Wei Liu^{1} and Kun Zhou^{1}

^{1}Siemens 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 = 90**^{0}) and short TR (FA < 90^{0}).### 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 imaging

^{1, 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 case

^{3}. 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 = 90

^{0}) and short TR (FA < 90

^{0}).

### 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