title: Dose calculation for permanent prostate implants incorporating spatially anisotropic linearly time-resolving edema.
abstract: OBJECTIVE
  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 of 125I, 103Pd, and 137Cs 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, delta, 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, RE(preplan), in a 5 x 5 x 5 cm3 volume for 125I (Oncura 6711), 103Pd (Theragenics 200), and 131Cs (IsoRay CS-1) seeds arranged in the Radiological Physics Center test case 2 configuration for a range of edema relative magnitudes (delta = [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, RE(preplan) for 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 delta and T. Values of RE(preplan) were 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., delta = 0.2 and T = 28 d, mean values of RE(preplan) in an axial plane located 1.5 cm from the center of the seed distribution were 8.3% for 131Cs seeds, 7.5% for 103Pd seeds, and 2.2% for 125I seeds. Maximum values of RE(preplan) in 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 RE(preplan) that 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.
authors.affiliation: Department of Medical Physics, Cross Cancer Institute, Edmonton, Alberta T6G 1Z2, Canada.
authors.forename: T T
authors.initials: TT
authors.lastname: Monajemi
authors.forename: Charles M
authors.initials: CM
authors.lastname: Clements
authors.forename: Ron S
authors.initials: RS
authors.lastname: Sloboda
mesh_terms: D016880:Anisotropy; D001918:Brachytherapy; D004487:Edema; D006801:Humans; D008297:Male; D008954:Models, Biological; D011467:Prostate; D019736:Prostheses and Implants; D011829:Radiation Dosage; D013997:Time Factors