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A Dual-Echo bSSFP Imaging Method for Proton Resonance Frequency-Based Thermometry and Analysis of Phase Behavior in bSSFP
Seohee So1, JaeJin Cho1, Kinam Kwon1, Byungjai Kim1, and HyunWook Park1

1School of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, Korea, Republic of

### Synopsis

Proton resonance frequency thermometry is useful to estimate temperature change that is proportional to the resonance frequency change. In this study, we propose a dual-echo bSSFP thermometry method that generates a high intensity signal and linear phase to the frequency shift. Off-centered acquisition in the balanced steady-state free precession creates an imperfect linear phase with respect to the frequency shift. The dual-echo acquisition method compensates for the phase nonlinearity and generates phase information that is linearly proportional to the frequency shift. This phase linearization makes it possible to accurately measure the proton resonance frequency shift caused by temperature change.

### INTRODUCTION

Magnetic resonance (MR) thermometry is a technique for monitoring and guiding thermal therapy. Proton resonance frequency (PRF) thermometry is one of the most preferred methods to estimate temperature change that is proportional to the resonance frequency change1. A balanced steady-state free precession (bSSFP) sequence is advantageous in terms of signal-to-noise ratio (SNR) and fast imaging time. However, the nonlinear phase response to the frequency shift is an obstacle for PRF based thermometry. In this study, we propose a dual-echo bSSFP method that generates a high intensity signal and linear phase to the frequency shift.

### METHODS

The signal acquired at echo time (TE), TE=TR/2, of bSSFP sequence does not have a linear relation between the phase of the transverse magnetization and the off-resonance frequency. However, if the echo time is shifted from TR/2, the phase information becomes proportional to the off-resonance frequency and the shifted time. However linearity of the phase with respect to the off-resonance frequency is not perfect and depends on $E_{1}=e^{-TR/T_{1}}$ and $E_{2}=e^{-TR/T_{2}}$. The nonlinearity is explained by relationship between free induction decay (FID) signal and echo signal in the bSSFP sequence. The FID signal and echo signal are the main components of the bSSFP signal2,3. Phase of the FID signal at TE is ${\delta}={\triangle}f{\times}TE$ and that of the echo signal is ${\delta}-{\theta}={\triangle}f{\times}TE-{\triangle}f{\times}TR$ where ${\triangle}f$ is the off-resonance frequency. The FID signal always has a higher signal intensity than the echo signal at every time. This intensity difference between the FID and echo signal results in the phase nonlinearity of the bSSFP signal in Figure 1(c). The phase of the bSSFP signal is biased toward the FID phase. The phase nonlinearity can cause a measurement error when it is used for thermometry. The bSSFP signal at TE is described as follows:

$$M_{xy}(TE)=|M_{FID}|e^{-TE/T_{2}^{*}}e^{i\delta}-|M_{echo}|e^{-TE/T_{2}}e^{i({\delta}-{\theta})}+(higher~order~terms)\hspace{3em}[1]$$

$$|M_{FID}|=M_{0}\cdot{\tan{\alpha/2}}\cdot\left\{1-\left(E_{1}-{\cos{\alpha}}\right)\left(1-E_{2}^{2}\right)/\sqrt{p^{2}-q^{2}} \right\}\hspace{3em}[2]$$

$$|M_{echo}|=M_{0}\cdot{\tan{\alpha/2}}\cdot\left(1/E_{2}\right)\cdot\left\{1-\left(1-E_{1}{\cos{\alpha}}\right)\left(1-E_{2}^{2}\right)/\sqrt{p^{2}-q^{2}} \right\}\hspace{3em}[3]$$

where $M_{0}$ is the magnetization at thermal equilibrium, $\alpha$ is the flip angle, $p=1-E_{1}\cos{\alpha}-E_{2}^{2}\left(E_{1}-\cos{\alpha}\right)$, and $q=E_{2}\left(1-E_{1}\right)\left(1+\cos{\alpha}\right)$.

In order to solve this nonlinearity problem, we employ a dual-echo method where two echoes are obtained at different TEs, respectively. From the two echo signals, the phase evolution between two echo times is measured by division of complex signals acquired from two different TEs as follows:

$$\angle\frac{M_{xy}(TE_{2})}{M_{xy}(TE_{1})}=\angle\frac{M_{0}\cdot\frac{\left(1-E_{1}\right)\cdot\sin{\alpha}}{p-q\cos{\theta}}{\cdot}e^{-TE_{2}/T_{2}}{\cdot}\left(1-E_{2}e^{-i\theta}\right){\cdot}e^{i\theta\left(TE_{2}/TR\right)}}{M_{0}\cdot\frac{\left(1-E_{1}\right)\cdot\sin{\alpha}}{p-q\cos{\theta}}{\cdot}e^{-TE_{1}/T_{2}}{\cdot}\left(1-E_{2}e^{-i\theta}\right){\cdot}e^{i\theta\left(TE_{1}/TR\right)}}=\left(TE_{2}-TE_{1}\right)\cdot\triangle{f}\hspace{3em}[4]$$

The phase difference between dual echo signals represents a perfectly linear proportion to $\triangle{f}$ in Eq. [4]. With two echoes symmetrically apart from the center of TR, we can efficiently measure the temperature change.

