Dosimetric impact of rotational errors on the quality of VMAT‐SRS for multiple brain metastases: Comparison between single‐ and two‐isocenter treatment planning techniques

Abstract Purpose In the absence of a 6D couch and/or assuming considerable intrafractional patient motion, rotational errors could affect target coverage and OAR‐sparing especially in multiple metastases VMAT‐SRS cranial cases, which often involve the concurrent irradiation of off‐axis targets. This work aims to study the dosimetric impact of rotational errors in such applications, under a comparative perspective between the single‐ and two‐isocenter treatment techniques. Methods Ten patients (36 metastases) were included in this study. Challenging cases were only considered, with several targets lying in close proximity to OARs. Two multiarc VMAT plans per patient were prepared, involving one and two isocenters, serving as the reference plans. Different degrees of angular offsets at various orientations were introduced, simulating rotational errors. Resulting dose distributions were evaluated and compared using commonly employed dose‐volume and plan quality indices. Results For single‐isocenter plans and 1⁰ rotations, plan quality indices, such as coverage, conformity index and D95%, deteriorated significantly (>5%) for distant targets from the isocenter (at> 4–6 cm). Contrarily, for two‐isocenter plans, target distances to nearest isocenter were always shorter (≤4 cm), and, consequently, 1⁰ errors were well‐tolerated. In the most extreme case considered (2⁰ around all axes) conformity index deteriorated by on‐average 7.2%/cm of distance to isocenter, if one isocenter is used, and 2.6%/cm, for plans involving two isocenters. The effect is, however, strongly associated with target volume. Regarding OARs, for single‐isocenter plans, significant increase (up to 63%) in Dmax and D0.02cc values was observed for any angle of rotation. Plans that could be considered clinically unacceptable were obtained even for the smallest angle considered, although rarer for the two‐isocenter planning approach. Conclusion Limiting the lesion‐to‐isocenter distance to ≤4 cm by introducing additional isocenter(s) appears to partly mitigate severe target underdosage, especially for smaller target sizes. If OAR‐sparing is also a concern, more stringent rotational error tolerances apply.


| INTRODUCTION
Stereotactic radiosurgery (SRS) is a well-established radiotherapy technique for the treatment of a variety of lesions, mainly in the brain. [1][2][3] Regarding the management of multiple brain metastases, SRS is being increasingly employed even in cases with more than 10 lesions. 4,5 However, increased conformity and presence of steep dose gradients in SRS treatment plans demand increased spatial accuracy in order to ensure effective treatment delivery, as spatial errors of just a few millimeters can induce considerable target underdosage, especially in tiny brain lesions. [6][7][8] Volumetric modulated arc therapy (VMAT) is commonly employed for SRS treatment delivery. Several studies have demonstrated that multiarc noncoplanar VMAT can deliver highly conformal plans to the target(s) and spare adjacent critical structures. [9][10][11][12][13][14][15][16] More recently, single-isocenter VMAT-SRS treatment techniques were introduced for dose delivery to multiple intracranial targets/lesions concurrently, with the latter being an attractive approach since treatment duration can be further reduced without necessarily compromising plan quality. [17][18][19] A single isocenter has been found sufficient for VMAT-SRS of multiple intracranial metastases, whereas minor improvements in plan quality can be achieved when additional isocenter(s) are used. 20 The main drawback of a single-isocenter VMAT-SRS technique is that it exhibits increased sensitivity to geometric uncertainties (compared to other approaches) and, therefore, its efficacy partly relies on the overall spatial accuracy. 9,12,17,18,[21][22][23][24] Patient positioning and immobilization is a typical source of translational and rotational uncertainties. 25 Thermoplastic masks are commonly used in intracranial frameless VMAT-SRS applications, and residual patient setup errors can be detected using appropriate image-guided techniques. 