A miscellany of new strategies, experimental techniques and theoretical approaches are
emerging in the ongoing battle against cancer. Nevertheless, as new, ground-breaking …

Mass balance equations typically adopted to describe tumor growth are to be closed by
introducing a suitable velocity field. The first part of this paper is devoted to a critical review …

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 …

In this paper the theory of mixtures is used to develop a two‐phase model of an avascular
tumour, which comprises a solid, cellular, phase and a liquid phase. Mass and momentum …

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 …

We extend the diffuse interface model developed in Wise et al.(2008) to study nonlinear
tumor growth in 3-D. Extensions include the tracking of multiple viable cell species …

We study solid tumor (carcinoma) growth in the nonlinear regime using boundary-integral
simulations. The tumor core is nonnecrotic and no inhibitor chemical species are present. A …

Introduction to Mathematical Oncology presents biologically well-motivated and
mathematically tractable models that facilitate both a deep understanding of cancer biology …

In this paper, we develop a thermodynamically consistent four‐species model of tumor
growth on the basis of the continuum theory of mixtures. Unique to this model is the …