Sulaiman A Al Hasani1, Zhaolin Chen 2, Gary F Egan2, and Jingxin Zhang3
1Department of ECSE, Monash University, Melbourne, Australia, 2Monash Biomedical Imaging, Melbourne, Australia, 3Swinburne University of Technology/School of Software and Electrical Engineering, Melbourne, Australia
Synopsis
Spread spectrum based encoding methods have recently been
investigated to spread the energy of MR signal in k-space and hence allowing
for optimal incoherent sampling and hence higher performance of CS
reconstruction. In this work, we extend the use of spread
spectrum based encoding to 3D GRE sequence. The proposed encoding scheme
can enhance the performance of multi-receive CS reconstruction at high
acceleration factors and preserve resolution of small anatomical structures
and preserve susceptibility contrast for Susceptibility-weighted imaging (SWI). Introduction
Compressed Sensing-MRI (CS-MRI) has shown effectiveness in accelerating data acquisition while preserving image quality [1]. The CS reconstruction is highly dependent on the level of signal (image) sparsity as well as the level of incoherent measurements [1]. Conventional Fourier encoded MRI concentrates the energy of the signal in the center of the k-space, this limits the sampling pattern to fully sampling the high energy center of k-space and inadequate sampling the peripherals of k-space hindering the performance of CS reconstruction at higher acceleration factors. Non-Fourier encoding methods have recently been investigated to spread the energy of MR signal in k-space and hence allowing for optimal incoherent sampling and higher performance of CS reconstruction. CS reconstruction of non-Fourier encoded data can preserve image resolution and contrast in small anatomical structures. In this work, we extend the use of spread spectrum based encoding (Chirp modulated Fourier encoding scheme) to 3D GRE sequence. This encoding scheme optimally spreads the energy of the image signal in the sensing domain “k-space” demonstrated in [2]. The proposed encoding scheme can enhance the performance of multi-receive CS reconstruction at high acceleration factors and preserve sufficient susceptibility contrast for Susceptibility-weighted imaging (SWI) [3].
Method
The measurement system for MRI is given by $$$y=\Theta x $$$ where $$$\Theta $$$ is the Kronecker product of encoding matrices along slice, readout and phase directions $$$E_{ss}$$$, $$$E_{ro}$$$ and $$$E_{ph}$$$ respectively. The proposed method uses tailored RF pulses to implement the Chirp modulated Fourier encoding scheme along the phase direction which is given by: $$E_{ph}= F{{\phi }_{n.n}}=F{{e}^{-i\left[ \frac{\Delta O.T}{2{{N}^{2}}}{{n}^{2}}+\frac{1}{8}\Delta O.T+\frac{\pi }{2} \right]}} (1) $$Where $$$\Delta O$$$ is the Chirp bandwidth, T is the duration of the pulse, N is number of phase encodes and $$$F$$$ is the Fourier matrix. We conducted a simulation on In-vivo acquired data to demonstrate the performance of the proposed encoding method. 3D GRE scans were performed on 3T Skyra (Siemens HealthCare, Erlangen, Germany) using a 32 channels head coil (TE/TR: 20/30 ms ; FOV: 230mm and Flip angle: 15°). Informed consent was taken from a healthy volunteer in accordance with the institution’s ethics policy.The phase encoding lines of the fully sampled k-space were then modulated using Chirp modulation matrix $$$ {{\phi }_{n.n}}$$$ to simulate the results of applying the proposed encoding scheme. The simulated dataset was then randomly under-sampled along the phase encoding direction $$$k_{y}$$$ and under-sampled with distribution along $$$k_{z}$$$ as shown in Figure 1. The under-sampled data were inputted in the multi-receive CS reconstruction pipeline proposed in [2]. The complex coil sensitivity maps were estimated from the fully acquired data and used in the CS reconstruction [4]. The Fourier encoded data were under-sampled with distribution in both $$$k_{y}$$$ and $$$k_{z}$$$. The SWI images were then calculated from the CS-reconstructed complex images for different acceleration factors. The homodyne filter in SWI was implemented using a Gaussian window with $$$\sigma = 2$$$.
Results
The simulation results were compared with those of Fourier encoding in multi-receive CS framework. The proposed encoding scheme achieves better resolution images (both phase and magnitude) at high acceleration factor (e.g. 4x) and preserve small anatomical structures that are viable for SWI analysis. Figure 2 shows phase and magnitude images at acceleration factor of 4. The insufficient sampling of the peripherals of k-space (i.e. high spatial frequencies) when using Fourier encoding and variable density under-sampling pattern, causes large reconstruction errors and blurs in fine anatomical structures such as blood vessels. Figure 2 (d)-(e) shows that the variance of the distribution of error values for all voxels in the phase image is reduced when using Chirp modulated Fourier encoding compared to Fourier encoding ($$$\sigma^2 = 1.0497\times 10^{-7}$$$ for the proposed encoding and $$$\sigma^2 = 1.263\times 10^{-6}$$$ for the conventional Fourier encoding). The mean of the distribution of error in the magnitude image is 0.045 for Chirp modulated Fourier encoding and 0.055 for Fourier encoding (figure 2 (i)-(j)). Figure 3 shows the SWI images and the enhanced delineation of venous blood vessels especially at acceleration factor of 4 when using the proposed encoding scheme for multi-receive CS-MRI.
Conclusion
In this work, we have extended the use of Chirp modulated Fourier encoding to 3D, which provides enhanced susceptibility contrast at acceleration factors 2 and 4 in comparison with Fourier encoding using the multi-receive CS reconstruction framework. Future work will include sequence implementation of Chirp modulated Fourier encoding for 3D GRE and perform QSM calculation.
Acknowledgements
No acknowledgement found.References
[1] Lustig, et al. MRM 2007. [2] S. AL Hasani, et al, ISMRM 2015. [3] E. Mark Haacke et al MRM 2004. [4] Chen, Z., et al NeuroImage. 2010.