On the use of the pion stopping distribution and the lesion additivity concept for the calculation of effective doses in pion treatment planning.

The large spatial variation in LET, and hence in RBE, is one of the main obstacles in the development of routine treatment planning of charged particle beams. Since the biological effect distribution of plans cannot be realistically measured for each patient, a simple scheme of relating effect to basic empirical physical measurement is required. For the case of a pion beam, the high LET dose distribution is correlated with that of the pion stopping density, which can be indirectly measured using several techniques. A scheme based on this spatial correlation has been developed. In this method, after partitioning the local dose into a high and a low LET fraction, the local effective dose is computed using a simple formula extracted from a recent analysis of radiobiological results for mixtures of radiations of different LET. This simple formula can also be derived from a mechanistic model of mixed radiation action developed using the hypothesis of additivity of common intermediate lesions. In this paper, the concept of spatial correlation between the high LET dose and the pion stars is merged with the concept of lesion additivity for mixed radiation, from which a simple computational scheme is formulated for the calculation of effective doses in the treatment planning of pions. Similar schemes can also be developed for other charged particle beams.