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Monte Carlo MC simulation techniques are presently considered to be the most reliable method for radiation therapy treatment planning.

Some of these manuwl MC codes are being used as a dose engine for MC-based treatment planning in the routine clinical setting. VRTs do not change the physics and therefore do not bias the results. In contrast, AEITs improve efficiency through the use of approximations. The use of sophisticated variance reduction and approximate efficiency improving techniques, combined with parallel processing in computer clusters and the continuing increase in computing power, will help beamncr MC-based treatment planning a mainstay option in radiation oncology departments.

Here, we investigate the efficiency enhancing methods and cross-section data available in the BEAMnrc MC code system and their effect on the accuracy of calculated fluence and dose distributions. Three main areas were considered. The initial number of histories was set to obtain approximately the same number of particles in the PHSP files, i.

The current version of BEAMnrc allows the user to choose three photon cross sections: The electron and photon cutoff energies were set to 0. The parameter values chosen for the different techniques are recommendations from previous published works 1930 or are considered to be reasonable estimates, based on information from the BEAMnrc developers.

The mean energy and planar fluence were extracted from the PHSP in circular ring bins of equal area, the spectral distribution in energy bins of equal bin width, and the angular distribution in angular bins of equal bin width. It has been reported that this option increases the efficiency of homogeneous phantom calculations, 38 however, no photon splitting or charged particle range rejection were employed.

An additional phantom with a 5 cm air gap embedded in water was also simulated for dose computations. All MC simulations were performed on a 2. In addition, the methods for performing the efficiency and statistical uncertainty calculations are described. The current version of BEAMnrc allows the user to choose three different photon cross sections: The default differential cross section for the bremsstrahlung interactions is Bethe—Heitler BH. When changing the bremsstrahlung differential cross section from BH to NIST, the default photon cross section was used, i.

In our study, ESAVE was set to 2 MeV in all component modules with the exception of the target where the electron cutoff energy value was used, as recommended in Sheikh—Bagheri et al. This is a technique, recently introduced in BEAMnrc18 that is more efficient than the standard range rejection scheme just described. Augmented range rejection accounts correctly for bremsstrahlung production, since charged particles surviving Russian Roulette and with their weight increased by a factor of NBRSPL still have a chance to undergo bremsstrahlung events.

The boundary crossing algorithm together with the electron transport algorithm constitutes the condensed history technique used by a particular MC code system. The three options for bremsstrahlung photon splitting were used in this study, i. Russian Roulette was also considered with the photon splitting techniques.

When using UBS, each bremsstrahlung event produces a predefined number of bremsstrahlung photons, each having a weight equal to the inverse of the splitting number NBRSPL times the weight of the electron that underwent the bremsstrahlung event. With SBS, the value of NBRSPL is changed in order to maximize the splitting of photons aimed into the field and to minimize unnecessary splitting of photons aimed away from the field.

When photon splitting was used together with the other techniques, only the cases with improved photon and electron fluence were considered, i.

Augmented charged particle range rejection is only available when used simultaneously with DBS. With photon interaction forcing, the user can force photons to interact up to a user-defined number of times, Nin specified component modules within a simulation.

A photon forced to interact is split into a scattered photon whose weight is equal to the probability of interaction and an unscattered photon carrying the remaining weight. Once it leaves the forcing zone, the unscattered photon may interact again, depending on the sampled path length. On the other hand, the scattered photon can be forced to interact again in the forcing zone, depending on how many forced interactions are still available.

The photon forcing parameters can also be passed onto secondary photons and this feature is particularly useful to improve calculation efficiency for bremsstrahlung photon interactions, especially when combined with bremsstrahlung photon splitting.

This efficiency gain is achieved through the use of variance reduction techniques and faster simulation of the electron transport. It is important to correctly define a measure of the overall uncertainty on the quantity of interest in order to accurately evaluate the efficiency of a particular MC simulation algorithm.

For the first three uncertainty calculations, only one bin is considered, i.

The CPU times were scaled to a single 2. CPU time is scaled to that of a single 2. When using only bremsstrahlung photon splitting, the greatest CPU time saving is when DBS is used with and without electron splitting, for both field sizes, i.

However, as demonstrated in Sec. In the megavoltage energy range, there are small but observable differences between the two differential cross sections refer to Fig.

### BEAMnrc: software tool to model radiation beams – National Research Council Canada

The uncertainty was calculated in five different ways, i. The photon forcing technique produces more photons, however, they are not statistically independent, thus yielding a lower efficiency although the corresponding PHSP file is generated the fastest.

For a particular beamnr enhancing technique used in BEAMnrcthe difference between the relative efficiencies obtained using the various estimates of the uncertainty increases as one changes from planar fluence to spectral distribution; this situation is clearly more evident for the larger field size see Figs.

