Monte Carlo evaluation of target dose coverage in lung stereotactic body radiation therapy with flattening filter-free beams

Abstract

Aim:

Previous studies showed that replacing conventional flattened beams (FF) with flattening filter-free (FFF) beams improves the therapeutic ratio in lung stereotactic body radiation therapy (SBRT), but these findings could have been impacted by dose calculation uncertainties caused by the heterogeneity of the thoracic anatomy and by respiratory motion, which were particularly high for target coverage. In this study, we minimized such uncertainties by calculating doses using high-spatial-resolution Monte Carlo and four-dimensional computed tomography (4DCT) images. We aimed to evaluate more reliably the benefits of using FFF beams for lung SBRT.

Materials and methods:

For a cohort of 15 patients with early stage lung cancer that we investigated in a previous treatment planning study, we recalculated dose distributions with Monte Carlo using 4DCT images. This included fifteen FF and fifteen FFF treatment plans.

Results:

Compared to Monte Carlo, the treatment planning system (TPS) over-predicted doses in low-dose regions of the planning target volume. For most patients, replacing FF beams with FFF beams improved target coverage, tumor control, and uncomplicated tumor control probabilities.

Conclusions:

Monte Carlo tends to reveal deficiencies in target coverage compared to coverage predicted by the TPS. Our data support previously reported benefits of using FFF beams for lung SBRT.

Introduction

Monte Carlo calculations of dose distributions in a simple geometric phantom (1), and a treatment planning study (2) showed that using flattening filter-free (FFF) beams can improve the therapeutic ratio in lung stereotactic body radiation therapy (SBRT). This study is an extension of that prior work. Calculation of doses to lung tumors is particularly challenging owing to the density difference between the lung and the tumor. Tumor motion and other anatomical changes caused by respiration are additional complicating factors. For these reasons, in this study we recalculated previously analyzed treatment plans (2) using Monte Carlo simulations. In these calculations, we accounted for intrafractional motion by calculating the dose distribution separately for each of the 10 phases of the respiratory cycle and then using a deformable registration algorithm to combine (sum) the doses and thereby generate the total accumulated dose delivered to a patient. In these calculations, we used 4-dimensional computed tomography (4DCT) image sets. We will refer to the above computational procedure as “4D Monte Carlo.” Our main aim was to evaluate the impact of dose calculation uncertainties on key findings of our treatment planning study (2) that used the analytical anisotropic algorithm (AAA, Varian Medical Systems, Palo Alto CA, USA).

Previous similar studies can be divided into 2 groups based on the type of dose calculation software they used: a commercial treatment planning systems (TPS) or Monte Carlo software. A few commercial TPSs offer a Monte Carlo dose calculation option. We assigned such studies to the second group. Below, we summarize the previous findings.

TPS-based studies.

