Commissioning and clinical implementation of the first commercial independent Monte Carlo 3D dose calculation to replace CyberKnife M6™ patient‐specific QA measurements

Abstract Purpose To report on the commissioning and clinical validation of the first commercially available independent Monte Carlo (MC) three‐dimensional (3D) dose calculation for CyberKnife robotic radiosurgery system® (Accuray, Sunnyvale, CA). Methods The independent dose calculation (IDC) by SciMoCa® (Scientific RT, Munich, Germany) was validated based on water measurements of output factors and dose profiles (unshielded diode, field‐size dependent corrections). A set of 84 patient‐specific quality assurance (QA) measurements for multi‐leaf collimator (MLC) plans, using an Octavius two‐dimensional SRS1000 array (PTW, Freiburg, Germany), was compared to results of respective calculations. Statistical process control (SPC) was used to detect plans outside action levels. Results Of all output factors for the three collimator systems of the CyberKnife, 99% agreed within 2% and 81% within 1%, with a maximum deviation of 3.2% for a 5‐mm fixed cone. The profiles were compared using a one‐dimensional gamma evaluation with 2% dose difference and 0.5 mm distance‐to‐agreement (Γ(2,0.5)). The off‐centre ratios showed an average pass rate >99% (92–100%). The agreement of the depth dose profiles depended on field size, with lowest pass rates for the smallest MLC field sizes. The average depth dose pass rate was 88% (35–99%). The IDCs showed a Γ(2,1) pass rate of 98%. Statistical process control detected six plans outside tolerance levels in the measurements, all of which could be attributed the measurement setup. Independent dose calculations showed problems in five plans, all due to differences in the algorithm between TPS and IDC. Based on these results changes were made in the class solution for treatment plans. Conclusion The first commercially available MC 3D dose IDC was successfully commissioned and validated for the CyberKnife and replaced all routine patient‐specific QA measurements in our clinic.


| INTRODUCTION
To ensure safe dose delivery in stereotactic radiotherapy, uncertainties and errors in dose delivery must be minimized by an extended and strict quality assurance (QA) protocol. An established part of a QA protocol is the patient-specific pre-treatment verification of the calculated dose, either by measurements or by checking the monitor units with an independent dose calculation (IDC). 1 Patient-specific QA measurements can be performed using chambers, film, or diode arrays. [2][3][4][5][6][7] Especially for stereotactic CyberKnife treatment plans, both measurement equipment and analysis require stringent quality criteria. Internationally acknowledged gamma criteria of 2% dose difference and 2 mm distanceto-agreement Γ(2,2) are insufficient to detect possible errors relevant during CyberKnife dose delivery. 2,4,8 However, measurements are costly by consuming valuable personnel and machine time.
Besides this, despite fulfilling the strict criteria, the relevant errors that can be picked up are limited and mainly refer to problems regarding the delivery system. [9][10][11] It is more efficient that these types of issues are addressed by proper commissioning and machine QA. 8 An alternative to pre-treatment measurements is an IDC. 1,8 This method recalculates the dose independent of a vendor treatment planning system (TPS), based on the treatment plan parameters for the given plan, and can range between a point dose calculation to a full three-dimensional (3D) Monte Carlo calculation. [12][13][14] Independent dose calculation platforms have been developed for the Cyber-Knife fixed cone and Iris™ collimators 15,16 and recently also for the newly developed MLC collimator. 17,18 None of these solutions offers a (MC) 3D IDC that is commercially available. This paper describes the commissioning and clinical implementation of the first commercially available 3D Monte Carlo dose engine (SciMoCa RT, Munich) for two CyberKnife ® M6™ robotic radiosurgery system (Accuray Inc., Sunnyvale, CA) in order to replace patient-specific QA measurements. To this end, the beam model provided by SciMoCa was compared to water tank reference measurements for all three collimator sets. Using SPC, treatment plans outside tolerances were detected in array measurements and IDCs and were further analysed. As the vast majority of our patient cohort is treated using the MLC collimator, retrospectively a set of 84 patient MLC plans was used for this evaluation.

2.A | Modeling of the CyberKnife accelerators
The SciMoCa algorithm has been described in Ref. [26] for general purpose linear accelerators with MLC. The CyberKnife implementation uses the same patient/phantom transport code, but differs in source and collimator models. The latter are purpose-built for fixed cones and Iris, whereas the MLC model was adapted from the model described in Ref. [26] with respect to transmission, leakage, and additional fixed collimation elements in the assembly. The source model is comprised of four virtual sources (primary, primary collimator and other head scatter, beam filter scatter, contamination electrons), whereby the scatter components amount to only about 3.3% of total energy fluence at the maximum field size of the MLC, and about 1.7% for the 60 mm cone.
The three beam models (one for each collimator type) of a CyberKnife M6 share the same source model, which was derived from water phantom depth dose curve (DDC) and output factor (OF) measurements obtained with the Incise2 MLC. Input for the models was identical to the data obtained during CyberKnife commissioning: a DDC, a set of off center ratios (depth 15, 50, 100, 200, and 300 mm) and an OF for each field size summarized in Table 1. For the MLC cross profiles were included. Reference depth for all collimators and field sizes was 1.5 cm.
Input DDCs and OFs for the fixed cones and Iris fields were

