Eclipse TPS 13.0 (Varian, Palo Alto, California, USA) is designed for performing KRT, IMRT, VMAT, SRS/SBRT and electron plannings. The Eclipse treatment planning system in our clinic includes Dose Volume Optimization (DVO), Plan Geometry Optimization (PGO), Progressive Resolution Optimizer (PRO), Multi-Resolution Dose Optimization (MRDC) Algorithms, Pencil Beam Convolution (PBC), Analytical Anisotropic Algorithm (AAA) and Acuros XB (AXB) dose calculation algorithms.

The AAA dose calculation model is a 3D pencil beam and convolution superposition algorithm consisting of separate models for electrons emitted from primary photons, scattered photons, and beam modulators (primary collimator, beam straightening filter, and wedge filter). The functional forms for the basic physical quantities initiate a process by adding device properties to the account. This often leads to a noticeable reduction in the calculation time required for such algorithms. Tissue heterogeneities are added to calculation as anisotropic using photon scattering kernels of the multiple lateral direction in the 3D neighborhood. The final dose distribution is formed by superimposing the contribution of photons and electron beams. The dose behind the air gap is a little over-calculated in the AAA algorithm with an error caused by the modeling of the scattered dose.

The Acuros XB (AXB) algorithm was developed for two strategic needs such as accuracy and speed in external photon beam treatment planning. AXB uses a complex technique to solve Linear Boltzmann Transport Equation (LBTE) and clarifies the patient dose calculation for heterogeneities originating entirely from lung, bone, air, and non-biological implants. LBTE, which is the linear form of the Boltzman Transport Equaiton (BTE) and defines the macroscopic behavior of the radiation particles, assumes that the interaction of the radiation particles in the medium is formed without interaction of each other and an external magnetic field. There are two solution approaches that try to explain LBTE. One of them is the Monte Carlo method, which does not clearly solve the commonly known LBTE and produces indirect solutions for LBTE. Second one is solving LBTE using numerical methods.

Monte Carlo and LBTE solution methods produce close results but fail to produce clear solutions, and mistakes are occured. The mistakes of Monte Carlo System are random and result from the fact that a limited number of particles are simulated. Systematic faults can occur when using Monte Carlo methodologies to expedite the solution time.

The source model of the AXB algorithm used in Eclipse TPS uses the existing AAA resource model. Within this model; there are primary photons, out-of-focus photons, contaminated electrons and scattered photons.

The AXB algorithm uses the mass density information obtained from the CT images in each voxel for dose calculation.

In order to measure the dosimetric difference between Analytical Anisotropic Algorithm and Acuros XB, measuring assembly was prepared as in Figure 1 and the 2 mm spaced computed tomography images were taken. A 5 cm Styrofoam layer was used to obtain the air cavity (HU = −1000) in measuring assembly. CT images of the measuring device were transferred to the Eclipse TPS. The calculation was made at the calculation grid size (CGS) of 2.5 mm for the SSD: 100 cm, 10 × 10 area and at 6 MV for the AAA and AXB. Dose measurement information at specified measurement points were recorded. At the same conditions, the point dose measurements were made with 0.015 cm³ pin point ion chamber (PTW, Freiburg-Germany) at predetermined measuring points by being performed irradiation in Trubeam STx device.

Planning CT scans of 20 patients with early-stage left breast cancer, after breast-conserving surgery, were used for this study (Table 1). Data were generated with patients in the supine position with one arm above the head in the breast board. For the treatment planning, the 7-field IMRT was planned with 6 MV rays of the Varian TrueBeam STx device in the Eclipse treatment planning system. Two treatment planning were made for each patient plan using AAA and AXB algorithms. The calculation grid size (CGS) of 2.5 mm was chosen for all plans to minimize errors due to calculation grid size (CGS) in treatment volume.

The median dose of target volume was 50.4 Gy in 1.8 Gy fractions (46.8 - 50.4 Gy). An additional dose of 10 Gy (200 cGy × 5 fractions) was given to the lumpectomy cavity of some patients. If necessary, the conventional photon rays of 10 MV were used with 6 MV for planning. The tissue heterogeneity corrections were used in all calculations.

Dose volum histograms (DVH) were evaluated for RTOG target volumes and OARs of each patient plan. While the treatment of the patients was being planned, the primary dose limitation was 95.0% of the target and 95.0% of the dose prescribed for chest or chest wall was provided to be received as PTV_breast. From each patient’s treatment planning; the V₅ Gy, V₂₀ Gy, mean (D_mean) doses were calculated for the ipsilateral lung, V₁₀ Gy, V₂₀, V₃₀ Gy and D_mean for the heart, V₅, V₁₀ and D_mean for the contralateral breast, V₅, V₁₀ and D_mean doses for the contralateral lung. Besides all these; Body-PTV doses which are not in the RTOG criteria were calculated. V₅ and V₂₀ doses were calculated separately for both algorithms, and small dose-volume responses of algorithms were investigated.

