A fuzzy convolution model for radiobiologically optimized radiotherapy margins

In this study we investigate the use of a new knowledge-based fuzzy logic technique to derive radiotherapy margins based on radiotherapy uncertainties and their radiobiological effects. The main radiotherapy uncertainties considered and used to build the model were delineation, set-up and organ motion-induced errors. The radiobiological effects of these combined errors, in terms of prostate tumour control probability and rectal normal tissue complication probability, were used to formulate the rule base and membership functions for a Sugeno type fuzzy system linking the error effect to the treatment margin. The defuzzified output was optimized by convolving it with a Gaussian convolution kernel to give a uniformly varying transfer function which was used to calculate the required treatment margins. The margin derived using the fuzzy technique showed good agreement compared to current prostate margins based on the commonly used margin formulation proposed by van Herk et al (2000 Int. J. Radiat. Oncol. Biol. Phys. 47 1121-35), and has nonlinear variation above combined errors of 5 mm standard deviation. The derived margin is on average 0.5 mm bigger than currently used margins in the region of small treatment uncertainties where margin reduction would be applicable. The new margin was applied in an intensity modulated radiotherapy prostate treatment planning example where margin reduction and a dose escalation regime were implemented, and by inducing equivalent treatment uncertainties, the resulting target and organs at risk doses were found to compare well to results obtained using currently recommended margins.