Epidural cerebellar stimulation drives widespread neural synchrony in the intact and stroke perilesional cortex

Cerebellar electrical stimulation has shown promise in improving motor recovery post-stroke in both rodent and human studies. Past studies have used motor evoked potentials (MEPs) to evaluate how cerebellar stimulation modulates ongoing activity in the cortex, but the underlying mechanisms are incompletely understood. Here we used invasive electrophysiological recordings from the intact and stroke-injured rodent primary motor cortex (M1) to assess how epidural cerebellar stimulation modulates neural dynamics at the level of single neurons as well as at the level of mesoscale dynamics. We recorded single unit spiking and local field potentials (LFPs) in both the intact and acutely stroke-injured M1 contralateral to the stimulated cerebellum in adult Long-Evans rats under anesthesia. We analyzed changes in the firing rates of single units, the extent of synchronous spiking and power spectral density (PSD) changes in LFPs during and post-stimulation. Our results show that post-stimulation, the firing rates of a majority of M1 neurons changed significantly with respect to their baseline rates. These firing rate changes were diverse in character, as the firing rate of some neurons increased while others decreased. Additionally, these changes started to set in during stimulation. Furthermore, cross-correlation analysis showed a significant increase in coincident firing amongst neuronal pairs. Interestingly, this increase in synchrony was unrelated to the direction of firing rate change. We also found that neuronal ensembles derived through principal component analysis were more active post-stimulation. Lastly, these changes occurred without a significant change in the overall spectral power of LFPs post-stimulation. Our results show that cerebellar stimulation caused significant, long-lasting changes in the activity patterns of M1 neurons by altering firing rates, boosting neural synchrony and increasing neuronal assemblies’ activation strength. Our study provides evidence that cerebellar stimulation can directly modulate cortical dynamics. Since these results are present in the perilesional cortex, our data might also help explain the facilitatory effects of cerebellar stimulation post-stroke.


Background
The cerebellum and M1 are heavily interconnected brain areas that play a vital role in motor control and learning [1,2]. Different classes of cerebellar neurons have been linked to different movement features. For example, deep cerebellar nuclei (DCN) neurons, the principal projection neurons from the cerebellum to M1, are tuned to cues leading to movement onset and duration in reaching tasks [3][4][5][6][7][8][9][10]. Purkinje cells, another principal cell type in the cerebellar cortex, are correlated to limb position, velocity, distance of limb movement and muscle activity during movement. Moreover, Purkinje cell activity becomes more synchronized during the learning of a skilled reaching task [3,4,[11][12][13][14][15][16][17][18]. In addition, studies have revealed a strong link between M1 neural plasticity and motor skill acquisition [19][20][21][22]. Consistent with these findings, other recent work has shown that inactivation of either area leads to a loss of kinematic precision in skilled reaching tasks [10,23].
Studies have also shown that cerebellar stimulation can modulate motor function, motor excitability and cerebellar plasticity [24][25][26][27][28]. This work, along with accumulating evidence that cerebellar stimulation can influence remote functional connectivity, has generated interest in assessing the role of cerebellar stimulation as a potential therapy for movement disorders, and in stroke rehabilitation [29][30][31][32][33]. Animal studies have stimulated DCN neurons in rodent stroke models. These results demonstrated that subjects showed subsequent improvements in motor behavior, and changes in MEPs, axonal growth protein and synaptogenetic markers in peri-infarct cortices [34][35][36]. Other animal work has shown that epidural stimulation of the cerebellum has a smoothing effect on corticomotor maps [24], and that cerebellar transcranial electric stimulation (tES) can entrain neurons in the cerebellar cortex and exerts its effects principally through modulation of Purkinje cells [37].
While these studies have provided key insights into the effects of cerebellar stimulation, our current understanding of how cerebellar stimulation impacts ongoing dynamics in the cortex at the level of single neurons or neural ensembles remains limited. Furthermore, how this stimulation modulates ongoing activity in the periinfarct cortex can help in understanding the facilitatory effects of cerebellar stimulation during stroke rehabilitation. Analyzing single neuronal activity at the cortical level can provide useful details that may aid in optimizing cerebellar stimulation paradigms. We were also interested in assessing coordinated firing of neural ensembles after cerebellar stimulation, as neuronal co-firing in a temporally coupled manner is known to be important for information processing and plasticity in the brain [38][39][40][41][42]. It is likely that such coordinated activity may play an important role in driving neural plasticity after injury and during neuromodulatory approaches such as cerebellar stimulation [34,35].
In this study, we have developed a model to study the effects of cerebellar stimulation on cortical activity using acute large-scale extracellular recordings of intact M1 and stroke-injured peri-infarct M1. We were particularly interested in understanding the diversity of single neuron responses to epidural cerebellar stimulation because epidural stimulation is less invasive than deep stimulation, and therefore presents a lower translational barrier [42,43]. It is unlikely that all neurons respond to cerebellar stimulation in the same manner due to differences in cell type, and the diversity of single neuron network connectivity [44]. We were also interested in assessing changes in neural synchrony, and examined the effects of cerebellar stimulation on M1 single neuron firing rates, as well as M1 ensemble dynamics like coordinated firing and neuronal pair coupling. We found that cerebellar stimulation could significantly change both the firing rate and the synchronous firing of neurons in the intact and stroke-injured perilesional M1. Together our results provide evidence that epidural cerebellar stimulation directly modulates neural dynamics in the intact and the periinfarct M1.