In the measuring assembly shown in Figure 1 which we prepared to demonstrate the differences in calculation between Analytical Anisotropic Algorithm and Acuros XB, the difference in dose between AAA and TPS was found to be 4% in A, which is the first dose measurement point after 5 cm air cavity, 7.8% in B, which is the second dose measurement point, and 9.5% in C.

Similarly; with AXB at the same measuring points, we achieved a difference of 1% at point A, 1.8% at point B and 3% at point C.

The dosimetric results for the treatment plan of 20 breast cancer patients formed using two different algorithms, are shown in Table 2. PTV_breast minimum, PTV_breast D_mean, PTV_breast D_95% doses; V₅ Gy, V₂₀ Gy and D_mean doses for the contralateral lung; V₁₀ Gy, V₂₀, V₃₀ Gy and D_mean doses for the heart; V₅, V₁₀ and D_mean doses for the contralateral breast; V₅, V₁₀ and D_mean doses for the contralateral lung are shown in Table 2.

In Table 2; V₅ and V₂₀ doses are shown separately for both algorithms by calculating the Body-PTV doses, which are not in the RTOG criteria.

Dose-Volume Histogram (DVH) for a patient calculated using the AAA and AXB dose algorithms is shown in Figure 2. There was a difference of 13% between the PTV_breast Dmin doses calculated by the AAA and AXB algorithms (p < 0.05). This may be related to the fact that the PTV_breast volume was calculated as high by the AAA algorithm although the PTV_breast volume was removed by 0.5 cm from the skin. There was no significant difference between the PTV_D95% dosescalculated by the AAA and AXB algorithms (p > 0.05).

There was a significant difference between the V₅, V₂₀ and D_mean doses calculated by AXB and AAA algorithms for the left side lung (p < 0.05). V₅, V₂₀ and D_mean doses of the left side lung are higher in all AAA plans than the dosimetric results of the AXB plans.

There was a significant difference between the V₁₀, V₂₀, V₃₀ and D_mean doses of the heart in all the plans of the AAA and AXB algorithms (p < 0.05).

Figure 3 shows comparison of dose distribution calculated using AAA and AXB dose calculation algorithms for a patient early-stage left breast cancer. The same 7 field IMRT plan recalculated using the AXB dose calculation algorithm (for the same patient, with the same dose scale).

When D_mean doses of the contralateral lung doses were evaluated, there was a significant difference between AAA plans and AXB plans (p < 0.05). There was also a significant difference between the doses of V₅ and V₁₀ in the contralateral lung (p < 0.05).

There was a significant difference between the D_mean, V₅ and V₁₀ doses of the contralateral breast (p < 0.05).

Finally; in our study comparing the V₅ and V₂₀ doses for Body-PTV, it was found that there was no significant relationship between AAA plans and AXB plans (p > 0.05)

Huang et al. showed that the calculation grid size (CGS) was related to the dose estimation in their studies of the lung streotactic radiotherapy (SBRT) planning [11] . To reduce this effect in our study, all plans for both algorithms were calculated at 2.5 mm CGS.

In a planning study performed for nasopharyngeal cancers by Kan et al., they reported that a lower dose between 3% and 6% was obtained with AXB on critical organs compared to AAA [12] .

Chung and Mittauer showed that CGS was effective on dose estimation for head and neck treatments [13] [14] . Ong et al. reported that the 1.0 mm CGS performed a more accurate dose calculation than the 2.5 mm CGS in AAA calculations [15] .

In our dosimetric phantom study, we detected that there was a 3% compliance was between the depth dose measurement and Acuros AXB algorithm. However, we found there was a dose difference of 9.5% between the depth dose measurement and AAA algorithm.

In the phantom study with 6 MV photon rays by Bush et al., they showed that there was difference of 4.5% between AXB and Monte Carlo algorithms in the transition from air to tissue and this difference increased to 13% between AAA and Monte Carlo algorithms [16] . In parallel with this study, Kan et al. found that there was a difference of 3% between the measurement and AXB algorithm in the transition from air to tissue and this difference reached 10% with AAA algorithm (12). In the rando phantom study study developed for head and neck treatments by Han et al., they found the maximum difference between measurement and calculation as 4.6% for AAA and 3.6% for AXB [17] .

In a study comparing the treatment plans of deep inspriation condition and free-breathing breast patients by Fogliata et al., they showed that Anisotropic Analytical Algorithm calculated a 1.6% more dose in PTV than Acuros XB [18] .

Padmanaban et al. compared the AAA and AXB algorithms using 3D Conformal and Rapid Arc techniques in the treatment of osefagus cancers and they found that the AXB algorithm determined a low dose in PTV (0.5 - 1.3 Gy) according to AAA. They showed that the low dose in PTV obtained for AXB was not related to the technique used [19] .