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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…
Employing a novel two-dimensional computational model we have simulated the feedback between angiogenesis and tumor growth dynamics. Analyzing vessel formation and elongation towards the concentration gradient of the tumor-derived…
Objective: Alterations of Young's modulus (YM) and Poisson's ratio (PR) in biological tissues are often early indicators of the onset of pathological conditions. Knowledge of these parameters has been proven to be of great clinical…
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…
Unstable dynamics characterizes the evolution of most solid tumors. Because of an increased failure of maintaining genome integrity, a cumulative increase in the levels of gene mutation and loss is observed. Previous work suggests that…
In solid tumors, cells constantly interact with the surrounding extracellular matrix. In particular cancer-associated fibroblasts modulate the architecture of the matrix by exerting forces and contracting collagen fibres, creating paths…
Several mathematical models of tumor growth are now commonly used to explain medical observations and predict cancer evolution based on images. These models incorporate mechanical laws for tissue compression combined with rules for…
Acidosis in tumors arises from reprogrammed metabolism and compromised vasculature, creating a harsh, acidic microenvironment that drives the evolutionary selection of acid-resistant cell phenotypes. A mathematical model is proposed to…
In this paper, we investigate a class of tumor growth models governed by porous medium-type equations with uncertainties arisen from the growth function, initial condition, tumor support radius or other parameters in the model. We develop a…
Growing experimental evidence highlights the relevant role of mechanics in the physiology of solid tumours, even in their early stages. While most of the mathematical models describe tumour growth as a volumetric increase of mass in the…
Tumor growth is a complex process characterized by uncontrolled cell proliferation and invasion of neighboring tissues. The understanding of these phenomena is of vital importance to establish appropriate diagnosis and therapeutic strategy…
We studied the effects of epidermal growth factor receptor (EGFR) density on tumor growth dynamics, both on the sub- and the multi-cellular level using our previously developed model. This algorithm simulates the growth of a brain tumor…
We developed a mathematical model to simulate the growth of tumor volume and its response to a single fraction of high dose irradiation. We made several key assumptions of the model. Tumor volume is composed of proliferating (or dividing)…
A limited mobility nonequilibrium solid-on-solid dynamical model for kinetic surface growth is introduced as a simple description for the morphological evolution of a growing interface under random vapor deposition and surface diffusion…
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…
The majority of solid tumours arise in epithelia and therefore much research effort has gone into investigating the growth, renewal and regulation of these tissues. Here we review different mathematical and computational approaches that…
In this manuscript, we study a nonlinear model of tumor growth, described by a coupled hyperbolic-elliptic system of partial differential equations. In this model, the compressible flow of tumor cells is modeled by a transport equation for…
Cancer is a disease that takes millions of lives every year. Then, to propose treatments, avoid recurrence, and improve the patient's life quality, we need to analyze this disease from a biophysical perspective with a solid mathematical…
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…
The work presents a study of the non-linear mathematical model of tumor growth, proposed by Kolev and Zubik-Kowal (2011). The model is described by a system composed of four partial differential equations that represent the evolution of the…