ON THE RELATION BETWEEN SIZE OF NECROSIS AND DIAMETER OF TUMOR SPHEROIDS

Purpose: In many previous experimental studies on multicellular tumor spheroids, the spheroid diameter at which central necrosis develops ha s been determined to be twice the thickness of the viable cell rim mea sured at a later stage of spheroid growth, This procedure tacitly assu mes that there is a linear relation between the diameter of necrosis a nd that of the whole spheroid over the entire range of emergence and g rowth of necrosis, However, some experimental investigations have demo nstrated that necroses do not grow gradually with spheroid diameter, b ut show a rapid initial increase, once a few cells have died, The pres ent article offers an explanation for this phenomenon, which is derive d from basic diffusion theory. Methods and Materials: A theoretical re lation between sizes of spheroids and of their central necroses is dev eloped, which is based on the assumption that formation of necrosis is caused by depletion of substrates or accumulation of metabolic waste products. In a second part, the theoretical model is fitted to experim ental data from the literature, and oxygen consumption rate as a funct ion of spheroid size is determined. Results: It turns out that the mod el closely mimics the experimentally observed behavior described above , These experimental results, therefore, do not furnish any evidence f or assuming other hypotheses of necrosis formation, Resulting O-2 cons umption rates are well in the range of previously published data, In a ll cases, approximations to the measured data are better than the corr esponding linear least squares fits. Conclusion: At least in some tumo r cell lines, depletion of substrates or accumulation of waste product s can explain formation of necrosis without the assumption of any addi tional mechanisms, Moreover, the model presented in this article offer s an alternative way of determining the turnover Fate of a substrate o r metabolic waste product provided that depletion/accumulation of this substance represents the cause for necrosis development.