Related papers: A note on a multi-layer tumor growth model
We derive various novel free boundary problems as limits of a coupled bulk-surface reaction-diffusion system modelling ligand-receptor dynamics on evolving domains. These limiting free boundary problems may be formulated as Stefan-type…
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…
Background and Objective: In an in-vivo situation, the tissue near the blood vessels is rich in oxygen supply compared to the one far from blood vessels. Hence, non-uniform oxygen distribution is observed in biological tissues. Our…
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…
Tumor growth from a single transformed cancer cell up to a clinically apparent mass spans many spatial and temporal orders of magnitude. Implementation of cellular automata simulations of such tumor growth can be straightforward but…
In the present work, we develop a comprehensive and rigorous analytical framework for a non-local phase-field model that describes tumour growth dynamics. The model is derived by coupling a non-local Cahn-Hilliard equation with a parabolic…
We report on a simple model of spatial extend anti-tumor system with a fluctuation in growth rate, which can undergo a nonequilibrium phase transition. Three states as excited, sub-excited and non-excited states of a tumor are defined to…
Recently, we have proposed a nutrient-limited model for the avascular growth of tumors including cell proliferation, motility and death \cite{jr}, that, qualitatively reproduces commonly observed morphologies for carcinomas {\it in situ}.…
We consider a particular phase field system which physical context is that of tumor growth dynamics. The model we deal with consists of a Cahn-Hilliard type equation governing the evolution of the phase variable which takes into account the…
We investigate a new dynamical system that describes tumor-host interaction. The equation that describes the untreated tumor growth is based on non-extensive statistical mechanics. Recently, this model has been shown to fit successfully…
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…
In this work, we investigate a distributed optimal control problem for an extended phase field system of Cahn--Hilliard type which physical context is that of tumor growth dynamics. In a previous contribution, the author has already studied…
Mathematical and computational modelling in oncology has played an increasingly important role in not only understanding the impact of various approaches to treatment on tumour growth, but in optimizing dosing regimens and aiding the…
The physics of solid tumor growth can be considered at three distinct size scales: the tumor scale, the cell-extracellular matrix (ECM) scale and the sub-cellular scale. In this paper we consider the tumor scale in the interest of…
In this paper, we develop a sharp interface tumor growth model in two dimensions to study the effect of both the intratumoral structure using a controlled necrotic core and the extratumoral nutrient supply from vasculature on tumor…
We study a stochastic phase-field model for tumor growth dynamics coupling a stochastic Cahn-Hilliard equation for the tumor phase parameter with a stochastic reaction-diffusion equation governing the nutrient proportion. We prove strong…
In this work, we investigate the population dynamics of tumor cells under therapeutic pressure. Although drug treatment initially induces a reduction in tumor burden, treatment failure frequently occurs over time due to the emergence of…
We investigate a partial differential equation model of a cancer cell population, which is structured with respect to age and telomere length of cells. We assume a continuous telomere length structure, which is applicable to the clonal…
We consider a diffuse interface model for tumour growth consisting of a Cahn--Hilliard equation with source terms coupled to a reaction-diffusion equation. The coupled system of partial differential equations models a tumour growing in the…
The uncontrolled proliferation of cancer cells and their interaction with healthy tissue poses a major challenge in oncology. This manuscript develops and analyzes mathematical models that describe tumor response to radiotherapy by…