This Timeline article charts progress in mathematical modelling of cancer over the past 50
years, highlighting the different theoretical approaches that have been used to dissect the …

Cancer is a complex, multiscale process in which genetic mutations occurring at a
subcellular level manifest themselves as functional changes at the cellular and tissue scale …

Agent-based modeling and simulation (ABMS) is a new approach to modeling systems
comprised of autonomous, interacting agents. ABMS promises to have far reaching effects …

Despite major scientific, medical and technological advances over the last few decades, a
cure for cancer remains elusive. The disease initiation is complex, and including initiation …

In this chapter we have presented mathematical modeling approaches to biological pattern
formation. While reaction-diffusion models are appropriate to describe the spatio-temporal …

Mathematical modeling, analysis and simulation are set to play crucial roles in explaining
tumor behavior, and the uncontrolled growth of cancer cells over multiple time and spatial …

Tumor progression, including metastasis, is significantly influenced by factors in the tumor
microenvironment (TME) such as mechanical force, shear stress, chemotaxis, and hypoxia …

The ability to invade tissue is one of the hallmarks of cancer. Cancer cells achieve this
through the secretion of matrix degrading enzymes, cell proliferation, loss of cell–cell …

In this paper we compare two alternative theoretical approaches for simulating the growth of
cell aggregates in vitro: individual cell (agent)-based models and continuum models. We …

The growth of solid tumours proceeds through two distinct phases: the avascular and the
vascular phase. It is during the latter stage that the insidious process of cancer invasion of …