A Stem Cell Model for Carcinogenesis ANNETTE KOPP-SCHNEIDER zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPON Abteilung Biostatistik, Deutsches Krebsforschungszentncm, D-69009 Heidelberg, Germany AND CHRISTOPHER J. PORTIER Division of Biometry and Risk Assessment, National Institute of Emironmental Health Sciences, Research Triangle Park, North Carolina 27709 ABSTRACT A modification to the well-known two-stage model of carcinogenesis with clonal expansion is proposed. A true stem cell is applied to the production of intermediate cells by incorporating a birth-death process with a reflecting barrier into the model. The distribution of the number of detectable intermediate cell clones is derived, and systems of differential equations are formulated for the cumulative distribution function for the appearance of malignant tumors. The model is applied to data on papilloma formation in a mouse skin painting experiment. Tests for the importance of intermediate cells in tumor incidence can be derived. 1. INTRODUCTION In recent years, several mathematical models of carcinogenesis have been proposed, and some of them have been applied to data from animal experiments and to epidemiological data. The stochastic models that have been proposed can be divided into two classes. One class, multistage models without clonal expansion, was first introduced by Nordling [20] and further investigated by Armitage and Doll [ll. The original model assumed that a normal cell is transformed into a neo- plastic cell by k 2 1 fundamental biological events. Later Armitage and Doll [3] restricted this model to cases in which these fundamental events must occur in one ordered sequence. Generally these biological events are held to invoke damage to the genetic material such as mutations at specific gene loci. Cells in the intermediate stages can be removed from the process by cell death or differentiation. The other class of models, multistage models with clonal expansion, can be viewed as an extension of the models of the Armitage-Doll type MATHEMATICAL BIOSCIENCES 120:211- 232 (1994) OElsevier Science Inc., 1994 211 655 Avenue of the Americas, New York, NY 10010 0025-5564/94/$7.00