Modeling of single cell cancer transformation using phase transition theory: application of the Avrami equation

The nucleation and growth theory, described by the Avrami equation (also called Johnson–Mehl–Avrami–Kolmogorov equation), and usually used to describe crystallization and nucleation processes in condensed matter physics, was applied in the present paper to cancer physics. This can enhance the popular multi-hit model of carcinogenesis to volumetric processes of single cell’s DNA neoplastic transformation. The presented approach assumes the transforming system as a DNA chain including many oncogenic mutations. Finally, the probability function of the cell’s cancer transformation is directly related to the number of oncogenic mutations. This creates a universal sigmoidal probability function of cancer transformation of single cells, as observed in the kinetics of nucleation and growth, a special case of a phase transition process. The proposed model, which represents a different view on the multi-hit carcinogenesis approach, is tested on clinical data concerning gastric cancer. The results also show that cancer transformation follows DNA fractal geometry.