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 …

Over the past two decades, a number of mathematical and computational models have been
developed to study different aspects of angiogenesis that span the spatial and temporal …

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 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 …

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 …

In this article, we present a new multiscale mathematical model for solid tumour growth
which couples an improved model of tumour invasion with a model of tumour-induced …

We develop a thermodynamically consistent mixture model for avascular solid tumor growth
which takes into account the effects of cell-to-cell adhesion, and taxis inducing chemical and …

Reaction-diffusion based tumor growth models have been widely used in the literature for
modeling the growth of brain gliomas. Lately, recent models have started integrating medical …

In this paper, we present and investigate a model for solid tumor growth that incorporates
features of the tumor microenvironment. Using analysis and nonlinear numerical …

We present a mathematical model for vascular tumor growth. We use phase fields to model
cellular growth and reaction-diffusion equations for the dynamics of angiogenic factors and …