Feasibility and Validity of the Proposed Technique

The key innovation of our technique is that it provides quantification of magnetic fields directly induced by tDCS currents as a means to visualize target engagement. This is in contrast to present in-vivo imaging approaches that use surrogate markers to record the brain’s neurovascular and neurophysiological responses to tDCS stimulation (e.g., BOLD/ASL fMRI, EEG and MEG). Proof of concept was established through the phantom experiment where the measured current-induced magnetic field was in excellent agreement with simulations (r = 0.84, p = 3.8 × 10−267, N = 989). The phantom results also demonstrated excellent specificity as no significant magnetic fields were detected in either the within-session control (Tube ‘B’), or during the control session (‘Sham’). In its present implementation, our technique is capable of detecting fields as low as one nT per mA of applied current (Supplemental S1) with a spatial resolution of a few millimeters.

The limb experiment demonstrated in-vivo feasibility of our technique in a relatively simple and electrically conductive biological tissue. While no field changes were detected during the ‘Sham’ session, magnetic field changes greater than 30nT/mA were observed during the ‘Active’ session. The experimental results also qualitatively matched the theoretically predicted magnetic fields based on a finite element model of the human calf (r = 0.43, p = 2.4 × 10−94; N = 2072). However, unlike the phantom experiment the experimentally detected magnetic fields were found to be greater than the simulated fields. This difference could be due to heterogeneity in the tissue conductivity leading to potential “hotspots” of electromagnetic fields that were detected by in-vivo experiment but not theoretical modeling. Another explanation could be variations in the tissue conductivity as well as boundary conditions employed by the computational modeling. These observations highlight the need for reliable in-vivo mapping of electromagnetic fields even for organs and limbs with relatively simple biological compositions.

Finally we performed the brain experiment with a common tDCS montage (bilateral-M1) on 12 healthy volunteers. A group level analysis revealed relatively weak (5–8nT/mA) yet statistically significant magnetic field reductions around the central sulcus (underneath the cathode) as well as in the precuneus region (around mid-way between the electrodes). Our observations are consistent with modeling studies which have predicted peak current densities to exist under the electrodes24 and for large electrodes (25–35 cm2) less than 10 cm apart, a single peak current density to exist between the electrodes25. Moreover, the magnitude of the experimentally detected fields, 0–10 nT/mA, was found to be the same order as that of simulated fields reported in a recent study21 (although the study used a different cathode positioning). Furthermore, although significant field changes were not detected under or around the anode in voxel-wise group analysis, an ROI analysis (Supplemental Fig. S1 with the method described in Supplemental S5) revealed significant field changes under both electrodes (and none during Sham). These field changes were also observed to have the same sign; which is intuitive given that the direction of tDCS current flow is the same (from anode to cathode) at both electrodes. However, it is not clear why the field changes were more significant under cathode than anode in our experiment. One potential explanation is the relatively large electrode size making the induced electromagnetic fields “diffuse” and such effect may be asymmetric between anode and cathode. With improved sensitivity of our technique (see below) and improved focality of tDCS montage (e.g., high-definition tDCS)20, we will be able to evaluate such hypothesis in future studies.

Advantages of the Proposed Technique

The proposed approach for visualizing tDCS target engagement through its induced magnetic fields is appealing since the magnetic field is directly induced by and linearly proportional to the applied current (as described by Ampere’s law). Moreover, the physical constant involved in the relationship between magnetic field and direct current is highly stable across biological tissues (variation of magnetic permeability is on the order of ~ppm26). In contrast, existing experimental techniques use surrogate markers of the brain’s response to tDCS stimulation (e.g., BOLD, ASL, EEG, MEG). These represent a secondary response to the applied stimulation and may extend beyond the site of stimulation due to brain networks. Additionally, unlike the physical relationship between magnetic fields and applied current, the relationship between these markers and the applied tDCS current is highly complicated and not easy to interpret.

