Thron C D
Cancer Res. 1984 Sep;44(9):4208-10.
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.
尤哈斯和李（《癌症研究》，38: 1528 - 1532，1978）提出了一种估算多细胞肿瘤球体生长层厚度的方法。然而，他们的方法假定生长层的厚度与球体半径无关；鉴于纯粹几何原因，小球体中的氧扩散距离大于大球体，这一假设似乎难以置信。在本论文中，基于伯顿（《生长》，30: 157 - 176，1966）的氧扩散模型计算了一个生长动力学模型的理论生长速率，结果表明，对于该模型，尤哈斯 - 李对生长层厚度的估算值比用于估算的两个球体中较大球体的该层真实厚度低10%至30%。为了推广到该特定模型之外，结果表明，对于任何生长层在小球体中比在大球体中更厚的模型，尤哈斯 - 李方法都会低估生长层的厚度。然而，至少对于我们的特定模型，尤哈斯 - 李估算中的偏差相当恒定且相对较小，因此这些估算可能相当有用，特别是对于纯粹的比较研究。
