Posted in Projects (This page is no longer updated. See NEWS page for the latest updates), Quantitative Neurophysiology with Applied Electric Fields

Preprint PDF: Rahman-Cellular-Effects-Acute-DCS-Somatic-Terminal

Asif Rahman

J Physiol. 2013 Mar 11.
Cellular Effects of Acute Direct Current Stimulation: Somatic and Synaptic Terminal Effects.

Rahman A, Reato D, Arlotti M, Gasca F, Datta A, Parra LC, Bikson M.
The City College of New York, CUNY;

Transcranial Direct Current Stimulation (tDCS) is a non-invasive brain stimulation technique to modulate cortical excitability. Although increased/decreased excitability under the anode/cathode electrode is nominally associated with membrane depolarization/hyperpolarization, which cellular compartments (somas, dendrites, axons and their terminals) mediate changes in cortical excitability remains unaddressed. Here we consider the acute effects of direct current stimulation on excitatory synaptic efficacy. Using multi-scale computational models and rat cortical brain slices we show: 1) Typical tDCS montages produce predominantly tangential (relative to the cortical surface) direction currents (4-12 times radial direction currents), even directly under electrodes. 2) Radial current flow (parallel to the somatodendritic axis) modulates synaptic efficacy consistent with somatic polarization, with depolarization facilitating synaptic efficacy. 3) Tangential current flow (perpendicular to the somatodendritic axis) modulates synaptic efficacy acutely (during stimulation) in an afferent pathway specific manner that is consistent with terminal polarization, with hyperpolarization facilitating synaptic efficacy. 4) Maximal polarization during uniform direct current stimulation is expected at distal (branch length is >3 times the membrane length constant) synaptic terminals, independent of and 2-3 times more susceptible than pyramidal neuron somas. We conclude that during acute direct current stimulation the cellular targets responsible for modulation of synaptic efficacy are concurrently somata and axon terminals, with the direction of cortical current flow determining the relative influence.



Figure 1. Multi-scale methods and outcome measures of uniform electric field directionality and effects. A1, Gyri-precise finite element models of current flow during tDCS indicate a uniform voltage gradient in cortical grey matter (GM) directly under the anode. A2, The induced electric field in the cortex can be decomposed into a radial component ( Ex ) that is parallel to the somatodendritic axis and a tangential component ( Ey ) that is orthogonal to the somatodendritic axis. A3, We quantified the relative occurrence of radial and tangential fields in cortical GM expressed as the ratio of the average of the field magnitude in the tangential direction to the average of the field magnitude in the radial direction ( Ey / Ex ). B1-2, The brain slice preparation was used to study the change in synaptic efficacy during a uniform radial or tangential field by recording evoked field potentials. The voltage gradient between parallel Ag/AgCl wires is superimposed on a schematic of a sagittal slice of the rat primary motor cortex. From the macroscopic to the mesoscopic scale we can approximate a uniform electric field along the length of a neuron (compare voltage gradients in A1 and B1). B3, The field EPSP provides a measure of synaptic efficacy through facilitation or inhibition of the response amplitude. C1, Compartment model simulations of morphologically reconstructed neocortical pyramidal neurons were used to provide a description of axon terminal polarization in a uniform electric field. C2, The polarization profile of a layer 5 pyramidal neuron in a radially directed uniform electric field indicates soma depolarization (red) corresponds to apical dendrite hyperpolarization (blue). Layer 2/3 neurons have a more complex polarization profile with long processes reaching maximal depolarization independent of the neuronal body. C3, Neurons in a uniform electric field directed tangential to the somatodendritic axis preferentially affects processes that are oriented along the tangential field.



Figure 2. Forward model of tDCS and HD-tDCS quantifying electric field direction metrics. During tDCS, current may be dominantly tangential (along the cortical surface) rather than radial, even in brain regions directly under the electrodes. A, MRI-derived finite element models of current distribution in a gyri-precise head model are used to quantify the relative occurrence of radial (normal to the cortical surface) and tangential (along the cortical surface) components of the electric field. Both conventional (top) and high definition (HD, bottom) tDCS montages produce radial ( Ex , normal to the cortical surface) and tangential current ( Ey , along the cortical surface) indicated by the global electric field distribution (V/m) across the head. In the HD-tDCS montage, current is focalized within the ring configuration (inset) with radial currents under the center electrode and tangential currents between the surround electrodes. Qualitative comparison of the electric field components indicate greater radial field magnitudes in the gyral wall and greater tangential field magnitudes in the gyral crown (compare insets). B, Regionally, the distribution of field component magnitudes indicate prevailing tangential currents under the anode, cathode and between electrodes as described by the ratio of tangential to radial field magnitude ( Ey / Ex ratio, see methods). However, most elements have both radial and tangential components, and the isolated highest electric fields are radial. The tangential and radial component for individual elements is shown for each sub-region in false color density plots, which show relative occurrence (relative density from absent (green) to maximal (red)). Axis histograms show relative distribution of elements with a given tangential or radial component electric field. Inset histograms describe the distribution of the % of elements in a region as a function of the normalized component magnitude (such that 1 indicates elements with dominant radial or tangential component). C, Cortical folding further influences the distribution of the electric field, therefore, sub-regional field component distributions are indicated for a gyral crown and wall. Tangential fields are dominant in magnitude in the gyral crown but are weaker in the walls where radial magnitudes are stronger, as observed in A.


