Abstract
Introduction
Stereotactic radiosurgery (SRS) has been broadly used to treat brain tumors. In this study, a dose kernel-based spot scanning (DKSC) treatment delivery has been developed for hypofractionated brain SRS.
Methods
DKSC treatments employs hundreds of confocal photon dose kernels. For such a delivery, a single continuous scanning path was first mapped within a 3D target volume, and then a series of dose kernels of variable sizes, shapes and beam weights were placed and then optimized along the path to produce highly conformal dose distributions. For implementation of DKSC delivery in a clinical setting, we specifically employed the Leksell Gamma Knife (LGK) system, where it is considered as the gold standard of modern SRS treatments.
Results
DKSC was successfully implemented for a patient treatment for the first time. General methodology as well as specific workflow and treatment planning caveats of implementing DKSC for the LGK is reported. To highlight the novelty of DKSC, we also compared DKSC against the conventional LGK-SRS treatment including its latest treatment planning optimization software.
Conclusion
DKSC has been demonstrated to be technically feasible, clinically implementable, and uniquely advantageous for hypofractionated brain SRS. Further studies are warranted toward testing DKSC for variable SRS modalities, different disease sites including extra-cranial lesions.
Introduction
Hypofractionated stereotactic radiosurgery (SRS) aims to deliver a tumoricidal dose to the target while sparing normal tissue by leveraging precision targeting as well as dose fractionation typically delivered in 3–5 fractions.1,2 Single fractional SRS was pioneered by Dr Lars Leksell in the 1950s 3 and was primarily engineered to treat relatively small lesions (e.g., typically < 2 cm in diameter) via a dedicated treatment unit, the Leksell Gamma Knife (LGK). Subsequent technological advancements have further expanded LGK's capability toward hypofractionated SRS for large (≥2 cm) lesion treatments in parallel with the developments of hypofractionated SRS for the S-band and X-band medical linear accelerators.1,2,4-8
For the purpose of treating brain lesions of large size (≥2 cm in diameter), LGK ICON (LGKI) system was introduced with on-board imaging guidance as well as a mask-based patient immobilization system for enabling hypofractionated treatments.1,5,9 The on-board imaging guidance employs a flat-panel partial-arc-reconstructed Cone-Beam Computed Tomography (CBCT) imager that is physically bolted onto the radiation unit of LGKI that houses 192 radioactive cobalt sources. 10 Most importantly, the CBCT imager is calibrated voxel-by-voxel to enable mapping predefined stereotactic coordinates of LGKI radiation unit unto the patient's skull images acquired while the patient being immobilized with a thermoplastic mask on the treatment couch.
To monitor the intrafractional target motions, an infrared high-resolution camera is mounted on the treatment couch to continuously monitor the movements of the patient's skull throughout the treatment delivery. A preset threshold value of 1 mm to 2 mm in the skull motions has been typically used for the entire treatment delivery. This threshold value is currently manually set by the user prior to the beam-on to account for uncertainties due to mask-based immobilization as compared to the traditional metal frame-based immobilization. The camera system can automatically trigger a beam-off signal when the maximum shift of the patient's skull is detected outside of the threshold level.
Previous studies assessed dosimetric effects associated with residual intrafractional motion that falls under these threshold values.11,12 A general dose smearing effect in analogous to what was observed from the fractionated linac-based treatment deliveries.11,12 Such a phenomenon can be interpreted via the central limit theorem governing the distribution of the sampling means of unknown probability distributions. Provided such an uncertainty and the need of preventing target missing or underdosing, the most common strategy is to add millimeter-level target margins allowing for the clinical target volume (CTV) to the planning target volume (PTV) expansion in millimeter levels, especially when treating a brain lesion with hypofractionation.
Aside from the CTV to PTV margin, an additional margin is often added when considering disease extension that yields a gross target volume (GTV)-to-CTV margin. It is worth noting that as the tumor grows bigger, the extensiveness of tumor microvascular network as well as presence of infiltrative tumor cells beyond the GTV surface tend to increase accordingly. With tumors of aggressive histology such as gliomas, a composite GTV-to-PTV margin on the order of 5 mm or larger is often required for hypofractionated SRS.
