Optimal radiation beam profiles considering the stochastic process of patient 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 fractions. For few fractions (less than or equal to 5), symmetry considerations reduce the problem so that it can be handled with ordinary numerical integration techniques. For the general case, including the frequently used 20-30 fractions, a Monte Carlo integration method has been developed. As may be expected, a linear response model for radiation sensitivity, based only on the total dose delivered, is insufficient for a large number of dose fractions with sharp beam edges. Under such circumstances the full linear quadratic model for cell survival has to be incorporated. The standard technique of opening up the fields to compensate for the positioning uncertainty is only feasible when the surrounding normal tissues tolerate radiation well. The present studies indicate that the probability of achieving tumour control without inducing severe injury to normal tissue can be increased if optimal non-uniform beams are used.