Stability of Recorded Neural Ensembles
Two macaque monkeys were first trained to manually perform delayed center-out reaching movements using a robotic exoskeleton that limited movements to the horizontal plane (i.e., manual control, MC). This commercially available robotic system allows precise and accurate measurement of kinematic parameters 
. Following implantation of microelectrode arrays in bilateral primary motor cortex (M1) (128 microelectrodes in each of the two monkeys), each animal was trained to perform the same center-out task in brain control (BC), in which the neural activity directly controlled the position of the cursor (). In each animal, we could record approximately 75–100 well-isolated units during each daily session. However, consistent with reports in the literature 
, several months postimplantation, a small ensemble of units were found to be extremely stable across a period of days to weeks. Past studies have demonstrated that ensembles of a similar size can be successfully used for two- or three-dimensional control of neuroprosthetic devices 
Experimental setup and stability of ensemble recordings.
In the specific experiments presented here, we ensured that the ensemble of neurons used for BC were stable over the time frame of the experiment (hereafter referred to as a “stable neural ensemble”). Stability of well-isolated units across days was first assessed by the stationarity and quality of waveforms (). In order to also quantify the stability of waveforms, we compared waveform characteristics across multiple days using principal components analysis (see Figure S1
). Recent studies have indicated that this is a valid metric of waveform stability across days 
. As an additional measure, we also ensured that the firing statistics (i.e., interspike interval [ISI] distribution) of each putatively stable single unit did not significantly change from day to day 
. shows three representative ISI distributions for three single units for two separate days. There were no significant changes in the distributions (p
>0.05, Kolmogrov-Smirnov Test). Finally, as a measure of ensemble stability across time, we periodically measured the directional tuning of each unit during daily MC sessions. As shown in Figure S2
, the ensemble tuning properties were also stable across time.
Brain Control Performance with Stable Ensembles
In this study, we were primarily interested in understanding the long-term neural adaptations to a fixed transform of neural activity into cursor movements (i.e., a fixed decoder across days). As in previous closed-loop BMI studies 
, we used a linear decoder optimized for physical movements of the upper limb. The linear decoder 
remains a straightforward and transparent method to transform neural activity into a control signal for closed-loop BMI experiments. As shown in , while the animal physically performed center-out movements during MC, the recorded M1 spike activity was regressed against the elbow and shoulder angular positions to generate correlations for each variable. We will use the term decoder
to refer to the combined transforms for both shoulder and elbow position. In BC mode (), this decoder allowed neural activity to control the computer cursor. For the initial set of experiments, BC performance was measured in the setting of (1) recordings from a stable ensemble of primary motor cortex (M1) neurons over days, and( 2) a linear decoder that was held constant after training during the MC session on day 1 (hereafter referred to as “fixed decoder”).
quantifies the daily performance of the center-out task in BC for two animals with a fixed decoder. Previous studies have used a variety of tasks to study BC. Because these tasks range from discrete to continuous control, it is difficult to directly compare task performance across studies 
. In this study, the cursor was under constant neural control, and the subject was required to perform multiple steps for a correct trial (including initiation by movement to the center followed by a brief hold period). Previous studies suggest that such continuous-control, multistep tasks are significantly more difficult than single-step tasks 
. Accordingly, longer periods of practice were initially required to learn this multistep task in BC. For the experiments from Monkey “P” and “R” shown in , ensembles of 15 units and ten units were used, respectively. For both subjects, with daily practice with a fixed decoder, there was a monotonic increase in BC performance and accuracy ().
Brain control performance with practice.
