Subthreshold electrical stimulation as a low power electrical treatment for stroke rehabilitation

As a promising future treatment for stroke rehabilitation, researchers have developed direct brain stimulation to manipulate the neural excitability. However, there has been less interest in energy consumption and unexpected side effect caused by electrical stimulation to bring functional recovery for stroke rehabilitation. In this study, we propose an engineering approach with subthreshold electrical stimulation (STES) to bring functional recovery. Here, we show a low level of electrical stimulation boosted causal excitation in connected neurons and strengthened the synaptic weight in a simulation study. We found that STES with motor training enhanced functional recovery after stroke in vivo. STES was shown to induce neural reconstruction, indicated by higher neurite expression in the stimulated regions and correlated changes in behavioral performance and neural spike firing pattern during the rehabilitation process. This will reduce the energy consumption of implantable devices and the side effects caused by stimulating unwanted brain regions.


Introduction
Stroke is a major brain injury that causes disabilities of body functions (e.g., movement, balance, swallowing) [1][2][3] . Clinically, functional recovery has been accomplished by exercise rehabilitation in the post-stroke phase and is caused by structural and functional remodeling that relies on plasticity perilesional cortex (PLC) or a remote area connected to the infarct area during the rehabilitation process [4][5][6][7] .
There have been various attempts to enhance plasticity for better functional rehabilitation using certain types of exercise 4,[8][9][10] . In addition to exercise rehabilitation, direct electrical stimulation to the brain has been used to mediate brain activity and enhance plasticity for stroke rehabilitation [11][12][13] . Direct electrical stimulation has been reported to promote activity-dependent neurotrophins, which enhance axonal and dendritic sprouting [14][15][16] . Micro-electrophysiology systems have provided a precise approach to target neural systems for stroke rehabilitation 17,18 . Here, the region damaged by stroke is functionally replaced by an electrical device that senses neural activities and stimulates a brain region to enhance the functional connection between two regions 17 . In addition, stimulation in timing sensitive manner affect the motor rehabilitation 19 . These precise neural recording-based approaches imply that the connection between two brain regions can be reconstructed after stroke and that Hebbian plasticity can be used to strengthen the functional connection. In previous studies, the focus was on scienti c reports of functional recovery by the addition of an electrical device. However, there has not been an engineering approach considering appropriate electrical stimulation power to enhance rehabilitation performance and to lower the system cost (i.e., energy consumption) and unexpected side effects. For the full implantation of an electrical treatment system, the energy consumption 20 and side effects must be considered in addition to the functional recovery.
In the current study, we aimed to promote functional recovery with less energy after stroke. We simulated engineering possibilities to reduce energy consumption. As an engineering target, spike timing-dependent plasticity (STDP), which is a major component of Hebbian plasticity, was utilized, and we achieved synaptic weight control with less energy. Using the knowledge acquired from the simulation study, we experimented with the engineering scenario in vivo and observed functional recovery with smaller electrical stimulation energy.

Subthreshold electrical stimulation for causal activation
In PLC after stroke, the population of gained and lost synapses is increased 21 for functional remapping.
Our engineering purpose was to promote the survival rate of newly made synaptic connections after stroke. While synaptic remapping was boosted with the gain and loss of synaptic connections 22 , we strengthened the synaptic weight to prevent synaptic connection loss. Based on this distinct mechanism of synaptic remapping after stroke (Fig. 1a), we studied the ability of STDP to control synaptic weight by manipulating synaptic activation. In STDP, the activation between pre-and postsynaptic neurons must be causal. To manipulate the synaptic weight using STDP, we proposed the application of subthreshold electrical stimulation (STES) of the population of postsynaptic neurons simultaneous to physical exercise to more strongly activate the population of presynaptic neurons (Fig. 1b). STES cannot make the membrane potential reach the action potential threshold. STES alone is a small bias. When there is additional potential from presynaptic neuron, the membrane potential reaches the action potential to re the neuron affected by STES. This process naturally makes causal activation between pre-and postsynaptic neurons. This causal activation is hypothesized to result in functional recovery based on the synaptic remapping process.
Using the two engineering points on the pre-and postsynaptic sides, we examined causal activation in silico (Fig. 1c). Since it is di cult to measure the quantitative weight change in synapse and the condition of pre-and postsynaptic neurons, we examined the initial idea of STES in computer simulation.
When stimulation was asynchronized, even though the presynaptic neuron red and caused an excitatory postsynaptic potential (EPSP), the postsynaptic neuron did not re an action potential. Since neither presynaptic input nor STES alone were able to initiate an action potential, the presynaptic neuron only red while the postsynaptic neuron was silent in the raster plot. On the other hand, when presynaptic input and STES occurred simultaneously, the overall membrane potential reached the action potential threshold, resulting in ring of the postsynaptic neuron. As a result, the raster plot shows that sequential causal activation resulted in postsynaptic ring following presynaptic ring. These asynchronous and synchronous cases are possible cases that can occur with STES.