Another important consideration is that the relative fluence efficiency, for a given splitting number, actually decreases with increase scoring zone area, a result derived mathematically in an article by Kawrakow.

Therefore, the actual relative efficiencies possible with DBS were underestimated.

### BEAMnrc, DOSXYZnrc and BEAMDP GUI users manual – NRC Publications Archive –

If the fluence distributions were reconstructed using equal area scoring zones e. Efficiencies are shown relative to the efficiency obtained for the BEAMnrc default case.

The mean energy, planar fluence, and angular and spectral distributions were used as quantities of interest and the estimate of the uncertainty was calculated in five different ways, i. The results presented emphasize the importance of using a proper measure of the uncertainty on the quantity of interest in the calculation of the efficiency of a MC simulation. Estimates of the uncertainty using a significant number of bins e. In addition, the relative efficiencies are dependent on the quantity of interest chosen, although one can claim from this study that BEAMnrc MC calculations with the directional bremsstrahlung splitting technique yields the highest efficiency for beaamnrc quantities of interest analyzed.

The percentage difference between bexmnrc and a selection of MC calculated central and off-axis dose profiles is also shown. For both field sizes, the results were normalized to the linac calibration point in cGy per MU, bsamnrc.

The percentage difference between measured and a selection of MC calculated central-axis dose profiles is also shown. The percentage difference, in the central region of the field and at different depths, between measured and a selection of MC calculated off-axis dose profiles is also shown. For both field sizes, the results are presented in Gy per incident particle.

The percentage difference between the two MC calculations is also shown. The percentage difference between the two MC calculated data is also shown. The percentage difference, in the central region of the field and at different depths, between the two MC calculated data is also shown. The two MC programs generate accurate PHSP files of the linear accelerator for subsequent planning or dosimetric verification purposes in a relatively short amount of time when the appropriate efficiency enhancing tools are used.

The efficiency of BEAMnrc PHSP simulations is significantly improved, beanmrc directional bremsstrahlung splitting combined with augmented charged particle range rejection, for beamndc two field sizes studied. Although significant differences in the mean energy, planar fluence, and angular and spectral distributions were observed when comparing the NIST and BH bremsstrahlung cross-section PHSP files, they were not reflected in the calculated dose distribution in a water phantom with and without an air gap.

There is another viewpoint concerning PHSP simulations of the linac treatment head, which should be considered. If one uses VRTs e. This occurs because of particle correlations which are introduced with the use of VRTs, such as bremsstrahlung splitting. Therefore, if one is concerned with the smallest statistical uncertainty variance in dose, then it is best to perform the treatment head PS simulation without VRTs.

The tradeoff is that the no-VRT simulation is much slower, although if this simulation is being performed just once for subsequent use then it is a reasonable approach. On the other hand, if one is interested in the most efficient Beajnrc simulation note that efficiency is the inverse product of variance and timethen it is necessary to use VRTs. The major advantage of using aggressive VRTs is the significant improvement in calculation time without a compromise in the accuracy of the patient dose computation.

This is essential if one is considering real-time MC simulation of the treatment head and patient. This work was supported in part by Grant Nos.

National Center for Biotechnology InformationU. Published online Nov 5. Author information Article notes Copyright and License information Disclaimer. This article has been cited by other articles in PMC. Monte Carlo, efficiency, variance reduction techniques, cross sections.

## BEAMnrc: software tool to model radiation beams

An investigation of the influence of different photon and bremsstrahlung cross-section data available in BEAMnrc on the accuracy of calculated fluence and dose distributions.

It is generally accepted that the cross-section data available in the megavoltage energy range are sufficiently accurate. A systematic study of the influence of efficiency enhancing methods available in BEAMnrc on the accuracy of calculated fluence and dose distributions.

The following efficiency enhancing methods were considered: Open in a separate window. Photon and bremsstrahlung cross sections The current version of BEAMnrc allows the user to choose three different photon cross sections: Boundary crossing algorithm The boundary crossing algorithm together with the electron transport algorithm constitutes the condensed history technique used by a particular MC code system. Variance reduction techniques Bremsstrahlung photon splitting, Russian Roulette, and electron splitting The three options for bremsstrahlung photon splitting were used in this study, i.

Table 2 Bremsstrahlung splitting techniques and the values used for the relevant parameters. Photon interaction forcing With photon interaction forcing, the user can force photons to interact up to a user-defined number of times, Nin specified component modules within a simulation.

Monte Carlo transport parameters Maximum electron step, smax cm 10 Maximum electron loss per step MeV 0. A 3— Springer, Berlin,pp. Springer-Verlag, Heidelberg,pp. Medical Physics, Windsor,pp. Academic, New York,Vol. PIRS E Data Tables 7 6— A 12 195— Data Tables 35 3— Data Tables 20 2— ;