As also evident in , there was a similar monotonic decrease in the mean time to reach targets. Whereas the initial cursor trajectories meandered, they became more direct with practice (, comparison of representative trajectories from day 3 and day 13 for Monkey P). It is important to note that the subjects were not required to follow a straight path from the center to each target. Interestingly, the mean trajectory to each target became increasingly stereotyped over time, suggesting that a relatively stable solution emerged for the path to each target. We quantified the similarity between each set of daily mean trajectories by performing pairwise correlations (see Materials and Methods
). As illustrated by the color map in , the correlation between the mean paths for each day initially increased and then stabilized. Similar results were obtained for Monkey R (see Figure S3
Daily Rapid Recall of Performance
We conducted a detailed examination of the performance during each daily session to identify whether BC “skill” could be transferred from one day to the next with practice under these conditions. Past studies have typically presented performance characteristics for an entire session 
. As evident in , with practice, subjects could attain accurate performance at the very start of each daily session. Closer examination of the first 5 min of performance each day produced striking evidence of this accuracy at the start of a session (). As expected, there was also a marked reduction in the variability of performance each day under these conditions. Identical levels of performance were also evident in a second animal (Monkey R). Thus, with daily practice in the setting of a stable neural ensemble and a fixed decoder, subjects developed a level of BC skill that could be readily recalled at the start of a session.
Dynamics of Changes in Ensemble Tuning Properties with Practice
We subsequently characterized the changes in M1 neural activity accompanying the sustained improvements in task performance. For the 19-d experiment shown in , a stable level of performance was evident after day 8. We first examined the neuron-behavior relationship during that period (i.e., days 9 through 19) by calculating the directional modulation of neural activity during BC 
. The directional modulation of neural activity was initially measured with respect to the intended target. Interestingly, we found that a remarkably stable neuron-behavior relationship was associated with proficient task performance. illustrate the directional modulation of two representative single units during a single BC session. The insets in illustrate the stability of this directional tuning relationship for BC across a period of 10 d (no significant changes in preferred direction [PD], bootstrap method, false detection rate [FDR] corrected for multiple comparisons). Overall, 14 of the 15 units did not experience a significant change in PD (bootstrap method, FDR corrected for multiple comparisons). We also evaluated whether this was evident at the level of the neural ensemble. As illustrated by the series of color maps in , we again calculated the daily directional tuning relationship for all units within the ensemble during BC. To compare each daily “ensemble map,” we performed pairwise correlations among each daily set of ensemble tuning properties 
. The similarity among daily ensemble maps initially increased and then stabilized ().
Stable task performance is associated with stabilization of ensemble tuning properties.
To compare the temporal course of skill acquisition with the process of map stabilization, we calculated a measure of map similarity across days. Thus, for each day, we calculated the mean correlation for comparisons between a given daily map and all other maps (i.e., mean of each column in the right panel of with exclusion of comparison to self). Remarkably, changes in map similarity closely tracked improvements in task performance for both animals (). Thus, stable task performance was strongly associated with the consolidation of an ensemble activation pattern (a “prosthetic motor map”).
We next examined in greater detail the temporal windows during “movement execution.” For instance, cursor control from the center to each target likely has an initial feedforward stage followed by a period in which visual feedback can lead to path corrections. We thus tested whether a similar stable map emerged when only taking into account the initial stages of execution. As shown in (dotted lines), a similar process of map stabilization also occurred for the first 200 ms of neural activity.
We also performed an additional set of analyses to exclude a potential confounder. As evident in , there was considerable variability in the path taken from the center to each of the targets. It is possible that the apparent evolution of ensemble tuning properties reflects changes in the path as opposed to changes in intrinsic neuronal properties. We thus took into account moment-to-moment changes in the cursor trajectories (i.e., 100-ms steps, see Materials and Methods
) when calculating the directional modulation of neural activity (). Unlike the previous analysis based on the intended target, this measure accounts for changes in tuning solely resulting from a modified cursor path. This analysis revealed that the tuning properties of neurons evolved during the period of learning independent of any changes in the actual cursor path.
