Xiaoxi Liu^{1}, Di Cui^{1}, Erpeng Dai^{2}, Edward S. Hui^{1,3}, Queenie Chan^{4}, and Hing-Chiu Chang^{1}

Propeller-EPI is a self-navigated multi-shot technique for high-resolution diffusion-tensor imaging. However, corrections for 2D Nyquist ghost and distortion for each blade data are necessary to obtain high-quality image. In this study, we aim to develop a self-calibrated and collaborative Propeller-EPI reconstruction (SCOPER) framework that can 1) allows the estimation of phase errors and off-resonance map from the blade data, and 2) collaboratively reconstruct fully-corrected Propeller-EPI image from all blade data and the thereof. Our results demonstrated that SCOPER shows improved SNR performance, compared with conventional Propeller-EPI reconstruction pipelines.

**Purpose**

**Methods**

**Signal model of Propeller-EPI**:

The k-space signal
along the j^{th} phase encoding line of the n^{th} blade
data from Propeller-EPI
acquisition for the $$$\gamma$$$^{th} coil can be written
as

$$S_{n,\gamma,k_{y|j}}=F_{n,k_{y|j}}(n\theta,j)C_{\gamma}\phi_{n,k_{y|j}}\psi_{k_{y|j}}\rho \qquad (1),$$

where $$$F_{n,k_{y|j}}(n\theta,j)$$$ represents the Fourier encoding matrix for the n^{th} blade with angle $$$n\theta$$$, $$$C_{\gamma}$$$ the coil
sensitivity, $$$\phi_{n,k_{y|j}}$$$ the 2D phase errors due to Nyquist ghost, and phase
variations associated with diffusion gradient, $$$\psi_{k_{y|j}}$$$ the 2D phase error due to off-resonance, and $$$\rho$$$ the unknown 2D image.

**SCOPER framework**: The entire
framework is summarized in Fig.1. In the pre-processing stage, the 2D phase
errors $$$\phi$$$ for the odd and even echoes for each blade were estimated
from the T2WI data. Nyquist ghosts were subsequently corrected for a pair of
blades with 0° and 180° rotation angles, and the pixel displacement map (DM) was subsequently measured by using the
reversed gradient method [4]. The
phase error $$$\psi$$$ caused by off-resonance was estimated from the DM. For DWI data, the
inter-shot phase variations are included in $$$\phi$$$. Finally,
all blade data are collaboratively reconstructed by solving a signal model
shown in Eq.(1) using the conjugate-gradient (CG) algorithm with a total
variation constraint[11].

**Experiments**: Human brain DTI data
sets with acquisition matrix of 128x128 were acquired using a 3.0T MRI scanner (Achieva
TX, Philips) using LAP-EPI with four different blade acceleration factor (i.e.,
R=1, 2, 3, and 4) and the following imaging parameters: 24 blades, blade rotation
of 15°, and blade size of
128x32. High-resolution DTI data sets with acquisition matrix of 192x192 were
acquired using LAP-EPI and SAP-EPI with the following parameters: 20 blades, blade
rotation of 18°, blade size of 192x20
(LAP-EPI) and 64x38 (SAP-EPI with 60% partial Fourier), and blade acceleration
factor of 3. All data were acquired with FOV of 240 mm, and b-value of 800 s/mm^{2}
in 6 diffusion directions. A multi-echo GRE sequence with same geometric
parameters as those of the DTI acquisition was performed for the estimation of
field map.

**Data reconstruction
and evaluations**: All Propeller-EPI data were reconstructed using four
different methods, namely 1) SCOPER, and conventional Propeller-EPI
reconstruction pipelines 2) without distortion correction, 3) with field map
correction, and 4) with reversed gradient correction. SNR was measured to
assess the quality of these four reconstruction methods.

**Results**

[1] Wang, Fu‐Nien; Huang, Teng‐Yi; Lin, Fa‐Hsuan; Chuang, Tzu‐Chao, et al. PROPELLER EPI: An MRI technique suitable for diffusion tensor imaging at high field strength with reduced geometric distortions. Magnetic Resonance in Medicine, November 2005, Vol.54(5), pp.1232-1240

[2] Skare, Stefan; Newbould, Rexford D.; Clayton, Dave B.; Bammer, Roland. Propeller EPI in the other direction. Magnetic Resonance in Medicine, June 2006, Vol.55(6), pp.1298-1307

[3] Chen, NK; Wyrwicz, AM. Optimized distortion correction technique for echo planar imaging. Magn Reson Med 2001; 45:525–528.

