This study aims to dosimetrically compare multi-leaf collimator (MLC)-based and cone-based 3D LATTICE radiotherapy (LRT) plans. Valley-peak ratios were evaluated using seven different 3D LATTICE designs. Target volumes of 8 cm and 12 cm were defined on the RANDO phantom. Valley-peak dose patterns were obtained by creating high-dose vertices in the target volumes. By changing the vertex diameter, vertices separation, and volume ratio, seven different LATTICE designs were generated. Treatment plans were implemented using CyberKnife and Varian RapidArc. Thermoluminescent dosimeter (TLD), EBT3 films, and electronic portal-imaging device (EPID) were employed for dosimetric treatment verification, and measured doses were compared to calculated doses. By changing the vertex diameter and vertices separation, the valley-peak ratio was exhibited little difference between the two systems. By changing the vertex diameter and volume ratio, the valley-peak ratio was observed nearly the same for the two systems. The film, TLD, and EPID dosimetry showed good agreement between the calculated and measured doses. Based on the results, we concluded that although smaller valley-peak ratios were obtained with cone-based plans, the dose-volume histograms were comparable in both systems. Also, when we evaluated the treatment duration, the MLC-based plans were more appropriate to apply the treatment in a single fraction.
INTRODUCTION
In the past decades, remarkable technological developments have arisen in the area of radiotherapy, such as intensity-modulated radiotherapy (IMRT), volumetric-modulated arc therapy (VMAT), which can be successfully applied with imaging guidance. However, the presence of radio-resistant tumors, including sarcomas, malignant melanomas, and necrotic tumors, may make these treatments inefficient. The inadequacy of conventional fractionated schemes has led to the need for ablative doses. Stereotactic ablative radiotherapy (SABR) delivers high radiation doses per fraction and is known as the effective treatment method in treating relatively small lesions. However, the application of high ablative doses in a hypo-fractionated regimen to large tumor sizes may lead to excessive toxicity. For this reason, the question of whether unconventional approaches can be introduced to improve the effectiveness of radiotherapy remains to be unanswered.
Spatially fractionated radiation therapy (SFRT) was proposed to irradiate sub-regions of a large target volume through small openings (1–4). 2D SFRT, also known as “GRID therapy”, was delivered by placing a physical custom-designed block on the gantry or by using multi-leaf collimators in a two-dimensional point of view (5–9). Instead of uniform dose distributions throughout the target volume, the inhomogeneous dose was delivered, creating high dose regions (peaks) and low dose regions (valleys), to keep dose values of adjacent normal tissues low. 2D GRID therapy subsequently allowed to deliver ablative doses without increasing toxicity in the treatment of radio-resistant, deeply seated, and bulky (>8 cm diameter gross tumor target volume) tumors (10). In the literature, several studies have presented the dosimetric properties and clinical outcomes of 2D GRID therapy (11–20).
In 2010, 3D LATTICE Radiotherapy (LRT) was introduced as a new approach to obtain GRID dose distributions in 3D point-of-view (21). Using this new concept, patient-specific LATTICE designs can be customized by tuning the vertex diameter and vertices separation. The heterogeneity of the 3D LRT dose distribution is often quantified in terms of the valley-peak ratio and recently recommended as the ratio of the mean dose of the LATTICE volume to the prescribed peak dose (22). The success of a 3D LRT plan depends on the volumetric design of the LATTICE layout in the target volumes (23). The optimal LATTICE design, however, has not been empirically or theoretically addressed in the literature. The differences between MLC-based and cone-based on LRT have also not been investigated.
The goal of this study is to dosimetrically evaluate 3D LRT implementations using the fixed cone collimators of the CyberKnife SRS unit and MLCs of the RapidArc Trilogy system. For this purpose, various 3D LATTICE designs based on vertex diameter and vertices separation were created. Dose distributions were measured in a RANDO phantom, and dose-volume histograms were compared in treatment planning systems. In addition, we evaluated the resulting valley-peak ratios by varying the vertex diameters and vertices separation. Furthermore, we investigated the impact of tumor size on the valley-peak ratios in two different ways. To our knowledge, this is the first dosimetric study to compare valley-peak ratios in 3D LRT using spherical dose islands by changing vertex diameter and vertices separation.
MATERIALS AND METHODS
Target Delineation and 3D LATTICE Design
Computed tomography (CT) images of the Alderson anthropomorphic RANDO phantom were acquired using the Toshiba Aquillon LB model CT scanner (Toshiba Co., Minato, Japan) with the slice thickness of 1 mm. CT images were transferred to an Eclipse v11.4.1 treatment planning system (Varian Medical Systems, Inc., Palo Alto, CA), and contouring was performed. Two large gross tumor volumes (GTVs), GTV1 with 8 cm diameter and GTV2 with 12 cm diameter, were virtually delineated in the brain and the lungs, respectively. The GTVs exemplified glioblastoma (GBM) and lung cancer.
DICOM files including CT images of Rando phantom and the delineated volumes were transferred to the DICOManTX software (developed by the Department of Radiation Oncology, University of Texas Southwestern Medical Center) to generate 3D LATTICE designs. The vertices, small spheres representing the high-dose regions, were delineated in the GTVs based on the LATTICE parameters. The residual volume between the vertices, named LATTICE volume, was acquired by subtracting total vertex volumes from the GTV. Both the high-dose vertices and LATTICE volume were defined inside the GTV. In the treatment planning, vertices were selected as LATTICE target volumes and exposed to the prescribed dose while LATTICE volume was spared as much as achievable. Tumor-specific 3D LATTICE designs with specified valley-to-peak (valley-peak) patterns were probed by switching the vertex diameter and the vertices separation. Table 1 list the vertex diameters, vertices separation, volume ratios (Vvertices/VGTV), and the number of vertices for the 8 cm GTV1 and the 12 cm GTV2. Figure 1 shows the 3D LATTICE designs of GTV1 and GTV2 for the 1 cm vertex diameter.
TABLE 1
3D LATTICE Parameters for 8 cm GTV1 and 12 cm GTV2

