Low-intensity electrical stimulation affects network dynamics by modulating population rate and spike timing

Abstract

Clinical effects of transcranial electrical stimulation with weak currents are remarkable considering the low amplitude of the electric fields acting on the brain. Elucidating the processes by which small currents affect ongoing brain activity is of paramount importance for the rational design of noninvasive electrotherapeutic strategies and to determine the relevance of endogenous fields. We propose that in active neuronal networks, weak electrical fields induce small but coherent changes in the firing rate and timing of neuronal populations that can be magnified by dynamic network activity. Specifically, we show that carbachol-induced gamma oscillations (25-35 Hz) in rat hippocampal slices have an inherent rate-limiting dynamic and timing precision that govern susceptibility to low-frequency weak electric fields (<50 Hz; <10 V/m). This leads to a range of nonlinear responses, including the following: (1) asymmetric power modulation by DC fields resulting from balanced excitation and inhibition; (2) symmetric power modulation by lower frequency AC fields with a net-zero change in firing rate; and (3) half-harmonic oscillations for higher frequency AC fields resulting from increased spike timing precision. These underlying mechanisms were elucidated by slice experiments and a parsimonious computational network model of single-compartment spiking neurons responding to electric field stimulation with small incremental polarization. Intracellular recordings confirmed model predictions on neuronal timing and rate changes, as well as spike phase-entrainment resonance at 0.2 V/m. Finally, our data and mechanistic framework provide a functional role for endogenous electric fields, specifically illustrating that modulation of gamma oscillations during theta-modulated gamma activity can result from field effects alone.

Figures

Figure 1.

Experimental and computational network methods. A, Experimental setup: spatially uniform electric fields were applied across hippocampal slices in an interface chamber. Recording of LFPs and intracellular potentials were performed in the CA3 region of hippocampus relative to an isopotential electrode in the bath (dotted line). The orientation of the pyramidal layer of the CA3c region was perpendicular to the applied field. B, Computational network model: 800 excitatory and 200 inhibitory neurons are synaptically connected with various synaptic strengths w. C, The electrical stimulation in the model was implemented as low-pass-filtered current (τE = 10 ms) that is proportional to the applied field E. D, The polarization of the single-neuron model of Izhikevich to a current injection (dashed blue line) exhibits low-pass characteristics. A better match to experimental data is observed with the additional low-pass filter. The combined model (solid red line) has a peak gain at ∼7 Hz.

Figure 2.

Gamma oscillations generated by carbachol application in vitro and in the computational network model. A, The 20 μM carbachol induces beta–gamma oscillations in rat brain slices, measurable as oscillatory activity of the LFP (25–35 Hz, low passed at 100 Hz). The activity is stable in power and frequency. B.1, Simulated LFP in the computational network model (low passed at 100 Hz). The LFP in the model is the average of the postsynaptic currents across the network. B.2, Raster plot representing the firing activity of excitatory (blue) and inhibitory (red) neurons during induced oscillations in the computational network model (sample of 80 excitatory and 20 inhibitory shown). B.3, Average excitatory and inhibitory currents (j̄e and j̄i) during the simulated oscillations.

Figure 3.

Changes in LFP oscillation during application of weak uniform fields in vitro. A, Left column, Mean spectrograms of the LFP (in dB) during the application of the uniform field with different waveforms (fields applied between 1.5 and 3.5 s). A.1, Negative DC stimulation (−6 V/m). A.2, Positive DC stimulation (+6 V/m). A.3, Low-frequency AC stimulation (2 Hz, 4 V/m). A.4, Higher frequency AC stimulation (28 Hz, 5 V/m). B, Right column, Summarizes the modulation of oscillatory power across slices. B.1, B.2, Modulation is measured relative to baseline during negative (B.1) and positive (B.2) DC stimulation. B.3, Modulation of power during low-frequency AC stimulation is measured as a ratio between enhancing and suppressing cycles (+, 2 Hz; ★, Hz; ∘, 7 Hz; □, 10 Hz; ◊, 12 Hz). B.4, Subharmonics power is measured at half the stimulation frequency relative to baseline power at the endogenous frequency (★, 20 Hz; +, 26 Hz; ∘, 28 Hz; □, 30 Hz; ◊, 40 Hz). Data from the same slice is indicated by color. Error bars indicated standard error of the mean.

Figure 4.