Animal preparation
Adult male Long-Evans rats were used in this study (n = 9, 250-400 g, ~ 8 weeks old, Charles River Laboratories). All animal procedures were performed according to the protocols approved by the Institutional Animal Care and Use Committee at Cedars-Sinai Medical Center, Los Angeles. This ensured that the animals that were used in this research were acquired, cared for, housed, used, and disposed of in compliance with the applicable federal, state and local laws and regulations, institutional policies and with international conventions to which the United States is a party. Animals were housed on a 14 h light and 10 h dark cycle (Photoperiod is from 6 am to 8 pm) in a climate controlled vivarium. One animal was excluded from the study due to significant recording drift and electrical noise in the recording. Thus n = 8 animals were used for the analysis. Out of these, four rats were assigned to the intact group and another 4 to the acute stroke group. Before starting the stimulation surgery, animals were briefly anesthetized using isoflurane, and then injected with a ketamine/xylazine cocktail (85 mg/ kg and 10 mg/kg, respectively). Supplemental ketamine (42.5 mg/kg) was given every 30-50 min as needed to maintain the anesthesia level. The ketamine-xylazine anesthetic state is predominantly characterized by slow wave oscillations in the neocortex [45], and has been used in other studies to investigate the effects of electric stimulation on ongoing cortical activity dominated by low-frequency oscillations [42,46]. In addition to anesthesia, atropine (0.05 mg/kg) was administered to counter respiratory or cardiac depression. Animals were perfused and their brains collected for staining on the same day after recordings.

Stimulation
After anesthetizing the animal, cranial screws were implanted in the skull in the configuration noted in Fig. 1a to act as epidural cerebellar stimulation electrodes. The stimulation screws were implanted over the cerebellar hemisphere contralateral to recorded M1. The location of the first screw was 11.5 mm posterior and 2.5 mm lateral to bregma. The second screw was placed 14 mm posterior and 3.0 mm lateral to bregma. This arrangement mimics a rostrocaudally oriented electric field, which has been shown to result in the greatest amount of Purkinje cell modulation [37,47]. Our stimulation electrode montage roughly encompassed the posterior lobe of the cerebellum; the anterior bone screw was connected to the cathode (current magnitude: − 175 μA), and the posterior screw served as the ground (Fig. 1a). A direct current stimulation (DCS) was applied for 30 min through these electrodes. DCS was applied directly onto the dura to ensure a defined contact area over the cerebellar cortex. Our current density was estimated at 0.25 mA/mm 2 based on our previous work [42]. This is comparable to that used in invasive human and non-human primate studies [48,49].

Electrophysiological recordings
We recorded extracellular neural activity using 32 channel tungsten microwire electrode arrays (MEAs, Tucker-Davis Technologies (Alachua, FL): each 33-μm polyimide-coated tungsten electrode). These were 8 × 4 arrays with 250 μm spacing in between each electrode in a row and 375 μm spacing between rows (total 4 rows). The long axis of the probe was placed mediolaterally in M1. Following a craniotomy and a durectomy over the forelimb area of M1, arrays were lowered down to 900-1500 μm from the surface of the dura mater. In the intact animals, the recording array was centered at 0.5-1 mm anterior to bregma and 2.5-3.5 mm lateral from midline, and in stroke rats, it was placed slightly anterior to the stroke site, centered at 3-3.5 mm anterior to bregma and 2.5-3.5 mm lateral to midline. Depth was finalized based on quality of recordings across the array. A ZIF-clip-based digital head stage with a TDT-RZ2 system was used for signal acquisition. We recorded spikes at 24,414 Hz and LFPs at 1017 Hz sampling frequencies. The average duration of recordings was 124.84 ± 8.31 min (mean ± s.e.m.) across all animals, where pre-stimulation baseline activity (Stim pre ) was recorded for 43.54 ± 4.46 min and post-stimulation

