Clinical implementation and evaluation of the Acuros dose calculation algorithm

Abstract Purpose The main aim of this study is to validate the Acuros XB dose calculation algorithm for a Varian Clinac iX linac in our clinics, and subsequently compare it with the wildely used AAA algorithm. Methods and materials The source models for both Acuros XB and AAA were configured by importing the same measured beam data into Eclipse treatment planning system. Both algorithms were validated by comparing calculated dose with measured dose on a homogeneous water phantom for field sizes ranging from 6 cm × 6 cm to 40 cm × 40 cm. Central axis and off‐axis points with different depths were chosen for the comparison. In addition, the accuracy of Acuros was evaluated for wedge fields with wedge angles from 15 to 60°. Similarly, variable field sizes for an inhomogeneous phantom were chosen to validate the Acuros algorithm. In addition, doses calculated by Acuros and AAA at the center of lung equivalent tissue from three different VMAT plans were compared to the ion chamber measured doses in QUASAR phantom, and the calculated dose distributions by the two algorithms and their differences on patients were compared. Computation time on VMAT plans was also evaluated for Acuros and AAA. Differences between dose‐to‐water (calculated by AAA and Acuros XB) and dose‐to‐medium (calculated by Acuros XB) on patient plans were compared and evaluated. Results For open 6 MV photon beams on the homogeneous water phantom, both Acuros XB and AAA calculations were within 1% of measurements. For 23 MV photon beams, the calculated doses were within 1.5% of measured doses for Acuros XB and 2% for AAA. Testing on the inhomogeneous phantom demonstrated that AAA overestimated doses by up to 8.96% at a point close to lung/solid water interface, while Acuros XB reduced that to 1.64%. The test on QUASAR phantom showed that Acuros achieved better agreement in lung equivalent tissue while AAA underestimated dose for all VMAT plans by up to 2.7%. Acuros XB computation time was about three times faster than AAA for VMAT plans, and computation time for other plans will be discussed at the end. Maximum difference between dose calculated by AAA and dose‐to‐medium by Acuros XB (Acuros_Dm,m) was 4.3% on patient plans at the isocenter, and maximum difference between D100 calculated by AAA and by Acuros_Dm,m was 11.3%. When calculating the maximum dose to spinal cord on patient plans, differences between dose calculated by AAA and Acuros_Dm,m were more than 3%. Conclusion Compared with AAA, Acuros XB improves accuracy in the presence of inhomogeneity, and also significantly reduces computation time for VMAT plans. Dose differences between AAA and Acuros_Dw,m were generally less than the dose differences between AAA and Acuros_Dm,m. Clinical practitioners should consider making Acuros XB available in clinics, however, further investigation and clarification is needed about which dose reporting mode (dose‐to‐water or dose‐to‐medium) should be used in clinics.


