Close relationship and role of fractal dimension, heterogeneous nucleation, dynamic transformations and cooperativity mechanisms in unperturbed tumor growth

Abstract

<title>Abstract</title> The cancer is the second leading cause of death worldwide and remains an enigma for researchers and medical doctors. The aim of this study is to propose a novel methodology that demonstrates the close relationship and role of fractal dimension, heterogeneous nucleation, dynamic transformations and cooperativity mechanisms in unperturbed tumor growth. We use the modified Kolmogorov-Johnson-Mehl-Avrami, Montijano-Bergues-Bory-Gompertz and Richards models and show that their respective parameters are connected. To this end, we normalized the last two models. The local Avrami exponent and the susceptibility are used to sense local changes and estimate regime changes during entire unperturbed tumor growth kinetics.The results demonstrate the correspondence between these three models, the interconnection between their parameters, which are fractal in nature. The entire tumor growth kinetics is characterized by discontinuities in contour fractal dimension and phase dynamics transitions with low activation energy. The behavior of the susceptibility order parameter demonstrates that both cooperative heterogeneous nucleation and competitive dynamics regimes are inherent at avascular and vascular phases of this growth kinetics, respectively. It is concluded that entire unperturbed tumor growth kinetics is a step wise dynamics, multiscale and intrinsically fractal with multiple cooperative phase transitions. It is governed by heterogeneous nucleation, competition dynamic regimes and impingement mechanisms. These features may be considered as another potential cancer hallmark.