Three-dimensional seed reconstruction in prostate brachytherapy using Hough transformations

In order to perform dosage analysis of prostate seed implants, 3D seed coordinates are ascertained for seed positions from conical x-ray projections. A conventional reconstruction approach uses back projection of x-ray data obtained at two or three gantry angles. The method, however, does not perform well when the seeds are obscured by other seeds in a projection. Additional x-ray projection data taken at different angles can resolve the overlapping seeds but the computational overhead increases dramatically. In this paper, we propose an alternate approach for 3D seed localization using Hough transformation. For each seed's coordinate in three dimensions, there exists a corresponding projection location in each of the views. Integrating each of these seed locations and placing the result in the 3D seed coordinate results in a high confidence score if there is a seed at the coordinate. This technique does not suffer from the problem of inability to reconstruct the overlapping seeds since the seed's path is unique for a particular seed. When seeds are overlapped, the paths intersect each other. From the seed's path, the overlapping seeds' coordinates can be determined. Our proposed method also has the ability to incorporate more views without incurring major computing cost. Using Hough transform parametric equations to describe the path of the seeds from one view to the next, the Hough transform weight of the 3D seed coordinates among the views can be calculated. Results from computer simulation and a physical phantom study are presented to illustrate the proposed approach. The results indicate that the Hough transform method can determine the 3D position of a brachytherapy seed even when the seed is undetected in some of the x-ray projections due to the seed overlap.