Anisotropic conductivity tensor imaging for transcranial direct current stimulation (tDCS) using magnetic resonance diffusion tensor imaging (MR-DTI)

Abstract

Transcranial direct current stimulation (tDCS) is a widely used non-invasive brain stimulation technique by applying low-frequency weak direct current via electrodes attached on the head. The tDCS using a fixed current between 1 and 2 mA has relied on computational modelings to achieve optimal stimulation effects. Recently, by measuring the tDCS current induced magnetic field using an MRI scanner, the internal current pathway has been successfully recovered. However, up to now, there is no technique to visualize electrical properties including the electrical anisotropic conductivity, effective extracellular ion-concentration, and electric field using only the tDCS current in-vivo. By measuring the apparent diffusion coefficient (ADC) and the magnetic flux density induced by the tDCS, we propose a method to visualize the electrical properties. We reconstruct the scale parameter, which connects the anisotropic conductivity tensor to the diffusion tensor of water molecules, by introducing a repetitive scheme called the diffusion tensor J-substitution algorithm using the recovered current density and the measured ADCs. We investigate the proposed method to explain why the iterative scheme converges to the internal conductivity. We verified the proposed method with an anesthetized canine brain to visualize electrical properties including the electrical properties by tDCS current.

Fig 1. Schematic diagram for DT-J-substitution algorithm.

(A) MR T₂-weighted image of the canine head with three pairs of surface electrodes. A current is diagonally injected from the left-top to the right-bottom. (B) MR magnitude image of the brain region. (C) Measured B_z image for the current injection. (D) Recovered projected current flow overlaid on the MR magnitude image. (E) Diagonal components of the estimated diffusion tensor. (F) Recovered scale parameter to connect the conductivity tensor and the diffusion tensor. (G) Recovered electrical conductivity tensor.

Fig 2. Internal current density in the brain region by injecting current.

(A) Cylindrical imaging structure attached a pair of electrodes to inject current. (B) Three dimensional current flow in the brain region. (C) Current flow streamlines overlap the T₂ weighted MR magnitude image in the first, second, and third slices.

Fig 3. Diffusion tensor images and recovered electrical property images.

(A) Six ROIs were overlaid on the T₂ image and diagonal components of the diffusion tensor of water molecule. (B) Case 1: reconstructed scale parameter η and diagonal components of the conductivity tensor using tDCS current. (C) Case 2: reconstructed scale parameter $\tilde{\eta }$ and diagonal components of the conductivity tensor using two independent injection currents.

Fig 4. Mean conductivity images in the first, second, and third imaging slices.

(A) Reconstructed mean conductivity images using tDCS current in the first, second, and third imaging slices. (B) Reconstructed mean conductivity images using two independent injection currents in the first, second, and third imaging slices.

Fig 5. Recovered electrical property images.

(A) Intensity of the projected current density, (B) Angle images between the twice updated velocity vector, D∇u², and the electric field ∇u, and (C) Reconstructed apparent isotropic conductivity images by using J-substitution algorithm.

Fig 6. Conductivity tensors inside the chosen rectangular ROI.

(A) Rectangular ROI marked in the T₂-weighted MR magnitude image. (B) and (C) Mean conductivities reconstructed using tDCS current and two injection currents, respectively. (D) and (E) Conductivity tensor images corresponding to (B) and (C) represented by tri-axial ellipsoids, respectively. The radii of each ellipsoid are proportional to the eigenvalues and their axes are oriented along the directions of the eigenvectors. The colors of the ellipsoid indicate the orientation of the principle eigenvector.