Dose calculation for permanent prostate implants incorporating spatially anisotropic linearly time‐resolving edema

Purpose: The objectives of this study were (i) to develop a dose calculation method for permanent prostate implants that incorporates a clinically motivated model for edema and (ii) to illustrate the use of the method by calculating the preimplant dosimetry error for a reference configuration ofI125,P103 d , andC137 s seeds subject to edema‐induced motions corresponding to a variety of model parameters.Methods: A model for spatially anisotropic edema that resolves linearly with time was developed based on serial magnetic resonance imaging measurements made previously at our center to characterize the edema for a group of n = 40 prostate implant patients [R. S. Sloboda et al. , “Time course of prostatic edema post permanent seed implant determined by magnetic resonance imaging,” Brachytherapy 9, 354–361 (2010)]. Model parameters consisted of edema magnitude, Δ , and period, T . The TG‐43 dose calculation formalism for a point source was extended to incorporate the edema model, thus enabling calculation via numerical integration of the cumulative dose around an individual seed in the presence of edema. Using an even power piecewise‐continuous polynomial representation for the radial dose function, the cumulative dose was also expressed in closed analytical form. Application of the method was illustrated by calculating the preimplant dosimetry error, R E p r e p l a n, in a 5 × 5 × 5   cm 3volume forI125(Oncura 6711),P103 d (Theragenics 200), andC131 s (IsoRay CS‐1) seeds arranged in the Radiological Physics Center test case 2 configuration for a range of edema relative magnitudes( Δ = [ 0.1 , 0.2 , 0.4 , 0.6 , 1.0 ] )and periods( T = [ 28 , 56 , 84 ]   d ) . Results were compared to preimplant dosimetry errors calculated using a variation of the isotropic edema model developed by Chen et al. [“Dosimetric effects of edema in permanent prostate seed implants: A rigorous solution,” Int. J. Radiat. Oncol., Biol., Phys. 47, 1405–1419 (2000)].Results: As expected, R E p r e p l a nfor our edema model indicated underdosage in the calculation volume with a clear dependence on seed and calculation point positions, and increased with increasing values of Δ and T . Values of R E p r e p l a nwere generally larger near the ends of the virtual prostate in the RPC phantom compared with more central locations. For edema characteristics similar to the population average values previously measured at our center, i.e., Δ = 0.2 and T = 28   d , mean values of R E p r e p l a nin an axial plane located 1.5 cm from the center of the seed distribution were 8.3% forC131 s seeds, 7.5% forP103 d seeds, and 2.2% forI125seeds. Maximum values of R E p r e p l a nin the same plane were about 1.5 times greater. Note that detailed results strictly apply only for loose seed implants where the seeds are fixed in tissue and move in synchrony with that tissue.Conclusions: A dose calculation method for permanent prostate implants incorporating spatially anisotropic linearly time‐resolving edema was developed for which cumulative dose can be written in closed form. The method yields values for R E p r e p l a nthat differ from those for spatially isotropic edema. The method is suitable for calculating pre‐ and postimplant dosimetry correction factors for clinical seed configurations when edema characteristics can be measured or estimated.