### Source Description:

Dimensions given in the paper by Williamson and Quintero are used for the 6702 source ^{ 1,2,3 } . The 6702 source consists of three resin spheres (resin density is 1.2 g/cm ^{ 3 } and has a molecular composition of C _{ 12 } H _{ 18 } NCl), each with a diameter of 0.600 mm. The spheres are coated with ^{ 125 } I which is assumed to have negligible thickness in this study. The spheres are encapsulated in a titanium tube with 0.050 mm thick walls and an outer diameter of 0.800 mm. End welds are 0.500 mm thick and are modelled as 0.400 mm hemispheres on top of solid cylinders that have a 0.400 mm radius and are 0.100 mm thick. The overall length is 4.50 mm and the active length is 3.30 mm (calculated using the TG-43 effective line source length with a seed spacing of 1.10 mm and N=3 sources). The maximum possible displacement of a source sphere from its nominal position is 1.45 mm along the seed axis and 0.050 mm in the radial direction.

### 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 | 1.000 | 0.004 |

R. E. P. Taylor, D. W. O. Rogers ^{ 7 } |
point | 1.003 | 0.003 |

H. Hedtjarn et al ^{ 8 } |
extrap (PTRAN) | 1.016 | |

E. Mainegra et al ^{ 9 } |
point (EGS4) | 1.009 | |

M. J. Rivard et al ^{ 10 } |
TG-43 Consensus Value | 1.036 | - |

### 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 ^{ 11 } .

*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 } |

0.05 | 10.00 | 1.9154E-03 | -2.6413E-02 | 1.1127E+00 | 2.9603E-01 | -3.4599E-02 | 1.3919E-03 | 3.0090E-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 ^{ o } . The anisotropy factor, φ _{ an } (r), was calculated by integrating the solid angle weighted dose rate over 0 ^{ o } ≤ ϑ ≤ 90 ^{ o } .

### References:

1. J. F. Williamson, F. J. Quintero, Theoretical evaluation of dose distributions in water models 6711 and 6702 ^{125}I seeds, Med. Phys., **15** , 891 -- 897, 1988

2. J. F. Williamson, Monte Carlo evaluation of specific dose constants in water for ^{125}I seeds, Med. Phys., **15** , 686 -- 694, 1988

3. J. F. Williamson, Comparison of measured and calculated dose rates in water near I-125 and Ir-192 seeds, Med. Phys., **18** , 776 -- 786, 1991

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. H. Hedtjarn *et al*, Monte Carlo-aided dosimetry of the symmetra model I25.S06 I^{125}, interstitial brachytherapy seed, Med. Phys., **27** , 1076--1085, 2000

9. E. Mainegra *et al*, Dose rate constants for ^{103}Pd, ^{125}I, ^{196}Yb, ^{192}Ir, brachytherapy sources: an EGS4 Monte Carlo Study, Phys. Med. Biol., **43** , 1557 -- 1566, 1998

10. M. J. Rivard *et al*, Update of AAPM Task Group No. 43 Report: A revised AAPM protocol for brachytherapy dose calculations, Med. Phys., **31** , 633 -- 674, 2004

11. 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.