Investigating the impacts of intrafraction motion on dosimetric outcomes when treating small targets with virtual cones

Abstract Purpose Intrafraction patient motion is a well‐documented phenomenon in radiation therapy. In stereotactic radiosurgery applications in which target sizes can be very small and dose gradients very steep, patient motion can significantly impact the magnitude and positional accuracy of the delivered dose. This work investigates the impact of intrafraction motion on dose metrics for small targets when treated with a virtual cone. Materials and Methods Monte Carlo simulations were performed to calculate dose kernels for treatment apertures ranging from 1 × 2.5 mm2 to 10 × 10 mm2. The phantom was an 8.2‐cm diameter sphere and isotropic voxels had lengths of 0.25 mm. Simulated treatments consisted of 3 arcs: 1 axial arc (360° gantry rotation, couch angle 0°) and 2 oblique arcs (180° gantry rotation, couch angle ±45°). Dose distributions were calculated via superposition of the rotated kernels. Two different collimator orientations were considered to create a virtual cone: (a) each treatment arc was delivered twice, once each with a static collimator angle of ±45°, and (b) each treatment arc was delivered once, with dynamic collimator rotation throughout the arc. Two different intrafraction motion patterns were considered: (a) constant linear motion and (b) sudden, persistent motion. The impact of motion on dose distributions for target sizes ranging from 1 to 10 mm diameter spheres was quantified as a function of the aperture size used to treat the lesions. Results The impact of motion on both the target and the surrounding tissue was a function of both aperture shape and target size. When a 0.5‐mm linear drift along each dimension occurred during treatment, targets ≥5 mm saw less than a 10% decrease in coverage by the prescription dose. Smaller apertures accrued larger penalties with respect to dosimetric hotspots seen in the tissues surrounding the target volume during intrafraction motion. For example, treating a 4‐mm‐sized target that undergoes 2.60 mm (3D vector) of continuous linear motion, the D5 in the concentric shells that extend 1, 2, and 3 mm from the surface of the target was 39%, 24%, and 14% smaller, respectively when comparing the delivery of a larger aperture (6 × 10 mm2) to a smaller aperture (2 × 5 mm2). Using a static collimator for shaping a virtual cone during treatment minimized the dosimetric impact of motion in the majority of cases. For example, the volume that is covered by 70% or more of the prescription dose is smaller in 60.4% of cases when using the static collimator. The volume covered by 50, and 30% or more of the prescription dose is also smaller when treating with a static collimator, but the clinical significance of this finding is unknown. Conclusions In this work, the dosimetric trade‐offs between aperture size and target size when irradiating with virtual cones has been demonstrated. These findings provide information about the tradeoffs between target coverage and normal tissue sparing that may help inform clinical decision making when treating smaller targets with virtual cones.

in the majority of cases. For example, the volume that is covered by 70% or more of the prescription dose is smaller in 60.4% of cases when using the static collimator. The volume covered by 50, and 30% or more of the prescription dose is also smaller when treating with a static collimator, but the clinical significance of this finding is unknown.
Conclusions: In this work, the dosimetric trade-offs between aperture size and target size when irradiating with virtual cones has been demonstrated. These findings provide information about the tradeoffs between target coverage and normal tissue sparing that may help inform clinical decision making when treating smaller targets with virtual cones.

