Synopsis
An
automated method for tissue phase and susceptibility estimation from
multichannel data is proposed. Using ESPIRiT with virtual body coil calibration
on multichannel data, phase-sensitive coil combination is achieved without an
additional reference acquisition. This is shown to perform similarly to SNR-optimal
Roemer combination that requires additional reference body and head coil acquisitions.
Estimation of the tissue phase from the combined data is posed as a regularized
inverse problem using the spherical mean value property. The extension of the
technique to single-step Quantitative Susceptibility Mapping is also
demonstrated on 2D, 3D and Simultaneous MultiSlice data. Purpose
We introduce an automated, data-driven coil combination method for
high-quality phase and susceptibility imaging that obviates the need for an
additional reference acquisition. The
technique is shown to perform similarly to SNR-optimal Roemer combination (1,2) that requires additional body and head coil acquisitions. For tissue phase estimation, an inverse problem using the spherical mean value (SMV) property was adopted (3,4), and extended to allow single-step
Quantitative Susceptibility Mapping (QSM) (5–7). Our
reconstruction approach is shown to enable streamlined phase and
QSM processing of multi-coil images from routinely acquired 2D, 3D and
Simultaneous MultiSlice (SMS) protocols.
Theory
The magnetic field created by background susceptibility sources is harmonic inside the brain
boundary, hence can be filtered out using an SMV kernel (3). Denoting the total
and tissue phase as φtot and φtis,
this
can be expressed as M(s*L(φtot))=M(s*φtis), where M is the brain mask,
s is an SMV filter and L is Laplacian unwrapping operator (8,9).
RESHARP
technique formulates SMV filtering as a regularized inverse problem
(10):
minφtis ||M(s*L(φtot)) - M(s*φtis)||22 + α·||φtis||22
Expressing
the convolution operations as multiplication with k-space kernel S=Fs, this
formulation is readily extended to single-step QSM:
minχ ||M(F'SFL(φtot)) - M(F'SDFχ)||22 + λ·TV(χ)
Here,
the susceptibility distribution χ is related to the tissue phase φtis via DFχ=φtis and λ is the Total Variation parameter. Nonlinear conjugate
gradients (11) were employed for optimization.
Automated data-driven
coil combination
Optimal-SNR coil combination requires estimation of coil sensitivities as well as the
receiver phase offsets, which need to be removed from the coil images for
constructive addition (1,2). This necessitates additional reference
images acquired with the body coil and head coil array, where the head coil images
are normalized by the body coil to remove anatomical information from the receiver
phase estimates. Virtual body coil concept (12) derives a homogenous reference from the head array
data, thus averting the need for an additional body coil acquisition. This is
achieved by computing the singular value decomposition (SVD) across channels,
and taking the dominant singular vector as the body coil reference, similar to
a “uniform-mode birdcage combination”. We propose to combine this concept with
ESPIRiT (13) for automated calibration of sensitivities. In
ESPIRiT, the relative receiver phase offset is arbitrary; hence the first coil
channel is assumed to be the reference. To make use of the virtual body coil
concept, we apply SVD compression (14) on the head array, and sort the virtual channels
in decreasing order of eigenvalues. This way, the first virtual channel corresponds
to the dominant singular vector, and therefore is the virtual body coil. Supplying
the SVD compressed data to ESPIRiT then uses the virtual body coil as the reference,
thus allowing coil sensitivity estimation without an additional acquisition
(Fig.1).
Data Acquisition &
Reconstruction
Three volunteers were scanned with
informed consent. Following BET brain masking (15) and Laplacian unwrapping, tissue
phase and QSM images were reconstructed using α and λ chosen with L-curve (16). A 32-channel head array was
used for reception and coil sensitivities were estimated from the central 16×16×16
k-space points of the acquired data using the proposed ESPIRiT with virtual
body coil concept. The following datasets were acquired:
(i) 3D-GRE at 3T with 1mm
isotropic resolution (Fig.2): FOV=240×192×120mm3,
TE/TR=24.8/35ms. For comparison against Roemer combination, additional
reference acquisitions with body and head coils were processed with ESPIRiT to
compute coil sensitivities.
(ii) 2D-GRE at 3T with 1.5mm isotropic resolution (Fig.3): FOV=192×192×144mm3, TE/TR=20/2630ms.
(iii)
SMS-EPI with blipped-CAIPI (17) at
7T with 2mm isotropic resolution (Fig.4): MultiBand 3× accelerated data were acquired at
3× in-plane acceleration with FOV=200×200×126mm3 and TE/TR=15/2040ms.
To mitigate SMS slice-group boundary artifacts stemming from large acquisition time
differences between adjacent slices at the slice-group boundaries, Laplacian
unwrapping was applied separately for each slice-group.
Results
Fig.2 demonstrates high-quality phase and QSM reconstructions where the difference from
Roemer combination is 2.6% and 2.3% RMSE respectively. Fig.3 shows high-fidelity
QSM images free of dipole artifacts. Arrows in Fig.4 point to the slice-group boundary
artifacts in the SMS phase images, which were largely mitigated in the tissue
phase and susceptibility results.
Discussion & Conclusion
Herein, an automated coil sensitivity
estimation technique that does not require additional reference scans has
been proposed. This is shown to yield detailed phase and QSM images with nearly
identical quality as the Roemer combination. This approach can be particularly
useful in cases where an adequate body coil reference is not available, such as
ultra-high field scanners. The technique is applicable to raw coil images from
2D, 3D and SMS acquisitions and performs in a data-driven fashion from as few
as 16×16 central k-space lines of the acquired data.
Acknowledgements
NIH NIBIB P41-EB015896, 1U01MH093765, R24MH106096, 1R01EB01943701A1 References
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