Controlling synaptic weight by STES with less energy
We explored the changes in synaptic weight caused by engineering in pre-and postsynaptic neurons.
Synaptic weight is regulated by the STDP mechanism in the simulation since STDP is one of the major properties of Hebbian plasticity 23 . We utilized the STDP model proposed by Song et al. 23 (for details see the Methods section). The STDP mechanism senses the ring timing difference between pre-and postsynaptic neurons and updates the weight as Δw. If there is postsynaptic ring following presynaptic ring, Δw is positive, and the synaptic connection is strengthened. On the other hand, if postsynaptic ring leads to presynaptic ring, the synaptic weight degrades, and the synaptic connection is weakened.
To focus on synaptic weight change by pre-and postsynaptic excitation, we designed one presynaptic neuron connected to one postsynaptic neuron. A Poisson random process was applied for presynaptic neurons to re randomly following the mean spikes per second (i.e., λ in the Poisson process). For the postsynaptic neuron, electrical stimulation was applied from 0 (no stimulation) to 100% of the threshold level (i.e., the minimum electrical stimulation level needed to cause an action potential). As shown in Fig. 2a, electrical stimulation at levels other than 0% (i.e., no stimulation) increased the synaptic weight. Notably, although STES (i.e., 0% < stimulation level < 100%) increased the synaptic weight, STES alone did not result in postsynaptic neuron ring due to the lack of the synchronous occurrence of the action potential in the presynaptic neuron and the electrical stimulation in the postsynaptic neuron. Since the presynaptic neuron res randomly, the ratio of the causal activation depends on the mean spikes in the Poisson process. As the mean spike rate increased, the gradient of the change in the synaptic weight increased (Fig. 2b). At higher mean spike rates, the synaptic weight is more frequently increased, indicating that higher activation in the presynaptic side results in a stronger connection between neurons.
Since the presence of just one presynaptic connection to one postsynaptic neuron is not physiologically representative, we added one more presynaptic neuron to add synaptic competition [23][24][25] . The activities of the two presynaptic neurons followed the Poisson process with the same mean spike rate but were designed to have an independent random process. The mean synaptic weight was measured by averaging the two synaptic weights. The results in Fig. 2c show that the gradients of each electrical stimulation level were less differentiated than those shown in the simulation with one presynaptic neuron (Fig. 2a). The electrical stimulation of more than 30% of the threshold level showed small performance variance comparing to the other levels (i.e., 0% = stimulation level ≤ 20%) (Fig. 2c). The 30% of the threshold level performed near the best that 50% of the threshold level did. Note that 30 % of the threshold level took 60% current level of the best performed current level but only have 3.5% weight difference at 30s. The overall gradient was halved because synaptic competition. Interestingly, the nosimulation case (i.e., 0% of stimulation level) showed presence in synaptic weight change due to the accumulation of the synaptic input potentials from the two presynaptic neurons. We explored the parameters of stimulation amplitude level and mean spike rate to obtain the best combination (Fig. 2d). The overall pattern of the gradient of synaptic weight change shows that there was small performance variance with stimulation amplitudes over 30% having less than 5% performance difference to the best combination at 50% of stimulation amplitude and 60 of mean spike level, implying that we may be able to reduce the electrical power for functional recovery after stroke. A low level of electrical stimulation has distinct advantages of saving power consumption. For example, a 30% stimulation amplitude reduces the power consumption to 9%, potentially saving power for implantable devices by combining presynaptic excitation and STES on the postsynaptic side.

