Related papers: Models, measurement and inference in epithelial ti…
We propose a multiscale model of the invasion of the extracellular matrix by two types of cancer cells, the differentiated cancer cells and the cancer stem cells. We assume that the epithelial mesenchymal-like transition between them is…
Multicellular tumor spheroids are an important {\it in vitro} model of the pre-vascular phase of solid tumors, for sizes well below the diagnostic limit: therefore a biophysical model of spheroids has the ability to shed light on the…
\emph{In vitro} experiments in which tumour cells are seeded in a gelatinous medium, or hydrogel, show how mechanical interactions between tumour cells and the tissue in which they are embedded, together with local levels of an…
Cancer, as the uncontrollable cell growth, is related to many branches of biology. In this review, we will discuss three mathematical approaches for studying cancer biology: population dynamics, gene regulation, and developmental biology.…
Comparing mathematical models offers a means to evaluate competing scientific theories. However, exact methods of model calibration are not applicable to many probabilistic models which simulate high-dimensional spatio-temporal data.…
This paper investigates cells proliferation dynamics in small tumor cell aggregates using an individual based model (IBM). The simulation model is designed to study the morphology of the cell population and of the cell lineages as well as…
Embryonic healing in epithelial tissues is distinct from adult wound healing, as it lacks inflammatory responses or immune cell recruitments, making it ideal to test models of wound healing driven primarily by epithelial dynamics. Many…
Inevitably, almost all cancer patients develop resistance to targeted therapy. Intratumor heterogeneity (ITH) is a major cause of drug resistance. Mathematical models that explain experiments quantitatively is useful in understanding the…
We investigate the dynamics of a nonlinear model for tumor growth within a cellular medium. In this setting the "tumor" is viewed as a multiphase flow consisting of cancerous cells in either proliferating phase or quiescent phase and a…
The transition from the epithelial to mesenchymal phenotype and its reverse (from mesenchymal to epithelial) are crucial processes necessary for the progression and spread of cancer. In this paper, we investigate how phenotypic switching at…
Survival of living tumor cells underlies many influences such as nutrient saturation, oxygen level, drug concentrations or mechanical forces. Data-supported mathematical modeling can be a powerful tool to get a better understanding of cell…
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…
In cancer, treatment failure and disease recurrence have been associated with small subpopulations of cancer cells with a stem-like phenotype. In this paper, we develop and investigate a phenotype-structured model of solid tumour growth in…
Environmental and genetic mutations can transform the cells in a co-operating healthy tissue into an ecosystem of individualistic tumour cells that compete for space and resources. Various selection forces are responsible for driving the…
The growth of cities has traditionally been studied from a population perspective, while urban expansion-its spatial growth-has often been approached qualitatively. However, characterizing and modeling this spatial expansion is crucial,…
Phase-field models of tumour growth have proved useful as theoretical tools to investigate cancer invasion. A key implicit assumption underlying mathematical models of this type which have so far been proposed, though, is that cells in the…
In this paper we study a tumor growth model with nutrients. The model presents dynamic patch solutions due to the contact inhibition among the tumor cells. We show that when the nutrients do not diffuse and the cells do not die, the tumor…
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…
A theoretical model for stratified epithelium is presented. The viscoelastic properties of the tissue is assumed to be dependent on the spatial distribution of proliferative and differentiated cells. Based on this assumption, a hydrodynamic…
Cellular signaling is essential in information processing and decision making. Therefore, a variety of experimental approaches have been developed to study signaling on bulk and single-cell level. Single-cell measurements of signaling…