects contribute to fracture and microdamage accumulation in trabecular bone?

Abstract

Failure of bone under monotonic and cyclic loading is related to the bone mineral density, the quality of the bone matrix, and the evolution of microcracks. The theory of linear elastic fracture mechanics has commonly been applied to describe fracture in bone. Evidence is presented that bone failure can be described through a non-linear theory of fracture. Thereby, deterministic size effects are introduced. Concepts of a non-linear theory are applied to discern how the interaction among bone matrix constituents (collagen and mineral), microcrack characteristics, and trabecular architecture can create distinctively differences in the fracture resistance at the bone tissue level. The non-linear model is applied to interpret pre-clinical data concerning the effects of anti-osteoporotic agents on bone properties. The results show that bisphosphonate (BP) treatments that suppress bone remodeling will change trabecular bone in ways such that the size of the failure process zone relative to the trabecular thickness is reduced. Selective estrogen receptor modulators (SERMs) that suppress bone remodeling will change trabecular bone in ways such that the size of the failure process zone relative to the trabecular thickness is increased. The consequences of these changes are reflected in bone mechanical response and predictions are consistent with experimental observations in the animal model which show that BP treatment is associated with more brittle fracture and microcracks without altering the average length of the cracks, whereas SERM treatments lead to a more ductile fracture and mainly increase crack length with a smaller increase in microcrack density. The model suggests that BPs may be more effective in cases in which bone mass is very low, whereas SERMS may be more effective when milder osteoporotic symptoms are present.

Figure 1

Predicted dependence of the normalized strength of trabeculae (σ_T / σ₀) and normalized fatigue strength of trabeculae (Δσ_T / Δσ₀) on normalized size Λ_S, Λ_F.

Figure 2

Schematic drawing of expected characteristics of mineralized collagen fibrils for Veh, BP and SERM treatment.