Forward treatment planning techniques to reduce the normalization effect in Gamma Knife radiosurgery

Abstract In Gamma Knife forward treatment planning, normalization effect may be observed when multiple shots are used for treating large lesions. This effect can reduce the proportion of coverage of high‐value isodose lines within targets. The aim of this study was to evaluate the performance of forward treatment planning techniques using the Leksell Gamma Knife for the normalization effect reduction. We adjusted the shot positions and weightings to optimize the dose distribution and reduce the overlap of high‐value isodose lines from each shot, thereby mitigating the normalization effect during treatment planning. The new collimation system, Leksell Gamma Knife Perfexion, which contains eight movable sectors, provides an additional means to reduce the normalization effect by using composite shots. We propose different techniques in forward treatment planning that can reduce the normalization effect. Reducing the normalization effect increases the coverage proportion of higher isodose lines within targets, making the high‐dose region within targets more uniform and increasing the mean dose to targets. Because of the increase in the mean dose to the target after reducing the normalization effect, we can set the prescribed marginal dose at a higher isodose level and reduce the maximum dose, thereby lowering the risk of complications.

(e.g., 90% and 70%) within targets; therefore, maintaining a sufficient target dose with a lower maximum dose is difficult.
In forward treatment planning, a single shot of radiation delivers the most concentrated dose to the target, as depicted in Fig. 1(a). A single-shot radiation pattern is characterized by its large portion of higher isodose lines in a small treatment volume, which permits uniform high-dose radiation to the target with a steep dose gradient and sharp fall-off of the dose outside the target margin. 6 On the basis of this concept, for situations where multiple shots must be used for the treatment of large or irregularly shaped targets, creating a radiation field that is generated by multiple shots but mimics the dose distribution of a single shot has been suggested. The dose distribution should consist of a large portion of higher isodose lines, which can conform to the target shape during treatment planning.
Achieving conformal coverage of the target with a large portion of higher isodose lines under the prescribed dose (PD) would enable the target to receive a more homogeneous high-dose radiation with an increased mean dose. When the target receives an increased mean dose, we can optimize the treatment dose by reducing the maximum dose delivered to the center of the target while maintaining the same dose in the margin. Accordingly, the surrounding normal tissues would receive less radiation, which would reduce the risk of complications.
While using multiple shots during treatment planning, however, a decrease in the proportion of the higher isodose coverage on the target should be avoided. In clinical practice, we generally define this phenomenon as the "normalization effect" between shots, as depicted in Fig. 1(c). Jitprapaikulsarn 7 described the normalization effect as the formation of a "hot spot" influenced by the locations and magnitude of the maximum doses of shots. In this report, we use a clinical definition to describe the normalization effect. The normalization effect occurs because the isodose lines from each shot overlap and dose contributions between shots are added. 7 After the interaction of two shots, the maximum dose (100% isodose level) in the new radiation field is renormalized and the shapes of the isodose lines change. Figure 1(b) illustrates the process of the normalization effect. Apparently, the normalization effect reduces the coverage proportion of 90% and 70% isodose lines.
A single shot has the largest proportion of high-value isodose line coverage. (b) Normalization effect. Two shots are placed close to each other, and the sum of their contributions was considered; star sign represents the maximum dose point contributed by the shots. (c) Normalization effect caused by the interaction of two shots in the treatment plan. Note that the 90% and 70% isodose lines are smaller after the normalization effect of the two shots.
The new collimation system of the Leksell Gamma Knife (LGK) Perfexion (PFX), consists of eight movable sectors, in which the collimator size can be adjusted among four settings (4, 8,16 mm, and blocked) independently and automatically. The PFX collimation system facilitates not only an increase in treatment efficiency but also the generation of composite shots to achieve more conformal treatments. 8,9 Studies on normalization effect reduction are scant. Therefore, this study evaluated the performance of forward treatment planning with and without the PFX collimation system for the normalization effect reduction. In addition, the clinical significance of the decreased normalization effect during treatment planning was elucidated.

