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 …

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 …

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 …

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 …

Clinical outcome prognostication in oncology is a guiding principle in therapeutic choice. A
wealth of qualitative empirical evidence links disease progression with tumor morphology …

We investigate a three-dimensional multiscale model of vascular tumour growth, which
couples blood flow, angiogenesis, vascular remodelling, nutrient/growth factor transport …

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 …

In the past 30 years we have witnessed an extraordinary progress on the research in the
molecular biology of cancer, but its medical treatment, widely based on empirically …

In this review we summarize our recent efforts using mathematical modeling and
computation to simulate cancer invasion, with a special emphasis on the tumor …

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 …