### Source Description:

The source dimensions for the Pd-1 seed ^{ 1,2,3 } are taken from the study by Chan and Prestwich. The DRAXIMAGE BrachySeed Pd-1 source consists of two 0.55 mm diameter aluminum silicate spheres containing a uniform distribution of ^{ 103 } Pd (spheres have a density of 2.53 g/cm ^{ 3 } and the composition by weight is 45.2% O, 23.8% Si, 18.4% Al, and 12.6% Na with a negligible amount of ^{ 103 } Pd). The two source spheres are separated by a 90% Pt / 10% Ir cylindrical rod that is 3.10 mm long and has a diameter of 0.380 mm. At the middle of the seed is a 1.19 mm long Ti annulus with inner and outer diameters of 0.380 mm and 0.691 mm, respectively. On either side of the annulus are two 1.19 mm long cylindrical Ti spacers with inner and outer diameters of 0.589 mm and 0.691 mm, respectively. These components are encapsulated in a 0.051 mm thick Ti capsule that is 3.60 mm long and has an outside diameter of 0.800 mm. The hemi-spherical ends are 0.065 mm thick on the longitudinal axis and 0.050 mm thick where they meet the cylindrical walls. The end welds are modelled using a 0.400 mm radius Ti hemisphere overlapped with a 0.349 mm radius air sphere with its center shifted by 0.0565 mm relative to the Ti sphere. The overall source length is 4.40 mm and the active length is 4.20 mm. The two spheres are free to move approximately 0.050 mm along the seed axis and 0.050 mm radially from the center of the seed.

### 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 the 30x30x30 cm ^{ 3 } water phantom, by the air kerma strength per history (scored * in vacuo * ). As described in ref. 4 , dose rate constants are provided for air kerma strenth calculated using voxels of 2.7x2.7x0.05 cm ^{ 3 } (WAFAC) and 0.1x0.1x0.05 cm ^{ 3 } (point) located 10 cm from the source. The larger voxel size averages the air kerma per history over a region covering roughly the same solid angle subtended by the primary collimator of the WAFAC ^{ 5,6 } at NIST used for calibrating low-energy brachytherapy sources and is likely the most clinically relevant value. The small voxel serves to estimate the air kerma per history at a point on the transverse axis.

Author |
Method |
Λ (cGy h-1 U-1) |
Abs. Uncertainty |

R. E. P. Taylor, D. W. O. Rogers ^{ 7 } |
WAFAC | 0.632 | 0.002 |

R. E. P. Taylor, D. W. O. Rogers ^{ 7 } |
point | 0.632 | 0.002 |

A. S. Meigooni et al ^{ 1 } |
point (MCNP) | 0.65 | 0.02 |

A. S. Meigooni et al ^{ 1 } |
TLD | 0.63 | 0.04 |

R. Nath et al ^{ 2 } |
TLD | 0.66 | 0.05 |

G. Chan, W. V. Prestwich ^{ 3 } |
extrap (CYLTRAN) | 0.613 | 0.018 |

### 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 0.05 cm to 10 cm. Fit parameters for a modified polynomial expression are also provided ^{ 8 } .

*Click image for higher res version*

Fitting coefficients for g _{ L } (r) = (a _{ 0 } r ^{ -2 } + a _{ 1 } r ^{ -1 } +a _{ 2 } + a _{ 3 } r +a _{ 4 } r ^{ 2 } + a _{ 5 } r ^{ 3 } ) e ^{ -a 6 r } |
||||||||

Fit range |
Coefficients |
|||||||

r _{ min } (cm) |
r _{ max } (cm) |
a _{ 0 } / cm ^{ 2 } |
a _{ 1 } / cm |
a _{ 2 } |
a _{ 3 } / cm ^{ -1 } |
a _{ 4 } / cm ^{ -2 } |
a _{ 5 } / cm ^{ -3 } |
a _{ 6 } / cm ^{ -1 } |

0.20 | 10.00 | 1.1862E-02 | -3.5324E-01 | 2.2129E+00 | -3.2497E-01 | 1.5973E-02 | 9.2637E-10 | 4.4630E-01 |

### Anisotropy function - F(r,θ):

Anisotropy functions are calculated using the line source approximation and tabulated at radii of 0.1, 0.15, 0.25, 0.5, 0.75, 1, 2, 3, 4, 5, 7.5 and 10 cm and 32 unique polar angles with a minimum resolution of 5^{° }. The anisotropy factor, φ_{an } (r), was calculated by integrating the solid angle weighted dose rate over 0^{° }≤ ϑ ≤ 90^{° }.

Click images for higher res versions

### References:

1. A. S. Meigooni * et al * , Theoretical and experimental determination of dosimetric characteristics for brachyseed Pd-103, model Pd-1, source, Appl. Radiat. Isotopes, ** 58 ** , 533--541, 2003

2. R. Nath * et al * , Experimental determination of dosimetric characterization of a newly designed encapsulated interstitial brachytherapy source of ^{ 103 } Pd-model Pd-1, Med. Phys., ** 29 ** , 2433--2434, 2002

3. G. Chan, W. V. Prestwich, Monte Carlo investigation of the dosimetric properties of the new ^{ 103 } Pd BrachySeed model Pd-1 source, Med. Phys., ** 29 ** , 1984--1990, 2002

4. 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

5. R. Loevinger, Wide-angle free-air chamber for calibration of low--energy brachytherapy sources, Med. Phys., ** 20 ** , 907, 1993

6. S. M Seltzer * et al * , New National Air-Kerma-Strength Standards for ^{ 125 } I and ^{ 103 } Pd Brachytherapy Seeds, J. Res. Natl. Inst. Stand. Technol., ** 108 ** , 337 -- 358, 2003

7. R. E. P. Taylor, D. W. O. Rogers, An EGSnrc Monte Carlo-calculated database of TG-43 parameters, Med. Phys., ** 35 ** , 4228--4241, 2008

8. R. E. P. Taylor, D. W. O. Rogers, More accurate fitting of ^{ 125 } I and ^{ 103 } Pd radial dose functions, Med. Phys., ** 35 ** , 4242--4250, 2008

Carleton Laboratory for Radiotherapy Physics

December 17 2007.