An automated, accurate, and efficient lung four-dimensional computed tomography (4DCT) image registration method is clinically important to quantify respiratory motion for optimal motion management. The purpose of this work is to develop a weakly supervised deep learning method for 4DCT lung deformable image registration (DIR). The landmark-driven cycle network is proposed as a deep learning platform that performs DIR of individual phase datasets in a simulation 4DCT. This proposed network comprises a generator and a discriminator. The generator accepts moving and target CTs as input and outputs the deformation vector fields (DVFs) to match the two CTs. It is optimized during both forward and backward paths to enhance the bi-directionality of DVF generation. Further, the landmarks are used to weakly supervise the generator network. Landmark-driven loss is used to guide the generator's training. The discriminator then judges the realism of the deformed CT to provide extra DVF regularization. We performed four-fold cross-validation on 10 4DCT datasets from the public DIR-Lab dataset and a hold-out test on our clinic dataset, which included 50 4DCT datasets. The DIR-Lab dataset was used to evaluate the performance of the proposed method against other methods in the literature by calculating the DIR-Lab Target Registration Error (TRE). The proposed method outperformed other deep learning-based methods on the DIR-Lab datasets in terms of TRE. Bi-directional and landmark-driven loss were shown to be effective for obtaining high registration accuracy. The mean and standard deviation of TRE for the DIR-Lab datasets was 1.20±0.72mm and the mean absolute error (MAE) and structural similarity index (SSIM) for our datasets were 32.1±11.6 HU and 0.979±0.011, respectively. The landmark-driven cycle network has been validated and tested for automatic deformable image registration of patients' lung 4DCTs with results comparable to or better than competing methods.
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