• Figure 1.
    Download figureOpen in new tabFigure 1. Location of the invasive recording electrodes and transcranial electrical stimulation electrodes in the 10 patients tested.

    Electrodes measuring from the cortical surface (64-contact grids, 8-contact strips) are indicated as black dots and depth electrodes (between 6–8 contacts each) as red dots. Square stimulation electrodes on scalp surface (2 cm), are shown in green with contact gel in red. Individual anatomy derived from the T1-weighted MRI is transparent to visualize electrode locations.

    DOI: http://dx.doi.org/10.7554/eLife.18834.002

    Figure 2.
    Download figureOpen in new tabFigure 2. Prediction of electric field with calibrated models for various electrode montages at 1 mA stimulation intensity.

    (B) Histogram of electric field magnitude for the montage used on Subject P03 (same as in Figure 5) and Subject P014. (C) Corresponding spatial distributions on cortical surface. (D) Cross-section plots showing predicted electric field intensity in mid-brain areas with hot spots underneath stimulation electrodes and adjacent to highly conducting ventricles.

    DOI: http://dx.doi.org/10.7554/eLife.18834.003

    Figure 3.
    Download figureOpen in new tabFigure 3. Voltage recordings across multiple intracranial locations for sinusoidal transcranial alternating current stimulation for the first subject tested (P03).

    Magnitude and sign are estimated by fitting a sinusoid to the voltage fluctuations at each electrode location. (A) Voltage recordings at multiple intracranial recording locations are linear with stimulation intensity up to 1 mA in this subject (each curve represents a different electrode). At higher intensities some channels saturate due to a limited dynamic range of the clinical recording equipment, which is demonstrated by the plateauing of measured voltage at intensities above 1.5 mA. (B) Intensities are constant with frequency in the range of 1–10 Hz. The drop-off at higher frequencies is due to the recording equipment. (C) Averaged measurements across three stimulation sessions (separated by approximately 1 min each) demonstrate stability of electric field measurements across sessions. (Here stimulation was 1 Hz and between 0.5–1 mA in stimulation current. The voltage values are calibrated to correspond to 1 mA stimulation). Error bars at each electrode indicate the variability across different stimulation blocks.

    DOI: http://dx.doi.org/10.7554/eLife.18834.004

    Figure 4.
    Download figureOpen in new tabFigure 4. Example of realistic model for Subject P06.

    Each patient's detailed anatomy was obtained by segmenting T1-weighted MR images into six tissue types: scalp, skull, CSF, gray matter, white matter, and air. Additionally, to capture the surgical details we modeled the craniotomy, cortical strips and depth electrodes as well as the subgaleal electrodes. Finite element models were built and solved to compute voltages and electric fields throughout the head. (A) Scalp, with stimulating pad electrode; configuration used here is the same as shown in Figure 1. (B) Skull, note the Jackson-Pratt Drain (blue), the subgaleal electrodes (green) and the craniotomy. (C) CSF, with the geometry of intracranial electrode strips. Craniotomy site was assumed to be filled with CSF. (D) Gray matter. (E) White matter. (F) Air cavities. (G) Spongy bone inside the skull. (H) Diffusion tensor distribution in one brain slice.

    DOI: http://dx.doi.org/10.7554/eLife.18834.005

    Figure 5.
    Download figureOpen in new tabFigure 5. Voltage and electric field for measurements and model.

    All values are calibrated to 1 mA stimulation. (A) False-color representation of measured voltages for patient P03. (B) Voltages from the corresponding individualized model across the cortical surface. (C) Absolute voltage difference between recording and model predictions. (D) Comparison of recorded voltages with values predicted by the individualized model for P03. Each point in the scatter plot represents an intracranial electrode as shown in (A), with black indicating cortical surface electrodes and red representing depth electrodes (mostly targeting hippocampus). (E) Projected electric field is measured in the direction of nearby electrodes (pairs connected by blue lines in (D)), and is calculated as the voltage difference divided by the distance between the two electrodes. Error bar at each point indicates the standard variation of the measured electric field at the corresponding electrode as shown in Figure 3C). (F) Projected electric field for cortical surface recordings and corresponding model predictions combining all the subjects. (G) Same as (F) showing all the depth electrodes.

    DOI: http://dx.doi.org/10.7554/eLife.18834.006

    Figure 5—source data 1.Animated 3D renderings of the recorded and model-predicted voltages for each subject, and the absolute difference between the two.

