Williams and Bjerknes proposed a simple stochastic growth model to describe the tumor growth in the basal layer of an epithelium. In this work we generalize this model by including the possibility of saturation in the tumor growth as it is clinically observed. The time evolution of the average...

Starting from theoretical results that we recently obtained in the field of rational thermodynamics, we develop a mathematical analysis of the dynamics of tumor interaction with the host immune system within the framework of a statistical cell model firstly proposed by Bellomo and Forni. A...

We demonstrate the power of genetic algorithms to construct a cellular automata model simulating the growth of 2D close-to-circular clusters, revealing the desired properties, such as the growth rate and, at the same time, the fractal behavior of their contours. The possible application of the...

Tumor growth has long been a target of investigation within the context of mathematical and computer modeling. The objective of this study is to propose and analyze a two-dimensional stochastic cellular automata model to describe avascular solid tumor growth, taking into account both the...

A new method, based on scaling analysis, is used to calculate fractal dimension and local roughness exponents to characterize in vivo 3-D tumor growth in the brain. Image acquisition was made according to the standard protocol used for brain radiotherapy and radiosurgery, i.e., axial, coronal...

All kinds of hypotheses have been proposed to explain the mechanism of tumorigenesis. Up until now, we have not had any generally acknowledged model that helps us understand the process. However, it is well accepted that cancer development and progression is dictated by a series of alterations...

We study the statistical properties of the star-shaped approximation of in vitro tumor profiles. The emphasis is on the two-point correlation structure of the radii of the tumor as a function of time and angle. In particular, we show that spatial two-point correlators follow a cosine law....

We propose a new model of cancer growth based on nonextensive entropy. The evolution equation depends on the nonextensive parameter q. The exponential, the logistic, and the Gompertz growth laws are particular cases of the generalized model. Experimental data of different tumors have been shown...

Most chemotherapeutic treatments use drugs that target proliferating cancer cells. Therefore, they do not affect quiescent cells which are naturally resistant. Surviving cancer cells can reactivate their cell cycles in the intervals between doses, becoming proliferative again and thus restarting...

A macroscopic approach to the tumor Gompertzian growth is proposed and successfully applied to the multicellular tumor spheroid data. It is based on the energetic balance among the different cell activities, related to the growth inhibitor factors. The main results can also be described by...