Tumor Growth, Proliferation and Diffusion in Osteosarcoma

Osteosarcoma is the most common primary bone cancer. According to medical and biological studies, it has a high genetic complexity, thus, to differentiate the mechanisms of appearance and evolution of this disease is a difficult task. In this paper, we use three simplest and well known mathematical models to describe the behavior of several cell lines of osteosarcoma. First, we use a potential law to describe the tumor growth in immunosuppressed mice; with it we show that the variation of tumor growth has a sublinear behavior without the blow-up phenomenon. Second, the logistic model is used to obtain a good aproximation to the rates of proliferation in cell confluency in in vitro experiments. Third, we use a linear reaction-diffusion model; with it, we describe the diffusion behavior for some cell lines. These three models allow us to give a classification of cell lines according to the rates of tumor growth and proliferation and to the diffusion coefficient. A relationship is found between the rates of the tumor growth, the diffusion coefficient and tumorigenicity. Experimental data are extracted from Lauvrak et al. (British Journal of Cancer 109(8):2228–2236, 2013).