Tangential currents to the cerebellar cortex can entrain Purkinje cell spiking activity
DOI: Pending DOI
Synopsis
In transcranial electrical stimulation, currents flow both parallel to the brain surface (tangentially) and inward toward deeper cortical layers. In this paper, we investigated whether tangential electric fields (E-fields) on the cerebellar cortex can entrain the spiking activity of Purkinje cells (PCs), which have dendrites extending toward the pial surface in a parasagittal plane. The results demonstrate that the entrainment of spiking activity is the strongest with E-fields that are oriented in the rostrocaudal direction in the plane of the PC dendritic tree, and lowest when the E-field is in orthogonal direction to the dendritic tree. These results suggest that tangential currents can be leveraged to selectively target the PCs in the cerebellar cortex using electrode designs that can steer the E-field direction.
Background
In non-invasive brain stimulation, cortical E-fields can be controlled to a certain extent through the choice of electrode montage. However, intervening layers under the electrodes such as the skin, skull, and cerebrospinal fluid (CSF) significantly distort the resulting field distribution [1, 2]. Computer simulations can provide insight into the E-field intensity and direction of the induced E-field at the meso- and macro-scales for a given electrode montage. There is also a great deal of diversity in morphology and electrophysiological properties of brain cells. These cellular characteristics together with the cell’s position and orientation relative to the externally applied E-field determine how the cell responds to the stimulation.
Previous reports have shown that the E-fields in the somatodendritic direction induce the largest perturbations of the transmembrane voltage at the soma [3-5]. Some of the largest cells of the cerebral and cerebellar cortices are oriented perpendicularly to the pial surface, which would make them most sensitive to E-fields in same direction. However, computer simulations predict that the applied current spreads through the CSF and predominantly flows parallel to the brain surface[LE1.1] [2], which is not the preferred directed for these large cells. PCs of the cerebellar cortex have a unique morphology with their dendritic trees mostly contained in a parasagittal plane and parallel to each other. We decided to study the effect of tangential AC currents for entrainment of PC spiking activity by systematically rotating the E-field in the plane parallel to the surface. We hypothesized that the unique morphology of the PCs would amplify sensitivity to lateral currents and result in a directional response within the tangential plane. Data revealed supportive evidence that E-fields aligned with rostrocaudal direction produced the strongest entrainment.
Methods
In ketamine/xylazine anesthetized rats, the entire posterior cerebellum was exposed by removing the skull. A flexible printed circuit board electrode with 16 contacts was custom-designed for producing lateral E-fields in different directions parallel to the cerebellar cortex. The transcranial stimulation electrode was positioned over the cerebellar surface and pressed against the dura to deliver the AC stimulation on lobule 7 of the vermis or crus II of the paravermal cortex. Extracellular recordings were obtained using a glass micropipette (3–4 MΩ) filled with normal saline. The micropipette was inserted perpendicular to the cerebellar cortex through the central opening of the stimulating electrode, near its center where the lateral electric field was presumed to be relatively uniform. Average recording depth was 0.8 ± 0.35 mm (mean±std).
Signals were amplified by a gain of 100 or 1000, and filtered at 10 Hz–10 kHz. Each trial consisted of 60 seconds of stimulation at frequencies ranging from 1 to 1000 Hz. Stimulus current amplitude was set to achieve an entrainment level corresponding to phase-locking value (PLV, see below for definition) of ~0.5. Cells were isolated using principal component analysis (PCA) of the spiking activity and validated using inter-spike interval (ISI) plots and the spike amplitude histograms. The ISIn−ISIn+1 plot (return plot, n is spike index) was utilized as an additional criterion. To identify the cell as a PC, the presence of silence after the complex spikes (CS) was used as the main criterion, along with the return plots.
The mean phase vector (MPV) was defined as MPV=e^iθ where θ denotes the phase of each spike relative to the stimulation cycle. The PLV was computed as the magnitude of the MPV, and the preferred phase (PPh) was defined as the phase of the MPV.
Results
Rotating the E-field in the tangential plane to the cortex during 100 Hz sinusoidal AC stimulation revealed a strong dependence of PC spike entrainment on field orientation. PC spikes exhibited phase locking to the stimulation waveform; however, both the PLV and PPh varied systematically with E-field direction (Figure (A) & (B)).