Vassiliev et al. (3) demonstrated the feasibility of lung SBRT with FFF beams and reported a substantial reduction in beam-on time when FFF beams were used for this type of treatment. Navarria et al. (4) compared the dosimetric characteristics and treatment outcomes of 86 patients who received three-dimensional (3D) conformal radiation therapy FF treatments and 46 patients treated with FFF volumetric modulated arc therapy (VMAT). They reported that at 1 year, the local control rate was 100% for patients treated with FFF beams compared with 92.5% for patients treated with FF beams. Additionally, they found significant reduction of ipsilateral lung doses and beam-on time in FFF mode. Prendergast et al. (5) retrospectively reviewed 99 lung and liver SBRT treatments, of which 36 used 10-MV FFF beams. They found that treatment and immobilization times with the FFF linac were 50% shorter than with a conventional linac. Gasic et al. (6) studied a cohort of 20 patients with early-stage lung cancer. For each patient, they developed 4 VMAT treatment plans that used 6- and 10-MV FF and FFF beams. They did not find significant differences in target coverage between FF and FFF plans, and they found comparable doses to organs at risk. FFF beams substantially improved beam delivery times. Lu et al. (7) addressed the question of the optimal energy for RapidArc® treatments with FFF beams. They found that lower doses to organs at risk were achieved with 6-MV FFF beams than with 10-MV FFF beams. This improvement translated into a normal tissue complication probability (NTCP) for the lung that was lower by a factor of 1.07–1.11 depending on the fractionation. Thus, 6-MV beams had a clear advantage over 10-MV beams. Tambe et al. (8) compared RapidArc® treatments with 6-MV FF, 6-MV FFF, and 10-MV FFF beams. Both FFF energies showed improvements in dose distributions over 6-MV FF treatments. The study confirmed that 6 MV is a better energy choice than 10 MV for FFF beams because 6-MV FFF plans had better coverage of the planning target volume (PTV) and lower doses to the spinal cord, esophagus, heart, lung, and chest wall. Pokhrel et al. (9) investigated VMAT treatments with 6-MV FF and FFF beams for 13 patients undergoing lung SBRT. They reported that FFF beams achieved modestly lower doses to some organs at risk, including the lung, and reduced beam-on time by a factor of 2.3. This groups has also reported early patient follow up data (10). The median follow up time was 8 months, and the range was 3–15 months. The local control rate was 100% and none of the patients developed acute lung or rib toxicity. In a treatment planning study, Vassiliev et al. (2) investigated lung SBRT treatments with 6-MV FF and 6-MV FFF beams for 15 patients. For the PTV, FFF plans improved several parameters: D₉₈, D₉₅, D₉₀, the homogeneity index (HI), and uncomplicated tumor control probability (UTCP). For the normal lung, FFF plans lowered the mean lung dose, V₁₀, V₂₀, V₃₀, and NTCP. For most patients, FFF beams also achieved lower doses to the esophagus, heart, spinal cord, and chest wall.

Overall, most of the above studies support the feasibility of achieving better dose distributions by replacing FF beams with FFF beams. The improvements they showed, however, were modest. Therefore, uncertainties in dose distributions associated with the limitations of commercial dose algorithms and with intrafractional anatomical changes that were not accounted for may have significantly impacted some of these findings. The following studies reduced dose uncertainties by using Monte Carlo algorithms and, in some cases, by accounting for respiratory motion.

Monte Carlo-based studies.