Combination of a motor task and STES for stroke rehabilitation
To validate the combination of presynaptic activation and STES on the postsynaptic side, we tested the engineering scenario described above the simulation in vivo. We combined a running task and micro electrical stimulation with STES to enhance the functional connection between the motor function and plasticity change in vivo. In order to induce presynaptic side activation, repeated rotarod running was performed; at the same time, STES was utilized to manipulate postsynaptic activity (Fig. 3a). This treatment process was performed twice a day with 30 trials per session beginning at poststroke day 3 or 4 and lasting for 16 days. The rotarod running task was chosen as the presynaptic activation stimulus to result in broad activation in the brain, and STES was performed in the right-hemispheric motor areas (M1). The performance of which during the preparatory period of a nger movement with the dominant right hand would be affected by stroke stress (Fig. S1a). The motor threshold (MT), which is the lowest injected current level necessary to force motor movement ( S2b shows that the multipolar stimulation with the vertical electrode formation resulted in a vertical current in cortex layer 5. Potential changes of approximately 100 and 30 mV were observed at 50 and 100 µm away from the STES location, respectively, in the simulation (Fig. S2d). This result suggests that the STES affects an area less than 100 µm from the stimulation site, which may minimize the stimulation of nontargeted brain areas.
Reversible ischemia (occlusion-reperfusion) was induced to make the transient middle cerebral artery occlusion (mCAO) model because middle cerebral artery failure is the most common type of ischemic stroke 28 . Then, we used four groups of trained rats with implanted electrodes: sham non-STES (STES(-)), sham STES(+), mCAO STES(-), and mCAO STES(+). To examine the details during the rehabilitation process, we performed certain analyses using a particular rehabilitation timeline (Fig. 3b). During the rehabilitation process following mCAO, behavioral and physiological analyses were simultaneously started at post-mCAO days 3 ~ 4. Rehabilitation with behavioral and physiological analyses continued until post-mCAO day 21. Baseline behavior and physiology levels were evaluated at phase N (before mCAO), and changes post mCAO were evaluated at phase R1 (less than 5 days after mCAO), R2 (6 to 10 days after mCAO), R3 (10 to 15 days after mCAO), and R4 (more than 15 days after mCAO).

STES with a motor task enhances motor function recovery
To address the effect of combining motor training with STES on motor function recovery, we evaluated the behavioral performance of mCAO rats performing motor running (i.e., rotarod running test). Rotarod running is regarded as the most sensitive and e cient method to detect motor impairment after brain injury [29][30][31] . For the behavioral performance analysis, the latency to fall from the rotarod was measured. Rats in the mCAO STES(+) condition exhibited signi cant improvement in their motor function compared to those in the mCAO STES(-) condition (P < 0.05 in the R2 ~ R3 session, P = 0.0128 in the R4 session), and the improvement was maintained throughout the rehabilitation process (Fig. 3d). Interestingly, rats in the sham STES condition did not show alterations or improvements in their behavioral performance compared to those in the sham STES(-) condition (Fig. 3c), suggesting that the effect of STES in mCAO rats is dependent on the mCAO environment. These data indicate that the enhanced motor performance resulting from STES plus motor training is accomplished by long-lasting M1 neuronal stimulation only under conditions of mCAO.

