Computation of cell survival in heavy ion beams for therapy

Abstract

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.

Review of Geant4-DNA applications for micro and nanoscale simulations

“…The authors concluded that the energy deposition clustering yields per event in the fragmentation region were approximately three times less than those induced by the 400 MeV/amu carbon beam within a few centimetres of the phantom surface. These calculations suggest an agreement with the RBE ratio of 3 between the entrance beam and the Bragg peak tail as measured by Scholz et al [98] in Chinese hamster ovary cells.…”

Applications of amorphous track models in radiation biology

“…Along with the ion kill-gamma kill (IGK) model of Katz, the models of Scholz and Kraft [16,17] and Wilson et al [18] have also used the radial dose and gamma-ray response to describe ion effects. We first discuss the approach of Katz and then the alternate features of other models.…”

“…The mutation efficiency is assumed to be directly proportional to this fraction multiplied by the total LET. This model differs from the approach of other amorphous track models [1][2][3][16][17][18] since the response of the bacteria to gamma-rays is not considered.…”

“…However, in the IGK model the gamma-kill and ion-kill modes both originate from the photon dose-response curve: ion-kill through the formation of the action crosssection, and gamma-kill directly in terms of the gammakill dose, which introduces the parameter σ 0 . In order to avoid the necessity of Monte Carlo sampling to include contributions from multiple tracks, Scholz et al [17] have introduced an approximation scheme where an α−β model for the ion dose response is used with the value of α from the one-track contribution and the β term an approximation to multiple-track contributions. This type of approximation is very useful for applications and, although done in a distinct manner, very much follows the spirit of ion-kill and gamma-kill modes introduced by Katz, and unavoidably introduces a new parameter to predict inter-track contributions.…”

“…The formation of chromosome aberrations is mediated by recombination processes [13,14], and a role for signal transduction is known [15], so even here there are no complete mechanistic descriptions, although there are models that may make such claims. Amorphous track models have had many useful applications where extrapolations of radiation biology data are needed to other doses or dose-rates, other particle types, and for mixed field environments [1][2][3][16][17][18][19]. Applications of the amorphous track models have been seen in radiobiology and cancer therapy with heavy ion beams, and in space radiation protection.…”