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Introduction

Brain Machine Interfaces (BMIs) hold promise for restoring motor functions in severely paralyzed patients [1]–[7]. State of the art BMIs take advantage of recent advances in electrophysiological techniques and neural decoding algorithms. Multi-electrode arrays facilitate simultaneous recordings from hundreds of neurons in multiple cortical areas. Movement related signals that modulate the activity of these neurons are extracted using neural decoding techniques and employed to control an external actuator. The BMI neural decoder includes free parameters that in typical BMI experiments with monkeys are determined from neural recordings during a training session with reaching movements. However, the requirement to produce similar movements through the BMI introduces a novel motor context, which may in turn affect the cortical modulations that drive the BMI.

During planning and execution of reaching movements, the modulations in the firing rate of cortical motor neurons reflect multiple motor, sensory, and cognitive variables [8]–[12]. Neural modulations that represent the direction and speed of the movement have been extensively studied during stereotypical reaching movements, and described computationally using tuning curves [13]–[16]. Recent BMI experiments indicate that neural tuning to movement direction [6] or velocity [7], [17] may change following BMI operation. However, changes in neuronal modulations beyond those related to movement kinematics have not been investigated.

The operation of a BMI presents a novel motor context in which the external actuator is controlled based on the predictions generated from a limited subset of neurons. During initial BMI operation, the movement of the actuator may deviate from the intended movement, and result in errors, as evident from the degradation in behavioral performance [7]. Here we addressed the effect of operating in this novel motor context on the nature of neuronal modulations in the motor cortex. Our spike-train analyses show that initial BMI operation was associated with increasing neuronal modulations, which were not merely associated with movement kinematics.

Firing-rate modulations are masked by neural noise, which hampers their unambiguous estimation form recorded spike-trains [18]. Averaging techniques that are applied to reduce the neural noise also diminish the effect of rate-modulating signals. Current rate-estimation methods focus on firing-rate modulations that are correlated with specific modulating signals, like the direction and speed of the movement. Such methods rely on identifying the relevant modulating signals and ignore potential contributions by other signals [19]. Instead of estimating the firing-rate, we focus in this paper on quantifying its variance, i.e., the variance of the neural activity that is associated with overall rate-modulations. This provided a scale for assessing the variance associated with specific modulating signals, which were estimated using linear regression. Using these tools we demonstrate that the variance associated with neuronal rate-modulations increased during initial BMI operation without a matching increase in the variance explained by the movement kinematics. Furthermore, the variance associated with neuronal modulations decreased with subsequent BMI training sessions. Possible hypothesis regarding the nature of these enhanced modulations are discussed to motivate further research.

Methods

Behavioral task and brain-machine interface operations

The BMI experiments were performed in two adult female monkeys (Macaca mulatta) and consisted of 10 BMI sessions for the first monkey and 23 for the second. The experiments are described in detail in [7] and briefly described here. Neural activity was recorded from N_n = 100−300 neurons in multiple cortical areas including the primary motor cortex (M1), dorsal premotor cortex (PMd), supplementary motor area (SMA), and primary somatorsensory cortex (S1) in one monkey and medial intraparietal (MIP) of the posterior parietal cortex (PP) in the second monkey.

Each experimental session started with a training session in which the monkey controlled the position of a cursor on a computer screen by moving a hand-held pole (pole control), with the task of acquiring a randomly placed visual target within 5 sec to obtain a juice reward. A linear filter was trained to predict the velocity of the movement from the binned spike-counts of the recorded neurons. After training, the filter generated real-time predictions of the velocity, which were reproduced by the cursor and/or a robotic arm (brain control). The monkeys continued to move the pole after brain control started (brain control with hand movements, BCWH), but later assumed a stationary arm posture after the pole was taken away (brain control without hand movements, BCWOH). Lack of muscle activity during BCWOH was demonstrated by EMG measurement from wrist flexors, extensors and biceps. Performance accuracy diminished after the transition from pole- to brain-control, and after the monkeys stopped moving their arms. However, the BMI task performance improved with further training in all the control modes, clearly indicating that motor learning was involved.

Percent Overall Modulation (POM)

Spike-trains can be considered as realizations of point processes [20], [21]. The number of spikes recorded in a bin of size b, N_b, depends on the average bin-rate in that bin Λ_b, which is modulated by the encoded signals, as depicted in Figure 1 (upper diagram). However this dependence is stochastic and the variance of the spike-count Var[N_b] may differ from the variance of the bin-rate Var[Λ_b]. While the variance of the spike-count can be measured directly, it is the variance of the bin-rate that is of interest here because it reflects signal modulations. In order to investigate these modulations, we defined the percent overall modulation (POM) as:
(1)
Since the variance of the bin-rate cannot be measured directly, the POM cannot be estimated without further assumptions. However, instead of restricting the analysis to firing-rate modulations that involve specific modulating signals, we made only basic assumptions about the nature of the spikes trains. In particular, we assumed that the spike trains are realizations of inhomogeneous Poisson processes, which are the simplest point processes that can describe rate modulations. We further generalized the analysis to additive noise models whose variance is proportional to the mean.