K E Y W O R D S
Monte Carlo, stereotactic radiosurgery, virtual cones

| INTRODUCTION
Highly conformal treatments of small cranial lesions utilize a technique known as Stereotactic Radiosurgery (SRS) which aims to achieve sub-mm target localization in all three spatial dimensions. 1 Compared with conventionally-fractionated treatments, singlefraction SRS and few-fraction stereotactic radiotherapy (SRT) are characterized by large doses per fraction, high dose conformity, and strict patient positioning tolerances. 2 Several approaches have been developed to deliver these treatments, including VMAT and stereotactic cones. In comparison to VMAT, cones have demonstrated better conformity for smaller target volumes (4 mm in diameter) when treating spherical lesions. 3,4 For certain indications such as trigeminal neuralgia (TN) where targets sizes become sufficiently small and dose limitations on surrounding tissues are stringent, 5 circular stereotactic cones are most commonly used for treatment delivery. 6 Recent literature has demonstrated that a combination of collimator rotations and apertures shaped by the multi-leaf collimator (MLC), referred to as a virtual cone, are capable of shaping dose distributions comparable to stereotactic cones for small targets. Popple et al aimed to create spherical dose distributions for the purpose of treating a small target like the trigeminal nerve with a virtual cone and found that performing an arc-based delivery with a 2.1 × 5 mm 2 aperture using two arcs with orthogonal collimator angles, produced a dose distribution comparable to a 4-mm stereotactic cone defined at the 50% isodose line. 7 Additional preliminary work with virtual cones investigated the treatment of functional disorders (e.g., thalamotomy of the nucleus ventralis intermedius (VIM)), which coupled high-resolution fMRI and SRS to delineate and ablate the VIM. 8 They found that a delivery with a fixed-MLC position and series of noncoplanar arcs can deliver a spherical dose distribution comparable to a 4-mm SRS shot with a cone. Another study using virtual cones for dorsal nerve root ganglion ablation therapy alluded to the potential of reducing treatment times (and therefore intrafraction motion) when using virtual cones, but did not quantify the dosimetric impact of intrafraction motion with virtual cones. 9 They found that the shape of the 60 Gy isodose surface was appropriate for the ablative doses used in therapy, and that the dose limits on surrounding organs at risk were satisfied. Furthermore, the conformity of the spherical dose profile shaped by virtual cones and arc arrangement eliminated the need for inverse planning and could be used as a standard template for most patients.
Historically, framed-based systems were used for immobilization during SRS treatments, 10-13 but many centers have moved away from invasive immobilization techniques in favor of non-invasive, thermoplastic mask-based methods. However, mask-based systems have been shown to allow larger intrafractional positioning errors that increase in magnitude with increasing treatment time. [14][15][16] There have been several studies that have investigated the magnitude of detected motion within different thermoplastic mask systems and imaging modalities. Using BrainLAB frameless masks and imaging with the Brainlab ExacTrac stereoscopic X-ray system, Gaevart et al reported the 3D displacement from intrafraction motion to be 0.66-3.16 mm. 17 Similarly, Bichay et al. found 3D displacements of 0.4-3.23 mm using a Civco mask, and aligning orthogonal images to digitally reconstructed radiographs (DRR). 18  | 61 median change in dose received to 95% (D 95 ) and 90% (D 90 ) of the target volume, the maximum dose (D max ), and mean dose (D mean ) for 8/9 subjects; whereas the dose received to 0.1% (D 0.1 ), 0.5%(D 0.5 ), 1%(D 1.0 ), and D max for the surrounding organs at risk (OAR) differed by −14% to 38%. 21 23 , and can reside an average of 2 mm away from the pons which is a radiologically sensitive structure. 24 Therapeutic situations such as these necessitate planning target volume (PTV) margins to be as small as possible. However, Guckenberg showed that using a 0mm PTV margin on cranial lesions could result in a 40% reduction in the conformity index when intrafraction motion occurs. 25  Results of this study provide insight into the robustness of both target dose metrics and surrounding tissue doses when the planning conditions (no motion) differ from the treatment delivery conditions (motion) as a function of target size and treatment aperture size. Such information will be of value to clinicians seeking to understand the risk-reward balance of highly conformal treatment apertures.

2.A | Monte Carlo Simulation
Dose kernels were created with the EGSnrc Monte Carlo system. 28 To simulate a dose kernel, a phase-space from the treatment head of the TrueBeam STx platform for a 6 MVFFF beam was provided by Varian Medical Systems through 54 phase space files (~69 Gb) that was validated down to a field size of 1 x 1 cm 2 . 29 The phase space was scored above the jaws at 73.3 cm from isocenter, and was used an input for SOURCE-21 containing a linac model with the jaws, HDMLC, and Mylar exit window within BEAMnrc. 30 The MLC-defined aperture was incident on an 8.2-cm diameter water sphere phantom in DOSXYZnrc, 31

2.B | Simulating treatment delivery
Treatments modeled in this study consisted of a set of 3 arcs: a 360°axial arc (couch angle = 0°) and 2 partial arcs (180°rotations) with the couch at AE45°. Dose distributions were calculated via superposition of the Monte Carlo-derived dose kernels described previously. To simulate the delivery, each arc was modeled as a series of discrete control points with 10°of gantry rotation between each control point. The kernel was rotated to account for the motion of the gantry, couch, and collimator. Rotations and translations were implemented in MATLAB utilizing tricubic interpolation.

2.D | Simulating intrafraction motion
To approximate positioning errors owed to intrafraction motion, six different motion traces were simulated as shown in Fig

