ArticleScientific reports2014
Entropy, complexity, and Markov diagrams for random walk cancer models.
Article in Scientific reports, 2014. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 18 papers.
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Who cites it
18 citing papers in PubMed.
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- Comparative analysis of the spatial distribution of brain metastases across several primary cancers using machine learning and deep learning models.Journal of neuro-oncology · 2024Article
- Modeling cancer immunoediting in tumor microenvironment with system characterization through the ising-model Hamiltonian.BMC bioinformatics · 2022Article
- A Temperature Conditioned Markov Chain Model for Predicting the Dynamics of Mosquito Vectors of Disease.Insects · 2021Article
- Modeling the Onset of Symptoms of COVID-19.Frontiers in public health · 2020Article
- Circulating Tumor Cells: High-Throughput Imaging of CTCs and Bioinformatic Analysis.Recent results in cancer research. Fortschritte der Krebsforschung. Progres dans les recherches sur le cancer · 2020Review
- Single cell correlation analysis of liquid and solid biopsies in metastatic colorectal cancer.Oncotarget · 2019Article
- Time-Series Analysis of Tumorigenesis in a Murine Skin Carcinogenesis Model.Scientific reports · 2018Article
- Development of metastatic brain disease involves progression through lung metastases inConvergent science physical oncology · 2017Article
- Analysis of healthy and tumour DNA methylation distributions in kidney-renal-clear-cell-carcinoma using Kullback-Leibler and Jensen-Shannon distance measures.IET systems biology · 2017Article
- Intracellular signaling entropy can be a biomarker for predicting the development of cervical intraepithelial neoplasia.PloS one · 2017Article
- The prisoner's dilemma as a cancer model.Convergent science physical oncology · 2016Article
- Investigating cellular network heterogeneity and modularity in cancer: a network entropy and unbalanced motif approach.BMC systems biology · 2016Article
- AN EVOLUTIONARY MODEL OF TUMOR CELL KINETICS AND THE EMERGENCE OF MOLECULAR HETEROGENEITY DRIVING GOMPERTZIAN GROWTH.SIAM review. Society for Industrial and Applied Mathematics · 2016Article
- Cell-to-cell communication in cancer: workshop report.NPJ breast cancer · 2015Article
- Spatiotemporal progression of metastatic breast cancer: a Markov chain model highlighting the role of early metastatic sites.NPJ breast cancer · 2015Article
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7 authors.
Funding
Abstract
The notion of entropy is used to compare the complexity associated with 12 common cancers based on metastatic tumor distribution autopsy data. We characterize power-law distributions, entropy, and Kullback-Liebler divergence associated with each primary cancer as compared with data for all cancer types aggregated. We then correlate entropy values with other measures of complexity associated with Markov chain dynamical systems models of progression. The Markov transition matrix associated with each cancer is associated with a directed graph model where nodes are anatomical locations where a metastatic tumor could develop, and edge weightings are transition probabilities of progression from site to site. The steady-state distribution corresponds to the autopsy data distribution. Entropy correlates well with the overall complexity of the reduced directed graph structure for each cancer and with a measure of systemic interconnectedness of the graph, called graph conductance. The models suggest that grouping cancers according to their entropy values, with skin, breast, kidney, and lung cancers being prototypical high entropy cancers, stomach, uterine, pancreatic and ovarian being mid-level entropy cancers, and colorectal, cervical, bladder, and prostate cancers being prototypical low entropy cancers, provides a potentially useful framework for viewing metastatic cancer in terms of predictability, complexity, and metastatic potential.
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