    The predicted values are from the individually optimized models.

    DOI: http://dx.doi.org/10.7554/eLife.18834.007

    Download source data [figure-5—source-data-1.media-1.ppt]
    Figure 6.
    Download figureOpen in new tabFigure 6. Electric field predicted with individually calibrated models under 1 mA stimulation.

    (A) Summary of electric field magnitudes for all subjects. The four different configurations of stimulation electrodes in Subject P014 are indicated as P014A–P014D. Also shown are values for a few stimulation montages commonly used in clinical trials simulated for Subject P03 (M1–SO, C3–C4, Cz–Oz). Whiskers indicate the maximal and minimal values of electric field magnitudes observed across the entire brain, and box indicates the 5% and 95% percentile across locations. Line inside the box indicates median value. (B) Electric field magnitudes as a function of depth, measured as the distance from the origin of the MNI coordinate system and normalized by diameter of the brain. Maximal field value is achieved at the cortical surface, which is approximately at distance of 0.55 (distance was divided by brain diameter in each MNI dimension). Locations exceeding 0.55 indicate mostly brain stem and cerebellum. Maximal value for each depth is indicated in green. (C) Summary of maximum for each of the 10 subjects and montages shown in (A) as a function of depth.

    DOI: http://dx.doi.org/10.7554/eLife.18834.008

    Figure 7.
    Download figureOpen in new tabFigure 7. Comparison of recorded values with model predictions using literature conductivity values for Subject P03 scaled to 1 mA.

    Points falling on the dashed blue line represent perfect prediction (slope s = 1). The literature values overestimate electric field magnitudes (measurements are 50% of predicted values, s = 0.50, green line). Skin, skull and brain conductivities are optimized to minimize prediction error for field projections (i.e. minimize mean square distance from dashed line in panel (B)) which corrects this magnitude mismatch, and is shown in Figure 5E.

    DOI: http://dx.doi.org/10.7554/eLife.18834.009

    Figure 9.
    Download figureOpen in new tabFigure 9. Performance of various modeling approaches.

    IM-CSF: This ‘intact model’ is based on the pre-surgical MRI and does not include craniotomy, recording electrodes, etc., and does not model CSF either; IM: intact model including CSF; RMcut: realistic model with all details as shown in Figure 4A–F, but truncated at the bottom of the skull due to the limited FOV of the clinical MRI scans; RM: realistic model with an extended FOV including the lower head and neck based on a standard head model; RM + 3skull: realistic model including 3-compartment skull as shown in Figure 4G; RM+DTI: realistic model including DTI as shown in Figure 4H. Four different ways to convert DTI ellipsoids into estimated anisotropic conductivity values were tested: direct method (DTI), volume normalized (DTI/VN), volume constrained (DTI/VC), and equivalent isotropic trace (DTI/EIT). What is demonstrated is that truncated head models may deteriorate prediction accuracy, and models accounting for CSF, multiple skull compartments or white matter tracts do not significantly improve model accuracy.

    DOI: http://dx.doi.org/10.7554/eLife.18834.012

  • Table 1.

    Models with different complexities

    DOI: http://dx.doi.org/10.7554/eLife.18834.013

    intact model without CSFgray, white, skull, scalp, air, stim electrodesIM-CSF
    intact modelgray, white, CSF, skull, scalp, air, stim electrodesIM
    realistic modelintact model with craniotomy and surgical instrumentRM
    realistic model with limited FOVsame as realistic model except truncated at the bottom of the skullRMcut
    realistic model with inhomogeneous skullskull is modeled as 3-layered structureRM + 3skull
    realistic model with anisotropic brain derived from DTI datadirect mappingRM+DTI
    volume normalizedRM+DTI/VN
    volume constrainedRM+DTI/VC
    equivalent isotropic traceRM+DTI/EIT
  • The following dataset was generated:

    Yu Huang, Anli A Liu, Belen Lafon, Daniel Friedman, Michael Dayan, Xiuyuan Wang, Marom Bikson, Orrin Devinsky, Lucas C Parra, 2016,Recordings of electrical potentials in the in vivo human brain induced by transcranial electrical stimulation., https://dx.doi.org/10.6080/K0XW4GQ1, Publicly available at Collaborative Research in Computational Neuroscience - Data sharing (http://crcns.org/)