Related papers: Does tumor growth follow a 'universal law'?
We argue that volumetric growth dynamics of a solid cancer depend on the tumor system's overall surface extension. While this at first may seem evident, to our knowledge, so far no theoretical argument has been presented explaining this…
In this article we shall trace the historical development of tumour growth laws, which in a quantitative fashion describe the increase in tumour mass/volume over time. These models are usually formulated in terms of differential equations…
Most physical and other natural systems are complex entities composed of a large number of interacting individual elements. It is a surprising fact that they often obey the so-called scaling laws relating an observable quantity with a…
Comparing both, the more conventional Gompertz tumor growth law (GL) and the ``Universal'' law (UL), recently proposed and applied to cancer,we have investigated the growth law's implications on various radiotherapy regimen. According to…
In this survey article, a variety of systems modeling tumor growth are discussed. In accordance with the hallmarks of cancer, the described models incorporate the primary characteristics of cancer evolution. Specifically, we focus on…
We have previously reported that a 'universal' growth law with fixed scaling exponent p, as proposed by West and collaborators for all living organisms, appears to be able to describe also the growth of tumors in vivo. Here, we investigate…
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…
We examine a lattice model of tumor growth where survival of tumor cells depends on the supplied nutrients. When such a supply is random, the extinction of tumors belongs to the directed percolation universality class. However, when the…
We investigate the dynamics of a nonlinear system modeling tumor growth with drug application. The tumor is viewed as a mixture consisting of proliferating, quiescent and dead cells as well as a nutrient in the presence of a drug. The…
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…
We propose a model for describing the growth on an untreated tumor, which is characterized in a simple way by a minimal number of parameters with a well-defined physical interpretation. The model is motivated by invoking the Master Equation…
Tumor growth has a number of features in common with a physical process known as molecular beam epitaxy. Both growth processes are characterized by the constraint of growth development to the body border, and surface diffusion of…
We investigate the evolution of tumor growth relying on a nonlinear model of partial differential equations which incorporates mechanical laws for tissue compression combined with rules for nutrients availability and drug application.…
We have previously reported that a universal growth law, as proposed by West and collaborators for all living organisms, appears to be able to describe also the growth of tumors in vivo. In contrast to the assumption of a fixed power…
Using our previously developed model we demonstrate here, that (1) solid tumor growth and cell invasion are linked, not only qualitatively but also quantitatively, that (2) the onset of invasion marks the time point when the tumor cell…
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…
Strong experimental evidence has indicated that tumor growth belongs to the molecular beam epitaxy universality class. This type of growth is characterized by the constraint of cell proliferation to the tumor border, and surface diffusion…
Integrating experimental data into ecological models plays a central role in understanding biological mechanisms that drive tumor progression where such knowledge can be used to develop new therapeutic strategies. While the current studies…
Determining the mathematical dynamics and associated parameter values that should be used to accurately reflect tumor growth continues to be of interest to mathematical modelers, experimentalists and practitioners. However, while there are…
In this paper we present a study of local dynamics of the growth of cancer tumor and healthy cells considering the presence of nutrients in the system. We also analyze the evolution of system if we take indirectly into account the level of…