Phase field models recently gained a lot of interest in the context of tumour growth models.
Typically Darcy-type flow models are coupled to Cahn–Hilliard equations. However, often …

The aim of this work is to develop a novel computational approach to facilitate the modeling
of angiogenesis during tumor growth. The preexisting vasculature is modeled as a 1D …

In this work, we study a model consisting of a Cahn--Hilliard-type equation for the
concentration of tumor cells coupled to a reaction-diffusion-type equation for the nutrient …

A mathematical analysis of local and nonlocal phase-field models of tumor growth is
presented that includes time-dependent Darcy–Forchheimer–Brinkman models of …

One of many important features of the tumour microenvironment is that it is a place of active
Darwinian selection where different tumour clones become adapted to the variety of …

Background Contemporary biological observations have revealed a large variety of
mechanisms acting during the expansion of a tumor. However, there are still many …

As a hallmark of cancer, angiogenesis is essential for tumor growth and metastasis. In the
process of tumor angiogenesis, a number of pathways are involved, which are regulated by …

Tumour-induced angiogenesis is affected by an interplay between different cell types, the
mechanical stresses in the extracellular matrix (ECM), and the cell signalling networks. The …

The tumour microenvironment is characterized by large chemical gradients and contains a
mixture of normal and tumour cells. 11 The presence of high gradients favours the formation …

A significant capability of computational modeling is the ability to integrate components into
a virtual system capable of reproducing complex behavior, incorporating circuits of …