Dosimetric comparison of pencil beam and Monte Carlo algorithms in conformal lung radiotherapy

Abstract Purpose In this study, lung radiotherapy target volumes as well as critical organs such as the lungs, spinal cord, esophagus, and heart doses calculated using pencil beam (PB) and Monte Carlo (MC) algorithm‐based treatment planning systems (TPSs) were compared. The main aim was the evaluation of calculated dose differences between the PB and MC algorithms in a highly heterogeneous medium. Methods A total of 6 MV photon energy conformal treatment plans were created for a RANDO lung phantom using one PB algorithm‐based Precise Plan Release 2.16 TPS and one MC algorithm‐based Monaco TPS. Thermoluminescence dosimeters (TLDs) were placed into appropriate slices within the RANDO phantom and then irradiated with an Elekta‐Synergy® Linear Accelerator for dose verification. Doses were calculated for the V5, V10, V20, and mean lung doses (MLDs) in bilateral lungs and D50, D98, D2, and mean doses in the target volume (planning target volume, PTV). Results The minimum, maximum, and mean doses of the target volumes and critical organs in two treatment plans were compared using dose volume histograms (DVHs). The mean dose difference between the PB and MC algorithms for the PTV was 0.3%, whereas the differences in V5, V10, V20, and MLD were 12.5%, 15.8%, 14.4%, and 9.1%, respectively. The differences in PTV coverage between the two algorithms were 0.9%, 2.7% and 0.7% for D50, D98 and D2, respectively. Conclusions A comparison of the dose data acquired in this study reveals that the MC algorithm calculations are closer to the 60 Gy prescribed dose for PTV, while the difference between the PB and MC algorithms was found to be non‐significant. Because of the major difference arising from the dose calculation techniques by TPS that was observed in the MLD with significant medium heterogeneity, we recommend the use of the MC algorithm in such heterogeneous sites.


| INTRODUCTION
The primary goal of radiotherapy was to achieve maximal tumor control with the optimal dose distribution while minimizing normal tissue exposure to avoid treatment-related complications. Many different medical linear accelerators and treatment planning systems (TPSs) along with different algorithms provided by several vendors are available in the modern radiotherapy era to help reach this goal.
Pencil beam (PB) and Monte Carlo (MC) are among the avaliable algorithms. Regarding photon beams, one of the most used calculation algorithms implemented in 3DCRT (three-dimensional conformal radiotherapy) is PB, and the most preferred algorithm of intensitymodulated radiotherapy (IMRT) is MC.
The algorithms used in radiotherapy treatment planning are categorized as correction-based, model-based, and MC. These algorithms have advantages or disadvantages in the calculation of the absorbed dose, particularly in cases of a transition from one medium to another, a tissue-air interface, the skin entrance or small-irregular treatment fields. Any of these algorithms may be used in 3DCRT planning, although they may have different speeds and accuracies.
To meet the International Commission on Radiation Units (ICRU) criteria, the dose calculation accuracy must be within 2%-3%. 1 PB is a correction-based algorithm in which dose calculation is performed on an infinitely narrow pencil beam dose distribution.
Dose kernels are acquired within a homogeneous medium such as water to calculate the absorbed dose. The PB algorithm takes into account the inhomogeneity correction for the longitudinal direction in the central beam axis but ignores lateral scatter. This condition may cause dose calculation inaccuracies for heterogeneous treatment sites such as the lung or chest wall. A patient's body contains different densities, requiring a correction factor for each beam causing beam attenuation. 2 The PB algorithm is very fast due to its use of a one-dimensional density correction, which does not accurately model the distribution of secondary electrons in heterogeneous media, 3,4 while its limitations in a heterogeneous medium are well known. The PB algorithm considers collimated photon beams incident on the patient as clusters of many small, narrow "pencil beams" each of which has central axis ray deposits with certain doses. The pattern of such dose deposits changes with the intensity and the beam spectrum incident on the patient. 5 MC is an algorithm in which mathematical phantoms are used to handle practical difficulties. Organ dose calculations are executed by performing a mathematical simulation of x ray interactions. In an MC algorithm, the distance traversed in a phantom or patient body by each photon of a certain x ray spectrum is monitored, and the energy released to the medium is detected using the interaction probabilities through its track. MC is the most accurate treatment planning method, but it is often not practical because it requires undesired long computational times. 6 The linear accelerator head, including its components, is simulated with the MC algorithm since model-based dose calculations require a great deal of attention to the details of the photon transport in the linear accelerator head.
The fluence and energy distribution of photons emerging from the accelerator can be obtained with MC. 7 The MC algorithm, which is considered the gold standard for dose calculation, 8,9 is the only dose calculation algorithm that can properly account for the lack of electronic equilibrium and the secondary buildup. However, the long calculation time required for MC calculations with present-day computers makes it impractical for application in a clinical setting, and routine patient dose calculations are performed with modelbased algorithms. 10 The MC technique explicitly tracks electron transport and is generally considered the gold standard in determining the electron disequilibrium dose distribution. 11,12 The calculation of dose distributions in inhomogeneities is a challenge; inhomogeneity corrections are needed in the air cavities, lung, bone and high-density environments, and these corrections should be implemented in clinical applications. 13 This step is even more important in high-density inhomogeneous media such as the lung and head and neck region, where air cavities are present. Low-density lung tissue can result in reduced photon attenuation and an increased range of secondary electrons, which can cause the algorithm to fail to accurately calculate the absorbed dose. 14 The purpose of this study was to address the existing problems related to dose calculations in a heterogenous medium to indicate the discrepancy between DVHs acquired by PB and MC algorithms using TLD measurement verification. The left side of Fig. 1 shows the RANDO phantom lung treatment site, and the right side shows a treatment plan created by Precise Plan. Gross target volume (GTV), clinical target volume (CTV), and planning target volume (PTV), along with critical organs such as the lungs, spinal cord, heart and esophagus, were contoured. TLDs were numbered and placed at predefined locations within the treatment site and field edges in the RANDO phantom, as shown in Table 1.

