Bone remodeling mathematical models using advanced discretization techniques: A review

This work presents a brief state of the art regarding bone remodeling models and their combination with numerical methods. The concept of bone remodeling arises from Wolff's law, in which it is suggested a relationship between the mechanical environment and bone's morphology. Since then, several models have tried to reproduce this adaptation process. Remodeling models first took into account only the mechanical component of the process, correlating the apparent density of the bone with its mechanical properties. Later, biochemical models emerged aiming to mathematically describe the dynamic interaction between bone cells and their controlling autocrine and paracrine signaling pathways. Currently, the trend is to create biomechanical models that simultaneously include bone cellular response to biochemical and mechanical stimuli. Therefore, in this work, some of the most relevant bone remodeling models are addressed along with a brief description of the remodeling process. Also, some applications resulting from the combination of these algorithms with distinct numerical techniques, including meshless methods, are presented.