Divya Varadarajan1,2, Robert Frost1,2, Andre van der Kouwe1,2, Leah Morgan1, Bram Diamond1, Emma Boyd1, Morgan Fogarty1, Allison Stevens1, Bruce Fischl1,2, and Jonathan R Polimeni1,2,3
1Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Boston, MA, United States, 2Harvard Medical School, Boston, MA, United States, 3Harvard-MIT HST, Cambridge, MA, United States
Synopsis
High-resolution multi-echo MRI at ultra-high field for ex vivo imaging is time consuming, SNR
starved and suffers from B0 inhomogeneity induced geometric distortions due to low-bandwidth
in the readout direction. Fieldmap-based correction cannot correct
singularities in regions of severe distortion, and reversed gradient (RG) approaches
double the scan time. We propose to combine an alternating-polarity acquisition
scheme for multi-echo MRI with a low-resolution fieldmap based novel distortion
correction algorithm that can correct singularities in half the scan time of RG
and enhance SNR while preserving edges. We show several ex vivo corrected results and demonstrate generalizability to in vivo MRI.
Introduction
B0 nonuniformity due to susceptibility
inhomogeneity causes geometric distortions in MRI whenever B0
offsets are large relative to the encoding bandwidth (BW). This is well studied
for EPI acquisitions1-4. However, here we focus on a lesser-known
case of high-resolution (100–150 μm), ultra-high field (7T), multi-echo ex vivo MRI, where air-tissue interfaces
(e.g. air bubbles) induce strong B0 offsets, and the low-BW required
to achieve high-resolution makes this data vulnerable to distortions spanning 100–1000 μm along the
readout axis5.
Ex vivo MRI is
used to study micro-architectonics, where even distortions at 100 μm are
problematic5. Conventional fieldmap1,2 methods cannot resolve singularities in the image such as
pile-up. Reversed-gradient3-4,6
(RG) methods can resolve singularities but require double the scan time because
two images with matching contrast and opposing distortions must be acquired. Long scan times of ex vivo
imaging make both acquiring a high-resolution fieldmap or an additional RG scan
impractical, rendering existing methods unusable.
Timing constraints often prevent the acquisition of multiple averages, resulting
in SNR-starved data.
In order to overcome these challenges, we propose a novel
acquisition and optimization framework that encodes opposing distortions in a
single multi-echo scan, incorporates a low-resolution fieldmap, and jointly
corrects all echoes using a shared edge constraint that enhances SNR and
corrects distortion singularities without additional high-resolution scans. We
show several ex vivo results and
demonstrate generalizability to in vivo MRI.Methods
Our
acquisition consists of a multi-echo gradient-echo pulse sequence where we
encode alternating echoes with opposite readout directions, positive and
negative; opposite readouts cause the distortions to be in opposing directions in
consecutive echoes to improve SNR efficiency7. Using a forward signal model7 we synthesize the opposite
polarity for every echo. That is, in a four-echo acquisition in which TE1 is
acquired with RO+, TE2 with RO−, TE3 with RO+,
and TE4 with RO−, we use echoes at TE2 and TE4 to
synthesize an image at TE3 with RO−. This ensures we
have both readout polarities for all contrasts and allows us to correct for
singularities using a single multi-echo acquisition.
Our method then jointly corrects distortion in all echoes by
solving a cost function given by, $$\arg\min_{\rho_0 \cdots \rho_N} \sum_{i=1}^N{\|K_i\rho_i-\tilde{y}\|^2+\lambda\|diag(\sqrt{\ell_i})D\rho_i\|^2},$$ where $$$N$$$is
the number of echoes, $$$i$$$
is an echo index,
$$$\rho_i$$$
is the undistorted echo, $$$y_i$$$
is the
acquired (distorted) echo and $$$\tilde{y_i}$$$ concatenates
the acquired and the synthesized opposite polarity echo. The first term is a least-squares data fidelity where
$$$K_i$$$ contains the linear
shift due to B0 inhomogeneity. We use a low-resolution fieldmap to calculate
$$$K_i$$$. The regularization term assumes that
echoes share the same edge locations corresponding to anatomy8. Here,
$$$\ell_i$$$ is the line
process prior9
calculated using the $$$L_{2,1}$$$ norm indicating group
sparsity i.e. common edges across echoes and $$$D$$$ is the finite
difference operator. The line process will be close to one in smooth regions of
the image, reducing the regularizer to a quadratic smoothness term that enhances
SNR. The regularization vanishes at common edges due to low values of $$$\ell_i$$$ thereby preserving them. The
optimization was solved using conjugate gradient.
We tested the proposed method by acquiring three ex vivo human brain hemisphere datasets
with a 4-echo protocol: two at 150 μm (TE=[5.65,11.95,18.25,24.55] ms, TR
=34 ms, FA=20°) and one at 100 μm (TE=[7.5,15.5,23.5,31.5] ms, TR=45 ms, FA=10°).
A 2-mm resolution fieldmap was additionally acquired in all sessions. We tested
generalizability of the proposed method to in
vivo multiecho MPRAGE (TE=[1.61,3.47,5.33,7.19] ms, TR=2.53 s, FA=7°)
data at 1 mm resolution.Results
Figures 1 and 2 show results of applying the proposed method
to the 150 μm ex vivo dataset.
Figure 1 zooms into the cerebellum (top row) and frontal lobe (bottom row) with
inhomogeneity of 100–650 μm. Figures 1c–f show the root-mean-square (RMS) combination
across all echoes and edge maps, with red and green edges corresponding to
echoes 0 and 1 respectively and yellow edges are regions of perfect alignment
between the echoes. RMS images of uncorrected data in Figs. 1c and e are blurry
or have unaligned edges (see arrows), while RMS images of the corrected data in
1d. and 1f. are sharper with well-aligned edges.
Figure 2 compares the proposed framework
with FSL’s topup4 applied to conventional RG data that require twice
the scan time to acquire. Both methods correct distortion well (blue arrow),
but the proposed method exhibits improved edge preservation (purple arrow) and
requires half the acquisition time.
Figure 3 shows a 100 μm sagittal
slice through visual cortex of the third echo, and edge maps of the third and
fourth echoes (in red and green) in a region of strong field inhomogeneity. The
edges align well after correction, and SNR is considerably improved without
blurring the anatomy.
Figure 4 shows an in vivo MEMPRAGE coronal slice with distorted temporal lobe. Distortion
is visible in 4b edge map where the consecutive echoes do not align. The
proposed method corrects the distortion well and accurately aligns the echoes.Conclusion
We presented a novel distortion correction framework for
high-resolution, 7T multi-echo ex vivo
data that enhances SNR and optimizes acquisition time. We also demonstrated that it extends to routine in vivo
MRI.Acknowledgements
This
work was supported in part by the NIH NIBIB (grants P41-EB015896), by the BRAIN Initiative (NIH NIMH grant
R01-MH111419), and by the MGH/HST Athinoula A. Martinos Center for Biomedical
Imaging; and was
made possible by the resources provided by NIH Shared Instrumentation Grants S10-RR023043 and S10-RR019371. References
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