ORRN: An ODE-Based Recursive Registration Network for Deformable Respiratory Motion Estimation With Lung 4DCT Images

Objective: Deformable Image Registration (DIR) plays a significant role in quantifying deformation in medical data. Recent Deep Learning methods have shown promising accuracy and speedup for registering a pair of medical images. However, in 4D (3D + time) medical data, organ motion, such as respiratory motion and heart beating, can not be effectively modeled by pair-wise methods as they were optimized for image pairs but did not consider the organ motion patterns necessary when considering 4D data. Methods: This article presents ORRN, an Ordinary Differential Equations (ODE)-based recursive image registration network. Our network learns to estimate time-varying voxel velocities for an ODE that models deformation in 4D image data. It adopts a recursive registration strategy to progressively estimate a deformation field through ODE integration of voxel velocities. Results: We evaluate the proposed method on two publicly available lung 4DCT datasets, DIRLab and CREATIS, for two tasks: 1) registering all images to the extreme inhale image for 3D+t deformation tracking and 2) registering extreme exhale to inhale phase images. Our method outperforms other learning-based methods in both tasks, producing the smallest Target Registration Error of 1.24 mm and 1.26 mm, respectively. Additionally, it produces less than 0.001% unrealistic image folding, and the computation speed is less than 1 s for each CT volume. Conclusion: ORRN demonstrates promising registration accuracy, deformation plausibility, and computation efficiency on group-wise and pair-wise registration tasks. Significance: It has significant implications in enabling fast and accurate respiratory motion estimation for treatment planning in radiation therapy or robot motion planning in thoracic needle insertion.