A possible bias in growth-kinetic estimates of the thickness of the growing layer in multicellular tumor spheroids.

Yuhas and Li (Cancer Res., 38: 1528-1532, 1978) have proposed a method for estimating the thickness of the growing layer in multicellular tumor spheroids. Their method assumes, however, that the thickness of the growing layer is independent of spheroid radius; this assumption seems implausible in view of the fact that, for purely geometrical reasons, oxygen diffusion distance is greater in small than in large spheroids. In this communication, theoretical growth rates are calculated for a growth kinetic model based on Burton's (Growth, 30: 157-176, 1966) model of oxygen diffusion, and it is shown that for this model the Yuhas-Li estimates of thickness of the growing layer are 10 to 30% below the true thickness of this layer in the larger of the two spheroids used for the estimation. To generalize beyond this particular model, it is shown that, for any model where the growing layer is thicker in small than in large spheroids, the Yuhas-Li method underestimates the thickness of the growing layer. However, for our particular model at least, the bias in the Yuhas-Li estimates is fairly constant and relatively small, so that these estimates may be quite serviceable, especially for purely comparative studies.