Super-Rough Dynamics on Tumor Growth

Abstract

The growth of a cultivated typical brain tumor is studied in this work. The tumor is analyzed both dynamically and morphologically. We have measured its fractal dimension to be ${d}_{f}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.21\ifmmode\pm\else\textpm\fi{}0.05$. From its dynamical behavior we determine the scaling critical exponents of this circular symmetry system which are compatible with the linear molecular beam epitaxy universality class. A very important feature of tumor profiles is that they are super-rough, which constitutes the first ( $1+1$)-dimensional experiment in literature with super-roughness. The results obtained from the dynamics study make manifest two very surprising features of tumor growth: Its dynamics is mainly due to contour cells and the tendency of an interface cell to duplicate is a function of the local curvature.