25 Translational setup errors are easily corrected for by adapting the treatment couch position. However, initial rotational errors can be accounted for only if a 6 degree-of-freedom (DOF) robotic couch is available, which is not always the case. [26][27][28] Nevertheless, regardless of pretreatment imaging and initial setup correction methods, significant intrafractional patient motion (including rotations) has been repeatedly reported for intracranial VMAT-SRS cases. 26,[28][29][30][31] In addition to patient positioning, other potential sources of rotational errors cannot be ruled out. For instance, the magnetic resonance imaging (MRI)-computed tomography (CT) spatial coregistration procedure could contribute to the overall spatial uncertainty budget. For a cranial case, the MR/CT registration uncertainty was estimated at 1.8 mm in a multi-institutional study. 32 Although rotational uncertainties were not separately reported, it can be expected that they may considerably contribute to the overall spatial uncertainty, especially for targets lying away from the MR isocenter where MR images inherently exhibit increased geometric warping. [33][34][35] Furthermore, geometric uncertainties stemming from the linac rotating parts (i.e., gantry, collimator or couch) or related to the angular alignment accuracy between the (i) on-couch imaging system (kV or MV CT), (ii) mechanical, and (iii) radiation delivery isocenters should also be taken into consideration. 36,37 Rotational errors are more important in single-isocenter multitarget cases, as lesions may lie several centimeters away from the isocenter and, therefore, induce considerable translations. As an instance, by performing off-axis Winston-Lutz tests, it was recently shown that radiation and on-couch imaging isocenters mis-alignment can induce offsets up to 1 mm at a distance of 60 mm from the isocenter. 36 Acknowledging the importance of spatial accuracy, several studies have investigated the dosimetric effect of rotational errors on linac-based SRS for brain metastases cases, mostly focusing on target/lesion underdosage and the potentially induced loss of coverage. [29][30][31]38 However, in all of the above studies the corresponding dosimetric impact on organs at risk (OARs) was not examined. In a recent study, Sagawa et al. 39 studied the dose-increase to the normal brain parenchyma but disregarded the effect on other critical structures such as the brainstem and the optic pathway. To our knowledge, the only work reporting on OAR-sparing focused on singletarget cranial SRS, where a small rotational error was found to have a significant dosimetric impact in cases with OARs in close proximity to the target volume. 24 In multitarget single-isocenter VMAT-SRS, due to the off-axis locations of targets and the steep dose gradients employed for sparing an adjacent OAR (e.g., the optic pathway), even a small geometric tilt could also result in significant overdosage to the OAR, especially when the adjacent off-axis target is also located away from the isocenter, which is not uncommon in multitarget single-isocenter SRS. Although not evaluated in their study, Roper et al. commented that the potential of rotational errors to overdose normal tissues is an important clinical concern and for lesions in close proximity to critical structures (e.g., optic nerves, chiasm, or brainstem), setup errors that result in collateral damage to these adjacent structures may be as critical as setup errors that underdose a target and, thus, require further investigation. 17 The scope of the present work was to study the dosimetric impact of rotational errors on target coverage and OAR-sparing in multitarget VMAT-SRS brain metastases cases, focusing on cases with OARs lying in close proximity to targets, located at various PRENTOU ET AL. The selected cases involved either three or four metastases (related to four and six patients, respectively), located in the brain parenchyma with at least one target lying in close proximity to OAR(s) (as indicatively shown in Fig. 1) (minimum target-to-OAR distance of approximately 0.5 cm). Other targets (not shown in Fig. 1) were more distant from critical structures or other targets, that is, resulted to increased interlesion distances. Details of the contoured targets are given in Table 1. In all selected cases, patients had been positioned in a Head-First Supine (HFS) position.
