Direct Current Stimulation Alters Neuronal Input/Output Function

Abstract

Background: Direct current stimulation (DCS) affects both neuronal firing rate and synaptic efficacy. The neuronal input/output (I/O) function determines the likelihood that a neuron elicits an action potential in response to synaptic input of a given strength. Changes of the neuronal I/O function by DCS may underlie previous observations in animal models and human testing, yet have not been directly assessed.

Objective: Test if the neuronal input/output function is affected by DCS METHODS: Using rat hippocampal brain slices and computational modeling, we provide evidence for how DCS modulates the neuronal I/O function.

Results: We show for the first time that DCS modulates the likelihood of neuronal firing for a given and fixed synaptic input. Opposing polarization of soma and dendrite may have a synergistic effect for anodal stimulation, increasing the driving force of synaptic activity while simultaneously increasing spiking probability at the soma. For cathodal stimulation, however, the opposing effects tend to cancel. This results in an asymmetry in the strength of the effects of stimulation for opposite polarities.

Conclusions: Our results may explain the asymmetries observed in acute and long term effects of transcranial direct current stimulation.

Keywords: DCS; Electrical stimulation; Excitability; Input-output; Two-compartment model; tDCS.

Figure 1

Neuronal input-output function under DCS. (A) In-vitro experimental set-up of electrophysiological recordings from rat hippocampal brain slices under DCS. DCS induces a uniform electric field across the slice indicated with the experimentally measured voltage gradient in false color. Dendritic and somatic activities are independently measured in CA1. Positive/negative field was defined as the positive/negative electrode near stratum pyramidale in CA1 corresponding to the conventional definition of “cathodal”/”anodal” stimulation. Panel A depicts a positive electric field. (B) Population measures. Orthodromic stimulation of presynaptic fibers releases neurotransmitters activating postsynaptic dendrites. Current flows into the population of neurons which can be measured as the fEPSP. This excitatory input induces action potentials in the population of neurons; the aggregation of this spiking activity is recorded as the population spike.(C) Input-output function. Increasing the orthodromic stimulation intensity produces bigger synaptic input measured as the fEPSP (gray traces to the right of the curve) with a corresponding increase in spiking output, measured as the population spike (gray traces on the left of the curve). (D–E) Hypothesis for how DCS may affect the I/O function of a neuron. (D) DCS may affect only synaptic input leaving the I/O function unchanged (control I/O is shown in black). Additionally, DCS may increase synaptic input as indicated by green arrows. The corresponding increase in firing as a direct consequence of the change in synaptic input is depicted as gray arrows. The I/O curve under DCS is shaped by the green points that fall on the original I/O curve. (E) DCS may affect synaptic input and amplify spiking output, shifting the I/O curve. Change in synaptic input is marked with horizontal green arrows; amplification of spiking output due to DCS is marked by the vertical green arrows. The I/O curve under DCS is shifted to the left indicating that neurons are in a more responsive state.

Figure 2

DCS modulate synaptic input and population firing. (A) Modulation of synaptic efficacy measured in hippocampal slices. fEPSP are significantly modulated (* p<0.05) by 35 V/m DCS. Error bars indicate SEM across slices. Representative traces are shown on the right; blue: −DCS, black: control, red: +DCS. (B) Modulation of recorded population spikes from hippocampal slices. −DCS significantly facilitates population spikes and +DCS inhibits them, but to a lesser extend. Representative traces depict the facilitation effect with −DCS (blue) and inhibition with +DCS (red). (C) Modulation of synaptic input in a single neuron computational model. Excitatory post-synaptic potentials (EPSP), measured at the somatic compartment, are modulated by DCS in the same direction as experimental data. The model is deterministic; therefore there are no error bars. (D) Modulation of population firing during DCS in the neuron computational model. Firing level, measured as the number of neurons that fire during DCS normalized by those during control, are modulated similar to the experimental data. The model is deterministic; therefore there are no error bars. (E) Schematic of two-compartment model. The dendritic compartment is formed by a leaky conductance (g_dl) and a capacitive current; voltage dependent conductances including: potassium (g_K), sodium (g_Na), persistent sodium (g_Nap) and slow voltage-dependent non-inactivating potassium (g_Ks). These are connected through a coupling conductance (g_C) to the axon/soma compartment including a potassium (g_K), sodium (g_NA) and a persistent sodium (g_Nap) conductance in addition to a leaky current (g_sl) and a capacitive current. The extracellular electric field was modeled as a voltage difference (V_E) across the compartments. The voltage traces on the right, show the membrane polarization induced in each compartment by +DCS and −DCS. The coupling constant (amount of polarization induced by each V/m) for the somatic voltage during −DCS is 0.12 mV/V/m and −0.11 mV/V/m for +DCS. In the dendritic compartment the coupling constant is 0.013 mV/V/m for + DCS and −0.08 mV/V/m for −DCS. (F) Synaptic efficacy modulation is independent of orthodromic stimulation orientation. Left, schematic of the experimental set-up, the bipolar stimulation electrode was placed in the middle of CA1. One recording electrode was located closer to CA3 (proximal location, to the left of the bipolar stimulation electrode), and the other was placed to the right of the stimulation electrode (distal location). The relative change of the fEPSP slope caused by the field in the proximal location versus the change in the distal location is shown.

