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Mathematical Modeling of Tumor Microenvironments
The environment of a tumor is crucial determining factor in its development.
A multiscale mathematical model of cancer invasion, which considers cellular and
microenvironmental factors simultaneously and interactively, which can forecast
how tumors grow and invade tissue (Anderson et al. 2006 ). The model simulations
predict that harsh tumor microenvironment conditions (e.g., hypoxia, heteroge-
neous extracellular matrix) exert a dramatic selective force on the tumor, which
grows as an invasive mass with fi ngering margins, dominated by a few clones with
aggressive traits. In contrast, mild microenvironment conditions (e.g. normoxia,
homogeneous matrix) allow clones with similar aggressive traits to coexist with
less aggressive phenotypes in a heterogeneous tumor mass with smooth, noninva-
sive margins. Thus, the genetic make-up of a cancer cell may realize its invasive
potential through a clonal evolution process driven by defi nable microenvironmen-
tal selective forces. The model shows a clear relationship between the shape of a
cancer tumor and how aggressive it is. Aggressive tumors tend to assume a spidery
shape in the model, while more benign growths are generally more spherical in
shape. The fi ndings would infl uence decision on how certain cancers are treated, by
considering the environment around the tumor to be a contributory factor in how
aggressive the cancer. Most of the current treatments are focused on making the
tissue environment as harsh as possible for the tumor in the hope of destroying it.
But this could allow the most aggressive cancer cells to dominate any residual
tumor left after treatment and develop resistance to treatment. Moreover, these
aggressive cells tend to be the more invasive resulting in an increased chance of
metastasis. With use of the tools of mathematical modeling and computer simula-
tion, cancer treatment will no longer be a trial and error game. With mathematics-
driven oncology research, it will be possible to determine which drugs will work at
which stage. In the future this research could help personalize treatment in a patient
specifi c manner.
Modeling Signaling Pathways to Reposition Anticancer Drugs
Computational modeling has been to derive specifi c downstream signaling path-
ways, cancer signaling bridges (CSB), which reveal previously unknown target-
disease connections and have the potential for systematic as well as fast-tracked
drug repositioning based on available patient gene expression data (Zhao et al.
2013 ). This model was applied to reposition known or shelved drugs for brain, lung,
and bone metastases of breast cancer with the hypothesis that cancer subtypes have
their own specifi c signaling mechanisms. To test the hypothesis, the authors
addressed specifi c CSBs for each metastasis that satisfy (i) CSB proteins are acti-
vated by the maximal number of enriched signaling pathways specifi c to a given
metastasis, and (ii) CSB proteins are involved in the most differential expressed
10 Personalized Therapy of Cancer