Joint oxygen-glucose deprivation as the cause of necrosis in a tumor analog.

The sandwich system was recently developed as an in vitro tumor analog. Like spheroids, sandwiches are organized, multicellular systems in which the interplay between diffusion and consumption leads to the formation of spatial gradients; a necrotic center and a viable cell border subsequently develop. Using sandwiches of the 9L and V79 cell lines, the effects of oxygen and glucose deprivation on the onset and formation of necrosis were investigated. The data indicate that in sandwiches necrosis is a result of a shortage of both substances. Complementary cell monolayer experiments to determine a number of consumption parameters were performed. On the basis of the data, we propose a joint oxygen-glucose deprivation model for V79 cell necrosis. It is assumed a cell dies when oxygen deprivation in conjunction with glucose deprivation lowers the cell's ATP production rate below a critical value. Interactions of the concentrations and consumptions of oxygen and glucose are analyzed theoretically; concentration profiles are obtained by numerically solving coupled non-linear integral equations arising from the diffusion equation. The predicted viable border widths are in good agreement with the observed values.