Interactions between cancer cells and their microenvironment are crucial for promoting tumor growth and invasiveness. In the tumor adaptive landscape model, hypoxic and acidic microenvironmental conditions reduce the fitness of cancer cells and significantly restrict their proliferation. This selects for enhanced motility as cancer cells may evolve an invasive phenotype if the consequent cell m...

The cancer stem cell hypothesis has evolved to one of the most important paradigms in biomedical research. During recent years evidence has been accumulating for the existence of stem cell-like populations in different cancers, especially in leukemias. In the current work we propose a mathematical model of cancer stem cell dynamics in leukemias. We apply the model to compare cellular properties...

In this chapter we present an overview of different mathematical and numerical approaches to describe stem cell proliferation and differentiation and the development of small cancer stem cell populations that are origins of neoplasm disease. The purpose of this chapter is not to scare the reader with complex mathematical and numerical analysis. Instead we aim to summarize the wide range of poss...

For aggressive brain cancers such as glioblastoma multiforme (gbm), much of the discussion on this web site and others are on clinical trials for new agents. This is largely because the existing arsenal of treatments is so weak. The clinical trials take drugs that seem promising and test them for safety and efficacy. The trials have prevented widespread use of agents that were dangerous, and ha...

The complex, constantly evolving and multifaceted nature of cancer has made it difficult to identify unique molecular and pathophysiological signatures for each disease variant, consequently hindering development of effective therapies. Mathematical modeling and computer simulation are tools that can provide a robust framework to better understand cancer progression and response to chemotherapy...

Background: Cervical cancer is the third most common cancer in women throughout the world. The human papillomavirus (HPV) E6 viral protein plays an essential role in proteasomal degradation of the cancer suppressant protein p53. As a result, p53 negative regulation and apoptosis relevant activities are abrogated, facilitating development of cervical cancer. Methods: A mathematical model of E6-p...