MR-based electrical conductivity mapping is important for SAR monitoring and has the potential for MR diagnosis^1,2. 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.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 (TE_eff). 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).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/TE_eff=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. By combining the four TSE data, high frequency components were enhanced while low frequency components still remained (for T₂=100ms, ~2.5% at TE_eff). 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.

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

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

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