Phase locking weakened at specific field orientations, with the PLV approaching zero, when the E- field was perpendicular to the plane of PC dendritic tree. Interestingly, the same orientations were associated with an abrupt inversion of the response phase. As the field orientation was advanced by a single 22.5° step near the PLV minimum, the PPh of the response shifted by approximately 180°. This transition was sudden, occurring within a single angular step and coinciding with the orientation that minimized PLV.
To assess if these observations can generalize, we analyzed 17 PCs recorded from 8 rats. Phase locking consistently depended on E-field orientation, with PLV exhibiting pronounced minima at specific field angles. These minima were clustered around two opposing orientations separated by approximately 180°, indicating that the minima occurred while the field direction is crossing a vertical plane. The E-field angles that produced the lowest PLV closely matched those showing an abrupt phase inversion, with points lying near the unity line in Figure (C), indicating a strong link between the two.
When PLV values from all cells were pooled, the dependence on E-field angle was evident. While individual measurements showed substantial variability, the mean normalized PLV from all cells revealed a clear angular dependence, with minima near 0° and 180° (field in mediolateral direction and perpendicular to the PC dendritic plane) and maxima near 90° and 270° (field in rostrocaudal direction and parallel to the dendritic plane). This angular dependence was statistically significant, as confirmed by a Kruskal–Wallis test followed by Bonferroni-corrected post hoc comparisons confirmed significantly (α = 0.05) lower PLV at mediolateral orientations (0° and 180°) than at rostrocaudal orientations (90° and 270°).
To examine whether anatomical location influences angle-dependent phase locking, cells were segregated based on recording site in the vermis versus crus II. This separation revealed differences in the angular structure of PLV modulation between the two regions. While both vermis and crus II cells exhibited PLV minima near opposing field orientations, crus II responses were more variable across angles. This increased variability may reflect differences in local folial geometry, as folia in crus II are more tilted, making precise alignment of the stimulation electrode with the folial axis more challenging.
To determine whether E-field orientation alters the frequency dependence of PC SS entrainment, we examined PLV across a coarse frequency sweep at multiple field orientations. Consistent with prior observations, PLV exhibited a tuning curve by stimulation frequency, where the strongest entrainment occurred in mid-frequencies and fell off at each side of the spectrum. Across E-field orientations, the overall magnitude of PLV varied, with some orientations producing weaker phase locking than others.
However, the shape of the PLV–frequency relationship remained qualitatively unchanged (Figure (D)). Normalization of PLV within each E-field orientation revealed nearly identical frequency-dependent profiles across angles, indicating that changes in field orientation primarily scaled the strength of entrainment without altering its frequency tuning. Frequencies that elicited strong phase locking at one orientation also did so at other orientations, and no field orientation selectively enhanced low-frequency or high-frequency modulation, except a small elevation at 1 Hz in two E-field orientations.
Discussion
In this paper, we show evidence that orthogonal E-fields to the somatodendritic axis can strongly entrain the spiking activity of the PCs of the cerebellar cortex and the preferred direction that maximizes the entrainment is approximately in the plane of the PC dendritic tree, in confirmation of our earlier report [6].
A metric based on the morphology of the cell (polar histogram coherence vector) was proposed where a net polarization vector was computed from stained images of the dendritic tree by finding the orientation of individual segments and taking the mean of their angles [4]. The projection of this vector on the axis of the E-field direction predicted how strongly the cell would be modulated. In this paper, despite our efforts to record from cells that are atop the folia, some of the PCs recorded were possibly closer to the folial walls and thus the somatodendritic axis of the cells may not be exactly orthogonal to the E-field applied. Furthermore, the horizontal asymmetry in the PC dendritic tree would tilt the direction of the net polarization vector from the assumed direction of the somatodendritic axis. For instance, the large basilar dendritic branches extend in the horizontal direction in PCs. Their proximity to the soma can make their asymmetry in the horizontal direction induce a large polarization of the soma.
In summary, the true polarization vector, particularly in PCs where the dendritic tree is extremely large, could deviate substantially from the somatodendritic axis of the cells that is assumed to be orthogonal to the folial surface. These factors probably played a role in generation of strong entrainment of the PC spiking activity in our data. Nonetheless, the results show that tangential currents can modulate the PCs and they should be taken into account while considering different electrode montages.
Disclosures
Supported by RF1NS122741 from NINDS/NIH.
References
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