This paper presents a critical review of selected topics related to the modelling of cancer
onset, evolution and growth, with the aim of illustrating, to a wide applied mathematical …

Cancer is a collection of diseases with the common feature of uncontrolled cellular growth.
Most tissues in the body can give rise to cancer, some even yield several types, and each …

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 …

Chemotaxis is a fundamental guidance mechanism of cells and organisms, responsible for
attracting microbes to food, embryonic cells into developing tissues, immune cells to …

We consider two simple conservative systems of parabolic-elliptic and parabolic-degenerate
type arising in modeling chemotaxis and angiogenesis. Both systems share the same …

Angiogenic sprouting requires functional specialisation of endothelial cells into leading tip
cells and following stalk cells. Experimental data illustrate that induction of the tip cell …

The purpose of this paper is to present a mathematical model for the tumor vascularization
theory of tumor growth proposed by Judah Folkman in the early 1970s and subsequently …

Two major mechanisms are involved in the formation of blood vasculature: vasculogenesis
and angiogenesis. The former term describes the formation of a capillary-like network from …

Vascular abnormalities contribute to many diseases such as cancer and diabetic
retinopathy. In angiogenesis new blood vessels, headed by a migrating tip cell, sprout from …

Blood vessels form either when dispersed endothelial cells (the cells lining the inner walls of
fully formed blood vessels) organize into a vessel network (vasculogenesis), or by sprouting …