Geometrical approach to tumor growth

Tumor growth has a number of features in common with a physical process known as molecular beam epitaxy. Both growth processes are characterized by the constraint of growth development to the body border, and surface diffusion of cells and particles at the growing edge. However, tumor growth implies an approximate spherical symmetry that makes necessary a geometrical treatment of the growth equations. The basic model was introduced in a former paper [C. Escudero, Phys. Rev. E 73, 020902(R) (2006)], and in the present work we extend our analysis and try to shed light on the possible geometrical principles that drive tumor growth. We present two-dimensional models that reproduce the experimental observations, and analyze the unexplored three-dimensional case, for which interesting conclusions on tumor growth are derived.

Figure 1

Evolution of the initial condition $r(\theta ,0)=10+9\cos \left(12\theta \right)$ (inner figure) given by Eq. (46). All the values of the parameters are set equal to unity, with the exception of $K_0=0$. The outer figure represents the surface at $t=5$.

Figure 2

Evolution of the initial condition $r(\theta ,0)=10+9\cos \left(12\theta \right)$ (inner figure) given by Eq. (46). All the values of the parameters are set equal to unity, with the exception of $K_2=0$. The outer figure represents the surface at $t=5$.