Recent translational research: computational studies of breast cancer

The dynamics of drug resistance: a mathematical perspective

Resistance to chemotherapy is a key impediment to successful cancer treatment that has been intensively studied for the last three decades. Several central mechanisms have been identified as contributing to the resistance. In the case of multidrug resistance (MDR), the cell becomes resistant to a variety of structurally and mechanistically unrelated drugs in addition to the drug initially administered. Mathematical models of drug resistance have dealt with many of the known aspects of this field, such as pharmacologic sanctuary and location/diffusion resistance, intrinsic resistance, induced resistance and acquired resistance. In addition, there are mathematical models that take into account the kinetic/phase resistance, and models that investigate intracellular mechanisms based on specific biological functions (such as ABC transporters, apoptosis and repair mechanisms). This review covers aspects of MDR that have been mathematically studied, and explains how, from a methodological perspective, mathematics can be used to study drug resistance. We discuss quantitative approaches of mathematical analysis, and demonstrate how mathematics can be used in combination with other experimental and clinical tools. We emphasize the potential benefits of integrating analytical and mathematical methods into future clinical and experimental studies of drug resistance.

Purinergic mechanisms in breast cancer support intravasation, extravasation and angiogenesis

Several advances have recently expanded models of tumor growth and promoted the concept of tumor homeostasis, the hypothesis that primary tumors exert an anti-proliferative effect on both themselves and subclinical secondary metastases. Recent trials indicate that the characterization of tumor growth as uncontrolled is inconsistent with animal models, clinical models, and epidemiological models. There is a growing body of evidence which lends support to an updated concept of tumor growth: tumor homeostasis. In the case of breast cancer, if not all metastasizing tumors, these advances suggest an inconvenient truth. That is, if breast tumor cells metastasize to distant sites early in the tumorigenesis process, then removal of a breast tumor may hasten the development of its metastases. We explore the heretofore unappreciated notion that nucleotides generated by tumor cells following the secretion of an ADP-kinase can promote metastasis and support angiogenesis. Evidence is presented that blockade of the actions of nucleotides in the setting of newly diagnosed breast cancer may provide a useful adjunct to current anti-angiogenesis treatment.

New concepts in breast cancer emerge from analyzing clinical data using numerical algorithms

A small international group has recently challenged fundamental concepts in breast cancer. As a guiding principle in therapy, it has long been assumed that breast cancer growth is continuous. However, this group suggests tumor growth commonly includes extended periods of quasi-stable dormancy. Furthermore, surgery to remove the primary tumor often awakens distant dormant micrometastases. Accordingly, over half of all relapses in breast cancer are accelerated in this manner. This paper describes how a numerical algorithm was used to come to these conclusions. Based on these findings, a dormancy preservation therapy is proposed.