Functional recovery relies on dendritic connections
We con rmed whether the infarct size was affected by the STES. Examination of the brains after all experimental procedures were completed. We found that mCAO induced an extensive infarction throughout all ipsilateral brain regions, including the cerebral cortical and subcortical areas, but not in contralateral brain regions (Fig. 4a), con rming that mCAO induced brain damage. Importantly, mCAO STES(+) did not decrease the size of the infarction area in the ipsilateral brain regions, and there were no signi cant differences in the size of the infarction area between the mCAO STES(+) and mCAO STES(-) conditions (STES(-), 195.9 ± 17.43; STES(+), 204.1 ± 17.29 (mm 3 )) (Fig. 4b).
Previous studies have clearly shown that functional remapping is mainly accomplished by neural plasticity in the target region 32 . The neuron-speci c protein microtubule-associated protein 2 (MAP2) is the most widely used marker of dendritic regions of neurons. Thus, the immunohistological intensity of MAP2 was used to represent neural plasticity. To examine changes in plasticity under the conditions tested here, we monitored MAP2 expression in the target regions. mCAO clearly resulted in decreased MAP2 expression. Furthermore, STES signi cantly upregulated MAP2 expression in the target regions of the mCAO rats to levels similar to those observed in the sham STES condition (Fig. 4c, d). Taken together, these results suggest that STES failed to prevent total structural damage from the infarction in the brain after mCAO but did modulate the neural plasticity that may promote recovery of motor function.

Functional rebuilding by STES with a motor task
To address changes in neural plasticity by combining motor training and STES in the mCAO group, multiunit spike ring was recorded and analyzed during stroke and the rehabilitation process. As shown in Fig. 5a, multi-unit recording was performed at STES training to measure neural ring during running and standing, representing a trained and nontrained motor task, respectively. Note that the stimulation and recording were performed separately to avoid recording contamination by electrical stimulation artifacts.
The detected spikes in the raster plot show different tendencies during the stroke and rehabilitation processes (N ~ R4) (Fig. 5b). In each phase, there was an increase in spike population density during rehabilitation in the mCAO STES(+) rats, while the spike population in mCAO STES(-) rats was sparser than in mCAO STES(+) rats after R1.
For quantitative analysis of the changes in neural plasticity, the number of multi-unit spikes (NMS) was measured. The NMS represents the number of spikes red in the running state compared to that at baseline in the R1 phase when rehabilitation began (Fig. 5c), with the NMS at R1 set to 0. Both the mCAO STES(-) and mCAO STES(+) rats exhibited a decrease in the NMS between N and R1 in the running state ( Fig. 5c), suggesting that the neurons near the electrodes red less due to the loss of synaptic connections caused by mCAO. After mCAO, the neural activity continued to decrease in the mCAO STES(-), even after rehabilitation. In contrast, the mCAO STES(+)recovered neural ring after R1, showing an increase in NMS. This result shows that STES with rotarod running promoted neural activity after mCAO.
To compare the spike ring tendency between the trained motor task (running) and the untrained motor task (standing), the spike ring ratio between the standing and running state (RSR) was monitored. The RSR represents a ratio indicating a normalized NMS between the running and standing state (for technical details see the Methods section) (Fig. 5d). The RSR for both groups showed that the neural activity was focused on the trained motor task after R1 in the mCAO STES(+). Interestingly, there was a signi cant increase in RSR between R1 and R3 in the mCAO STES(+), suggesting that the population of synaptic connections related to the trained motor task survived more than the other functional connections, resulting in a ring pattern biased to the trained motor task. This functional rebuilding is highlighted in the correlation analysis between the behavioral test results and spike ring patterns. There was a highly correlated rehabilitation tendency between motor function recovery and neural plasticity change with a 0.99 normalized cross-correlation coe cient (the maximum is 1) between the behavioral test and spike ring rate change in the mCAO STES(+), comparted to a 0.77 normalized cross-correlation coe cient in the mCAO STES(-).

