Qing Li^{1}, Congyu Liao^{1}, Huihui Ye^{1}, Ying Chen^{1}, Hongjian He^{1}, Qiuping Ding^{1}, and Jianhui Zhong^{1}

A squeezed variable density spiral (SVDS) trajectory was proposed to reduce SAR and peak RF power in 2D RF pulse design using parallel transmission (pTX). SVDS was generated by applying a pointwise squeezing factor to conventional variable density spiral (CVDS) trajectory. Compared to CVDS, SVDS can reduce peak RF and SAR by close to 40%, with minimal increase in the normalized root mean square error (NRMSE) of the excitation profile and pulse duration.

**Purpose**

A
method based on Fourier transformation of the target excitation pattern ^{3}
was used. First, RF pulse was designed based on the excitation k-space traversal
trajectory. SAR was denoted as the time integral of the RF power. Squeezing
factors were then determined via minimizing the SAR. Next, the k-space trajectory was
divided into dozens of groups based on the local RF peaks. Since most of the SAR
was contributed by the peaks of RF pulses, the goal was to minimize the SAR of
each group by squeezing the k-space points whose RF power was lower within the
group towards the point with the highest RF power. The proposed SAR optimization
problem was solved by an evolutionary algorithm called Backtracking Search
Optimization Algorithm (BSA) ^{4}.

More specifically the CVDS trajectory $$$K =re^{j\theta(r)}$$$ was designed with a controllable excitation FOV (XFOV) method where $$$r$$$ is the distance to the k-space center and $$$\theta$$$ is the azimuthal angle defined as $$$\theta(r) = 2\pi\int_{0}^{r}FOV(\rho)d\rho$$$. Squeezing factor $$$S = \lambda e^{j\phi}$$$ is defined to describe the squeezing towards the k-space center by the squeezing strength parameter $$$\lambda$$$ and along the tangential direction by the squeezing angle $$$\phi$$$, which can be analytical defined as $$\lambda = 0.5(1-\lambda_{0}(r))\cdot cos(\kappa_{1}(\theta+\kappa_{2})) +0.5(1+\lambda_{0}(r))$$ and $$\phi = \phi_{0}(r)\cdot sin(\kappa_{1}(\theta+\kappa_{2})),$$ where $$$\lambda_{0}(r)$$$ and $$$\phi_{0}(r)$$$ are the referential k-space energy-based squeezing strength and squeezing angle; $$$\kappa_{1}$$$ and $$$\kappa_{2}$$$ are the polar number and rotation angle. Finally, the SVDS trajectory was generated as the product of CVDS trajectory and the squeezing factor, which then be optimized to satisfy the system limitations.

Fig. 1 shows
several target excitation profiles and their corresponding k-space energy
distribution as well as the squeezing factors. Measurements were performed on a
Siemens 3T Prisma scanner equipped with 2 independent pTX channels.
High-resolution MRI with SVDS trajectory was tested on both phantom and human
brain. The pTX RF pulse was designed with a spatial domain pulse design method ^{5}.
B1^{+} maps were obtained by a presaturation TurboFLASH pulse sequence.
Images were acquired using a SE-pTX sequence with the following parameters:
matrix size = 192 × 192, TR/TE = 400/12
ms, slice thickness = 2 mm, FOV = 20 × 20 cm^{2}
for full FOV acquisition and FOV = 10 × 10 cm^{2}
for a reduced FOV (rFOV) imaging.

**Results and Discussion**

Fig 2 shows the RF pulses and Bloch simulated excitation performances of a rectangular pattern designed by the CVDS and SVDS. The black arrows over (c) and (d) indicate that RF peaks in CVDS has been dispersed to the squeezed-in points in SVDS. Thereby, the RF peak amplitude has been reduced in SVDS as shown in (b). The result is in agreement with the squeezing theory where k-space points with low RF amplitude will be squeezed towards the local RF peaks. In the rectangular excitation, SVDS has reduced the SAR and peak RF by 37% and 39% respectively, with 0.15% loss of excitation accuracy and 260 µs pulse extension.

In Fig. 3, three
types of patterns, square, slab and slice, were excited with CVDS and SVDS on a
fixed maximum transmission voltage 200V as measured on the scanner. SVDS provides
higher signal intensity level in square and slab excitation than CVDS. For the
square excitation, SVDS shows a more uniform excitation profile than the
referential SE image because the B1^{+} distributions have been
involved in the SVDS RF pulse design. Fig. 4 shows the ability of SVDS to increase
the imaging resolution by 4 times without prolonging the scan time.

1. Lee D, Grissom W A, Lustig M, et al. VERSE-guided numerical RF pulse design: A fast method for peak RF power control. Magnetic Resonance in Medicine, 2012, 67(2): 353-362.

2. Xu D, King K F, Liang Z, et al. Variable slew-rate spiral design: Theory and application to peak B1 amplitude reduction in 2D RF pulse design. Magnetic Resonance in Medicine, 2007, 58(4): 835-842.

3. Katscher, U., Börnert, P., Leussler, C, et al. Transmit SENSE. Magnetic Resonance in Medicine, 2003, 49: 144–150.

4. Civicioglu P. Backtracking Search Optimization Algorithm for numerical optimization problems. Applied Mathematics and Computation, 2013, 219(15): 8121-8144.

5. Grissom W A, Yip C, Zhang Z, et al. Spatial domain method for the design
of RF pulses in multicoil parallel excitation. Magnetic Resonance in
Medicine, 2006, 56(3): 620-629.

Fig.
1. Different
target excitation profiles and their k-space power distribution as well as the
corresponding squeezing factors plotted in polar coordinates. Polar number in
(a, d, f) is 4, in (b, e) is 2. Rotation
angle in (a, b, c) is 0 and in (d, e, f) are respectively 45°, 90° and
a variable value with *r*.

Fig.
2. Comparing the performance of CVDS and SVDS with Bloch simulation. (a, c) and
(b, d) are the designed RF pulses, k-space trajectories and the excitation
profile for CVDS and SVDS. The k-space trajectories in (c) and (d) are colored by
the normalized RF in (a) and (b) with the colorbar at the left side. (e) is the
numerical comparison of CVDS and SVDS. Note that SAR and peak RF of SVDS in (e)
have recalculated as their relative value to CVDS.

Fig.
3. Phantom validation of square, slab and slice excitation with CVDS and SVDS
pulses. The maximum transmission voltage of all the RF pulses has been fixed to
200V. Images from the first row to the third row are corresponding to the
target profiles of square, slab and slice rounded by the dash line. (c), (f)
and (i) compare the signal intensity of the white lines in CVDS, SVDS and the referential
spin-echo (SE) image. All images share the same colorbar at the left corner.

Fig.
4. High resolution images with SVDS 2D RF excitation. Images from the first
column to the third column are respectively the full FOV image, SVDS 2D RF
excited full FOV image and rFOV image. The first and second row are images for
phantom and in vivo, respectively.