Treatment Planning
DICOM files including LATTICE structures were then transferred to the MultiPlan v3.5 (Accuray Inc.) treatment planning system. Three plans for the GTV1 and four plans for the GTV2 were implemented and evaluated. 6D-skull and X-sight vertebra tracking techniques were used in the treatment planning of the GTV1 and the GTV2, respectively. The dose was set to 15 Gy in a single fraction using fixed collimators. Sequential optimization was performed using a ray-tracing algorithm. For MLC-based LRT planning, the same DICOM files were transferred to the Eclipse v11.4.1 treatment planning system as a second step. The volumetric modulated arc therapy (VMAT) treatment technique was used for planning. Two full arcs were applied for each plan. The collimator angles were set to 45° and 315°. The dose calculation was performed using the analytical anisotropic algorithm (AAA). All measurements were performed in an Alderson RANDO phantom under 6 MV X-ray energy. Figure 2 shows the GTV1 dose distributions of the treatment plans for CyberKnife and VMAT.
Dose Measurements
Ten LiF: Mg,Ti dosimeters (TLD-100) were placed in a RANDO phantom. The TLDs were calibrated at the maximum depth dose of 1.6 cm with 100 cm SSD and field size of 10 × 10 cm2. Irradiation was performed three times. After each irradiation, dose values were recorded using a Harshaw 3500 TLD reader. The measured and calculated dose values were then compared.
For the film calibration process, Gafchromic EBT3 films were cut into squares of 5 × 5 cm2. Films were placed at dmax with SSD of 100 cm and 10 × 10 cm field size. The eight dose values of 50, 100, 200, 300, 400, 500, 600, and 650 cGy were applied to obtain the calibration curve. A non-irradiated film was reserved to verify the calibration. Films were scanned using an Epson 10000 XL flatbed scanner after waiting 24 h to ensure color stabilization. The measurements were analyzed using the PTW Verisoft 6.2 software program.
Delivery quality assurance were prepared for each plan using the Eclipse treatment planning system. Dosimetric verification was performed using an electronic portal-imaging device (EPID). The measured and calculated values were compared by the gamma analysis method using the portal dosimeter software available in the system. In our study, the results were evaluated with the parameters of 3% dose difference and 3 mm distance-to-agreement.
RESULTS
Dosimetric Comparison for GTV1 and GTV2
Tables 2 and 3 show the dose-volume histogram parameters of vertices and LATTICE volume for GTV1 using CyberKnife and VMAT treatment plans. dose-volume histogram parameters represent D95, D90, D10, D5, Dmax, and Dmean of the vertices and the LATTICE volume separately.
TABLE 2
Vertices Dose Comparison between CyberKnife and VMAT for GTV1 3D LATTICE Designs

