Simulating cancer behavior across multiple biological scales in space and time, ie,
multiscale cancer modeling, is increasingly being recognized as a powerful tool to refine …

Using mathematical models to simulate dynamic biological processes has a long history.
Over the past couple of decades or so, quantitative approaches have also made their way …

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 …

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 …

If we had to formulate in one sentence what this book is about, it might be “How partial
differential equations can help to understand heat explosion, tumor growth or evolution of …

The book aims to provide an introduction to mathematical models that describe the
dynamics of tumor growth and the evolution of tumor cells. It can be used as a textbook for …

This paper deals with a chemotaxis-haptotaxis model of cancer invasion of tissue
(extracellular matrix (ECM)). The model consists of a parabolic chemotaxis-haptotaxis PDE …

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 devise second-order accurate, unconditionally uniquely solvable and unconditionally
energy stable schemes for the nonlocal Cahn–Hilliard (nCH) and nonlocal Allen–Cahn …

Cancer is a complex disease that starts with mutations of key genes in one cell or a small
group of cells at a primary site in the body. If these cancer cells continue to grow successfully …