Related papers: Joint fitting reveals hidden interactions in tumor…

Tumors are defined by their intense proliferation, but sometimes cancer cells turn senescent and stop replicating. In the stochastic cancer model in which all cells are tumorigenic, senescence is seen as the result of random mutations,…

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.…

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…

Cancer stem cells have been shown to be critical to the development of a variety of solid cancers. The precise interplay mechanisms between cancer stem cells and the rest of a tissue are still not elucidated. To shed light on the…

Major efforts to sequence cancer genomes are now occurring throughout the world. Though the emerging data from these studies are illuminating, their reconciliation with epidemiologic and clinical observations poses a major challenge. In the…

Cancer cells are known to modify their micro-environment such that it can sustain a larger population, or, in ecological terms, they construct a niche which increases the carrying capacity of the population. It has however been argued that…

The interactions between tumor cells and the immune system play a crucial role in cancer evolution. In this study, we explore how these interactions influence cancer progression by modeling the relationships among naive T cells, effector T…

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…

A general model for the ontogenetic growth of living organisms has been recently proposed. Here we investigate the extension of this model to the growth of solid malignant tumors. A variety of in vitro and in vivo data are analyzed and…

Collective migration dominates many phenomena, from cell movement in living systems to abiotic self-propelling particles. Focusing on the early stages of tumor evolution, we enunciate the principles involved in cell dynamics and highlight…

In this work we present a flexible tool for tumor progression, which simulates the evolutionary dynamics of cancer. Tumor progression implements a multi-type branching process where the key parameters are the fitness landscape, the mutation…

It is proposed that cancer results from the breakdown of universal control mechanisms which developed in mutual association as part of the historical process that brought individual cells together into multi-cellular communities. By…

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…

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…

Stochastic resonance induced by external factor is considering to investigate the complex dynamics of tumor. The surrounding environment and the treatment effects on the tumor growth are considered as additive and multiplicative noises in…

A cell-molecular based evolutionary model of tumor development driven by a stochastic Moran birth-death process is developed, where each cell carries molecular information represented by a four-digit binary string, used to differentiate…

Phenotype variations define heterogeneity of biological and molecular systems, which play a crucial role in several mechanisms. Heterogeneity has been demonstrated in tumor cells. Here, samples from blood of patients affected from colon…

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…

Several mathematical models of tumor growth are now commonly used to explain medical observations and predict cancer evolution based on images. These models incorporate mechanical laws for tissue compression combined with rules for…