Variable Order Differential Models of Bone Remodelling*. Issue 1 (July 2017) - Pinheiro Neto, Joana; Moura Coelho, Rui; Valério, Duarte; Vinga, Susana; Sierociuk, Dominik; Malesza, Wiktor; Macias, Michal; Dzieliński, Andrzej
Abstract: Bone is a living tissue undergoing a constant remodeling process that involves different cell types, in particular osteoclasts and osteoblasts. This process can be modeled using differential equations, accounting for the biochemical coupling between the referred bone cells. These models have also been extended to include the effects of bone diseases in its dynamics, such as tumor metastizations. Due to the high number of parameters involved in the existing physiological models for bone remodeling, a new approach to this system is here presented. Variable order derivatives are introduced as a method to simplify its structure, providing more compact models that lead to similar results to those of the original formulations. These new models also allow for anomalous diffusion to be accounted for. These models are expected to serve in clinical decision systems such as personalized therapy schemes.