Synopsis

High acceleration is an effective tool to achieve whole brain coverage with acceptable total acquisition times. A limitation of parallel imaging is high noise amplification at high acceleration factors. In this work, an algorithm for parallel imaging of RASER in two dimensions implemented. The noise enhancement is theoretically derived and experimentally validated. Results show that even at high acceleration noise amplification remains low and high resolution whole brain images can be obtained with RASER.

Introduction

Methods

RASER is ultrafast imaging method using spatiotemporal encoding (SPEN) (Fig. 1)^{1, 2}. The signal in the SPEN-dimension is sequentially excited by a chirp-pulse and in same order recorded during an echo readout train. The signal is localized as result of signal dephasing in the periphery of the quadratic phase profile generated by frequency-sweep of the chirp-pulse. The vertex of the quadratic phase moves along the SPEN-dimension encoding an image profile. The signal in the SPEN-dimension is, hence, acquired in the image domain. Parallel imaging in the SPEN-dimension was achieved by using multi-band excitation. The phase-encoded slab-selective dimension is undersampled for acceleration.

All experiments were performed on a 7 T scanner (Siemens, Erlangen, Germany) with Nova 8Tx 32Rx head coil. Full reference scans with two to four bands were acquired of a spherical phantom filled with silicone oil. Other imaging parameters were spatial resolution (2 mm)³, acquired matrix size: 200 x # bands·24 x 64. T_E = 75 ms, T_R = 800 ms. Acceleration along the SPEN-dimension was simulated by superimposing excitation bands. For the subject data, a full reference scan with short T_R (800 ms) was acquired in addition to the T₂-weighted accelerated scan with long T_R (2 s). Imaging parameters are spatial resolution (1.25 mm)³, T_E = 70 ms, multi-band 4, acceleration in the phase-encoded slab-selective dimension 4.

Images were reconstructed using GRAPPA according to the flow diagram in Fig. 2. The pseudo multiple replica method³ was used to compute g-factors from image SNR. G-factors were also theoretically derived from GRAPPA-weights.

Theory

To perform GRAPPA in the SPEN-dimension the signal, which is acquired in image space I, has to be Fourier-transformed to generate k-space data s:

$$s^{acc}_{\mu}=\sum_{\nu=1}^{N_{SPEN}}\tilde{I}_\nu\exp\left\{-\frac{2\pi i}{N_{SPEN}}\mu\nu\right\}$$[1]

where $$$\tilde{I}_\nu=\sum_{b=1}^{M_B}I_{B\nu}$$$ represents the superimposed signals from multi-band excitation. Considering the noise n during acquisition one obtains

$$s^{acc}_{\mu}+n'^{acc}_{\mu}=\sum_{\nu=1}^{N_{SPEN}}\tilde{I}_\nu\exp\left\{-\frac{2\pi i}{N_{SPEN}}\mu\nu\right\}+\sum_{\nu=1}^{N_{SPEN}}n^{acc}_\nu\exp\left\{-\frac{2\pi i}{N_{SPEN}}\mu\nu\right\}$$[2]

Assuming the noise is random and uncorrelated in respect to the frequency-encoded, SPEN- and phase-encoded slab-selective dimension the noise variance of the k-space signal is

$${\sigma^{2}}\left({n'^{acc}_{c}}\right)=N_{SPEN}{\sigma^{2}}\left({n^{acc}_{c}}\right)$$[3]

For the reference scan the noise propagation is

$$s^{full}_{\mu}+n'^{full}_{\mu}=\sum_{\nu=1}^{M_{B}N_{SPEN}}I_\nu\exp\left\{-\frac{2\pi i}{M_{B}N_{SPEN}}\mu\nu\right\}+\sum_{\nu=1}^{M_{B}N_{SPEN}}n^{full}_\nu\exp\left\{-\frac{2\pi i}{M_{B}N_{SPEN}}\mu\nu\right\}$$[4]

Hence, the noise variance in the reference scan is

$${\sigma^{2}}\left({n'^{full}_{c}}\right)=N_{SPEN}{\sigma^{2}}\left({n^{full}_{c}}\right)$$ [5]

Hence, the noise ratio in k-space before applying GRAPPA-reconstruction is

$$\frac{{\sigma^{2}}\left({n'^{acc}_{c}}\right)}{{\sigma^{2}}\left({n'^{full}_{c}}\right)}=\frac{1}{M_{B}}\frac{{\sigma^{2}}\left({n^{acc}_{c}}\right)}{{\sigma^{2}}\left({n^{full}_{c}}\right)}$$[6]

Using the definition of the g-factor in reference⁴ one obtains for multi-band acceleration

$$\frac{SNR_{full}}{SNR_{acc}}=\frac{1}{M_B}g;g^2=\frac{1}{N_z}\sum_{z=1}^{N_z}g^2_z$$[7]

where g_z is the g-factor for each phase-encoding step in the slab-selective dimension.

Results

Conclusion

Acknowledgements

References

1. Chamberlain R, Park JY, Corum C, Yacoub E, Ugurbil K, Jack CR, Garwood M. RASER: A new ultrafast magnetic resonance imaging method. Magn Res Med 2007;58(4):794-799.

2. Goerke U, Garwood M, Ugurbil K. Functional magnetic resonance imaging using RASER. NeuroImage 2011;54(1):350-360.

3. Robson PM, Grant AK, Madhuranthakam AJ, Lattanzi R, Sodickson DK, McKenzie CA. Comprehensive quantification of signal-to-noise ratio and g-factor for image-based and k-space-based parallel imaging reconstructions. Magn Res Med 2008;60(4):895-907.

4. Breuer FA, Kannengiesser SAR, Blaimer M, Seiberlich N, Jakob PM, Griswold MA. General Formulation for Quantitative G-factor Calculation in GRAPPA Reconstructions. Magn Res Med 2009;62(3):739-746.