Figure 3

DCS modulates the threshold of the neuronal input-output function. (A) Model prediction of the DCS effect on the input-output function. Spiking output is characterized by the probability of firing and synaptic input by the average EPSP slope magnitude measured at the soma. The direction of the field relative to the model is plotted in the upper inset, −DCS (blue) and +DCS (red). (B) Neuronal input-output function is affected by DCS in hippocampal brain slices. Spiking output is measured as the population spike amplitude (PS) and synaptic input as the fEPSP slope. The I/O curve of a representative slice shows the threshold shift (X₅₀) induced by −35 V/m DCS (blue) and a smaller change in the opposite direction for +35 V/m DCS (red). Dashed lines mark the X₅₀ value for each curve. Gray area depicts the fEPSP slopes and PS values plotted on (D). The direction of the electric field relative to the slice is plotted in the upper inset. (C) Threshold changes predicted by model and measured in experimental data. Percentage changes are quantified by normalizing the parameters in the field condition by the control condition and calculating the deviation. Gray points indicate the change for each slice; black lines on top of the bars indicate standard error. Note that the model yields one neuronal input-output function in each condition; therefore there are no error bars for the model parameters. (D) DCS affects population firing for an equal synaptic input. Values within the I/O curve with the same synaptic input were chosen (gray area in B), fEPSP traces are plotted on the left and population spikes on the right column for each condition: control (black), −DCS (blue), +DCS (red). The three conditions are overlaid in the lower plot.

Figure 4

DCS alters firing time. (A) Time delay determined by the two-compartment model. Left, representative voltage traces of single spike timing, at determined pre-synaptic stimulation intensity. Time delay (ΔT) is calculated as the spike latency in control condition (black) minus the time of the action potential during DCS (−DCS: blue, +DCS: red). During −DCS neurons fire faster, resulting in a negative ΔT; the opposite occurs for +DCS. Right, ΔT was measured for both polarities under different orthodromic stimulation intensities (to emulate experimental data). −DCS advances firing time for all orthodromic stimulation intensities (B) Time delay quantified for experimental data. Left, representative physiological traces of population firing with fix orthodromic stimulation intensity. ΔT is measured comparing population spike latency (short line underneath each trace) under control versus DCS condition. The population of neurons fire faster during −DCS (blue) and viceversa for +DCS (red). Right, ΔT measured across orthodromic stimulation intensities for each slice (n=15). −DCS significantly advances population firing and +DCS delays firing. Gray dots indicate the mean ΔT across orthodromic stimulation intensities for each slice. Lines on top of the bars indicate standard error.

Figure 5

I/O function model for population of neurons predicts different excitability changes under the anode versus cathode. (A) Single-neuron model predicts modulation for various field intensities and orientations. (A.1) Horizontal shift of the I/O function for multiple field magnitudes. Orientation of the field is aligned with the somato-dendritic axis. The computational model predicts a monotonic modulation (approximately linear) of the horizontal shift of the I/O curve (x₅₀ shift). Sensitivity to the field intensity varied between positive and negative fields. Resulting in an approximate change of −0.45% of the X₅₀ compared to control per V/m applied for negative fields and 0.04% shift per V/m for positive fields. (1) and (2) indicate the change of the I/O function shown in A.2.(A.2–A.4) For a fixed field amplitude (35 V/m) the relative orientation was varied from 0° (A.2) to 45° (A.3) to 90° (A.4), inset indicates direction and polarity of the field. (B) The single-neuron model was coupled with a multi-scale model of macroscopic currents in the human brain (Rahman, 2013). We simulated the effect of polarizing currents on the I/O function for neurons distributed across the cortex under the anode and cathode. (B.1) A conventional M1-SO montage was simulated. (B.2) The current flow intensity alternated regularly across the cortex (false color map shows the electric field along the somato-dendritic axis) (B.3) Schematic of the cortical gyrius and the neuronal orientation relative to the current flow. Gray arrows depict the direction of the current. The polarization effect on the I/O function is shown for each group on neurons in the gyrius (I/O functions plotted outside the schematic gyrius). The aggregate effect is calculated as the average across the population of neurons (I/O curve in the center of the gyrius). When current flows inward neurons experience a soma depolarization (blue) resulting in a larger shift of the I/O function to the left. The opposite effect occurs for neurons on the contralateral area of the gyrus. (B.4) Probability density function of the radial component of the electric field underneath the anode and the cathode. The gradient indicates the type of cell body polarization (blue, depolarizing; red, hyperpolarizing). (a) and (c) refer to the 5_th percentile; (b) and (d) refer to the 95_th percentile. (B.5) Schematic representation of the mean effect on the I/O function of all neurons that are exposed the electric field distribution in (B.4). Upper, the population effect under the anode is a leftward shift shown in blue. Lower, the population effect under the cathode is a rightward shift, plotted in red. (B.6) I/O function change for the population underneath the anode and the cathode quantified as % change of the X₅₀ threshold per V/m applied. (B.7) I/O function modulation for the population of neurons that experience the peak electric fields under the electrodes. (a,c) 5% of neurons that are exposed to the strongest negative fields (soma depolarizing) under the anode. (b,d) 5% of neurons affected by the strongest positive fields (soma hyperpolarizing) under the anode/cathode.