[4] Chang, H.C.; Chuang, T.C.; Lin, Y.R.; Wang, F.N. et al. Correction of geometric distortion in Propeller echo planar imaging using a modified reversed gradient approach Quant Imag Med Surg, 3(2) (2013), p.73

[5] Chang HC, Chen NK, Chuang TC, Juan CJ, Wu ML and Chung HW, “PROPELLER-EPI improved by 2D phase cycled reconstruction”, ISMRM, 20th Annual Meeting, Melbourne, Australia, May 2012.

[6] Chuang TC1, Huang TY, Lin FH, Wang FN, Juan CJ, Chung HW, Chen CY, Kwong KK. PROPELLER-EPI with parallel imaging using a circularly symmetric phased-array RF coil at 3.0 T: application to high-resolution diffusion tensor imaging. Magn Reson Med. 2006 Dec;56(6):1352-8.

[7] Chuang, T-C.; Huang, T-Y.; Wang, F-N. and Chung H-W. Advantages of long-axis PROPELLER EPI via k-space weighting: comparison of point spread function with short-axis PROPELLER EPI. ISMRM 2006; abstract no. 2955

[8] Aksoy, Murat; Skare, Stefan; Holdsworth, Samantha; Bammer, Roland. Effects of motion and b-matrix correction for high resolution DTI with short-axis PROPELLER-EPI. NMR in Biomedicine, August 2010, Vol.23(7), pp.794-802

[9] Voss, Henning U.; Watts, Richard; Uluğ, Aziz M.; Ballon, Doug. Fiber tracking in the cervical spine and inferior brain regions with reversed gradient diffusion tensor imaging. Magnetic Resonance Imaging, 2006, Vol.24(3), pp.231-239

[10] Block, Kai Tobias; Uecker, Martin; Frahm, Jens. Undersampled radial MRI with multiple coils. Iterative image reconstruction using a total variation constraint. Magnetic Resonance in Medicine, June 2007, Vol.57(6), pp.1086-1098

Fig.1:
The reconstruction
flowchart of SCOPER. In the pre-processing stage, we firstly derive the 2D
phase errors $$$\phi_{n,k_{y|j}}$$$ between
odd and even echoes from T2WI data for all blades. Afterward, the Nyquist ghosts are corrected for a pair of
blades with 0° and
180° rotation
angles, and the
displacement map (DM) is subsequently measured by using reversed gradient
method. For DWI data, the inter-shot phase variations are included in derived
2D phase errors $$$\phi_{n,k_{y|j}}$$$. Finally, all blade data are collaboratively reconstructed by solving a
signal model with k-space encodings, 2D phase errors, coil sensitivity, and
off-resonance effect taken into account.

Fig.2: The 128x128 T2WI and averaged DWI images reconstructed
from LAP-EPI data (24 blades, 32 k-lines/blade, and 15° rotation) using (a)
conventional Propeller-EPI reconstruction, (b) SCOPER with off-resonance
information derived from an external field map measured from multi-echo GRE
imaging, and (c) SCOPER with off-resonance
information derived from displacement map (DM) measured internally from the raw
data. The images produced from conventional Propeller-EPI reconstruction show
the signal-loss and blurring due to off-resonance effect (yellow arrows). The
proposed SCOPER framework can reduce the artifacts due to off-resonance effect
in Propeller-EPI acquisition.

Fig.3: (a)-(d) The 128x128 T2WI and DWI images reconstructed
from LAP-EPI data acquired with four different blade acceleration factors
varying from 1 to 4 (24 blades, 15° rotation, and 32 k-lines for full-sampled
blade data). All data were reconstructed with three different conventional
Propeller-EPI reconstruction pipelines and proposed SCOPER framework. The three
conventional Propeller-EPI reconstructions employ different strategies to
reduce the artifacts associated with off-resonance effect, including 1)
applying triangle weighting to each blade, 2) distortion correct of each blade
using fieldmap, and 3) distortion correction of each pair of blades using reversed
gradient method.

Fig.4:
The comparison of 192x192 DTI data (with 1.25 x 1.25 mm^{2} in-plane
resolution) acquired by using either (a) LAP-EPI or (b) SAP-EPI, with an acceleration
factor of 3 for each blade data acquisition. All data were reconstructed with
three different conventional Propeller-EPI reconstruction pipelines and
proposed SCOPER framework. The resulted images demonstrate that the proposed
SCOPER framework can successfully reconstruct either LAP-EPI or SAP-EPI data,
with reduced noise amplification due to parallel imaging reconstruction and
minimized artifacts caused by off-resonance effect.

Fig.5: The SNR
measurements of T2WI and averaged DWI images reconstructed from (a) 128x128
data set with LAP-EPI acquisition (as shown in Figure 3), and (b) 192x192 data
set with either LAP-EPI or SAP-EPI acquisition (as shown in Figure 4). The
quantitative measurements show prefect agreement in improved SNR performance by
using SCOPER reconstruction framework.