Improving the damage accumulation in a biomechanical bone remodelling model

We extend, reformulate and analyse a phenomenological model for bone remodelling. The original macrobiomechanical model (MBM), proposed by Hazelwood et al. [J Biomech 2001; 34:299-308], couples a population equation for the cellular activities of the basic multicellular units (BMUs) in the bone and a rate equation to account for microdamage and repair. We propose to account for bone failure under severe overstressing by incorporating a Paris-like power-law damage accumulation term. The extended model agrees with the Hazelwood et al. predictions when the bone is under-stressed, and allows for suitably loaded bones to fail, in agreement with other MBM and experimental data regarding damage by fatigue. We numerically solve the extended model using a convergent algorithm and show that for unchanging loads, the stationary solution captures fully the model behaviour. We compute and analyse the stationary solutions. Our analysis helps guide additional extensions to this and other BMU activity based models.