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

Multi-band Magnetic Resonance Fingerprinting
can be achieved using UNFOLD-like acquisition and dictionary matching without
using parallel methods. However, the MR parametric maps after dictionary matching
in one slice suffers from artifacts due to the high frequency components of
other simultaneously acquired slices. In this work, a new acquisition strategy was
proposed for the multi-band acquisition, where spiral-in-out trajectory was
used to provide extra* k _{z}* encoding.
A modified sliding window reconstruction was also proposed to reduce the high
frequency oscillations.

A FISP-MRF [4] sequence was used and the readout
gradient of our proposed sequence is shown in Fig 1a and the associated spiral-in-out
trajectory in Fig 1b. The flip angle (FA) and repetition time (TR) trains are respectively
shown in Figs 1c and 1d. The additional *G _{z}*
blip (the green trapezoid in Fig 1a) is inserted in between the spiral-in and
spiral-out readout portion, thereby introducing a $$$\Delta k_{z}$$$ shift between the two readouts. The additional

Given our proposed sampling strategy, the image
series of different slices are encoded with unique phase pattern that favors UNFOLD.
An example for MB factor of 3 is illustrated in Fig 3. The dictionary matching
process is to search the maximum inner product between the acquired MR signal and
dictionary $$$\sum_{t=0}^N m_{i,j}(t) = \sum_{t=0}^N s_{i}(t)d_{j}(t)$$$ where $$$\textbf{s}_i$$$ and $$$\textbf{d}_j$$$ respectively indicate the signal evolution vector
for the *i*^{th} voxel and the *j*^{th} dictionary vector, $$$\textbf{m}_{i,j}=\textbf{s}_i\cdot\textbf{d}_j$$$, and $$$s_{i}$$$, $$$d_{j}$$$ and $$$m_{i,j}$$$ are their *t*^{th} elements, and *N* is the number of TR. If $$$\textbf{S}_{i}$$$, $$$\textbf{D}_{j}$$$ and $$$\textbf{M}_{i,j}$$$ are Fourier transform of $$$\textbf{s}_i$$$, $$$\textbf{d}_j$$$ and $$$\textbf{m}_{i,j}$$$, then $$$\textbf{M}_{i,j}=\textbf{S}_{i}\circledast\textbf{D}_{j}$$$, where $$$\circledast$$$ indicates convolution, so $$$\sum_{t=0}^N m_{i,j}(t) = M_{i,j}(0)=\sum_{\omega=0}^N S_{i}(\omega)D_{j}(-\omega)$$$. Then the target low frequency component in
signal is chosen by $$$D_{j}(\omega)$$$.
Due to the high in-plane undersampling factor, the high frequency components of
signal are not neglectable. The low frequency component is then collapsed with
the high frequency components of other slices. With the extra encoding of *k*_{z}, the frequency of different
slices became more sparsely distributed, thus rendering less effect on each
other.

To further reduce the high frequency
artifact, a modified sliding window reconstruction method was proposed. As
shown in Fig 2e, sliding window gridding was performed for each *k _{z}* so that the combined k-space
data still followed the desired sampling pattern in

All data were acquired with a 3T MRI
scanner (Achieva TX, Philips Healthcare) with 8-channel head coil. An in-house
FISP-MRF sequence was used with imaging parameters: TE = 6ms, TI = 20ms, FOV =
300 x 300 mm^{2}, image resolution = 1.17 x1.17 x 5 mm^{3}, acquisition
matrix size = 256x256. The acquisition window is 8.4ms, with a rotation increment
of gold angle 222.5 degree for different dynamics, and TR varied between 12~14
ms.

Results and Discussion

Figs 4 and 5 show the parameter maps with MB = 3 and MB = 4 respectively. For 2D MRF, spiral-in-out trajectory can reduce the error caused by off-resonance effect, especially with long acquisition window. For MB-MRF, the use of our proposed spiral-in-out trajectory in conjunction with an additional[1] Ma, D., Gulani, V., Seiberlich, N., Liu, K., Sunshine, J. L., Duerk, J. L., & Griswold, M. A. (2013). Magnetic resonance fingerprinting. Nature, 495(7440), 187.

[2] Madore, B., Glover, G. H., & Pelc, N. J. (1999). Unaliasing by Fourier‐encoding the overlaps using the temporal dimension (UNFOLD), applied to cardiac imaging and fMRI. Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine, 42(5), 813-828.

[3] Cao, X., Liao, C., Wang, Z., Chen, Y., Ye, H., He, H., & Zhong, J. (2017). Robust sliding‐window reconstruction for Accelerating the acquisition of MR fingerprinting. Magnetic resonance in medicine, 78(4), 1579-1588.

[4] Jiang, Y., Ma, D., Seiberlich, N., Gulani, V., & Griswold, M. A. (2015). MR fingerprinting using fast imaging with steady state precession (FISP) with spiral readout. Magnetic resonance in medicine, 74(6), 1621-1631.

[5] Zahneisen, B., Poser, B. A., Ernst, T., & Stenger, V. A. (2014). Three‐dimensional Fourier encoding of simultaneously excited slices: generalized acquisition and reconstruction framework. Magnetic resonance in medicine, 71(6), 2071-2081.

[6] Ma, D., Jiang, Y., Chen, Y., McGivney, D., Mehta, B., Gulani, V., & Griswold, M. (2018). Fast 3D magnetic resonance fingerprinting for a whole‐brain coverage. Magnetic resonance in medicine, 79(4), 2190-2197.

Fig 1. (a)
Our proposed spiral-in-out readout for MB-MRF sequence. The additional Gz blip (green) was
introduced to provide extra kz
encoding. (b) Spiral-in-out
trajectory. (c) Flip angle and (d) TR trains.

Fig 2. Multi-band MRF acquisition strategy in kz-t domain for the case of
MB factor of 3 (a) without and (b) with extra kz encoding; MB factor of 4 (c) without and (d) with
extra kz encoding. (e) Our proposed modified sliding
window reconstruction method.

Fig 3. (a)
MR signal evolution from MB-MRF with MB factor of 3. (b) Simulated signal of related dictionary entry. (c) The Fourier transform of the signal
in b, and (d) the Fourier transform of the signal in a. (e)-(g) MR signal
evolutions of the 3 simultaneously acquired slices in a. The shaded area indicated the low frequency components of the
signal from one slice in e, which is
collapsed with the high frequency components of the signal from the other two
slices in f and g.

Fig 4. MR parametric maps from MB-MRF with MB
factor of 3 obtained from (a) single
slice MRF result[MOU1] , (b) without and (c) with
additional kz encoding, (d) with modified sliding window, and (e) with additional kz encoding and modified
sliding window.
[MOU1]What do you mean by reference?

Fig 5. MR parametric maps from MB-MRF with
MB factor of 4 obtained from (a) single
slice MRF result[MOU1] , (b) without and (c) with
additional kz encoding, (d) with modified sliding window, and (e) with additional kz encoding and modified
sliding window.
[MOU1]What do you mean by reference?