TABLE 3
LATTICE Volume Dose Comparison between CyberKnife and VMAT for GTV1 3D LATTICE Designs

The dose-volume histogram results for the GTV2 from both CyberKnife and VMAT treatment plans are listed in Table 4 and Table 5.
TABLE 4
Vertices Dose Comparison between CyberKnife and VMAT for GTV2 3D LATTICE Designs

TABLE 5
LATTICE Volume Dose Comparison between CyberKnife and VMAT for GTV2 3D LATTICE Designs

Dose-volume histograms demonstrated that heterogeneous dose distribution was delivered to the tumors by different CyberKnife and VMAT LRT plans. For the GTV1 and GTV2, the 95% dose coverage of vertices exhibited a little difference between CyberKnife and VMAT.
If we compare the two systems, the mean doses of the high-dose vertices for all vertex diameters were similar using either technique, whereas the maximum doses in GTV2 were higher using CyberKnife. LATTICE volume's mean doses decreased with increasing vertex diameter and vertices separation for both systems.
The produced valley-peak patterns for GTV1 and GTV2 are shown in Figs. 3 and 4. Figure 3 shows the example of the GTV1 3D LATTICE valley-peak pattern using a 1-cm vertex diameter and 1.5-cm vertices separation for the CyberKnife plan.
FIG. 3
CyberKnife: Panel a: 3D LATTICE cose distribution from transverse plane. Panel b: 3D view of dose distribution pattern (1 cm vertex diameter and 1.5 cm vertices separation).

FIG. 4
VMAT: Panel a: 3D LATTICE dose distribution from transverse plane. Panel b: 3D view of dose distribution pattern (1 cm vertex diameter and 3.5 cm vertices separation).

Figure 4 shows the example of the GTV2 3D LATTICE valley-peak pattern using a 1-cm vertex diameter and 3.5-cm vertices separation for the VMAT plan.
In our study, the valley-peak ratio was calculated as the ratio of the LATTICE volume's mean dose to the high-dose vertices' mean dose. Tables 6 and 7 indicate the valley-peak ratios, treatment durations, and MU values, of the 8 cm GTV1 and 12 cm GTV2 for CyberKnife and VMAT, respectively.
TABLE 6
Valley-Peak Ratios, Treatment Durations and MU Values, for the 8 cm GTV1 using CyberKnife and VMAT

TABLE 7
Valley-Peak Ratios, Treatment Durations and MU Values, for the 12 cm GTV2 using CyberKnife and VMAT

