Simplifying biochemical tumorous bone remodeling models through variable order derivatives

Bone is a living tissue that is constantly being renewed, where different cell types can induce a remodeling action to its structure. These mechanisms are typically represented through differential equations, accounting for the biochemical coupling between osteoclastic and osteoblastic cells. Remodeling models have also been extended to include the effects of tumorous disruptive pathologies in the bone dynamics.This article provides a novel approach to existing biochemical models, acting on two different stages. First, the models are said to physiologically better explain an osteolytic metastatic disease to the bone than the multiple myeloma previously considered. Second, and most importantly, variable order derivatives were introduced, for the first time in biochemical bone remodeling models. This resulted in a set of equations with less parameters that describe tumorous remodeling, and provide similar results to those of the original formulation. A more compact model, that promptly highlights tumorous bone interactions, is then achieved. Comparison of simulations and parameters is provided.Such results are a one-step-closer insight to, in a near future, easily provide clinical decision systems ensuring tailored personalized therapy schemes, for more efficient and targeted therapies.