Application of k-space energy spectrum analysis to susceptibility field mapping and distortion correction in gradient-echo EPI.
ABSTRACT 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.
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ABSTRACT: Head motion and static magnetic field (B0) inhomogeneity are two important sources of image intensity variability in functional MRI (fMRI). Ideally, in MRI, any deviation in B0 homogeneity in an object occurs only by design. However, due to imperfections in the main magnet and gradient coils, and, magnetic susceptibility differences in the object, undesired B0 deviations may occur. This causes geometric distortion in Cartesian EPI images. In addition to spatial shifts and rotations of images, head motion during an fMRI experiment may induce time-varying field-inhomogeneity changes in the brain. As a result, correcting for motion and field-inhomogeneity effects independently of each other with a static field map may be insufficient, especially in the presence of large out-of-plane rotations. Our primary concern is the correction of the combined effects of motion and field-inhomogeneity induced geometric distortion in Cartesian EPI fMRI images. We formulate a concurrent field-inhomogeneity with map-slice-to-volume motion correction, and develop a motion-robust dual-echo bipolar gradient echo static field map estimation method. We also propose and evaluate a penalized weighted least squares approach to dynamic field map estimation using the susceptibility voxel convolution method. This technique accounts for field changes due to out-of-plane rotations, and estimates dynamic field maps from a high resolution static field map without requiring accurate image segmentation, or the use of literature susceptibility values. Experiments with simulated data suggest that the technique is promising, and the method will be applied to real data in future work. In a separate clinical fMRI project, which is independent of the above work, we also formulate a current density weighted index to quantify correspondence between electrocortical stimulation and fMRI maps for brain presurgical planning. The proposed index is formulated with the broader goal of defining safe limits for lesion resection, and is characterized extensively with simulated data. The index is also computed for real human datasets. Ph.D. Electrical Engineering: Systems University of Michigan, Horace H. Rackham School of Graduate Studies http://deepblue.lib.umich.edu/bitstream/2027.42/60787/1/tbyeo_1.pdf
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ABSTRACT: A robust modification of echo-planar imaging dubbed double-shot echo-planar imaging with center-out trajectories and intrinsic navigation (DEPICTING) is proposed, which permits imaging at ultra-short echo time. The k-space data is sampled by two center-out trajectories with a minimal delay achieving a temporal efficiency similar to conventional single-shot echo-planar imaging. Intersegment phase and intensity imperfections are corrected by exploiting the intrinsic navigator information from both central lines, which are subsequently averaged for image reconstruction. Phase errors induced by inhomogeneities of the main magnetic field are corrected in k-space, recovering the superior point-spread function achieved with center-out trajectories. The minimal echo time (<2 msec) is nearly independent of the acquisition matrix permitting applications, which simultaneously require high spatial and temporal resolution. Examples of demonstrated applications include anatomical imaging, BOLD-based functional brain mapping, and quantitative perfusion imaging.Magnetic Resonance in Medicine 09/2010; 65(1):165-75. · 3.27 Impact Factor
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ABSTRACT: Electrical stimulation of the rat forepaw and hindpaw was employed to study the spatial distribution of BOLD fMRI. Averaging of multiple fMRI sessions significantly improved the spatial stability of the BOLD signal and enabled quantitative determination of the boundaries of the BOLD fMRI maps. The averaged BOLD fMRI signal was distributed unevenly over the extent of the map and the data at the boundaries could be modeled with major and minor spatial components. Comparison of three-dimensional echo-planar imaging (EPI) fMRI at isotropic 300 μm resolution demonstrated that the border locations of the major spatial component of BOLD signal did not overlap between the forepaw and hindpaw maps. Interestingly, the border positions of the minor BOLD fMRI spatial components extended significantly into neighboring representations. Similar results were found for cerebral blood volume (CBV) weighted fMRI obtained using iron oxide particles, suggesting that the minor spatial components may not be due to vascular mislocalization typically associated with BOLD fMRI. Comparison of the BOLD fMRI maps of the forepaw and hindpaw to histological determination of these representations using cytochrome oxidase (CO) staining demonstrated that the major spatial component of the BOLD fMRI activation maps accurately localizes the borders. Finally, 2-3 weeks following peripheral nerve denervation, cortical reorganization/plasticity at the boundaries of somatosensory limb representations in adult rat brain was studied. Denervation of the hindpaw caused a growth in the major component of forepaw representation into the adjacent border of hindpaw representation, such that fitting to two components no longer led to a better fit as compared to using one major component. The border of the representation after plasticity was the same as the border of its minor component in the absence of any plasticity. It is possible that the minor components represent either vascular effects that extend from the real neuronal representations or the neuronal communication between neighboring regions. Either way the results will be useful for studying mechanisms of plasticity that cause alterations in the boundaries of neuronal representations.NeuroImage 07/2011; 57(2):526-38. · 6.25 Impact Factor
Application of k-space energy spectrum analysis to susceptibility field mapping and distortion correction in gradient-echo EPI
N-K. Chen1, K. Oshio1,2, L. P. Panych1
1Radiology, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, United States, 2Diagnostic Radiology, Keio University, Tokyo, Japan
Echo planar imaging (EPI), with its high temporal resolution, has become an important technique for various dynamic studies, such as functional
MRI and contrast agent enhanced imaging. It is well known that EPI is geometrically distorted by Bo field inhomogeneity. In order to remove the
geometric distortions, an extra field mapping scan can be performed prior to EPI based dynamic imaging (Jezzard and Balaban, MRM, 1995, 34:65).
