Related papers: A Single Equation Explains Go-or-Grow Dynamics in …
We consider a minimal go-or-grow model of cell invasion, whereby cells can either proliferate, following logistic growth, or move, via linear diffusion, and phenotypic switching between these two states is density-dependent. Formal analysis…
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…
Tumor cells develop different features to adapt to environmental conditions. A prominent example is the ability of tumor cells to switch between migratory and proliferative phenotypes, a phenomenon known as go-or-grow mechanism. It is…
In the study of cancer evolution and therapeutic strategies, scientific evidence shows that a key dynamics lies in the tumor-environment interaction. In particular, oxygen concentration plays a central role in the determination of the…
We propose and study a strongly coupled PDE-ODE-ODE system modeling cancer cell invasion through a tissue network under the go-or-grow hypothesis asserting that cancer cells can either move or proliferate. Hence our setting features two…
A fundamental feature of collective cell migration is phenotypic heterogeneity which, for example, influences tumour progression and relapse. While current mathematical models often consider discrete phenotypic structuring of the cell…
In this thesis we develop minimal models of the relationship between motility, growth, and evolution of cancer cells. We utilise simple simulations of a population of individual cells in space to examine how changes in mechanical properties…
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…
We consider a mathematical model for the evolutionary dynamics of tumour cells in vascularised tumours under chemotherapy. The model comprises a system of coupled partial integro-differential equations for the phenotypic distribution of…
Go-or-grow approaches represent a specific class of mathematical models used to describe populations where individuals either migrate or reproduce, but not both simultaneously. These models have a wide range of applications in biology and…
We provide a short review of existing models with multiple taxis performed by (at least) one species and consider a new mathematical model for tumor invasion featuring two mutually exclusive cell phenotypes (migrating and proliferating).…
Existing studies comparing individual-based models of growing cell populations and their continuum counterparts have mainly focused on homogeneous populations, in which all cells have the same phenotypic characteristics. However,…
Hypoxia and acidity act as environmental stressors promoting selection for cancer cells with a more aggressive phenotype. As a result, a deeper theoretical understanding of the spatio-temporal processes that drive the adaptation of tumour…
Recent evidence suggests that nongenetic (epigenetic) mechanisms play an important role at all stages of cancer evolution. In many cancers, these mechanisms have been observed to induce dynamic switching between two or more cell states,…
We consider the mean-field approximation of an individual-based model describing cell motility and proliferation, which incorporates the volume exclusion principle, the go-or-grow hypothesis and an explicit cell cycle delay. To utilise the…
In the study of therapeutic strategies for the treatment of cancer, eco-evolutionary dynamics are of particular interest, since characteristics of the tumour population, interaction with the environment and effects of the treatment,…
In this paper we study a reduced continuous model describing the local evolution of high grade gliomas - a lethal type of primary brain tumor - through the interplay of different cellular phenotypes. We show how hypoxic events, even…
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…
Tumor cell migration within the microenvironment is a crucial aspect for cancer progression and, in this context, hypoxia has a significant role. An inadequate oxygen supply acts as an environmental stressor inducing migratory bias and…
We propose a two-component reaction-transport model for the migration-proliferation dichotomy in the spreading of tumor cells. By using a continuous time random walk (CTRW) we formulate a system of the balance equations for the cancer cells…