Dose uncertainties associated with a set density override of unknown hip prosthetic composition

Abstract The dosimetric uncertainties associated with radiotherapy through hip prostheses while overriding the implant to a set density within the TPS has not yet been reported. In this study, the uncertainty in dose within a PTV resulting from this planning choice was investigated. A set of metallic hip prosthetics (stainless steel, titanium, and two different Co‐Cr‐Mo alloys) were CT scanned in a water bath. Within the TPS, the prosthetic pieces were overridden to densities between 3 and 10 g/cm3 and irradiated on a linear accelerator. Measured dose maps were compared to the TPS to determine which density was most appropriate to override each metal. This was shown to be in disagreement with the reported literature values of density which was attributed to the TPS dose calculation algorithm and total mass attenuation coefficient differences in water and metal. The dose difference was then calculated for a set density override of 6 g/cm3 in the TPS and used to estimate the dose uncertainty beyond the prosthesis. For beams passing through an implant, the dosimetric uncertainty in regions of the PTV may be as high as 10% if the implant composition remains unknown and a set density override is used. These results highlight limitations of such assumptions and the need for careful consideration by radiation oncologist, therapist, and physics staff.


| INTRODUCTION
Treatment of patients with single or bilateral hip replacements requires careful consideration due to the dose effects produced through radiation interactions with the metal prostheses. Much work has already been conducted in quantifying the dosimetric effect of metal prostheses and determining the relevant properties of materials. [1][2][3][4][5][6] A greater body of literature has been collected in AAPM's TG63 report. 7 TG-63 also provides clear recommendations on how to undertake accurate treatment of a patient with a hip prosthetic.
In the interest of accuracy, the report concerns itself with the scenario when the hip prosthetic material is already known, either in the patient records or measured through methods suggested and subsequently demonstrated in the literature. 8 Many centers, including Adelaide Radiotherapy Centre (ARC), do not ascertain the hip prosthetic material but instead override any hip prosthetic to a set density in the treatment planning system (TPS).
There have been many documented issues with the handling of prostheses by computed tomography (CT) including image artifacts and incorrect CT to density conversion. 9,10 Integer storage limitations through a phantom measurement with varying density inserts, ranging from lung density to titanium. The titanium insert receives the greatest CT number possible (2 12 À 1001 = 3095). Materials with density greater than titanium saturate CT number and are thus indistinguishable from each other on the image. Some 12-bit scanners are able to perform reconstructions at higher CT numbers through increased bin sizes although this method reduces fidelity. Alternatively, a centre might make improvements to dosimetric accuracy through acquisition of a 16-bit scanner, 10 although a 16-bit CT image dataset imported into a 12-bit TPS will have higher CT numbers truncated. Even if all CT information was importable, there still be may be issues with the TPS treatment of the high density regions. 9 Some centers have evaluated the accuracy of their dose calculation algorithm using the raw density values provided by the CT scanner without override, 9 whereas others choose to override the prosthetic to some predetermined densitywhich is the chief concern of this paper. While several authors have used Monte Carlo simulations to assess the accuracy of dosimetric calculations by the TPS in proximity to metallic implants with varying results, 12,13 to our best knowledge this paper is the first to investigate dose accuracy with realistic prosthesis geometries.
Because the prosthetic material remains unknown, there is uncertainty in the dose distribution from assuming a particular override value. Presently, there is insufficient data in the literature to calculate such uncertainties. Two experiments were conducted. First, it was determined which values of density override best correspond with measurement. These were compared to values obtained from the literature. Second, the uncertainty in dose was quantified from assuming a particular override value.  Table 1.

| MATERIALS AND METHODS
The prosthetic pieces were placed individually in a water bath and scanned on a Somatom â Emotion â 6 CT (Siemens AG, Munich, Germany) scanner at 100 kVp. The CT image datasets were then exported to Pinnacle 3â 9.8 (Koninklijke Philips N.V., Amsterdam, the Netherlands).
In the TPS, fields of 6 MV and 10 MV (respective TPR 20,10 values of 0.680 and 0.733) were added at a gantry angle of 0°. The isocenter was set to a point 4 cm below the prosthetic. This distance is greater than the buildup distances involved and is a good representation of the distance between the femoral head and the planned target volume (PTV) (a distance of 3 cm is common for prostate-bed patients). The streaking and image artifacts were removed by overriding the water bath to a density of 1 g/cm 3 . Contours were created for the prosthetic pieces as per their physical dimensions, to obviate issues with metal artifacts in the CT image set, particularly the concave shape of the Vitallium implant. Although vitally important to clinical implementation, the challenges of and solutions to metal artifact reduction in CT are well documented elsewhere. 14,15 The prosthetic pieces were each overridden to a series of densities ranging from 3 to 10 g/cm 3  The MapCheck â device was used as the higher resolution of film was not necessary for the particular purpose. Through a series of open field measurements the MapCheck â has been cross-calibrated against an ion chamber whose calibration is traceable to a primary standards laboratory and it is routinely used for absolute dose measurements of modulated treatment plans. MapCheck measurements were further supported through measurement of absolute dose using a calibrated RAZOR TM Chamber (IBA Dosimetry GmbH, Schwarzenbruck, Germany) in a solid water slab. Measured dose at a point behind the metallic implant was compared to TPS calculations using density overrides from 3 to 10 g/ cm 3 in order to find the most optimal, or effective, density override.