Discussion
Engineering plasticity for stroke rehabilitation Our engineering approach appeared to generate behaviorally relevant circuits through changes in neural plasticity. According to a previous study, sporadic diffuse reconnection may provide some level of longterm innate recovery from stroke except in directly damaged regions of the brain 4 . Speci cally, Hebbian plasticity plays a key role in making novel connections in undamaged brain regions especially in PLC 33,34 . Electrical stimulation has been reported to upregulate MAP2 expression in undamaged brain regions, implying that stimulation changes the neural plasticity during rehabilitation. Along with the histological observation, neural spike ring was also upregulated when STES was combined with motor training (Fig. 5c). Taken together, our results suggest that combining STES with motor training may lead to motor function recovery associated with changes in neural plasticity even without structural reconstruction in the infarct area.
In the rehabilitation process, brain stimulation can improve recovery from stroke by elaborating plasticity, in the form of gaining or losing synaptic connections 33 . This plasticity involves simultaneous pre-and postsynaptic activation related to the repeated training 21 . Because synaptic plasticity is dependent on the spike timing of pre-and postsynaptic neurons, the rehabilitation protocol must be designed to ensure that the postsynaptic neurons re immediately after the presynaptic neurons. To create speci c circumstances, we adopted a combination of two distinct and independent variables in our rehabilitation scheme. One was the existing concept of rehabilitation upregulating innate plasticity in undamaged brain regions within the critical period after stroke 21 . The other was adopting STES combined with motor training to upregulate and focus plasticity in an extrinsic manner. Importantly, the repeated motor training and STES were applied simultaneously. The STES simulation study suggested that the low stimulation level (30% of the MT) caused more bias in the trained motor task, increasing the background potential around the electrodes, potentially resulting in causal excitation between presynaptic neurons that are afferent neurons to the M1 cortex and neurons in the M1 cortex. Using STDP, our engineering approach provides an environment encouraging the strengthening of synaptic connections rather than the loss of connections. Therefore, functional recovery was accomplished by increasing the survival of neural connections during dendritic remapping after stroke.
Our physiological results from the multi-unit spike ring analysis suggest that connections between brain regions may be strengthened by STES with motor training early in rehabilitation (R1 ~ R2), together with a dramatic improvement in behavioral performance in this period. During this early critical rehabilitation stage, a certain range of circuits related to the trained motor task may be increased and enhanced. After R2, there was no signi cant increase in the number of spikes; similarly, the enhancement in behavioral performance also stalled. Because the nervous system has a certain range of recovery capacities to change the properties of its circuits [35][36][37] , this constraint of plasticity may be a physiological limitation. The most interesting part of our rehabilitation process was R2 ~ R3, immediately following R1 ~ R2. Although the R2 ~ R4 period showed a similar tendency in the behavioral performance and spike ring results, the tendency for the spike signal to be focused toward motor training constantly increased during this speci c period of the rehabilitation process (R2 ~ R3), indicating that a certain range of circuits related to the trained motor task was speci cally reinforced during the late critical rehabilitation stage.

Reducing power consumption and side effects
As implanted electronic systems require durable systems in a small package 20 , battery size is an important matter for system design. Compared to sensing and monitoring devices, electrical stimulation devices consume a relatively large amount of power, and the effort is limited by the development of a low-impedance electrode 38,39 . In the current study, performing STES based on the STDP mechanism provided the capability of reducing the energy consumption for electrical stimulation to achieve functional recovery. Even with just 9% ((30% stimulation amplitude) 2 ž impedance) of the stimulation power necessary to result in neural excitation, our engineering approach achieved functional recovery after stroke. This concept enables engineering approaches to reduce power consumption in electrical stimulation, not only improving electrode manufacturing techniques but also informing future systematic approaches to physiological engineering.
Although direct electrical stimulation has the bene t of manipulating neural activation and promoting functional recovery after stroke, the technique is limited by the production of undesired stimulation effects (e.g., motor and speech problems) 40,41 . The side effects are mainly caused by the stimulation of a large population of cells, including unwanted neurons around the stimulation site. In order to reduce the side effects, optogenetic stimulation has been applied in animal experiments. However, optogenetic tools cannot be the solution in clinical application because their use in the clinic is prohibited 42 . STES may be an alternative solution to avoid side effects. As the amplitude of the electrical stimulation decreases, the size of the affected area shrinks exponentially, reducing the exposure of untargeted brain regions to electrical stimulation. Therefore, STES provides the advantage of reducing power consumption as well as avoiding side effects.

