Numerous mathematical models have been proposed to study the bone remodeling process influenced by different types of precursors, hormones and vitamins for example. Unfortunately, none of them have analyzed the effects of electrical fields. The main focus of this contribution is to proposed a mathematical model for net bone formation and to analyze theoretically and numerically the effects of electrical field on osteoblast cells associated with bone production.
The proposed model was conceived following a second order bio-kinetic model limited by precursor availability and controlled by endogenous decay. In particular, osteoblast cellular specific growth rate was modeled using an Arrhenius type function, electrical field dependent.
Preliminary results indicates that electrical fields have a significant impact on bone formation. Increased levels of osteoblast cells are predicted when different order of magnitude of the electrical field are imposed on the system. These results provide important insights into the development of new treatment protocols for patients with bone injuries, diseases, and/or implants.