Volumetric modulated arc therapy (VMAT) is widely used in clinical practice as it can deliver precise dose coverage to the target while minimizing radiation exposure to the surrounding healthy tissues [1-3]. The VMAT planning process relies on an optimization algorithm within a treatment planning system (TPS) that uses an inverse planning approach. Although the optimization automatically determines the optimal beam parameters based on dose-volume constraints for targets and organs at risk (OARs), it still requires user-defined inputs such as prescription doses, collimator and couch angles, and gantry rotation settings [4,5].

In the Monaco TPS (Elekta AB), users must specify gantry arc increment (GAI) values, which define the angle for each sector of the arc [5,6]. The number of sectors is calculated by dividing the total gantry angle by the GAI. Within each sector, the multi-leaf collimator (MLC) moves in a consistent direction, reversing direction in the subsequent sector [5-8]. Increasing the number of sectors can enhance plan quality by allowing for more precise MLC modulation [7,8]. Although GAI significantly affects plan quality and treatment time, few studies have investigated the optimal GAI.

Nithya et al. [7] observed similar plan qualities with GAI values of 15°, 20°, 30°, and 40° in VMAT for patients with esophageal cancer, concluding that 40° was optimal due to its higher dose homogeneity and improved monitor unit (MU) efficiency. Similarly, Chen et al. [8] demonstrated that GAI values of 30° and 40° enhanced the plan quality and comparable deliverability in VMAT for patients with cervical cancer. However, the optimal GAI for plans requiring relatively higher degrees of modulation is poorly understood. Moreover, the impact of GAIs on treatment sites requiring different modulation levels is unclear. In this study, we examined VMAT plans for two clinical treatment sites requiring varying modulation levels: head and neck (HN) and prostate cancer, which require high and low modulation, respectively.

1. Patient selection, computed tomography scanning, and OAR contouring

Twenty patients (10 for HN, 10 for prostate) were selected following institutional review board approval (IRB No. 2405-164-068). Informed consent was waived due to the retrospective nature of the study. All patients underwent computed tomography (CT) scans using a Big Bore RT CT Simulator (Philips Health Systems) with appropriate immobilization devices and a slice thickness of 2 mm. After the scans, OARs were automatically contoured using the Contour ProtégéAI^TM module in MIM^® software (Version 7.2.10; MIM Software Inc.). A radiation oncologist reviewed and confirmed the OAR contours and manually contoured the clinical target volume (CTV) according to established guidelines [9-14]. The planning target volume (PTV) was generated by expanding the CTV with a 3 mm margin in all directions for the HN cases and a 5 mm margin in all directions except for a 1 mm margin posteriorly for the prostate cases.

2. Treatment planning

VMAT plans were created using the Monaco TPS (Version 6.1.2; Elekta AB). Users must specify the GAI, with options ranging from 5° to 45°. Elekta recommends a 30° GAI value for general VMAT plans, which can be reduced if more modulation is needed [6]. To evaluate the effects of a smaller GAI, we compared increments of 30° and 15°, the latter being the vendor-recommended value. For the planning of HN and prostrate cases, 6 MV and 10 MV photon beams were utilized, respectively. Collimator angles of 45° and 315° were selected for each field, as a 90° difference between these angles is known to optimize the sparing of OARs, with literature showing no significant differences with other angle combinations [15,16]. A Monte Carlo dose calculation algorithm was employed with a statistical uncertainty of 1.0% per calculation and a dose grid resolution of 2 mm [4,17].

For both HN and prostate cases, the PTV was prescribed to receive 70 Gy in 35 fractions. The OAR constraints are summarized in Table 1. The plans were optimized to ensure that 95% of the PTV received 70 Gy, with the dose of 0.03 cc (D_0.03cc) of the PTV not exceeding 110% of the prescribed 70 Gy. After the optimization, the plans were normalized to ensure that 70 Gy covered 95% of the PTV.

Table 1 . Dose constraints used in this study.

Case	OAR	Dose-volumetric parameter	Constraint
HN	Spinal cord	Dmax	<45 Gy
	Brain stem	Dmax	<54 Gy
	Left parotid gland	Dmean	<26 Gy
	Right parotid gland	Dmean	<26 Gy
Prostate	Bladder	V50Gy	<50%
		V70Gy	<30%
	Rectum	V50Gy	<50%
		V70Gy	<25%
	Left femoral head	V50Gy	<5%
	Right femoral head	V50Gy	<5%

3. Evaluations

The quality of the plans was assessed in terms of dose-volumetric parameters listed in Table 1. The D_mean for OARs in prostate cases was also evaluated. Further, conformity number (CN), homogeneity index (HI), and gradient index (GI) were calculated as follows [18-21]:

where V_T is the volume of the PTV, V_T,100% is the volume covered by the prescription dose, V_x% is the volume receiving x% of the prescription dose, and D_y% is the dose received by y% of the PTV.