While physically necessary to account for microscopic disease extension as well as intrafraction uncertainties associated with a thermos mask-based immobilization, a 5 mm or higher margin has raised significant concerns of elevated normal tissue toxicity due to presence of a substantial amount of normal brain parenchyma encompassed in the GTV-to-PTV margin area. A previous study has found that the probability of the adverse radiation risk tended to increase drastically in a non-linear manner with increasing margin sizes. 13 To alleviate such a risk, our current clinical practice is to prescribe a homogeneous dose distribution (eg, with the prescription isodose line value ≥ 85% of the maximum dose) for all hypofractionated SRS treatments involving margin expansion of 3 mm or larger. Another rationale of this requirement is to prevent random dose hot spots accidentally shifted into the marginal area due to intrafraction uncertainties that would further elevate the risk of radiation necrosis from excessively irradiation of the normal brain.
As expected, mandating homogeneous dose distribution has created a major technical challenge for LGK. Due to pre-fixed collimation size (i.e, 0 mm or blocked, 4 mm, 8 mm, and 16 mm), it has been a well-established practice for LGK-SRS treatments to be prescribed to a relatively low value isodose line such as 50% of the maximum dose, resulting a significant dose inhomogeneity for the treatment.
To overcome such a challenge, we proposed the concept of dynamic delivery, 14 where the treatment couch moves continuously with the radiation beam is always turned on. However, engineering hurdles incurred by the idea has yet been solved to render dynamic delivery possible to date. However, with recent enhancements in the LKGI system especially more robust source positioning motorization controls, the total number of shots that can be delivered by LGKI has drastically increased compared to the previous models. This drives us to develop DKSC to create homogenous dose distribution that potentially rivals a dynamic delivery.
Conceptually, DKSC is analogous to the spot-scanning intensity-modulated proton therapy (IMPT) approach, except the spot scanning in DKSC was created by moving the patient's head versus steering of an ion beam possessing a Bragg peak, i.e., an intrinsic dose kernel by default. To implement DKSC, we have built an in-house dose computing architecture for treatment planning and integration with the clinically approved Leksell Gamma Plan. Technical caveats and clinical workflow associated with this first-time DKSC implementation is reported here.
Materials and Methods
The first step of the DKSC implementation is to map out a 3D scanning path that aims to facilitate fast dose optimizations. Figure 1 illustrates the process flow chart of the algorithm, where (a) illustrates an example of a brain tumor target to be treated, where the delineated target contour and its maximum length (L = 3.37 cm) are shown. (b) shows the Dicom image contours extracted and then filled with trajectory-forming points within the target volume, which was created by sequentially shrinking the contour dataset in a layer-by-layer fashion similar to peeling an onion. (c) shows 2D projection of the contours from the entire imaging series, where the full ranges of the stereotactic coordinates along x-, y- and z-direction were computed. (d) and (e) show the surface rendering and stacked image rendering of the point-filled contour dataset. Note that the number of points in each layer were by design made proportional to the layered shell volumes. As a result, more points are located toward the exterior portion of the target volume versus inner portion of the target volume. Finally, (f) shows the 3D scanning path created from the above process by connecting all the point via the Traveling Salesman (TS) algorithm.

Illustration of the scanning path generation process for creating the initial test solution for DKSC.
As illustrated above, the 3D convex hull target volume after step (e) was in effect rendered into a point cloud, where proportionally more points were distributed toward the surface of the target than toward the center. The final 3D scanning path was created by simply connecting these points via the TS algorithm which yielded the shortest total path length, thus minimizes the total spot-scanning distance for all the shot isocenters.
The shot isocenters were subsequently placed along the scanning path with a fix spacing of Δ. In theory, Δ should be set to match the hardware resolution of the Patient Positioning System (PPS) in movement step of 0.1 mm. However, this produces the number of shots that exceeded the current maximum shot limit of N = 500. As a result, we selected an initial value of Δ = L/500, where L is the total length of the scanning path of step (f), which largely depends on the shape and the size of the target.
