Summary

While many studies on cancer research have been published from a biological perspective, much less is known from a quantitative approach. Nowadays, applied mathematics is helping to fight cancer by integrating quantitative models of tumor growth, as the Gompertzian phenomenon and the power law, which behaviour is thought to have a fractal nature. In this project, developed at Institut de Física d’Altes Energies, it is considered a chaotic dynamical simulation model of tumor growth and metastasis process, sensitive to initial conditions, which is compared to the experimental breast cancer growth of two different cell tumor lines, namely MCF7 and MDA-231, obtained at Institut de Recerca Biomèdica Barcelona Foundation. Moreover, a three-dimensional strange attractor based on the designed model is constructed, which is dependent on the ratio between cell division and cell death probabilities, the tumor oxygen consumption and the releasement of pro-angiogenic factors, and the experimental parameters of which could be used to intercept the geometry of the tumor. A detailed analysis of the intercorrelation of the different variables is also provided. Hence, this project offers a new cutting-edge technique from a physical perspective using the properties of the fractal tumor’s nature, the principle of minimum energy of which here is considered for the first time and proved successfully.