Plan deliverability was evaluated based on the total MUs and the modulation complexity score for VMAT (MCS_v). MCS_v, a plan complexity metric developed by McNiven et al. [22] for intensity-modulated radiation therapy and later adapted by Masi et al. [23] for VMAT, measures plan complexity by evaluating aperture area variability (AAV) and leaf sequence variability (LSV). First, the maximum leaf position changes for each control point (pos_max(CP)) was calculated using the following formula:

Next, LSV_cp and AAV_cp were calculated as follows:

After that, MCS for each arc (MCS_arc) was calculated as:

Finally, MCS_v was calculated as:

A lower MCS_v indicates higher plan complexity, while a higher MCS_v reflects lower complexity. Therefore, MCS_v is adopted as a surrogate metric for plan deliverability.

Given the relatively small sample size in this study, we employed the Wilcoxon signed-rank test for statistical analysis, which is particularly advantageous for paired samples and small sample sizes [24]. Differences with P-values <0.05 were considered statistically significant. Statistical analysis was performed using the Real Statistics Resource Pack software (Release 9.1.1) plug-in for Excel.

1. Plan quality comparisons

Dose-volumetric analysis results are summarized in Table 2. Figs. 1 and 2 show the dose distributions and dose-volume histograms for the representative cases. For HN cases, the D_0.03cc, HI, and GI for the PTV were similar across the groups. However, plans using 15° GAI values demonstrated significantly better conformity than those using a 30° increment. While the D_0.03cc for the brainstem was lower in the 15° plans than in the 30° plans, this difference was not statistically significant. However, the D_0.03cc for the spinal cord and the D_mean for the left and right parotid glands were significantly lower in the 15° plans than those in the 30° plans.

Table 2 . Dose-volumetric analysis results and statistical significances.

Case	Organ	DV parameter	30° GAI	15° GAI	P-value
HN	PTV	D0.03cc (Gy)	76.25±0.75	76.48±1.03	0.097
		CN	0.85±0.04	0.86±0.04	0.019*
		HI	0.06±0.01	0.06±0.01	0.246
		GI	3.03±0.56	2.93±0.46	0.097
	Spinal cord	D0.03cc (Gy)	23.86±6.03	20.84±4.78	0.003*
	Brainstem	D0.03cc (Gy)	16.18±16.33	15.81±16.76	0.216
	Left parotid gland	Dmean (Gy)	26.79±11.20	24.75±11.20	0.032*
	Right parotid gland	Dmean (Gy)	32.74±14.74	30.27±15.18	0.032*
Prostate	PTV	D0.03cc (Gy)	74.70±0.55	74.86±0.38	0.188
		CN	0.84±0.02	0.84±0.03	0.278
		HI	0.05±0.01	0.05±0.00	0.097
		GI	4.75±0.54	4.69±0.56	0.246
	Bladder	V70Gy (%)	27.74±17.06	27.41±17.03	0.053
		V50Gy (%)	47.62±18.92	48.10±18.26	0.326
		Dmean (Gy)	46.99±9.77	47.63±9.77	0.216
	Rectum	V70Gy (%)	2.92±1.38	2.55±0.96	0.097
		V50Gy (%)	19.86±5.31	18.32±4.54	0.097
		Dmean (Gy)	33.51±3.73	33.06±4.33	0.423
	Left femur head	V50Gy (%)	0.13±0.40	0.25±0.79	0.250
		Dmean (Gy)	19.18±1.80	18.95±2.30	0.385
	Right femur head	V50Gy (%)	0.10±0.22	0.04±0.09	0.250
		Dmean (Gy)	17.36±2.43	18.64±2.47	0.003*

Figure 1. Sample dose distributions for representative cases in head and neck cancer with GAIs of (a) 30° and (b) 15°, and in prostate cancer with GAIs of (c) 30° and (d) 15°. GAI, gantry arc increment; PTV, planning target volume.

Figure 2. Sample dose-volume histograms for representative cases in (a) head and neck and (b) prostate cancer. The dotted and solid lines represent plans using 30° and 15° gantry arc increments, respectively. PTV, planning target volume.

For prostate cases, the D_0.03cc, CN, HI, and GI were comparable across groups with no significant differences. Additionally, none of the dose-volumetric parameters for OARs showed statistical significance.

