Abstract Katz, R. The Parameter-Free Track Structure Model of Scholz and Kraft for Heavy-Ion Cross Sections. Radiat. Res. 160, 724–728 (2003). The “parameter-free”, “local effects” theory of Scholz and Kraft is an extension to mammalian cells of the theory of RBE for dry enzymes and viruses of Butts and Katz. Its claim for parameter freedom has been challenged elsewhere. Here we examine its conceptual base and find errors in its use of the physical concept of cross section and its neglect of the radiobiological relationship between target size and radiosensitivity in evaluating the radiation damage to “point targets”.

The d-ray theory of track structure is compared with experimental data for the radial dose from heavy ion irradiation. The effects of electron transmission and the angular dependence of secondary electron ejection are 95 included in the calculations. Several empirical formulas for electron range and energy are compared in a wide variety of materials in order to extend the application of the track-structure theory. The model of Rudd for the U secondary electronspectrum in proton collisions, which is based on a U modified classical kinematics binary encounter model at high energies and a 34 molecular promotion model at low energies, is employed. For heavier en projectiles, the secondary electron spectrum is found by scaling the effective on charge. Radial dose calculations for carbon, water, silicon, and gold are discussed. The theoretical data agreed well with the experimental data.

The phenomenological track-structure model of cell damage is discussed. A description of the application of the track-structure model with the NASA Langley transport code for laboratory and space radiation is given. Comparisons to experimental results for cell survival during exposure to monoenergetic, heavy-ion beams are made. The model is also applied to predict cell damage rates and relative biological effectiveness for deep-space exposures.

Track theory is combined with a realistic model of a heavy ion beam to study the effects of nuclear fragmentation on cell survival and biological effectiveness. The effects of secondary reaction products are studied as a function of depth in a water column. Good agreement is found with experimental results for the survival of human T-1 cells exposed to monoenergetic carbon, neon, and argon beams under aerobic and hypoxic conditions. The present calculation, which includes the effect of target fragmentation, is a significant improvement over an earlier calculation because of the use of a vastly improved beam model with no change in the track theory or cellular response parameters.

Response parameters that describe the production of recessive lethal mutations in C. elegans from ionizing radiation are obtained with the Katz track structure model. The authors used models of the space radiation environment and radiation transport to predict and discuss mutation rates for C. elegans on the IML-1 experiment aboard STS-42.

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The average track model describes the response of physical and biological systems using radial dose distribution as the key physical descriptor. We report on an extension of this model to describe the average distribution of electron spectra as a function of radial distance from an ion. We present calculations of these spectra for ions of identical linear energy transfer (LET), but dissimilar charge and velocity to evaluate the differences in electron spectra from these ions. To illustrate the usefulness of the radial electron spectra for describing effects that are not described by electron dose, we consider the evaluation of the indirect events in microdosimetric distributions for ions. We show that folding our average electron spectra model with experimentally determined frequency distributions for photons or electrons provides a good representation of radial event spectra from high-energy ions in 0.5–2 μm sites.

An analytic method is described for evaluating the average radial electron spectrum and the radial and total frequency-event spectrum for high-energy ions. For high-energy ions, indirect events make important contributions to frequency-event spectra. The method used for evaluating indirect events is to fold the radial electron spectrum with measured frequency-event spectrum for photons or electrons. The contribution from direct events is treated using a spatially restricted linear energy transfer (LET). We find that high-energy heavy ions have a significantly reduced frequency-averaged final energy (yF) compared to LET, while relativistic protons have a significantly increased yF and dose-averaged lineal energy (yD) for typical site sizes used in tissue equivalent proportional counters. Such differences represent important factors in evaluating event spectra with laboratory beams, in space- flight, or in atmospheric radiation studies and in validation of radiation transport codes. The inadequacy of LET as descriptor because of deviations in values of physical quantities, such as track width, secondary electron spectrum, and yD for ions of identical LET is also discussed.

In the track structure model, the inactivation cross section is found by summing an inactivation probability over all impact parameters from the ion to the sensitive sites within the cell nucleus. The inactivation probability is evaluated by using the dose response of the system to gamma rays and the radial dose of the ions and may be equal to unity at small impact parameters. We apply the track structure model to recent data with heavy ion beams irradiating biological samples of E. Coli, B. Subtilis spores, and Chinese hamster (V79) cells. Heavy ions have observed cross sections for inactivation that approach and sometimes exceed the geometric size of the cell nucleus. We show how the effects of inactivation may be taken into account in the evaluation of the mutation cross sections in the track structure model through correlation of sites for gene mutation and cell inactivation. The model is fit to available data for HPRT (hypoxanthine guanine phosphoribosyl transferase) mutations in V79 cells, and good agreement is found. Calculations show the high probability for mutation by relativistic ions due to the radial extension of ions track from delta rays. The effects of inactivation on mutation rates make it very unlikely that a single parameter such as LET (linear energy transfer) can be used to specify radiation quality for heavy ion bombardment.

The assessment of biological damage from the galactic cosmic rays (GCR) is a current interest for exploratory class space missions where the highly ionizing, high-energy, high-charge ions (HZE) particles are the major concern. The relative biological effectiveness (RBE) values determined by ground-based experiments with HZE particles are well described by a parametric track theory of cell inactivation. Using the track model and a deterministic GCR transport code, the biological damage to mammalian cell cultures is considered for 1 year in free space at solar minimum for typical spacecraft shielding. Included are the effects of projectile and target fragmentation. The RBE values for the GCR spectrum which are fluence-dependent in the track model are found to be more severe than the quality factors identified by the International Commission on Radiological Protection publication 26 and seem to obey a simple scaling law with the duration period in free space.

Risk assessment calculations are presented for the preliminary proposed solar minimum and solar maximum orbits for Space Station Freedom (SSF). Integral linear energy transfer (LET) fluence spectra are calculated for the trapped proton and GCR environments. Organ dose calculations are discussed using the computerized anatomical man model. The cellular track model of Katz is applied to calculate cell survival, transformation, and mutation rates for various aluminum shields. Comparisons between relative biological effectiveness (RBE) and quality factor (QF) values for SSF orbits are made.

The effects of nuclear reactions on integral low-linear-energy-transfer (LET) protons spectra are studied, behind typical levels of spacecraft and body shielding, for the historically largest flares using the high-energy transport code BRYNTRN in conjunction with several biological damage models. The cellular track model of Katz provides an accurate description of cellular damage from heavy ion exposure. The track model is applied with BRYNTRN to provide a LET decomposition of survival and transformation rates for solar proton events. In addition, a fluence-based risk coefficient formalism is used to estimate Harderian gland-tumor induction in rodents and cataractogenesis in rabbits from solar flares, and a LET analysis is used to assess the relative contribution from target fragments on these biological endpoints.