Bone metastasis modeling based on the interactions between the BMU and tumor cells

In recent years there has been a multidisciplinary effort by the scientific community to understand the mechanisms of bone metastasis. In order to obtain more information about the significant factors that give support to the cancer invasion, we propose a nonlinear differential model to describe the dynamics between the tumor cells and the main BMU cells (osteoclasts and osteoblasts). The model is based on a power law functional that represents the paracrine signaling between the BMU cells along with a logistic growth for cancer cells. A stability analysis is carried out and the obtained results provide biological information regarding the success or failure of the invasion of bone metastasis. Numerical simulations are performed in order to illustrate theoretical results. Diverse dynamical interactions of the tumor-osteoclast-osteoblast cells are shown which are consistent with observed experimental behavior.