相关论文: A Three-dimensional tumor growth model and its bou…

We consider a biphasic continuum model for avascular tumour growth in two spatial dimensions, in which a cell phase and a fluid phase follow conservation of mass and momentum. A limiting nutrient that follows a diffusion process controls…

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…

In this paper, we consider a 3-dimensional free boundary problem modeling tumor growth with the Robin boundary condition. The system involves a positive parameter $\mu$ which reflects the intensity of tumor aggressiveness. Huang, Zhang and…

In this paper, we develop a sharp interface tumor growth model to study the effect of the tumor microenvironment using a complex far-field geometry that mimics a heterogeneous distribution of vasculature. Together with different nutrient…

In the present article the diffusion equation is used to model the spatio-temporal dynamics of a tumor, taking into account the heterogeneous of the medium. This approach makes it possible to take into account the complex geometric shape of…

In this paper, we use the Bayesian inversion approach to study the data assimilation problem for a family of tumor growth models described by porous-medium type equations. The models contain uncertain parameters and are indexed by a…

Tumor growth has long been a target of investigation within the context of mathematical and computer modelling. The objective of this study is to propose and analyze a two-dimensional probabilistic cellular automata model to describe…

This paper studies asymptotic behavior of solutions of a free boundary problem modeling the growth of tumors with two species of cells: proliferating cells and quiecent cells. In previous literatures it has been proved that this problem has…

Understanding the dynamics of brain tumor progression is essential for optimal treatment planning. Cast in a mathematical formulation, it is typically viewed as evaluation of a system of partial differential equations, wherein the…

In this paper we deal with a free boundary problem modeling the growth of nonnecrotic tumors.The tumor is treated as an incompressible fluid, the tissue elasticity is neglected and no chemical inhibitor species are present. We re-express…

We derive a course grained, continuum model of the 2D vertex model, applicable for different underlying geometries, and allowing for analytical analysis of an otherwise numerical model. Using a geometric approach and out--of--equilibrium…

We consider a diffuse interface model for tumor growth recently proposed in [Y. Chen, S.M. Wise, V.B. Shenoy, J.S. Lowengrub, A stable scheme for a nonlinear, multiphase tumor growth model with an elastic membrane, Int. J. Numer. Methods…

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…

We develop an existence and regularity theory for solutions to a geometric free boundary problem motivated by models of tumor growth. In this setting, the tumor invades an accessible region $D$, its motion is directed along a constant…

Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which 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…

For tumor growth, the morphological instability provides a mechanism for invasion via tumor fingering and fragmentation. This work considers the asymptotic stability of a free boundary tumor model with a periodic supply of external…

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…

We study a free boundary problem modelling the growth of non-necrotic tumors with fluid-like tissues. The fluid velocity satisfies Stokes equations with a source determined by the proliferation rate of tumor cells which depends on the…

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.…