Photothrombotic stroke
After the craniotomy, rose bengal dye (20 mg/kg) was injected into the femoral vein over a 2 min period using an intravenous catheter. Next, the M1 area of the brain was illuminated with a green laser (532 nm, Laserglow Technologies) through a 2-mm aperture (centered 0.5 mm anterior and 2.5 mm lateral to bregma) for 12 min, while the remaining exposed cortex was covered with a custom aluminum foil mask to prevent light penetration. After induction, a probe was implanted in the perilesional cortex immediately anterior to the stroke site [42,50]. The craniotomy or implanted electrodes were covered with a layer of silicone (Kwik Sil ™ ).

Data analysis Single unit analyses
After spike sorting, further single unit analyses were performed in MATLAB (Rb2018a) using a combination of custom written routines. We started by selecting high amplitude units for subsequent analyses. In order to identify units with high amplitude, we calculated the signal-to-noise ratio (SNR) for every recorded unit using the following equation [50,51]: where A is the peak-to-peak voltage of the mean spike waveform and SD noise is the standard deviation of the baseline noise floor. Our single unit analysis was typically done on units with SNR > 3.5. For during-stimulation analyses in intact animals, we chose neurons with SNR > 6.

Firing rate analysis
Firing rate was calculated from the spike trains of isolated single units by counting the number of spikes in the 50 ms bins. Using this method, we calculated the mean firing rate in the Stim pre Stim dur and Stim post periods. Firing rates were calculated for the entire duration of all periods. A significant change in firing was estimated by calculating the mean post-stimulation firing rate and checking if it was outside of the 95% distribution of prestimulation firing rate. Neurons that increased their firing rate were classified as positively modulated (M + ), while ones that decreased their firing rate were classified SNR = A 2 * SD noise as negatively modulated (M − ). The rest of the units were classified as non-modulated (NM) units.

Spike train cross-correlation
We began by equaling the spike counts in pre-and poststimulation periods. We then computed cross-correlation histograms (CCH) using 10 ms bins for all neuronal pairs. Furthermore, we constructed pseudo-random spike train CCHs with simulated spike counts of equal length for every pairing in Stim pre and Stim post conditions. Such simulations were run 300 times (Monte Carlo Simulations) [52]. CCH counts were converted to probability. Thereafter, to quantify pairwise coincident firing from Stim pre to Stim post , we took the mean of the simulated CCH probability within ± 400 ms around the center and subtracted it from the mean of real CCH probability in the same window for Stim pre and Stim post conditions, respectively (Δ CCH ).

Ensemble activation analysis
Next, we wanted to assess changes in the activity patterns of neural ensembles. For this, we characterized the neural activity patterns in Stim pre and Stim post by comparing it to a template that was created by performing principal component analyses (PCA) on a baseline Stim pre neural activity matrix. This method can detect cell assembles or neurons with shared activity patterns [40,[52][53][54]. To perform these analyses, we computed a pairwise unit activity correlation matrix from baseline activity during Stim pre . Stim pre spike trains were binned (t bin = 500 ms) for each neuron. These spike trains were z-transformed, and then organized into a 2-D matrix of neurons (rows) by time (columns). From this spike count matrix, we calculated the correlation matrix and then calculated the eigenvector for the largest eigenvalue from this correlation matrix and used it as the ensemble baseline activity template. We then equaled the number of spikes in Stimpre and Stim post , and then projected the ensemble baseline activity template back onto them. This projection is a linear combination of Z-scored binned neural activity from the two blocks above, weighted by the principal component (PC) ensemble (i.e., the eigenvector) that was calculated from the baseline activity matrix. This linear combination has been described as the "activation strength" of that particular ensemble. Typically, the significance of a PC is determined by λ max , which is the highest eigenvalue that arises out of an equivalently sized random matrix based on the Marchenko-Pastur law. We got 1-3 significant PCs from the baseline activity, but the first PC explained the highest variance of the data so we focused our analysis on that one. Using this method, we compared the activation strength of the first PC in each animal during Stim pre and Stim post . Stim dur time periods were excluded from ensemble analyses as we restricted during-stimulation analyses to a limited number of very high SNR neurons, and ensemble analyses are more wellsuited to datasets with a larger number of neurons.

