### INTRODUCTION

^{1,}

^{2,}

^{4-}

^{6,}

^{12,}

^{13)}. Since, this is based on a single-fraction high dose treatment strategy, independent verification of the Leksell GammaPlan® (LGP) is important for ensuring patient safety and minimizing the risk of treatment errors

^{10,}

^{13)}. Previous methods for verifying LGP by various algorithms were reported by Tsai et al.

^{13),}Marcu et al.

^{11),}Hur et al.

^{9)}and Zhang et al.

^{14)}.

^{14)}could calculate only treatment times, which were accurate only without plugs. Other methodologies only tested around the center of the target

^{13)}. Additionally, these studies uniformly lacked statistical analysis. Instead of showing statistical agreement between their method and LGP findings, only the size of errors was reported

^{11,}

^{13,}

^{14)}. Another significant limitation was that previous studies were tested exclusively on single treatment target. None of the previous studies showed accuracy for multiple targets. This means that findings from these previous investigations are not applicable to all LGK procedures, because a large portion of LGK treatment involves multiple targets.

### MATERIALS AND METHODS

^{9)}. For this, the patient's skull is viewed as an ellipsoid with the center at the mammillary body. The ellipsoid is expressed as following equation

_{s}, y

_{s}, z

_{s}) are the coordinates of the shot center coordinate system (SCCS), (l, m, n) are the coordinates of the mammillary body in the SCCS and α=γ-90°, β is the angle rotated counterclockwise about the z'

_{s}-axis of the skull. A single beamlet from the 201 collimators was defined as follows

_{p,i}, y

_{p,i}, z

_{p,i}), (i=1,····, 201) are the geometrical locations of the 201 collimators in the SCCS. Dose rate for a single beamlet at the arbitrary point (p) is determined by the equation

_{cal,18}(0) is the calibration dose rate for the 18 mm collimator helmet, ω

_{c}is the collimator factor, d

_{i}is the "i" beamlet depth, PW

_{i}is the plug weight (either 0 or 1), and F(ω

_{c}; r

_{i}) is the dose profile function related to dose distribution on the transverse plane of the beam axis. Therefore, the dose rate for one shot at point (p) is calculated with the formula

_{s}(LGP) is the shot time calculated by LGP.

### Dose for 50 points in each patient

### Maximal dose points

### Target volume

### Statistical analysis

*p*value of less than 0.05 was considered statistically significant. We also created a Bland-Altman plot to graphically compare the dose rates for 50 points as calculated by the two systems

^{8)}. The Bland-Altman plot is constructed with the MedCalc software program (MedCalc®, Mariakerke, Belgium, http://www.medcalc.be/).

### RESULTS

### DISCUSSION

^{9,}

^{11,}

^{13,}

^{14)}. Additionally, results of these studies were compared only in under certain conditions for limited parameters although many different LGP parameters are instantly available in clinical settings.

^{13)}. Thus, these modalities are not applicable to all matrix points. Tsai et al.

^{13)}applied average target depth from MRI images or ruler measurements. Since this group used a three-dimensional dose profile referred in unplugged condition, plugged treatments may produce errors depending on the numbers and location of plugs

^{13)}. They explained that the discrepancies are due to the high dose gradient, especially when a plug pattern is used for the helmet. Their method revealed a 23.1% maximal dose rate mismatch for certain locations. Because this method produces errors in off-center points, it cannot be used for multiple targets. Marcu et al.

^{11)}used a constant radius R based on a spherical head. The accuracy of their method depended inversely on the deviation of the shape of a patient's head from a sphere. The method utilized by Zhang et al.

^{14)}adopted the tissue-maximum ratio for each of the 201 beams. Their method is related to accurately to the multiple-shot treatment plan because the accumulated error affects the normalization factor. Overall, the previous methods had limitations to be applicable for multiple targets.

^{11)}. Only a few authors have reviewed results of multiple shot treatments. The method used by Marcu et al.

^{11)}had error ranges of 5% for a single shot and 3% for multiple shots, and did not provide a description of multiple targets. Zhang et al.

^{14)}neglected to mention whether or not their study was performed on multiple targets

^{14)}. Multiple targets are subject to greater error because matrix points are more dispersed in the cranium. Minimum requirements for multiple target treatment are as follows : 1) a dose verification method with accuracy of off center points; 2) the ability to calculate the dose at all points in N matrices (N×31×31×31 points); 3) an off axis dose profiles complying with four collimator types; and 4) inherent error not multiplied over the number of targets. Unless any of these requirements are satisfied, dose verification cannot be performed accurately.

^{3)}. This method was more appropriate than correlation analysis when the reference method is low in error results

^{7)}. LGP also exhibits inherent error when Gamma Knife® is used in an actual clinical setting. For example, bubble head measurements are subject to uncertainty due to orientation of the ruler against the surface of patients' head as well as the impact of existing scalp hair and its elasticity

^{13)}. The aim of agreement analysis is to verify that two methods concur such that they can be used interchangeably.