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A stochastic Markov chain model to describe lung cancer growth and metastasis

Newton, Paul K ; Mason, Jeremy ; Bethel, Kelly ; Bazhenova, Lyudmila A ; Nieva, Jorge ; Kuhn, Peter Ermentrout, Bard

PloS one, 2012-04, Vol.7 (4), p.e34637-e34637 [Periódico revisado por pares]

United States: Public Library of Science

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Título:
A stochastic Markov chain model to describe lung cancer growth and metastasis
Autor: Newton, Paul K ; Mason, Jeremy ; Bethel, Kelly ; Bazhenova, Lyudmila A ; Nieva, Jorge ; Kuhn, Peter
Ermentrout, Bard
Assuntos: Analysis ; Autopsies ; Autopsy ; Bayesian analysis ; Biology ; Cancer ; Cancer metastasis ; Cell Adhesion - physiology ; Cell Movement - physiology ; Chain dynamics ; Computer Science ; Computer simulation ; Construction sites ; Diagnostic software ; Diagnostic systems ; Disease Progression ; Entropy ; Humans ; Iterative methods ; Lung cancer ; Lung diseases ; Lung Neoplasms - physiopathology ; Markov analysis ; Markov Chains ; Markov processes ; Mathematical models ; Mathematics ; Medicine ; Metastases ; Metastasis ; Models, Biological ; Monte Carlo simulation ; Neoplasm Metastasis - physiopathology ; Optimization ; Population (statistical) ; Random variables ; Seeds ; Steady state ; Stochastic Processes ; Stochasticity ; Time Factors ; Tissue analysis ; Transition probabilities ; Tumors
É parte de: PloS one, 2012-04, Vol.7 (4), p.e34637-e34637
Notas: ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
Conceived and designed the experiments: PN JM PK. Performed the experiments: PN JM. Analyzed the data: PN JM KB LB JN PK. Contributed reagents/materials/analysis tools: PN JM. Wrote the paper: PN JM PK.
Descrição: A stochastic Markov chain model for metastatic progression is developed for primary lung cancer based on a network construction of metastatic sites with dynamics modeled as an ensemble of random walkers on the network. We calculate a transition matrix, with entries (transition probabilities) interpreted as random variables, and use it to construct a circular bi-directional network of primary and metastatic locations based on postmortem tissue analysis of 3827 autopsies on untreated patients documenting all primary tumor locations and metastatic sites from this population. The resulting 50 potential metastatic sites are connected by directed edges with distributed weightings, where the site connections and weightings are obtained by calculating the entries of an ensemble of transition matrices so that the steady-state distribution obtained from the long-time limit of the Markov chain dynamical system corresponds to the ensemble metastatic distribution obtained from the autopsy data set. We condition our search for a transition matrix on an initial distribution of metastatic tumors obtained from the data set. Through an iterative numerical search procedure, we adjust the entries of a sequence of approximations until a transition matrix with the correct steady-state is found (up to a numerical threshold). Since this constrained linear optimization problem is underdetermined, we characterize the statistical variance of the ensemble of transition matrices calculated using the means and variances of their singular value distributions as a diagnostic tool. We interpret the ensemble averaged transition probabilities as (approximately) normally distributed random variables. The model allows us to simulate and quantify disease progression pathways and timescales of progression from the lung position to other sites and we highlight several key findings based on the model.
Editor: United States: Public Library of Science
Idioma: Inglês

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A stochastic Markov chain model to describe lung cancer growth and metastasis

Newton, Paul K ; Mason, Jeremy ; Bethel, Kelly ; Bazhenova, Lyudmila A ; Nieva, Jorge ; Kuhn, Peter Ermentrout, Bard

United States: Public Library of Science

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