Evaluation of dose calculation accuracy of treatment planning systems at hip prosthesis interfaces

Abstract There are an increasing number of radiation therapy patients with hip prosthesis. The common method of minimizing treatment planning inaccuracies is to avoid radiation beams to transit through the prosthesis. However, the beams often exit through them, especially when the patient has a double‐prosthesis. Modern treatment planning systems employ algorithms with improved dose calculation accuracies but even these algorithms may not predict the dose accurately at high atomic number interfaces. The current study evaluates the dose calculation accuracy of three common dose calculation algorithms employed in two commercial treatment planning systems. A hip prosthesis was molded inside a cylindrical phantom and the dose at several points within the phantom at the interface with prosthesis was measured using thermoluminescent dosimeters. The measured doses were then compared to the predicted ones by the planning systems. The results of the study indicate all three algorithms underestimate the dose at the prosthesis interface, albeit to varying degrees, and for both low‐ and high‐energy x rays. The measured doses are higher than calculated ones by 5–22% for Pinnacle Collapsed Cone Convolution algorithm, 2–23% for Eclipse Acuros XB, and 6–25% for Eclipse Analytical Anisotropic Algorithm. There are generally better agreements for AXB algorithm and the worst results are for the AAA.

of the bone, and potential failure of the prosthetic device. Avoiding these complications may become a controlling factor in planning treatments near high-z materials.
The effect of high-z materials in external beam radiation therapy has been studied extensively. Das 3 studied the backscatter dose at the interface of materials ranging from bone to lead. By comparing the dose at a reference depth in a homogeneous polystyrene block and that at the same depth with the introduction of a slab of high-z material, backscatter dose factors (BSDFs) were calculated. The BSDF, as determined by Das, for common prosthetic device materials such as stainless steel, titanium, or cobalt-chromium-molybdenum, fall somewhere between 1.2 and 1.35. Erlanson 4 studied the dose enhancement in the periphery of hip prosthesis and reported a dose enhancement of 25% at the vicinity of prosthesis.
Even though the common practice is to avoid the beams passing through high-z prosthesis, this may not be possible in all situations.
Overcoming the shadow effects of placing the prosthesis between the radiation source and the intended treatment volume may be problematic. Williams 5 proposed a method to overcome the shadow effects by using an initial field and adding an additional boost field in the area where the prosthesis was located to deliver the intended dose to the treatment site. In addition, the treatment beams often exit through the prosthesis.
Metallic implants also present a challenge in imaging the treatment volume because they lead to poor quality CT scans. High-z materials absorb and harden the beam which leads to streaking artifacts when the image is reconstructed. Poor quality CT images can lead to degraded diagnosis and identification of treatment planning regions of interest, and incorrect assignment of density for dose calculations. The reduction of treatment planning errors from reconstruction artifacts was studied by Bazalova. 6 Aubin 1 used megavoltage CT to complement standard CT images. Both sets of images were acquired and then co-registered. Target volumes that were not readily visualized on the standard CT were able to be differentiated on the MV CT.
Whether the enhanced dose at and near the surface of prosthesis is accurately predicted by the modern treatment planning systems was the goal of this study. There have been previous studies on the accuracy of various treatment planning algorithms in the vicinity of prosthesis. Ding 7 evaluated the accuracy of a correction-based dose calculation algorithm in predicting the dose in the vicinity of hip prosthesis by comparing it with Monte Carlo (MC) and concluded that the algorithm underestimated the attenuation by the prosthesis. Roberts 8 evaluated a pencil beam algorithm's accuracy when the beam passes through a prosthesis using measurements and pointed to an 11-15% overestimation of the dose by the planning system beyond the prosthesis. Lin 9 evaluated the accuracy of a convolutionbased algorithm in predicting the dose through a prosthesis in a simple geometry by comparison with MC and concluded that it underestimates the dose upstream and downstream from the prosthesis.
Keall 10 compared MC, superposition, and pencil beam algorithms in the presence of hip prosthesis, and concluded that all of them fail in predicting backscattered dose from the prosthesis. More recently, Ojala 11 evaluated the accuracy of Acuros XB algorithm in predicting the dose when the beam traverses a prosthesis using MC and measurements and showed a small underestimation of the dose downstream from the implant, but a larger one at the interface.
These studies often used highly reproducible volumes easily defined with good geometries and a single field to evaluate the effect of the high-z material on dose calculation, often distal from the prosthesis. The current study focuses on two modern treatment planning systems (three dose calculation algorithms) and their ability to calculate accurate doses near the surface of a prosthetic device with multiple fields in a geometry representative of clinical cases.
Three megavoltage beam energies were used in this study.

| METHODS
A Johnson and Johnson (DePuy) Ultima cobalt-chromium-molybdenum (Co-Cr-Mo) artificial hip prosthesis was used for this study. The AAPM TG 63 report and Hazuka 12 detail the physical properties of several common hip prostheses. The density of Co-Cr-Mo is approximately 7.9 g/cm 3 with an electron density of 6.79-6.9 relative to that of water and an effective atomic number of 27.6.
A cylindrical phantom, shown in Fig. 1, was constructed of AdTech LUC4105 casting urethane. A casting urethane was chosen for its low cost and ease of molding. The initial density of the casting urethane was 1.73 g/cm 3 . The density was lowered to near that of soft tissue by the introduction of hollow lightweight glass beads. TLDs. The TLDs were not annealed at a low temperature prior to analysis. Instead, the glow peaks that decay quickly were eliminated The plans were delivered to the phantom using an Elekta Synergy linear accelerator (Elekta). The TLDs were positioned prior to delivery in the phantom and promptly removed following irradiation.
Each plan was delivered to the phantom three times. As with the determination of calibration factors, the TLDs were read approximately 36 h post irradiation.
The plans were also delivered to phantom with the OSLDs in place to compare measured and calculated doses at points far from interface. In addition, a mixed energy (6, 10, 18 MV) AP/PA plan was also generated and delivered to the phantom with the OSLDs in place. This plan served as a control one as the beams did not traverse the prosthesis. The OSLDs were read after approximately 30 min using a MicroStar InLight reader (Landauer). Due to dose dependence of OSLDs, three sets of calibration curves, a low dose, high dose, and an ultra high one, were created to convert the emitted light to dose.

| RESULTS
The calculated and measured doses and their percentage differences are shown in Tables 1-3     The size of the implant should not have any effect on backscattered radiation but will, of course, affect the transmission. So the size may affect the magnitude of the dose at points downstream from the prosthesis but does not affect the underestimation of the dose due to backscatter. Should the implant be at shallow depths, which is unlikely for hip implants, the results may vary because of the uncertainty of dose calculations in the buildup region.

| CONCLUSION S
The Pinnacle 3 treatment planning system and its CCC dose calculation algorithm, as well as Eclipse treatment planning system and its AAA and AXB algorithms were evaluated for their ability to predict the dose at the surface of a hip prosthesis within the treatment field.
The results indicate that there is a consistent underprediction of the dose at the interface, irrespective of the energy and algorithm used.
The dose enhancement at the interface could lead to additional complications for patients with high-z hip implants including premature failure of the prosthesis from bone necrosis or demineralization.
With greater understanding of the dose distribution, treatment planners can make more informed decisions regarding high-density prosthetic materials in the treatment field and potentially improve longterm patient outcomes.

CONF LICT OF I NTEREST
The authors have no conflict of interest to report.