The Exponential-Gompertzian Tumor Growth Model: Data from Six Tumor Cell Lines in Vitro and in Vivo. Estimate of the Transition point from Exponential to Gompertzian Growth and Potential Cinical Implications

Abstract

The published growth data were examined for six tumor cell lines (FSA, Line 1, MCA-11, EMT6/RO, MGH-U1, MLS) grown in vivo and in vitro as monolayer cultures and as multicell spheroids cultured under different experimental conditions. Serial estimates of tumor sizes were fitted by Gompertzian equations obtained with a non-linear computerized program. When the growth equations of the same tumor growing in different experimental conditions were compared, the Gompertzian parameters alpha 0 (initial specific growth rate) and beta (retardation factor) showed a strong linear correlation in all the examined lines, with no exception. This occurrence supports the exponential-Gompertzian growth model, where an early exponential phase (which is virtually not influenced by exogenous factors) is followed by a Gompertzian phase, the characteristics of which are greatly dependent on environmental conditions. The transition between the two phases was estimated to occur when tumor size reached 10(2)-10(4) cells, depending on the cell line. This kinetic change in tumor growth may be clinically relevant as regards cytotoxic treatments. It could explain some consequences of delays in adjuvant (postoperative) chemotherapy observed in clinical trials on primary breast cancer.