Figure 1.
(a) Left: EEGs are voltage drops of extracellular currents, the origins of which are dendric currents of pyramidal neurons, between the EEG electrodes; Right: When a transcranial extracellular impedance control (tEIC) is applied, i.e., a shunt resistor is attached to two EEG electrodes to reduce the extracellular resistance, the extracellular currents increase, and the intracellular currents increase accordingly because these two currents are continuous; i.e., they must be equal at the cell boundary. (b) Left: Effects on pyramidal neuron 1. It is called the tEIC intracellular effect when the intracellular current modulation of a pyramidal neuron is caused by the current from the neuron itself. The increasing currents increase the voltage drop, and the membrane potential increases. Right: Effects on pyramidal neuron 2. It is called the tEIC intercellular effect when the modulation is caused by currents from other neurons. tEIC intra- and inter-cellular effects nearer the soma have a greater effect on firing. Note that the + and – marks show only the effects of intra- and inter-cellular currents on membrane potentials neglecting the resting potential, and the current branches that do not pass through the tEIC resistor are omitted.
Figure 2.
(a) According to Ho-Thevenin’s theorem, a head including the brain as seen from two EEG electrodes can be electrically approximated by a very simple circuit. (b) Left and middle: The resistance versus voltage and resistance versus current characteristics are calculated on the basis of the theorem. These characteristics are symmetric with respect to the points [–Re{Z}, E] and [–Re{Z}, 0]. Thus, Type I tEIC positively increases (or enhances) the current I (a portion of the extracellular currents), and Type II tEIC “negatively” increases (or depresses) it. Right: The negative resistor here is an Ohmic resistor having a negative slope. (c) The superposition theorem resolves the head circuit under tEIC into a number of circuits, each including one active EEG generator (the others are replaced with a short circuit) and the tEIC (a Type I or Type II resistor). Each resolved circuit indicates that a tEIC resistor enhances or depresses each active EEG generator. This is the tEIC intracellular effect. (d) It also demonstrates that a current source (e.g., tDCS, tRNS, and tACS) can stimulate a bunch of EEG generators (actually replaced with a short circuit) regardless of whether each of them is active.
Figure 3.
The implementations of Type I tEIC (positive amplification of extracellular currents) and Type II tEIC (negative amplification of them) are different from each other, and two implementations for each type are illustrated. (a) and (b) are respectively implementations of tEIC with two voltage followers and a voltage-to-current convertor (VCC) for Type II and Type I tEICs, respectively. (c) and (d) are implementations with a voltage follower and a common negative impedance circuit. Every circuit has a switch (SW1 and SW2 are interlocked) for choosing two conditions; one is for the tEIC condition, i.e., applying the current to the brain and the other is for the sham condition, i.e., applying the current to a dummy head resistor. The device parameters are listed at the bottom of this figure; the Type I (Type II) implementation functioned as –R1 Ω (–R2 Ω) above 4 Hz without a phase delay.
Figure 4.
(a) Two EEG generators E1 (20 Hz sine) and E2 (10 Hz cosine) were in the brain, and a two-channel (α and β) EEG was observed (indifferent reference: right earlobe). (b) The basic mutual interaction between the EEG generators was given by the gray T-circuit. (c) The EEG observation on channel α (β) was given by the blue (red) T-circuit bifurcated from the gray T-circuit. The direct path between channels α and β was given by the magenta connection. The bottom surface of the cubic circuit was connected to the reference. Resistors were set such that channel α (β) was more sensitive to E1 (E2). (d) tEIC resistor r was connected to EEG channel α and the reference. (e) Circuit for Simulation A. (f) tEIC-conditional current waveforms of the EEG generators (top row) and their powers resolved into E1- and E2-originated currents (bottom row). Type I enhanced and Type II depressed the intrinsic currents (E1-originated current in I1 and E2-originated current in I2) compared with the Sham condition. This is the tEIC intracellular effect. Type I depressed and Type II enhanced the interference currents (E2-originated current in I1 and E1-originated current in I2) compared with the Sham condition. This is the tEIC intercellular effect. Thus, the synergetic tEIC effect clearly occurred; i.e., Type I differentiated and Type II merged the EEG generator activities. (g) tEIC-conditional voltage waveforms of the EEG observations (top row) and their powers resolved into E1- and E2-originated voltages (bottom row). The results in the top left panel show that the tEIC-conditional waveform changed on the basis of Ho-Thevenin’s theorem.
Figure 5.
A selective response (mouse-click) task for visually presented stimuli was performed. (a) Top: Visual stimulus sequence. Each stimulus is presented for a duration of 1/15 s with a stimulus onset asynchrony (SOA) of 0.8–1.2 s at a random location along the four-degree visual angle circle (the circle was invisible). Bottom: Images L and R for the selective mouse-click. (b) A total of 512 trials (128 trials×4 runs) were divided into 32 blocks (16 trials for each block). The tEIC conditions, Sham, Type I, Type II, and Noise, were randomly switched every block (the Noise condition was excluded from further analyses due to electronics problems). Note that tEIC was simultaneously (not in a before-and-after manner) applied to the behavioral experiment.
Figure 6.
EEG results of the tEIC-applied behavioral experiment.
(a) tEIC-conditional EEG grand averages at EEG channels F3 (tEIC channel), F4, and O2 for 14 validated subjects (duration: from −0.1 to 0.5 s, stimulus onset: 0 s). The averaged magnitudes for the post-trigger duration (from 0 to 0.5 s) were statistically tested (*: significant difference among the averaged magnitudes, p<0.05 with Bonferroni correction; see Fig. S3 for all the channels). These grand averages were consistent with the expectations with reference to Ho-Thevenin’s theorem. (b) Normalized EEG grand power spectrum averages for the post-trigger duration (not the power spectra of the EEG grand averages). Type I at F3 and F4 and Type II at O2 showed temporal-high-pass-filter-like characteristics. Since tEIC was designed not to have any frequency response above 4 Hz, this would be caused by spatial frequency responses. (c) Alpha band (8–13 Hz) results. Top: Topography of the normalized EEG grand power averages for the post-trigger duration for Sham; Bottom: Ratios of the normalized grand power averages for the post-trigger duration on a logarithmic scale: log10(Type I/Sham), log10(Type II/Sham), and log10(Type II/Type I) (*: significant difference among the normalized power averages, p<0.05 with Bonferroni correction). (d) Lower beta band (20–25 Hz) results. (e) Upper beta band (25–30 Hz) results. (f) Lower gamma band (30–35 Hz) results. The presentation styles of (d)–(f) are the same as in (c). The EEG generators of the alpha band seemed to be densely distributed in the occipital area, whereas those of the other bands seemed to be densely distributed in the frontal area (top panels in (c)–(f)). Type I enhanced (depressed) the power of the area in which the EEG generators were densely (sparsely) distributed, whereas Type II enhanced (depressed) for the area in which the EEG generators were sparsely (densely) distributed (bottom panels in (c)–(f)). These results imply that tEIC works as a spatial filter (Type I: spatial high-pass filter, Type II: spatial low-pass filter) due to the synergetic tEIC effect; i.e., Type I differentiates and Type II merges EEG generator activities.
Figure 7.
Behavioral results of the tEIC-applied behavioral experiment.
(a) tEIC-conditional means of reaction times for 14 validated subjects. Individual reaction times are superimposed on these results. Type I showed a significant improvement effect in reaction time compared with Sham (p<0.05 with Bonferroni correction). (b) tEIC-conditional means of accuracy rates over the subjects. The presentation style is the same as in (a). No significant differences were observed.