A biomathematical model for calculating the dose delivered by I-125 or Pd-103 seeds to the edematous prostate

Purpose/Object: In many institutions, post-implant CT scans are obtained to determine the dose delivered by an I-125 or Pd-103 prostate implant. However, if the prostate is edematous at the time of imaging, parameters such as the minimum prostatic dose and dose coverage will be underestimated. Conversely, if the imaging is delayed until the edema dissipates, these dosimetric parameters will be overestimated. The purpose of this study is to define a model which accounts for edema in the dose calculation, so that the question of optimum time to image prostate implants can be investigated. Materials and Methods: Based on analysis of serial post-implant CT scans, it is found that the edema caused by the insertion of the implantation needles decays exponentially with time with an edema half-life (T(e1(2)), time for the edema to decrease by (1(2))) ranging from 3 to 23 days (mean 8.5 days). The model for calculating the dose is numerical integration of the accumulated distribution of dose within the prostate as a function of time, in which both the prostate volume, seed locations, and source strength change and are updated with time. The change in the prostate is described by an exponential function (c0+c1e-λT) in which the parameters c0, c1 and λ are determined by fitting the edema curve defined by analysis of serial CT scans. The model utilizes contours of the prostate volume and the location of seeds as obtained from a CT scan taken on the day of the implant. A 3-D matrix of grid points enclosed by the contours are used to represent the prostate. Dose was calculated on the grid points by taking into account the change of the coordinates for the grid points and for the seeds, and the decay of source strength as a function of time. By assuming that edema regresses isotropically, the change in the relative positions between grid points and seeds also follows the exponential function. Results: The model has been used to calculate the dose delivered by both I-125 and Pd-103 seed implants for which the magnitude and duration of edema is documented by serial CT scans. These results indicate that if a single post-implant CT scan is to be obtained for dosimetric evaluation, a scan obtained at approximately 2T(e1(2)) provides a more accurate assessment of dose coverage than CT scans obtained immediately after the implant procedure or after the edema had dissipated. Conclusion: A biomathematical model has been developed for calculating the dose delivered to an edematous prostate. This model indicates that the optimum time for obtaining a post-implant CT scan is 2T(e1(2)) after the implantation procedure. However, patients exhibit a wide range of edema half-lives which can only be determined by serial CT scans. This model will be used to explore the error associated with CT scans obtained at a fixed time intervals after implantation to define the optimal fixed time for a post-implant CT scan