Related papers: Initial/boundary-value problems of tumor growth wi…
Models of tumor growth, now commonly used, present several levels of complexity, both in terms of the biomedical ingredients and the mathematical description. The simplest ones contain competition for space using purely fluid mechanical…
Tumor growth beyond a critical size relies on the development of a functional vascular network, which ensures adequate oxygen and nutrient supply. In this work, we present a modeling framework based on an optimization-based 3D-1D coupling…
Primary tumors often emerge within genetically altered fields of premalignant cells that appear histologically normal but have a high chance of progression to malignancy. Clinical observations have suggested that these premalignant fields…
We consider a coupled bulk-surface system of partial differential equations with nonlinear coupling modelling receptor-ligand dynamics. The model arises as a simplification of a mathematical model for the reaction between cell surface…
Motivated by a mathematical model for the transport of morphogenes in biological systems, we study existence and uniqueness of entropy solutions for a mixed initial-boundary value problem associated with a nonlinear flux--limited diffusion…
Development of resistance limits efficiency of present anticancer therapies and preventing it remains big challenge in cancer research. It is accepted, at intuitive level, that the resistance emerges as a consequence of cancer cells…
The well known nonlinear model for describing the solid tumour growth [Byrne HM., et al. Appl Math Letters 2003;16:567-74] is under study using an approach based on Lie symmetries. It is shown that the model in the two-dimensional (in…
Brain-related experiments are limited by nature, and so biological insights are often restricted or absent. This is particularly problematic in the context of brain cancers, which have very poor survival rates. To generate and test new…
The transformation of the regular vasculature in normal tissue into a highly inhomogeneous tumor specific capillary network is described by a theoretical model incorporating tumor growth, vessel cooption, neo-vascularization, vessel…
In this paper, we derive an effective macroscale description suitable to describe the growth of biological tissue within a porous tissue-engineering scaffold. As in our recent work (Holden \textit{et al.} "A multiphase multiscale model for…
In the present review, we describe three hot topics in cancer research such as circulating tumor cells, exosomes, and 3D environment models. The first section is dedicated to microfluidic platforms for detecting circulating tumor cells,…
Central to the quest for a deeper understanding of the cancer growth and spread process, the naturally multiscale character of cancer invasion demands appropriate multiscale modelling and analysis approach. The cross-talk between the tissue…
This study presents a mathematical model formulated as a system of first-order non-linear ordinary differential equations, aimed at examining the effects of different factors, classified as local and systemic factors on a wound healing…
We present a mathematical model that describes how tumour heterogeneity evolves in a tissue slice that is oxygenated by a single blood vessel. Phenotype is identified with the stemness level of a cell, $s$, that determines its proliferative…
A mathematical model of infiltrative tumour growth taking into account cell proliferation, death and motility is considered. The model is formulated in terms of local cell density and nutrient (oxygen) concentration. In the model the rate…
The aim of this work is studding the behavior of solutions of initial boundary problem for degenerated nonlinear parabolic equation of the second order, conditions of existence and non-existence in whole by time solutions, is establish.
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 study a mathematical model for the growth of nonnecrotic solid tumor. The tumor is assumed to be radially symmetric and its radius R(t) is an unknown function of time t as tumor growth, and the model is in the form of a…
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…
The aim of this paper is to draw attention to an interesting semilinear parabolic equation that arose when describing the chaotic dynamics of a polymer molecule in a liquid. This equation is nonlocal in time and contains a term, called the…