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Estimation of transceive phase via LORE-GN algorithm and its use in MREPT1Electrical and Electronics Engineering, Bilkent University, Ankara, Turkey
Synopsis
Balanced steady state free precession (bSSFP) is a widely used MR sequence since it has high speed, high SNR, motion insensitivity and automatic eddy current compensation. Besides all these advantages, bSSFP sequence is susceptible B0 inhomogeneity and banding artifact occurs in certain off-frequency regions. In this paper, one of the correction methods, LORE-GN, is utilized to obtain transceive phase free from the distortions originating from B0 inhomogeneity. As an application, acquired transceive phase maps are used to obtain conductivity maps.
Introduction
Magnetic Resonance Electrical Properties Tomography (MREPT) aims to reconstruct electrical properties (conductivity ($$$\sigma$$$) and permittivity ($$$\epsilon$$$)) by utilizing transceive phase ($$$\phi^{tr}$$$). To obtain transceive phase, many MRI sequences can be used. Among them, bSSFP sequence is favourable since it has high speed, high SNR, motion insensitivity and automatic eddy current compensation1. However, bSSFP suffers from B0 inhomogeneity and the concomitant “banding artifact”.
Methods that involve phase-cycled acquisitions are already offered to remove such artifacts in bSSFP images2-4. Linearization for Off-Resonance Estimation – Gauss-Newton Nonlinear Search (LORE-GN) is one of such correction methods that produces M0, T1, T2, B0 maps, and also transceive phase image.
In bSSFP imaging, complex image value at an arbitrary pixel in the slice of the interest for the nth phase-cycled image can be expressed as:
$$S=KM_0\frac{(1-E_1)sin\alpha}{1-E_1cos\alpha-(E_1-cos\alpha)E_2^2}e^{-TE/T_2}e^{i\Omega TE}\frac{1-ae^{-i(\Omega+\Delta\Omega_n)TR}}{1-bcos[(\Omega+\Delta\Omega_n)TR]}$$
where
$$a=E_2$$
$$b=E_2\frac{1-E_1-E_1cos\alpha+cos\alpha}{1-E_1cos\alpha-(E_1-cos\alpha)E^2_2}$$
$$E_{1,2}=e^{-TR/T_{1,2}}$$
K is the complex-valued coil sensitivity, $$$\Omega$$$ is off-resonance related term as $$$\Omega=2\pi f_{OR}$$$ and $$$\Omega_nTR$$$ is the user-controlled phase increment. LORE-GN implements a two step algorithm to estimate the unknowns, namely $$$\Omega, Re(KM_0), Im(KM_0), T_1$$$ and $$$T_2$$$3. First step involves converting non-linear problem into a linear one by using parametrization. Second step aims to minimize the nonlinear least squares criterion.
Since phase of K is equal to transceive phase, LORE-GN algorithm can be easily used to obtain transceive phase as
$$\phi^{tr}=\angle(K)=tan^{-1}\bigg(\frac{Im(KM_0)}{Re(KM_0)}\bigg)$$
The purpose of the study is to investigate the usage of the corrected transceive phase, which is obtained by utilizing LORE-GN algorithm, in MREPT.
Methods
For LORE-GN algorithm, 16 different phase-cycled bSSFP images are obtained in phantom and human experiments. RF phase increments in each TR are selected as $$$180^\circ-(n-1)\cdot22.5^\circ$$$ where n is the number of corresponding phase-cycled images. For phantom experiments, a cylindrical z-independent experimental phantom with diameter of 20 cm and height of 25 cm was constructed. For background, agar-saline solution (20 gr/L agar, 2 g/L NaCl, 0.2 g/L CuSO4) was used, and for anomalies, saline solution (6 g/L NaCl, 0.2 g/L CuSO4) was prepared. Anomaly regions have diameters as 0.5, 1.5 and 2.5 cm. Human experiment was performed on a 24 years old healthy male volunteer. Experiments were conducted on 3T Siemens Tim Trio MR scanner using quadrature body coil. Generalized phase-based MREPT is used to obtain conductivity maps from transceive phase5.Results
Figure 1 displays magnitude images, phase images and resulting conductivity maps of first phase-cycled image (Figs. 1a,d,g), ninth phase-cycled image (Figs. 1b,e,h), and LORE-GN corrected image from 16 phase-cycled bSSFP images (Figs. 1c,f,i). Banding artifacts are shown by white arrows (Figs. 1b and 1e) and their presence distorts the final conductivity map significantly (Fig. 1h).
