The Associated Volume sampling algorithm as an alternative method for the calculation of ionisation cluster size distributions in computational nanodosimetry

In computational nanodosimetry, Monte Carlo Track Structure (MCTS) simulations are employed to calculate ionisation cluster size distributions (ICSDs), which are crucial for characterising mixed radiation fields at the nanoscale. The Uniform Sampling (US) algorithm, commonly used for this purpose, is inefficient when evaluating ICSDs conditioned on clusters exceeding a given size $\nu$ threshold. This study investigates a more efficient alternative - the Associated Volume (AV) algorithm - against the US approach for computing conditional ICSDs ($\nu \ge 1$) from proton tracks simulated with Geant4-DNA. Two configurations of the AV algorithm were evaluated: the standard AV-Overlap, allowing sensitive volumes to overlap (with a 1/$\nu$ correction), and the novel AV-No Overlap, which prevents overlap. We compared the conditional ICSDs, mean cluster size ($M_1$), complementary cumulative frequencies ($F_k$ for $k \in [2,7]$), and overall execution time per run and per event. Deviations exceeding two standard deviations of the mean difference were considered statistically significant. Although statistically significant differences in ICSDs, $M_1$ and $F_k$ were observed, the relative differences in the AV-Overlap rarely exceeded 5%, whereas the No Overlap configuration they ranged from $\lt$ 1% to approximately 15% at the higher $F_k$. Both AV configurations achieved execution times one to two orders of magnitude shorter than the US algorithm. Our findings indicate that the AV-Overlap algorithm may be a preferred alternative for calculating conditional ICSDs and derived nanodosimetric quantities, offering a substantial gain in computational efficiency without compromising accuracy.