  This paper aims to create a deep learning framework that can estimate the
deformation vector field (DVF) for directly registering abdominal MRI-CT
images. The proposed method assumed a diffeomorphic deformation. By using
topology-preserved deformation features extracted from the probabilistic
diffeomorphic registration model, abdominal motion can be accurately obtained
and utilized for DVF estimation. The model integrated Swin transformers, which
have demonstrated superior performance in motion tracking, into the
convolutional neural network (CNN) for deformation feature extraction. The
model was optimized using a cross-modality image similarity loss and a surface
matching loss. To compute the image loss, a modality-independent neighborhood
descriptor (MIND) was used between the deformed MRI and CT images. The surface
matching loss was determined by measuring the distance between the warped
coordinates of the surfaces of contoured structures on the MRI and CT images.
The deformed MRI image was assessed against the CT image using the target
registration error (TRE), Dice similarity coefficient (DSC), and mean surface
distance (MSD) between the deformed contours of the MRI image and manual
contours of the CT image. When compared to only rigid registration, DIR with
the proposed method resulted in an increase of the mean DSC values of the liver
and portal vein from 0.850 and 0.628 to 0.903 and 0.763, a decrease of the mean
MSD of the liver from 7.216 mm to 3.232 mm, and a decrease of the TRE from
26.238 mm to 8.492 mm. The proposed deformable image registration method based
on a diffeomorphic transformer provides an effective and efficient way to
generate an accurate DVF from an MRI-CT image pair of the abdomen. It could be
utilized in the current treatment planning workflow for liver radiotherapy.
