Microdosimetric structure of heavy ion tracks in tissue

Abstract

Energy dissipation in tracks of high energy heavy ions in tissue shows a lateral spread of several to many microns depending on the energy of the primary particle. Complete dosimetric characterization, therefore, requires in addition to the Linear Energy Transfer (LET) information on the radial energy distribution. The theory of track structure distinguishes two regions: core and penumbra. The core is a narrow central zone with a radius in tissue far below 1 micron where energy deposition occurs mainly in processes of excitation and electron plasma oscillation. According to the Equipartition Principle, half of the total energy dissipation accrues in this manner. The penumbra is a peripheral zone enveloping the core where energy deposition occurs mainly in ionization events by energetic secondary electrons released by the primary particle in the center of the core traveling at rather high speed thus spreading laterally. The extension of the penumbra depends in a complex manner on the maximum transferable energy to electrons which in turn depends on the speed of the primary particle. Local energy density in the penumbra decreases with the square of increasing radius. It therefore amounts only to a very small fraction of the core density already a few microns away from the center. In general terms, track structure can be described as exhibiting a core of enormous energy density with lateral dimensions remaining entirely on the submicroscopic level surrounded by a penumbra where energy density drops precipitously to very small levels. The relationships are illustrated with micrographs of different sections of a heavy particle track in nuclear emulsion and their counterpart graphical plots.

Effect of Recombination between a Molecular Ion and an Electron on Radial Dose in the Irradiation of a Heavy Ion

“…We take t max to be 5 fs, 50 fs, and 100 fs for Figures 4 (a) and (b) and to be only 100 fs for Figures 4 (c -f). We also show our previous results (Moribayashi, 2014a) that correspond to R D obtained from excluding TBR and the conventional distributions (Katz & Kobetich, 1969, Chatterjee & Schaefer, 1976, Magee & Chatterjee, 1980.…”

“…Two types of radial dose distributions have been available (Kase et al, 2008), where we call them 'Katz type distribution' (Katz & Kobetich, 1969;Kraft et al, 1992) and 'Chatterjee type distribution' (Chatterjee & Schaefer, 1976;Magee & Chatterjee, 1980), respectively in this paper after the name of first developers of these distributions. There is a different feature in the region near the incident ion path between these distributions although this region is the most important to estimate the cell survival (Kase et al, 2008).…”

“…The paradigms employed in these distributions are the free electron gas (Lindhard & Winther, 1964;Ziegler et al, 2008) and the binary collision models (Katz & Kobetich, 1969;Kraft et al, 1992), respectively. In the Chatterjee type distribution (Chatterjee & Schaefer, 1976;Magee & Chatterjee, 1980) where the free electron gas model is employed, the electric field due to the induced polarization produces plasma oscillation that enhances the radial dose. However, in this model, the ionization energy of a molecule in the target is ignored.…”

“…The solution provided by Bloch indicates that we must consider the ionization energy of a molecule in the weak scattering because it becomes comparable with the energy transfer. It should be noted that the free electrons, which are produced from the weak scattering, forms the plasma oscillation and that this oscillation enhances radial dose in the Chatterjee type distribution (Chatterjee & Schaefer, 1976;Magee & Chatterjee, 1980). In our model, which is based on the binary collision model, we consider not only the impact processes between each individual charged particle (ion, free electron etc.)…”

Radially restricted linear energy transfer for high-energy protons: A new analytical approach

“…Two approaches have been widely used. Chatterjee et al (1973) and Chatterjee and Schaefer (1976) presented an equation for the radial energy deposition around the trajectory of a heavy charged particle in water, the core and penumbra model. It is assumed that excitations form a core of high-energy deposition in the center of the particle track, while the ~ electrons transport their energy away from the core and form a penumbra around it.…”