Physics-Informed Principal Component Analysis–Sinusoidal Modeling of Respiratory Motion from 4DCT for Radiation Oncology Applications

Purpose: Respiratory-induced motion constitutes a major source of geometric uncertainty in thoracic radiotherapy.While four-dimensional computed tomography (4DCT) permits direct assessment of respiratory motion, it produces high-dimensional deformation datasets that are difficult to interpret and analyze directly.This study presents a physics-informed framework integrating principal component analysis (PCA) with sinusoidal representation to provide a concise and interpretable description of dominant respiratory motion patterns derived from 4DCT data.Methods: Anonymized 4DCT datasets were analyzed as imaging-derived motion signals.Deformable image registration between respiratory phases generated deformation vector fields.PCA was then applied to minimize dimensionality and identify dominant motion components.The temporal amplitudes of the leading principal components were subsequently modeled using loworder sinusoidal functions.Model performance was assessed using quantitative agreement metrics, including root mean square error, coefficient of determination (R²), and Bland-Altman analysis.Results: Respiratory motion demonstrated marked anisotropy, with the greatest displacement observed along the superior-inferior direction.PCA achieved effective dimensionality reduction, with only a few components capturing the majority of respiratory motion variance.Sinusoidal modeling reproduced the predominant temporal dynamics of the PCA-derived motion components, with variable agreement across components reflecting differences in periodicity.Bland-Altman analysis indicated good overall agreement with no appreciable evidence of systematic bias. Conclusions:The proposed PCA-sinusoidal framework offers a compact, quantitative, and physically interpretable representation of respiratory motion derived from 4DCT deformation fields.This methodological approach may facilitate respiratory motion characterization in radiotherapy and medical imaging applications where model transparency and physical interpretability are prioritized.