| METHODS
Treatment plans were created using identical parameters (1 cm margin for PTV, two-opposing fields, the same fields and angles of the beams, the same normalization procedure and the same isocenter depth as that for PTV, 2 Gy/fraction and a total prescribed dose ELCIM ET AL.  Table 1.
After isocenter verification at the AP and LAT positions using Iview image guidance, irradiation was performed on the phantom according to the appropriate plan shown in Fig. 1. Figure 1

| RESULTS
The comparative assessment of point doses calculated by TPSs using the PB and MC algorithms are shown in Table 1 Monaco treatment planning (on the right) are shown in Fig. 6.    We also used the AAPM TG-142 Report of the quality assurance of medical accelerators 15     the PB algorithm calculates an underdose due to it is lack of a lateral scatter calculation. This undercalculation may mislead the physicist and physician, causing them to have less concern than they should in terms of clinical toxicities during the treatment planning phase as well as future considerations such as re-irradiation.
Our study reveals that calculations using the PB and MC algorithms are reliable and consistent with each other in terms of the mean dose for the target volume; additionally, the results of both algorithms were generally in good agreement with the measurements. Minimum dose values are important for assessing target volume coverage; that is, higher minimum doses indicate improved target volume coverage. As shown in Table 2, the difference between the MC and PB algorithms with regard to the GTV, CTV, and PTV minimum doses were 2.9%, 2.6%, and 0.6%, respectively.
The PTV minimum dose was better with the MC algorithm, but the difference was not significant.   24 The magnitude of the difference may be higher in the case of small treatment volumes and negligible in the case of large GTVs.
In our study, the treatment volume was not small; however, inhomogeneities due to air-lung tissue interfaces in the treatment field may have a substantial effect on the calculated dose differences between the PB and MC algorithms. The PTV volume was 88 cc in our study, and the calculated differences between the PB and MC algorithms were 2% for V20, 3% for V10, and 3% for V5. Our results support the use of the MC algorithm for small treatment volumes.

| CONCLUSION
In planning 3DCRT treatment, a homogeneous distribution of the mean dose in the target volumes of the GTV, CTV, PTV, and achieving high minimum doses is desirable. TPS, which is the only tool to create a radiation treatment plan, requires an accurate algorithm to accurately calculate the absorbed dose to assess the treatment plan before delivery. In this study, the absolute dose calculations by TLDs and the differences between the calculated absolute doses created by the PB and MC algorithms were evaluated by assessing the relevant DVH. In conclusion, the results are generally in good agreement with the TLD measurements. However, differences between the doses were more evident in areas of inhomogeneous transitions close to and within critical organs.
While both algorithms provided compatible results in calculating the target volume in 3DCRT, the MC algorithm was superior to the PB algorithm in a heterogeneous medium or in critical organ dose calculations.

CONFLI CT OF INTEREST
The authors have no relevant conflicts of interest to disclose.