Conductivity Tensor Imaging Reconstruction Protocol

Conductivity tensor images were reconstructed using an MRCI toolbox which is available at http://iirc.khu.ac.kr/toolbox.html (Sajib et al., 2017 (link)). The raw data was extracted from the k-space of the MR spectrometer. To minimize geometrical mismatches, the B1 phase maps and DWI were registered with the anatomical T2-weighted images after denoising and bias corrections. The B1 phase map, which is the spatial sensitivity distribution of the applied RF coil measured via MRI, is used to obtain σ_H (Katscher et al., 2009 (link)). From the MEMS data obtained after imaging experiment, the multiple echoes were combined to achieve a higher signal-to-noise ratio (SNR) using a weighting factor. The optimized phase maps were used to reconstruct σ_H (Gurler and Ider, 2017 (link)). The multi-b-value DWI data were corrected for eddy-current effects and geometrical distortions. The averaged images at b = 0 were linearly co-registered to the magnitude images of MEMS data, and the affine transformation matrix was used to non-linearly co-register the multi-b-value DWI (Smith, 2002 (link)). The conductivity of extracellular space can be defined as the product of ion concentration and mobility of charged particles. The following CTI formula was used for all conductivity tensor image reconstructions (Sajib et al., 2018 (link)): ${\sigma }_L=\alpha {\sigma }_e=\alpha \overline{c_e}{\mu }_e$ where σ_L is the low-frequency conductivity; α is the extracellular volume fraction; σ_e is the conductivity of extracellular space; $\overline{c_e}$ is the ion concentration; ${\mu }_e$ is the ion mobility. The apparent extracellular ion concentration $\overline{c_e}$ can be estimated as suggested by Sajib et al, (2018) (link). $\overline{c_e}=\frac{{\sigma }_H}{\alpha d_e^w+\left(1-\alpha \right)d_i^w\beta }$ where β is the ion concentration ratio of the intracellular and extracellular spaces; d_e^w and d_i^w are the extracellular and intracellular water diffusion coefficients, respectively. Since the ion concentration inside and outside of the giant vesicles are almost similar (β = 1), the low-frequency isotropic conductivity σ_L can be expressed as follows: ${\sigma }_L=\frac{\alpha {\sigma }_H}{\alpha d_e^w+\left(1-\alpha \right)d_i^w\beta }{d}_{\mathrm{e}}^w$
The details of the conductivity tensor reconstruction procedures followed those outlined in the works of Katoch et al, (2019) (link).