Table 1 Characteristics of the different VBDM investigated

Monte Carlo (MC)

F(M _ijk , N _ijk , ρ _ijk , E _90Y )

E _90Y is the beta energy spectra per disintegration

Local deposition (LD)

\( {N}_{ijk}\cdot \frac{E_{avg}}{\rho_{ijk}\cdot \Delta V} \)

E _avg (0.937 MeV) is the average energy of the beta particle per disintegration. ΔV is the volume of a voxel.

Soft-tissue kernel (SK)

N _ijk  ⊗ K _{i ' j ' k '}

K _{i ' j ' k '} is obtained from a MC simulation of infinite uniform soft-tissue material with density of 1.04 g/cc.

Soft-tissue kernel with density correction (SKD)

\( \left({N}_{ijk}\otimes {K}_{i^{\hbox{'}}{j}^{\hbox{'}}{k}^{\hbox{'}}}\right)\cdot \frac{1.04}{\rho_{ijk}} \)

Assumes ρ _ijk is in units of g/cc