Theoretical considerations for improving tumour targeting.

To determine the relative importance of factors influencing tumour uptake of antibodies, we used a mathematical model to simulate intravenous injection of substances of varying molecular sizes and tumour-binding affinities at several dose levels. The FACSIMILE program was used to simulate the time course of tumour uptake of the tumour-binding substance by calculating the instantaneous tumour content (TC) and tumour:background uptake ratios (UR). Relative total doses to tumour and normal tissue were calculated by integration of TC/time curves. The model was used to make theoretical predictions on the effects of altering different parameters. The size of the injected dose in relation to the number of tumour receptors was crucial:if too low, uptake could not be improved by manipulating other variables, and if too high, the UR for large binding molecules was reduced. Using the standard scanning dose of labelled antibody, absolute numbers of labelled molecules binding to tumour could be increased by injection of a large excess of unlabelled molecules. Given an adequate dose, peak tumour content increased with increasing affinity up to receptor saturation. The peak uptake ratio rose progressively with affinity for a small ligand, but reached a relatively low plateau for antibody due to constant high background levels. At low doses such as those currently administered for diagnostic scanning with antibody, no effect of increasing affinity was predicted.