The main mechanisms that control the organization of multicellular tissues are still largely open. A commonly used tool to study basic control mechanisms are in vitro experiments in which the growth conditions can be widely varied. However, even in vitro experiments are not free from unknown or...

Cancer development can be viewed as an example of spatio-temporal pattern formation. Several attempts have been made to model and predict malignant tumor behavior and also to account for immune system response and the impact of possible clinical treatments. Modeling started from a macroscopic...

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...