Figure 3. Electrophysiology of direction-specific uniform DC electric fields in synaptic pathways of the rat motor cortex. A, Schematic of electrophysiology setup where uniform extracellular electric fields were generated in all experiments by passing constant current across parallel Ag-AgCl wires positioned in the bath across the slice. Activity was monitored in layer II/III or layer V with a glass microelectrode. An additional field electrode (REF) was positioned in an iso-potential to remove the uniform field artifact. Activity was evoked with a bipolar stimulating electrode (S1-S4) positioned 500 μm from the recording electrode in either layer II/III or layer V targeting one of four distinct synaptic pathways corresponding to different orientations of afferent axons: posterior horizontal layer II/III (S1), anterior horizontal layer II/III (S2), posterior horizontal layer V (S3), and vertical layer V to II/III (S4). B, Diagram summarizing the primary synaptic circuits in this study. Line thickness and diameter of the filled circles, which represent synapses, are correlated with the strength of the synaptic input. C, Schematic of the expected polarization in distinct synaptic pathways exposed to radial and tangential fields. Somas, dendrites, axons and axon terminals are depolarized (red), hyperpolarized (blue), or not affected (black) by DC fields. D, Characteristic fEPSP and field spike waveforms from the layer V pathway. The fEPSPs, but not earlier field-spike, were suppressed by the non-NMDA receptor antagonist DNQX.



Figure 4. Modulation of pathway-specific synaptic efficacy by radial and tangential DC fields. Application of DC currents in cortical slice demonstrates that tangential current are as effective in modulating pathway-specific synaptic efficacy as radial currents, though pathway-average effects result only for radial electric fields. A, Input-output curve of fEPSP response amplitude and peak latency in the horizontal layer V pathway. Horizontal grey bars indicates 25th and 75th percentile of fEPSP peak latency. B, Relative fEPSP amplitude in the vertical layer V to II/III pathway at different radially oriented electric field intensities (correlation coefficient R2 of linear fit=0.96). The fEPSP waveform inset shows a characteristic change in fEPSP amplitude with positive (+8 V/m, red) and negative radial fields (-8 V/m, blue) from control (no field, black). C, fEPSP responses are significantly (P < 0.05, *) facilitated with +8 V/m fields (left) and reduced with -8 V/m (right) in three pathways. In each pathway, individual slice averages are indicated with colored circles. Grouped average fEPSP amplitudes across all synaptic pathways indicate a 7% polarity-specific modulation of synaptic efficacy with 8 V/m radial fields. Circles in the grouped average represent the across slice means of distinct pathways (blue, red, green, and yellow are S1, S2, S3, and S4 pathways, respectively). D, fEPSP amplitude was significantly modulated by tangential electric fields in all three horizontal pathways but with direction sensitivity and not in the vertical pathway, all consistent with terminal polarization. Although tangential fields affected individual pathways, grouped average of fEPSP amplitudes across all pathways was not significant.


Figure 5. Terminal polarization by uniform DC electric fields using neuron compartment model and analytical/hybrid approximations. Maximum terminal polarization ( Vt ) depends on the length ( l ) of the last axonal branch and becomes uncoupled from the bend point at distant terminals ( l > 3λ ), however for short branches the terminal membrane potential is coupled with the membrane potential at the bend (V0 ). In all cases, numerical simulations applied 1 V/m electric fields. A, For a typical cortical pyramidal neuron, the maximum terminal polarization (Vt ) is a plotted with the corresponding optimal polarization angle ( θ ) of the branch relative to the electric field and the length ( l ) of terminating axon branch. B1-2, Relative terminal polarization (Vt normalized by the axonal length constant and by the electric field) as a function of branch electrotonic length and angle (circle color). B3, Considering the optimal polarization angle the relative polarization asymptotically approaches magnitude 1 with branch length (equivalently, terminal polarization reaches the maximal polarization Eλ for increasing lengths). C1-2, Schematic of a branched and straight axon in a uniform electric field with analytical solutions (see Methods). The straight axon is a special case of the branched axon with infinite final branch length. For long branches, where l >> λ , the terminal membrane potential becomes independent of the branch point and approaches Eλ cosθ . C3, The branched axon model approaches maximal terminal polarization Eλ for l > 3λ . D, Error of approximations (analytical vs. numerical estimates) for branched (blue) and straight (red) axons.