Mechanobiological bone growth: comparative analysis of two biomechanical modeling approaches

Mechanobiological growth is the process whereby bone growth is modulated by mechanical loading. Analytical formulations of mechanobiological growth have been developed by Stokes et al. (J Orthop Res 17(5):646–653, 1990) and Carter et al. (J Orthop Res 6:804–816, 1988). The purpose of this study was to compare these two modeling approaches in a finite element model of a vertebra to investigate whether growth pattern induced by these models were equivalent. A finite element model of a thoracic vertebra, integrating a conceptual model of the growth plate, was developed and combined with the mechanobiological growth models. This model was further used to simulate vertebral growth modulation resulting from different physiological loading conditions. Different growth magnitudes were obtained under compression and combined tension/shear loading, whereas dissimilar growth patterns were triggered by shear forces and combined compression/shear. These two models represent mechanobiological bone growth under limited mechanical environment. Carter’s model takes into account three-dimensional stress stimuli, but does not intrinsically incorporate the resulting growth orientation. Stokes’ model adequately represents the mechanobiological contribution of axial stresses but does not take into account the contribution of non-axial stresses, which can occur in complex mechanical environment.