Session Item

While Monte Carlo (MC) simulations are the gold standard for accurate dose calculation, their computational overhead often encourage the use of approximate pencil-beam (PB) algorithms, especially for demanding applications like the quantification of uncertainty through random dose scenario sampling.
Thus, while the inferior accuracy of PB in comparison to MC is extensively studied, it is not clear if and how such results translate to uncertainty estimates like mean and standard deviation (std. dev.) of dose given specific set-up and range uncertainties.
Here, we present a comparison of uncertainty estimates computed with MC and PB dose samples for a phantom and two patient cases.

We used the PB algorithm of the open source treatment planning system matRad with base data fitted to TOPAS MC simulations.
For matRad’s water box phantom, a paraspinal and a lung case, 100 samples were drawn from a multivariate normal distribution describing range and set-up errors (3.5% & 2mm std. dev., respectively).
For each sample, an MC simulation with TOPAS (cloud: 8 VMs w/ 28 cores) as well as a PB computation with matRad (Desktop, 8 cores) was performed, followed by calculation of mean and std. dev. of all dose scenarios.
Additionally, a fully analytical, PB-based uncertainty propagation was performed with analytical probabilistic modeling (APM). The resulting means and std. devs. were compared using a γ-analysis.
As reference, a similar comparison was performed for the nominal dose from PB and MC.

The table below shows γ-pass-rates comparing PB and APM calculations against MC using a criterion of 3%/3mm which had to be chosen over a more strict criterion in order to stay robust against statistical MC uncertainty (up to 1% of the prescribed dose).
To examine bias in the std. dev. calculation, the average std. dev. from MC and APM calculations is shown as well (PB nearly similar values as APM).

The large deviations for the std. dev. γ-pass-rates for the box phantom also manifested when comparing APM to PB, but could be raised to 99.8% when using more PB samples (5000) than the default 100.
Additionally, the figure below visualizes the mean and std. dev. of the dose for the lung case (with the worst γ-pass-rates).

The runtime varied by case (2-6 days for 100 MC simulations, 1-3 hours for 100 PB simulations).

Transferring the discrepancies known between MC and PB dose calculation to respective uncertainty is not trivial. Here, agreement between mean MC and PB estimates was substantially better than in the nominal case, whereas the std. dev. exhibited worse agreement. Yet, due to systematic overestimation of the std. dev., PB or APM may be acceptable for conservative uncertainty estimates. Further, limited statistical accuracy is achievable with MC due to runtime, which can efficiently be mitigated with APM or better PB statistics, which might justify the use of PB for estimating uncertainty and applications like probabilistic treatment planning even in heterogeneous cases.