Long-Term Changes in the Mean Firing Rate and the Depth of Modulation
The analysis described above focused on changes in preferred direction during learning and long-term use of a neuroprosthetic device. However, past studies have also indicated that other changes in neural properties can also be present 
. We thus examined the daily changes in the mean firing rate and the depth of modulation of the neural tuning curves. We first compared the mean changes in firing with practice. For Monkey P, eight of 15 units were found to experience long-term changes in the mean firing rate with practice (p
-test comparing days 1–5 with days 15–19, FDR correction for multiple comparisons). Of the eight neurons, seven experienced a net increase, and one demonstrated a slight but significant increase. For Monkey R, six of the ten neurons experienced a significant increase in the mean firing rate with time.
We next evaluated for systematic changes in the depth of modulation associated with long-term neuroprosthetic use. illustrate representative examples of units with a persistent increase in the depth of modulation (p<0.05. t-test, FDR correction for multiple comparisons). For Monkeys P and R, respectively, seven of 15 and five of ten units demonstrated similar persistent increases in the depth of modulation. The remaining units did not experience significant changes in the depth of modulation. Taken together, these results further highlight the long-term stability of changes in neural properties that tracked improvements in task performance for both animals.
Stable long-term changes in the depth of modulation.
Importance of the Ensemble Map for Brain Control
Our results thus far suggest that a stable pattern of neural activity is associated with stable BC performance. We next examined whether the entire ensemble is actually involved in BC. For instance, it is possible that only a small fraction of neurons are actually being used for closed-loop BC. We thus generated an “online” neuron dropping curve to quantify the effects of ensemble size on BC performance. After a session in which BC performance was demonstrably accurate (>95% accuracy), a random number of neurons were excluded during subsequent closed-loop BC. Each of these sessions lasted 10 min. We subsequently confirmed that the level of performance returned to the previous baseline. These experiments were performed for both the ten- and the 15-neuron ensembles. As shown in , removal of three neurons (i.e., 20% vs. 30% of neurons, depending on the ensemble size) resulted in a greater than 50% drop in accuracy. Moreover, for correct trials under such conditions, it took significantly longer to reach each target (mean time to target of 2.5 s vs. 5.3 s, p<0.05, t-test). These results indicate that once a neural representation for neuroprosthetic control is consolidated, the entire ensemble map appears to be actively involved in BC.
Dependence of BC performance on size of the neural ensemble.
Stable Ensemble Map Formation with a Shuffled Decoder
Our results suggest that an ensemble of motor cortex neurons can settle upon a remarkably stable activation pattern for prosthetic control in response to a constant decoder. We tested the limits of this conclusion by evaluating whether ensembles of neurons can learn an arbitrary, fixed transform. We thus applied a “shuffled” version of a decoder trained during a MC session. In comparison to the reliable predictions of the actual decoder shown in , the “shuffled decoder” could not reliably predict limb position across time as expected (new ensemble in Monkey P, n
41 neurons). Surprisingly, accurate prosthetic control was achieved after several days of BC practice in the presence of the shuffled decoder (days 3–8: correct trials
94±1%, mean±standard deviation [SD]; mean time to target
2.5±0.3 s, mean±SD). Moreover, a stable prosthetic motor map also emerged under these conditions (). In addition to suggesting that a decoder unrelated to arm movements (i.e., a nonbiomimetic decoder) can be learned, this experiment further supports the notion that a stable decoder is crucial for the formation of a stable cortical representation for prosthetic control.
Map stabilization with a shuffled decoder.
Specificity of Neural Adaptations
We subsequently tested the specificity of neural adaptations to the initial fixed decoder. Although many options are available to perturb the transform of neural activity to cursor movements 
, we chose to retrain the linear decoder prior to select BC sessions. The linear decoder was created using multivariate linear regression techniques 
. It is well known that multivariate linear regression can result in variable model parameters when multiple colinearity is present in the dataset 
. Thus, two models can be equally effective in predicting a parameter but have different model structures. For prediction of movement parameters from neural data, this can result in slightly different decoder structures (i.e., weight given to each neuron) even while the overall movement prediction is stable 
. Such variability in the weights can occur for sequential datasets from the same recording session 
. As shown in (upper panel), similar findings were also evident when two decoders were trained on different days. We thus used daily retraining of the decoder as a means to perturb the transform of neural activity to cursor movements.
