Relaxation based Conductivity Weighted Imaging (rCWI)
Jaewook Shin1, Min-Oh Kim1, Jun-Hyeong Kim1, and Dong-Hyun Kim1

1Electrical and Electronic engineering, Yonsei University, Seoul, Korea, Republic of

Synopsis

To reduce the noise amplification of the conductivity imaging, the direct calculation of the Laplacian operator was substituted by appropriate k-space weighted sampling scheme by the combination of four TSE data with alternating PE directions.

Purpose

MR-based electrical conductivity mapping is important for SAR monitoring and has the potential for MR diagnosis1,2. However, during the reconstruction process (especially, calculation of Laplacian operator (Eq.1)), high frequency noise is amplified thereby demanding additive denoising process3. As a result, boundary artifact spill into homogenous regions and degrade the effective resolution of conductivity map. In this study, rather than direct calculation of Laplacian operator, a k-space weighted acquisition scheme mimicking the Laplacian operation was devised using four turbo spin echo (TSE) data with alternating phase-encoding directions. Additional low frequency suppression filter was adapted to match to the Laplacian.

Theory

For conventional MR electrical property tomography (MREPT)4, conductivity map (σ) is retrieved from magnetic field information (H) (Eq.1). In the frequency domain, calculation of the Laplacian operator ($$$\triangledown^{2}=\partial^{2}/\partial x^{2}+\partial^{2}/\partial y^{2}$$$) is transformed as multiplication of high-pass filter (HPF, $$$F\left(k_{x},k_{y}\right)=k_{x}^{2}+k_{y}^{2}$$$) in Fig.1a. To replace the direct calculation of Laplacian operator, high frequency weighted k-space data can be used. Here, this was achieved by employing a TSE sequence with linear k-space ordering (Fig. 1b). The TSE sequence has a T2 dependent point spread function (PSF) which can be modeled as Eq. 2. In this study, to mimic the frequency response of the Laplacian operator, four TSE data with different phase-encoding directions (AP, PA, LR and RL) were linearly combined. The effective frequency response is given in Fig. 1c. The effective PSF is dependent on T2 relaxation time of each tissue and imaging parameters such as echo-spacing (ESP) and effective TE (TEeff). Therefore, the effective PSF depends on T2 value of each tissue. After combining four TSE data, the conductivity weighting was generated by dividing with the SE phase term (Eq. 3).

Method

Tube phantoms with different conductivity (NaCl (0.5/1.0/1.5%)) and T2 (CuSO4 (0.1/0.15 g/L)) values were designed (Fig. 2a) and tested. Phantom and brain imaging were performed in a 3T clinical scanner (3T Siemens Tim Trio MRI scanner) with 2D FSE sequence (resolution=1x1x5mm3, TR/TEeff=2000/371ms, Echo Train Length (ETL)=64 for phantom and 96 for brain, four different PE directions with 4 averages each, total acquisition time=64sec) and a 2D SE sequence (TR/TE=2000/10ms, two opposite readout-directions for eddy current compensation, total acquisition time~8min for phantom and 12min for brain). In the proposed method, an additional butterworth filter was applied to suppress residual low frequency component of the combined TSE data. For comparison, a phase-based approach5 was applied for conventional MREPT. A Gaussian filter (FWHM=2.0mm and 3.0 mms) was applied to reduce the high frequency noise.

Results & Discussion

By combining the four TSE data, high frequency components were enhanced while low frequency components still remained (for T2=100ms, ~2.5% at TEeff). After applying the additional low frequency suppression filter, the proposed method showed conductivity contrast (Fig.2e). However, T2 contrast still remains in the resultant image which was compensated by dividing with by T2 weighting at effective TE (Fig. 2b, 2f). After T2 compensation, conductivity dependent contrast was dominant (Fig.3). Compared with the conventional method (Fig. 2c and d), the proposed method (Fig.2f) showed less boundary artifact. However, blurring was observed due to imperfect T2 kernel design (Fig.1c). In vivo results are given in Fig. 4. Conductivity contrast can be observed similar with the conventional EPT method. Since the effective PSF has T2 dependency, blurring of long T2 components such as CSF (>400ms) may be remained in the conductivity weighted image. Further investigations about optimal scan parameters and kernel designs can be extended for in-vivo conductivity weighted imaging.

Equations

$$\sigma=imag\left\{ \frac{\triangledown^{2}H}{i\omega\mu_{0}H} \right\} \left(1\right)$$

$$F_{TSE}\left(k_{x},k_{y}\right)=exp\left( -\frac{k\left(k_{x},k_{y}\right)}{T_{2}} \right)F\left(k_{x},k_{y}\right) \left(2\right)$$

$$r\sigma WI =-imag\left\{ \frac{exp\left( i\cdot arg\left( \sum_{j=1}^{4} TSE_{j} \right) \right)}{exp\left( i\cdot arg\left( SE \right) \right)} \right\} \left(3\right)$$

Acknowledgements

No acknowledgement found.

References

1. Shin J, Kim MJ, Lee J, Nam Y, Kim M, Choi N, Kim S, Kim D-H. Initial study on in vivo conductivity mapping of breast cancer using MRI. J Magn Reson Imaging 2015;42:371–378.

2 Balidemaj, E, van Lier, A. L, Crezee, H, Nederveen, A. J, Stalpers, L. J, van den Berg, C. A., Feasibility of electric property tomography of pelvic tumors at 3T. Magn Reson Med, 2015. 73(4): p. 1505-13.

3. Seo JK, Kim MO, Lee J, et al. Error analysis of nonconstant admittivity for MR-based electric property imaging. IEEE Trans Med Imaging 2012;31(2):430-437.

4. Katscher U, Voigt T, Findeklee C, Vernickel P, Nehrke K, Dossel O. Determination of electric conductivity and local SAR via B1 mapping. IEEE Trans Med Imaging 2009;28(9):1365-1374.

5. Voigt T, Katscher U, Doessel O. Quantitative conductivity and permittivity imaging of the human brain using electric properties tomography. Magn Reson Med 2011;66(2):456-466.

Figures

Figure 1. Frequency response of (a) ideal Laplacian operator and (b) four T2 point spread function (PSF) with alternating PE directions and combined T2 PSF. (T2 = 100ms, ETL=128 and EPS=6ms)

Figure 2. (a) Agarose phantom model (1%) with different NaCl(0.5/1.0/1.5%) and CuSO4(0.1/0.15g/L) concentration. (b) Corresponding T2 map acquired using multi-echo SE. Conductivity map reconstructed from phase-based EPT method with Gaussian filtering (c). FWHM=2.0mm, (d). FWHM=3.0mm. Proposed conductivity weighted imaging (e) before T2 correction and (f) after T2 correction.

Figure 3. ROI analysis for each NaCl and CuSO4 concentration (green:0.15g/L, brown:0.1g/L). Mean value and standard deviation of conductivity weighted image intensity (a) before T2 compensation and (b) after T2 compensation.

Figure 4. (a) Brain T2 map. Conductivity weighted imaging (b) before T2 correction and (c) after T2 correction. (d) Conductivity map reconstructed from phase-based EPT method with fitting technique.



Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
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