Neuron and STDP model
In order to examine the effects of STDP, a simple neuron model was adopted for simulation. A neuron was modeled with two compartments, cell body and dendrite. The dendrite part contained an embedded passive channel for current leaking with a conductance of 0.001 S/cm 2 and a reversal potential of 65 mV.
For the cell body, the Hodgkin-Huxley mechanism was included to simulate the active process of neurons.
Sodium, potassium and leak conductance were set at 0.12 S/cm 2 , 0.036 S/cm 2 , and 0.0003 S/cm 2 , respectively, and a reversal potential of -54.3 mV was applied. The neurons were isolated so as not to be affected by the electrical propagation from the other. One synapse was built to monitor the synaptic modi cation caused by STDP between the two neurons. The basal activity of neurons was modeled by a Poisson random process, and in the presynaptic neuron, event-related activation was added following a Poisson random process with λ.
For the STDP model in the current study, the STDP model proposed by Song et al. 23 was employed. The model provides a symmetric and asymmetric form of STDP and updates the synaptic weight as follows: where w max is the maximum weight, A + and A − are the step size for weight increase and decrease, respectively, t pre and t post are the spike timing in the pre-and postsynaptic neuron, and τ + and τ − are the time constant, respectively. In the current study, A − τ − /A + τ + = 1.06 as in Song et al. 23 .
The simulation was performed by the NEURON simulator (version: 7.5) under a python environment (version: 2.7). Current was utilized as the source type of the electrical stimulation. Electrical stimulation directly injected current into the cell body membrane and modulated the membrane potential. The level of the current amplitude, stimulation timing and time duration were controlled.

Experimental cerebral ischemic stroke
We induced reversible ischemia (occlusion-reperfusion) to make the mCAO model. Brie y, 30 animals were randomly divided into experimental (n = 16 [electrical stimulation: 8; electrical nonstimulation: 8]) or sham (n = 14 [electrical stimulation: 8; electrical nonstimulation: 6]) groups. Under anesthesia by iso urane inhalation in medical-grade oxygen, their sternocleidomastoid muscle was dissected, and the right common carotid artery (CCA), external carotid artery (ECA), and internal carotid artery (ICA) were exposed. The arteries were separated from the surrounding nerves and connective tissue. The ECA was coagulated for 2 hours using lament insertion. At the end of the ischemic period, the animals were reanesthetized, and the lament was gently retracted to allow reperfusion of the ischemic region.
Quanti cation of the stroke volume The Animal Care and Use Committee of the Daegu Gyeongbuk Institute of Science and Technology (DGIST) approved all animal protocols. Also, this study was carried out in compliance with the ARRIVE guidelines. After all rehabilitation procedures, the rats were euthanized under anesthesia after reperfusion, and the brains were rapidly removed. Coronal sections were cut into 2-mm-thick slices and stained with standard 2% TTC for 20 min at 37°C 30,43 . The pale-appearing infarcted areas and the uninfarcted areas were digitally analyzed using the NIH ImageJ software. The area of infarction from each slide was summed and presented as a percentage of the volume of the uninfarcted hemisphere.

Behavioral motor testing
All animals were housed in individual cages. Before induction of ischemia, all animals received training in the rotarod test (20 rpm) for 14 days. The rotarod test was used to examine balance and coordination [44][45][46] . The rotating drum was accelerated from 0 to 50 rpm over 3 min, and the latency in seconds for the animals to fall off the drum was recorded. Each session included three consecutive trials with a maximum time of 600 s, and the mean fall latency was calculated from three trials.