In theory, LORE-GN algorithm requires only 3 different phase-cycled images. The effect of introducing additional phase-cycled images can be seen in Figure 2. It can be observed that addition of extra phase-cycled images reduce noise further and increase the quality of the conductivity maps.
Human experiment is shown in Figure 3. Despite the similarity between the phase of the first phase-cycled image and the phase of the LORE-GN corrected image (Figs. 3a and 3b), using LORE-GN algorithm removes the distortion related to B0 inhomogeneity on conductivity maps (Figs. 3c and 3d).
Discussion and Conclusion
Correction for B0 inhomogeneity in bSSFP transceive phase images has already been done for MREPT6,7. However, LORE-GN algorithm brings new advantages, especially in acquisition time. This is because introducing B0 and T2 to the steady state equation, by Ozdemir and Ider,6 requires additional and lengthy B0 and T2 mapping, while PLANET7 requires at least 6 different phase-cycled images (LORE-GN requires only 3). Therefore, with the usage of LORE-GN algorithm, acquisition time for phase-based MREPT can be significantly reduced.Acknowledgements
This study was partially supported by TUBITAK 114E522 research grant. Experimental data were acquired using the facilities of UMRAM, Bilkent University, Ankara.References
1. Katscher U, Kim D, Seo J. Recent Progress and Future Challenges in MR Electric Properties Tomography. Comput Math Methods Med. 2013;2013:1-11.
2. Bangerter NK et al. Analysis of Multiple-Acquisition SSFP. Magn Reson Med. 2004;51(5):1038–47.
3. Björk M et al. Parameter estimation approach to banding artifact reduction in balanced steady-state free precession. Magn Reson Med. 2013;72(3):880-892.
4. Shcherbakova Y et al. PLANET: An ellipse fitting approach for simultaneous T1 and T2 mapping using phase-cycled balanced steady-state free precession. Magn Reson Med. 2017;79(2):711-722.
5. Gurler N, Ider Y. Gradient-based electrical conductivity imaging using MR phase. Magn Reson Med. 2016;77(1):137-150.
6. Ozdemir S, Ider YZ. bSSFP phase correction and its use in magnetic resonance electrical properties tomography. Magn Reson Med. 2018;00:1–13.
7. Gavazzi S et al. Sequences for transceive phase mapping: a comparison study and application toconductivity imaging. In Proceedings of the 26th Annual Meeting of ISMRM, Paris, France, 2018.
Figures
Figure 1: For phantom experiment, magnitude, phase and conductivity maps that are obtained from first phase-cycled image (a,d,e), ninth phase-cycled image (b,e,h), and corrected image by using LORE-GN algorithm (c,f,i). The deteriorating effect of banding artifact on conductivity map is clearly seen in (h).
Scan parameters were: FOV = 225 mm, FA = 40, TE/TR = 2.29/4.58 ms, 60 slices, 16 phase-cycled images, duration for each phase-cycled image is 36 seconds.
Figure 3: For human experiment, phase and conductivity maps that are obtained from (a,c) first phase-cycled image, (b,d) LORE-GN corrected image with 16 phase-cycled images, (e) magnitude of the first phase-cycled image.
Scan parameters were: FOV = 225 mm, FA = 40, TE/TR = 2.29/4.58 ms, 60 slices, 16 phase-cycled images, duration for each phase-cycled image is 36 seconds.