In our institute, the Precision MC was installed in November 2017 and after commissioning and validation it was clinically introduced for patient treatments . For this purpose, during the commissioning phase, the Precision MC source model parameters were adjusted such that calculated output factors (OF), dose profiles and tissue-phantom ratio (TPR) curves match to the corresponding measurements.
The Precision MC dose calculation algorithm is described by Ma et al.  with implementation details information given by Heidorn et al.  and only a brief summary is provided here. A measurement based virtual source model is used to sample photons generated in the treatment head. A single virtual source, consistent with the linac target, is included, and its properties (energy spectrum, source point distribution, and direction distribution) are commissioned by comparison of measured and calculated TPR, dose profile, and OF. A CT based patient model is derived by determining a mass density and material type at each voxel. Mass density is assigned from a user defined Hounsfield unit (HU) to mass density calibration curve. Material type is assigned based on mass density to be either air, soft tissue, or bone. Material type is only used for photon interaction calculations. During dose calculation, each photon sampled from the source model is transported through the CT based patient model. Photon interactions are calculated using material type and mass density. At each interaction site a pre-simulated particle track (containing the details of all subsequent interactions and energy loss) is selected at the appropriate energy, aligned with the photon track and overlaid onto the patient model. Energy deposition is calculated using the pre-generated steps in this track, scaled by local mass density. These pre-simulated tracks are generated in a uniform water phantom and provided as a data library with Precision MC. This track repeating method, together with other variance reduction methods such as Russian Roulette, photon splitting, and forced photon interaction enables an efficient MC-based handling of the transport of charged particles and leads to reduced simulation times when compared to full MC simulations. Table 1 provides details about the CT conversion and interaction handling in Precision MC. In this study, Precision version 1.1.1 was used for all calculations. This was running on a Dell T7910 with 2 × 2.40 GHz CPU and 64 GB RAM.
The IDC framework has been described in  and is used in this work for benchmarking the Precision MC algorithm. For this purpose, the IDC was commissioned based on measured OFs, dose profiles and depth dose data from the same CyberKnife M6 system. It is important to note that the IDC framework was not intended to work as a clinical tool for treatment planning but was developed in order to serve either as a patient specific QA tool or to serve as a benchmark tool (as in this study). Also for the IDC, EGSnrc served as a basis but in contrast to Precision MC, the IDC framework simulates all particles within a specific material according to the methods described in . By this means, there is no pre-simulation applied resulting in computation times, which are expected to be longer than those of Precision MC. More details about the IDC implemented method is given in Table 1. All MC transport parameters remained identical to  with a global photon cut energy of 10 keV and 700 keV for electrons. Bremsstrahlung cross-sections were Bethe-Heitler and photon cross sectional data were read from the XCOM library.
In order to benchmark the accuracy and general performance of Precision MC, cases were either created artificially or originated from clinical routine (i.e. were clinical cases previously treated with CyberKnife using fixed size cone or Iris collimators and now re-planned using MLC and Precision MC). Starting with simplified situations (academic cases), complexity is increased to treatment plans applied to phantoms (phantom cases) and finally to clinical cases as detailed below.
The benchmark consists of the comparison of the calculated dose distribution of Precision MC and the corresponding dose distribution as either calculated by IDC or measured on the CyberKnife M6 system.
The basic setup for the benchmarking study is similar to the setup used to commission the IDC system , but now compared to matching calculations from Precision MC. A homogeneous water tank with a size of 201 × 201 × 200 mm3 is used. Within this water tank OFs, dose profiles, and depth dose curves are measured by a PTW 60019 microDiamond (PTW-Freiburg GmbH, Freiburg, Germany) detector or calculated using IDC and Precision MC. For this purpose, rectangular fields were shaped by the Incise MLC and different field sizes ranging from 7.6 mm × 7.7 mm to 115.0 mm × 100.1 mm were investigated. These dose quantities have already been used for the commissioning of both the IDC  and Precision MC models. It should be noted, however, that this measured dataset is similar, but not identical. First of all a different detector was used for the commissioning: Specifically, during commissioning, the dose profiles, the TPR’s at all field sizes, and OF’s at the smallest field size were measured using a SFD diode detector (IBA Dosimetry GmbH, Schwarzenbruck, Germany) instead of the microDiamond. No corrections were applied to the OF measured using either detector. Moreover, TPR data were used for the commissioning of the Precision MC model, while PDD data was used for IDC commissioning as well as the benchmarking study. Therefore, the simple academic test described here allows not only to validate the dose calculation accuracy but also the quality of the commissioning itself. As a first step, commissioning quality is assessed. Based upon this, data from 3D dose distributions is compared to measurements. Only then can data from Precision MC be benchmarked against IDC. These steps are illustrated in Fig. 1 for the example of OFs.
