An investigation of nanodosimetric parameters for realistic geometries and a novel study of the track structure Penumbra region
Relative Biological Effectiveness (RBE) used in radiotherapy can be derived from the study of nanodosimetric parameters of particle track structure (TS). In nanodosimetry, the ionization component of charged particle TS is characterized by the measurement or calculation of the frequency distribution of ionizations in target volumes that are used to simulate nanometric sites in liquid water. In the current study, Monte Carlo simulation tools and software analysis techniques are employed in the mapping of nanodosimetric parameters radially from and along proton tracks. Two approaches were used to study the radial dependence of nanodosimetric quantities around protons tracks. A heuristic approach was ultimately used to evaluate changes along the track pathlength, and secondly, a more accurate approach was used to provide a detailed analysis of both the core and penumbra regions. For the first approach, a nanodosimetric TS analysis attempt is presented to address the issue of RBE variation in a Spread-Out Bragg Peak (SOBP) of protons. The Geant4-DNA simulation package is used for the simulation and capture of the ionization component of protons of 100 MeV initial energy and their secondary electrons propagating in water. The frequency distribution of ionization clusters formed in target volumes corresponding to a 10 base-pairs segment of Deoxyribonucleic Acid (DNA) was obtained as a function of the radial distance between target and proton trajectory for a set of positions along the proton path. The radial dependence of nanodosimetric parameters was analyzed using a heuristic model function to obtain an Effective Track Cross-Section (ETCS) derived from the integration of the model as a function of the proton’s residual range. The results were convolved with weighted range distributions suggested in the literature for the construction of the SOBP. In the second approach, a more detailed investigation into the nanodosimetric properties of the track structure of protons in water at energies relevant for proton radiotherapy follows from the heuristic study above. The ionization component of the tracks is still simulated using Geant4-DNA for proton start energies between 1 MeV and 100 MeV. From the simulation results, the frequency distribution of ionization clusters formed in nanometric target volumes was obtained dependent on the impact parameter of the proton trajectory vii with respect to the target centre. In the track core, targets of cylindrical shape and a size comparable to a short segment of DNA were used for scoring ionization cluster size distributions. For the penumbra region, three different options for defining the cylinder shell segments were investigated, with each cylinder shell segment volume the same as the cylinder target volume. The radial distributions were numerically integrated to obtain the effective track cross-sections with respect to different nanodosimetric parameters. Graphically displaying the radial dependence in a similar way as microdosimetric distributions allowed elucidating the contribution of different radial distances to the overall radial integral of the quantities under consideration. Furthermore, it was tested how well the radial dependence of the nanodosimetric parameters could be fitted with a model function derived in literature for the radial energy deposition in proton tracks. The calculated ionization cluster size distribution from charged particle radiation tracks depend heavily on the size, geometry, and material of the target volume. The geometry of the target, specifically its orientation relative to the direction of the primary track, is investigated in this study. Simulations performed in the first approach are used to investigate the dependence of nanodosimetric parameters on target orientation. A related investigation involved the ion counter nanodosimeter at the Physikalisch Technische Bundesanstalt (PTB), where both the electrical field and the extraction aperture define the size and shape of the sensitive volume. In this study, a procedure to determine a cylindrical effective measurement target that is based on the second moments of the detection efficiency map is presented. The efficiency map is represented by an analytical model used in the investigation of the dependence of the simulated site size on the nanodosimeter’s operating parameters. The ETCS derived from the heuristic model shows an increase in the distal end region of the SOBP in qualitative agreement with radiobiological observations of enhanced cell damage in this region. The results demonstrate that nanodosimetric track characteristics may be used for qualitatively predicting the variation of the probability for induction of lethal lesions in cells. In the second approach, it was found that the model function from literature allows describing only the radial dependence of the total frequency of nanometric targets where ionizations occur. The deviation from a 1⁄���� dependence of the radial dependence of the frequency of targets receiving more than a minimum number of ionizations (exceeding one) includes a second peak centred around 10 nm radial distance from the proton trajectory. Calculated nanodosimetric parameters are found to have some dependence on the orientation of the target. With respect to the investigation for the derivation of the wall-less target in a nanodosimeter, the results show that within the limits of the simplifying assumptions, the model of an effective cylindrical target gives a reasonable approximation of the efficiency map.
A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy to the Faculty of Science, University of the Witwatersrand, 2021