Electric Current Detection Based on the MR Signal Magnitude Decay

Abstract

Purpose: Conventional current density imaging method, which relies on the detection of the magnetic field induced by the current in an image phase, is demanding and difficult to perform. In this study, a much simpler signal-magnitude-decay (SMD)-based current detection method is proposed.

Methods: Conductive test and biological samples were imaged at various TE times using the gradient- or spin-echo imaging sequences with superimposed constant or bipolar currents, respectively. The SMD curve was sampled for each image voxel, which enabled voxel-vise current density calculation by fitting an appropriate SMD model curve to the measured SMD curve. Effect of the voxel size on the signal decay and precision of the current density calculation was studied as well.

Results: It was shown theoretically, as well as verified by experiments on test and biological samples, that the current flowing though the sample creates an inhomogeneous magnetic field, which, as a consequence has a faster signal decay. Estimated current density from the measured signal decay increase agreed reasonably well with the actual current density, especially with the larger voxel sizes and longer times to signal acquisition. The sensitivity of the SMD method is up to $1/\sqrt{6}$ the sensitivity of the current density imaging method.

Conclusion: SMD method of current detection is not limited to any particular sample orientation or geometry, and any pulse sequence capable of acquisition of the current-induced signal evolution in a voxel can be used for it. This widens the scope of its application from tissues to in vivo studies on animals and humans.

Keywords: current-induced magnetic field gradient; electric current detection; gradient-echo imaging; signal magnitude decay.

FIGURE 1

The sketch and photo of the sample (A) that was used for testing in the proposed signal decay current detection method. The sample consisted of 2 concentric cylindrical containers with the diameters of 4 mm and 10 mm, both which were filled with 2% saline. Only the inner cylinder was connected by the electrodes to the voltage supply of 10 V, and it was conducting current of 28 mA during the electric pulses. Axis of the cylinders were perpendicular to the direction of the static magnetic field B ₀ to maximize the z‐component of the magnetic field change $B_{c_z}$. Dependence of $B_{c_z}$ along the y‐axis (B) and its profile in the yz‐plane (C). It can be seen that $B_{c_z}$ increases linearly in the inner cylinder and decreases proportionally with the reciprocal radial distance from the cylinder axis in the outer cylinder. The scheme of gradient‐echo (D) and of spin‐echo (E) sequences with superimposed bipolar electric pulses that enables current detection by the signal magnitude decay (SMD).

FIGURE 2

Graphs in the left column show the average signal magnitude from the voxel in the inner cylinder as a function of time t (from signal excitation to signal acquisition) for different imaging matrix sizes (voxel sizes L = 117, 234, 469 μm). Signals S _c (orange curve) and S (blue curve) correspond to the case with and without current flowing through the inner cylinder, respectively. The graphs in the right column show the normalized signals f(t) (ratios between signals S _c and S) as a function of time t by experimental points (red triangles), and the best fit model curves for the signal magnitude decay model in Equation 7 (violet curve) and for its simplification in Equation 9 (green curve). All signals for the graphs were obtained from the images in Supporting Information Figure S2

FIGURE 3

Images in the upper rows show measured normalized signals $S_c/S$ that were obtained by dividing “current” with the corresponding “no‐current” magnitude images from Supporting Information Figure S2, acquired by the gradient‐echo sequence in Figure 1D. Images of the normalized signals are shown for different current injection times t and voxel sizes L = 117, 234, and 469 μm (imaging matrices 128 × 128, 64 × 64, and 32 × 32). Images in the lower rows show current density $j_{\perp }$ calculated pixel‐wise using 4 different ways. By multi‐point analyses: a) model function $f(t)=A\left|\sin (\mathit{Ct})\right|/(\mathit{Ct})$ or b) simplified model function $f(t)=A\left(1-{(\mathit{Ct})}^2/6\right)$ was first fitted to $S_c/S$ data to obtain the parameter C, which was then utilized to calculate the corresponding current density $j_{\perp }$ using Equation 8. In single‐point analyses, current density $j_{\perp }$ was calculated from a single normalized signal value using the simplified model in Equation 10 for 2 different times: c) t = 34 ms and d) t = 44 ms. Maps e) show theoretically expected current density $j_{\perp }$ that was calculated from magnetic field gradient given in Equation 4 for the inner cylinder

FIGURE 4

The current density imaging by the SMD method on the biological (lower chicken thigh) sample ex vivo. The sample was imaged in a single transversal 4 mm thick slice perpendicular to the static magnetic field and to the needle electrodes spaced by 11 mm; bipolar electric pulses of 30 V and 40 mA were delivered to the electrodes. Position of the electrodes in the sample is shown in the grayscale image. Images in the upper row show measured normalized signals $S_c/S$ that were obtained by dividing “current” with the corresponding “no‐current” magnitude images from Supporting Information Figure S4 acquired by the spin‐echo sequence in Figure 1E. These images are shown for 3 different current injection times t and voxel size L = 469 μm (imaging matrix 64 × 64). Images in the lower row show current density $j_{\perp }$ calculated pixel‐wise using the same 4 different methods utilizing for the test sample in Figure 3, that is, by using: (a) model function $f(t)=A\left|\sin (\mathit{Ct})\right|/(\mathit{Ct})$, (b) simplified model function $f(t)=A\left(1-{(\mathit{Ct})}^2/6\right)$, (c) single‐point analysis with t = 40 ms, and (d) single‐point analysis with t = 60 ms