Evaluation of a new secondary dose calculation software for Gamma Knife radiosurgery

Abstract Current available secondary dose calculation software for Gamma Knife radiosurgery falls short in situations where the target is shallow in depth or when the patient is positioned with a gamma angle other than 90°. In this work, we evaluate a new secondary calculation software which utilizes an innovative method to handle nonstandard gamma angles and image thresholding to render the skull for dose calculation. 800 treatment targets previously treated with our GammaKnife Icon system were imported from our treatment planning system (GammaPlan 11.0.3) and a secondary dose calculation was conducted. The agreement between the new calculations and the TPS were recorded and compared to the original secondary dose calculation agreement with the TPS using a Wilcoxon Signed Rank Test. Further comparisons using a Mann‐Whitney test were made for targets treated at a 90° gamma angle against those treated with either a 70 or 110 gamma angle for both the new and commercial secondary dose calculation systems. Correlations between dose deviations from the treatment planning system against average target depth were evaluated using a Kendall’s Tau correlation test for both programs. The Wilcoxon Signed Rank Test indicated a significant difference in the agreement between the two secondary calculations and the TPS, with a P‐value < 0.0001. With respect to patients treated at nonstandard gamma angles, the new software was largely independent of patient setup, while the commercial software showed a significant dependence (P‐value < 0.0001). The new secondary dose calculation software showed a moderate correlation with calculation depth, while the commercial software showed a weak correlation (Tau = −.322 and Tau = −.217 respectively). Overall, the new secondary software has better agreement with the TPS than the commercially available secondary calculation software over a range of diverse treatment geometries.


| INTRODUCTION
Gamma Knife (GK) radiosurgery has become a popular technique for the treatment of a variety of intracranial diseases, such as acoustic neuroma, pituitary adenoma, trigeminal neuralgia, vascular malformations, and malignant metastases. 1,2 Using 192 collimated Co-60 sources focused at an isocenter, a patient will be stereotactically positioned to place the target at the source ray intersections to submillimeter accuracy. 3 GK treatments are characterized by large doses delivered in a single, or more recently, hypofractionated schemes utilizing rigid thermoplastic masks with cone beam CT image guidance, and very sharp dose gradients outside of the target. 4,5 Because of the uniqueness of this system and treatments, quality assurance (QA) is of the utmost importance, including patient specific secondary dose calculations. 6 Secondary independent dose calculations play an important role in radiation therapy, and given the high precision associated with GK radiosurgery, secondary dose checks become even more important to reduce the risk of doing serious harm to the patient. 7,8 Given the complicated geometry of GK treatments, establishing an accurate methodology to incorporate secondary dose calculations into the clinic workflow has been cumbersome. 8 There have been several publications working to satisfy this clinical need, but many of the secondary dose calculation techniques suggested will still fail in certain situations, most notably when the patient is setup with a 110 or 70°gamma angle, or when the calculation point is at a shallow depth near the skull surface. It has been suggested that these difficulties in accurate secondary dose calculation arise from modeling the skull geometry, and constant density assumptions near the skull surface. 8 Different skull rendering techniques have been proposed, including modeling the skull as a sphere or using measured skull data from the use of a skull scalar instrument. [8][9][10] These methods work well for standard patient and target geometries, but significant discrepancies from the treatment planning system (TPS) are still evident when the target is at a shallow depth or when the patient setup uses a non 90°gamma angle. 11 It has been suggested that using an image thresholding technique may be the best method to accurately construct the patients skull for dose calculation. 12 Image thresholding makes use of an image data set such as CT or MRI and binarily assigns a voxel of the dataset to be within or beyond the skull boundary based upon a determined threshold image scale value. Skull rendering using this method minimizes uncertainties from measurement interpolation and produces an accurate representation of the true patient surface geometry.
Our institution installed the Leksell Gamma Knife Icon (Elekta Medical Systems, Stockholm, Sweden) in November of 2017. The Icon treatment system utilizes 192 Co-60 sources divided into eight sectors that can be individually blocked, or collimated to 4, 8, and 16 mm shot sizes. The Icon is unique in that it utilizes on-board cone beam computed tomography (CBCT) imaging system to enable fractionated and frameless treatments. 13 The specifics on commissioning and QA for the Icon system can be found in the literature. [13][14][15][16] Dose is calculated for Icon patients using the TMR10 algorithm. 17 This algorithm requires only dose rate calibration given by the user and a configurable collimator output factors that are provided by manufacturer. The TMR10 uses an exponential attenuation computation to the point of interest that is specific to each source location. The attenuation length (i.e. depth of the point of interest in the patient) for each source is calculated based on the source focal point, the distance from the focal point to the point of interest, and the distance to the rendered skull surface. 18 For each GK Icon target treated, a secondary dose calculation using a commercially available software is completed prior to treatment per institution policy. This commercial secondary check software reportedly uses the same TMR10 dose calculation formalism as the TPS, and reconstructs the patient skull using 24 scalar measurements either input directly by the user or inferred from a CT dataset. 19 The same user inputs were utilized for the second check software as the TPS. Our experience is similar to Xu et al., 11 especially where the commercially available software performs poorly in the presence of a nonstandard gamma angle, in some cases deviating from the TPS by more than 10%. This known issue presents a clinical difficulty in that treatment cannot proceed unless the TPS and secondary dose calculation agree to within 5%, as is the recommendation taken from AAPM Task Group 40 and our clinical policy. 7 In many cases, the problem is circum- The combination of these two methods may result in more accurate calculation conditions for both standard and nonstandard gamma angles which in turn will provide a more robust secondary calculation engine that can be used in the clinical setting. After each target was imported into the new secondary calculation software, the patient skulls were constructed using the image thresholding technique, in contrast with the derived scalar measurements used in the commercial software (Gamma Check, MU Check, Oklahoma City, OK), available with the program (Fig. 1). In most cases, the skulls were rendered from a CT image dataset. However, in approximately 10% of the patient plans a CT dataset was not available and the patient's skull was rendered using an MRI dataset.

