PhysMorph: A biomechanical and image-guided deep learning framework for real-time multi-modal liver image registration

Background and purpose: Accurate registration of pretreatment Magnetic Resonance Imaging (MRI) to onboard Cone Beam Computed Tomography (CBCT) is critical for liver Stereotactic Body Radiation Therapy (SBRT) but is challenged by poor CBCT soft-tissue contrast and respiratory motion. We developed and validated PhysMorph, a physics-informed deep learning framework designed to provide rapid, anatomically plausible MR-CBCT image registration of the liver. Materials and methods: We developed PhysMorph, a registration framework that incorporated finite element method (FEM) simulations as biomechanical regularization alongside image similarity metrics. The framework was validated on two datasets: (1) simulated data with a known ground-truth deformation derived from longitudinal MR-Linac scans, and (2) clinical MR-CBCT pairs from liver SBRT patients. Performance was assessed using target registration error (TRE), mean surface distance (MSD), and metrics of biomechanical fidelity. Results: On clinical data, PhysMorph achieved a mean TRE of 2.2 ± 1.4 mm and a MSD of 1.60 ± 0.05 mm, significantly outperforming VoxelMorph (4.11 ± 1.53 mm) and SynthMorph (4.41 ± 1.67 mm) while maintaining high biomechanical fidelity. The framework reduced registration time from over 10 min for conventional finite element methods to 103.4 ms, enabling practical real-time application. Conclusions: PhysMorph enables fast, accurate, and physically realistic registration of pretreatment MRI to on-board CBCT for liver SBRT. By integrating MRI's superior soft-tissue visualization while ensuring anatomical plausibility, our approach facilitates precise tumor localization that could enable smaller planning target volumes and more conformal dose distributions, potentially enhancing tumor control while reducing radiation exposure to healthy tissues.