This article proposes a model of bone remodeling that encompasses mechanical and electrical stimuli. The remodeling formulation proposed by Weinans and collaborators was used as the basis of this research, with a literature review allowing a constitutive model evaluating the permittivity of bone tissue to be developed. This allowed the mass distribution that depends on mechanical and electrical stimuli to be obtained. The remaining constants were established through numerical experimentation. The results demonstrate that mass distribution is altered under electrical stimulation, generally resulting in a greater deposition of mass. In addition, the frequency of application of an electric field can affect the distribution of mass; at a lower frequency there is more mass in the domain. These numerical experiments open up discussion concerning the importance of the electric field in the remodeling process and propose the quantification of their effects.

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The patella is a sesamoid bone embedded within the quadriceps tendon and the patellar tendon that articulates with the femur. However, how is it formed is still unknown. Therefore, here we have evaluated, computationally, how three theories explain, independently, the patella onset. The first theory was proposed recently, in 2015. This theory suggested that the patella is initially formed as a bone eminence, attached to the anterodistal surface of the femur, while the quadriceps tendon is forming. Thereafter, a joint develops between the eminence and the femur, regulated by mechanical load. We evaluated this theory by simulating the biochemical environment that surrounds the tendon development. As a result, we obtained a patella-like structure embedded within the tendon, especially for larger flexion angles. The second and third theories are the most accepted until now. They state that the patella develops within tendons in response to the mechanical environment provided by the attaching muscles. The second theory analyzed the mechanical conditions (high hydrostatic stress) that (according to previous Carter theories) lead to the differentiation from tendon to fibrocartilage, and then, to bone. The last theory was evaluated using the self-optimizing capability of biological tissue. It was considered that the development of the patella, due to tissue topological optimization of the developing quadriceps tendon, is a feasible explanation of the patella appearance. For both theories, a patella onset was obtained as a structure embedded within the tendon. This model provided information about the relationship between the flexion angle and the patella size and shape. In conclusion, the computational models used to evaluate and analyze the selected theories allow determining that the patella onset may be the result of a combination of biochemical and mechanical factors that surround the patellar tendon development.