A simple dosimetric approach to spatially fractionated GRID radiation therapy using the multileaf collimator for treatment of breast cancers in the prone position

Abstract The purpose of this study was to explore the treatment planning methods of spatially fractionated radiation therapy (SFRT), commonly referred to as GRID therapy, in the treatment of breast cancer patients using multileaf collimator (MLC) in the prone position. A total of 12 patients with either left or right breast cancer were retrospectively chosen. The computed tomography (CT) images taken for the whole breast external beam radiation therapy (WB‐EBRT) were used for GRID therapy planning. Each GRID plan was made by using two portals and each portal had two fields with 1‐cm aperture size. The dose prescription point was placed at the center of the target volume, and a dose of 20 Gy with 6‐MV beams was prescribed. Dose‐volume histogram (DVH) curves were generated to evaluate dosimetric properties. A modified linear‐quadratic (MLQ) radiobiological response model was used to assess the equivalent uniform doses (EUD) and therapeutic ratios (TRs) of all GRID plans. The DVH curves indicated that these MLC‐based GRID therapy plans can deliver heterogeneous dose distribution in the target volume as seen with the conventional cerrobend GRID block. The plans generated by the MLC technique also demonstrated the advantage for accommodating different target shapes, sparing normal structures, and reporting dose metrics to the targets and the organs at risks. All GRID plans showed to have similar dosimetric parameters, implying the plans can be made in a consistent quality regardless of the shape of the target and the size of volume. The mean dose of lung and heart were respectively below 0.6 and 0.7 Gy. When the size of aperture is increased from 1 to 2 cm, the EUD and TR became smaller, but the peak/valley dose ratio (PVDR) became greater. The dosimetric approach of this study was proven to be simple, practical and easy to be implemented in clinic.


| INTRODUCTION
Clinical results have indicated that megavoltage spatially fractionated radiation therapy (SFRT, or simply called GRID therapy hereafter) provided by modern linear accelerator machines can significantly improve the therapeutic window in the treatment of bulky tumors. [1][2][3][4][5] Researchers have attributed the therapeutic advantages identified in the GRID radiation field to the bystander effect, which is stronger in the high gradient field 6 ; although the underlying reasons for improved responses can be explained by other mechanisms, 7 in which the potential therapeutic advantage of GRID therapy was derived from the radiobiological modeling results based on the different radio-sensitivities of normal and cancerous cells in the target volume. As reported by Zwicker et al. 8 and Zhang et al., 9,10 in theory the GRID therapy takes advantage of the fact that normal cells interspersed in the cancerous cells in the target volume in general have superior repair capabilities over cancer cells. When normal tissue cells are spared by GRID therapy in low dose zones, those lower-irradiated areas can serve as centers of regrowth for normal tissues. In the high dose zones, however, there will be an intensive killing of cancer cells and normal cells as well, consequently the communications between the cancer cells are obstructed throughout the tumor volume. With the spatially fractionated radiation fields, the cancer cell killing rate is maintained, whereas the normal cell survival is increased due to the existence of the cold zones and normal cell repair, thereby providing a clinical advantage shown by the tumor shrinkage and increased radiation tolerance. The latest study by Zhang et al. 7 demonstrated that GRID therapy provided a pronounced therapeutic advantage in both hypofractionated and traditionally fractionated regimens as compared with the results seen with singlefraction, open debulking field regimens. However, from the radiobiological modeling results, the true therapeutic advantage (after separating the benefit of fractionation) exists only in hypofractionated GRID therapy. 7 Of note, clinical outcomes and theoretical studies have indicated that a course of open-field radiotherapy is needed to further control tumor growth after a large-fraction dose with GRID therapy as the equivalent uniform dose (EUD) of GRID therapy is significantly less than standard prescription doses. 1,3,4,7,10 Clinical trials of GRID therapy continue adding useful data each year and patients with bulky cancer have shown benefit from this unique treatment; yet researchers are still striving for better techniques to deliver GRID therapy. One effort is avoiding using heavy and inconvenient Cerobend GRID block collimators which are not able to take into account tumor shape and normal structure sparing. 11,12 New GRID therapy approaches, which use the existing technology of tomotherapy, 12 or high precision multileaf collimators (MLCs) 11,[13][14][15] or stereotactic radiotherapy apparatus 16 found in most modern radiotherapy linear accelerator machines, are expected to facilitate the use of GRID therapy in the radiation oncology clinic.
It has been shown that such techniques can alleviate the work intensity and collateral damage concerns of the large dose impact of GRID therapy to the adjacent organs. 14 In this study, the GRID therapy plans were developed by utilizing a treatment planning system (TPS) associated with an MLC capable linear accelerator machine for breast cancer patients in the prone position. The prone position was chosen because the supine position poses a potential concern for increased lung and heart dose. 17 It has been reported that the prone position can significantly reduce the dose to the organs at risks (OARs) in the setting of breast EBRT, 18 thus choosing prone position for breast GRID therapy was expected to mitigate the concern of high dose streaks made by the GRID field. show the dosimetric results achieved by the plans. The dose of 20 Gy was selected as this GRID fraction dose has been widely used in various clinics and proven to be safe and effective. [3][4][5]14 During the treatment, the patients were setup in the prone posi-  Radiation Oncology Systems, Fitchburg, WI) version 9.10 treatment planning software was used for planning. Two opposed tangential angles were used in each plan. The medial and lateral tangent gantry angles were selected based on patient anatomy to avoid the contralateral breast in the beams and to further minimize entry/exit dose into the heart and lung. The GRID was formed using two fields on each side of tangents, thus each plan has four fields (Fig. 1). This approach was utilized because, we discovered that if every hot spot is designed as an individual radiation field, 13 the total treatment monitor units (or time) would be far beyond the practical range. In this simple two pairs of fields approach, in each field every other MLC was extended to the opposing collimator jaw in order to create a series of striped blocks that are 1 cm wide. The field was copied and the collimator was then rotated 90 degrees to form a second field. This process was repeated on the opposing tangent fields. The combination of the two fields per tangent created a 1 by 1 cm grid in the sagittal direction. In addition, some MLCs were closed to account for the patient's anatomy (Fig. 1). The fields were weighted to produce a homogenous population of hot spots. Also, an initial collimator rotation of 0-20 degrees was used and designed according to patient's anatomy to minimize MLC leakage into the heart and lung.

