The surface area effect: How the intermediate dose spill depends on the PTV surface area in SRS

Abstract Purpose Stereotactic radiosurgery (SRS) is rapidly becoming the standard of care for many intracranial targets. The characteristics of the planning target volume (PTV) can affect the intermediate dose spill and thus normal brain volume dose which is correlated with brain toxicity. R50% (volume receiving 50% of prescription dose divided by PTV volume) is a useful metric to quantify the intermediate dose spill. We propose a novel understanding of how the PTV surface area (SAPTV) affects the intermediate dose spill of SRS treatments. Methods Using a phantom model provided by a computed tomography (CT) of the IROC Head Phantom® and Eclipse® Treatment Planning System, we investigate the relationship of R50% and SAPTV in single‐target SRS treatments. The planning studies are conducted for SRS treatments on a Varian TrueBeam® linear accelerator with high‐definition MLC and a 6 MVFFF beam mode. These data are analyzed to ascertain trends in R50% related to SAPTV. Since SAPTV is not available as a structure property in the Eclipse RTPS, we introduce an Eclipse script to extract PTV surface area of arbitrary‐shaped PTVs. We compare a physically reasonable theoretical prediction of R50%, R50%Analytic, to the R50% achieved in treatment planning studies. Results The SRS phantom study indicates good correlation between the plan R50% and SAPTV. A near‐linear relationship of plan R50% vs SAPTV is observed as predicted by the R50%Analytic model. Agreement between plan R50% values and R50%Analytic predictions is good for all but the very smallest PTV volumes. Conclusions We demonstrate dependence of the intermediate dose spill measured by R50% on the SAPTV. We call that dependence the surface area effect. This dependence is explicit in the R50%Analytic prediction model. The predicted value of R50%Analytic for a given PTV could be used for guidance during SRS treatment plan optimization, and plan evaluation for that PTV.