The first step is assessing the quality of the commissioning by comparing OFs from Precision MC beam data tables (originating from the commissioning process itself and thus only available in Precision MC) to measurements. Building upon this, OFs, dose profiles at 15 mm depth and depth dose curves are extracted from 3D dose distributions and compared to measurements. The third step then compares OFs, dose profiles and depth dose curves from 3D dose distributions between IDC and Precision MC. While IDC commissioning results have been presented previously for SFD measurements , this work updates results with microDiamond measurements. All dose profiles, depth dose curves and OFs are measured and calculated with a source-to-surface distance (SSD) of 785 mm. Calculation in the homogeneous water tank is performed using a voxel size of 1 × 1 × 1 mm3.
For benchmarking purposes of a dose calculation algorithm, it is important to investigate the impact of inhomogeneities . In radiation therapy, this is typically accomplished using phantoms such as lung or pelvis phantoms. In this study, one lung and two prostate treatment plans were generated on a thorax and a male pelvis phantom, respectively (CIRS IMRT thorax / CIRS IMRT pelvic 3D phantom, CIRS, Inc., Norfolk, VA). Besides the thorax phantom plan, all treatment plans were generated using sequential optimization and Table 2 summarizes treatment plan characteristics of these cases.
The thorax phantom is outfitted with a 20 mm diameter soft tissue equivalent spherical volume representing a tumor. A simplified treatment plan referred to as case 1 is generated, containing a single MLC shaped beam conformed to the tumor volume insert. For this case a single dose of 46 Gy to the 80% isodose line was prescribed and corresponding dose distributions were calculated by Precision MC, IDC and, additionally for illustration purposes, the finite size pencil beam (FSPB) algorithm implemented in Precision (the lateral kernel scaling option was not used).
For the first prostate treatment plan (case 2), a dose of 33.13 Gy was prescribed to the 80% isodose line. Sequential optimization was used to create a treatment plan with 47 beams and 151 segments. To avoid calculation uncertainties in small fields, a subset of this treatment plan was created (case 3) by manually erasing small MLC apertures (so called “perimeter shapes”, which can be enabled during optimization to fill possible underdosage at the edge of the PTV). This subset retained 26 beams and 84 segments. The number of MU of the remaining beams was unaltered, resulting in a prescribed dose of 32.58 Gy.
In order to investigate the difference between Precision MC and IDC, clinical cases were used and dose distributions were recalculated by both algorithms. By this means, dose distributions of 7 lung treatment plans were calculated using Precision MC as well as IDC. A dose prescription of 50 Gy by 5 fractions or 60 Gy by 3 fractions to the 74–79% isodose lines was used. Depending on the case, this results in 19–24 beams and 31–58 segments.
Dose distributions calculated in Precision MC targeted a statistical uncertainty of 1% for phantom and 2% for lung cases after smoothing, and were calculated at the native CT voxel resolution (i.e. as shown in the CT voxel size column of Table 2). Dose distributions from Precision MC are smoothed with a Gaussian kernel. IDC dose calculations were also performed with the calculation volume and voxel size equaling the 3D CT data set. IDC dose distributions were calculated to mean statistical uncertainties of < 1.9% in voxels receiving 50% of the respective dose maximum for all cases. For analysis, the resolution of each dose distribution (Both Precision MC and IDC) was reduced by a factor of two along any axis with a voxel edge length of < 1.5 mm. Analysis was then performed with the voxel size given in Table 2 under “averaged voxel size”.
Resulting dose distributions were benchmarked by analyzing dose differences, DVHs and by performing 3D gamma evaluation . In all DVHs, the dose axis represents dose relative to the Precision MC dose maximum (100%) and volume relate to the volume of each contoured structure. Gamma evaluation was performed with 2% dose difference (global, relative to Precision MC dose maximum), 1 mm distance to agreement criteria and a global 10% dose threshold and IDC calculated dose was set as reference for gamma evaluation. Furthermore, mean dose to the PTV and relative lung volume receiving 20 Gy or more (lung V20) were compared between Precision MC and IDC. To analyze efficiency, calculation times for the 7 clinical lung cases were recorded in Precision MC.