Robert Katz

The radial distribution of dose around the path of a heavy ion in liquid water

Abstract Monte Carlo calculations of the radial distribution of dose in liquid water, incorporating energy deposition due to primary excitations and ionizations, have been performed for protons of energy 1, 10, 20, 50 and 100 MeV. By combining these results with earlier semi-empirical formulae used in track structure theory calculations, a corrected analytic formulation has been developed which on radial integration closely reproduces the value of stopping power for protons in the energy range 0.1–1000 MeV. After including a β-dependent ‘effective charge’ formula, this corrected formulation is tested against all published measurements of radial distribution of dose from energetic ions in gaseous media. Though some inconsistencies at the closest and the farthest reaches of the radial distribution of dose remain, the overall agreement is very satisfactory, indicating that the ‘effective charge’ Z∗, and Z∗2/β2 scaling are phenomenologically valid concepts for describing the radial dose from heavy ions of energies above ∼ 0.5 MeV/amu.

THEORY OF RBE FOR HEAVY ION BOMBARDMENT OF DRY ENZYMES AND VIRUSES.

The response of dry enzymes and viruses to heavy ion bombardment may be predicted from their response to γ-irradiation (and no further knowledge of their size and structure). The molecules are appr...

Inactivation of Cells by Heavy Ion Bombardment

The tracks formed in nuclear emulsion by energetic heavy ions are made up of grains sensitized by the passage of a single ion. Cells may also be inactivated by the passage of a single ion, in a mod...

TRACK STRUCTURE THEORY IN RADIOBIOLOGY AND IN RADIATION DETECTION

Abstract The response of biological cells, and many physical radiation and track detectors to ionizing radiations and to energetic heavily ionizing particles, results from the secondary and higher generation electrons ejected from the atoms and molecules of the detector by the incident primary radiation. The theory uses a calculation of the radial distribution of local dose deposited by secondary electrons (delta-rays) from an energetic heavy ion as a transfer function, relating the dose-response relation measured (or postulated) for a particular detector in a uniform radiation field (gamma-rays) to obtain the radial distribution in response about the ions path, and thus the structure of the track of a particle. Subsequent calculations yield the response of the detector to radiation fields of arbitrary quality. The models which have been used for detector response arise from target theory, and are of the form of statistical models called multi-hit or multi-target detectors, in which it is assumed that there are sensitive elements (emulsion grains, or biological cell nuclei) which may require many hits (emulsion grains) or single hits in different targets (say, cellular chromosomes) in order to produce the observed end-point. Physically, a hit is interpreted as a ‘registered event’ caused by an electron passing through the sensitive site, with an efficiency which depends on the electrons speed. Some knowledge of size of the sensitive volume and of the sensitive target is required to make the transition from gamma-ray response to heavy ion response. Critical differences in the pattern of response of biological systems and physical detectors to radiations of different quality arise from the number of electrons which must pass through the sensitive volume to produce the recorded end-point. For biological cells this is typically 2 or more. This characteristic multi-hittedness results in survival curves with shoulders, or supralinear dose-response relations for gamma-irradiation, and for an ‘RBE’ which can exceed 1 at appropriate values of the ‘LET’. One-hit detectors cannot mimic the response of biological cells to radiations of different quality. From the beginning it has been clear that SSNTDs (etchable plastics) are not 1-hit detectors. But even now, we do not know their characteristic response to gamma-rays. We are not able to produce a satisfactory theory of track structure in these detectors. There is only a hint, that etching rate is nominally proportional to the quantity z 4 β 4 of the incident ion, suggesting the possibility of a ‘2-or-more’ hit detector. Recent work has demonstrated that many-hit physical detectors do exist. From both emulsion sensitometry and from the structure of tracks of heavy ions, we are able to show that emulsion-developer combinations exist which yield many-hit response. There is also some evidence that the supralinearity in thermoluminescent dosimeters arises from a mixture of 1-hit and 2-hit response, perhaps of different trap structures within the same TLD crystal. These detectors can be expected to mimic the response of biological cells to radiations of different quality. Their patterns of response may help us to understand better the structure of particle tracks in SSNTDs.

Radial Distribution of Dose and Cross-Sections for the Inactivation of Dry Enzymes and Viruses

A new semi-empirical algorithm for the radial distribution of dose is compared with available data. The algorithm is used to calculate the inactivation cross section for dry enzymes and viruses using an extended target model of a 1-hit detector. Agreement with data is at about the 15% level, approximating the precision of the data itself.

Supralinearity of peak 5 and peak 6 in TLD-700

Abstract Track theory has been applied to calculate the response of peak 5 and peak 6 in LiF (TLD-700) for H, He, C, O and Ne bombardment. Calculations reproduce experimental features of the heavy-ion response of TLD-700 and provide means of connecting the gamma and high-LET responses in thermoluminescent dosimeters.

Effects of track structure and cell inactivation on the calculation of heavy ion mutation rates in mammalian cells

It has long been suggested that inactivation severely effects the probability of mutation by heavy ions in mammalian cells. Heavy ions have observed cross sections of inactivation that approach and sometimes exceed the geometric size of the cell nucleus in mammalian cells. In the track structure model of Katz 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 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 for some ions. We show how the effects of inactivation may be taken into account in the evaluation of the mutation cross sections from heavy ions in the track structure model through correlation of sites for gene mutation and cell inactivation. The model is fit to available data for HPRT mutations in Chinese hamster cells and good agreement is found. The resulting calculations qualitatively show that mutation cross sections for heavy ions display minima at velocities where inactivation cross sections display maxima. Also, calculations show the high probability of mutation by relativistic heavy ions due to the radial extension of ions track from delta-rays in agreement with the microlesion concept. The effects of inactivation on mutations rates make it very unlikely that a single parameter such as LET or Z*2/beta(2) can be used to specify radiation quality for heavy ion bombardment.

Biological Effectiveness of High-Energy Protons: Target Fragmentation

High-energy protons traversing tissue produce local sources of high-linear-energy-transfer (LET) ions through nuclear fragmentation. We examine the contribution of these target fragments to the biological effectiveness of high-energy protons using the cellular track model. The effects of secondary ions are treated in terms of the production collision density using energy-dependent parameters from a high-energy fragmentation model. Calculations for mammalian cell cultures show that at high dose, at which intertrack effects become important, protons deliver damage similar to that produced by gamma rays, and with fragmentation the relative biological effectiveness (RBE) of protons increases moderately from unity. At low dose, where sublethal damage is unimportant, the contribution from target fragments dominates, causing the proton effectiveness to be very different from that of gamma rays with a strongly fluence-dependent RBE. At high energies, the nuclear fragmentation cross sections become independent of energy. This leads to a plateau in the proton single-particle-action cross section, below 1 keV/micron, since the target fragments dominate.

Electron Energy Dissipation

Abstract A new algorithm for the computation of the energy dissipated by normally incident, monoenergetic electron beams, provides good agreement with experimental data and with the computations of Spencer.

An analytic representation of the radial distribution of dose from energetic heavy ions in water, Si, LiF, NaI, and SiO2

Abstract An earlier representation of the radial distribution of dose about the path of a heavy ion in liquid water is modified and extended to include silicon, lithium fluoride, sodium iodide, and silicon dioxide.