Nonlinear modeling and control strategies for bone diseases based on TGF β and Wnt factors

Bone remodeling is regulated by numerous signaling pathways being transforming growth factor- β (TGF β ) and Wnt crucial for coupling bone formation and elimination activities. Bone diseases, such as osteoporosis and bone metastasis, develop when the bone cells cross-talk is corrupted which causes unbalanced bone mass production. In this work, we explore the effects of TGF β and Wnt in bone dynamics based on a proposed mathematical model, and thereby study different disease control strategies. In particular, we find steady-states of proposed mathematical models, and show bifurcation diagrams that indicate nonlinear dynamical behavior, such as Hopf bifurcations and hysteresis. The implications of these findings on dynamical behavior are then discussed in the context of bone diseases. Finally, using control theory, we also address the question about how input or inhibition combination therapies may help in the control of osteoporosis and cancer-induced bone disease. Numerical simulations are performed to simulate the dynamical behavior of the bone microenvironment and to analyze different treatment combinations (conventional and novel). A discussion of the results is carried out.