2.E | Dosimetric analysis
For treatment simulations that did not involve motion, for each aperture size, a dose volume histogram (DVH) was calculated for target sizes ranging from 1 to 10 mm in diameter. For each target volume (TV), the dose matrix was normalized such that 99% of that target volume was covered by the prescription dose (which will be defined as D 99 ). For simulations where motion was present, the distributions were not renormalized to achieve the same coverage. To evaluate the dosimetric impact of motion, the ratio of the Paddick conformity indices was calculated for the case of motion to the case without motion 33 : where TV M refers to the volume within the target covered by the prescription dose for the case of motion, PIV M is the prescription isodose volume for the case of motion; both of these parameters are determined using the prescription isodose in the case of no motion.
TV NO refers to the volume within the target covered by the prescription dose for the case of no motion, PIV NO is the prescription isodose volume for the case of no motion. A value of unity would indicate that the conformity index for the case of motion is equivalent to the case without motion.
To evaluate the steepness of the dose gradient for different plans, the gradient index (GI) was calculated by conventional means 34 : Movement traces for different intrafraction motion patterns. L 0.5 mm, L 1.0 mm, L 1.5 mm, represent linear motion up to 0.5, 1.0, and 1.5 mm in each dimension respectively. S 1/4, S 1/2, S 3/4, represents a linear motion of 2 mm in each dimension at ¼, ½, and ¾ of the way through treatment respectively. The shaded regions represent the first co-planar arc and the two non-coplanar arcs in order from left to right.
where V 50 is the volume receiving 50% of the prescription dose, and V 100 is the volume receiving 100% of the prescription dose. For this analysis, the dose distributions were normalized such that the prescription dose was defined as 100%.

3.A | Effect of aperture size on target coverage
The impact of different sized apertures on target coverage is demonstrated by the black lines in Fig. 2 for the static collimator case. In In Table 2 the minimum dose received by 100% of a volume (D m ), and the minimum dose received by 5% of a volume (D 5 ) are shown for a fixed target size with varying aperture sizes. Values are expressed as a percentage of the prescription dose. This table is representative of the trends seen within the data, which is that larger apertures (effective area) produce lower D 5 at the expense of delivering a higher D m to the surrounding concentric shells.

3.B | Effect of collimator orientation
The impact of collimator rotation throughout gantry motion is depicted in Fig. 3 for various circumstances. In Fig. 3.A. a collimator size of 4 x 5 mm 2 is used to irradiate a 5-mm spherical target. Differences between the static and dynamic collimator deliveries were minimal for both the TV and the surrounding shells. However, as shown in Fig. 3(b), when irradiating with a dynamic collimator and a 1 x 5 mm 2 aperture, a smaller D 5 is observed for the 1st, 2nd, and    Analyzing the DVHs for two representative cases with the static collimator case; the dosimetric trade-offs for different aperture sizes when intrafraction motion is present can be evaluated. In Fig. 7(a). and Fig. 7(b). these trade-offs become apparent for an irradiation of a 4-mm target irradiated with a 2 x 5 mm 2 , and 6 x 10 mm 2 -sized field, respectively. As shown above in previous sections, irradiating with a smaller field has the potential to produce a sharper dose gradient as the surrounding concentric shells receive less dose. However, when intrafraction motion is present, small field sizes result in larger relative increases to the hotspots in the surrounding shells of tissue. In the example of Fig. 7, the increase in the D 5% for the smaller aperture (2 x 5 mm 2 ) in the 1st, 2nd, and 3rd concentric shell was 39%, 24%, and 14% larger respectively when compared with the delivery using the larger aperture (6 x 10 mm 2 ). While treating with a larger aperture minimizes the relative penalties of intrafraction motion, this comes at the expense of delivering a larger integral dose to the surrounding tissues.

3.C | Impact of motion on dosimetry
The dosimetric impact of motion on targets that reside off-axis are visualized in Fig. 8  F I G . 4. Absolute volumetric differences between the volumes receiving 30 and 10% or more of the prescription isodose defined as V 30 and V 10 respectively for the different collimator deliveries. Volumes <0 cc indicate a smaller relative volume for the dynamic collimator case. Blacked out tiles represent plans that delivered a D max >200%.
F I G . 5. Dose map for a delivery with a 2 x 5 mm 2 aperture with the static collimator case. The black-dashed contour line represents delivery without motion and red lines represents with the same delivery characteristics but the phantom has been linearly moved 1.0 mm along each dimension by the end of treatment.
3 cm off-axis, respectively. Similarly, the differences in V 100 are less than 8 x 10 -4 cc for the three target locations when simulating a delivery with Monte Carlo.
In Fig. 9, the R C is shown for all field sizes and each different type of motion trace. Predictably, the magnitude of conformity loss increases with increasing magnitude of linear drift. A similar trend is observed for the large shifts that occur at different time points, where earlier shifts producing larger losses of conformity. Interestingly, for the case of large shifts occurring a set time points in Figure D, E, and F, there is a trend of worsening conformity with increasing effective aperture area. The average R C for the different cases of motion are summarized in Table 3.
For any given target volume, the choice of an aperture, and collimator orientation technique will vary dose hot-spots as well as the low-intermediate dose wash which influence the dosimetric conformity delivered to the target. This is visualized in Fig. 10 where dosimetric profiles along three orthogonal axes through isocenter have been extracted for the treatment of a 5-mm target. The profiles are normalized to ensure that 99% of the target volume is covered by the prescription dose. In this figure, it is shown that while squarelike apertures (4 x 5 mm 2 ) produce a steeper dose-gradient outside of the target volume when compared with rectangular-like aperture (3 x 7.5 mm 2 ), they deliver a larger dosimetric hotspot (~5.2% larger), which could pose a larger detriment to surrounding sensitive structures; and the steepness of the dose gradient could lead to a larger decrement in target volume coverage when motion is present. The use of collimator rotation can be implemented to reduce the dosimetric hotspot (~8.4% as is depicted in the case of the 2 x 10 mm 2 aperture) reducing the dosimetric risk to surrounding tissues when motion is present. While this also leads to a larger distribution of low-intermediate dose to surrounding tissues, this could minimize the decrements to conformity when motion is present for specific cases. For example, as is shown in Fig. 9(a)-9(c) when treating a 3mm-sized target with a 1 x 2.5 mm 2 , 2 x 2.5 mm 2 , or 3 x 2.5 mm 2 field when linear motion is present, using a dynamic collimator produces a 12% AE 3% higher R C . Seen across Fig. 9(a)-9(c) is the trend of a higher R c with more rectangular apertures, as well as some values of R c greater than unity. This effect is due to the relative shrink-