| MATERIALS AND METHODS
The current versions of the TPS support image thresholding skull definition from both types of imaging modalities. Individual beamlet rotations were also made for patient setups using non-standard gamma angles. Dose was re-calculated with the new software, and the agreement to the TPS was evaluated. This was done using the percent difference for each individual target. The median and range of the percent differences per target was calculated over the entire cohort. A further comparison of deviation between TPS and secondary calculation doses with respect to average calculation depth was completed using a Kendall's Tau correlation test to evaluate any dependencies the secondary software has on target location depth in the skull. The target cohort was then binarily categorized by gamma angle (standard 90°and nonstandard 70/110°). Using a Mann-Whitney U test, differences between the two categories with respect to agreement with the TPS were evaluated for statistical significance.
A Wilcoxon Signed Rank Test (WSRT) was used to evaluate significant differences in the deviation from the TPS calculated dose over the entire 800 treatment targets for both calculation software packages. Using the same techniques as described for the new secondary dose calculation software, dependencies on agreement to the TPS of the commercially available software dose calculation as it pertains to gamma angle and average calculation depth were evaluated and compared to the dependencies of the new secondary dose calculation software.
The new secondary dose calculation software has the capability to render the skull for dose calculation using discrete scalar measurements if these measurements were used in the TPS for planning. To isolate the robustness of the beamlet rotation algorithm employed for nonstandard gamma angles by the new software, the target with a nonstandard gamma angle patient setup that showed the largest discrepancy from the TPS by the commercially available software was replanned in GammaPlan using skull scalar measurements. The plan was reimported to the new software and the skull was rendered using the discrete measurements. Dose was recalculated using the new software and compared with the TPS.  As the purpose for a secondary dose calculation is to give the user confidence that the primary dose calculation from the TPS is accurate, an absolute dose measurement was also employed for comparison against both the TPS and the two secondary dose calculation engines. In the two plans where the TPS estimated dose and the commercially available secondary dose software differed the greatest, the shot arrangement and gamma angle in the patient plan was copied to an anthropomorphic phantom and a film measurement was taken. Using EBT3 gafrchormic film cross calibrated to an ADCL calibrated ionization chamber, an optical density to dose calibration curve was created by irradiating a 16 mm shot to 2, 3, 4 and 5 Gy.
Next, the patient plan was scaled to a max dose of 4 Gy, and delivered on an anthropomorphic head phantom. The maximum measured dose was then compared to the TPS, a calculation from commercially available software, and what the new secondary dose calculation software predicted. Each of the film measurements, including calibration films, were repeated three times.

| RESULTS
Over the entire target cohort, the new secondary dose calculation software showed excellent agreement with the TPS. The differences from the TPS ranged from 0.00% to 3.33%, with a median and mean value of 0.6% and 0.68%, respectively, which is well within our clinical tolerance. The agreement between the TPS and the commercially available dose calculation software showed larger deviations, ranging from 0.00% to 10.25% and a median and mean value of 0.833% and 1.15%, with 13 above clinical tolerance. These data are shown in

| CONCLUSION
Currently, secondary dose calculation in Gamma Knife radiosurgery is not robust and current methods of computing dose accurately depend on the simplicity of treatment geometry. In complex patient setups, these current secondary calculation methods fail, leading the user to make difficult clinical decisions on whether to proceed with treatment that may not be warranted due to the inaccuracy of secondary dose calculation. In this study, a new secondary dose calculation software for Gamma Knife radiosurgery using image threshold skull rendering and beamlet rotation technique was evaluated and compared to a commercially available software for 800 targets treated with our Icon system. The new software clearly excels where the commercial software falls short, especially in the presence of 110 and 70°gamma angles in patient setup. This will make a large impact for the Gamma Knife physicist for plan QA by providing confidence to the user that the planned dose calculated by the TPS is accurate, regardless of complexity of calculation geometry.

ACKNOWLEDG MENTS
The authors thank the Lifeline Software Development Team for all of their help and support for this project

CONFLI CT OF INTEREST
The department of radiation oncology physics division received funding in aiding the implementation of previous work from our department into a secondary dose calculation program for Gamma Knife from Lifeline Software Inc.