Recent advances in positron emission tomography (PET) targeting prostate specific membrane antigen (PSMA) allow highly specific and sensitive identification of intra/extraprostatic tumors. Combination of PSMA PET and intraoperative transrectal ultrasound (TRUS) images enables to further improve the standard of care in brachytherapy, allowing the physician to precisely tailor the dose to the individual's tumor. The key step of PET-determined focal prostate brachytherapy is the preoperative PET/CT and intraoperative TRUS image fusion, which enables mapping of PSMA PET to intraoperative imaging. In this paper, we propose a deformable image registration algorithm for PET/CT-TRUS image fusion based on a structural descriptor map (SDM). The SDM is computed by solving Laplace's equation based on the prostate segmentations. The solution to the Laplace's equation with a boundary condition provides equipotential surfaces within the prostate that describe smooth transitions from the midline to the boundary while preserving the prostate shape and geometry. Therefore, the computed equipotential surface distribution can be considered as a structural descriptor and used for deformable registration. The proposed SDM-based CT-TRUS registration algorithm has been evaluated on five prostate brachytherapy patient data sets in which intraoperative end-of-implantation TRUS and day 1 post-implant CT were registered. Target registration errors computed by using the implanted seeds as the anatomical landmarks were 2.25±1.36 mm on average, which is clinically acceptable.