2.B.3 | Establishing action levels
For every new QA method, appropriate action levels need to be established to identify differences between dose calculated by the TPS and delivered dose. Action levels for IDCs were determined using statistical process control (SPC). 22 This method has been described previously for radiotherapy quality assurance, such as linac QA, 23 image-guidance QA, 24 IMRT dose verification 25 and similar to our application, independent monitor unit calculation 26 and the replacement of patient-specific QA measurements by IDCs. 27 Using SPC, chronological processes such as patient-specific QA can be evaluated in control charts that show how the process randomly varies over time. Control charts typically show a central average line and statistically determined upper and lower control limits. In control charts, in contrast to the general conception in radiotherapy, systematic errors are defined as points outside the action levels. Besides systematic errors, the charts will show if the average or the random variation changes due to alterations in the treatment process. To set action levels in CyberKnife plan QA, two charts were used; an average chart, displaying the average and random spread of the measurements and a range chart that displays the difference between successive measurements and their average value. The range R was calculated according to Eq. (1).
where x represents an individual, successive QA measurements. This leads to the following equations for the center lines and upper and lower thresholds in the average (A) and range (R) charts: The factors d 2 and d 3 are tabulated and are valid for a subgroup size of n ¼ 2 where each measurement can be treated as an independent data point. 23,28 In this case R l will be effectively set to 0.

2.C | Comparison to pre-treatment measurements
The intended use of the SciMoCa IDCs is to replace patient-specific QA measurements. To ensure that this can be safely done, a risk assessment of the QA program, in line with AAPM TG100, needs to take place. As part of this, for the same set of 84 patients that received an IDC, individual pre-treatment measurements were reevaluated using the SPC method. Identical gamma criteria as in IDCs were used: Γ(2,1), using the global maximum, and a 10% dose cutoff.
Plans outside the action levels were further analyzed.  resolution area (5.5 × 5.5 cm 2 ) is 2.5 mm. In the low resolution area, filling the remainder of the 11 × 11 cm 2 area, the distance between the chambers is 5 mm. The use of the 1000SRS array for the Cyber-Knife has been investigated and found sufficiently accurate for patient-specific QA measurements. 4,6 Our 1000SRS array has a fixed geometry with a slab phantom in which a set of three fiducial markers are embedded. Pre-treatment alignment on the CyberKnife is based on a fiducial match between two stereoscopic x-ray images with digitally reconstructed radiographs based on the treatment planning CT, ensuring optimal alignment between planned and delivered geometry.

2.C.1 | Measurements of QA plans
A 2D gamma analysis was performed in Verisoft (v 7.0, PTW, Freiburg, Germany) for the two CyberKnife systems separately. No additional geometrical shift of the dose planes, to obtain optimal pass rates, was allowed in the analysis to prevent biased gamma results.

3.A | Validation of the beam models
Absolute DDCs and OFs, and relative cross profiles calculated by SciMoCa were compared to measurements in a homogenous water phantom using a Γ(2,0.5) and Γ(1,0.5), respectively. 18 Figure 1 shows measured versus calculated dose profiles (crossplane) and depth curves for increasing fields sizes of the Incise2 MLC.
Of the calculated OF for both CyberKnife systems 99% agreed within 2% and 81% within 1%, the maximum deviation of 3.2% is associated with a cone size of 5 mm (Table 2).    previous work on in-house developed IDCs. [15][16][17][18] The agreement in dose calculated by Multiplan and SciMoCa is very high. The average gamma pass rate Γ(2,1) 98% and mean 0.27 found in this work for 3D IDCs are well above the advised numbers of AAPM TG 135 of Γ(2,2) ≥ 90%. 8 The pass rates agree well with earlier work on CyberKnife patient-specific QA. 2,15,17,18 Previously, similarly high agreement between Acuros and SciMoCa calculated dose distributions had been reported. 30 T A B L E 3 Pass rates from the comparison between water tank validation measurements and calculations by SciMoCa for two CyberKnife systems. This can be attributed to the use of a dedicated CyberKnife QA phantom and the beam delivery perpendicular to the array surface, to avoid angular correction of the array response.

3.B.3 | Comparison of IDCs and measurements
Action levels for gamma pass rate and gamma mean were set using SPC. Plans exceeding the action levels were further analyzed.
In the measurements 5 out of 6 systematic errors could be explained by a scaling factor in the dose attributable to the initial absence of a dedicated phantom. The fourth case corresponds to a plan with a large target volume, due to which the high dose gradients over- | 309 a systematic error in both IDC and measurements seems a coincidence, as the origin of the deviation was different. Based on these results and an extensive period of testing the MLC, 31  In this study, we focused on gamma parameters, however, the IDC method also allows us to look at clinically relevant differences in DVHs parameters. This is often used in our clinical practice and is a valuable additional tool to detect issues in treatment planning. 32 Also, potential future development of log file analysis could further boost the confidence in the actual delivered dose, bridging the gap between machine QA and machine settings during dose delivery. 33,34

| CONCLUSION
Commercially available 3D Monte Carlo IDC software was successfully commissioned and validated. Good agreement was observed between the dose calculation algorithms provided by the Multiplan TPS and SciMoCa based on reference measurements in water. The use of the IDC in clinical practice has been validated by analyzing a set of 84 patient plans using SPC and a comparison to pre-treatment measurements. After a risk assessment of our QA program, independent dose calculations using SciMoCa have replaced regular patientspecific QA measurements for the CyberKnife in our institute.

CONF LICT OF I NTEREST
MA and MS are associated with Scientific RT (SciMoCa). In collaboration, the product for the Cyberknife was developed. However, there has been no influence of Scientific RT on the results described in this paper. There is no commercial interest for MM and MH.