Flip Angle Optimization in Diffusion-Weighted Imaging using Simultaneous Multi-Slice Acceleration
Wei Liu1 and Kun Zhou1

1Siemens Shenzhen Magnetic Resonance Ltd, Shenzhen, China, People's Republic of

### Synopsis

In this study, an automatic optimization scheme was proposed in diffusion-weighted imaging using simultaneous multi-slice (SMS) acceleration to determine an appropriate flip angle based on a short TR, which is capable to obtain similar contrast of a pair of tissue type compared to the one with long TR scan. With this optimization scheme, minimal TR in SMS case is practically achievable and there is no obvious contrast deviation between images from long TR (FA = 900) and short TR (FA < 900).

### PURPOSE

Recently simultaneous multi-slice (SMS) accelerated single-shot EPI (ss-EPI) and readout segmented EPI (rs-EPI) have been introduced as a robust method for reducing scan time in diffusion imaging1, 2. This technique relies on exciting multiple slices simultaneously and the overall TR can therefore be reduced, leading to an acquisition time reduced almost by the same factor. Usually a 900 excitation is preferred in diffusion scan to maximize signal intensity and TR should be much longer than T1 to allow a substantial recovery of longitudinal magnetization. If the perturbed magnetization is not fully recovered to its equilibrium, image intensity will be decreased and contrast will be also altered. So in SMS study, the reduced TR should not only depend on the slice acceleration factor but also on the longitudinal magnetization recovery. Other values of the flip angle can be used with shorter TR to enable a better longitudinal magnetization recovery and increase signal or maximize the contrast between a particular pair of tissue types in this case3. In this study, an automatic optimization scheme was proposed to determine an appropriate flip angle (FA) based on a short TR, which is capable to obtain similar contrast of a pair of tissue type compared to the one with long TR scan. With this optimization scheme, there is no obvious contrast deviation between images from long TR (FA = 900) and short TR (FA < 900).

### METHODS

The signal in a diffusion acquisition can be derived by considering the longitudinal magnetization at various points within the pulse sequence. Readout-segmented Echo Planar Imaging (rs-EPI) is shown in Figure 1 as an example. In the derivation, the transverse magnetization at point G is assumed to be negligible because of spoiler gradient and neglect the T1 relaxation during the RF excitation pulses. Let the equilibrium longitudinal magnetization be M0 and use the steady state condition MA = MG and assume θ2 = 180o, MZ and signal intensity S at point G could be expressed as $$M_{G}=M_{0}\frac{2E_{2}E_{3}-E_{1}E_{2}E_{3}-2E_{3}+1}{1-\cos\theta_{1}E_{1}E_{2}E_{3}}$$ $$S=M_{G}\sin\theta_{1}\sin^{2}(\theta_{2}/2)e^{-TE_{1}/T_{2}}e^{-bD}$$ where $E_{1}=e^{-TE_{1}/2T_{1}}, E_{2}=e^{-TE_{2}/2T_{1}}$, $E_{3}=e^{-(TR-TE_{1}/2-TE_{2}/2)/T_{1}}$, b value controls the degree of diffusion weighting in the image, and D is the diffusion coefficient along the direction of the applied diffusion gradient. Please note that the second refocusing pulse is used to collect navigator data but not imaging data, which only affects the longitudinal magnetization equilibrium. Then a contrast between a particular tissue pair A and B can be expressed as: $$Contrast_{T_{1A}-T_{1B}}=\frac{M_{G}(T_{1A}, TR, TE_{1}, TE_{2}, \theta_{1})e^{-TE_{1}/T_{2A}e^{-bD_{A}}}}{M_{G}(T_{1B}, TR, TE_{1}, TE_{2}, \theta_{1})e^{-TE_{1}/T_{2B}e^{-bD_{B}}}}$$ Assume an optimization condition $$Contrast_{T_{1A}-T_{1B}}(TR_{long}, \theta_{1}=90) = Contrast_{T_{1A}-T_{1B}}(TR_{short}, \theta_{1})$$ and $$TE_{1}, TE_{2} << TR, \theta_{1opt}=PI-\arccos(\frac{a+c-ab-1}{b-ac-bc+abc})$$where $$a=(1-e^{-\frac{TR_{long}}{T_{1A}}})/(1-e^{-\frac{TR_{long}}{T_{1B}}}), b=e^{-\frac{TR_{short}}{T_{1B}}}, c=e^{-\frac{TR_{short}}{T_{1A}}}$$ All measurements were performed using a Siemens MAGNETOM Spectra 3T system. Experimental data were obtained on healthy volunteer using a non-product SMS accelerated rs-EPI sequence with FA optimization scheme. The Scan parameters were TE = 79ms, slice thickness = 5mm, matrix = 224×224, number of slices = 20, echo spacing = 0.36ms, b = 0, 1000 s/mm2, in-plane GRAPPA factor = 2, slice acceleration factor =2. The original SMS acquisition with TR = 4800ms had a total scan time of 4:12 min; the SMS acquisition with/without FA optimization with TR = 2000ms had a total scan time of 1:52 min.

### RESULTS

A comparison of sample images results from original SMS rs-EPI with different TRs and modified SMS rs-EPI with optimized FAs is shown in Fig.2. In the original SMS case, image contrast drops a lot along the decrease of TR, especially for the contrast between CSF and GM/WM (Fig.2 B). According to a proposed FA optimization scheme, reasonable san time is achieved with comparable image contrast compared to original SMS case with a long TR. Please note that the image contrast improvement is also visible in b = 1000s/mm2 images, indicated with red circle. The magnified images of the marked region are also displayed. Furthermore, the images from the proposed scheme outperformed the images from ss-EPI, but can be acquired in the similar scan time.

### DISCUSSION AND CONCLUSION

The proposed method enables a comparable contrast for specific T1 values of tissue pair in a short TR acquisition, compared to the one acquired with a long TR. Therefore minimal TR in SMS case is practically achievable without noticeable contrast alteration. In general, the previous derivation of a FA optimization could be simply adapted to ss-EPI diffusion sequence, with small modifications related to the number of refocusing pulses. It is also feasible for other sequence types with a perfect spoiler at the end of the sequence.

### Acknowledgements

No acknowledgement found.

### References

1. Setsompop K, Gagoski BA, Polimeni JR, et al. Blipped-controlled aliasing in parallel imaging for simultaneous multislice echo planar imaging with reduced g-factor penalty. Magn Reson Med, 2012; 67:1210-24.

2. Frost R, Jezzard P, Douaud G, et al. Scan time reduction for readout-segmented EPI using simultaneous multislice acceleration: Diffusion-weighted imaging at 3 and 7 Tesla. Magn Reson Med, 2014.

3. M. A. Bernstein, K. F. King and X. J. Zhou, Handbook of MRI pulse sequences,. Elsevier Academic Press, 2004, ISBN: 0-12-092861-2

### Figures

Figure 1. The timing points A-G used to calculate the steady state of longitudinal magnetization in rs-EPI acquisition

Figure 2. (A-B) original accelerated image, b = 0 s/mm2, TR = 4800/2000 ms; (C) accelerated image with FA optimization, b = 0 s/mm2, TR = 2000 ms, EFA= 49 degree, optimized based on T1A = 1500 ms ,T1B = 4000 ms. (D) comparable image using ss-EPI. (E-H) corresponding images with b = 1000 s/mm2. Magnified images of the marked region are also shown.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
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