Related papers: A level-set approach for a multi-scale cancer inva…
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.…
Cancer cell invasion is recognised as one of the hallmarks of cancer and involves several inner-related multiscale processes that ultimately contribute to its spread into the surrounding tissue. In order to gain a deeper understanding of…
We present multiscale models of cancer tumor invasion with components at the molecular, cellular, and tissue levels. We provide biological justifications for the model components, present computational results from the model, and discuss…
Local cancer cell invasion is a complex process involving many cellular and tissue interactions and is an important prerequisite for metastatic spread, the main cause of cancer related deaths. Occurring over many different temporal and…
We formulate a cell-scale model for the degradation of the extra-cellular matrix by membrane-bound and soluble matrix degrading enzymes produced by cancer cells. Based on the microscopic model and using tools from the theory of…
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…
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…
The dynamic interplay between collective cell movement and the various molecules involved in the accompanying cell signalling mechanisms plays a crucial role in many biological processes including normal tissue development and pathological…
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…
Local cancer invasion of tissue is a complex, multiscale process which plays an essential role in tumour progression. Occurring over many different temporal and spatial scales, the first stage of invasion is the secretion of matrix…
We analyse a novel mathematical model of malignant invasion which takes the form of a two-phase moving boundary problem describing the invasion of a population of malignant cells into a population of background tissue, such as skin. Cells…
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…
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…
Most biological tissues grow by the synthesis of new material close to the tissue's interface, where spatial interactions can exert strong geometric influences on the local rate of growth. These geometric influences may be mechanistic, or…
The ability to locally degrade the extracellular matrix (ECM) and interact with the tumour microenvironment is a key process distinguishing cancer from normal cells, and is a critical step in the metastatic spread of the tumour. The…
At the continuous level, we consider two types of tumor growth models: the cell density model, which is based on the fluid mechanical construction, is more favorable for scientific interpretation and numerical simulations; and the free…
This paper concerns a model for tumor cell migration through the surrounding extracellular matrix by considering mass balance phenomena involving the chemical interactions produced on the cell surface. The well-posedness of this model is…
Cancer invasion of the surrounding tissue is a multiscale process that involves not only tumour cells but also other immune cells in the environment, such as the tumour-associated macrophages (TAMs). The heterogeneity of these immune cells,…
Microscale oxygenation plays a prominent role in tumour progression. Spatiotemporal variability of oxygen distribution in the tumour microenvironment contributes to cellular heterogeneity and to the emergence of normoxic and hypoxic…
A major goal of modern computational biology is to simulate the collective behaviour of large cell populations starting from the intricate web of molecular interactions occurring at the microscopic level. In this paper we describe a…