This article presents a comprehensive review of numerical methods and models for interface
resolving simulations of multiphase flows in microfluidics and micro process engineering …

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 …

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 …

A balanced force refined level set grid method for two-phase flows on structured and
unstructured flow solver grids is presented. To accurately track the phase interface location …

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 …

The flow of interstitial fluid and the associated interstitial fluid pressure (IFP) in solid tumors
and surrounding host tissues have been identified as critical elements in cancer growth and …

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 …

Ductal carcinoma in situ (DCIS)—a significant precursor to invasive breast cancer—is
typically diagnosed as microcalcifications in mammograms. However, the effective use of …