In order to better serve the scope of this study, effort was made to involve a wide range of lesion-to-isocenter distances, whether a single-or a two-isocenter plan (see section 2.B) is created. The resulting lesion-to-isocenter distances are also given in Table 1. Since the simulated rotational errors occurred with respect to the plan's isocenter, it is geometrically expected that the induced spatial offset will be more enhanced at target locations distant from the isocenter. 17 For each patient, two plans were prepared. The first approach involved a single isocenter with its location defined by the geometric center of all targets considered. In order to prioritize high target coverage, planning goals assured V 20Gy ≥ 98%, that is, the prescription isodose covers 98% of each target volume. During plan optimization, the clinical procedure was followed in order to achieve the intended planning goals such as high-dose conformity and steep dose gradients. Regarding OARs, the dose criteria given in Table 2 were considered and strictly met in all cases. The aforementioned planning method has been repeatedly implemented in other independent studies. 11,13,14 For the comparison purposes of this study, two-isocenter plans were also prepared with all other planning and calculation parameters kept constant. However, isocenter positioning followed a different approach in order to involve two isocenters. Regarding cases of four brain metastases, the first isocenter was placed at the geometric center of the two targets lying closest to each other, whereas the second isocenter was positioned at the geometric center of the remaining two targets. In a similar way, for cases with three brain metastases (indicatively shown in Fig. 2), the first isocenter was placed at the geometric center of the two closest targets and the second one at the center of the remaining target. In this way the maximum lesion-to-isocenter distance was limited to 4 cm, for the patients included in this study, in contrast to corresponding distances of up to 6.55 cm occurring for plans of one isocenter (Table 1). Each isocenter was associated with the same four noncoplanar arcs as the ones considered for the singleisocenter planning approach, with MLCs and jaws collimated to include only the respective target(s). 20 In all cases, the two isocenters were optimized simultaneously using the same optimization criteria as with the single-isocenter plans.

2.C | Rotational errors simulation
In order to simulate and estimate the dosimetric effect of rotational errors, the reference dose distributions (corresponding to the reference plans, section 2.B) were rotated around the plan isocenter(s).
To accomplish that, planning data were exported from the TPS in

2.D | Plan evaluation and comparison
Reference and rotated dose distributions were analyzed and compared in MATLAB using in-house routines or using BrachyGuide Dose-volume metrics related to OARs were in agreement with plan quality criteria considered during treatment planning, although all cases were rather challenging with one or more OARs located very close to metastases (indicatively shown in Fig. 1). Consequently, D max values were just below the allowed dose limits (see Table 2) for the brainstem, optic pathway and lenses. Regarding brain parenchyma, V 7Gy was in the range of 3.5% -6.2% for the singleisocenter technique, whereas the corresponding range using two isocenters was reduced to 3.3% -4.9%. Accordingly, V 12Gy and V 13Gy slightly improved for the two-isocenter reference plans. An indicative example (patient #5) of plan conformity and dose-volume metrics for the two planning techniques is presented in Table 3.
However, the treatment planning techniques resulted to substantially different beam-on times, as expected. If two isocenters are used, monitor units increase by nearly 1.5-fold which is expected to increase overall treatment duration by a factor of up to 2.

3.B.2 | Dosimetric effect on targets
The dosimetric impact of rotational errors on dose distributions is illustrated in Fig. 3, indicatively for patient #5 and an angular offset of 2°around all three axes. Loss of target conformality to the 20Gy isodose (i.e., the prescription dose) due to the rotation is more evident for the single-isocenter case [ Fig. 3(a)].
The effect is quantitatively represented by the box-whisker plots shown in Fig. 4 Fig. 4(b)] do not exceed 5%. Even for 2°, the induced effect is considerably reduced, although significant V 20Gy and D 95% changes (of the order of 10%) were detected.
Results shown in Fig. 4 are characterized by increased spread, in addition to not being normally distributed. Effort was put to correlate the observed underdosage of targets with physical characteristics and, particularly, the lesion volume and distance to nearest isocenter. Indicative results are given in the following figures. In specific, Fig. 5 presents DVHs calculated for a fairly large (2.1cc) and a small lesion (0.9cc, same patient) for both reference plans and certain simulated rotational errors (±1°, ±2°) around the three axes. For the larger target volume, the induced underdosage can be hardly noticed for the two isocenters plan, whereas the effect is increased but still limited for the single-isocenter plan, even for rotations of 2°.
