相关论文: On a phenotype-structured phase-field model of nut…

We present a mathematical model that describes how tumour heterogeneity evolves in a tissue slice that is oxygenated by a single blood vessel. Phenotype is identified with the stemness level of a cell, $s$, that determines its proliferative…

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 present a mathematical study of the emergence of phenotypic heterogeneity in vascularised tumours. Our study is based on formal asymptotic analysis and numerical simulations of a system of non-local parabolic equations that describes the…

We consider a phenotype-structured reaction-diffusion model of avascular glioma growth. The model describes the interaction dynamics between tumour cells and oxygen, and takes into account anisotropic cell movement and oxygen diffusion…

In cancer, treatment failure and disease recurrence have been associated with small subpopulations of cancer cells with a stem-like phenotype. In this paper, we develop and investigate a phenotype-structured model of solid tumour growth in…

We consider a mathematical model for the evolutionary dynamics of tumour cells in vascularised tumours under chemotherapy. The model comprises a system of coupled partial integro-differential equations for the phenotypic distribution of…

Since the discovery of a cancer initiating side population in solid tumours, studies focussing on the role of so-called cancer stem cells in cancer initiation and progression have abounded. The biological interrogation of these cells has…

The transition from the epithelial to mesenchymal phenotype and its reverse (from mesenchymal to epithelial) are crucial processes necessary for the progression and spread of cancer. In this paper, we investigate how phenotypic switching at…

We introduce a new diffuse interface model for tumour growth in the presence of a nutrient, in which we take into account mechanical effects and reversible tissue damage. The highly nonlinear PDEs system mainly consists of a Cahn-Hilliard…

The phenotypic equilibrium, i.e. heterogeneous population of cancer cells tending to a fixed equilibrium of phenotypic proportions, has received much attention in cancer biology very recently. In previous literature, some theoretical models…

Tumour progression has been described as a sequence of traits or phenotypes that cells have to acquire if the neoplasm is to become an invasive and malignant cancer. Although the genetic mutations that lead to these phenotypes are random,…

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 tumor can be thought of as an ecosystem, which critically means that we cannot just consider it as a collection of mutated cells but more as a complex system of many interacting cellular and microenvironmental elements. At its simplest, 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…

This paper concerns multiphase models of tumor growth in interaction with a surrounding tissue, taking into account also the interplay with diffusible nutrients feeding the cells. Models specialize in nonlinear systems of possibly…

In a previous paper we have introduced a phenomenological model of cell metabolism and of the cell cycle to simulate the behavior of large tumor cell populations (Chignola R and Milotti E, Phys. Biol. 2 (2005) 8-22). Here we describe a…

In this work, we present a phase-field model for tumour growth, where a diffuse interface separates a tumour from the surrounding host tissue. In our model, we consider transport processes by an internal, non-solenoidal velocity field. We…

Melanoma is an aggressive form of skin cancer. Survival rates are excellent if it is detected early but fall markedly if it metastasises. A key step in early tumour progression is the formation of cell clusters, which can promote…

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…

Collective cell migration plays a crucial role in numerous biological processes, including tumour growth, wound healing, and the immune response. Often, the migrating population consists of cells with various different phenotypes. This…