Biophysics-Enhanced Neural Representations for Patient-Specific Respiratory Motion Modeling

Implicit neural representations (INRs) are well suited to cardiac motion estimation, providing continuous, compact representations of motion fields. However, fitting an INR to each image sequence is time-consuming and sensitive to the optimisation trajectory. Learned priors can help guide optimisation towards plausible motion fields and enable faster adaptation, but learning priors for cardiac motion INRs remains under-explored. In this work, we compare four strategies for learning cardiac motion priors, including a population prior learned by joint optimisation, a consensus prior obtained by weight averaging, auto-decoders, and meta-learning. Using short-axis tagged cardiac magnetic resonance images from the UK Biobank, we evaluate their impact on tracking accuracy, motion behaviour, and adaptation trajectory. All learned priors substantially improved early adaptation performance compared with random initialisation. While the simple consensus prior was effective, auto-decoders recovered large deformations faster during early adaptation. Meta-learning achieved strong early performance and maintained the best adaptation trajectory over 50 iterations.

Bronchoscopic navigation relies on registering endoscopic video to a preoperative CT scan, but respiratory motion deforms the airway by 5-20 mm, creating CT-to-body divergence that limits localization accuracy. In practice, this is mitigated through breath-hold protocols, which attempt to match the intraoperative anatomy to a static CT, but are difficult to reproduce and disrupt clinical workflow. We propose to eliminate the need for breath-hold protocols by leveraging patient-specific respiratory modeling. Paired inhale-exhale CT scans, already acquired for planning, implicitly define the patient-specific deformation space of the breathing airway. By registering these scans, we reduce respiratory motion to a single scalar breathing phase per frame, constraining all reconstructions to anatomically observed configurations. We embed this representation within a mesh-anchored Gaussian splatting framework, where a lightweight estimator infers breathing phase directly from endoscopic RGB, enabling continuous, deformation-aware reconstruction throughout the respiratory cycle without breath-holds or external sensing. To enable quantitative evaluation, we introduce RESPIRE, a physically grounded bronchoscopy simulation pipeline with per-frame ground truth for geometry, pose, breathing phase, and deformation. Experiments on RESPIRE show that our approach achieves geometrically faithful reconstruction, over 20x faster training, and 1.22 mm target localization accuracy (within the 3mm clinically relevant tolerances) outperforming unconstrained single-CT baselines. Please check out our website for additional visuals: https://asdunnbe.github.io/RESPIRE/

Deformable image registration models implicitly encode deformation priors through their parametrization and optimization. In this work, we conduct a validation study on continuous registration methods to examine how these implicit priors affect performance across different registration tasks. Classic B-Spline transformations impose locality, smoothness, and scale through their control-point structure, whereas recent INR-based methods impose different priors through neural parameterization and optimization. We compare INR-Dense (IDIR), which directly models a dense displacement field using a SIREN-based INR; INR-BSCP (SINR), which predicts B-Spline control points with an INR; D-BSCP, which directly optimizes single-scale B-Spline control points; and MR-D-BSCP, which adds a multiresolution coarse-to-fine scheme. Experiments on inter-subject brain MR registration (OASIS) and intra-subject exhale-to-inhale lung CT registration (DIR-LAB 4DCT) reveal different behavior across deformation regimes. On OASIS, where deformations are moderate but locally complex, D-BSCP matches or slightly outperforms INR-BSCP, suggesting that the B-Spline parameterization accounts for much of INR-BSCP's effectiveness. On DIR-LAB 4DCT, where respiratory motion is larger and more coherent, single-scale B-Spline methods (D-BSCP and INR-BSCP) are less suitable, while INR-Dense and MR-D-BSCP are more effective. Across both tasks, MR-D-BSCP achieves the best performance among the tested continuous parameterizations. These findings highlight that registration accuracy depends strongly on matching the induced deformation prior to the target motion pattern, and support prior-deformation matching as a practical design principle for medical image registration. Our code will be available at https://github.com/HengjieLiu/RightPriorDIR.