In an effort to better demonstrate the effect of target size, all 36 lesions were grouped according to their volume (<1cc, 1-2cc, >2cc) and the maximum change in V 20Gy was detected for each group and all rotational errors simulated. Results are presented in Fig. 6. In all cases, the two-isocenter planning technique is less sensitive to rotational errors. Still, for the smallest targets considered and using two isocenters, V 20Gy dropped up to 15% (for an angular offset of 2°), which can be considered clinically unacceptable. Contrarily, for targets larger than 2cc the corresponding maximum detected loss of coverage was limited to 4% (Fig. 6).
Dependence of target susceptibility to rotational errors on lesion-to-isocenter separation is quantified in Fig. 7. Detected PCI changes (with respect to reference plans) are plotted against distance to the nearest isocenter for both planning techniques. A fitted linear trendline is also given. Indicatively, for the worst case of a 2°r  Table 4) is the combined geometric effect of an angular offset at the given distance from the isocenter, the ratio of

3.B.3 | Dosimetric effect on OARs
Regarding OARs lying in the vicinity of targets, maximum doses either increased or decreased depending on the magnitude, direction and axis of rotation assumed, as well as relative locations of neighboring targets. As an instance, in [ Fig. 3(a) relevant orientation and axis between the structure of interest and the proximal target. In accordance to target-related results, the magnitude of the effect is also associated with distance to the nearest isocenter. According to the results presented in Table 5, compromised OAR-sparing can occur if rotational errors are not accounted for.
The increased dose delivery to critical organs in several cases resulted in dose-volume indices exceeding the original dose constraints considered during reference treatment planning (see Table 2), that is, rotated plans could be considered clinically unacceptable, even for rotations of 0.5°in a few cases. However, it should be noted that for all angles of rotations investigated, violation of the dose constraints occurred less frequently and to a lesser degree if two isocenters were used.

| DISCUSSION
Overall results of this work suggest that the degree and direction of rotational errors, as well as the distance to nearest isocenter could suggesting considerable intrafractional patient motion. Such errors were related to reduced target coverage by >5% in 14% of the patients included in the analysis. In another study, for isocenter-tolesion distances up to 75 mm, intrafractional patient positioning uncertainties of up to 1.8 mm were calculated even if a robotic couch is used. 29 Recently, using kV imaging, it was shown that intrafractional motion is not statistically correlated with treatment duration and can exceed 1.5 mm for cranial multitarget SRS. 28 In a simulation study involving two metastases per case and one isocenter, rotational errors were introduced around all axes simultaneously. 17 For errors of 0.5°, D 95% and V 95% values for all cases were found >95%. Briscoe et al. also investigated cases with two brain metastases using one isocenter. 38 Loss of target coverage was associated with increasing distance from the isocenter. However, only one target was located at a distance of more than 4 cm, whereas the effect was not studied for more than two lesions per case. Stanhope et al. additionally reported that optimal conformity and gradient indices are achieved when the lesions are located within close proximity to the isocenter and quantified the effect with respect to distance to isocenter, with or without the use a six DOF couch. 30 The effect was more pronounced for smaller targets (<1cc). In this study, the impact of rotational errors on target dosimetry was studied under a comparative perspective between single-and twoisocenter treatment planning methods. Induced median spatial offsets were reduced by at least 35% if the latter approach is considered. Based on V 20Gy and D 95% results [ Figs. 4 and 6], it is implied that 1°rotational errors are not tolerated in the case of a single isocenter, especially if targets are located several centimeters (typi-cally>~4 cm) from the isocenter (Fig 7). This remark is in-line with the recommendations of Briscoe et al.. 38 Using an additional isocenter all targets lay at distances < 4 cm from the nearest isocenter and corresponding plans were found to be less sensitive to rotational errors, with angular offsets of 1°generating clinically acceptable dose distributions. However, reduced lesion-to-isocenter separations may result in minimizing target displacement but smaller target sizes are still very sensitive to rotational errors (Fig. 6). The dosimetric impact can be clearly correlated with the target-displacement to target-diameter ratio, as shown in Fig. 8, which is independent to the planning technique employed.
