A novel mechanical parameter to quantify the microarchitecture effect on apparaent modulus of trabecular bone: a computational analysis of ineffective bone mass

Abstract

Introduction: Previous studies showed microarchitecture can vary the apparent modulus of trabecular bone independent of bone volume fraction (BV/TV). However, the modulus is a mechanical quantity and there is no mechanical explanatory parameter. This study aims to reveal a novel mechanical parameter to quantify the microarchitecture effect on the apparent modulus of trabecular bone. Methods: Fourteen human vertebrae were scanned with DXA followed by micro-CT. Four trabecular specimens were obtained per vertebrae and converted to micro–finite element models. The apparent modulus (E) was computed using linear micro–finite element analysis. Ineffective bone mass (InBM) was the bone mass with a negligible contribution to load-resistance, quantified as the low von Mises stress ratio (LSVMR), which is the ratio of the number of InBM elements to the total number of elements in the model. Correlation between E* and LSVMR was analysed, with the experimental optimal stress threshold. Multiple linear regression of E against both BV/TV and LSVMR was further analysed. Results: BV/TV alone can explain 59% of the variation in E (E=2254.64BV/TV1.04, R2=0.59, p<0.001), and LSVMR can explain 48% of the variation in E (E=1696.4 - 1647.1LSVMR, R2=0.48, p<0.001). Combining these two predictors, 95% of the variation in E can be explained in a multiple linear regression model (E=1364.89 + 2184.37BV/TV - 1605.38LSVMR, adjusted R2=0.95, p<0.001). Conclusion: LSVMR can be adopted as the mechanical parameter to quantify the microarchitecture effect on the apparent modulus of trabecular bone.