Functional magnetic resonance electrical impedance tomography (fMREIT) sensitivity analysis using an active bidomain finite-element model of neural tissue

Abstract

Purpose: A direct method of imaging neural activity was simulated to determine typical signal sizes.

Methods: An active bidomain finite-element model was used to estimate approximate perturbations in MR phase data as a result of neural tissue activity, and when an external MR electrical impedance tomography imaging current was added to the region containing neural current sources.

Results: Modeling-predicted, activity-related conductivity changes should produce measurable differential phase signals in practical MR electrical impedance tomography experiments conducted at moderate resolution at noise levels typical of high field systems. The primary dependence of MR electrical impedance tomography phase contrast on membrane conductivity changes, and not source strength, was demonstrated.

Conclusion: Because the injected imaging current may also affect the level of activity in the tissue of interest, this technique can be used synergistically with neuromodulation techniques such as deep brain stimulation, to examine mechanisms of action.

Keywords: brain imaging; deep brain stimulation; electrical conductivity; electrophysiology; functional magnetic resonance imaging.

Figure 1

Model composition showing (a) cross-sectional and (b) oblique views and dimensions of the sample chamber, current injection ports and modeled tissue. The tissue portion of the model was 2.25 mm in diameter and 0.75 mm thick. Each electrode port was a 1.25 mm cube. The octagonal sample chamber was 6.25 mm high. Distances between opposing faces were also 6.25 mm. Voltages in the sample chamber and current injection ports were solved for using the bath (Vo) equation, while all other variables (Ve, Vm, m, h and n) were solved on the tissue compartment. The cylindrical isotropic current source had 70 μm diameter. Source location and scale is indicated in both panels.

Figure 2

Schematic showing (black) MREIT current source waveforms (A and B), (green) internal source waveform, (red) resulting membrane conductance (Gm) at active tissue center and (blue) membrane voltage Vm at active tissue center. Relative scales and timings of for internal source and MREIT imaging current waveforms are shown above. Main scale applies to membrane conductance and voltage. Gm and Vm values were calculated directly from finite element data at the center of the bidomain tissue (within the internal current source). The echo time TE typically used in imaging is marked on the scale for comparison with other figures.

Figure 3

Spin-echo-based MREIT pulse sequence. MREIT imaging currents are applied after each RF pulse, with the second pulse reversed to preserve phase. The echo time TE, and repetition time TR, are marked on the sequence. Typical MREIT images are acquired first with positive current (A) after the first RF pulse of each TR (‘Positive Current Injection’), and negative current after the refocusing pulse (B). The sequence is repeated with reversed polarity (A′ and B′) after the first RF pulse (‘Negative Current Injection’). The two images are then complex divided to remove background phase and double signal.

Figure 4

Distributions created by MREIT imaging fields. (a) Example of B_z distribution formed by MREIT current flow from electrode 5 to electrode 1 shown in a slice centered on the electrode plane. Maximal B_z values were of the order of 100 nT. (b) Current density distribution formed in center plane at 1 mA current amplitude. The tissue portion of the model was removed to maintain continuity in the current density data. Profile lines shown in this image are used in the graph of (c). Colored dots on the profile lines delineate the boundary of the tissue model shown in (a). (c) Value of activating function (Δ²V_e), within the sample chamber, plotted along the profile lines shown in (b), calculated for a 5.6 μm diameter myelinated nerve model with 500 μm internodal spacing, as per (26). The distribution shown is for a 1 mA imaging current amplitude.

Figure 5

ΔB_z distributions found in slice centered on electrode plane for six model cases. (a) ΔB_z distribution formed for a source strength of 500 pA and no imaging current. (b) ΔB_z distribution when PASSIVE image was subtracted from FULL B_z data gathered with 1 mA MREIT imaging current, 500 pA source current. (c) as for (b) but with 2 mA MREIT imaging current. (d) ΔB_z distribution formed for a source strength of 2.5 nA and no imaging current, (e) ΔB_z distribution when PASSIVE image was subtracted from FULL B_z data gathered with 1 mA MREIT imaging current, 2.5 nA source current (f) as for (e) but with 2 mA MREIT imaging current. All data were averaged over a TE of 18.3 ms. Each voxel was 70 μm x 70 μm x 500 μm³.

Figure 6

Histograms of ΔB_z distributions within active tissue voxels only, for cases shown in Fig. 5. Histogram data were compiled from all three modeled slices. Values are plotted as a fraction of the total active tissue volume. Numbers above the lines in each plot show the number of averages required to achieve a baseline noise level of about 0.1 nT using voxels of 70 x 70 x 500 μm³ (black), 140 x 140 x 500 μm³ (red) and 280 x 280 x 500 μm³ (green).

Figure 7

Laplacians of ΔB_z data in Fig. 6. Data from the active tissue are highlighted only.

Figure 8

Reconstructed Laplacians of conductivity difference distributions formed using the Harmonic B_z algorithm, based on the data shown in Fig. 7 with added noise. Data from the active tissue are highlighted only. No data are shown in Fig. 8 (a, b) because these cases do not correspond to MREIT experiments.

Figure 9

Plot of median ΔB_z values found for all imaging cases as a function of internal source strength, for each imaging current amplitude.