Tissue-level failure accumulation in vertebral cancellous bone: A theoretical model

Abstract

Vertebral compression fractures are a potentially severe injury, which is characteristic to osteoporotic elderly. Despite being a significant healthcare problem, the etiology of compression fractures is not fully understood, and there are no biomechanical models in the literature that describe the development of these fractures based on cancellous bone failure accumulation. The objective of this study was therefore to develop a computational model of tissue-level failure accumulation in vertebral cancellous bone, which eventually leads to compression fractures. The model predicts the accumulated percentage of broken trabeculae delta in a vertebral region of interest (ROI) over 60 years, by employing Euler's theory for elastic buckling. The accumulated failure delta is calculated as function of the daily activity characteristics and rate of annual bone loss (RABL) with aging. An RABL of unity represents the normal bone loss attributed to aging per se, whereas RABL>1 is assumed to represent pathological bone metabolism such as osteoporosis. Simulations were conducted for a range of RABLs, to determine the effect of changes in bone metabolism on the accumulation of bone failure. Results showed that bone failure rapidly increased with RABL. Generally, trabecular failure was shown to become more severe for RABL>4. Total failure was exhibited at RABL=7.5 for the central ROI, and at RABL=8.5 for the sub-endplate ROI. We concluded that vertebral compression fractures advance monotonically between the age of 50-55 years and 70 years, and may accelerate thereafter if RABL is high (~8). Additionally, the model identified weight lifting as the action that most dramatically accelerated the destruction of osteoporotic spinal cancellous bone. The present biomechanical model is useful for understanding the etiology of compression fractures, and potentially, depending on further experimental characterization of RABL, for considering the effects of medications that influence bone metabolism on patient prognosis.