Specificity of neural adaptations to the decoder.
Interestingly, substitution of the learned decoder (DecoderOLD in , black bar in upper panel) with a newly trained decoder (DecoderNEW, green bar) caused a drop in BC performance. However, the animal could rapidly resume accurate BC upon reinstatement of the well-learned decoder. A significant drop in overall performance was evident for multiple experiments conducted on different days for both animals (). These results suggest that small but significant changes in the model weights are sufficient to prevent an established cortical map from being transformed into a reliable control signal.
We subsequently tested whether a stable prosthetic motor map can emerge in the presence of variability in the decoder. For example, the brain may settle upon a solution that takes into account the inherent variability of the neuron–cursor relationship. We again specifically made use of the variability in the model parameters present with retraining the decoder each day. Under such conditions, more variable daily performance was observed, likely the result of having to relearn the relationship for cursor control each day (see Figure S4A
). Moreover, there was no similar trend of cortical map stabilization within the timeframe of the experiment (see Figure S4B
). Thus, variability in the decoder impedes the emergence of a stable cortical map for prosthetic control.
Coexistence of Two Ensemble Maps
The results presented above further indicate that the formation of a stable and readily recalled prosthetic map is closely associated with stable task performance. Once stabilized, is a specific prosthetic motor map resistant to interference from learning a second map? To address this question, we examined whether an animal could simultaneously learn and recall cursor control for two distinct biomimetic decoders using the same set of neurons. As shown by our results, a retrained decoder can prevent accurate transformation of neural activity (). We thus allowed a subject to practice BC each day using both a “new” biomimetic decoder and a well-consolidated (“old”) biomimetic decoder (). The new decoder was trained during a MC session on day 1. In comparison to the old decoder, there were significant changes in four of the 15 weights (p<0.05. t-test, FDR correction for multiple comparisons) for the elbow decoder, and seven of the 15 weights for the shoulder decoder (p<0.05. t-test, FDR correction for multiple comparisons).
Simultaneous retention of two maps without interference.
As expected, introduction of the newly trained decoder reduced task performance (, day 1). Reintroduction of the consolidated decoder, however, rapidly restored BC performance. Over the course of several days, the subject demonstrated skilled performance with each of the two decoders (day 4, 97.5% vs. 99% trials correct, mean time to target of 2.3 vs. 2.4 s). Surprisingly, the prosthetic motor map was distinct for each of the two decoders. shows examples of changes in directional tuning during BC under each condition (insets i and iii). Nine of 15 units exhibited significant changes in directional tuning (bootstrap, p
<0.05, FDR corrected). Moreover, although the previously consolidated map remained stable (n
6 comparisons, R
0.86±0.03, mean±SD), the new prosthetic motor map was less similar to previous maps (n
As suggested previously, these changes in directional tuning could be the result of a change in the cursor path. As the subjects were not required to reach the targets with a straight path, there was some variation between the cursor paths for trials under each of the two decoders (See Figure S5
). We next tested whether changes in the path could account for the observed change in directional tuning. We again computed the directional modulation of neural activity with respect to the actual cursor path during the first 200 ms (as opposed to direction of intended movement to a given target). Using this measurement, the calculated PDs were somewhat different for each neuron (compare tuning curves in with those in Figure S6
). This likely reflects the difference between the actual curved paths taken in comparison to an idealized straight path (i.e., directional modulation based on the intended direction). As such, there was a systematic shift in the respective PDs for each neuron (e.g., vs. Figure S6
: [i] PDnew decoder
29° vs. 96°; [ii] PDnew decoder
352° vs. 74°). Most importantly, even after taking into account the variations in the actual path of the cursor, significant changes in neural tuning were evident during BC with each of the two decoders (see Figure S6