Related papers: Interface Dynamics in a Two-phase Tumor Growth Mod…
A novel numerical technique has been proposed to solve a two-phase tumour growth model in one spatial dimension without needing to account for the boundary dynamics explicitly. The equivalence to the standard definition of a weak solution…
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…
The stochastic discrete space-time model of an immune response on tumor spreading in a two-dimensional square lattice has been developed. The immunity-tumor interactions are described at the cellular level and then transferred into the…
We propose a strange-attractor model of tumor growth and metastasis. It is a 4-dimensional spatio-temporal cancer model with strong nonlinear couplings. Even the same type of tumor is different in every patient both in size and appearance,…
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…
We propose a model for describing the growth on an untreated tumor, which is characterized in a simple way by a minimal number of parameters with a well-defined physical interpretation. The model is motivated by invoking the Master Equation…
In this work, we present and analyze a mathematical model for tumor growth incorporating ECM erosion, interstitial flow, and the effect of vascular flow and nutrient transport. The model is of phase-field or diffused-interface type in which…
The comprehension of tumor growth is a intriguing subject for scientists. New researches has been constantly required to better understand the complexity of this phenomenon. In this paper, we pursue a physical description that account for…
We study a non-local variant of a diffuse interface model proposed by Hawkins--Darrud et al. (2012) for tumour growth in the presence of a chemical species acting as nutrient. The system consists of a Cahn--Hilliard equation coupled to a…
We present a multiphase mathematical model for tumor growth which incorporates the remodeling of the extracellular matrix and describes the formation of fibrotic tissue by tumor cells. We also detail a full qualitative analysis of the…
We consider two minimal mathematical models for cancer dynamics and self-adaptation. We aim to capture the interplay between the rapid progression of cancer growth and the possibility to leverage and enhance self-adaptive defense mechanisms…
Motivated by the incompressible limit of a cell density model, we propose a free boundary tumor growth model where the pressure satisfies an obstacle problem on an evolving domain $\Omega(t)$, and the coincidence set $\Lambda(t)$ captures…
Percolation theory from statistical physics has been applied to several aspects of tumor progression. Tumor growth on percolation clusters has been used to model spatial expansion, vascular percolation to describe nutrient supply and…
We consider a diffuse interface model of tumor growth proposed by A.~Hawkins-Daruud et al. This model consists of the Cahn-Hilliard equation for the tumor cell fraction $\varphi$ nonlinearly coupled with a reaction-diffusion equation for…
In the present article we demonstrate a new hybrid model of tumor growth. Our model is stochastic by tumor population development and strongly deterministic in cell motility dynamics and spatial propagation. In addition, it has excellent…
We consider the asymptotic limit of a diffuse interface model for tumor-growth when a parameter $\varepsilon$ proportional to the thickness of the diffuse interface goes to zero. An approximate solution which shows explicitly the behavior…
In this paper we study the growth of a tumor colony of multilayer type and focus on how the tumor grows from a near flat (when compared to the length of the tumor as, for instance, in the case of a bone tumor in a femur) initial colony. In…
Various models of tumor growth are available in the litterature. A first class describes the evolution of the cell number density when considered as a continuous visco-elastic material with growth. A second class, describes the tumor as a…
Known as one of the hallmarks of cancer [30], cancer cell invasion of human body tissue is a complicated spatio-temporal multiscale process which enables a localised solid tumour to transform into a systemic, metastatic and fatal disease.…
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…