M. I. Romero Rodríguez, J. C. Vargas Pino, E. L. Sierra-Ballén
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引用次数: 0
Abstract
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).
期刊介绍:
Acta Biotheoretica is devoted to the promotion of theoretical biology, encompassing mathematical biology and the philosophy of biology, paying special attention to the methodology of formation of biological theory.
Papers on all kind of biological theories are welcome. Interesting subjects include philosophy of biology, biomathematics, computational biology, genetics, ecology and morphology. The process of theory formation can be presented in verbal or mathematical form. Moreover, purely methodological papers can be devoted to the historical origins of the philosophy underlying biological theories and concepts.
Papers should contain clear statements of biological assumptions, and where applicable, a justification of their translation into mathematical form and a detailed discussion of the mathematical treatment. The connection to empirical data should be clarified.
Acta Biotheoretica also welcomes critical book reviews, short comments on previous papers and short notes directing attention to interesting new theoretical ideas.