Empirical evidence and theoretical studies suggest that the phenotype, ie, cellular-and
molecular-scale dynamics, including proliferation rate and adhesiveness due to …

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

Glioblastoma, the most malignant form of brain cancer, is responsible for 23% of primary
brain tumors and has extremely poor outcome. Confounding the clinical management of …

Recently we considered a stochastic discrete model which describes fronts of cells invading
a wound [E. Khain, LM Sander, and CM Schneider-Mizell, J. Stat. Phys. 128, 209 (2007)]. In …

We propose a two-component reaction-transport model for the migration-proliferation
dichotomy in the spreading of tumor cells. By using a continuous time random walk (CTRW) …

In this work, a cellular Potts model based on the differential adhesion hypothesis is
employed to analyze the relative importance of select cell-cell and cell-extracellular matrix …

Invasion of malignant glioma is a highly complex phenomenon involving molecular and
cellular processes at various spatio-temporal scales, whose precise interplay is still not fully …

Gliomas are very aggressive brain tumours, in which tumour cells gain the ability to
penetrate the surrounding normal tissue. The invasion mechanisms of this type of tumour …

We study the in vitro dynamics of the malignant brain tumor glioblastoma multiforme. The
growing tumor consists of a dense proliferating zone and an outer less dense invasive …