| RESULTS AND DISCUSSION
An example of a MapCheck measured profile and TPS export comparison is shown in Fig. 3 and a plot of gamma pass rates with TPS density override is presented in Fig. 4.   This study observed that while titanium had effective density overrides that were within uncertainty of the reported values, stainless steel (and to a lesser extent, Cr-Co-Mo) required a lower density override in order to calculate dose accurately. This indicated that the Pinnacle â CCC algorithm is more likely to underdose as physical density increases.
Like other convolution algorithms, Pinnacle â CCC considers different density media to be density-scaled water. If the familiar total mass attenuation coefficient plot is considered comparing water and lead, the coefficients for water are known to keep decreasing for energies less than 100 MeV. 16 However, due to the strong Z 2 dependence of the pair production interaction, the total mass attenuation coefficient for cobalt begins to increase beyond 5 MV [the pair production atomic attenuation coefficients for metals at 10 MV are indistinguishable from 6 MV nominal energies 17 ]. So while Pinnacle â will treat an implant as "super dense water" with the same attenuation properties, in reality the attenuation will be different due to pair production.
The underdosing observed may be due to the total mass attenuation coefficient actually being greater for water than for metal at the effective beam energies concerned. This is represented in a plot of tabulated NIST data below 18 (Fig. 5). With an atomic number of 27, cobalt is a good surrogate for both stainless steel and Co-Cr-Mo (see Table 1). Then for the energies utilized, the total mass attenuation coefficient for water is around 15% greater than for Cobalt.
Since Pinnacle â treats everything as density-scaled water, this is consistent with the results that the TPS may underdose behind higher atomic number alloys. This result is consistent with predictions from the Monte Carlo simulations performed by Kairn et al. 12 Given an ideal scenario where a patient presents with a prosthetic of known material, the appropriate density override can be selected based on material and beam energy. For situations where the prosthetic composition remains unknown, a generic override density can be used with the aim to reduce the uncertainty in the dose calculation. In order to minimize the uncertainty for any one material, a generic density of 6 g/cm 3 was chosen as it represents the midpoint of the maximum and minimum effective override densities. The dose difference in the dose shadow was assessed for this case by dose map comparison with TPS exported profiles with a 6 g/cm 3 override for the MapCheck and dose point comparison for the RAZOR. This is shown in Fig. 6. The dose differences and uncertainty, has been shown in Table 3.
An override of 6 g/cm 3 is denser than the most accurate effective override for titanium so the TPS will obviously underestimate dose. Similarly, 6 g/cm 3 is less dense than the optimal overrides for stainless steel and the Co-Cr-Mo alloys so the TPS will overestimate dose. The dose error is not expected to be constant throughout the PTV as it will change slightly with distance from the implant. 9 However, since the distance of 4 cm represents a point inside or close to the edge of the PTV it is a dose uncertainty of potential significance.
Thus given a patient with an unknown hip prosthesis material with beams passing through the implant, the uncertainty in dose calculation at regions within the PTV may range between +7% and À10% for 6 MV and between +7% an À9% for 10 MV. These uncertainties T A B L E 2 Effective override physical densities for different prosthetic materials at different beam energies in Pinnacle 3â 9.8. Uncertainties in effective density come from the 2.2% calibration uncertainty of the RAZOR chamber and the choice of sampling resolution of density overrides for the MapCheck. could be clinically significant 19 and steps should be taken by radiotherapy departments to minimize the impact of these uncertainties.

Alloy
It is recommended to utilize a value of 6 g/cm 3 for overriding hip prostheses within Pinnacle for the 6 and 10 MV beams as this value is a good compromise between the "effective" densities of Ti, stainless steel and Co-Cr-Mo. The very small difference in maximum dosimetric uncertainty between 6 and 10 MV as well as the very similar mean "effective" densities (Table 2) support a value of 6 g/cm 3 . This recommendation is made in the absence of presentation rates of the different implant materials. If this information was available, one may elect to push the value higher (toward stainless steel) or lower (toward Ti) to minimize the uncertainty for the most common implants.

| CONCLUSION
A set of metallic hip replacement pieces were used to determine the dosimetric uncertainty associated with prostate planning protocols that involve a set override value for implants. An effective override density was found for each case that best matched the measured dose map. The dose difference was then calculated for the case where a set density override of 6 g/cm 3 was chosen. PTV dose uncertainty in the dose shadow was found to be as much as 10%, highlighting the need for careful planning and dose consideration when allowing beams to pass through metallic implants. In instances where the composition of the metallic implant remains unknown, we recommend the use of a density override value of 6 g/cm 3 .

ACKNOWLEDGMENTS
Thanks go to Jason Morton for the hip prosthetics.

CONFLI CT OF INTEREST
The authors declare no conflict of interest.
T A B L E 3 Greatest dose differences from MapCheck and RAZOR when an override of 6 g/cm 3 is chosen. MapCheck is able to show greater dose differences because it samples many more points than the RAZOR.