Differences between the valley-peak ratios are dependent on the 3D LATTICE design. If the 3D LATTICE design used the different vertex diameter and vertices separation, the valley-peak ratio was exhibited little difference between the two systems for the 8 cm of GTV1. Also, the valley-peak ratio difference decreased as the vertex diameter and vertices separation increased between the two systems. For the CyberKnife and VMAT plans using 2 cm vertex diameter, the valley-peak ratio was lowest compared to the other two vertex diameters. As presented in Table 6, if the volume ratio was remained constant, the valley-peak ratio decreased with increasing the vertex diameter and vertices separation for both systems.
In the 12 cm of the GTV2 target volume, when the 3D LATTICE design with the smallest vertex diameter and volume ratio was used, the valley-peak ratio was lowest for both systems. Also, the vertex diameter and volume ratio increased, the valley-peak ratio was observed nearly the same for the two systems. Similarly, as the vertex diameter and volume ratio increased, the valley-peak ratio was obtained to be higher for both systems. For example, as demonstrated in Table 7, using a 2-cm vertex diameter and the volume ratio of 0.5, the valley-peak ratio was the highest for the CyberKnife and VMAT plans. Regarding the constant vertices separation, the valley-peak ratio increased moderately with increasing the vertex diameter and volume ratio.
Comparing the two systems in terms of treatment duration, CyberKnife plans were completed in approximately 4–6 h, whereas VMAT plans could be implemented in minutes as shown in Tables 6 and 7. The results indicate that even though CyberKnife plans produce the lowest valley-peak ratios, they cannot be implemented clinically in a single fraction, whereas VMAT plans are clinically applicable because of the treatment duration.
Dosimetry
Film dosimetry showed good agreement between the calculated and measured doses. The gamma-passing rate for different 3D LATTICE designs ranged between 90.1% and 94.6% (3-mm distance-to-agreement and 3% dose differences). The profile comparison of the measured dose (Fig. 5b, blue line) with the film and the calculated dose (Fig. 5b, brown line) distribution is shown in Fig. 5a and b for the CyberKnife film irradiation and in Fig. 6a and b for the VMAT film irradiation.
FIG. 5
CyberKnife: Panel a: Illustration of the EBT3 film irradiated with 1 cm vertex diameter 3D LATTICE design. Panel b: Dose profile in a 3D plane.

FIG. 6
VMAT: Panel a: Illustration of the EBT3 film irradiated with 1 cm vertex diameter 3D LATTICE design. Panel b: Dose profile in a 3D plane.

