(250k) Mathematical Analysis of Bone Remodeling under Influence of Electrical Field

Bone remodeling, defined as the replacement of bone tissue, is a process consisting of two basic mechanisms, bone resorption and bone formation. It has been found that bone formation can be influenced by the presence of an electrical field. If this finding continues to test true, applications of electrical fields may lead to novel treatments in this area of study, including bone fractures, transplant, and osteoporosis.

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.