However, the acquired field map may become invalid if the subject's position changes during dynamic EPI scans. Furthermore, the experimental time
will be increased when an extra field map scan is performed.
Here, a novel algorithm termed k-space energy spectrum analysis is presented to map the susceptibility field gradients directly from gradient-echo
EPI data. Neither extra field mapping scan nor EPI pulse sequence modification is needed. Based on the calculated susceptibility field gradient maps,
the Bo field inhomogeneity map can be derived and used to remove the geometric distortions in EPI data.
Theory and Methods
Echo-shifting effect in gradient-echo EPI: In the presence of susceptibility field gradients, gradient-echo EPI's echo signals deviate from the center
of the k-space and the degree of this echo-shifting effect depends on (1) the effective echo time, (2) echo-spacing time, (3) image field of view (FOV),
and (4) the susceptibility field gradients. If the echo-shifting effects, corresponding to different image-domain regions, can all be measured directly from
gradient-echo EPI data, the susceptibility field gradients can be quantified without an extra field mapping scan.
K-space energy spectrum analysis: We have developed a k-space energy spectrum analysis algorithm to map EPI's echo-shifting effect along both
readout and phase-encoding directions. The procedure for mapping the echo-shifting effect along the phase-encoding direction consists of the following
two steps. First, a selected number of ky lines are truncated (in post-processing) and replaced by values calculated from the un-truncated data using
Cuppen's partial Fourier technique (van Cuppen and van Est, MRI, 1987, 5:526). The modified k-space data are then Fourier transformed to an image.
The signal intensity of the reconstructed image will resemble the full-Fourier image, if the peak of the corresponding k-space signals is located in the un-
truncated area. On the other hand, if the peak of the k-space signals is located in the truncated k-space, there will be significant signal loss in the
reconstructed image. Second, by varying the number of truncated/replaced ky lines in the first step, a series of images are obtained. The pattern of pixel-
wise signal variation in those images is determined by the k-space echo shifting effect originating from the susceptibility field gradients. The measured
pixel-wise signal variation pattern is therefore termed k-space energy spectrum, in which abrupt signal changes occur when the peaks of k-space echo
signals are being truncated. For example, Figure 1a presents an EPI image and Figure 1b shows the phase-encoding k-space energy spectrum of three
selected pixels. As indicated by arrows in Figure 1b, the echo-signal peaks are located in ky line number 27, 48, and 74, respectively, as a result of
spatially varying susceptibility field gradients. The above two steps can also be applied to measure the k-space echo-shifting effect along the readout
direction, by truncating different number of kx lines in EPI data and calculating the corresponding k-space energy spectrum.
Measurement of susceptibility field gradients and EPI distortion correction: Once the spatially dependent echo-shifting effects along both readout
and phase-encoding directions are measured (Nx and Ny), the susceptibility field gradients along these two directions (Gx and Gy) can be calculated
based on Equation 1 and Equation 2, where tDW is the dwell time, TEeff is the effective echo time, and tESP is the echo-spacing time.
γ FOVx[Nx× τDW+ (TEeff+ Ny× τESP)] ......... 
For example, the phase-encoding susceptibility field gradient map calculated from the EPI data in Figure 1a is shown in Figure 1c. When the RF
excitation pulse frequency is chosen to be the averaged Larmor frequency of the imaged slice, Bo field inhomogeneity maps can be derived from the
susceptibility field gradients, and then used to remove EPI's nonlinear geometric distortions through the previously reported phase modulation method. If
the RF pulse frequency is set to off-resonance, there may remain residual global translation after nonlinear distortion correction. This remaining image
translation can easily be detected and corrected with rigid body image registration.
Human brain and phantom EPI data acquired at 1.5 T and 3 T GE systems were processed with the proposed k-space energy spectrum analysis
algorithm. The susceptibility field gradients were calculated based on Equations 1 and 2 (without the need of extra field mapping scan) and then used to
correct EPI geometric distortions through the phase modulation method (Chen and Wyrwicz, MRM, 1999, 41:1206).
Results and Discussion
Phantom EPI images acquired at 3T under three different shim settings are shown in Figure 2a. Using the proposed k-space energy spectrum
analysis and distortion correction technique, the nonlinear geometric distortions in EPI data are removed, as shown in Figure 2b. Examples of distortion
correction in human brain EPI are presented in Figure 3. As shown, there exist significant geometric distortions in human brain EPI (Figure 3a), and
these artifacts can be reliably removed using the proposed data processing algorithm (Figure 3b).
The proposed method is superior to conventional field map based EPI correction methods in three ways. First, using k-space energy spectrum
analysis algorithm, the field maps can be obtained without
performing additional field mapping scan. Second, in the
presence of subject movement during dynamic EPI scans,
the valid field maps corresponding to different scan times
can be reliably obtained with the proposed post-processing
method. Third, in the proposed algorithm, complicated in-
plane phase unwrapping procedure that is required in most
conventional field mapping methods can be avoided. It
should be noted that this EPI distortion correction
technique is also compatible with parallel imaging methods.
Even though the EPI distortions can generally be reduced
when data are acquired with parallel imaging schemes, the
residual distortions may still degrade the spatial accuracy,
especially at high field. Using the proposed post-processing
algorithm, the residual distortion in parallel EPI can be
γ FOVy(N ×τESP+ TEeff) ......... 
Proc. Intl. Soc. Mag. Reson. Med. 13 (2005)