相关论文: The model muddle: in search of tumour growth laws

Most human tumors result from the accumulation of multiple genetic and epigenetic alterations in a single cell. Mutations that confer a fitness advantage to the cell are known as driver mutations and are causally related to tumorigenesis.…

Despite internal complexity, tumor growth kinetics follow relatively simple macroscopic laws that have been quantified by mathematical models. To resolve this further, quantitative and discriminant analyses were performed for the purpose of…

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…

Mechanical models for tumor growth have been used extensively in recent years for the analysis of medical observations and for the prediction of cancer evolution based on imaging analysis. This work deals with the numerical approximation of…

We develop a field theory-inspired stochastic model for description of tumour growth based on an analogy with an SI epidemic model, where the susceptible individuals (S) would represent the healthy cells and the infected ones (I), the…

In this paper, a two-dimensional model for the growth of multi-layer tumors is presented. The model consists of a free boundary problem for the tumor cell membrane and the tumor is supposed to grow or shrink due to cell proliferation or…

In this study, we model avascular tumour growth in epithelial tissue. This can help us to get a macroscopic view of the interaction between the tumour with its surrounding microenvironment and the physical changes within the tumour…

In this paper we present a method for estimating unknown parameters that appear on an avascular, spheric tumour growth model. The model for the tumour is based on nutrient driven growth of a continuum of live cells, whose birth and death…

Mathematical modelling of tumor growth is one of the most useful and inexpensive approaches to determine and predict the stage, size and progression of tumors in realistic geometries. Moreover, these models has been used to get an insight…

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…

Cancer is a very complex phenomenon that involves many different scales and situations. In this paper we consider a free boundary problem describing the evolution of a tumor colony and we derive a new asymptotic model for tumor growth. We…

Using formal asymptotic methods we derive a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour or other biological tissue. The mathematical model takes the form of a closed…

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…

In this paper a macroscopic model of tumor cord growth is developed, relying on the mathematical theory of deformable porous media. Tumor is modeled as a saturated mixture of proliferating cells, extracellular fluid and extracellular…

The dynamics of tumour evolution are not well understood. In this paper we provide a statistical framework for evaluating the molecular variation observed in different parts of a colorectal tumour. A multi-sample version of the Ewens…

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…

We consider a one--spatial dimensional tumour growth model [2, 3, 4] that consists of three dependent variables of space and time: volume fraction of tumour cells, velocity of tumour cells, and nutrient concentration. The model variables…

We investigate the dynamics of a nonlinear model for tumor growth within a cellular medium. In this setting the "tumor" is viewed as a multiphase flow consisting of cancerous cells in either proliferating phase or quiescent phase and a…

A mathematical model of infiltrative tumour growth taking into account cell proliferation, death and motility is considered. The model is formulated in terms of local cell density and nutrient (oxygen) concentration. In the model the rate…

Tumour cells have to acquire a number of capabilities if a neoplasm is to become a cancer. One of these key capabilities is increased motility which is needed for invasion of other tissues and metastasis. This paper presents a qualitative…