| INTRODUCTION
Stereotactic radiosurgery (SRS) and stereotactic radiotherapy (SRT) both refer to the highly conformal delivery of a very high dose, with very high spatial precision, to a target typically in the cranium.
Stereotactic radiosurgery is a term reserved for a single fraction delivery while SRT can be three to five fractions. SRS/SRT is becoming standard of care for a host of small planning target volumes (PTVs) within the cranium. 1,2 Stereotactic radiosurgery/SRT is delivered on a variety of machine types including Gamma Knife (Elekta Instrument AB, Stockholm, Sweden), CyberKnife (Accuray, Sunnyvale, California), TomoTherapy (Accuray, Sunnyvale, California), and conventional C-arm linear accelerators (linac) such as the Varian TrueBeam STx ® with 120 leaf HD MLC or Edge radiosurgery system (Varian Medical Systems, Palo Alto, CA) and Elekta Versa HD (Elekta Instrument AB, Stockholm, Sweden). Photon energies of 6 MV and 60 Co are commonly used. Current technology makes linac-delivered SRS/SRT a good clinical option using both volumetric modulated arc therapy (VMAT) and dynamic conformal arc therapy (DCAT) techniques. 1,2 An important objective of SRS treatment planning and delivery is to minimize the nontarget brain dose by tightly conforming the prescription (Rx) dose to the target lesion with steep dose fall-off outside the target surface, with the goal of minimizing the intermediate dose spill. The degree to which normal brain tissue is irradiated in SRS is known to be associated with complications such as radiation necrosis. 3 Various SRS studies have evaluated the effect of dose delivered to normal brain tissue in the dose fall-off region on the development of complications from radionecrosis. 3,4 For example, Flickinger et al. 3 developed a predictive model for symptomatic postradiosurgery brain injury (necrosis) when treating arteriovenous malformations using SRS techniques based in part on the parameter V12 Gy (brain Volume receiving 12 Gy or more, a volume dose statistic). A similar study was conducted by Minniti and co-workers 5 when treating brain metastases using SRS. That study showed evaluated risk of developing radionecrosis associated with brain volumespecific doses between 10 and 16 Gy (i.e., V10-V16 Gy). These and other studies have shown that minimizing intermediate dose spill in SRS planning is an important goal when minimizing the risk of complications due to brain radionecrosis.
Various metrics have been devised to assess the level of dose fall-off, or intermediate dose spill, in radiotherapy planning. In stereotactic body radiation therapy (SBRT), it is common to use the metric R50%, defined as the ratio of the 50% Rx isodose cloud volume (V IDC50% ) to the volume of the PTV (V PTV ). 6 The metric GI is commonly used in SRS planning when evaluating competing plans.
Paddick 7 defines the GI as the ratio of the 50% Rx isodose cloud volume (V IDC50% ) to the 100%Rx isodose cloud volume (V IDC100% ). This is essentially the form of GI as written by Zhao et al. 1 Clearly, if the plan is perfectly conformal, V IDC100% is equivalent to and spatially coincident with the PTV volume (V PTV ) and GI is equivalent to R50%. But if V IDC100% is not perfectly conformal to the PTV, plan flaws can be masked. For example, a V IDC100% larger than V PTV is possible and, in such a case, the GI would not adequately account for the normal tissue that falls within V IDC100% but is outside the PTV surface. As a consequence, a plan with an acceptable GI could be an inferior plan in terms of the normal tissue outside of the PTV being radiated to a high dose. In a study of linac-based RapidArc ® There are many factors that may influence the intermediate dose spill including PTV location, PTV volume, beam geometry, delivery method, and the distribution of critical structures. In this work, we focus on a limited number of factors, namely V PTV and PTV surface area (SA PTV ). It is common in the literature for authors to organize treatment planning outcomes as a dependence on V PTV as this parameter is readily available in the radiation treatment planning system (RTPS) contour statistics. 4,5,7,[9][10][11] Examples include optimal Isodose Rx line or V12 Gy vs V PTV . One characteristic that is typically observed in these published studies is a dispersion of results for a cohort of PTVs with similar V PTV . At least one study attempted to reconcile the nature of this observed dispersion by considering the PTV shape and surface area but were unable to incorporate shape in any effective manner. 10 We believe the SA PTV (i.e., a shape dependency) plays an important role in achievable intermediate dose spill metrics such as R50% in highly conformal approaches such as SRS and we have conducted a study to test this hypothesis. This work explores SA PTV as was done previously in our study of R50% in SBRT, 12 but here we examine R50% in cranial SRS. This work also builds on our previous efforts which derived a semi-empirical equation for an approximation of R50%, which we refer to as R50% Analytic , based on V PTV and SA PTV in lung SBRT. 13 The R50% Analytic value is considered to be a prediction of the R50% result that may be achieved in highly conformal treatment techniques given SA PTV and V PTV for the treated PTV. Utilizing an DESAI ET AL.
| 187 anthropomorphic head phantom study, we have applied the R50% Analytic approach devised in the lung SBRT study to cranial SRS.
We demonstrate that the dependence of the achievable R50% on the SA PTV is consistent with previous lung SBRT results. 12    Alto CA). Image segmentation was performed using the Contouring module in Eclipse. For the purpose of this study, we ignore the IROC PTV and create unique sets of centrally located PTVs in the cranial cavity with well-controlled characteristics. Plans were created for delivery on a Varian TrueBeam STx ® linac, 6XFFF mode, and having a 120 leaf HD MLC. Treatment delivery utilizes a RapidArc ® VMAT approach.

2.A | Phantom model
Beam geometry consisted of five hemi-arcs each spanning 150 arc degrees. To maximize the degree of non-coplanar beam delivery, each hemi-arc used a unique couch angle including 355°, 315°, 270°, 45°, and 5°. The geometric configuration of gantry, collimator, couch, and phantom is shown Fig. 1. This geometry is both clinically reasonable and highly conformal for a central cranial tumor treated on a conventional C-arm linac because it utilizes a nearly full 2π solid angle beam entry geometry and no beam line overlaps with another beam line other than when close to the target.
A fixed SRS Rx dose of 18 Gy in one fraction was used for each plan with the requirement that 99% of the PTV volume receive the Rx dose (i.e., D99% Rx condition). 14 The Eclipse automatic Normal Tissue Objective (NTO) as well as standard dose-limiting shells were utilized in the optimization to minimize dose gradient and encourage high-dose conformality. 11,15,16 Each plan was optimized with the same set of criteria seeking a minimum R50% and high-dose conformality. Conformality was assessed using the standard Conformity Index (CI) defined as the ratio of the prescription dose volume to the PTV volume. 8 The Eclipse algorithm PO v15.6 was used for all optimizations. Eclipse AAA convolution v15.6 was used for the final dose distribution calculation implemented on a 1-mm grid point spacing matrix. R50% values so obtained were compared to SA PTV and the prediction given by the R50% Analytic methodology.