For any shot or isocenter placed on the scanning path, the relative beam weights and its size (i.e., 4 mm, 8 mm or 16 mm) were adjusted offline to generate an initial solution of DKSC via a previously published method.15-17 The resulting shot parameters (i.e., x-, y-, z-stereotactic coordinates, size, relative beam weights) were finally programmed into a script file protocoled by the manufacturer. This script file of all the shot configuration was imported into the clinical treatment planning system (Leksell Gamma Plan version 11) for composite dose calculations and manual adjustments required to satisfy the machine constraints that will be discussed later. The goal of this last step is important as it allows the computation of the final dose distribution on a clinically commissioned and FDA-approved medical software, i.e., Leksell Gamma Plan version 11 afore mentioned. It is worth mentioning that without scripting, all the shot parameters may be manually typed into the LGP system as was attempted during the initial stage of the project. However, this incurred substantial labor, human errors, and time delay especially under the pressure of patient's waiting, which was another major barrier for clinical adoption of DKSC until we acquired the scripting functionality from the manufacturer.
As part of the clinical implementation, a conventional LGKI plan was also created and served as the benchmark of the DKSC plan in terms of all the dose volume histogram (DVH)-based parameters such as conformity and gradient indices. Despite this, we found that it was impossible to create a conventional LGKI plan by prescribing to the 85% isodoseline with the conventional methods and tools, especially the manual trial-and-error approach. Nonetheless, a conventional LGKI plan of the same dose prescribing to 50% isodoseline for the case was created for the purpose of benchmarking the treatment quality of DKSC of the same patient case.
Results
The dose distribution for the first clinical case of DKSC is shown in Figure 2. For the case, the prescribed dose was 30 Gy delivered in 5 fractions with a prescription isodoseline value of 85% for a PTV of 14.1 cm3 (3.1 cm × 2.5 cm × 4.4 cm in diameter along anterior-posterior, lateral, and superior-inferior direction respectively). The patient suffered from an aggressive brain tumor possessing a diffusive histology that required urgent medical care, and DKSC was the only radiation treatment option compounding medical insurance considerations.

Results of axial dose distribution computed on the clinical treatment planning system (LGP Version 11) prior to the DKSC treatment delivery. The small circular dots indicate the isocenter locations (N = 120) within the target, and other treatment parameters are provided in the insert such as the treatment time (T = 34.5 min) under a nominal reference dose rate of 2.3 Gy/min.
The number of shots for the treatment yielded 120 after the software eliminated 380 low-weighted shots that bear negligible contributions to the composite dose distribution. A manual shot adjustment of 6 shots was found necessary to satisfy the lowest timer setting of the current GK system for each shot. This was primarily caused by a lower per-fraction dose (e.g., 4-6 Gy) for an hypofractionated treatment compared to the single-fraction SRS treatment of prescribing 20 Gy per fraction. To deliver a dose of 6 Gy per session, for example, at the 85% isodose line via 120 shots, this means that on average a shot may only deliver 6 Gy /0.85/100 = 0.06 Gy. With a nominal dose rate of 2 Gy/min at the isocenter, that timer setting for the shot on average would be 0.03 min. This is significantly lower than the machine timer limit of 0.05 min per each shot.
To overcome this problem, we manually added sectoring blocking for the affected shots to lowering their dose rates in order to raise the timer setting for the shots over the threshold of the hardware limit. This in effect prolonged the total beam on time by approximately 1 min per fraction, which is <3% of total treatment delivery time that fortuitously did not hinder the treatment for the case.
The results of the isodose overlay between DKSC and the conventional plan (prescribed to the 50% isodose line) are shown in Figure 3, where (a) shows the isodose comparison between the conventional (solid smooth line) and the DKSC (thin jagged line) treatment plan. and (b) shows the three dose-volume-histogram (DVH) comparison of DKSC, conventional plan as well as the LGP Lightening Optimization (LO), which was released after the DKSC implementation and the patient treatment.

The axial, coronal and sagittal planar isodose plot is shown in (a), where the shaded area shows PTV reconstructed from the Image DICOM data set, the solid isodose lines in the overlay plot of (a) are from the convention treatment while the jagged lines denote the DKSC treatment plans. The dose volume histogram curves are shown in (b), where the conventional treatment plan (Conv), the Lightenting Optimization (LO), and the DKSC treatment plan are shown.
From the results of Figure 3b, PTV target volume coverage (Cov = 98%), selectivity index (SI = 0.88) and gradient index 18 (GI = 3.71) were achieved to be identical for all the treatments, especially noting that the DVH curves of the skull (Fig 3b) overlapped with each other at the dose-volume defining points of these indices. Despite such an observation, notable difference still existed in the shapes of the prescription and other isodose lines as shown in Figure 3a. It is also worth mentioning that SI is the Paddick conformity index 19 normalized by the target volume coverage (Cov) by definition in LGP.
