Seohee So^{1}, Hyunseok Seo^{2}, and HyunWook Park^{1}

Conventional parallel imaging methods reconstruct MR images from subsampled data, which utilizes spatial sensitivity information of multi-channel RF coil. In this study, localization of receiving coil sensitivity along readout direction (x) is introduced to efficiently utilize the coil sensitivity for parallel imaging. In the x-ky space, localization window is applied for estimation of missing data. Sensitivity localization in the readout direction makes near channels more weighted than distant channels for calculating estimation kernel. The proposed reconstruction method for parallel imaging considers the correlation between spatial sensitivities along the readout direction of receiving channels and region to be reconstructed.

We conducted computer simulations to validate the proposed
reconstruction method. Six-channel birdcage RF coil was designed^{5}
and sensitivity of each channel was calculated using Biot-Savart’s law^{6}
as shown in Figure 2. Modified Shepp-Logan phantom image with a matrix size of 256×256 was created and sensitivity of each channels was multiplied to
the image. With a reduction factor of three, GRAPPA estimation kernel size of
2(PE)×5(RO), ACS lines of 24, conventional GRAPPA reconstruction and the
proposed localized reconstruction were performed. In
order to show the effect of sensitivity localization, GRAPPA estimation kernels
were compared between the conventional GRAPPA and the proposed localized
reconstruction. The conventional GRAPPA shares one estimation kernel for
estimating all of the missing data. The proposed reconstruction has one estimation
kernel for estimating data in each window. Figure 2 shows that kernel weights
of the proposed method for higher sensitivity channels are greater than that of
the conventional method. This means the influence of distant channels is small
and the influence of near channels is large for the proposed method. The reconstructed
images and differences from the reference image that was reconstructed from fully
sampled data are shown in Figure 3. Noise from the proposed method is smaller
and more restricted than that from the conventional reconstruction method.

In order to show the effect of sensitivity localization, number of channels were changed and performance of the proposed reconstruction methods was analyzed. Number of channels increased only in the radial direction of the birdcage-shaped coil. As the channel sensitivities are localized, the performance of the proposed method increases as shown in Figure 4.

1. Deshmane, A., Gulani, V., Griswold, M. A., et al. Parallel MR imaging. Journal of Magnetic Resonance Imaging. 2012; 36(1): 55-72.

2. Griswold, M. A., Jakob, P. M., Nittka, M., et al. Partially parallel imaging with localized sensitivities (PILS). Magnetic Resonance in Medicine. 2000; 44(4): 602-609.

3. McVeigh, E. R., Bronskill, M. J., Henkelman, R. M.. Phase and sensitivity of receiver coils in magnetic resonance imaging. Medical physics. 1986; 13(6): 806-814.

4. Griswold, M. A., Jakob, P. M., Heidemann, R. M., et al. Generalized autocalibrating partially parallel acquisitions (GRAPPA). Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine. 2002; 47(6): 1202-1210.

5. Hayes, C. E., Edelstein, W. A., Schenck, J. F., et al. An efficient, highly homogeneous radiofrequency coil for whole-body NMR imaging at 1.5 T. Journal of Magnetic Resonance. 1969; 63(3): 622-628.

6. Giovannetti, G., Landini, L., Santarelli, M. F., et al. A fast and accurate simulator for the design of birdcage coils in MRI. Magnetic Resonance Materials in Physics, Biology and Medicine. 2002; 15(1-3): 36-44.

Schematic
diagram of the proposed method

(a) is
simulated phantom image, (b) is six-channel birdcage coil and their
sensitivities. (c) and (d) are kernels to estimate data of channel1 using
GRAPPA algorithm and the proposed algorithm for green line data in (a),
respectively. Six 2×5 kernels are shown in (c). Top left kernel in (c) is a
kernel for estimating channel1 data from subsampled channel1 data and bottom
right kernel is for estimating channel1 data from subsampled channel6 data. (e)
and (f) are estimation kernels to estimate data of channel3 using GRAPPA
algorithm and the proposed algorithm for blue line data in (a), respectively.

(a) is the fully sampled ground truth. (b) and (c) are the reconstructed
phantom images from the conventional GRAPPA algorithm and the proposed
algorithm, respectively. Absolute difference images and mean square errors
between the reconstructed images and ground truth for (d) the conventional
GRAPPA algorithm and (e) the proposed algorigthm.

Number of RF coil channels versus mean square error decrement compared
with the conventional GRAPPA reconstruction. 0% MSE decrement means MSE of the
proposed method is same as GRAPPA. Five different window sizes are tested.
Circle lines represent the proposed reconstruction algorithm that only one
central readout point is used in a single window and the window shifts into
next point along the readout direction. Star lines represent the proposed
reconstruction algorithm that whole points are used in a single window and the window
shifts with a size of window along the readout direction.