The dynamics of tumorgrowth and cells pattern morphology - Elena Izquierdo-Kulich; Margarita Amigó de Quesada; Carlos Manuel Pérez-Amor; Magda Lopes Texeira; José Manuel Nieto-Villar (Mathematical Biosciences and Engineering)
The mathematical modeling of tumor growth is an approach to explain thecomplex nature of these systems. A model that describes tumor growth wasobtained by using a mesoscopic formalism and fractal dimension. This modeltheoretically predicts the relation between the morphology of the cellpattern and the mitosis/apoptosis quotient that helps to predict tumorgrowth from tumoral cells fractal dimension. The relation between the tumormacroscopic morphology and the cell pattern morphology is also determined.This could explain why the interface fractal dimension decreases with theincrease of the cell pattern fractal dimension and consequently with theincrease of the mitosis/apoptosis relation. Indexes to characterize tumoralcell proliferation and invasion capacities are proposed and used to predictthe growth of different types of tumors. These indexes also show that theproliferation capacity is directly proportional to the invasion capacity.The proposed model assumes: i) only interface cells proliferate and invadethe host, and ii) the fractal dimension of tumoral cell patterns, canreproduce the Gompertzian growth law.