Computational representations for electron microbeam microdosimetric quantities in one micron diameter spherical targets

Michael Todd Batdorf

In this study, computational tools were developed to gather, process, and fit simulated data resulting from the Monte-Carlo simulation of low energy electron particle tracks in liquid water using the Positive Ion Track Simulation (PITS) code set. To gather the data, the simulation space was packed with one micron diameter spheres in concentric rings to exploit angular symmetry, three million tracks were generated for initial beam energies ranging from 20 keV to 80 keV in 5 keV increments on a 16 node PC cluster, and histograms for stochastic quantities were tabulated for each sphere and placed in an XML file for archiving. Computational routines wrapping a preexisting B-spline library were then created to approximate the probability distributions and summary statistics for any stochastic quantity over a domain of target location and beam energy. Because of their biological significance, three particular quantities were chosen to illustrate the methods under varying conditions: the conditional mean of energy imparted ( [mu] E ), which is a summary statistic with a relatively simple nature; the probability of a track reaching a target ([phi]), which is a summary statistic with large peaks in its data set; and the energy deposited per unit tracklength of the primary particle ([lambda]), which is a stochastic whose distributions are approximately lognormal. For each of these quantities, approximations were created at various levels of refinement, with each approximation being tested for its storage requirements and its accuracy against a test data set. A second method of approximation using lognormal probability distribution curves and the method of least squares was pursued on the distributions of [lambda] for a set of locations and beam energies. Goodness-of-fit testing showed that these distributions may appear to be lognormal but are not statistically lognormal. Finally, an investigation was undertaken to determine whether the representations developed for the one micron diameter spheres could be applied to larger targets by packing the targets with the spheres and somehow aggregating the results. No methods were found for the stochastic representations, and methods that were assumed to work for summary statistics were shown to be inefficient.

Computational representations for electron microbeam microdosimetric quantities in one micron diameter spherical targets

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