A stochastic model for the formation of metastatic foci at distant sites
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.
formation of metastatic focu at distant sites
probability distributions of metastatic foci at distant sites
scientific article; zbMATH DE number 4179183