Optimal Matching for Prostate Brachytherapy Seed Localization with Dimension Reduction

Abstract

In prostate brachytherapy, x-ray fluoroscopy has been used for intra-operative dosimetry to provide qualitative assessment of implant quality. More recent developments have made possible 3D localization of the implanted radioactive seeds. This is usually modeled as an assignment problem and solved by resolving the correspondence of seeds. It is, however, NP-hard, and the problem is even harder in practice due to the significant number of hidden seeds. In this paper, we propose an algorithm that can find an optimal solution from multiple projection images with hidden seeds. It solves an equivalent problem with reduced dimensional complexity, thus allowing us to find an optimal solution in polynomial time. Simulation results show the robustness of the algorithm. It was validated on 5 phantom and 18 patient datasets, successfully localizing the seeds with detection rate of ≥ 97.6 % and reconstruction error of ≤ 1.2 mm. This is considered to be clinically excellent performance.

Prostate Brachytherapy Seed Reconstruction Using C-Arm Rotation Measurement and Motion Compensation

“…2. As it can be seen the reconstruction algorithm shows consistently successful performance over a wide range of C-arm translational position errors, while the performance without motion compensation decreases with measurement errors [3]. It can be seen in Figs.…”

“…In order to solve the matching problem, we rely on a linear programing approach introduced by Lee et al [3] which, for sake of completeness, we outline in Section 2.1. The motion compensation method is discussed in detail in Section 2.2.…”

“…Equation (1) can be written as a constrained linear programing problem by concatenating the x ijk and c ijk into vectors. The unknowns that correspond to a cost higher than a specified threshold are removed and the linear programing problem with reduced dimensions is solved to find the correct seed matching solution [3].…”

“…1(a)). Three dimensional reconstruction of the seeds has several benefits such as intraoperative dosimetry modifications and quantitative assessment, and has been proposed previously [1,2,3].…”

“…Seed reconstruction entails solving a seed matching problem -assigning the shadows of a seed in different images to each other-which has been solved using simulated annealing [1], Hungarian algorithm [2] and linear programing [3]. rotation of the C-arm around the primary axis (PA) and the world coordinate system, and (c) the scaling problem.…”