LFP power analysis
LFP analyses were conducted using a combination of custom-written routines in Matlab, along with functions from the Chronux toolbox (http:// chron ux. org/) [55]. Pre-processing for LFP analyses involved the elimination of periods with artifacts and the removal of broken channels and noisy segments of LFPs by offline visual inspection. Additionally, ± 10 s of LFP data around the start and end of stimulation was removed to reduce segments with artifacts. We calculated power on a total of 32 channels across eight animals. The electrodes we implanted in M1 were 32-channel arrays that were arranged as eight shanks in four rows (375 μm row separation). We selected one channel from each row for these analyses, totaling four channels from each animal. Power analyses were performed by time matching the Stim pre and Stim post time periods or Stim pre and Stim dur time periods to the shortest recording period, splitting them into 10 s segments and then finding the mean power across the segments. We used a time-bandwidth product of 10 with 19 tapers for multitaper spectral analyses [46]. Mean power was calculated across the δ-band (0.3-4 Hz, which is the predominant oscillation with ketamine anesthesia), and all the values in this frequency range were averaged together on each channel. Statistical analyses were performed on the average power estimates of this frequency band respective to Stim pre , Stim dur and Stim post values (see section below).

Staining for stroke
After the acquisition of brain electrophysiological recordings was complete, the rats were re-anesthetized with isoflurane inside a desiccator jar and intracardially perfused with phosphate buffered saline (PBS) for 10 min followed by 4% paraformaldehyde in PBS for 30 min. The brains were harvested and post-fixed in 4% paraformaldehyde in PBS for 4 h at the end of which they were transferred to 30% sucrose (w/v) in 0.1 M PBS until equilibrated. The tissue was embedded in Tissue-Tek O.C.T. compound, cryosectioned into 50 µm sagittal sections and stored in 0.1% Sodium Azide in PBS at 4 °C. For Fluoro-Jade C staining, the free-floating sections were given three washes with PBS followed by mounting and air drying at room temperature. The slides were then incubated with gentle shaking in the following solutions in sequence: 1% sodium hydroxide in 80% ethanol for 5 min, 70% ethanol for 2 min, distilled water (DW) for 2 min, 0.06% potassium permanganate for 15 min, and DW for 2 min. The slides were protected from light during the subsequent steps: incubation with freshly prepared 0.0001% Fluoro-Jade C (Chemicon International, CA) in 0.1% acetic acid with DAPI for 30 min, 3 washes with DW (2 min each time), air dry for 5 min, and placement on slide warmer at 65 °C for 10 min. Finally, the dried slides were cleared in Xylenes and coverslipped using DPX mounting medium. Digital images of the stained sections were collected on an Olympus BX51W1.

Statistical analysis
In this study, we performed statistical analyses by implementing routines in MATLAB (Rb2018a). The linear mixed-effects model (implemented using MATLAB fitlme) was used to compare the differences between Stim pre and Stim post groups shown in Figs. 1c, 2c, 4d, 5b, 6b-d, 7b, d, e, f and 8b-d. This model accounts for the 'nested' datasets wherein multiple observations have been collected from the same research subject [42,56]. In Fig. 3, we computed the differences in firing rates of all individual neurons from Stim pre to Stim post and correlated them with the difference between the mean ΔCCH change of the respective neuron with all other neurons from Stim pre to Stim post . We used linear regression (implemented using MATLAB fitlm) to evaluate changes in firing rate and coincident firing changes after cerebellar stimulation for pairs of neurons showing an increase (Fig. 3a), decrease (Fig. 3b) or no change in firing rate from Stim pre to Stim post (Fig. 3c).

Cerebellar stimulation modulates neural firing in intact M1
We first analyzed the effects of cerebellar stimulation on the firing rate of M1 neurons in the intact cortex (Fig. 1). The majority of recorded neurons showed a significant change in their firing rate following stimulation. Examples of both a significantly positively modulated (M + , Stim pre firing rate = 0.56 ± 0.01 Hz, Stim post firing rate = 7.40 ± 0.02 Hz, p < 0.05) and a significantly negatively modulated (M − , Stim pre firing rate = 1.97 ± 0.01 Hz, Stim post firing rate = 0.848 ± 0.007 Hz, p < 0.05) neuron are shown in Fig. 1b. Additionally, we observed a significant change in the firing rate of neurons at the population level (n = 154 neurons, mixed-effect model, p < 10 -7 , see Fig. 1c), and found that at the individual neuron level 56% of neurons showed increased firing, 20% showed decreased firing and 23% showed no significant change in firing in Stim post (Fig. 1d).
To ensure that fluctuations in baseline firing rate were not due to anesthesia, we analyzed firing rate changes from early and late Stim pre , and found that they did not change significantly (n = 154 neurons, baseline change = 0.037 ± 0.01 Hz, mixed-effect model, p > 0.05). Additionally, we found no significant change in baseline LFP power in the δ-band within Stim pre (mixed-effect model, p > 0.05).