Chan et al. (11) analyzed data for 25 lung cancer patients treated with a CyberKnife® system (Accuray, Sunnyvale CA, USA), which does not have a flattening filter. All the calculations were performed within the MultiPlan® TPS, which includes a Monte Carlo dose algorithm and tools for deformable image registration. The study compared Monte Carlo calculations for static 3D representations of patient anatomy with Monte Carlo calculations performed using 4DCT image sets, thereby accounting for respiratory motion. It found that the 3D-based calculations overestimated the volume receiving the prescribed dose by 5.2% on average and D₉₉ for the gross tumor volume (GTV) by 2.6%. Doses to normal tissues, however, did not substantially differ between 3D- and 4D-based calculations. Li et al. (12) compared the accuracy of the XiO superposition dose algorithm with that of the Monaco Monte Carlo algorithm (both by CMS, Inc., St Louis MO, USA) using 15 study sets from the Radiation Therapy Oncology Group 0236 trial. They found that Monte Carlo doses were higher; the ratios of 100% and 50% prescription isodose volumes to PTV, the maximal dose at 2 cm from PTV, and V₂₀ for the lung were higher by 9%, 12%, 7%, and 18%, respectively. Gete et al. (13) evaluated the accuracy of the algorithm by comparing it to that of the BEAMnrc/DOSXYZnrc Monte Carlo system (14,15). They generated dose distributions for 9 lung cancer patients. The average differences between the 2 algorithms were under 0.2% for lung dosimetric indices and 0.3 Gy for maximum doses to normal tissue. The AAA algorithm overestimated minimum dose to the PTV by 3.8% on average. Chetty et al. (16) compared several commercial dose algorithms with a Monte Carlo algorithm in a large cohort of 133 patients with lung cancer who were treated with SBRT. They found that D₉₅ for the PTV calculated with the commonly used AAA and collapsed cone convolution (CCC) algorithms agreed with Monte Carlo within 0.6 %. Discrepancies in the tumor control probability (TCP), however, were larger, reaching an average of 3% for small tumors. This suggests that some dosimetric indices were more sensitive to dose uncertainties than D₉₅ was. Differences between AAA, CCC, and Monte Carlo in mean lung dose were mostly within 2%. Ojala et al. (17) compared several commercial algorithms and the BEAMnrc/DOSXYZnrc Monte Carlo system (14,15). Monte Carlo doses were calculated only for 4 patients and compared only to the Acuros XB (AXB) algorithm (Varian Medical Systems, Palo Alto CA, USA). AXB is a new-generation algorithm (18) that performs better than AAA in challenging cases (19). Nevertheless, in the worst case, the difference between Monte Carlo and AXB for PTV D₉₅ was 11%. In contrast, the maximum differences for lung V₃₀ and for the maximum dose to the spinal cord were only 1.5%. Zhao et al. (20) compared dose distributions calculated with CCC and Monte Carlo algorithms. They used the Oncentra Masterplan TPS (Elekta, Stockholm, Sweden) with CCC and the BEAMnrc/DOSXYZ Monte Carlo system (14,15). For each of 24 cancer lung patients, they developed both 3D conformal and intensity-modulated radiation therapy treatment plans. They found that the CCC algorithm overestimated key dosimetric indices for the lung, but only by 1% to 2%. The differences between CCC and Monte Carlo were substantially larger for the PTV. For example, the differences in D₉₈ and D₉₅ for the GTV exceeded 5%. Vassiliev et al. (1) calculated dose distributions delivered to a simple thorax phantom by 6-MV FF and FFF beams at a spatial resolution of 0.5 mm to 1 mm. They investigated the impact of tumor size and lung density on the differences between FF and FFF doses in a lung tumor and its vicinity. With FFF beams, consistent, albeit modest, target dose enhancement was reported. Freislederer et al. (21) performed 4D Monte Carlo dose calculations for 5 lung patients using Hyperion software (Elekta, Stockholm, Sweden). The study reported that Monte Carlo 4D and 3D doses were “comparable.”

In summary, most of the above studies reported small, 1% to 2%, differences between Monte Carlo and TPS doses to organs at risk. However, discrepancies were consistently larger and often not negligible for dosimetric indices characterizing target coverage. Only 2 studies (11,21) accounted for respiratory motion by using 4D Monte Carlo algorithms, and only 2 (1,11) considered FFF beams. Of the 2 that used FFF beams, one (11) considered a CyberKnife® accelerator, and the other (1) considered a geometric phantom, not patient CT images. Chan et al. (11) did not compare FFF and FF beams. Our study extends and complements this previous work. We calculated dose distributions for 15 patients who had lung tumors treated with SBRT. Each patient had 2 treatment plans: the original plan with FF beams, which was used for the treatment, and a new plan that we developed for comparison using a TrueBeam™ accelerator (Varian Medical Systems, Palo Alto Ca, USA) in the high-intensity mode (i.e., FFF). We performed all calculations using the BEAMnrc/DOSXYZ Monte Carlo software (14,15) and with 4DCT image sets to account for respiratory motion.

Methods and materials

Patient cohort.

This retrospective study was approved by our Institutional Review Board. We selected 15 patients treated for early-stage lung cancer at our institution. The main selection criterion was the use of SBRT. We aimed to include tumors of different sizes and locations. All the treatments used 6-MV FF photon beams. The patients’ characteristics are summarized in Table 1. The table includes the average ipsilateral lung density because we had previously shown that it affects the tumor dose coverage (1). We derived the density using a method described by Pokhrel et al. (22).

Table 1.

Patient characteristics.