In applications involving milliampere currents, the primary challenge for detecting current-induced magnetic fields is the weak signal relative to noise (SNR). Existing techniques to detect weak magnetic fields attempt to overcome the SNR limitation primarily through enhancing the ‘signal’, e.g., by increasing the current intensity and/or using time varying currents (~1 Hz or higher)27,28,29. In contrast, our technique addresses the SNR limitation by statistically modeling out a range of ‘noise’ sources by exploiting the linear relationship between applied-current and induced magnetic fields and is thus able to detect small magnetic fields with high sensitivity and spatial resolution.

In the proposed technique, a general linear model (GLM) was employed to model a set of magnetic field maps with applied current as well as systematic noise sources, similar to linear regression analysis commonly used in fMRI. Our choice of a GLM is supported by the fact that the relationship between applied current and measured magnetic field is linear (Ampere’s Law) and by ensuring the stochastic-noise distribution is Gaussian (see Supplemental S5, ‘Preprocessing’). Another advantage of using GLM is that many statistical methods developed for fMRI can be adapted for the proposed technique. For instance, in an experimental paradigm involving tasks, tDCS induced signals could be separated from task-related brain signals30 by designing the tDCS and task stimuli to be sufficiently orthogonal (similar to optimal stimulus design in fMRI). In one possible implementation, a study could involve two identical task sessions: one with ‘Active’ tDCS currents and another with ‘Sham’. The contrast between ‘Active’ and ‘Sham’ sessions would detect magnetic field changes specifically induced by tDCS, controlling for task related brain-activity signals. The use of a GLM does assume (implicitly) the invariance of current path with different intensities of applied currents. This assumption is reasonable considering the small magnitude of currents used (will not induce neuronal discharge) and the fact that all currents were applied in the same direction.

Potential Clinical Applications

In the present study, we were able to visualize tDCS current-induced magnetic fields in human brains at the group level. This is a significant first step to experimental verification of target engagement. In addition to verification, our technique can also help advance focal stimulation, which has been shown to be more efficient than conventional tDCS31. By identifying group-wide peak-intensity areas from imaging studies (performed for conventional tDCS), our technique can potentially (a) provide target engagement confirmation for a conventional tDCS trial; and if treatment effects are observed, (b) identify target sites for future studies with focal stimulations with a reasonable expectation of the same treatment effects. Once we reach the capability for reliable mapping of electromagnetic fields induced by tDCS in individual subjects with the proposed technical developments (see below), our technique may open the door to a new field of individualized, precise, noninvasive neuromodulation using tDCS.

Limitations and Future Developments

With the present implementation (single-channel coil and standard field mapping sequence), we were able to reliably detect significant field changes during the head experiment at the group level but not in individual subjects. To address this shortcoming, future studies will use faster field mapping sequences to increase the number of measurements per session (thereby increasing statistical power) together with multi channel coils to improve SNR. The increased SNR may also improve the sensitivity of the proposed technique (~1.2 nT/mA of the present implementation, see Supplemental S1). The capability to reliably map tDCS current-induced fields in individual subjects may also overcome the potential averaging effects of group analysis, given the variability of cortical geometry and current distribution across subjects and allow direct comparison with computational models.

It should be noted that our present technique maps only the magnetic field changes along B z . In the absence of additional information, mapping electric current requires measuring all three spatial components of the induced field. One possible solution is to map the induced fields of a subject in at least three different orientations, which may be feasible with an open magnet. Alternatively, constraining computational current prediction models with a single experimentally verified component of the induced field could improve the accuracy for predicting current distribution.

A promising direction for research involves integrating fMRI with our field mapping technique. While our technique uses the phase information in an MRI image, most existing fMRI methods use magnitude information. Since every MRI acquisition generates phase and magnitude images, it is conceivable that target engagement (through mapping tDCS induced magnetic fields) and ensuing neurophysiological effects (through BOLD/ASL fMRI) could be simultaneously measured during a single tDCS session. One such promising technique is ASL with dual-echo EPI32 readout to simultaneously map current induced fields, perfusion and blood oxygenation.