We present a mathematical model for vascular tumor growth. We use phase fields to model
cellular growth and reaction-diffusion equations for the dynamics of angiogenic factors and …

Although extensive research effort and resources have been dedicated to the development
of nanotherapeutics to treat cancer, few formulations have reached clinical application. A …

We propose a coupled mathematical modelling system to investigate glioblastoma growth in
response to dynamic changes in chemical and haemodynamic microenvironments caused …

Tumor vasculature, the blood vessel network supplying a growing tumor with nutrients such
as oxygen or glucose, is in many respects different from the hierarchically organized arterio …

The avascular multiphase model for tumor growth, developed by the authors in previous
works, is enhanced to include angiogenesis. The original model comprises the extracellular …

Podocytes are mainly involved in the regulation of glomerular filtration rate (GFR) under
physiological condition. Podocyte depletion is a crucial pathological alteration in diabetic …

Recognised as a key stage in cancer growth and spread in the human body, the cancer cell
invasion process is crucial for metastatic spread and the subsequent development of …

We consider and solve numerically a mathematical model of tumour growth based on
cancer stem cells (CSC) hypothesis with the aim of gaining some insight into the relation of …

A tumour invasion model has been developed to examine the influence of diffusible matrix
metalloproteinases (MMPs) and the mediated proteolysis of non-diffusible, membrane type …

The tumor-associated microvasculature is one of the key elements of the microenvironment
that helps shape, and is shaped by, tumor progression. Given the important role of the …