Application of k-space energy spectrum analysis to susceptibility field mapping and distortion correction in gradient-echo EPI

Echo-planar imaging (EPI) is widely used in functional MRI studies. It is well known that EPI quality is usually degraded by geometric distortions, when there exist susceptibility field inhomogeneities. EPI distortions may be corrected if the field maps are available. It is possible to estimate the susceptibility field gradients from the phase reconstruction of a single-TE EPI image, after a successful phase-unwrapping procedure. However, in regions affected by pronounced field gradients, the phase-unwrapping of a single-TE image may fail, and therefore the estimated field maps may be incorrect. It has been reported that the field inhomogeneity may be calculated more reliably from T2*-weighted images corresponding to multiple TEs. However, the multi-TE MRI field mapping increases the scan time. Furthermore, the measured field maps may be invalid if the subject's position changes during dynamic scans. To overcome the limitations in conventional field mapping approaches, a novel k-space energy spectrum analysis algorithm is developed, which quantifies the spatially dependent echo-shifting effect and the susceptibility field gradients directly from the k-space data of single-TE gradient-echo EPI. Using the k-space energy spectrum analysis, susceptibility field gradients can be reliably measured without phase-unwrapping, and EPI distortions can be corrected without extra field mapping scans or pulse sequence modification. The reported technique can be used to retrospectively improve the image quality of the previously acquired EPI and functional MRI data, provided that the complex-domain k-space data are still available.