Distributions of oxygen, nutrient, and metabolic waste concentrations in multicellular spheroids and their dependence on spheroid parameters.

The distribution of oxygen, nutrients and metabolic wastes in multicellular tumor spheroids and its dependence on the parameters characterizing the spheroid (i.e., spheroid geometry, diffusivity, and consumption/production rates of biological substances) have been investigated by a theoretical analysis: 1. Parameter dependence is qualitatively demonstrated and visualized. 2. Reduction of the number of variables by specific coordinate transformations made it possible to generate nomograms from which concentration distributions for any choice of parameter values may easily be obtained. In particular, these nomograms may also be used for estimating concentration profiles of metabolic waste pro…