Comparison of the Convolution algorithm with TMR10 for Leksell Gamma knife and dosimetric verification with radiochromic gel dosimeter

Abstract The Convolution algorithm, implemented in Leksell GammaPlan® ver. Here, 10, is the first algorithm for Leksell Gamma Knife that takes heterogeneities into account and models dose build‐up effects close to tissue boundaries. The aim of this study was preliminary comparison of the Convolution and TMR10 algorithms for real clinical cases and dosimetric verification of the algorithms, using measurements in a phantom. A total of 25 patients involved in comparison of the Convolution and TMR10 algorithms were divided into three groups: patients with benign tumors close to heterogeneities, patients with functional disorders, and patients with tumors located far from heterogeneities. Differences were observed especially in the group of patients with tumors close to heterogeneities, where the difference in maximal dose to critical structures for the Convolution algorithm was up to 15% compared to the TMR10 algorithm. Dosimetric verification of the algorithm was performed, using a radiochromic gel dosimeter based on Turnbull blue dye in a special heterogeneous phantom. Relative dose distributions measured with the radiochromic gel dosimeter agreed very well with both the TMR10 and Convolution calculations. We observed small discrepancies in the direction in which the largest inhomogeneity was positioned. Verification results indicated that the Convolution algorithm provides a different dose distribution, especially in regions close to heterogeneities and particularly for lower isodose volumes. However, the results obtained with gamma analyses in the gel dosimetry experiment did not verify the assumption that the Convolution algorithm provides more accurate dose calculation.


| INTRODUCTION
The Leksell Gamma Knife â Perfexion TM stereotactic radiosurgery system operating with submillimeter accuracy offers two-dose calculation algorithms for Leksell GammaPlan â (LGP): TMR10 and a Convolution algorithm. Until the Convolution algorithm was introduced in LGP, the radiosurgery treatment planning system ignored heterogeneity corrections and dose calculations were based solely on attenuation in water. Brain tissue is relatively homogeneous but beams pass through air-filled cavities and bones, and substantial differences can exist in the dose distribution when homogeneity is not assumed. 1 Moskvin et al. (2004) reported that the dose delivered to the target area is underestimated by up to 7% by the algorithm assuming homogeneous media geometry. 2 In the Convolution algorithm, an added software module enables accurate dose calculation for treatment of heterogeneous tissue. The algorithm takes into account build-up effects as well as heterogeneity effects. 3 The aim of this study was the preliminary comparison of the Convolution algorithm with TMR10 on real clinical cases and dosimetric verification. Verification of a new dose calculation algorithm should precede its implementation in routine clinical use.
In stereotactic radiosurgery, the selection of a suitable detector is not a trivial task. Gel dosimeters, as truly 3D dosimeters, are a promising tool for three-dimensional dose measurements in highdose-rate radiosurgery. Polymer gel dosimetry with PAGAT (Polyacrylamide gelatine gel fabricated at atmospheric conditions) and magnetic resonance imaging have a long history of use for this application. 4 However, temperature stabilization, toxicity, and access to an MR scanner for evaluating the PAGAT gel response makes radiochromic gel dosimeters more user-friendly for clinical applications. 5 A radiochromic gel dosimeter based on Turnbull blue dye formed by irradiation (TB gel) is an integral chemical dosimeter introduced by Solc et al. 6 The response can be evaluated, using both cone-and laser-beam optical CT. Basic properties of the TB gel dosimeter are summarized by Solc et al. 7 and Vavru et al. 8 It offers several advantages such as inhibited diffusion, linear response from 0 Gy up to at least 400 Gy, easy preparation, and nontoxic composition. The main disadvantages of TB gel dosimeters are lower sensitivity that requires a longer irradiation time, and gel aging caused by the spontaneous interactions of ferric ions with organic compounds of the gel. Gel response is stable if the gel is refrigerated in the dark, and evaluation of the irradiated TB gel should be performed within a few days following irradiation.

