One of the most remarkable differences between classical engineering materials and living
matter is the ability of the latter to grow and remodel in response to diverse stimuli. The …

We briefly review spatially homogeneous mechanistic mathematical models describing the
interactions between a malignant tumor and the immune system. We begin with the simplest …

This monograph presents a general mathematical theory for biological growth. It provides
both a conceptual and a technical foundation for the understanding and analysis of …

In this paper we present an overview of agent-based models that are used to simulate
mechanical and physiological phenomena in cells and tissues, and we discuss underlying …

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 …

This review will outline a number of illustrative mathematical models describing the growth
of avascular tumors. The aim of the review is to provide a relatively comprehensive list of …

This is the first paper in a two-part series in which we develop, analyze, and simulate a
diffuse interface continuum model of multispecies tumor growth and tumor-induced …

The application of mathematical models to explain the dynamics of biological pattern
formation started with the work of D'Arcy Thompson who showed that mathematics cannot …

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 …

Angiogenesis, the growth of a network of blood vessels, is a crucial component of solid
tumour growth, linking the relatively harmless avascular growth phase and the potentially …