Transcranial direct current stimulation (tDCS) is an emerging non-invasive neuromodulation technique that has been shown to improve symptoms in a range of neurologic and psychiatric disorders (epilepsy, Parkinson’s disease, chronic pain, depression and stroke [1,2,3]). Determining the spatial distribution of the applied current is critical to evaluate targeting and improve efficacy of tDCS montages. A MR current mapping technique has recently been introduced for visualizing tDCS induced electromagnetic field changes based on Ampere’s law [4,5]. The goal of the present study was to validate the MR current mapping technique in a conductive phantom model through comparison with theoretical calculations based on the Biot-Savart law.

Ampere’s Law states that an applied direct current (DC) induces a magnetic field with its magnitude proportional to the current intensity and its direction orthogonal to the current. The along-B₀ component of this induced field can be detected as phase changes using MRI field mapping. A field mapping experiment was performed using a cylindrical phantom fitted with an electrolyte filled plastic U-shaped tube (‘A’) (Fig 1). All applied currents were confined to this tube. An identical U-shaped tube(‘B’) was included as a control. Currents (0.5-1.5mA) were applied in a pseudo random order (Fig 2) over three sessions: ‘Active’, ‘–Active’ and ‘Sham’. The polarity of currents in ‘–Active’ was reversed relative to ‘Active’, while currents were switched off during ‘Sham’. Field mapping data was acquired concurrently with each applied current using a standard field mapping sequence (Quadrature volume coil, field mapping TE1/TE2=4.92/14.76 msec, TR=1.15 sec, FA = 25⁰, 65 slices, 2x2x3mm³ Voxel, Matrix: 128 x128, BW=750 Hz/pix) on a Siemens 3T PRISMA scanner. With these parameters, the minimum detectable field was calculated as ~0.6nT/mA.

Analysis: Acquired phase data was SNR thresholded to preserve voxels with Gaussian noise [6]. Data was subsequently unwrapped using the Region Growing algorithm (implemented in PhaseTools [7]). Phase was modeled as:

Φ_m = Φ₀ + Φ_Current + Φ_Non-Current + Φ_Drift + Φ_Noise

where Φ_m is the measured phase, Φ₀ is the baseline phase, Φ_Current is phase due to current-induced fields, Φ_Non-Current is phase due to non-current sources (e.g. off resonance), Φ_Drift represents the MRI inter-scan field drift and Φ_Noise is Gaussian noise. Unwrapped data was modeled voxel-wise using a general linear model (GLM) with applied currents as predictor. By using the phase difference ΔΦ_m between two TE’s in our analyses, Φ₀ was eliminated. ΔΦ_Non-Current by definition does not vary across currents, and is modeled by the intercept. ΔΦ_Drift was modeled by interpolating a polynomial to the zero current scans. The degree of the polynomial was adapted to avoid overfitting. The regression coefficient of the predictor (applied current) represents the induced-phase at unit current, and was converted to induced-magnetic field at unit current.

Simulations: The induced magnetic field was simulated from current density using a finite element implementation of the Biot-Savart law. The current density in turn was calculated from the geometry of Tube ‘A’ and the assumption of the electrolyte conductivity being uniform and isotropic. It should be noted that while the Biot-Savart law predicts the magnetic field at a point, MRI measures the induced field averaged over a voxel. Our simulation addresses this by averaging the induced magnetic fields over 175 equi-spaced points within each voxel.

Figure 3a shows the simulated current-induced field. Induced magnetic fields as low as 5nT/mA were reliably detected in the ‘Active’ session (Fig. 3b), and were highly consistent with simulations. The induced fields in the ‘–Active’ session(Fig. 3c) were observed to be similar in magnitude, while opposite in sign. This is expected, since reversing the current polarity reverses the direction of the induced fields (Ampere’s Law). No current-induced fields were detected for the ‘Sham’ session (Fig. 3d), or in the intra-session control tube ‘B’.Our results provide a validation of the MR current mapping technique for in vivo studies. Through the phantom experiment, we demonstrated reliable detection of current induced field changes as low as ~5nT/mA. Our technique also demonstrates excellent specificity: No fields were detected in the ‘Control’ session or the intra-session control (Tube ‘B’). One unique advantage of our technique is that it uses information from phase images. Traditional fMRI techniques mapping neurophysiological markers mostly utilize magnitude images. Since every MRI acquisition measures a phase and a magnitude image, it is conceivable that the two techniques may be combined to enable simultaneous measurement of applied current and the brain response from a single MRI experiment.