Assessing Microdosimetric Uncertainties In Monte Carlo Simulations Due to Quantum Effects In Low-Energy Electron Transport
Abstract
Purpose
This study investigates the magnitude of systematic uncertainties that arise from ignoring quantum effects in semi-classical Monte Carlo (MC) simulations of low-energy electron transport through biological systems. We focus on microdosimetric quantities often relevant to targeted radiotherapy such as number of ionizations, distance between ionizations, radial energy deposition profiles, and shellwise specific energies per history.
Methods
We build upon existing methods involving simplified quantum systems of point scatterers by further including ionization processes. This addition of ionizations allows for the novel concept of a quantum history, whose probabilistic nature leads naturally to a treelike branching structure. On each quantum history (QM) we extract various microdosimetry quantities, and compare these to the predictions of an analogous MC method. Both QM and MC simulations involve electrons originating from the centre of a 2 nm sphere, use identical energy-dependent cross sections, and assert a single binding energy near the threshold energy of water or DNA.
Results
Relative to QM, MC methods overestimate the average number of ionizations by 20% and underestimate the average distance between ionizations by 17%. Considering energy deposited in each spherical shell, MC results are up to 10% lower than QM for initial kinetic energies above 64 eV, but this increases to 18% for 32 eV and 36% for 16 eV. The average relative error of specific energy deposited in spherical shells increases from -11% at 256 eV to -39% at 16 eV.
Conclusion
We have successfully implemented a tool to carry out simplified quantum simulations of electron transport and ionization, and can now predict select microdosimetric quantities. Across energy ranges relevant for radiotherapy, trends in relative error (e.g., ionization count overestimates; energy deposition underestimates) will contribute to uncertainty assessments in nanoscale research contexts, e.g. optimizing targeted radiotherapy with Auger emitters.