In this paper, we review multi-scale models of solid tumour growth and discuss a middle-out
framework that tracks individual cells. By focusing on the cellular dynamics of a healthy …

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 …

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 present an unconditionally energy stable and solvable finite difference scheme for the
Cahn-Hilliard-Hele-Shaw (CHHS) equations, which arise in models for spinodal …

Mathematical modeling has recently been added as a tool in the fight against cancer. The
field of mathematical oncology has received great attention and increased enormously, but …

The process in which a growing tumor transforms a hierarchically organized arterio-venous
blood vessel network into a tumor specific vasculature is analyzed with a theoretical model …

We use the Glazier-Graner-Hogeweg model to simulate three-dimensional (3D), single-
phenotype, avascular tumors growing in an homogeneous tissue matrix (TM) supplying a …

The physics of solid tumor growth can be considered at three distinct size scales: the tumor
scale, the cell–extracellular matrix (ECM) scale and the sub-cellular scale. In this paper we …

INTRODUCTION Cancer growth, and as a particular example in this paper, solid tumor
growth, is a complicated phenomenon involving many interrelated processes across a wide …

Solute transport coupled with biomass growth and/or mineral precipitation/dissolution is a
complex and challenging nonlinear problem. Important applications in biomedical systems …