| INTRODUCTION
Intensity-modulated radiation therapy (IMRT) and volumetric-modulated arc therapy (VMAT) can produce highly conformal radiation dose distributions and enhance treatment localization, but these complex treatment techniques also place higher demands on dose calculation algorithms in terms of both accuracy and computation speed. 1,2 With the increasing popularity of IMRT and VMAT techniques in clinics, accuracy in treatment planning systems (TPSs) has always been a concern in modern radiotherapy. To address that concern, analytical anisotropic algorithm (AAA) was implemented in the Eclipse (Varian Medical Systems) treatment planning system to replace the pencil beam (PBS) for the calculation of dose distributions for photon beams.
The first characterization of the AAA algorithm in water was published by Fogliata et al. 3 in their investigation of the configuration module of the AAA algorithm, they compared dose calculated by AAA with measurements and reported an accuracy of 1%-2% for output factors of open and wedged beams, respectively, a 1%, 1 mm average accuracy in the calculated depth dose curves and an accuracy within 1% for the central region of the profiles. Esch et al. 4 reported that AAA improves the accuracy of dose calculations compared to PBS and can achieve 5% agreement with measurements in thoracic phantom.
Even though with the significant improvement, AAA still lacks the accuracy of Monte-Carlo dose calculation algorithm which is often accepted as the golden standard. Over the past years, it has become a common belief that precise dose calculation will necessitate the use of Monte-Carlo methods to take correctly into account the electron transport governing the dose deposition process. However, Monte-Carlo methods are presently still too time consuming to be used in routine clinical environments. Hence, the impetus for providing a fast and accurate alternative to the golden standard of Monte-Carlo-based calculations, especially when inhomogeneous tissues are involved, resulted in the exploration of new strategies.
One such strategy is the application to external beam radiotherapy of a deterministic solution of the linear Boltzmann transport equation (LBTE). A benefit of the deterministic radiation transport solutions of the LBTE compared to Monte Carlo simulations is the lack of statistical noise in the calculated dose. An algorithm using this technique, born on the prototype solver called Attila, 5 was first used in the radiotherapy environment for dose calculation in brachytherapy treatments giving accurate radiation transport solutions for implanted radioactive sources. 5,6 Based on this prototype, a dose calculation algorithm for external photon beams has been developed on the same methods and implemented in the Varian Eclipse external beam treatment planning system (Varian Medical Systems, Palo Alto, CA, USA). This new algorithm is the Acuros XB Advanced Dose Calculation algorithm (Acuros XB) and was first benchmarked by Fogliata et al. 7 in water, and further validated by Han et al. 8  All of the studies show the advantage of Acuros XB compared with AAA in terms of accuracy. The prior studies warrant further validation and exploration of the advantages of using Acuros in clinics.
Hence, the purpose of this study was to present implementation of Acuros XB for a Varian Clinac iX linac, and further validate Acuros XB by comparing it with measurements and the AAA algorithm using homogeneous and inhomogeneous phantoms. Dose distribution differences in VMAT plans on phantoms as well as on patients were also compared. The differences between doses calculated by AAA and Acuros dose-to-water and dose-to-medium on patient plans were also compared Before presenting the methods and materials, it would be helpful to first give a short description of the algorithms used in this study.
The two algorithms implemented in the Eclipse treatment planning system for all dose calculations in this study were the Acuros XB version 11 and the AAA version 11. The AAA is a kernel based convolution/superposition method and was originally developed to improve the dose calculation accuracy in heterogeneous media. The kernels, representing the energy transport and dose deposition of secondary particles stemming from a point irradiation, are not usually accessible through measurements but are very simple to calculate by use of Monte Carlo particle transport codes. The AAA corrects for heterogeneities by performing density scaling of Monte Carlo derived kernel for a homogeneous medium such as water. The common approach is to scale all dose fractions of a point kernel h q0 s; r ð Þ, calculated for a homogeneous medium of mass density q 0 , by the mean electron density between the point s of energy release and the point r of energy deposition, that is, in which q rel is the relative number of electrons per volume as compared with the reference medium (Tillikainen et al. 10 ).
Similar to the Monte Carlo method, Acuros XB also belongs to one of the approaches of obtaining open form solution to the LBTE.
In general, Monte Carlo method refers to the method in which random sampling of known probability distribution is used to solve a mathematical or physical problem. In the case of calculating dose, instead of directly solving the LBTE, Monte Carlo method indirectly obtains the solution by following the histories of a large number of particle transports through successive random samplings in media.
The random sampling of known probability distribution function inevitably produces stochastic uncertainties when insufficient number of particle histories are followed. To achieve a certain level of accuracy, a huge amount of particle histories need to be sampled,  to 40 9 40 cm 2 on the same water tank and the measurements were compared with dose calculated by AAA and Acuros.
The dose calculation grid resolution can be set by users from 1 to 5 mm for AAA and 1 to 3 mm for Acuros XB during the treatment planning. In this study, the dose grid size was set at 2.5 mm which is typically used in our clinics.

2.B | Verification phantoms
All measurements on homogeneous phantom were carried out using    Historically, radiotherapy dose measurements and calculations have been performed in, or specified in terms of the absorbed doseto-water (D w,m ). Like Monte Carlo dose calculation, Acuros provides two dose reporting mode dose-to-water (Acuros_D w,m ) and dose-tomedium (Acuros_D m,m ). Whether one should eventually use Acur-os_D m,m in place of Acuros_D w,m in clinical prescriptions is an interesting research topic [12][13][14] . Since AAA has been used in clinics for years, hence, to make a correct transition from AAA to either Acur-os_D w,m or Acuros_D m,m , it is important to evaluate the differences between dose calculated by AAA and Acuros_D w,m (and Acuros_D m, m ). Therefore, three lung VMAT plans were chosen, and, for each of the VMAT plans, doses calculated by AAA and Acuros_D w,m (Acur-os_D m,m ) were compared. The three plans has been approved and 3 | RESULTS

3.A | Results on homogeneous phantom
Measured and calculated (AAA and Acuros XB) doses for 6X photon beams of variable field sizes are reported in Table 2. Relative standard errors (RSE) which is defined as (std/mean) of measurements * 100 are also listed in the For both Acuros XB and AAA, the differences between calculations and measurements were within 3% and the differences were larger for higher energy beams.

