Sensitivity of helium beam-modulator design to uncertainties in biological data

The goal in designing beam-modulating devices for heavy charged-particle therapy is to achieve uniform biological effects across the spread-peak region of the beam. To accomplish this, the linear-quadratic model for cell survival has been used to describe the biological response of the target cells to charged-particle radiation. In this paper, the sensitivity of the beam-modulator design in the high-dose region to the values of the linear-quadratic variables alpha and beta has been investigated for a 215-MeV/u helium beam, and implications for higher LET beams are discussed. The major conclusions of this work are that, for helium over the LET range of 2 to 16 keV/mu, uncertainties in measuring alpha and beta for a given cell type which are of the order of 20% or less have a negligible effect on the beam-modulator design (i.e., on the slope of the spread Bragg peak); uncertainties less than or equal to 10% in the dose-averaged LET at each depth are unimportant; and, if the linear-quadratic variables for the tumor differ from those used in the beam-modulator design by a constant factor between about 0.5 and 3, then the resultant nonuniformity in the photon-equivalent dose delivered to the tumor is within +/- 25%. It is also shown that for any ion, if the nominal values of alpha or beta used by the beam-modulator design program differ from their actual values by a constant factor, then the maximum errors possible in the beam-modulator design may be characterized by two limiting depth-dose curves such that the ratio of the dose at the proximal end of the spread Bragg curve to the dose at the distal end of the spread peak is given by alpha distal/alpha prox for the steepest curve, and square root of beta distal/beta prox for the flattest curve.