2.C | R50% Analytic methodology and the dependence on PTV surface area
It is common in the literature for authors to organize treatment planning outcomes as a dependence on V PTV as this parameter is readily available in the RTPS structure statistics. 4,5,7,[9][10][11] PTV shape and therefore the SA PTV are typically unknown or not reported. Within these reported results, for a cohort of PTVs of given, nominal PTV volume, one can often observe dispersion in obtained plan metrics such as R50% which we surmise is an indication of the effect of the PTV surface area or shape on the observed outcome. The R50% Analytic methodology developed in our previous work in lung SBRT 13 attempts to incorporate the effects of PTV shape through the PTV surface area. As the details are available elsewhere, we only reproduce the final result for the form of R50% Analytic as follows: where and r PTV is the radius for an effective spherical shape for the given conditions. Given the near-2π distribution of beam directions using this delivery geometry, we expect isodose surfaces to be essentially spherical. Since the PTVs are also spheres, Δr would be readily obtainable from the difference of the radii of the 50%Rx isodose cloud (r SphVIDC50% ) and the PTV (r SphPTV ). The Eclipse RTPS provides a useful tool for this purpose known as the Gradient Measure (GM). In general terms, GM 9 is defined for any shape 50%Rx isodose cloud and 100%Rx isodose cloud as follows: where r EqSphVIDC50% and r EqSphVIDC100% are the radii of spheres that are equal in volume to the actual V IDC50% and V IDC100% , respectively.  Table 3.

3.A | Phantom study for the determination ofΔr
Estimates of Δr obtained in the phantom study are summarized in 3.B | R50% Analytic methodology and the dependence on PTV surface area Figure 3 and Table 1   T A B L E 3 Characteristics of PTVs used in the SRS R50% phantom study. Also shown are the CI and R50% obtained from treatment planning and the R50% Analytic result. The R50% Analytic value is in good agreement with planned R50% obtained as indicated in the last column.  shapes ranged from "pencil-like" to "coin-like" and indicates the R50% dependence is truly related to SA PTV and not some artifact of the orientation or aspect ratio of the cylindrical PTVs. Considering that the PTV surface represents the interface between the target volume and the normal tissue, it should not be surprising that the SA PTV has a marked effect on the amount of normal tissue subjected to the intermediate dose spill as quantified by R50%. For SRS, brain is the primary normal tissue of interest and, therefore, SA PTV serves as the basis for the normal brain tissue volume susceptible to high doses. Given the same degree of conformality, a larger PTV surface area in a cranial SRS plan means more healthy brain tissue is exposed to the highest dose region. That exposure would propagate out to all isodose clouds outside the target including the 50% isodose cloud defining the R50%. Furthermore, the surface area effect would be a characteristic of any treatment modality capable of high conformality since the SA PTV is a property of the PTV and not the radiation delivery technology. We note similarity of this PTV surface area study to a statement in the publication of Goldbaum et al. 10 In that work, the authors hypothesized that for a cohort of PTVs with nearly equal volumes "an increase in TV12 could be related to an increase in the surface area of the target" (note TV12 is the equivalent V12 Gy). Goldbaum and co-workers attempted to use effective ellipsoids to quantify PTV surface area but the approached proved ineffective at improving results. Yet as we see from this work, the PTV surface area effect is an important factor in predicting the plan R50%.

ACKNOWLEDG MENTS
The authors thank Deborah Olsen Desai for formatting tables and figures, editing, and proofreading the manuscript.

D A T A V A L U E S T A T E M E N T
The data that support the findings of this study are available from the corresponding author upon reasonable request.