Volume estimation of multicellular colon carcinoma spheroids using Cavalieri's principle

Multicellular tumour-spheroids are regarded as suitable models for cancer research, similar to avascular tumour parts. As a size parameter of the spheroids, usually their maximum diameter is used, estimated on a section presumed to be equatorial or near equatorial. Estimation of the volume of spheroids is of interest for the detection of subtle changes in different kinds of investigations. Since spheroids are often not truly spherical, and because model-based methods for volume determination may be biased, Cavalieri's principle, rediscovered recently for stereology, was used to determine the volume of the spheroids. Here we report the results of the volume estimation of colon carcinoma spheroids, together with an outline of the basic stereological principle and formulas used. The spheroids investigated had a volume between 1.4 and 92.3 mm3 (mean 33.9). The volume fraction of necrotic to viable tissue cells was between 0.6:1 and 2.2:1. The coefficient of error (CE) was remarkably low with 3.7% for the volumes. Both inter- and intraobserver-variability were extremely low with correlation coefficients (r2) of 99%. Thus, the high precision of the stereological method, combined with a low workload, make it ideally suitable for routine volume estimation.