Cerebellar stimulation increases neural synchrony
To analyze changes in neural synchrony post cerebellar stimulation in the intact brain, we looked at how the magnitude of cross-correlation between pairs of M1 units changed from Stim pre to Stim post (Fig. 2a). We analyzed a total of 2425 neuron pairs for this analysis. An example of an increase in cross-correlation from Stim pre to Stimpost is shown in Fig. 2b. At the population level, we calculated the magnitude of the difference between the peaks of Stim pre and Stim post from a shuffled correlogram (Δ CCH , see "Methods"). We found a significant increase in correlated firing post-stimulation (mean Stim pre to Stim post change 29.51%; mixed-effect model, p < 10 -67 , see Fig. 2c). Thus, even though firing rates were diversely modulated following cerebellar stimulation, neural activity became consistently more synchronized.

Neural synchrony is independent of changes in M1 firing rate
As shown above, cerebellar stimulation significantly modulated neural firing rates and correlated firing between neurons. While we equaled the number of spikes in Stim pre and Stim post before making cross-correlograms (see "Methods"), it is possible that our observed changes in coincident firing were related to the changes in the firing rate. We therefore examined whether there was a relationship between the firing rate changes of a neuron and the change in Δ CCH of that neuron with other neurons. We specifically wanted to check if neurons that increased their firing rate (i.e., M + neurons) also experienced an increase in neural synchrony. Similarly, we also wanted to check if the neurons that decreased their firing rates (M − neurons) experienced a reduction in their cross-correlograms. Hence, we focused on the correlations changes of neurons that were part of either M + -M + or M − -M − pairs. We also performed another regression for neurons of NM-NM pairs and their respective crosscorrelations to compare to M + /M − neurons. We found that only 3.5% of the variation in change of Δ CCH was explained by firing rate changes of M + neurons (Fig. 3a), 0.02% was explained by M − neurons (Fig. 3b) and 3.02% was explained by NM neurons (Fig. 3c). These results indicate that changes in correlated firing were not correlated with the firing rate changes of positively modulated, negatively modulated or non-modulated neuron pairs. This suggests that the effects of cerebellar stimulation on M1 neural synchrony are independent of its effects on the firing rates. . On the right is the average LFP power in the slow frequency band across all animals (right, *p < 1 × 10 -2 ; Stim pre power is same in Fig. 5 but y-axis scale is adjusted to accommodate Stim dur power)

Activation strengths of M1 cell assemblies is strengthened after epidural cerebellar stimulation
Having demonstrated large-scale cerebellar stimulationdependent changes in firing rate and correlated firing among neural pairs, we next examined whether cerebellar stimulation boosted the activation of M1 cell assemblies over their baseline level of activation (Stim pre ) in the intact brain. To investigate this, we used principal component analyses (PCA) to identify patterns of neural activity (i.e., neural ensembles) and then probed their activation magnitude before and after stimulation (see "Methods" for details).
Ensemble activation during the Stim pre and Stim post periods was quantified by applying a PCA-generated template of spontaneous baseline neural activity from pre-stimulation recordings. PCA resulted in a number of principal components (PCs or "ensembles") that reflected patterns of common variance across the recorded single-units, with each component comprised of weights that reflected the contribution of each neuron to that particular ensemble (Fig. 4a, b). To represent the activity of a particular ensemble, the traditional method is to multiply the weights from each neuron in the ensemble with the z-scored activity matrix of the recorded neurons. The ensemble defined from the spontaneous pre-stimulation recording period was multiplied by the z-scored neural activity recorded during the Stim pre and Stim post , resulting in a one-dimensional vector that represents the "activity" of that ensemble before and after stimulation (Fig. 4c).

