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A method for finding optimal primary fluence profiles for multiple field external beam radiation therapy techniques has been developed using a radiobiologically based objective function that quantifies the probability of achieving complication-free tumor control, P+. The objective function P+ has the valuable property of giving the highest possible dose to the tumor without causing severe damage to normal tissues at risk. This radiobiologically based objective function selects suitable dose levels but also takes into account the dose homogeneity in the target volume to the extent that it is not causing an excessive risk of local recurrence or damage to surrounding normal tissues. The biological parameters used can either be patient specific, as determined by a predictive assay on biopsy specimens, or taken from a library of radiobiological parameter values characteristic for different tissue types of a reference patient. In its present form the method can be used to determine the optimum incident photon fluence profiles for each beam. The method has been used to investigate for a given target volume a large number of combinations of beam entry directions to find the best beam orientations with respect to the probability of achieving complication-free tumor control. It is demonstrated that when nonuniform dose delivery is available it is unsuitable to combine parallel opposed beams in two-beam techniques and to a lesser extent also to use perpendicular beams. In two-beam techniques the best angle between the beams is generally in the 100 degrees-120 degrees range. The major symmetry characteristics of the P+ phase space for two-beam techniques are also identified. The method can easily be extended from two to three dimensions and noncoplanar geometry, but it is presented here in its two-dimensional form for clarity and speed of calculation.
Södertröm et al. (Thu,) studied this question.