Implant Sciences Corporation, HDR Yb169, 4140

Source Description:

Dimensions for the HDR 4140 source are taken from the study by Medich et al ¹. The 4140 source consists of a 3.60 mm long ytterbium oxide core (6.9 g/cm³) with a diameter of 0.73 mm enclosed in a stainless steel capsule (assumed to be AISI 306 with a density of 7.80 g/cm³). The encapsulation includes a 0.50 mm thick end weld composed of a 0.45 mm radius hemisphere with its center shifted 1.95 mm from the center of the source and attached to a 0.050 mm thick solid cylinder. The end weld is attached to a 3.70 mm long hollow cylindrical section that has inside and outside diameters of 0.73 mm and 0.90 mm, respectively. The hollow portion of the encapsulation is attached to a solid cylindrical section that is 0.60 mm thick and 0.90 mm in diameter. The empty space between the end weld and the source element is assumed to be filled with air. The cable is assumed to be a solid cylinder of AISI 306 stainless steel with a density of 6.90 g/cm³, a diameter of 0.90 mm and a length of 1.95 mm. The active length of the source is 3.6 mm. The mean photon energy calculated on the surface of the source is 117.07 keV with statistical uncertainties < 0.002%.

Dose Rate Constant - Λ :

Dose rate constants, Λ , are calculated by dividing the dose to water per history in a (0.1 mm)³ voxel centered on the reference position, (1 cm, Π/2), in a 80x80x80 cm³ water phantom, by the air-kerma strength per history factor (scored in vacuo). Air kerma per history is always calculated using a tracklength estimator in a 10x10x0.05 cm³ air voxel located in vacuo on the transverse axis 100 cm away from the source and then corrected (k_r² = 1.00217) for the lateral and thickness dimensions of the scoring voxel to give the air kerma per history on the central axis at a point 100 cm from the source’s mid-point as described in our previous study ^2, 3. Low-energy photons emitted from the source encapsulation are suppressed in the air-kerma calculations by discarding all photons with energy less than 10 keV (i.e. PCUT set to 10 keV in EGSnrc). egs_brachy uncertainties are only statistical uncertainties (k=1).   

Note: decreasing  the PCUT from the recommended 10 keV to 1 keV increases the value of the air-kerma strength per history factor  by 2.8% and decreases the dose-rate constant to 1.1541(4), i.e., 2.8% lower.

Note: DRC calculated using electron transport in phantom is 1.1874 cGy h^-1 U^-1 which is about 0.03%  higher than the value of  1.1871 cGy h^-1 U^-1 without electron transport, i.e., the same well within statistical uncertainties.

Radial dose function - g(r):

The radial dose function, g(r), is calculated using both line and point source geometry functions and tabulated at 36 different radial distances ranging from 0.2 cm to 20 cm. 

 Note: There is no significant difference (<0.1%) between the g(r) with and without electron transport for radii >0.1 cm although can differ considerably very close to the source.

Anisotropy function - F(r,θ):

Anisotropy functions are calculated using the line source approximation and tabulated at 13 radii from 0.25 cm to 20 cm and 47 unique polar angles with a resolution of 5^° or better. The anisotropy factor, φ_an (r), was calculated by integrating the solid angle weighted dose rate over 0^° ≤ ϑ ≤ 180^°.

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F(1.00,θ)	F(5.00,θ)
F(10.00,θ)

Along-Away Dose Data:

Along-away dose data are tabulated at 16 away distances from 0 cm to 20 cm and 29 along points from -20 cm to 20 cm. Doses are normalized to S_K,  the air-kerma strength.

Primary and Scatter Separated (PSS) Dose Data: D_ii (r,θ):

Primary and Scatter Separated (PSS) dose data are tabulated at 12 radii from 0.3 cm to 20 cm and 47 unique polar angles with a resolution of 5° or better. High resolution (Δr = 1 mm, ΔΘ = 1°) primary scatter dose data are also available in .csv files. For the purposes of these calculations, any photon escaping the source encapsulation is considered a primary. Only photons which scatter within the phantom are counted in the scatter tallies. Doses are normalized to the total photon energy escaping the encapsulation.  The "ii" subscript labeled in the D_ii(r, θ) represent the total scatter as D_to(r, θ), the primary photons as D_pr(r, θ), the single scatter photon as D_ss(r, θ), and the multiple scatter photons as D_ms (r, θ) .

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Dii (r,90°)*r 2	Dii (1.00,θ)
Dii (5.00,θ)	Dii (10.00,θ)

Photon Energy Spectra

Photon energy spectra generated by the source model are calculated using the egs_brachy surface count scoring option to get the spectrum on the surface of the source. The plotted values are the counts per MeV in 1 keV bins, normalized to 1 count total in the spectrum. The MC calculations have a statistical uncertainty less than 0.002% on the mean energy.  The spectrum data are available in xmgrace format below.

References:

1. D. C. Medich et al , Monte Carlo characterization of an ytterbium-169 high dose rate brachytherapy source with analysis of statistical uncertainty, Med. Phys., 33 , 163-172, 2006
2. R. E. P. Taylor et al , Benchmarking BrachyDose: voxel-based EGSnrc Monte Carlo calculations of TG-43 dosimetry parameters, Med. Phys., 34 , 445 - 457, 2007                                                 

3. D. W. O. Rogers, Inverse square corrections for FACs and WAFACs, Appl. Radiat. Isot.,153 ,108638, 2019                     
4. H. Safigholi, M. J. P. Chamberland, R. E. P. Taylor, M. P. Martinov, D. W. O. Rogers, and R. M. Thomson, Update of the CLRP TG-43 parameter database for high-energy brachytherapy sources,  to be published (Current calculation).                
5. R. E. P. Taylor, D. W. O. Rogers, EGSnrc Monte Carlo calculated dosimetry parameters for 192 Ir and 169 Yb brachytherapy sources, Med. Phys., 35, 4933-4944, 2008