Patient	Tumor location	Fractio-nation	GTV, cm3	PTV, cm3	Average ipsilateral lung density, g/cm3
1	upper right, island	4×12.5 Gy	1.8	35.6	0.283
2	upper left, c.w. attached	4×12.5 Gy	8.1	30.6	0.350
3	middle right, c.w. attached	7×9 Gy	35.6	86.4	0.335
4	middle right, mediast. attached	7×10 Gy	53.4	117.6	0.281
5	upper right, c.w. attached	7×10 Gy	99	280.1	0.222
6	middle right, c.w. attached	4×12.5 Gy	4.8	19.6	0.269
7	upper right, c.w. attached	7×10 Gy	66.4	138	0.240
8	lower left, c.w./diaph. attached	7×10 Gy	60	229	0.355
9	upper right, island	4×12.5 Gy	5.4	56.7	0.314
10	lower left, c.w. attached	4×12.5 Gy	5	60.9	0.269
11	upper right, c.w. attached	4×12.5 Gy	1.8	34.5	0.240
12	middle left, island	4×12.5 Gy	15.3	41.1	0.343
13	upper right, c.w. attached	4×12.5 Gy	0.6	5.5	0.249
14	upper right, c.w. attached	4×12.5 Gy	1.4	9.2	0.252
15	middle right, island	4×12.5 Gy	9	70.3	0.407
Median (range)			8.1 (0.6, 99)	56.7 (5.5, 280)	0.281 (0.222, 0.407)

Abbreviations: GTV, gross tumor volume; PTV, planning target volume; c.w., chest wall; mediast., mediastinum; diaph., diaphragm.

Treatment planning.

We imported the original treatment plans from our clinical data base into the Eclipse 13.6 TPS (Varian Medical Systems, Palo Alto CA, USA). Then, in all the plans, we changed all beams to the 6-MV FFF mode without changing the beam setup. Next, we reoptimized each plan, aiming to achieve the same tumor coverage as in the original plan while minimizing dose to the organs at risk. We used the AAA algorithm for dose calculation because it is one of the most commonly used algorithms and belongs to the same category, “type b” (23), as another widely used algorithm, CCC. We used the average CT image for planning. The beams were static and the MLC mode was step-and-shoot. The calculation grid size was 2.5 mm. A complete dosimetric analysis of the new FFF plans is given elsewhere (2). The main finding was that by using FFF beams, doses to organs at risk could be lowered without compromising tumor coverage.

Monte Carlo dose calculation.

We used the BEAMnrc/DOSXYZnrc Monte Carlo system (14,15) and representative phase space files for TrueBeam™ provided by the manufacturer in support of Monte Carlo research. The files store parameters such as phase coordinates for all particles that reach a plane immediately upstream of the movable jaws. The phase space files have been validated for both FF and FFF beams (24–26). In our simulations, particle trajectories begin in the phase space plane. Below this plane, the design of the TrueBeam™ beamline is very similar to that of the Clinac 2100 accelerator (27). Hence, we can use our previously validated model of a 2100 series accelerator (28), which includes a detailed representation of the Millennium™ 120 multileaf collimator (MLC) (Varian Medical Systems, Palo Alto CA, USA) (29).

For all the patients in the study cohort, 4DCT image sets were acquired. Each set consisted of 10 three-dimensional computed tomography (3DCT) images corresponding to the 10 phases of the respiratory cycle. We converted each 3DCT image into a voxelized phantom and saved the phantom data to a file in a format suitable for import into the DOSXYZnrc program. The phantom did not include CT slices that were above or below the 1% isodose. Those slices that were included in the phantom were not truncated in the axial plane. All the phantom voxels were 2-mm cubes.

We performed the simulations in 2 steps. In the first step, we transported particles through the jaws and the MLC. MLC leaves were moving in the step-and-shoot manner following the instructions recorded in the DICOM treatment plan file. For each beam, a phase space file was created where parameters of all particles that reached a plane immediately below the MLC were recorded. In the second step, these phase space files served as a source of particles incident on the voxelized patient phantom. This source accounted for the gantry, couch, and collimator rotation angles, again using the data stored in the treatment plan file. For each patient, the same phase space files were used for each of the 10 phantoms representing the 10 phases of the respiratory cycle. The total number of particles incident on each phantom per beam was 6 billion. The number of beams was 6 to 9 per plan. The statistical uncertainties (1σ) of the calculated dose in a voxel were lower than approximately 0.4% in those voxels that received more than 80% of the maximum dose. These voxels were located in the PTV and the volume surrounding it. The dosimetric indices that we report are integral quantities that involve large numbers of voxels and therefore have much lower uncertainties than the voxel dose.

