Technical Note: Monte Carlo calculations of the AAPM TG‐43 brachytherapy dosimetry parameters for a new titanium‐encapsulated Yb‐169 source

Abstract Due to a number of distinct advantages resulting from the relatively low energy gamma ray spectrum of Yb‐169, various designs of Yb‐169 sources have been developed over the years for brachytherapy applications. Lately, Yb‐169 has also been suggested as an effective and practical radioisotope option for a novel radiation treatment approach often known as gold nanoparticle‐aided radiation therapy (GNRT). In a recently published study, the current investigators used the Monte Carlo N‐Particle Version 5 (MCNP5) code to design a novel titanium‐encapsulated Yb‐169 source optimized for GNRT applications. In this study, the original MC source model was modified to accurately match the specifications of the manufactured Yb‐169 source. The modified MC model was then used to obtain a complete set of the AAPM TG‐43 parameters for the new titanium‐encapsulated Yb‐169 source. The MC‐calculated dose rate constant for this titanium‐encapsulated Yb‐169 source was 1.19 ± 0.03 cGy·h−1·U−1, indicating no significant change from the values reported for stainless steel‐encapsulated Yb‐169 sources. The source anisotropy and radial dose function for the new source were also found similar to those reported for the stainless steel‐encapsulated Yb‐169 sources. The current results suggest that the use of titanium, instead of stainless steel, to encapsulate the Yb‐169 core would not lead to any major change in the dosimetric characteristics of the Yb‐169 source. The results also show that the titanium encapsulation of the Yb‐169 source could be accomplished while meeting the design goals as described in the current investigators’ published MC optimization study for GNRT applications.


| INTRODUCTION
Over the years, various designs of Yb-169 sources have been described in the published literature. [1][2][3][4][5][6][7][8][9][10][11][12][13] As summarized previously, 13 the relatively low energy photon spectrum of Yb-169 would provide multiple advantages including the possibility of in vivo shielding of essential organs and tissues via shielded applicator (e.g., using 0.5-1.0 mm thick lead foils in the applicator system to reduce bladder and rectal doses in gynecological malignancies 3 ), reduced radiation exposure to personnel, simplified high dose rate (HDR) room shielding, streamlined after-loading units, and overall reduced costs. [1][2][3][4]7,[9][10][11][12] Additionally, Yb-169 has been suggested as an almost ideal radioisotope for the brachytherapy implementation of so-called gold nanoparticle-aided radiation therapy (GNRT), 13,14 because its gamma ray spectrum (average energy of 93 keV just above the K-absorption edge of gold) can lead to more advantageous (e.g., larger or/and more uniform) dose enhancement characteristics with gold nanoparticles (GNPs) than other radioisotopes being used for brachytherapy purposes (e.g., Ir-192, I-125, Pd-103, etc.). To follow-up on this suggestion, we designed a new titanium-encapsulated Yb-169 source optimized for GNRT applications, 13 based on our Monte Carlo (MC) investigation of the effects of the Yb-169 source encapsulation on the photon spectra, and more importantly the secondary electron spectra that are directly responsible for the dose enhancement characteristics for a given concentration of GNPs. After our initial MC source design study, 13 we proceeded to produce novel titanium-encapsulated Yb-169 sources in collaboration with a source manufacturer (Source Production & Equipment Co., Inc., St. Rose, LA, USA).
In the current MC study, we determined a complete set of brachytherapy dosimetry parameters for the aforementioned titanium-encapsulated Yb-169 source model, following the American Association of Physicists in Medicine (AAPM) Task Group 43 (TG-43) formalism. 15,16 The key results from the current investigation were compared with those from the previous investigations of various Yb-169 source models, in light of GNRT as well as general brachytherapy applications.

2.A | Source design
As described in our previous publication, 13 the new Yb-169 source optimized for GNRT applications was designed similar to a previously investigated HDR Yb-169 source, 7,12,17 with the exception of the encapsulation material (i.e., titanium vs. stainless steel). While its specific design was slightly different from that described in our previous publication, 13 the new Yb-169 source manufactured from this investigation maintained the key features of our original source design, most notably the titanium encapsulation as compared to a more conventional stainless steel encapsulation. As depicted in Fig. 1, the new Yb-169 seed source had an active Ytterbium core (3.5 mm in length, 0.6 mm in diameter, and 7.0 mg mm À3 in density) encapsulated by American Society for Testing and Materials (ASTM) grade 2 titanium (4.54 mg mm À3 in density). This source had an air gap between the active Ytterbium core and titanium encapsulation, which was included in our MC model ( Fig. 1) following the specifications provided by the source manufacturer. It should be noted that, while intended for eventual HDR applications, Yb-169 sources produced during the current investigation had their activities on the order of 10 mCi for the ease of handling and testing.

2.B | Monte Carlo calculations of TG-43 parameters
The MC radiation transport code, Monte Carlo N-Particle Version 5 (MCNP5), was used to compute all the necessary quantities to characterize the Yb-169 source as defined by TG-43. The source and encapsulation geometry were modeled exactly as shown in Fig. 1.
The active region of the source was modeled with a uniform activity distribution. Table 1 shows the Yb-169 photon spectrum used for the current MC study excluding all photons with intensity lower than 0.1% and energy lower than 5 keV as specified in TG-43. 15 The air-kerma rate was then calculated from K MC and converted to units of cGy Á mCi À1 Á h À1 by: where I c is the total number of photons per disintegration of the source. The air-kerma rate may also be written in terms of the unit U (cGy Á cm 2 Á h À1 ) as specified in TG-43. 15,16 The dose distribution surrounding the source was computed by simulating the source centered in a spherical water phantom with a radius of 50 cm, an appropriate size to approximate full-scatter conditions of a semi-infinite water phantom. An array of tally regions was modeled to collect the dose at radial distances of 0.5 cm and 1- were developed by Luxton et al. 18 and compare the factor  The geometry function G L r; h ð Þ (Table 2) represents the effective inverse-square correction based on the line-source approximation.
The function shows it effectively becomes point sources for r ! 5cm: The radial dose functions are shown in Table 3 and the fit to 5 th order polynomial as specified in the updated report of TG-43 15 is shown in Fig. 2. Table 4 presents the values of 2D anisotropy function F r; h ð Þ from the current study. Figure 3 shows a comparison of the source anisotropy at r = 1.0 cm between the current titaniumencapsulated Yb-169 source and a previously described stainless steel encapsulated Yb-169 source. 7

| DISCUSSION
In a previous study, 13 we showed that titanium-encapsulation of the Yb-169 core would allow more low energy photon being transmitted through the source filter and, as a result, lead to an increased dose enhancement during GNRT, compared to stainless steel-encapsulation. Additionally, we pointed out that the increased structural integrity of titanium over stainless steel might also provide the possibility to shrink the size of the source encapsulation, thereby further improving the dose enhancement characteristics of the source. 13

CONF LICT OF I NTEREST
No conflict of interest to declare.

R E F E R E N C E S
F I G . 3. Comparison of the source anisotropy data at r = 1.0 cm, F r ¼ 1:0 cm; h ð Þ , between the current titanium encapsulated Yb-169 source and a previously reported stainless steel encapsulated Yb-169 source. 7