Bone remodeling simulation using spatial influence function in macroscopic cube case

Bone has the capability to adapt its density in response to mechanical stimuli through a process known as bone remodeling, which has been simulated <i>in silico</i> using various algorithms in several studies, with Strain Energy Density (SED) being a commonly used driving parameter. A spatial influence function has been introduced in addition to the remodeling algorithm, which accounts for the influence of neighboring regions on local mechanical stimuli, thereby reducing artificial mesh dependency and mimicking cellular communication in bone. However, no study has implemented the SED-driven algorithm with spatial influence function on a macroscopic 3D bone structure, and there is no physiological explanation on the value used in remodeling parameter. The goal of this study was to assess the effect of the spatial influence function's parameters on the resulting 3D simple cubic structure under compressive loading through a sensitivity analysis. The results demonstrated that the spatial influence function enabled the density distribution to propagate in directions not only aligned with external loads, thus simulating the work of cellular communication. This study also underscores the importance of selecting appropriate parameter values to accurately reflect physiological conditions in bone remodeling simulations, since different parameters influence not only bone mineral density but also the architecture of the resulting bone structure. This work represents a step forward in understanding the interplay between mechanical stimuli and bone remodeling in three dimensions, providing insights that could improve the accuracy of computational models in simulating physiology and pathophysiology.