Changes in LFP during simulation of weak-field stimulation in the computational model. A, Left column, Spectrograms of the local field potential (in dB) during the application of fields with different waveforms (fields applied between 1.5 and 3.5 s). A.1, Negative DC stimulation (ΔV = −1.18 mV). A.2, Positive DC stimulation (ΔV = 1.34 mV). A.3, Low-frequency AC stimulation (2 Hz, ΔV = 1.09 mV). A.4, Higher frequency AC stimulation (25.5 Hz, ΔV = 0.86 mV). B, Right column, Summarizes the effects of the fields on the ongoing gamma activity for two different values of the e-e synaptic coupling constant w̄ee, 0.325 (blue line) and 0.275 (red line) capturing some of the variability seen in slice. The range of field magnitudes applied is the same in all cases (E ∈ [0, 12] V/m), but horizontal axis is given in terms of the resulting average cellular polarization, ΔV, to reflect frequency-dependent gain g. B.1–4, Power modulation is measured as in the slice data. Error bars indicated SEM.

Figure 5.

Analysis of the computational model results. A, Integrated synaptic drive Qe′ and Qi′ (total charge delivered relative to baseline) during DC stimulation at various field intensities. Each point indicates data from repeated runs of the model averaged >30 frames (blue for w̄ee = 0.325 and red for w̄ee = 0.275). Clusters reflect results for 11 field intensities tested indicating that the network converges to the same stable balance point. B, The instantaneous synaptic network drive in the computational model is represented as a point in the (j̄i, j̄e) space. The trajectory of the points represents the instantaneous level of excitation/inhibition (following a 5 point moving average) before (black line) and during field application (green line). The stimulation amplitudes applied are the same as in the spectrograms in Figure 4A and in the raster plots in Figure 6A. B.1, B.2, Hyperpolarizing and depolarizing DC stimulation; B.3, 2 Hz stimulation; B.4, 25.5 Hz stimulation. C, Frozen-input condition for different waveforms applied in the computational model. Firing rate change during the application of the field under normal conditions (red line) and frozen-input conditions (blue line) as a function of the average single-neuron polarization ΔV. C.1, DC stimulation. C.2, 2 Hz AC stimulation. C.3, 25.5 Hz AC stimulation. Error bars indicate SD.

Figure 6.

Model predictions for spiking activity and validation with intracellular recordings. A, Raster plots on the left column indicate spiking activity for a sample of model neurons during electrical stimulation (blue for excitatory and red for inhibitory). The frequencies and amplitudes of the applied fields are the same as in Figure 4A. A.1, Negative DC stimulation. A.2, Positive DC stimulation. A.3, Low-frequency AC stimulation (2 Hz). A.4, Higher frequency AC stimulation (25.5 Hz). B, Right column, Illustrative intracellular recordings in slices during electrical stimulation (6 V/m). B.1, Negative DC stimulation. B.2, Positive DC stimulation. B.3, Low-frequency AC stimulation (2 Hz). A.4: Higher frequency AC stimulation (26 Hz). Quantitative comparison between the model and the intracellular recordings requires aggregating data over multiple frames (see Fig. 7).

Figure 7.

Quantitative comparison of the intracellular recordings with the computational model predictions. A, The experimental data (circles) are compared with the results of the model (blue box indicating median and 75th percentile, outliers not plotted). DC and 2, 7, 13, and 26 Hz were tested using 6 V/m fields corresponding in the computational model to ΔV = 0.5 mV for the DC case. A.1, Firing rate change (relative to baseline) during the application of positive and negative DC stimulation. A.2, Firing rate change (relative to baseline) during the application of AC stimulation. A.3, Coherence between the spikes and the applied AC fields. A.4, Mean angle between the spikes and the applied AC fields. B, Phase-entrainment resonance induced for very low-amplitude fields (0.2 V/m) in the experiments (circles) and the model (solid blue line). B.1, Coherence measured as vector strength of the phase of spike time relative to the applied oscillating field. Frequencies of the applied field are normalized to the endogenous frequency to facilitate comparison. B.2, The p-value for coherence measures (p = 0.05, dotted line).

Figure 8.

Model results for multiple frequencies and field intensities. A, Main frequency of the endogenous activity during the field application. Inset, Main frequency of the oscillations applying frequencies close to double the endogenous. B, Relative power change at the main frequency of the oscillations before and during the stimulation. C, Mean coherence between spike times and applied fields. D, Average firing rate of pyramidal neurons during the field application.

Figure 9.

Modulation of gamma power when applying a waveform approximating endogenous hippocampal theta oscillations. A.1, B.1, Spectrograms (in dB) of the effects of 7 Hz, 1 V/m AC fields on the oscillations in the experiments and the model (IE = kEE = 0.067). B.1, Spectrogram of the LFP (in dB) during the application of a theta field in the model. B.2, Phase distribution of spikes relative to the field applied as in B.1 for all excitatory neurons in the simulated network.