Optimal bone density distributions: numerical analysis of the osteocyte spatial influence in bone remodeling

In this paper a control and optimization procedure for bone remodeling simulations was adopted to study the effect of the osteocyte influence range on the predicted density distribution. In order to reach this goal, the osteocyte network regulating bone remodeling process in a 2-D bone sample was numerically simulated. The assumed proportional-integral-derivative (PID) bone remodeling rule was related to the error signal between the strain energy density and a selected target. Furthermore the control parameters and the target were optimally determined minimizing a suitable cost index: the goal was to minimize the final mass and the energy thus maximizing the stiffness. The continuum model results show that the developed and adapted trabecular structure was consistent with the applied loads and only depended on the external forces, the value of the cost index, the maximum attainable elastic modulus value (hence, the maximum density value) and the value of the energy target. The remodeling phenomenon determined the number and thickness of the trabeculae which are formed from a uniform distribution of mass density in the considered domain; this number and these thicknesses are controlled by the values assigned to the parameters of the model. In particular, the osteocyte decay distance (D) of the influence range affected the trabecular patterns formation, showing an important effect in the adaptive capacity of the optimization numerical model.