Performance of DBS in a Broad Beam

We also tested the performance of DBS in the simulated 6 MV SL25 photon beam by examining fluence efficiency at the SSD (100 cm) with the jaws widened to give a 40$\times$40 cm$^2$ field. The jaws simulated in this case were the ``standard" jaws (10 cm thick, comprising 5 cm of tungsten and 5 cm of lead) instead of the jaws for use with a multi-leaf collimator that were used to determine performance of DBS with a 10$\times$10 cm$^2$ field in this accelerator (see section IV. above). Other than the jaws and their settings, the simulation geometry and other parameters were identical to those used with the 10$\times$10 cm$^2$ field.

The splitting parameters used for all splitting routines were those found to optimize performance in the 6 MV SL25 accelerator with a 10$\times$10 cm$^2$ field (see section IV.B. above), with the exception of the splitting field size, FS, in SBS and the splitting field radius in DBS. For SBS, FS was set to 60 cm. This setting is based on the performance of SBS as a function of FS in the 10$\times$10 cm$^2$ beam (see section IV.B.2. above), where little improvement in photon fluence efficiency was observed for values of FS $>$ field size + 20 cm. The splitting radius used in DBS was 30 cm. This radius completely encloses the 40$\times$40 cm$^2$ field, allowing for 2 cm beyond the corners of the field. Note that with such a large splitting radius, the difference in efficiency with a small change in the splitting radius (eg reducing it by 2 cm so that it exactly encloses the field) is expected to be negligible.

For the purposes of scoring fluence, the phase-space surface at SSD=100 cm was divided into 6561 (81$\times$81) 1$\times$1 cm$^2$ scoring zones. As with the study of photon fluence efficiency in the 10$\times$10 cm$^2$ beam, efficiency of all splitting algorithms is expected to increase as the area of the scoring zones is decreased (see section IV.A. above). Unlike the 10$\times$10 cm$^2$ field case, the 1$\times$1 cm$^2$ scoring zones were used for both photon and electron fluence efficiency profiles.

Figure: Photon (a) and electron (b) fluence efficiency vs X (at Y=0) at the SSD (100 cm) for a simulated 6 MV SL25 photon beam with jaws expanded to give a 40$\times$40 cm$^2$ field. Efficiencies are relative to the efficiency with no splitting. The arbitrarily normalized photon and electron fluence profiles at Y=0 are also shown for comparison. For UBS, NBRSPL was set to 250. For SBS, NBRSPL=1000 and the splitting field size, FS, was set to 60 cm. For DBS, NBRSPL=1000, splitting field radius was 30 cm, Z of the electron splitting plane was 15.66 cm (the back of the flattening filter), and Z of the Russian Roulette plane was 15.5 cm.

Figure 11 shows the photon (a) and electron (b) fluence efficiency profiles (efficiency vs X at Y=0) at SSD=100 cm in the 40$\times$40 cm$^2$ beam. Efficiencies are relative to efficiency with no splitting. Photon and electron fluence profiles are also shown for reference. The fluctuations in relative electron fluence efficiency with DBS visible in Figure 11b are due mainly to fluctuations in efficiency with no splitting (i.e., the normalizing quantity) ultimately caused by the small scoring zones.

It is clear from the figures that, in the broad beam, DBS still offers a substantial improvement in efficiency over the other splitting routines. In the case of photon fluence within the field ($-$20 cm $\leq$ X $\leq$ 20 cm), DBS is between 5.5 (at the centre of the field) and 7 (at the edges of the field) times more efficient than SBS and is $\approx$12 times more efficient than UBS. Between the edges of the field and the edge of the splitting field (20 cm $\leq$ $\vert$X$\vert$ $\leq$ 30 cm), the relative photon efficiency with DBS increases, resulting in the ``horns" in Figure 11(a). This increase is due to the high uncertainty (low efficiency) in the photon fluence with no splitting in this region. In the case of electron fluence, the efficiency using DBS is $\approx$8 times greater than with SBS and $\approx$14 times greater than with UBS in the field.

The efficiency of DBS in the broad beam is significantly lower than in the 10$\times$10 cm$^2$ beam (Figure 6), with photon fluence efficiency inside the field dropping by a factor of $\approx$1.7 and electron fluence efficiency inside the field dropping by a similar amount. In comparison, photon fluence efficiency inside the field using SBS drops by a factor of only 1.1 (at the centre of the field) to 1.5 (at the edges of the field) in the broad beam, with electron fluence efficiency dropping by a factor of only $\approx$1.2. In the case of UBS, the drop in photon and electron fluence efficiency in the broad beam compared to the 10$\times$10 cm$^2$ beam is insignificant.

The directional splitting routines (SBS and DBS) are less efficient in the broad beam simply because of the required increase in splitting field size. In the case of DBS, this results in both fewer photons being eliminated by Russian Roulette and more photons being generated by the do_smart_brems and do_smart_compton subroutines. In the case of SBS, this results in a higher splitting number over a greater range of incident electron directions/energies. The reason that the overall efficiency drop in the broad beam is relatively greater for DBS than for SBS may be due to the increased number of split Compton interactions in DBS (SBS does not split these interactions). In the case of UBS, the change in field size does not change the number of split photons that must be tracked, resulting in no significant efficiency change.

It is interesting to note that for a given splitting routine in both broad beam and 10$\times$10 cm$^2$ cases, the relative electron fluence efficiency is of the same order as the relative photon fluence efficiency which is useful since electron contamination plays a more important role in the broad beams.