OPTIMAL RADIATION BEAM PROFILES CONSIDERING THE STOCHASTIC-PROCESS OFPATIENT POSITIONING IN FRACTIONATED RADIATION-THERAPY

We present a solution to the problem of finding optimal beam profiles in fractionated radiation therapy when taking the uncertainty in beam patient alignment into account. The problem was previously solved for the special cases of one single dose fraction and infinitely many frac tions. For few fractions (less than or equal to 5), symmetry considera tions reduce the problem so that it can be handled with ordinary numer ical integration techniques. For the general case, including the frequ ently used 20-30 fractions, a Monte Carlo integration method has been developed. As may be expected, a linear response model for radiation s ensitivity, based only on the total dose delivered, is insufficient fo r a large number of dose fractions with sharp beam edges. Under such c ircumstances the full linear quadratic model for cell survival has to be incorporated. The standard technique of opening up the fields to co mpensate for the positioning uncertainty is only feasible when the sur rounding normal tissues tolerate radiation well. The present studies i ndicate that the probability of achieving tumour control without induc ing severe injury to normal tissue can be increased if optimal non-uni form beams are used.