| DISCUSSION
For the majority of the analysis considered in this work, many of the pairings of aperture size for a given target volume would be clinically impractical. The purpose of performing the analysis was to F I G . 6. Dose profiles extracted along the three orthogonal axes intersecting isocenter for dose distributions when treating 3 mm spherical target with a 2 x 5 mm 2 aperture with 1.0 mm of linear motion along each axes. Black lines represent the case without motion, red lines represent the case with motion. demonstrate the benefits and compromises one must make when considering TV coverage, hot spots, and magnitude of dose received to abutting tissues, and dose-gradients. In the past decade, irradiation of lesions <1 cc. using VMAT, or dynamic conformal arc therapy have appeared for Brain Metastases 26,27 and Trigeminal Neuralgia. 24 Popple et al. were the first to implement the use of a virtual cone with an arc-based delivery for treating small targets such as trigeminal neuralgia with arc-based and static port deliveries, respectively. 7 That work determined that the target volume coverage by the 50%  [21][22][23]25 and furthermore, to utilized average trends of motion that have been observed in the literature for cranial SRS. [14][15][16][17][18][19][20] Neither of the collimation methods (static or dynamic) demonstrated a consistent dosimetric benefit; albeit, the 10% isodose line In this work, the impact of motion in the context of the volume receiving the prescription dose was highly variable across different aperture sizes, target sizes, and different magnitudes of motions. For F I G . 9. Ratio of the Paddick conformity index for deliveries with varying intrafraction motion. (A), (B), and (C) are plots for L 0.5 mm, L 1.0 mm, L 1.5 mm, which represents linear motion up to 0.5, 1.0, and 1.5 mm in each dimension respectively. (D), (E), and (F) are plots for S 3/4, S 1/2, and S 1/4, which represents a linear motion of 2 mm in each dimension at ¾, ½, and ¼ of the way through treatment respectively. Open-face symbols represent the static collimator case and closed-face symbols represent the dynamic collimator case. The dashed line at unity represents the situation where a delivery with motion produces equal conformity to a delivery without motion.
T A B L E 3 Average ratio of Paddick conformity index for the various cases of motion. The magnitudes and standard deviations are determined from averages across all apertures shown in Fig. 9 Type of Motion

| CONCLUSIONS
In this work, we have demonstrated the dosimetric trade-offs between aperture size and target size when irradiating with virtual cones. Larger apertures (effective area) produce smaller hotspots (D 5 ) at the expense of delivering larger absolute doses to surrounding tissues. We have also shown the dosimetric impact of intrafraction motion consistent with previously published data derived from thermoplastic mask immobilization systems. For a given target size, the relative dosimetric penalties of intrafraction motion are smaller for larger aperture. In a representative example, the D 5% for a larger aperture (6 x 10 mm 2 ) in the 1st, 2nd, and 3rd concentric shell was 39%, 24%, and 14% smaller, respectively, when compared with the delivery using the smaller aperture (2 x 5 mm 2 ). Rotating the collimator throughout delivery is beneficial in minimizing the volumes covered by the intermediate dose wash in the majority of cases (50% and 30% of the prescription dose), but the clinical significance of these findings are unknown. Apertures with a larger length to width ratio minimized the reduction in conformity when motion is present. The data from this work illustrates the growing urgency and necessity for sub-mm positioning when treating smaller targets.

| DATA STATE MENT
The data that support the findings of this study are available from the corresponding author upon reasonable request.

FIN ANCIAL DISCLOSURES
CC, DP, and AS have no financial disclosures.