Computation of cell survival in heavy ion beams for therapy. The model and its approximation

A simplified method for the calculation of mammalian cell survival after charged particle irradiation is presented that is based on the track structure model of Scholz and Kraft [1, 2]. Utilizing a modified linear-quadratic relation for the x-ray survival curve, one finds that the model yields linear-quadratic relations also for heavy ion irradiation. If survival is calculated as a function of specific energy, z, in the cell nucleus--thus reducing the stochastic fluctuations of energy deposition--the increase in slope of the survival curve and therefore the coefficient beta z can be estimated with sufficient accuracy from the initial slope, alpha z. This permits the tabulation of the coefficients alpha z for the particle types and energies of interest, and subsequent fast calculations of survival levels at any point in a mixed particle beam. The complexity of the calculations can thereby be reduced in a wide range of applications, which permits the rapid calculations that are required for treatment planning in heavy ion therapy. The validity of the modified computations is assessed by the comparison with explicit calculations in terms of the original model and with experimental results for track-segment conditions. The model is then used to analyze the influence of beam fragmentation on the biological effect of charged particle beams penetrating to different depths in tissue. In addition, cell-survival rates after neuron irradiation are computed from the slowing-down spectra of secondary charged particles and are compared to experimental observations.