2.A | Patient selection and treatment setup
In a commonly used and commercially available GRID block collimator (High Dose Radiation Grid; Radiation Products Design, Albertville, MN), the aperture diameter of the GRID collimator is 0.60 cm on the upper surface and 0.85 cm on the lower surface.
The center-to-center spacing of holes on the collimator is 1.15 cm.
The aperture diameter and center-to-center spacing are 1.3 and 1.8 cm, respectively, as projected in the plane of isocenter. 9 So, the aperture size of our GRID plans is close to the commercial GRID block collimator. In order to understand the dosimetric impact of the aperture size, three cases were replanned with the same approach but in a 2-cm aperture. The plans with 1 and 2-cm apertures were dosimetrically compared. standards aiming for heart mean dose below 1 Gy, ipsilateral lung V10 Gy < 35% and V5 Gy < 50%.

2.C | Dosimetric and planning criteria
Another calculation point was set at the center of the GTV, in order to make sure a GRID hot spot was arranged at this point, in case the point is not onto the CAX. The dose at the GTV center reaches the prescription dose 20 Gy.

2.D | Peak/valley dose ratio (PVDR) of MLC-based GRID therapy plan
Traditional Cerrobend-based GRID block field has a clear peak/valley dose ratio, 9 but for MLC-based 3D GRID therapy, a single point of peak dose and single point of valley dose might be misrepresenting the true spatial dosimetric modulation of a GRID plan. A term of D10/D90, a ratio between the dose covering 10% of target volume and dose covering 90% of target volume was recommended by this study to represent the peak/valley dose ratio.
The PVDR for all plans were calculated. dose. This model has been found to more closely predict the radiobiological responses to large dose sizes. 19 The equation of MLQ model is as follows,

2.E |
SF i is the survival fraction at the dose D i. α and β are radiosensitivity  23 found the breast cancer treatment can benefit from a nonuniform dose field radiotherapy regardless of their radiosensitivity. In this study, both of these breast cancer cell lines (α/β = 4 and 10 Gy) were used and respectively named as the acutely responding breast cancer (C1, α/β = 10 Gy) and the slowly responding breast cancer (C2, α/β = 3.846 Gy). The reason is simply because at the same dose, a cell line with a larger α/β ratio can have a smaller survival fraction (more death) than the one with a smaller α/β ratio. For this study, T 1/2 was set at 1 h and the shift factor δ was set at 0.15 as a standard, consistent with the findings of Guerrero and Li. 21 The radiation delivery time T was set as 0.25 h (15 min). The MLQ parameters of cancer and normal cells used in this study are listed in the Table 1.
The average survival fraction SF was calculated by the Eq. (3) using the MLQ parameters of Table 1.
f i is the fraction of target volume receiving dose Di. The average survival fraction was then utilized to solve the MLQ Eq. (4) for deriving the equivalent uniform dose (EUD).
Similar biological modeling considerations were applied to the interspersed normal tissue of target volume. The average surviving fraction of normal tissue in a GRID field, SF N Grid ð Þ was calculated by using the same methodology as was used for the cancer cell line but with the normal cell MLQ parameters (N1, N2, and N3 in Table 1).
The ratio between the value SF N Grid ð Þ and the surviving fraction of normal cells using the EUD, that is, SF N ðEUDÞ will define the therapeutic ratio (TR) of GRID therapy.
Because it is implied that the GRID field and open field with the same EUD will achieve the same cancer cell killing rate, a therapeutic advantage on normal tissue sparing by the GRID field is implied if TR is >1, as the GRID therapy has spared more normal tissue. However, if TR is <1, more normal cell death in the GRID field is implied, and thus a uniform dose therapy would be preferable over GRID in this scenario.  24 The equation is as follows:

3.A | Dose-volume histograms
Using the TPS for dosimetric planning with MLCs, six left and six right breast cancer GRID therapy plans were generated. Figure 2 shows the isodose lines of a typical breast GRID therapy plan.   (Tables 2 and 3). Table 2 indicates that the 100% isodose line (20 Gy) only covered <3% of PTV, 50% of isodose (10 Gy) covered more than 63% of PTV, and 20% of prescription isodose line (4 Gy) will cover more than 98% of PTV. F I G . 2. Typical isodose distribution from the corona, sagittal, and axial view. Two dark stripes shown in the breast are due to the artifacts caused by the breast support board. The mass density was changed by the artifacts from 0.9 to 0.8 g/cm 3 in the dark strips the dosimetric impact was confirmed by treatment planning system as negligible.

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The ratio of D10/D90, which is envisioned to replace the traditional PVDR, is found in the range between 2.34 and 2.92. Average PVDR is about 2.72. (Table 3).

3.B | Doses to the OARS
Because the patients were treated in prone position, the dose received by lung and heart is minimal.

3.C | EUDs, TRs, and MUs
The  3.D | Dosimetric metrics of 2-cm aperture GRID plans Figure 5 shows a comparison between 1-cm and 2-cm aperture GRID therapy plans for the same patient. Figure 6 shows the c-DVH and d-DVH curves of 2-cm aperture GRID plans of three patients. Table 5 shows the results of the TRs, EUDs, PVDRs, and MUs from 2-cm aperture plans compared with 1-cm aperture GRID plans for the same patients. The 2-cm aperture plans were found to have a smaller TR, EUD, and MU but greater PVDRs than their 1-cm counterparts (Table 6).

| DISCUSSIONS
Spatially fractionated GRID radiation therapy has primarily been used for debulking large tumors or for increasing radio-immuno response in order to arrange an effective conventional treatment or for palliative treatment. To date, ample clinical evidence has accumulated for the high symptomatic and clinical response and minimal toxicity of  GRID therapy in palliatively and definitively treated tumors with excessive bulk and/or therapy resistance. [1][2][3][4][5][25][26][27][28][29][30][31][32][33] EUD is an important parameter for assessing GRID therapy plan.
EUDs calculated by Niemierko's equation were found to be greater than that obtained from the MLQ model. This is understandable because, when the killing of 2 Gy is extended to the dose >10 Gy, the killing rate will be overestimated because of neglected cell repair which is more important at high dose range, 19 16 demonstrated that, a stereotactic radiotherapy apparatus which was initially designed for making breast SBRT, can be used to make a breast lattice radiotherapy therapy plan as well. The dosimetric parameters of aforementioned plans are similar to our plans. The advantages of our dosimetric approach are: (a) the patient anatomic structures are maximally protected from the high dose strips of grid fields by using a prone position, (b) no need to purchase an additional apparatus, (c) it can accurately report the doses to the target volume and OARs (Tables 2, 3, and 4), and (d) it also can reduce the OAR doses via adjusting the beam shapes, orientations, and intensity, the dosimetric data can ensure that the plan is safe and can achieve similar and even potentially better treatment outcomes because of closely tailoring the target dose and normal structure considerations. With our presented dosimetric approach that uses two gantry angles, multiple beams, prone position, and modern radiotherapy TPS, the toxicities are expected to be less than the treatments using the Cerrobend GRID block with single angry angle, single beam, supine position, and no consideration for target and OAR geometries.

| CONCLUSION S
GRID therapy for breast cancer is feasible with a modern external beam TPS and onboard multileaf collimator (MLC). The plans T A B L E 6 TRs, EUDs, and PVDRs of 1-cm and 2-cm aperture GRID plans for three randomly picked patients. Breast cancer cell line C1 and radiosensitive normal tissue N1 are used in TR calculations.