3.B | Results on inhomogeneous phantom
Tables 6 and 7 present percentage differences between calculated (AAA and Acuros XB) and measured doses on the inhomogeneous phantom. "test 3" was not measured for the asymmetrical field T A B L E 2 Percentage dose differences between calculations (Acuros_D w,m and AAA) and measurements for 6MV photon beams on homogeneous phantom. | 199 (8 9 15) since it is outside the field. Also "test 5" was not measured for wedged fields since it is very similar to "test 4" and "test 6".
Compared with AAA, Acuros XB significantly improved the dose calculation accuracy for the points located beyond (downstream) the inhomogeneous region, that is, points "test 4", "test 5" and "test 6".
For most of them, doses calculated by Acuros XB were within 3% of measurements while the maximum difference between measurement and calculation by AAA was more than 8%.
T A B L E 3 Percentage dose differences between calculations (Acuros_D w,m and AAA) and measurements for 23 MV photon beams on homogeneous phantom.   Acuros and AAA and their differences (Acuros -AAA) on the QUA-SAR phantom are shown side-by-side in Fig. 3. Most of the differences between AAA and Acuros XB were between 1 and 2.5 percent and they were mainly in low density region. Also when calculating the differences, dose calculated by AAA was subtracted from the dose calculated by Acuros XB (Acuros XB dose -AAA dose). The differences were mostly in the lung insert region, and this implied that dose calculated by Acuros XB was higher than the dose calculated by AAA in this region and it is consistent with what we observed in Table 8.  Table 9 shows percentage differences between doses calculated by AAA and doses calculated by Acuros (Acuros_D w,m and Acuros_D m,m , respectively) at the isocenter. The isocenters were all located inside the PTV. The differences between doses calculated by AAA and Acuros_D w,m were less than 2%, but the maximum differences between AAA dose and Acuros_D m,m was 4.3%.
Similar to Table 9, Table 10 shows percentage differences between maximum spinal cord dose calculated by AAA and Acur-os_D w,m (Acuros_D m,m ). In general the differences between AAA dose and Acuros_D w,m were less than or equal to 1%, but the differences between AAA dose and Acuros_D m,m for the spinal cord were more than 3%. Figure 5 compares the DVHs' differences for GTVs of the three lung patients. For all three plans, the differences between AAA and Acuros_D w,m is smaller than the differences between AAA and Acuros_D m,m . Another dosimetric criterion often used to evaluate the plan quality is D 100 of GTV, and normally, D 100 should be no less than prescribed dose in clinics. Table 11 shows the D 100 calculated by AAA, Acuros_D w,m and Acuros_D m,m for the same plan.
The differences in D 100 between AAA and Acuros_D w,m were less than 2%, but the differences between AAA and Acuros_D m,m were more than 3% and the maximum difference was 11.3%. Dose distributions calculated by AAA and Acuros_D w,m (Acuros_D m,m ) along with GTVs (PTV for patient 3) were shown side-by-side in Figs.
6-8. By visual inspection, the differences between AAA and Acur-os_D m,m was larger than the differences between AAA and Acur-os_D w,m .

| DISCUSSION
In this work, the implementation of a new photon dose calculation algorithm, Acuros XB, was described and its accuracy was validated against measurements and compared with our clinically used AAA  cases. Acuros XB and AAA calculations were also compared on patient CTs, and the differences indicate that AAA calculations were lower in lung region and higher in normal tissue (Fig. 4)  to evaluate the quality of a plan. Generally, D 100 of GTV should be no less than prescribed dose. Table 11 shows that D 100 calculated by AAA for the three VMAT plans all satisfied this criterion, but when the same plans were calculated by Acuros_D m,m , all three plans failed. For patient 2, the difference of D 100 was 11.3% between the plan calculated by AAA and the plan calculated by Acuros_D m,m . If Acuros_D m,m was used, then the plans for patient 1 and 2 should be rejected and plan for patient 3 was on the borderline. By comparing the DVHs (Fig. 5) and visually inspecting the dose distributions of Gladstone 14 , etc. recommends that, for MC or grid-based Boltzmann solver (GBBS) algorithms such as Acuros XB, conversion of D m,m to D w,m should be avoided, rather, D m,m computed inherently by these algorithms should be reported. Currently, our cancer center is participating NRG clinical trials and our AAA algorithm has been validated by Radiological Physics Center (RPC) and is used in clinics.
Due to the large inconsistency between AAA and Acuros_D m,m , we decided to continue to use AAA until the root cause of the discrepancies are found. As a first step, we collaborated with a physicists from VARIAN and performed preliminary examinations, and tentatively concluded that the discrepancies were due to different type of tissue present in lung patients. However, to completely confirm this, more extensive tests are needed. To make such tests more robust and thorough, it would be better for us to collaborate with other institutions and VARIAN to perform such study with the goal of understanding whether the discrepancies seen in this study are inherent to Acuros XB and Monte Carlo. One particular test would be to commission Monte Carlo on our Clinic iX machine and use it to calculate the three plans and see whether Monte Carlo will report similar differences between AAA dose and dose-to-medium calculated by Monte Carlo. We leave these studies to our future work.

| CONCLUSION
In general, the accuracy of Acuros XB photon dose calculation algorithm was found to be equivalent to that of AAA on homogeneous phantom and better than AAA on inhomogeneous phantom. It also achieves better agreement with measurements than AAA for clinically used VMAT plans in low density region on the QUASAR phantom. By comparing the point doses, DVHs of GTV and dose distributions calculated by AAA, Acuros_D w,m and Acuros_D m,m , we can conclude that the differences between AAA dose and Acur-os_D w,m is smaller than the differences between AAA dose and Acuros_D m,m . In some cases, the differences are clinically significant, and hence, further clarification and guidance is needed before switching from AAA to Acuros_D m,m in clinics.