Growth in solid heterogeneous human colon adenocarcinomas: comparison of simple logistical models

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Abstract
Three models of simple logistical growth were used to describe volumetric growth in heterogeneous tumours. Two clonal subpopulations (designated as clone A and clone D) originally obtained from a human colon adenocarcinoma were used to produce solid xenograft tumours in nude mice. Volumetric growth of tumours produced from pure cells alone was compared to that produced from 50% A:50 D, 88% A:12% D, and 9% A:91% D admixtures. Gompertzian analysis of the in vivo growth data indicated significant differences in both the initial growth rates and final asymptotic limiting volumes of the pure versus the admixed tumours. Verhulstian and modified Verhulstian models were also used to derive regression curves from the same data. The fit of the curves was compared with each other using standard (Akaike, 1974; Schwartz, 1978) information criteria. In four of the five tumour populations the Gompertz equation fitted best. Only in the 88% A:12% D tumors did the modified Verhulst model fit best. The deviations from the regression curves, the residuals, for all three models were systemically distributed. These systematic errors are likely to be the result of using simplified logistical models to describe the growth kinetics of interacting populations in heterogeneous tumours.