  Purpose: To develop and evaluate a free-breathing respiratory motion
compensated 4D (3D+respiration) $T_2$-weighted turbo spin echo sequence with
application to radiology and MR-guided radiotherapy.
  Methods: k-space data are continuously acquired using a rewound Cartesian
acquisition with spiral profile ordering (rCASPR) to provide matching contrast
to the conventional linear phase encode ordering and to sort data into multiple
respiratory phases. Low-resolution respiratory-correlated 4D images were
reconstructed with compressed sensing and used to estimate non-rigid
deformation vector fields, which were subsequently used for a motion
compensated image reconstruction. rCASPR sampling was compared to linear and
CASPR sampling in terms of point-spread-function (PSF) and image contrast with
in silico, phantom and in vivo experiments. Reconstruction parameters for
low-resolution 4D-MRI (spatial resolution and temporal regularization) were
determined using a grid search. The proposed motion compensated rCASPR was
evaluated in eight healthy volunteers and compared to free-breathing scans with
linear sampling. Image quality was compared based on visual inspection and
quantitatively by means of the gradient entropy.
  Results: rCASPR provided a superior PSF (similar in ky and narrower in kz)
and showed no considerable differences in images contrast compared to linear
sampling. The optimal 4D-MRI reconstruction parameters were spatial
resolution=$4.5 mm^3$ and $\lambda_t=10^{-4}$. The groupwise average gradient
entropy was 22.31 for linear, 22.20 for rCASPR, 22.14 for soft-gated rCASPR and
22.02 for motion compensated rCASPR.
  Conclusion: The proposed motion compensated rCASPR enables high quality
free-breathing T2-TSE with minimal changes in image contrast and scan time. The
proposed method therefore enables direct transfer of clinically used 3D TSE
sequences to free-breathing.
