  Purpose: This study extends the Fast ROtary Nonlinear Spatial ACquisition
(FRONSAC) method to include 3D acquisitions and reconstructions. It also
presents a transform domain reconstruction that makes 3D reconstructions
practical and provides new insights into how parallel imaging performance is
enhanced by FRONSAC encoding. Methods: This work developed the first examples
of FRONSAC incorporated into a 3D acquisition. 3D FRONSAC was tested on human
subjects with both simple gradient echo and MPRAGE Cartesian acquisitions. The
quality of the 3D FRONSAC images was evaluated using structural similarity
index measure (SSIM), and normalized root mean square error (NRMSE). Results:
FRONSAC encoding did not significantly modify the contrast obtained in either
sequence, but it substantially improves the image quality of undersampled
reconstruction. FRONSAC images have reduced undersampling ghosts and
consistently improved SSIM and NRMSE. Conclusions: Acquisition and
reconstruction of 3D FRONSAC images are feasible, and the additional FRONSAC
encoding improves image quality in highly undersampled images.
