W.E. Wilson, J.H. Miller, D.J. Lynch, K. Wei and A. Kurtulus
Washington State University-TriCities, Richland, WA 99352, USA
Dosimetry calculations supporting the design of several low-LET irradiation facilities and the interpretation of experiments performed with them will be described. The computations involve event-by-event, detailed-histories Monte Carlo simulations of low energy electrons and soft x-rays interacting in a low-Z homogeneous medium. The spatial variation of absolute event frequency and the distribution in specific-energy are typically obtained from which one can estimate the dose for arbitrary cellular mono-layers growing on a thin substrate. This approach is an extension of Berger's point-kernel treatment into the microdosimetry realm.
Cellular Targets:
Preliminary calculations were performed with realistic cell-like target boundaries obtained by confocal microscopy of HeLa-cell monolayers 1). Two typical cell types (designated A and B) were selected for dosimetry calculations. The average radii of nuclei and cytoplasm were similar, except the thickness of the nuclear volume of cell A was approximately 25% greater than that of B, even though the total cellular thickness was comparable (6 and 7 micrometers respectively for A and B). Therefore, the cytoplasm above the nucleus was much thinner for cell A than cell B. This difference in cellular components had a significant effect on the mean energy imparted in the two cases and emphasizes that the actual cell morphology will be important in evaluating the dosimetry in radiobiology experiments.
25 keV Electrons:
Extensive dosimetry calculations have been made aimed at characterizing the spatial variation of the energy deposited by the slowing and stopping of individual energetic electrons independent of target size and shape 2). Electrons of 25 keV were simulated and energy deposition distributions scored in one micrometer spheres located at varied penetration and radial distances up to 15 micrometers from the entry point. The one micrometer scoring-sphere size was selected as a compromise between large enough to get reasonable statistics within acceptable computational time and still small compared to a real mammalian target cell. The 25 keV energy was selected for initial work because the energy deposited will be contained mostly within a typical mammalian cell. Single tracks were scored because their energy deposition distributions are fundamental. Computations for higher doses (multiple tracks) are underway and results will be compared with single-track mean values combined via binomial statistics.
Over the range of 15 micrometers in penetration, h, and radial distance, r, the event frequency decreases from 1 to less than 10-6. After the first micrometer, the event frequency decreases along the h direction approximately exponentially. The event frequency is more varied radially; at small penetration the event frequency decreases rapidly with radial direction, reflecting the low probability of very large angle scattering by the electron near its initial energy. At deeper penetration, the event frequency dependence takes on a more isotropic shape, as a result of many random small-angle scatterings. The variation of the mean specific energy deposited varies from about 0.2 Gy at the lowest to roughly 0.8 Gy near the end of the electron range. The mean specific energy initially decreases along the h-direction, passes through a minimum at about 4 micrometers, then increases again. As the electrons penetrate two things happen; they scatter away from their initial direction, and they slow down, i.e. their stopping power increases. These two effects account for the variation of energy deposition with penetration. Near the starting point the electrons will have nearly diametric paths across the 1 micrometer diameter site. As they penetrate and before they have lost significant energy, scattering begins to have an effect; some electrons will have shorter paths within the site and hence deposit less energy on average. This accounts for the initial decrease of energy deposition with penetration, h. Eventually the slowing, with associated greater stopping power, dominates and specific energy increases with further penetration and radial distance.
Soft X-rays:
A soft x-ray module has been added to our PITS suite of Monte Carlo radiation simulations tools. It is specifically designed to simulate the interactions of low energy photons, e.g., the characteristic x-rays of Carbon (278 eV), Aluminum (1487 eV) and Titanium (4509 eV). The three important interactions, photo electric effect, coherent (Rayleigh) scattering, and incoherent (Compton) scattering are included. The photo effect, since it is the more frequent, is simulated by "table-lookup". The other two interactions are simulated via the Monte Carlo rejection method using Klein-Nishina theory and published form factors and scattering functions. Bremsstrahlung production and beam focusing are features yet to be included. Atomic additivity is assumed for the absorbers and appropriate atomic source data have been assembled for all elements through Calcium plus Iron. Preliminary calculations are underway for the cell A and B target morphologies described above.
References:
1) J. H. Miller et al., Radiat. Environ. Biophysics 39 (2000) 173-177.
2) W. E. Wilson et al., Radiat. Res. 155 (2001) 89-94.
3) W. E. Wilson and H. Nikjoo, Radiat. Environ. Biophysics., 38 (1999) 97-104.
Acknowledgement: Work supported by the US Departmemt of Energy, Office of Biological and Environmental Research, under Grant No. DE-FG03-99ER62860.