A stochastic model for the formation of metastatic foci at distant sites
type: Item
instance of: scholarly article
title: A stochastic model for the formation of metastatic foci at distant sites
zbMATH Open document ID: 0715.92010
DOI: 10.1016/0895-7177(89)90230-6
published in: Mathematical and Computer Modelling
publication date: 1989-01-01T00:00:00Z
review text: The purpose of this paper is to develop a stochastic model describing how metastatic foci are formed at distant sites from metastatic tumor cells. This type of problems was first considered by \textit{L. A. Liotta, J. Kleinerman} and \textit{G. M. Saidel} for deterministic and homogeneous stochastic models [Cancer Res. 34, 997-1004 (1974) and Biometrics 32, 535-550 (1976; Zbl 0341.92014)] to predict the number of metastatic foci at a primary distant site. However, these results are obtained under oversimplified assumptions which were implicitly assumed. Further, because of genetic instability of tumor cells and the heterogeneity of tumor cell populations, the metastatic processes are naturally not time homogeneous. Therefore, the author proceeds to extend the Liotta-Saidel-Kleinerman model to more general nonhomogeneous cases, to develop probability distributions of metastatic foci at distant sites and to extend the results to cases involving several different tissues such as the lung, the brain and the liver.
Mathematics Subject Classification ID: 92C50
Mathematics Subject Classification ID: 60J85
zbMATH DE Number: 4179183
zbMATH Keywords: formation of metastatic focu at distant sites
zbMATH Keywords: probability generating functions
zbMATH Keywords: waiting time distributions
zbMATH Keywords: cancer progression
zbMATH Keywords: stochastic model
zbMATH Keywords: metastatic tumor cells
zbMATH Keywords: nonhomogeneous cases
zbMATH Keywords: probability distributions of metastatic foci at distant sites
author: Wai-Yuan Tan
MaRDI profile type: Publication
full work available at URL: 0895-7177(89)90230-6
OpenAlex ID: W2024082795
cites work: Stochastic Model of Metastases Formation
cites work: Q3345540
description: scientific article; zbMATH DE number 4179183