相关论文: Necrotic tumor growth: an analytic approach

In this paper, we studied phase-space analysis of a certain mathematical model of tumor growth with an immune responses and chemotherapy therapy. Mathematical modelling of this process is viewed as a potentially powerful tool in the…

During the last decades, medical observations and multiscale data concerning tumor growth are mounting. At the same time, contemporary imaging techniques well established in clinical practice, provide a variety of information on real-time,…

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…

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…

In this paper, we investigate the tumor instability by employing both analytical and numerical techniques to validate previous results and extend the analytical findings presented in a prior study by Feng et al 2023. Building upon the…

We consider weak solutions to a problem modeling tumor growth. Under certain conditions on the initial data, solutions can be obtained by passing to the stiff (incompressible) limit in a porous medium type problem with a Lotka-Volterra…

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…

This paper provides a unified mathematical analysis of a family of non-local diffuse interface models for tumor growth describing evolutions driven by long-range interactions. These integro-partial differential equations model cell-to-cell…

Background: Radiotherapy outcomes are usually predicted using the Linear Quadratic model. However, this model does not integrate complex features of tumor growth, in particular cell cycle regulation. Methods: In this paper, we propose a…

We study a free boundary problem modeling tumor growth with a T-periodic supply $\Phi(t)$ of external nutrients. The model contains two parameters $\mu$ and $\widetilde{\sigma}$. We first show that (i) zero radially symmetric solution is…

In this paper we analyse a differential system related to a Glioblastoma growth. Using numerical simulations, we prove that model captures different kind of growth changing adequately the parameters of the model. Firstly, we make an…

We prove an existence result for a free boundary problem inspired by the modelization of accretive growth. The growth process is formulated through a level-set approach, leading to a boundary-value problem for a Hamilton-Jacobi equation…

We briefly review the properties of radially growing interfaces and their connection to biological growth. We focus on simplified models which result from the abstraction of only considering domain growth and not the interface curvature.…

Initiation and development of a malignant tumor is a complex phenomenon that has critical stages determining its long time behavior. This phenomenon is mathematically described by means of various models: from simple heuristic models to…

We study the spatial evolutionary dynamics of solid tumors as they obtain additional driver mutations. We start with a cancer clone that expands uniformly in three dimensions giving rise to a spherical shape. We assume that cell division…

We introduce a free boundary model to example the effect of vesicle transport onto neurite growth. It consists of systems of drift-diffusion equations describing the evolution of the density of antero- and retrograde vesicles in each…

We consider a class of stochastic partial differential equations arising as a model for amorphous thin film growth. Using a spectral Galerkin method, we verify the existence of stationary mild solutions, although the specific nature of the…

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…

This paper deals with some mathematical models arising in the theory of epitaxial growth of crystal. We focalize the study on a stationary problem which presents some analytical difficulties. We study the existence of solutions. The central…

Williams and Bjerknes proposed a simple stochastic growth model to describe the tumor growth in the basal layer of an epithelium. In this work we generalize this model by including the possibility of saturation in the tumor growth as it is…