M1 LFP power remains unchanged after cerebellar stimulation
Next, we examined the mesoscopic changes in M1 activity by looking at LFP signals. The ketamine-xylazine anesthetic state is predominantly characterized by slow wave oscillations in the neocortex as depicted in Fig. 5a [45]. These slow oscillations are similar in frequency to recently described low-frequency oscillations (LFOs) that can serve as a biomarker for stroke recovery [42], and hence have been studied to assess the effects of electric stimulation [42,46]. We analyzed power changes in lowfrequency bands (i.e., δ-band, 0.3-4 Hz). Our LFP analysis revealed no significant change in δ-band LFP power post cerebellar stimulation (14.82%, mixed-effect model, p = 0.69, Fig. 5b).

Changes in M1 activity start to set-in during cerebellar stimulation
Whether the above-described changes in M1 activity started to set in with the onset of stimulation requires an analysis of during-stimulation changes (Stim dur ). Due to increased noise levels during cerebellar stimulation, we considered only neurons with very high amplitudes (SNR > 6) for this analysis. We found that the changes in firing rate of positively (M + ) and negatively modulated (M − ) neurons start to set in during stimulation. An example of an M + neuron is shown in Fig. 6a. The distribution of changes in the firing rates of units before and during cerebellar stimulation across M + and M − groups is c Representative cross-correlogram of a pair of peri-infarct M1 units, before and during cerebellar stimulation (left). Mean change in Δ CCH is shown as mean ± s.e.m., across four animals (right). *p < 5 × 10 -2 . d An example LFP power from a single animal before and after cerebellar stimulation (left). Grey shaded area shows the slow frequency band (0.3-4 Hz). The average LFP power in the slow frequency band across four animals is shown in the inset (Stim pre power is same as the Fig. 7 but y-axis is adjusted) shown in Fig. 6b. These units show significant changes in their firing rates during stimulation (mixed-effect model, p < 0.05). We also observed that coincident firing starts to increase during stimulation (Fig. 6c), but this increase was not significant (n = 59 pairs, mixed-effect model, p = 0.36). Furthermore, we looked at δ-band LFP power during stimulation. We found a significant increase in power from Stim pre to Stim dur (276.12%, mixed-effect model, p < 0.05, Fig. 6d). These changes in power spectrum show that low-frequency oscillatory activity in M1 is boosted during cerebellar stimulation. However, the power spectral changes were not long-lasting and ended by Stim post , while the firing rate changes and coincident firing changes persisted. Together, these results indicate that the effects of cerebellar stimulation on single units persist long after stimulation has ceased, and that they start to set in during stimulation.

Changes in peri-infarct M1 during cerebellar stimulation
In our next set of experiments we wanted to check for concordance of the results we observed in healthy animals with acutely stroke-injured animals. We induced a photothrombotic stroke in M1 in four animals and recorded activity directly anterior to the site of stroke in peri-infarct M1 before, during and after cerebellar stimulation (Fig. 7a). Since there was a paucity of neurons that we could record after stroke, our analyses were done on all neurons with SNR greater than 3.5 (n = 57). We first looked at the firing rate of units in intact and stroke brain. We found that firing rates of units in the stroke perilesional cortex were lower than the firing rates of units in the intact M1 during Stim pre (Fig. 7b). Thereafter, we looked at changes in the firing rates of peri-infarct M1 neurons during cerebellar stimulation. An example of an M + neuron is shown in Fig. 7c. The units from stroke perilesional cortex showed significant changes in their firing rates during stimulation (Fig. 7d, mixed-effect model, p < 10 -3 ). We also looked at changes in the coincident firing of peri-infarct M1 units. Although coincident firing starts to increase during stimulation, this increase was not significant (Fig. 7e, mixed-effect model, p = 0.60). Next, we looked at δ-band LFP power during stimulation, and found a significant increase in power from Stim pre to Stim dur (376.70%, mixed-effect model, p < 0.01, Fig. 7f ). Overall, recordings from stroke-injured rats show similar trends to recordings in intact rats during cerebellar stimulation.

Changes in peri-infarct M1 post cerebellar stimulation
We also looked at the Stim post changes in peri-infarct M1 activity. The firing rate changes that start to set in during stimulation persist after stimulation as well. An example of an M + neuron with a sustained increase in spiking activity is shown in Fig. 8a. At the population level, units from peri-infarct M1 showed significant changes in their firing rates after stimulation (mixed-effect model, p < 10 -7 ) and 88% of cells changed their firing rate significantly (Fig. 8b). Furthermore, we observed a significant change in the coincident firing of peri-infarct M1 units post cerebellar stimulation (Fig. 8c, mixed-effect model, p < 0.05). Our LFP analysis from Stim post in stroke-injured rats showed a nonsignificant increase in δ-band LFP power (34.73%; mixed-effect model, p = 0.66, Fig. 8d).