### RESULT

A numerical phantom consisting of a homogeneous circular object at the center is generated to verify the proposed MR thermometry method. At the center of the object, temperature increases 10℃. The temperature change at the other position of the object follows bioheat equation4 explaining heat dissipation. In addition, field inhomogeneity and noise are introduced in the simulation. TR=10ms and TE=0 and 10ms for two echoes, respectively, are used, which is an ideal scan condition for maximum efficiency, and phase cycling of π radian is applied. Figure 2(l) represents the result of the proposed method. The proposed method using dual echo signals effectively compensated for the nonlinearity and accurately estimated the temperature change.

A cylindrical CAGN phantom5 was made for experiments, which mimicked prostate tissue. Because actual temperature change could not be generated in our experimental conditions, the frequency shift from temperature change was substituted by a change of local field strength. The estimated frequency shift from the phase information using the proposed method are coincident with the applied local field.

### DISCUSSION

We proposed the dual-echo acquisition in a bSSFP sequence for thermometry based on PRF imaging. The proposed dual-echo acquisition solved nonlinearity problem of single off-centered echo and generated a linear phase according to the frequency shift. The high signal intensity from the bSSFP sequence and the phase amplification by combining dual echo signals are advantages of the proposed dual-echo bSSFP method. In addition, anatomical images with high SNR and CNR make guidance for thermal therapy easier and more accurate.

### Acknowledgements

This research was supported by a grant of the Korea Health Technology R&D Project through the Korea Health Industry Development Institute (KHIDI), funded by the Ministry for Health and Welfare, Korea (HI14C1135) and the Technology Innovation Program(#10076675) funded by the Ministry of Trade, Industry & Energy (MOTIE, Korea).

### References

1. Hindman, J. C.. Proton resonance shift of water in the gas and liquid states. The Journal of Chemical Physics. 1966; 44(12): 4582-4592.

2. Gyngell, M. L.. The steady-state signals in short-repetition-time sequences. Journal of Magnetic Resonance 1969; 81(3): 474-483.

3. Freeman, R., & Hill, H. D. W.. Phase and intensity anomalies in Fourier transform NMR. Journal of Magnetic Resonance 1969; 4(3): 366-383.

4. Pennes, H. H.. Analysis of tissue and arterial blood temperatures in the resting human forearm. Journal of applied physiology. 1948; 1(2): 93-122.

5. Hattori, K., Ikemoto, Y., Takao, W., et al. Development of MRI phantom equivalent to human tissues for 3.0‐T MRI. Medical physics. 2013; 40(3).

### Figures

(a) A sequence diagram of the proposed dual-echo bSSFP imaging method. (b) and (c) are the magnitude and phase profiles of the conventional bSSFP for various TEs. When TE<TR/2, the phase decreases as θ increases. On the other hand, the phase and θ have a positive proportional relation when TE>TR/2. The phase difference between two echoes acquired with (a) shows the phase profile in (d), which is completely linear with respect to θ. The slope of the phase profile in (d) is proportional to the time difference between the two echoes.

Simulation data before and after heating and estimated temperature changes. (a, b) and (c, d) are the magnitude and phase of the reconstructed images from the first and second echoes, respectively, before heating. (e, f) and (g, h) are those after heating. The temperature changes are estimated from the first echo only (j), the second echo only (k) and the proposed dual echoes (l). (m) shows cutview graphs of temperature maps representing the center horizontal position marked as a dotted horizontal line in (i). (j) is underestimated and (k) is overestimated in comparison with the true temperature change (i).

Results of phantom experiments. The applied local field is horizontally modulated by a shim coil. For two methods of SPGR and the proposed method, five different frequency modulations from 1Hz/pixel to 5Hz/pixel are carried out. (a) and (c) are the phases for various frequency modulations. (b) and (d) represent cutviews of the temperature changes measured from the phase information along the horizontal dotted line in the first image of (a). Solid lines are the estimated frequency and dotted lines are the real frequency for every local field modulation (1~5Hz/pixel).

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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