Calculation of accumulated dose.

After dose distributions for all respiratory phases were calculated, we mapped those distributions onto the CT image taken at the end of exhalation. We used the hybrid intensity and structure-based deformable registration algorithm implemented in the RayStation TPS (RaySearch Laboratories, Stockholm, Sweden). A multi-institutional study (30) evaluated performance of several commercial deformable image registration algorithms in the thoracic region. They found that the average 3D registration error for the algorithm that we used was 1.26 mm, lower than the values reported for other algorithms. For each patient, we summed the resulting 10 dose distributions and thereby calculated the distribution of the total dose delivered to a patient’s target volume over the treatment course. The summation reduced the statistical uncertainties in dose per voxel to about 0.1% and less in voxels that received more than 80% of the maximum dose.

Parameters of dose distribution.

For each FF or FFF treatment plan, we calculated multiple dose-volume histogram indices characterizing target coverage. Doses to the organs at risk were reported in our previous study (2). We also calculated the HI, defined as HI = (D₂ − D₉₈)/D₅₀ (31), and the conformity index (CI), which is the ratio of the volume receiving at least the prescription dose, V(Dx), to the PTV.

Treatment outcome predictors.

We described calculation of the TCP and NTCP in our previous paper (2). Briefly, to calculate the TCP we followed the method formulated by Chetty et al. (16), Webb and Nahum (32), and Guckenberger et al. (33). We calculated NTCP for the normal lung (i.e. lung minus GTV) using the method developed by Selvaraj et al. (34). The model was a Lyman-Kutcher-Burman type with a logistic local dose-effect relation for perfusion loss derived from single-photon emission CT imaging data. We also calculated the UTCP, which is the product TCP × (1 − NTCP).

Statistical analysis.

Continuous variables are summarized by the median and range across subjects. All reported p values comparing the FF and FFF beams were obtained from the Wilcoxon signed-rank test using the paired values for FF and FFF for each subject. A p-value < 0.05 was considered to be significant. Analysis was performed in Matlab R2017b and R version 3.5.0.

Results and Discussion

TPS versus 4D Monte Carlo.

First, we compared target dose distributions generated by the TPS with accumulated doses calculated with Monte Carlo. The data are summarized in Table 2. The overall trend was that 4D Monte Carlo calculations produced worse target dose coverage than that predicted by the TPS. Figure 1 compares ratios, Monte Carlo to TPS, of several dosimetric indices for the PTV. For most patients, the TPS over-predicted indices characterizing low-dose regions: D₁₀₀, D₉₈, and D₉₅. Similarly, the Monte Carlo-calculated HI and CI were worse than the TPS predictions. The differences between Monte Carlo and TPS were significant (p < 0.05) for D₁₀₀ and CI. For the GTV, the same trend was observed for D₁₀₀, HI, and CI, whereas there were no systematic differences in D₉₈, D₉₅, and D₉₀. Figures 2 and 3 show dose-volume histograms for patients 8 and 10, who had relatively large and small tumors, respectively. The case shown in Figure 2 is interesting in that Monte Carlo calculations revealed a cold spot in the GTV, a small volume where the dose was lower by 9.3 Gy than that predicted by the TPS. Figure 3 shows a more typical case in which the TPS only slightly over-predicted the dose to a relatively large part of the GTV. In this case, in 14% of the GTV, the Monte Carlo dose was lower by ~0.6 Gy than that calculated by the TPS. Dose coverage of the PTV showed a similar pattern, with Monte Carlo dose lower than the TPS dose by 0.2 to 0.5 Gy in about 2% of the volume. In Figure 4, we compare target dose distributions for patients 7 (Fig. 4, A and B) and 8 (Fig. 4, C and D). Both tumors were close to 5 cm in diameter, which exceeded the depth of ~1.5 cm needed to achieve electronic equilibrium. The data in Figure 4 are representative of the general pattern of discrepancies between the TPS (Fig. 4, A and C) and Monte Carlo calculations (Fig. 4, B and D). The differences were only about 1 to 2 Gy and were more likely to be seen near lung-tumor interfaces. This is consistent with a previous Monte Carlo analysis that used a simple geometric phantom (1). However, in contrast to the phantom calculations, the patterns of discrepancies shown in Figure 4 are rather irregular because of the heterogeneities and the modulation of the beam intensity. Good agreement between the TPS and Monte Carlo doses is seen in Figures 4C and 4D in the region where the tumor is adjacent to the chest wall and where, therefore, electronic equilibrium was likely achieved.

