Viability of the EUD and TCP concepts as reliable dose indicators

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Abstract
The concept of equivalent uniform dose (EUD) was introduced to provide a method of reporting radiotherapy dose distributions which takes account of the nonlinearity of tissue dose-response, whilst not attempting to make predictions of absolute outcome. The purpose of this investigation was to determine the level of sensitivity of EUD to model parameters for significant variations in dose distribution and consequently the reliability of the factor as a dose-indicator, and to compare EUD with the more familiar index, tumour control probability (TCP). EUD and TCP, derived from the linear-quadratic formalism, were investigated for a test tissue being irradiated non-uniformly. Variations in the parameters of the model (tissue cell characteristics, dose heterogeneity, fractionation parameters) indicated the sensitivity of EUD and TCP to them. For time independent factors--cell density, cell radiosensitivity, radiosensitivity heterogeneity (population averaged) and ratio alpha/beta--EUD was found to vary insignificantly in comparison with TCP, though this is a function of the actual form of the dose distribution under consideration. For fractionated treatments where the mean dose per fraction is varying (due to dosimetric/positioning errors for example), both EUD and TCP showed little variation with the degree of dose non-uniformity. For other time dependent factors, fractionation rate and cell repopulation times, TCP again showed significant variation relative to EUD. The relative insensitivity of EUD implies that this index will be useful for dose evaluation when parameters are not known with accuracy, for the intercomparison of dose control studies and as a radiobiologically based optimization objective. However, given confidence in model parameters, the sensitivity of TCP would make it a more reliable tool for indicating potentially successful and unsuccessful irradiation strategies. It is suggested that both parameters be used in conjunction, with EUD and TCP results viewed with an appreciation of the characteristics of each model.