As for target dose homogeneity, DKSC drastically decreased the point maximum dose by 41% from 60 Gy of conventional plan to 35.2 Gy. Depending on the volume and value of the hot spots, such a decrease can be as much as 50%. This has led to > 100% decreased in the area-under-the-curve (AUC) when integrated from the prescription dose value of 30 Gy to the maximum dose for the DVH of PTV between DKSC and the conventional treatment, which is a surrogate of the total energy deposited inside the PTV.
A small but notable increase on the order of 3% in the low dose spillage at 10–15% of the prescribed isodose level was noted for the DKSC versus the conventional treatment prescribing to 50% isodose line. The increase was reviewed and deemed clinically insignificant. Such a phenomenon was likely from the scattering dose of increased number of shots used to achieve a uniform dose distribution and it warranted further study. Of note, the total beam-on time was 31.0 min for the conventional treatment (50% isodose line) versus 34.5 min for the DKSC treatment, inclusive of hardware constraint considerations.
In concert with the conventional treatment of prescribing to 50% of isodose line, LO failed to produce a feasible solution that satisfied the clinical mandate of prescribing to 85% or higher isodose. The highest isodose line achieved with LO was 70% (Figure 3b). In addition, LO yielded significantly different dose hot-spot distribution patten from DKSC and conventional treatment plan as shown in the PTV DVH curves of Figure 3b. The normal brain DVH curves were similar for all the plans, noting that DKSC was the only one that satisfied the clinical requirement in term of target volume coverage, selectivity, and the PTV dose uniformity.
Discussion & Conclusion
This is the first report of DKSC for hypofractionated brain SRS via confocal photon beams. Compared to other deliveries such as Linac-based SRS, DKSC on LGK presents a unique delivery paradigm where the patient was shifted in hundreds or even thousands of couch control points versus immobilizing the patient and varying the beam field size via hundreds or thousands of control points of a multi-leaf collimator (MLC). The results of our current study distinctively demonstrated the potentials of DKSC in expanding capabilities and functionalities of conventional gold-standard LGK-SRS, especially noting previous comparison studies have suggested superior dose interplay of LGK-SRS over linear-based SRS platforms.20-22 Another direct benefit of the uniform target dose created by DKSC for LGK-SRS is a drastically improved workflow for concomitant boost treatments,23,24 where a complex dose boosting pattern can now be directly superimposed. This is an active area of research for our on-going studies.
The specific finding on the dose rate from the study was also interesting. Clearly, DKSC delivery favors or requires a low dose-rate radiation delivery machine. This finding suggests that the conventional rule of thumb of resourcing a LGK unit every 5–7 years for the single fraction SRS purposes may not be always useful for hypofractionated SRS treatments when a homogeneous dose distribution is required or in the situation that requires a large number of shots. Against rapid developments of ultra-high dose rate linac-based SRS platforms, our study suggests that there is still room and benefit of deploying a low dose rate machine for SRS. More stringent beam transport and dosimetry studies would be expected when implementing DKSC on an ultra high-dose-rate machine such as the flattening-filter-free linac.
Besides dose-rate requirements, another potential limitation of DKSC is the finite spot-scanning size, e.g., 4-mm in the case of LGK-SRS. Evidently, a finite spot-scanning size can limit dose painting resolution as well as the dose uniformity that is ideally achievable, both of which requires further investigations, especially toward optimally defining appropriate target and margin sizes for clinical implementations of DKSC.
In summary, DKSC has been successfully developed and demonstrated in clinical settings for hypofractionated SRS treatments. Further studies are warranted toward defining clinical endpoints of DKSC as well as toward implementation for linac-based SRS/SBRT treatment deliveries.
Footnotes
Acknowledgements
We acknowledge technical supports from Juan Gutiérrez on LGP script import connectivity.
Ethical Considerations
Formal ethics approval was not required as treatment was clinically indicated and approved through standard institutional procedures using the Leksell GammaPlan system. Informed consent was obtained for treatment and publication.
Funding
The author(s) received no financial support for the research, authorship, and/or publication of this article.
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
