Related papers: Tumor boundary instability induced by nutrient con…
We investigate the large time behavior of an agent based model describing tumor growth. The microscopic model combines short-range repulsion and cell division. As the number of cells increases exponentially in time, the microscopic model is…
The influence of random fluctuations on the recruitment of effector cells towards a tumor is studied by means of a stochastic mathematical model. Aggressively growing tumors are confronted against varying intensities of the cell-mediated…
Understanding the untreated tumor growth kinetics and its intrinsic findings is interesting and intriguing. The aim of this study is to propose an approximate analytical expression that allows to simulate changes in surface charge density…
This paper is concerned with a multi-dimensional free boundary problem modeling the growth of a tumor with two species of cells: proliferating cells and quiescent cells. This free boundary problem has a unique radial stationary solution. By…
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…
The intratumor heterogeneity has been recognized to characterize cancer cells impairing the efficacy of cancer treatments. We here propose an extension of constraint-based modeling approach in order to simulate metabolism of cell…
At the continuous level, we consider two types of tumor growth models: the cell density model, which is based on the fluid mechanical construction, is more favorable for scientific interpretation and numerical simulations; and the free…
In this paper we study a free boundary problem for the growth of multi-layer tumors in necrotic phase. The tumor region is strip-like and divided into necrotic region and proliferating region with two free boundaries. The upper free…
Analysis of invasion front has been widely used to decipher biological properties, as well as the growth dynamics of the corresponding populations. Likewise, the invasion front of tumors has been investigated, from which insights into the…
We consider a non-local tumour growth model of phase-field type, describing the evolution of tumour cells through proliferation in presence of a nutrient. The model consists of a coupled system, incorporating a non-local Cahn-Hilliard…
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…
Radiation Therapy (XRT) is one of the most common cancer treatment methods. In this paper, a new mathematical model is proposed for the population dynamics of heterogeneous tumor cells following external beam radiation treatment. According…
I consider how cell shape and environmental geometry affect the rate of nutrient capture and the consequent maximum growth rate of a cell, focusing on rod-like species like \textit{E.\ coli}. Simple modeling immediately implies that it is…
We study an initial-boundary value problem (IBVP) for a coupled Cahn-Hilliard-Hele-Shaw system that models tumor growth. For large initial data with finite energy, we prove global (local resp.) existence, uniqueness, higher order spatial…
In this paper, we study a distributed optimal control problem for a diffuse interface model for tumor growth. The model consists of a Cahn-Hilliard type equation for the phase field variable coupled to a reaction diffusion equation for the…
The flow of the laminar boundary layer on a flat plate is studied with simulation of Navier-Stokes equations. The mechanisms of flow instability at external edge of the boundary layer and near the wall are analyzed using the energy gradient…
This paper investigates dynamic behaviors of the tumor-immune system perturbed by environmental noise. The model describes the response of the cytotoxic T lymphocyte (CTL) to the growth of an immunogenic tumour. The main methods are…
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 an optimal control problem for a stochastic model of tumour growth with drug application. This model consists of three stochastic hyperbolic equations describing the evolution of tumour cells. It also includes two stochastic…
In this paper, we address a distributed control problem for a system of partial differential equations describing the evolution of a tumor that takes the biological mechanism of chemotaxis into account. The system describing the evolution…