To Based on the results of this study (Table 5), rotation tolerances in multitarget single-isocenter applications are more stringent, asin a few casesplans that could be considered clinically unacceptable were obtained even for rotations of as low as 0.5°. If two isocenters are employed, increase in dose to OARs is substantially reduced (  30 Another study suggested that target coverage is assured if a margin of 2 mm is applied. 47 Regarding intrafractional motion, a 1-mm margin was proposed. 31 However, none of these recommendations take into account OAR-sparing. As an instance, margins of just a few millimeters result in an increase in F I G . 6. Bar charts of the maximum change in V 20Gy are presented for all 36 targets, grouped according to their volume (<1cc, 1-2cc, >2cc). The bars in blue color are related to the results for (a) singleisocenter planning technique, whereas the bars in red color are related to the results for (b) two-isocenter planning technique. Rotations occurred around all three axes.
dose to normal brain parenchyma and, consequently, increased risk of radiation-induced brain necrosis. [48][49][50] Furthermore, according to the results of this study, tolerance levels of rotational errors related to OAR-sparing (e.g., maximum dose to brainstem, Table 5) are more stringent compared to considering target coverage alone. As an alternative or complement to the introduction of margins, limiting lesionto-isocenter distances (using additional isocenter(s)) appears to also mitigate the induced dosimetric effect.
A number of limitations of this study are noteworthy. The singleand two-isocenter reference plans were similar and clinically acceptable but not identical in terms of plan quality. Using a second isocenter resulted in slightlyyet systematicallysuperior plans, as expected. 20  effect of this approximation can be considered negligible which was also confirmed in the work of Roper et al. 17 Another limitation of this study is that presented results depend on the given spatial distribution, size and shape of targets included in the analysis. Investigation of larger (>4cc) target volumes was not performed, although it has been shown that the induced dosimetric effect could also vary accordingly. 24 The maximum lesion-to-isocenter distance included in this analysis was limited to 6.5 cm. However, in single-isocenter SRS treatment planning, larger separations can be encountered, exceeding 10 cm in a few cases. 17,30 In addition, up to four targets per patient were studied, despite the fact that the number of lesions considered treatable by SRS has recently increased. 4,5 Assuming a larger number of metastases per case would result in increased average lesion-to-isocenter distances, and tolerance of rotational uncertainties is expected to be much more stringent in such distant targets and adjacent OARs. Therefore, presented results should be regarded as indicative for cases similar to the ones presented herein.
Image guidance and a stringent patient setup protocol are essential in order to minimize potential setup errors in single-isocenter multitarget VMAT-SRS. In absence of a six DOF couch and for patients with three or more brain metastases and adjacent OARs, limiting lesion-to-nearest isocenter distance to~4 cm (by introducing additional isocenter(s)) appears to be a safe-side treatment planning approach that partly mitigates the effect on targets and OARs.
However, in specific cases and orientations of rotational errors, plans that could be considered clinically unacceptable were obtained even for angles of as low as 0.5°. Despite that the effect was rare for plans of two isocenters, still, OAR-sparing cannot be guaranteed.
Employing a six DOF robotic couch could minimize the required margins and/or number of isocenters, although intrafractional patient motion still remains a concern. 26,30,31 Future work will focus on the the lesion-to-isocenter distances to~4 cm (by introducing additional isocenter(s)) appears to partly mitigate severe target underdosage.
However, smaller target sizes (especially < 1cc) may still exhibit increased sensitivity to rotational errors. In any case, lesion size and distance to isocenter are two factors governing the impact of rotational errors on target underdosage and thus the later was found to be clearly correlated with the target-displacement to target-diameter ratio, a factor that takes into account the increased sensitivity of smaller target sizes to rotational errors. Moreover, if OAR-sparing is also a concern (i.e., OARs lying in close proximity to targets), more T A B L E 5 The maximum and median deviations (with respect to reference plans) for clinically used dose-volume metrics for all patients and OARs considered and all three simulated angles, irrespective of the axis and sign of rotational error assumed. Results are presented for the (a) single-and (b) two-isocenter planning techniques, to assist comparison.

CONF LICTS OF INTEREST
None.