We simulate the growth of a benign avascular tumour embedded in normal tissue, including
cell sorting that occurs between tumour and normal cells, due to the variation of adhesion …

In this paper, we develop a simple mathematical model of the vascularization and
subsequent growth of a solid spherical tumour. The key elements that are encapsulated in …

We consider the dynamic growth of a tumour, concentrating on the possible development of
a necrotic region and examine some simple tumour geometries in detail. The growth and …

The structure and function of biological systems are considered to be closely related. The
present study addresses the question of how histological patterns of tumours are related to …

A nutrient-limited model for avascular cancer growth including cell proliferation, motility, and
death is presented. The model qualitatively reproduces commonly observed morphologies …

In this paper, a mathematical model is presented to describe the evolution of an avascular
solid tumour in response to an externally-supplied nutrient. The growth of the tumour …

During the initial avascular phase of solid tumour growth, it is the balance between cell
proliferation and cell loss that determines whether the tumour colony expands or regresses …

Tumor growth has long been a target of investigation within the context of mathematical and
computer modeling. The objective of this study is to propose and analyze a two-dimensional …

We develop a discrete model of malignant invasion using a thermodynamic argument. An
extension of the Potts model is used to simulate a population of malignant cells experiencing …

A flexible, cell-level, and lattice-based technique, the cellular Potts model accurately
describes the phenomenological mechanisms involved in many biological processes …