2. MU and complexity comparisons

The statistics for MU and MCS_v are summarized in Table 3. For both HN and prostate cases, the mean MU for plans with 30° and 15° increments showed no significant difference. However, the mean MCS_v for plans with 30° and 15° increments exhibited a statistically significant difference (P <0.05) in both cases.

Table 3 . Statistics for MU and MCS_v.

Case	Metric	30° GAI	15° GAI	P-value
HN	MU	1,268.21±225.92	1,309.73±223.15	0.216
	MCSv	0.17±0.08	0.09±0.01	0.007*
Prostate	MU	1,320.52±382.78	1,367.72±338.26	0.138
	MCSv	0.29±0.13	0.13±0.06	0.003*

This study demonstrated dose-volumetric analysis and plan deliverability for HN and prostate VMAT plans using different GAIs. While no significant differences in doses to OARs and targets were observed in prostate cases, plans using a 15° increment in HN cases achieved notable dose reductions, specifically in the D_0.03cc for the spinal cord and the D_mean for both parotid glands. In both cases, plans with a 15° increment had higher MUs and lower MCS_v than those with a 30° increment, although only the difference in MCS_v was statistically significant.

Previous studies, such as those by Nithya et al. [7], demonstrated that using a larger increment (40°) improved the plan quality with fewer MUs in VMAT for patients with esophageal cancer. Similarly, Chen et al. [8] found that while plans with a 30° increment in VMAT for patients with cervical cancer had advantages, such as shorter treatment times, dose reductions with different increments did not show significant differences. While the findings for prostate cases in this study were consistent with previous research, HN plans using smaller GAIs might significantly reduce doses to OARs, albeit with increased plan complexity. Plan complexity for VMAT in HN cases is generally greater than that in prostate cases due to the typically irregular and elongated shape of the target volume in HN cases and the proximity of multiple OARs [23]. The complexity of plans using a 15° GAI was more pronounced than those using a 30° increment in both cases. These findings indicate that VMAT plans with smaller GAIs may offer potential benefits in reducing OAR doses in cases requiring higher modulation.

This study has some limitations. First, the sample size is relatively small for each case. To address this, we used the Wilcoxon signed-rank test for statistical analysis, as it is well-suited for small sample sizes and non-normally distributed data. Due to the limited sample size, the impact of dose reduction in prostate cases may not be as apparent. However, despite this limitation, the smaller GAI still demonstrated a significant OAR-sparing effect in HN cases. Another limitation is that plan deliverability was assessed using complexity metrics rather than performing a gamma analysis based on actual delivery. Although studies have shown that various complexity metrics are highly correlated with gamma passing rates [23], directly evaluating plan deliverability through gamma analysis might benefit future research.

Despite several limitations, our results showed that OAR doses can be potentially reduced with smaller GAIs, albeit with a slight increase in complexity. While the quality of VMAT plans is often determined by user-defined dose-volumetric parameters, a thorough understanding of the physical properties of the TPS and the mechanical parameters of the linear accelerator can enhance plan quality and deliverability, offering significant clinical benefits.

VMAT plans with a smaller GAI (15°) can significantly reduce OAR doses compared to those with a 30° GAI in HN cases. However, no significant dose reduction was observed with a smaller GAI in prostate cases. Although plan complexity and total MUs may slightly increase, using a smaller GAI can potentially reduce OAR doses in the Monaco TPS.

This work was supported by Korea Institute of Energy Technology Evalutaion and Planning (KETEP) grant funded by the Korea government (MOTIE) (20227410100040, Development of patch-type flexible personal dosimeter and real-time remote monitoring system using high-performance inorganic perovskite).

The authors have nothing to disclose.

All relevant data are within the paper and its Supporting Information files.

Conceptualization: Minsoo Chun. Data curation: Hyejo Ryu. Formal analysis: Hyejo Ryu, Lee Yoo. Funding acquisition: Seonghee Kang. Investigation: Seonghee Kang, Do Hoon Oh, Minsoo Chun. Methodology: Minsoo Chun. Project administration: Seonghee Kang. Resources: Hyejo Ryu, Do Hoon Oh. Software: Lee Yoo. Supervision: Minsoo Chun. Validation: Hyejo Ryu, Do Hoon Oh. Visualization: Hyejo Ryu, Lee Yoo. Writing – original draft: Seonghee Kang, Minsoo Chun. Writing – review & editing: Seonghee Kang, Hyejo Ryu, Minsoo Chun.

The study was approved by the Institutional Review Board of Chung-Ang University Gwang Myeong Hospital (IRB approval number; 2405-164-068).