Histology and immunohistochemistry
Animals were anesthetized by intraperitoneal injection of 65 mg/kg ketamine with 5 mg/kg xylazine. The rats were then transcardially perfused with prechilled phosphate-buffered saline (PBS, pH 7.6) 47 . The heads were removed, skinned, and post xed overnight in 4% paraformaldehyde in PBS at 4°C 48 . The mandibles were discarded, and the trimmed heads were skinned and xed by immersion in the same xative for 1 week at 4°C. The heads were decalci ed in 10% EDTA (pH 7.0) for 1 week at 4°C. After decalci cation, the specimens were washed, dehydrated in increasing concentrations of ethanol, and transferred into xylene for tissue clearing. The specimens were in ltrated with Paraplast and embedded.
Frontal sections (coronal, 6 µm) were cut serially from the tip of the nose to the posterior extension of the cortex layer, and each section was preserved on MAS-coated slides (Matsunami Glass, Japan).

Electrode implantation and electrical stimulation
A single shank electrode (A1x16-3mm-100-703, NeuroNexus) was placed at the primary motor cortex (M1, AP = + 1 mm, ML = + 2 mm, DV= -2 mm) on the gray matter in the brain, and the reference electrode was located on the skull. The implanted electrode had a sixteen-channel vector array with a 1.5-mm-long recording area for which the recording sites were evenly distributed. A repeated pattern of [E, G] was applied to the electrode, for which E is the electrical stimulation site (active site) and G is the ground site. A biphasic pulse with 50 Hz of stimulation frequency and 30% of the MT was applied. The anodic duration and cathodic duration were 200 µs, and the gap between them was 40 µs.

Spike detection and sorting
Intracortical recording was performed with the Tucker-Davis Technologies (TDT) neurophysiology system (RZ2, TDT) with a 24-kHz sampling frequency using the implanted 16-channel single shank electrode. The signals were ltered by a high pass lter at 800-3000 Hz. After ltering, threshold-based spike detection was performed by taking the spikes above the threshold. The threshold was set by calculating four times the standard deviation of the signal recorded for all the recording days as 1 where is the recorded data at channel on day with the data point , and μ is the mean calculated as 2 Note that the threshold is determined by long-term (i.e., D days) measurement data instead of one-day measurement data.
Spike sorting was performed after spike detection. Three principal components were used for the features, and K-means clustering with k = 9 sorted the spikes. The spike ring time was measured for each sorted spike and marked as a dot in the raster plot in Fig. 5b.
The NMS, RSR, and normalized cross correlation The number of spikes detected in the running and standing state at phases N ~ R4 was counted. The NMS was calculated by counting the spikes in each phase and then subtracting the number of spikes where is the expectation operator, and is the counted spike ring at the days in the phase in the state .
The RSR was calculated to evaluate whether the spike ring pattern was biased to the running or standing state. The number of daily ring spikes in the running and standing state was normalized by dividing the total number of spikes in each day. Because the running state was recorded two times longer than the standing state, in the normalization, the spike number was multiplied by different weights (i.e., 1 for the running state and 2 for the standing state). Then, the normalized spike ring was compared, and the baseline (i.e., normalized spike ring at R1) was subtracted as 4 The mean of the NMS and the behavior motor test result were compared by normalized cross correlation. The data range in both graphs was rescaled (i.e., min = 0 and max = 1). Then, the normalized cross-correlation coe cient was calculated as 5 where and are the rescaled NMS and behavioral motor test results, respectively, and σ is the standard deviation.
Electromagnetic (EM) simulation with a rat phantom EM simulation was performed with the Sim4life (ver. 2.2, SPEAG) software platform. The 3D electrode model was implanted into the brain of a small male rat phantom model (198 g, Sprague Dawley) (Fig.   S1a). The EM low frequency solver (EM LF) was used to estimate the physics of the EM propagation with Maxwell's equation. The vector of the electric eld and the electrical potential were estimated with a quasi-static approximation.

Statistical analysis
All data are presented as the mean (±) SEM. One-way ANOVA followed by Dunnett's post hoc test was used, and the criterion for statistical signi cance was set at P < 0.05.