Table 2.

Target coverage: treatment planning system (TPS) vs Monte Carlo (MC), both FF; and FF vs FFF, both MC. The dosimetric indices are reported as a percentage of the prescription dose.

Parameters	TPS-FF		MC-FF		MC-FFF
	Median	Range	Median	Range	Median	Range
GTV
D90, %	112	101, 136	112	101, 137	113	101, 132
D95, %	111	100, 135	111	100, 135	112	99.5, 130
D98, %	110	98.8, 135	110	97.3, 134	111	97.1, 128
D100, %	106	88.6, 134	103	78.8, 133	108	81.2, 119
HI	0.0915	0.0269, 0.168	0.0967	0.0238, 1.70	0.0693	0.0272, 0.141
CI	4.75	1.12, 25.3	5.01	1.07, 30.1	5.54	1.08, 32.1
TCP	1.00	1.00, 1.00	1.00	1.00, 1.00	1.00	1.00, 1.00
UTCP	0.959	0.914, 0.983	0.959	0.914, 0.983	0.960	0.916, 0.987
PTV
D02, %	120	105, 148	121	105, 147	119	105, 145
D50, %	111	94.6, 131	111	95.4, 132	112	97.2, 131
D90, %	104	78.9, 124	105	78.6, 125	106	82.5, 125
D95, %	102	76.9, 121	102	76.3, 121	102	79.2, 123
D98, %	100	69.3, 118	98.7	65.0, 119	97.2	65.2, 121
D100, %	88.8	42.7, 109	78.4	29.4, 106	84.5	36.9, 106
HI	0.153	0.0670, 0.449	0.154	0.0586, 0.501	0.170	0.0608, 0.488
CI	1.40	0.406, 2.32	1.46	0.387, 2.72	1.36	0.390, 2.90
TCP	1.00	0.08, 1.00	1.00	0.00, 1.00	1.00	0.00, 1.00
UTCP	0.958	0.0765, 0.983	0.958	0.00, 0.983	0.957	0.00, 0.987

Abbreviations: GTV, gross tumor volume; HI, homogeneity index; CI, conformity index; TCP, tumor control probability; UTCP, uncomplicated tumor control probability; PTV, planning target volume.

Figure 1.

Ratios of dosimetric indices for the PTV calculated with Monte Carlo (MC) to those predicted by the TPS. Red lines are the medians, blue boxes are interquartile ranges, black dashed lines are ranges, and red crosses are outliers. HI, homogeneity index; CI, conformity index.

Figure 2.

Dose-volume histogram for patient 8. The prescription dose is 70 Gy. Data for GTV and PTV, FF and FFF plans, calculated with Monte Carlo and a TPS are shown as indicated in the key.

Figure 3.

Dose-volume histogram for patient 10. The prescription dose is 50 Gy. Data for GTV and PTV, FF and FFF plans, calculated with Monte Carlo and a TPS are shown as indicated in the key. Based on Monte Carlo data, in this case doses to all organs at risk in the FFF pans were lower or the same as in FF plans. For example, NTCPs for the lung were 2.4 (FFF) and 2.7% (FF).

Figure 4.

Target coverage for patients 7 (A,B) and 8 (C,D). Comparison of dose distributions predicted by a TPS (A,C) with those calculated with Monte Carlo (B,D).

