a stochastic markov chain model to describe lung cancer growth and metastasis一个随机马尔可夫链模型来描述肺癌生长和转移.pdfVIP

A Stochastic Markov Chain Model to Describe Lung Cancer Growth and Metastasis 1 1 2 3 4 5 Paul K. Newton *, Jeremy Mason , Kelly Bethel , Lyudmila A. Bazhenova , Jorge Nieva , Peter Kuhn 1 Department of Aerospace Mechanical Engineering and Department of Mathematics, University of Southern California, Los Angeles, California, United States of America, 2 Scripps Clinic Torrey Pines, La Jolla, California, United States of America, 3 UCSD Moores Cancer Center, La Jolla, California, United States of America, 4 Billings Clinic, Billings, Montana, United States of America, 5 The Scripps Research Institute, La Jolla, California, United States of America Abstract 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 distrib