Delivery quality assurance for the VMAT plans was performed using EPID. The results indicated that the gamma passing rate was above 95% using the 3%/3 mm agreement criteria. In addition, for TLD measurements, the calculated and measured point dose difference was less than 10% at all points where TLDs were placed. The mean discrepancies between calculated and measured point dose were 3.3% for the CyberKnife plans and 4.1% for the VMAT plans. These results indicate good agreement between the planned and delivered doses.
DISCUSSION
Spatially fractionated radiation therapy via 2D GRID is an effective tumor debulking radiotherapy method for patients with large lesions. For deep-seated large targets, new technologies have been devised to deliver GRID dose distribution inside a target volume without high dose spillage outside the target, such as GRID in tomotherapy, GRID in VMAT, etc. 3D LRT goes one step further. It “cuts” needle-like high-dose regions which is the typical dose pattern for GRID therapy in a physical grid block or through 2D MLC modulation, to multiple pieces aiming to further enhance GRID therapy effectiveness. This study presents the results of dose comparison between 3D LRT dose distributions by CyberKnife and VMAT technologies. Such a LRT comparison study using spherical dose vertices throughout the tumor by changing vertex number, vertices separation, volume ratio has not been done before. It showed that LRT in VMAT is dosimetrically comparable to CyberKnife LRT making it a clinically practical radiation method.
In the literature, limited studies are investigating the dosimetric parameters of 3D LRT. Wu et al. showed the feasibility of 3D LRT using the CyberKnife and RapidArc (21). Similarly, Zhang et al. investigated the patient-specific LRT using helical tomotherapy (23). However, those studies in the literature are mainly focusing on comparing the dosimetric characteristics between the physical 2D GRID block and virtual 3D LATTICE template. This work studied dose differences between LRT doses by CyberKnife and VMAT and resulted that VMAT is an effective method for LRT as shown in some publications that reports the clinical outcomes using VMAT technique (24–27). Although a similar comparison study has already been published by Sheikhet et al., they compared tomotherapy-based plans with VMAT and 3DCRT planning techniques using cylindrical target structures instead of spherical LATTICE points (28).
In our study, we proposed that the valley-peak ratio should be defined as a ratio of mean doses of LATTICE volume and high-dose vertices for the LRT. Since the virtual LATTICE designs are not a physical block. The minimum dose is not similar throughout the target volume and cannot represent the actual valley dose. Therefore, we believe that the valley-peak pattern is not obtained more realistically calculating as a ratio of minimum dose to maximum dose within GTV. Furthermore, Sheikh et al. was calculated the peak-valley ratio similarly (28). Also, Wu et al. and Zhang et al. recommended that the valley-peak ratio should be calculated as the ratio of DMean of the LATTICE volume to the prescribed peak dose and D90/D10, respectively (22, 29).
As shown in Tables 6 and 7, our study showed that VMAT plans had a relatively larger valley-peak ratio compared to the CyberKnife plans for both tumor volumes. For the GTV1, as the vertex diameter and vertices separation increased, the valley-peak ratio decreased (from 0.60 to 0.45 for the CyberKnife plans and from 0.64 to 0.48 for the VMAT plans) for both systems. For the GTV2, as the vertex diameter and volume ratio increased, the valley-peak ratio increased (from 0.33 to 0.59 for the CyberKnife plans and from 0.39 to 0.58 for the VMAT plans) for the two systems. Thus, according to our treatment planning system findings, the valley-peak ratio was reasonably affected by varying the vertex diameter, the vertices separation and the volume ratio.
However, as compared to treatment duration, the approaches for having a LRT plan using CyberKnife would need hours for the existing clinical dose rate. The lengthy treatment time makes it impractical. For fewer number dose vertices, CyberKnife has proven to be viable. Still, we used the same number of vertices to acquire a comparable plan. In the future, LRT may become applicable with new delivery techniques such as ultra-high dose-rate irradiation for CyberKnife.
LRT plans using VMAT have been reported by Amendola et al., previously (24–27). They used this technique and presented the clinical outcomes. However, their approaches were not dose comparison work and they have given the limited details on the LRT planning parameters. A comprehensive dosimetric analysis for LRT was conducted by Wu et al. (22). Grams et al. described a planning approach to VMAT grid therapy (30). They contoured the dose vertices manually for two patient samples and placement of vertices was variable. The valley-peak ratios were not evaluated. Differently, we used variable vertex diameter, vertices separation, and volume ratio to design the LATTICE layout for a given tumor. The effect of LATTICE parameters on the valley-peak ratio was evaluated and compared between different 3D systems. Also, Jiang et al. reported the clinical outcomes for the LRT case of non-small cell lung cancer treated with CyberKnife system (31).
Furthermore, the present study investigated the effect of tumor volume on the valley-peak ratio in two different ways. First, for a constant vertices separation, vertex diameter, and volume ratio, it was observed that as the tumor volume increased, the valley-peak ratio increased by 31% for the CyberKnife plans and by 21% for the VMAT plans. Second, for the constant vertex diameter (1 cm), the use of different vertices separation and different volume ratios, decreased the valley-peak ratio by 81% for the CyberKnife plans and by 64% for the VMAT plans as the tumor volume increased.
This work has also some limitations that have to be pointed out. The first limitation is that this work was conducted only on the phantom settings. However, the comparison of these parameters was not analyzed for real patients. The second limitation is that all comparisons were evaluated inside the target volume. The organs at risk (OAR) doses were not compared, as we did not focus on the normal tissues. We intended to evaluate the dose distributions within the target volumes only. In addition, this study is solely a dosimetric comparison work. We did not focus on the setup uncertainty, patient motion, and respiratory motion. However, these parameters, especially the respiratory motion may significantly change the valley-peak ratios. Although the collimator size or optimization method for CyberKnife and MLC leaf-width, collimator angle, or the number of arcs for VMAT would lead to different effects on the plan qualities, the effects of these parameters were not analyzed in this study. In the future, it is recommended that the obtained valley-peak ratios should be assessed through the clinical cases to evaluate how the calculated values translate to clinical outcomes.
CONCLUSIONS
In conclusion, heterogeneity was successfully and accurately achieved using both cone-based and MLC-based plans via various LATTICE layouts. However, despite the lower valley-peak ratios obtained using the CyberKnife LRT plans, the treatment duration was too long to apply in a single fraction. In contrast, VMAT LRT plans can be applied within minutes. In addition, dosimetric verification results demonstrated that the plans obtained using both cone-based and MLC-based plans can be implemented accurately. In the present study, the vertex diameter, the vertices separation and the volume ratio were found as influencing factors to produce the optimal LATTICE design by using modern 3D treatment machines for defined conditions.
ACKNOWLEDGMENT
This work was supported by the Scientific and Technological Research Council of Turkey (TUBITAK) (grant number: 318S233).