Discussion
Our work shows that epidural cerebellar stimulation can significantly change neural firing rates and induce M1 plasticity that lasts 30-45 min after the end of stimulation. Moreover, neural synchrony as measured through coincident firing changes (Δ CCH ) increased significantly irrespective of the direction of the change in firing rate after stimulation. These changes occurred over a mesoscale oscillatory backdrop of low-frequency oscillations due to ketamine-xylazine anesthesia, and we observed these changes in the intact and stroke-injured M1. These results suggest that cerebellar stimulation can directly modulate M1 dynamics and increase cortical neural synchrony. Our study helps support other recent findings that report the facilitatory effects of cerebellar stimulation in stroke recovery [34-36, 57, 58].

Relation to previous models of cerebellar stimulation
Previous studies have shown that cerebellar stimulation can alter functional connectivity and excitability in cortical areas [24,26,27]. These changes have been evaluated using functional imaging [26], which is an indirect measure of neural activity. Moreover, cerebellar stimulation has been shown to increase cortical excitability in rodent and human studies as evaluated through MEPs induced either through transcranial magnetic stimulation (TMS) or intracortical microstimulation (ICMS) [27,36]. Both deep brain stimulation (DBS) and transcranial direct current stimulation (tDCS) have been studied extensively for their applications in abnormal motor behavior. Our work can be likened to tDCS studies as we stimulated the cerebellum epidurally. Cerebellar tDCS is shown to induce polarity specific modulation in the cerebellar cortex [59]. This work suggested that anodal tDCS excites the cerebellar cortex, whereas cathodal tDCS exerts an inhibitory effect. Furthermore, computational modeling work has shown that tDCS directly affects cerebellar circuitry, and that stimulation currents are contained within the cerebellum [60]. An index of cerebellar brain inhibition (CBI) has been used to evaluate the impact of cerebellar modulation [61], and it was noted that cathodal tDCS reduces CBI and anodal tDCS increases CBI (although another study found that anodal tDCS reduces CBI [62]). These observed effects have been explained either through a direct effect of tDCS on inhibitory neurons in the cerebellar cortex or on cerebello-thalamo projections to inhibitory interneurons of M1. Epidural cerebellar stimulation in animal models supports these findings, where it has been shown that epidural cerebellar stimulation via anodal current injection focuses corticomotor maps by augmenting inhibition. Meanwhile, cathodal epidural stimulation has the reverse effect [24]. New work recently showed that epidural cerebellar stimulation principally affects the main inhibitory cell in the cerebellar cortex, the Purkinje cell [37]. The cerebellar cortex strongly inhibits the cerebellar nuclei. Hence, inhibiting the cerebellar cortex can result in excitatory overdrive along the dentato-thalamo-cortical (DTC) pathway [63]. This work is indicating that there are polarity-dependent site-specific effects of direct current stimulation in the cerebellar cortex, similar to that which has been reported in cerebral cortex [64,65]. Our work is in agreement with these findings, as we placed a cathode over cerebellar posterior lobes and largely observed an increase in contralateral M1 neurons' firing rates.
Furthermore, DBS of the DTC pathway in rodents has also shown very promising results, extending the early studies that showed that single pulse stimulation of the dentate nucleus modulated cerebral cortical excitability [66][67][68]. This novel DBS approach used a continuous stimulation that targeted the DTC pathway, and reported that low-frequency beta-band stimulation enhanced cortical excitability and promoted functional recovery [34,69]. This work also showed that DBS helped reduce crossed cerebellar diaschisis [70,71]. Our work is also consistent with the facilitatory effects of lateral cerebellar nuclei (LCN) stimulation in these studies, as we find that cerebellar stimulation induces a heightened neural synchrony in the contralateral periinfarct M1 that is amenable to plasticity.
Our work adds to this body of literature and shows how M1 activity is directly affected by cerebellar stimulation. Specifically, our work has demonstrated three main points: First, epidural cerebellar stimulation can directly modulate the firing patterns of M1. This is demonstrated by the changes in firing rates of single neurons. Second, the diverse changes in neural firing rate we found suggest a more complex neural response to cerebellar stimulation. A better understanding of the diversity of responses and their neural bases, possibly through the study of their underlying connectivity, might help improve the efficacy of cerebellar stimulation. Third, our results suggest that cerebellar stimulation may act by changing spontaneous firing rate or neural synchrony.

