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 products, e.g. of lactate, which are expected to accumulate in the tumor spheroids. 3. An additional set of nomograms is given which is more convenient for determining time courses of these concentrations during spheroid growth. 4. A quantitative sensitivity analysis of parameter dependencies is performed to identify those parameters upon which a concentration of interest depends most critically in a given experimental situation.