Cell proliferation kinetics and multistage cancer risk models

Cell-kinetic multistage (CKM) cancer-risk models account for clonal proliferation of postulated intermediate (initiated, premalignant) cell populations during tumorigenesis. To date, almost all CKM models considered have assumed that intermediate, premalignant cells may proliferate exponentially over time in vivo. This "exponential growth" assumption, however, may not always be as biologically plausible as the alternative assumption that cells tend to grow geometrically in time. The general CKM model and applications of it that presume exponential cell growth are reviewed here. Geometric CKM models are then considered, previous erroneous analyses of these models are reviewed, and a corrected mathematical treatment is provided. It is pointed out that the presumption of exponential instead of geometric proliferation kinetics may lead to underestimates of small increments in CKM-predicted cancer risk above background if the geometric assumption is true. An evaluation of pertinent biological evidence is provided, which indicates that precancerous cells may typically proliferate geometrically. Consequently, if CKM models are used for environmental risk assessment, it may be prudent for one to presume geometric cell growth unless specific data support an alternative assumption.