Weakly Supervised Spatial Implicit Neural Representation Learning for 3D MRI-Ultrasound Deformable Image Registration in HDR Prostate Brachytherapy

Purpose: Accurate 3D MRI-ultrasound (US) deformable registration is critical for real-time guidance in high-dose-rate (HDR) prostate brachytherapy. We present a weakly supervised spatial implicit neural representation (SINR) method to address modality differences and pelvic anatomy challenges. Methods: The framework uses sparse surface supervision from MRI/US segmentations instead of dense intensity matching. SINR models deformations as continuous spatial functions, with patient-specific surface priors guiding a stationary velocity field for biologically plausible deformations. Validation included 20 public Prostate-MRI-US-Biopsy cases and 10 institutional HDR cases, evaluated via Dice similarity coefficient (DSC), mean surface distance (MSD), and 95% Hausdorff distance (HD95). Results: The proposed method achieved robust registration. For the public dataset, prostate DSC was $0.93 \pm 0.05$, MSD $0.87 \pm 0.10$ mm, and HD95 $1.58 \pm 0.37$ mm. For the institutional dataset, prostate CTV achieved DSC $0.88 \pm 0.09$, MSD $1.21 \pm 0.38$ mm, and HD95 $2.09 \pm 1.48$ mm. Bladder and rectum performance was lower due to ultrasound's limited field of view. Visual assessments confirmed accurate alignment with minimal discrepancies. Conclusion: This study introduces a novel weakly supervised SINR-based approach for 3D MRI-US deformable registration. By leveraging sparse surface supervision and spatial priors, it achieves accurate, robust, and computationally efficient registration, enhancing real-time image guidance in HDR prostate brachytherapy and improving treatment precision.