2.A | Algorithm comparison for clinical cases
As required for implementation of the Convolution algorithm, a calibration curve for the CT scanner (Somatom Definition Flash; Siemens Healthcare GmbH, Erlangen, Germany) was measured, using a CIRS Electron Density Phantom Model 062M (Head Insert) (Norfolk, VA, USA) with eight different tissue equivalent inserts, using a head protocol (120 kVp, 1 mm slice thickness). For clinical implementation of the Convolution algorithm, the calibration curve between Hounsfield units and relative electron density had to be adjusted to avoid problems with streaking artifacts at the edge of the CT scan. Relative electron densities lower than~0.2 were considered to be air, and since a high density insert was not available for the CIRS phantom, the calibration curve was extrapolated to include the high density fixation screws (Fig. 1).
A total of 25 patients were involved in the clinical testing of the Convolution algorithm. Patients were divided into three groups: Group 1 (12 patients) with benign tumors close to heterogeneities (vestibular schwannomas and pituitary adenomas); Group 2 (7 patients) with functional disorders (trigeminal neuralgia); Group-3 (6 patients) underwent a full-head CT scan and contained mostly patients with centrally located brain metastases, uveal melanomas, or meningiomas far from heterogeneities.
A treatment plan was created for each patient, using the TMR10 algorithm and then recalculated with the Convolution algorithm keeping all other planning parameters fixed. Treatment plan parameters are summarized in Table 1. Various parameters were used for the comparison: isodose volumes (prescription isodose, 30% and 20% isodoses), tumor coverage, Paddick conformity index, 9 gradient indexes, treatment time, and doses to critical structures.

2.B | Gel dosimetry verification
A TB gel was prepared, using the procedure suggested by Solc et al. 7 It is composed of a gel matrix -0.25% (w/w) phytagel, 0.5 mM potassium ferricyanide, and 0.5 mM ferric chloride compound dissolved in 1 mM sulphur acid medium. The prepared gel was poured into two glass cylindrical flasks (0.2 l, with a diameter of 6 cm), with one gel sample used for irradiation and one sample for background.
Gel dosimeters were stored in a refrigerator at 5°C. Solidification of the TB gel took roughly 48 h.
Verification of the new algorithm required design of a special heterogeneous phantom. One of the gel dosimeters described above The phantom shape (skull definition) and electron densities were defined, using the CT data. A treatment plan was generated, using the TMR10 algorithm. The phantom was irradiated with a single 8mm shot, positioned at the center of the TB gel dosimeter to a prescription dose of 50 Gy to the 50% isodose, requiring a treatment time of 60.6 min for a dose rate of 1.873 Gy/min. Irradiation took place in a dark treatment room. A second, nonirradiated gel sample was stored separately in a dark at room during the experiment at the same temperature. An identical plan was recalculated with the Convolution algorithm and both plans were exported in DICOM format.
The TB gel dosimeter was removed from the phantom and scanned, using a homemade optical CT scanner 2 h after irradiation. 10 The nonirradiated gel sample was also scanned to obtain a background reading. The optical CT scanner, described in more detail by

3.A | Algorithm comparison for clinical cases
Differences between the two algorithms were observed particularly in Group 1, with tumors close to heterogeneities. Differences between the two algorithms are shown in Fig. 3 on dose distribution for pituitary adenoma treatment. We observed that the Convolution algorithm reduced the prescription isodose volume by 2.4% (range À4.8% to À1.2%), and in the case of 30% isodose and 20% isodose, by 4.3% (range À8.3% to À1.8%), and 5.3% (range À10.5% to À1.6%), respectively. Tumor coverage decreased by 0.7% (range À2.1% to 0%), Gradient index decreased by 2.9% (range À12.6% to 0.4%) and the Paddick Conformity index increased on 2.9% (range À0.9% to 7.1%). Treatment time increased by 3.2%. Deviation in maximal doses to 1 mm 3 of critical structures observed in the T A B L E 1 Parameters of treatment plans for 25 patients was involved in clinical testing of the Convolution algorithm.

3.B | Gel dosimetry verification
Comparisons between gel measurements and TPS calculations are presented in the form of 1D x and y profiles (Fig. 4) | 141 (Fig. 5), 2D gamma maps with 3% dose difference, and 1 mm distance to agreement criteria calculated for the central slice (Fig. 6) and three-dimensional gamma analyses, using 3% dose difference and 1 mm distance to agreement and 10% dose threshold criteria (Fig. 7). The measured relative dose distributions agreed very well with the both TMR10 and Convolution calculations. We observed small discrepancies in the direction of the y axes, where the largest inhomogeneity (air filled flask) was positioned, and in the z direction (the remainder of the upper part of the gel dosimeter was filled with air). However, the results obtained by gamma analyses show minimal differences between both algorithms. Two-dimensional gamma anal- Carlo simulation.

ACKNOWLEDG MENTS
The paper was supported by the Grant Agency of the Czech Technical University in Prague grant No. SGS15/217/OHK4/3T/14.

CONFLI CT OF INTEREST
Josef Novotny Jr. is employed as consultants of Elekta Instruments AB, Stockholm.