Our results are consistent with findings of previous Monte Carlo based studies. For example, Li et al. (12) noted that Monte Carlo calculations produced a ratio of prescription isodose volume to the PTV (i.e. CI) that was higher by 9% than that predicted by a superposition algorithm. Our calculations, similarly, showed that Monte Carlo CI was higher by 7.6% on average than the AAA result. Gete et al. (13) found that the AAA algorithm overestimated the minimum PTV dose by 3.8% on average. Our data also showed overestimation but by 9.5% on average. According to Chetty et al. (16), D₉₅ values for the PTV calculated with the AAA algorithm were higher than Monte Carlo values by 0.84% on average. In our calculations the average overestimation of D₉₅ for the PTV by the AAA algorithm was 0.36%. Some differences in the above average values can be attributed to patient-to-patient variability and to differences in computational methods.

FFF versus FF.

Next, we compared target dose distributions for FF and FFF plans; both are accumulated doses that we calculated with Monte Carlo using 4DCT data sets. The data are summarized in Table 2. For most patients, replacing FF beams with FFF beams improved target coverage. Figure 5 shows box plots of FFF-to-FF ratios for several indices characterizing dose distribution in the GTV. For about three-fourths of the patients, FFF beams improved D₉₀, D₉₅, D₉₈, and D₁₀₀ (i.e., the minimum dose). Higher doses delivered to the GTV by FFF beams resulted in improved TCP. However, only UTCP improvements were significant. Similar, but more modest, improvements were achieved with FFF beams in PTV dose distributions, and again only the UTCP improvements were significant. These findings reflect our approach to treatment planning with FFF beams: we prioritized lowering doses to organs at risk over improving target coverage that was achieved in FF plans. FFF beams elevate doses compromised by electronic disequilibrium near the tumor edge (1). This property allowed us to lower doses to organs at risk without compromising target coverage. These improvement were particularly consistent for the lung resulting in better UTCPs.

Figure 5.

Ratios of dosimetric indices for the GTV for FFF plans to those for FF plans. All dose distributions were calculated with Monte Carlo. Red lines are the medians, blue boxes are interquartile ranges, black dashed lines are ranges, and red crosses are outliers. HI, homogeneity index; CI, conformity index.

The dose-volume histogram shown in Figure 3 is an example of the substantial improvement of target coverage that can be achieved with FFF beams. Doses to both the GTV and PTV were improved. For the GTV, use of FFF beams increased the minimum dose by 2.9 Gy and produced a more uniform dose distribution. For some patients, however, FFF plans did not improve GTV coverage (Fig. 5).

Differences in target volumes dose distributions were small. For this reason in most cases our analysis did not produce statistically significant conclusions. To overcome this limitation a much larger cohort size is required. In this study we performed full Monte Carlo simulations at a high spatial resolution, for each of the ten phases of respiratory motion. This is a computationally expensive approach that is not feasible for a substantially larger cohort. For treatment planning we used a “type b” algorithm, the AAA. It would be interesting, in a future study, to compare our findings with a similar analysis based on a “type c” algorithm, such as AXB.

Conclusions

Calculation of dose distributions in the thoracic region is challenging owing to the large density gradients and respiratory motion that causes tumor displacement, deformation of the entire region, and changes in lung density. In this study, we focused on the dose distribution in the target volume because previous studies reported relatively low uncertainties in doses to organs at risk. We found that Monte Carlo simulations tended to reveal worse target dose coverage, especially in colder regions of the target volume, than a commercial TPS predicted. The discrepancies between Monte Carlo and TPS calculations ranged from negligible to, in rare cases, moderate. These findings were consistent with most of the previous studies that we reviewed. The results of this study are, overall, consistent with our previous treatment planning study (2) in that using FFF beams tended to improve target coverage. This improvement was modest because in FFF treatment planning we prioritized lowering doses to organs at risk over improving target coverage that was achieved in FF plans. To compare the overall quality of treatment plans, we calculated UTCP, which accounts for both tumor control and risks of normal tissue complications. We found that in the plans with FFF beams, UTCPs were significantly higher than they were in the FF plans. In summary, our data support the feasibility of improving the therapeutic ratio in lung SBRT by using FFF beams instead of FF beams.