A system of nonlinear partial differential equations is proposed as a model for the growth of
an avascular-tumour spheroid. The model assumes a continuum of cells in two states, living …

Research on resistance to cancer treatment was mainly focused for 20 years on multidrug
resistance (MDR). No useful method of reversing MDR, suitable for clinical use, has yet …

The partial pressure of oxygen (pO2) and pH play critical roles in tumor biology and therapy.
We report here the first combined, high-resolution (≤ 10 μm) measurements of interstitial pH …

Histopathologic knowledge that extensive heterogeneity exists between and within tumors
has been confirmed and deepened recently by molecular studies. However, the impact of …

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 …

In this paper we present a hybrid mathematical model of the invasion of healthy tissue by a
solid tumour. In particular we consider early vascular growth, just after angiogenesis has …

Oxygen and nutrient limitation are common features of the tumor microenvironment and are
associated with cancer progression and induction of metastasis. The inefficient …

In this chapter we have presented mathematical modeling approaches to biological pattern
formation. While reaction-diffusion models are appropriate to describe the spatio-temporal …

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 …

To what extent the growth dynamics of tumors is controlled by nutrients, biomechanical
forces and other factors at different stages and in different environments is still largely …