Does Cancer Growth Depend on Surface Extension?

We investigate a new dynamical system that describes tumor-host interaction. The equation that describes the untreated tumor growth is based on non-extensive statistical mechanics. Recently, this model has been shown to fit successfully exponential, Gompertz, logistic, and power-law tumor growths. We have been able to include as many hallmarks of cancer as possible. We study also the dynamic response of cancer under therapy. Using our model, we can make predictions about the ...

Understanding the untreated tumor growth kinetics and its intrinsic findings is interesting and intriguing. The aim of this study is to propose an approximate analytical expression that allows to simulate changes in surface charge density changes at cancer-surrounding healthy tissue interface during the untreated solid tumor growth. For this, the Gompertz and Poisson equations are used. Simulations reveal that the unperturbed solid tumor growth is closely related to changes i...

A small but growing number of people are finding interesting parallels between ecosystems as studied by ecologists (think of a Savanna or the Amazon rain forest or a Coral reef) and tumours1-3. The idea of viewing cancer from an ecological perspective has many implications but fundamentally, it means that we should not see cancer just as a group of mutated cells. A more useful definition of cancer is to consider it a disruption in the complex balance of many interacting cellu...

The problem of the onset and growth of solid tumour in homogeneous tissue is regarded using an approach based on local interaction between the tumoral and the sane tissue cells. The characteristic sizes and growth rates of spherical tumours, the points of the beginning and the end of spherical growth, and the further development of complex structures (elongated outgrowths, dendritic structures, and metastases) are derived from the assumption that the reproduction rate of a po...

Cancer is a disease that takes millions of lives every year. Then, to propose treatments, avoid recurrence, and improve the patient's life quality, we need to analyze this disease from a biophysical perspective with a solid mathematical formulation. In this paper we introduce a novel deterministic model for the evolution of tumors under several conditions (untreated tumors and treated tumors using chemotherapy). Our model is characterized by a second-order differential equati...

A nutrient-limited model for avascular cancer growth including cell proliferation, motility and death is presented. The model qualitatively reproduces commonly observed morphologies for primary tumors, and the simulated patterns are characterized by its gyration radius, total number of cancer cells, and number of cells on tumor periphery. These very distinct morphological patterns follow Gompertz growth curves, but exhibit different scaling laws for their surfaces. Also, the ...

In this paper we study and extend the mechanistic mean field theory of growth of cellular populations proposed by Mombach et al in (Mombach J. C. M. et al., Europhysics Letter, 59 (2002) 923) (MLBI model), and we demonstrate that the original model and our generalizations lead to inferences of biological interest. In the first part of this paper, we show that the model in study is widely general since it admits, as particular cases, the main phenomenological models of cellula...

The majority of solid tumours arise in epithelia and therefore much research effort has gone into investigating the growth, renewal and regulation of these tissues. Here we review different mathematical and computational approaches that have been used to model epithelia. We compare different models and describe future challenges that need to be overcome in order to fully exploit new data which present, for the first time, the real possibility for detailed model validation and...

The comprehension of tumor growth is a intriguing subject for scientists. New researches has been constantly required to better understand the complexity of this phenomenon. In this paper, we pursue a physical description that account for some experimental facts involving avascular tumor growth. We have proposed an explanation of some phenomenological (macroscopic) aspects of tumor, as the spatial form and the way it growths, from a individual-level (microscopic) formulation....

Tumor growth is a complex process characterized by uncontrolled cell proliferation and invasion of neighboring tissues. The understanding of these phenomena is of vital importance to establish appropriate diagnosis and therapeutic strategy and starts with the evaluation of their complexity with suitable descriptors, such as those produced by scaling analysis. In the present work, scaling analysis is used for the extraction of dynamic parameters that characterize tumor growth ...