Mathematical Oncology: Using Math to Fight Cancer


SIAM News Publishes Professor Tannenbaum's Complex Network Research

In April the Society for Industrial and Applied Mathematics (SIAM) published Professor Allen Tannenbaum's research, Robustness of Complex Networks with Applications to Cancer Biology

The work attacks the battle against cancer mathematically by garnering ideas from geometric network mathematics. As Tannenbaum states in the article, the "research is part of the emerging field of mathematical oncology" which will hopefully "help in the development of new treatments."  Researchers are very interested in geometric network framework, particularly as it relates to cancer. The cancer biology connection results from the ability to model many cellular gene and protein networks as weighted graphs. The overall goal is to investigate how curvature and other intrinsic geometric/topological properties affect cell features.  As shown on the figure to the right, created by Liangjia Zhu, network curvature, robustness, and entropy are all positively correlated. 

Researchers are developing analytical methods for "quantitatively describing the functional robustness of cancer networks to identify genes/proteins with treatment potential." Ideally, analytical methods will lead to treatments involving targeted drug agents, combined with immunotherapy and more traditional chemical agents. 

While studying possible gateways to treatment, mathematical researchers are also analyzing possible mechanisms of resistance. The example posed in the article is if certain key pathways can increase robustness in neighboring pathways and thus contribute to an escape route from a given therapy. The methods detailed in the article characterize the processes that lead to differentiation and targeted anticancer therapies take into account the tumor as a whole and the likelihood that drug-resistant subclones. 

About the Researcher

Allen Tannenbaum is a SUNY Distinguished Professor of Computer Science and Applied Mathematics at Stony Brook University, part of the College of Engineering and Applied Sciences. He joined Stony Brook in 2013 and he also holds positions with the Departments of Radiology and Biomedical Informatics. Tannenbaum earned a PhD in Mathematics from Harvard University and his main fields of interest are algebraic geometry, systems and control, invariant theory, computer vision, medical imaging, and complex networks.