Cerebellar stimulation and neural plasticity
Cerebellar stimulation induced plasticity appears to affect recorded M1 neurons differently. While most neurons experienced a change in firing rate, the extent and the direction of change was variable. We can envision several possible mechanisms for this diversity. Recent work that stimulated the cerebellum using transcranial alternating current showed that multiunit activity of the cerebellar cortex was enhanced during the negative phase of stimulation, while the positive phase suppressed activity [37,47]. This work also showed that Purkinje cells were the main cell type that was affected by transcranial epidural cerebellar stimulation [37]. Similarly, anodal DCS over the cerebellum has been shown to have a 'smoothing' effect on corticomotor maps [24]. Finally, theta burst stimulation has been shown to induce cerebellar plasticity [24]. The cerebellar cortex sculpts its output to M1 by adjusting the firing rate and timing of the neurons in the DCN. It is thus likely that our observations of changes in neural synchrony in M1 are due to input from the cerebellum. It is also possible that repetitive stimulation of inputs to an area can result in short-term homeostatic regulation of network dynamics [72][73][74].
Cerebellar stimulation could also trigger activitydependent synaptic plasticity [75,76]. In general, brief periods of activity can trigger long-term potentiation and long-term depression, depending on the specific patterns of activation [72,77]. Such activity can also increase or decrease the intrinsic excitability of presynaptic neurons [72], which might explain the observed diversity of single neuron plasticity following stimulation. It may also be possible, in future studies, to predict specific plasticity effects at the single neuron level by quantifying network connectivity with emerging computational methods [38].
Another possibility is that the observed changes in M1 firing result from network plasticity in the cerebello-cortical system. Epidural DCS of the cerebellum has been shown to 'focus' corticomotor maps, by reducing the magnitude of corticomotor responses, and enhance afferent inhibition associated with peripheral stimuli [24]. Moreover, cerebellar stimulation can trigger changes in TMS, DCS and ICMS evoked MEPs [24,36,[78][79][80]. The cerebellum projects mainly to cortical layers IV and V of M1 via the ventrolateral thalamic nuclei [81]. These inputs can adjust M1 circuitry in several ways, such as by modulating the efficacy of interconnections between M1 neurons. Furthermore, the cerebellum receives numerous projections that predict and update sensory events through the interactions of mossy fibers and climbing fibers [82]. Thus, it is reasonable to suppose that largescale network dynamics are modulated by cerebellar stimulation. It is also possible that observed changes in M1 could be a result of plasticity at other sites.

Increased neural synchrony during low frequency oscillations
It is important to note that the increases in neural synchrony and cell assembly activation strengths we observed occurred when the LFPs principally showed δ-waves, or LFOs [42,83]. We didn't observe a change in the LFP power of LFOs following stimulation. This suggests that changes in input to M1 are not a main driver of the observed effects, as LFP is widely believed to be a measure of synaptic inputs [39,44]. So what might be the broader physiological consequences of cerebellar stimulation-induced changes in correlated firing under LFO-like oscillations? It is known that this low frequency oscillatory activity commonly occurs during ketamine anesthesia [42,83], but studies have shown that LFOs also occur at the spiking and LFP level in M1 during reaching tasks [41,42,83,84]. It is hypothesized that LFOs represent an intrinsic property of motor circuits that are involved in the production of fast and accurate movements. Stroke disrupts these movement related potentials in humans, which is highly correlated to motor impairments and recovery [42,84]. Interestingly, our other recent work showed that parameters for the modulation of LFOs under anesthesia also generalized to awake skilled reaching [42]. Since, in this study, cerebellar stimulation enhanced neural synchrony while M1 was predominantly characterized by LFOs, cerebellar stimulation might be particularly useful for modulating neural dynamics during cortical slow-wave oscillations. Therefore, future work could examine whether cerebellar stimulation similarly modulates movement-related spiking in intact and peri-infarct cortices in awake behaving animals. This might reveal one mechanism through which cerebellar stimulation could improve motor function in stroke patients.

Conclusions
To summarize, a brief period of cerebellar stimulation resulted in long-lasting M1 plasticity. We found that the firing rates and correlated firing changed significantly in response to stimulation, and that neural ensemble activation was boosted. Our findings here will help optimize cerebellar stimulation paradigms for those with motor disabilities post-stroke, or other movement disorders.