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On the Selection of Slice Profile for Through-Plane Resolution in Multi-Slice MR Imaging
Eric G. Stinson1, Soudabeh Kargar2, Roger C. Grimm1, and Stephen J. Riederer1

1Radiology, Mayo Clinic, Rochester, MN, United States, 2Biomedical Engineering and Physiology, Mayo Clinic, Rochester, MN, United States

### Synopsis

Multislice imaging is a mainstay of clinical MR exams, but image reformatting is limited by through-plane resolution. Some methods aim to overcome this by acquiring overlapping slices and deconvolving the slice profile. However, slice profiles which have zero crossings in the Fourier (spatial frequency) domain preclude the recovery of those spatial frequencies. Here, we describe the problem and provide a solution in the form of slice profiles without zero crossings in $k_Z$-space.

### Introduction

Multi-slice imaging is a mainstay of clinical MRI exams, often used to provide T2-weighted contrast. However, the through-plane resolution of these datasets is usually low, on the order of 3-4 mm slice thickness, typically 3-8$\times$ coarser than the in-plane resolution. Reformatting the acquired images into the other two planes is sub-optimal. One approach to overcoming this limitation is to sample the object with overlapping slices and then deconvolve the effect of the slice profile (1,2); however, depending on the slice profile used for the sampling, some spatial frequencies may not be recoverable. For example, a “rect” slice profile, generally regarded as optimum for conventional multi-slice imaging, has zero crossings within the desired passband of through-plane spatial frequencies. In this work, that passband is termed the “$k_Z$ bandwidth ($BW_{k_Z}$)” and the response within the band (the Fourier transform of the slice profile) is termed "$k_Z$ response." The spatial frequency response in $Z$ of the overall imaging process (including any slice profile demodulation) is described by the modulation transfer function (MTF).

Figure 1 shows the theoretical $k_Z$ response (A) and MTF (after regularized slice profile deconvolution) (B) for three different functions: a windowed sinc (corresponding to the conventional rect slice profile), a Gaussian, and a shifted cosine. Due to the zero crossing in the windowed sinc function, there is a dropout in the resolution response as shown by the MTF (B).

The purpose of this work is to demonstrate the resolution loss from zero crossings within $BW_{k_Z}$ and propose alternative slice profiles without zero crossings.

### Methods

Three $k_Z$ response functions were chosen to: (a) cover the desired $BW_{k_Z}$ ($\pm$0.625 mm$^{-1}$ in Figure 1), (b) be spatially limited in image space, to prevent through-slice cross-talk in a multislice acquisition, and (c) have slice thickness to provide adequate signal-to-noise ratio. The $k_Z$ response functions were: (i) a windowed sinc, which is taken as the control, (ii) a Gaussian function, and (iii) a shifted cosine function defined as one period of the form $1+cos(A k_Z)$ where $A - arccos(2b-1)/BW_{k_Z}$ is a scaling factor to ensure that the response at $\pm$$BW_{k_Z}$ is $b$. The Gaussian pulse was scaled to the same $b$. From the desired $k_Z$ response, ideal slice profiles were computed (through Fourier transform) and Shinnar-Le-Roux RF Pulse methods (3) were used to design the RF pulses. Slice profiles were measured with a readout in the slice-selection direction, and reasonably matched the desired $k_Z$ response.

A 3D-printed continuously-variable comb resolution phantom (Figure 2) was submerged in deionized water and imaged. The resolution combs vary from 0.152 to 0.625 line pairs per mm (LP/mm). Scan parameters are shown in Table 1. The through-slice direction was chosen to traverse the short dimension of the phantom and allow the resolution bar fidelity to reflect through-plane resolution.

Images were reconstructed with and without slice profile demodulation. Estimated empirical MTFs were measured by analyzing line profiles ($p$) through the resolution combs over the length of the phantom. Empirical MTF was defined as $MTF_{emp} = \frac{max(p) - min(p)}{max(p) + min(p)}$ (4).

### Results

Reformatted multi-slice imaging stacks (A) and estimated empirical MTFs (B) are shown in Figure 3 for each of the designed $k_Z$ response profiles. No slice profile deconvolution was performed on these images. Finer resolution bars are resolvable in the images acquired with the Gaussian and shifted cosine pulses than with the windowed sinc. Additionally, the empirical resolution response for the windowed sinc is reduced at the zero crossing as expected.

The images in Figure 4A were reconstructed using slice deconvolution processing in $k_Z$-space with Tikhonov regularization and $\lambda$ = 0.025. Empirical MTF (B) is closer to unity for many spatial resolutions, but still suffers from resolution dropout when the windowed sinc pulse is used. The Gaussian and shifted cosine pulses do not suffer from this drawback and show near unity response out to and beyond 0.5 LP/mm, indicating that sub-mm resolution is possible.

### Discussion

We have shown that in multi-slice imaging through-plane resolution is limited by the spatial frequency response of the slice profile. Zero crossings within the desired $BW_{k_Z}$(such as in conventional windowed sinc pulses) indicate spatial frequencies to which the slice is not sensitive. When zero crossings are avoided (e.g. Gaussian and shifted cosine pulses) the finer structures may be resolved. The greater extent in $k_Z$ space of the alternative pulses effectively reduces the slice thickness; however, avoiding zero crossings is also critical for resolution recovery.

### Conclusion

In terms of through-plane resolution of multi-slice imaging, the conventional rect profile is non-ideal because of zero crossings within the passband. However, Gaussian or cosine-shaped selective RF pulses can be devised to provide fidelity for all spatial frequencies as high as 0.5 LP/mm.

### Acknowledgements

No acknowledgement found.

### References

1. Okanovic M et al. Magn Reson Med 2018;80:1812–1823.
2. Riederer SJ et al. International Society for Magnetic Resonance in Medicine (ISMRM). 2018 #4492.
3. Pauly J et al. IEEE Trans Med Imaging 1991;10:53–65.
4. Bushberg JT. Lippincott Williams & Wilkins; 2002.

### Figures

Figure 1 - A: The desired $k_Z$ responses of three different slice profiles - a windowed sinc, a Gaussian, and a shifted cosine function - that extend out to $\pm$0.625 mm$^{-1}$. Note that the windowed sinc includes a zero crossing at $\pm$0.3125 mm$^{-1}$. The zero crossing corresponds to a drop-out in the modulation transfer function (MTF) as shown in (B). The Gaussian and shifted cosine pulses do not have a zero crossing which is reflected in the MTF showing a smoother resolution response.

Figure 2 - Photographs of the continuously variable comb resolution phantom used in this work. Note the fiducial notches in the base indicating the resolutions demarcated by the dotted yellow lines. (In B the lines indicate the resolution combs at the top of the phantom, and due to optical distortion do not line up with the notches in the base.)

Figure 3 - Before any deconvolution of the slice profile, the spatial resolution response of the acquisition is seen to differ between the different slice profiles (A). When an empirical modulation transfer function is plotted (B), a reduction in the resolution response is seen at the zero crossing of the windowed sinc pulse, but not in the Gaussian or shifted cosine pulse (as in the theoretical plots in Figure 1A).

Figure 4 - Deconvolution of the slice profile results in sharper images of the continuously variable comb phantom (A). Additionally, the empirical MTF plots show a more uniform response for the Gaussian and shifted cosine $k_Z$ responses, but the resolution dropout due to the zero crossing in the windowed sinc is not recovered.

Table 1: Scan parameters of the fast-spin echo imaging sequence used in this work. Field of view and matrix size are reported as LR$\times$AP$\times$SI, and the slice selection direction was SI.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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