For gamma sources such as I-125, the radial dose function g(r) defines the falloff of dose rate along the transverse axis of the source due to absorption and scattering in the medium. For β emitters such as Ru-106, g(r) is a beta point kernel function.

To expedite the dose calculation, Plaque Simulator uses a 2001 element extended g[r] lookup table covering the range 0..40 mm at increments of 0.02 mm. The lookup table can be calculated from 5th order polynomial coefficients such as those published in Table VII of AAPM TG43 which are valid for r < 7 cm (Medical Physics, Vol. 22, 1995, page 215), or interpolated from a table of 20 data pairs describing the curve in the range 0..40 mm. The coefficients from Table VII of TG43 have been installed in Plaque Simulator's resources.

For r > 40 mm (unlikely in plaque dosimetry) the TG43 polynomial equation is used directly if the lookup table was calculated from the coefficients. If the lookup table was interpolated from data pairs, g(r) for r > 40 mm is calculated using only the a0,a1, and a2 coefficients and the following equations:

• For I-125: g(r) = a0 * exp(a1 * (r - a2)) r > 40 mm
• For Ir-192 and Pd-103: g(r) = a0 + (a1*r) + (a2*r²) r > 40 mm

For Ru106-Rh106 β plaques, the g(r) function is actually a point source attenuation kernel. The kernel lookup table covers the range 0.02 to 40 mm at a resolution of 0.02 mm. The default point kernel data was taken from Table VI in Cross, W.G. et al, Calculation of beta-ray dose distributions from ophthalmic applicators and comparison with measurements in a model eye, Med. Phys. 28(7), 2001, page 191. The values in the table are expressed in mm and nGy/h per Bq multiplied by r². The point kernel calibration parameter d is a distance offset into this attenuation kernel. You may also elect to generate the beta kernel using Cross's formula and parameters v,C,R,k,b,a (see the Dose Constants tab) and to further optimize those parameters for a better fit the tablulated data. Cross's Monte Carlo derived point kernel is now Plaque Simulator's default because it is conceptually simple, it has been compared to measurement, other Monte Carlo codes, and empirical expressions derived by Cross, and it yields dosimetric results a few percent closer to BEBIG's central axis calibration measurements than the earlier MIRD formalism.

You may still elect to use the earlier MIRD formalism for Ru106 which was calculated from the Fβ (r/r₉₀) scaled absorbed-dose distribution data in Table 12, MIRD pamphlet 7, 1971, page 20, according to the equation:

• g(r) = Fβ / (4πρ r² r₉₀) for r/r₉₀ <= 1.8
• g(r) = 0 for r/r₉₀ > 1.8

where ρ (g/cm³) is the density of the medium and r₉₀ is the 90 percentile distance. The 90 percentile distance is the distance in mm from the source within which 90% of the energy is absorbed.