Mathematical Modeling, Avascular Tumor Growth, and Cancer Research

A wealth of experimental cancer research data exists that requires systematic analysis before it can be used to fight this deadly disease. Researchers believe that mathematics can make huge contributions to numerous areas of experimental cancer investigation by utilizing modeling techniques to interpret this data. Models also provide a framework to investigate a problem and make intuitive predictions.

One important application of modeling in cancer research is the study of avascular tumor growth. Although complex in its own right, avascular tumor growth is easier to replicate experimentally, much simpler to model mathematically and yet contains many of the phenomena that researchers and mathematicians will need to address when modeling vascular tumors growth. Modeling avascular tumor growth is the first step toward building models for fully vascularized tumors and thus more thoroughly understanding cancer.

As close collaboration between mathematicians and experimentalists develops, the pathways from model hypothesis to testing of model predictions will become more rigorous.

Definitions
Mathematical models
A mathematical model is a representation of a physical, biological, or social system in mathematical language. It allows the tools of mathematics, statistics, and computation to be utilized to understand the system and make quantitative predictions.

Avascular tumor growth
Avascular tumor growth is the growth of tumors without blood vessels. These are less complex than vascular tumors. Avascular growth is a distinct phase in cancer development and is the stage before the tumor develops its own blood supply and continues to grow (vascular growth).

 

Source:
Mathematical Models of Avascular Tumor Growth
Tiina Roose, S. Jonathan Chapman, Philip K. Maini
SIAM Review, 49 (2007), pp 179-208
Pub date 1 May 2007
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