Background: Several analytical models have been developed in the past to analyze the specific role of osteocytes in the process of bone remodeling, which can be considered as the response of bone material to functional requirements. Most of them considered both the number of osteocytes and their spatial distribution in one area of influence, while others suggested in addition to include considerations of the size of the basic multi-cellular unit. Methods: Taking advantage of previous works, the standard model equation is revisited by incorporating two complementary parameters: (a) the possibility of resorption of osteocytes, apoptosis or function inhibition during remodeling process triggered by the transduction phase of osteocytes embedded within the bone matrix and; (b) the interference of influence zones for the same osteocyte. Results: Bone density evolution has been calculated starting with a medical imaging of an implanted femur. It is shown that the management of interference zone and the possibility of resorption or inhibition of osteocytes have a direct impact upon the value of the mechanical stimulus and hence on the recruitment of Bone Multicellular Units (BMUs). From a mathematical point of view, this effect has been considered by modifying mechanical stimulus of the standard model such that it is impacted by a scalar factor ranged in the interval (0.5–1). Conclusion: It is clearly demonstrated that predicted of the added bone mass amount shows that the new model is more active in low density regions where requiring rapid adaptation to the behavior of the implant, and that the standard model takes the lead in the regions with high density.

This paper aims to construct a general framework of coupling tumor–bone remodeling processes in order to produce plausible outcomes of the effects of tumors on the number of osteoclasts, osteoblasts, and the frequency of the bone turnover cycle. In this document, Komarova’s model has been extended to include the effect of tumors on the bone remodeling processes. Thus, we explored three alternatives for coupling tumor presence into Komarova’s model: first, using a “damage” parameter that depends on the tumor cell concentration. A second model follows the original structure of Komarova, including the tumor presence in those equations powered up to a new parameter, called the paracrine effect of the tumor on osteoclasts and osteoblasts; the last model is replicated from Ayati and collaborators in which the impact of the tumor is included into the paracrine parameters. Through the models, we studied their stability and considered some examples that can reproduce the tumor effects seen in clinic and experimentally. Therefore, this paper has three parts: the exposition of the three models, the results and discussion (where we explore some aspects and examples of the solution of the models), and the conclusion.