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

The theoretical framework is well-conceived: the diffeomorphic flow formulation using time-dependent velocity fields $v^{\bm{\theta}}$ integrated via Euler schemes provides a continuous representation of respiratory cycles without fixed reference states. The ablation study convincingly demonstrates that temporal regularization $\mathcal{R}_{t}$ is crucial for extrapolation performance, while spatial regularization $\mathcal{R}_{ph}$ alone provides limited benefits outside the interpolation regime. The neohookean hyperelastic regularizer $\mathcal{R}_{ph}(\varphi^{\bm{\theta}})=\mathrm{trace}(\mathbf{C})-3-\mathrm{log}(|\mathbf{J}|^{2})+\lambda(|\mathbf{J}|-1)^{2}$ is physically motivated for lung tissue and produces visibly smoother displacement fields compared to the sequential baseline.

The most significant concern is the performance gap in the critical extrapolation scenario: PRISM-RM achieves 2.83mm mean TRE versus 1.86mm for the sequential approach, representing a 52% larger error that could translate to clinically meaningful dose delivery inaccuracies. The dataset is limited to only 11 patients with 10-14 breathing states each, raising questions about statistical power and generalization across diverse breathing patterns. The improvement over the prior INR method (3.66mm to 2.83mm), while statistically significant, is modest in absolute terms and comes at substantial computational cost (40s per epoch versus 11-29s for ablated variants). Regarding the biophysical constraints, the neohookean model assumes homogeneous tissue properties, whereas lung regions contain heterogeneous structures (tumors, vessels, airways) with varying elastic moduli that a single $\lambda$ parameter cannot capture.

The comparison to the sequential two-stage approach of Wilms et al. (2014) is appropriate and serves as a rigorous baseline, though the authors' claim that PRISM-RM 'improves the extrapolation ability' requires qualification—it improves upon their prior INR method but not upon the clinical standard. The evidence supports that trajectory-aware sampling with $n(n-1)$ image pairs versus $n-1$ provides more robust training, but the advantage is insufficient to overcome the inherent generalization limitations of coordinate-based neural networks when predicting motion at surrogate signal values outside the training distribution $\mathcal{S}$. The landmark-based evaluation using manually placed anatomical points is appropriate for respiratory motion assessment, though the exclusion of neighboring breathing states in the extrapolation experiment represents a relatively severe test that may not fully represent incremental extrapolation scenarios seen in clinical practice.

Reproducibility is partially supported but incomplete. The architectural details are thoroughly specified: a sinusoidal activated INR with three hidden layers of 256 neurons, learning rate $1\times10^{-5}$, and hyperparameters $\alpha_{ph}=0.001$, $\alpha_{t}=0.1$, $\lambda=1$. The training procedure describes sampling 10,000 points per epoch with a 40/60 split between observed and interpolated surrogate signals. However, critical implementation details for the Euler integration are underspecified—the exact number of integration steps between arbitrary time points $t_j$ and $t_k$ is not stated, and the network initialization scheme for the SIREN architecture is not confirmed. The code is not publicly available, though the dataset (Wilms et al., 2014) can be obtained from the corresponding author upon request.