| MATERIAL AND METHODS
Our Gamma Knife center is equipped with a PFX and GammaPlan 9.0 treatment planning system. In forward treatment planning using multiple shots for radiosurgery, we typically first place a main shot in the region of the target center and choose a best-fit collimator size for the main shot to cover the TV in the most thorough and conformal manner possible. Subsequently, we cover the remaining TV by adding multiple small shots to generate an ideal isodose line to fit the shape of the target margin. In treatment planning, the contribution of the radiation dose from the main shot is generally the maximum in the dose distribution. Figure 2(a) depicts an example of a dose plan with a 16-mm large shot (A1), which delivers the maximum contribution to the reference point. For some large targets, we may use several large shots that deliver the greatest contribution to the reference point.
During treatment planning, frequent monitoring should be performed to detect the occurrence of the normalization effect after the delivery of a new shot that causes the shrinkage of the higher isodose lines covering the target. To minimize the normalization effect of the dose distribution, we intended to reduce the overlap of the higher isodose lines between shots. During multiple-shot treatment planning, we adjusted the position and weighting of each shot to allow the 50-60% isodose lines to fit the target margin and the 70% isodose line to cover approximately 70-80% of the TV. 10,11 For the adjustment of shot positions, our strategy was to separate each shot appropriately to reduce the overlaps of higher isodose lines.
For the adjustment of shot weightings, our strategy involved F I G . 2. Example of a Gamma Knife treatment plan for a target with a volume of 10.2 cm 3 , using one large shot with a 16-mm collimator, eighteen 8-mm small shots, and one composite shot with 8-mm and 4-mm collimators. A1 is the main shot of this treatment plan. We maintained the maximum contribution of A1 to the reference point during treatment planning.
reducing certain shot weightings for attaining a lower dose contribution and less volume coverage to reduce the overlap of higher isodose lines.
After the normalization effect reduction, we can increase the proportion of coverage of high-value isodose lines on the target.
Once we achieve this goal which means that the uniformity of the  high-dose region within the target would increase and the mean dose to the target would increase; then we can set the PD at a higher isodose level with an acceptable target coverage (at least 95% of the TV covered by the PD in our treatment plans). Because we set out prescription marginal dose at a higher isodose level, the maximum dose can be reduced. The PFX collimation system provides another method for reducing the normalization effect, which entails using composite shots.
Our strategy involved the selection of some sectors with smaller collimator sizes (4 or 8 mm) or a blocked collimator in the junction of the large shots. This concept of combining sectors to form a composite shot is similar to the adjustment of shot weightings mentioned previously, but reduces the dose in a shot only partially from parts of sectors with smaller collimators.
During dose planning, if shrinkage of higher isodose lines coverage occurs on the target, we should determine which shot other than the main shot has a greater contribution to the reference point compared to that from other shots. If a small, non-main shot is excessively strong such that it causes the normalization effect in the dose distribution, we should adjust the position of that shot away from the main shot, reduce its weighting, or use composite shots. Figure 3 shows the different forward treatment planning methods for the normalization effect reduction.  Table 1 presents the dosimetric comparisons between the treatment plans with and without the normalization effect reduction for these two cases.      to the target, a PD can be set at a higher isodose level with an acceptable target coverage (at least 95% of the TV covered by the PD in our treatment plans). Therefore, the maximum dose delivered to the target center can be reduced, and a sufficient mean target dose can be maintained. Theoretically, because the maximum dose is reduced, the surrounding normal tissues receive low radiation, thus lowering the risk of complications.

3.A | Case illustration
Conventionally, the PD to the target margin is set at the 50% isodose level because of the rapid fall-off of the dose outside the target margin. 14,15 From our experience, we suggest that a large-volume target should be treated with the PD at a slightly higher isodose level (55-60% in most cases); moreover, the ideal target conformity and sharp dose gradient are maintained. This strategy can reduce the maximum dose and prevent an overdose to the target.
In this report, we presented two case examples of large-volume lesions treated with GKRS. The dosimetric variables of the treatment were compared between the two treatment plans (with and without the normalization effect reduction; Table 1). The variables included the conformity index (CI; based on the Paddick CI), 16  (PIV 50%PD ), percentage of TV covered by the 70% isodose line, the volume of TV covered by 15 Gy (130% of the PD) in case (a) and 21 Gy (130% of the PD) in case (b), the volume of brainstem receiving 50% of the PD, and 12-Gy volume that correlates with the risk of radiation necrosis. 17,18 Case (a): In both treatment plans, the target margins received 11.5 Gy. Although plan (1) had a higher isodose level at the target margins than plan (2) (11.5 Gy at 58% vs. 11.5 Gy at 51%), plans (1) and (2)

| CONCLUSION S
We proposed different forward treatment planning techniques to reduce the normalization effect during forward treatment planning by adjusting shot positions and shot weightings and by using composite shots. The reduction of the normalization effect increases the proportion of coverage of higher isodose lines on the target; thus, the mean dose to the target increases. This increased homogeneous radiation maintains a sharp dose gradient and conformal treatment to the target.
Through this method, we can maintain a sufficient mean treatment dose for a large or irregularly shaped tumors or AVM. Moreover, the maximum dose of the treatment can be reduced by setting an effective marginal dose at a higher isodose level; while normal tissues receive less radiation, the risk of complications may be lowered.

ACKNOWLEDG MENTS
The authors would like to thank all the physicists and neurosurgeons from Department of Radiation Oncology and Department of Neurosurgery of Shuang Ho Hospital, Taipei Medical University for their generous encouragement.

CONFLI CT OF INTEREST
The authors declare that they have no conflicts of interest.