  Purpose: This study aims to propose a model-based reconstruction algorithm
for simultaneous multi-slab diffusion MRI acquired with blipped-CAIPI gradients
(blipped-SMSlab), which can also incorporate distortion correction.
  Methods: We formulate blipped-SMSlab in a 4D k-space with kz gradients for
the intra-slab slice encoding and km (blipped-CAIPI) gradients for the
inter-slab encoding. Because kz and km gradients share the same physical axis,
the blipped-CAIPI gradients introduce phase interference in the z-km domain
while motion induces phase variations in the kz-m domain. Thus, our previous
k-space-based reconstruction would need multiple steps to transform data back
and forth between k-space and image space for phase correction. Here we propose
a model-based hybrid-space reconstruction algorithm to correct the phase errors
simultaneously. Moreover, the proposed algorithm is combined with distortion
correction, and jointly reconstructs data acquired with the blip-up/down
acquisition to reduce the g-factor penalty.
  Results: The blipped-CAIPI-induced phase interference is corrected by the
hybrid-space reconstruction. Blipped-CAIPI can reduce the g-factor penalty
compared to the non-blipped acquisition in the basic reconstruction.
Additionally, the joint reconstruction simultaneously corrects the image
distortions and improves the 1/g-factors by around 50%. Furthermore, through
the joint reconstruction, SMSlab acquisitions without the blipped-CAIPI
gradients also show comparable correction performance with blipped-SMSlab.
  Conclusion: The proposed model-based hybrid-space reconstruction can
reconstruct blipped-SMSlab diffusion MRI successfully. Its extension to a joint
reconstruction of the blip-up/down acquisition can correct EPI distortions and
further reduce the g-factor penalty compared with the separate reconstruction.
