The Dynamic Evolution of the Power Exponent in a Universal Growth Model of Tumors

We have previously reported that a universal growth law, as proposed by West and collaborators for all living organisms, appears to be able to describe also the growth of tumors in vivo. In contrast to the assumption of a fixed power exponent p (assumed by West et al. to be equal to 3/4), we show in this paper the dynamic evolution of p from 2/3 to 1, using experimental data from the cancer literature and in analogy with results obtained by applying scaling laws to the study of fragmentation of solids. The dynamic behaviour of p is related to the evolution of the fractal topology of neoplastic vascular systems and might be applied for diagnostic purposes to mark the emergence of a functionally sufficient (or effective) neo-angiogenetic structure.