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Entropy, complexity, and Markov diagrams for random walk cancer models
Paul K Newton1, Jeremy Mason1, Brian Hurt1
1Viterbi School of Engineering, Department of Mathematics, and Norris Comprehensive Cancer Center, University of Southern California, Los Angeles, CA 90089-1191, USA.
Scientific Reports
|December 20, 2014
Summary
Entropy analysis reveals cancer complexity. High entropy cancers like skin and lung are more complex and unpredictable than low entropy cancers such as colorectal and prostate. This framework aids understanding metastatic potential.
Area of Science:
- Computational biology
- Cancer research
- Network science
Background:
- Cancer metastasis is a complex process.
- Understanding metastatic patterns is crucial for treatment.
- Current models may not fully capture cancer complexity.
Purpose of the Study:
- To quantify cancer complexity using entropy.
- To compare complexity across 12 common cancers.
- To correlate entropy with metastatic predictability.
Main Methods:
- Analysis of autopsy data for metastatic tumor distribution.
- Application of power-law distributions, entropy, and Kullback-Liebler divergence.
- Development of Markov chain dynamical systems and directed graph models.
Main Results:
- Entropy values successfully characterized complexity for 12 cancers.
- Entropy correlated with graph structure complexity and conductance.
- Cancers were grouped into high (skin, lung), mid (stomach, ovarian), and low (colorectal, prostate) entropy categories.
Conclusions:
- Entropy provides a framework for understanding cancer metastatic complexity.
- This approach offers insights into predictability and metastatic potential.
- Grouping cancers by entropy may refine treatment strategies.
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