Figure 1. Inhomogeneous Poisson process and implied variance distribution.

doi:10.1371/journal.pone.0000619.g001

The simplest point process, the homogenous Poisson process, is characterized by a constant rate and thus is inadequate for describing task-related firing rate modulations. Despite their constant rates, homogeneous Poisson processes generate spike trains with highly variable spike-counts, whose variance equals the mean, i.e., Var[N_b] = E[N_b]. Taking the homogeneous Poisson process as a model of neural activity with no modulations, we conclude that the resulting variance, which equals the mean rate, is attributed to the neural noise.

The inhomogeneous Poisson process, which is characterized by time-varying rate that is independent of the history of the spike train, is the simplest point process that can describe firing rate modulations [20], [21], [22]. For inhomogeneous Poisson processes, the variance of the spike-count Var[N_b] is related to the variance of the bin-rate Var[Λ_b] according to Var[N_b] = Var[Λ_b]+E[N_b] [20]. This relationship can be interpreted as a decomposition of the total variance in the binned spike-count into the variance of the underlying information bearing parameter, or bin-rate Var[Λ_b], and the variance that would have occurred if N_b was generated by a homogenous Poisson process, E[N_b], i.e., the neural noise (Figure 1). Thus, the variance of the modulated bin-rate is the excess variance of the binned spike-count beyond the level expected from a homogeneous Poisson process. The resulting POM can be evaluated from the statistics of the binned spike-count as (Figure 1):
(2)
where is the Fano factor [23], [22]. Given spike-trains of finite duration, we estimated the POM using the sample-mean and sample-variance of the binned spike-counts, instead of the mean and variance, respectively.

The POM analysis can be extended to cases where the binned spike-count include signal-dependent zero-mean noise, i.e., N_b = Λ_b+e [24]. The probability distribution of the noise e is assumed to be conditionally normal with signal dependent variance: f(e|Λ_b)~N(0,γ²Λ_b). Note that this model converges to the inhomogeneous Poisson process for large rates and γ = 1. Since for any signal level the error is zero mean, the variance of the spike counts is given by: Var[N_b] = Var[Λ_b]+γ²E[N_b], as shown in the Supplemental text (Text S1). The resulting POM can be evaluated as:
(3)
where POM(1) is the POM of an inhomogeneous Poisson process (γ = 1) as defined in Equation (2). Thus, the results and conclusions based on the POM defined in Equation (2) can be easily extended for the general case of additive signal-dependent noise. In particular: , so increasing/decreasing trends in estimated POM based on Equation (2) reflect increasing/decreasing trends in POM(γ).

Significantly Modulated Neurons

The POM of spike-trains that are evoked by homogeneous Poisson processes is zero. However, when estimated from finite spike-trains, the sample-POM is randomly distributed and may take non-zero, either positive or negative, values. Under the homogeneous Poisson process assumption, the distribution of the sample-POM, estimated from a finite sample of n bins, is asymptotically normal with zero mean and variance of 2/n. We defined neurons as significantly modulated if their estimated POM indicated that the homogeneous Poisson process hypothesis could be rejected at 95% confidence level for at least one control mode (pole, BCWH, or BCWOH). For a typical sample of 12000 bins (20 minutes of an experiment with 100 msec bins), the standard deviation of the sample- POM is 1.3%. Note that neurons that are significantly modulated in only one or two control modes may exhibit zero of even negative sample-POM in the other mode(s) due to the limited length of the analyzed spike-train.

Percent Velocity Modulation (PVM)

Velocity tuning is often determined in center-out reaching experiments, where the direction of movement is approximately constant [13], [16]. For general arm movements, this method was generalized to characterize the tuning of the neural activity to the velocity at a specific time lag [17]:
(4)
where k is the index of the current time-bin, N(k) is the spike counts (in bins of 100msec), V_x and V_y are the x- and y-components of the velocity, is the speed, l is the relative lag (positive/negative l corresponds to rate-modulations preceding/ succeeding the velocity measurement, respectively), a_x(l), a_y(l) and a_s(l) are the tuning parameters, a_c(l) is a bias parameter, and ε(k, l) is the residual error. The coefficient of determination of the single-lag regression R²(l) quantifies the fraction of the variance in the neural spike-count that is attributed to, or explained by, the velocity at lag l. However, since the velocity values at different lags are correlated, the lag-by-lag analysis cannot be used to determine the fraction of the variance that is attributed to the spatio-temporal velocity profile. Hence, we further generalized the analysis to account for the tuning of the neural activity to the spatio-temporal velocity profile in the surrounding window according to:
(5)
where ε(k) is the residual error, and L₁ and L₂ are the number of preceding and succeeding lags in the velocity profile, respectively. We used L₁ = L₂ = L = 9 to include a 1900-ms window around the current bin. The regression in Equation (5) was evaluated using truncated Singular Value Decomposition to stabilize the solution despite the large condition number of the spatio-temporal velocity matrix (around 10⁶) [25], [26]. Truncation was performed at the singular value that preserved 95% of the variance in the velocity measurements.

The coefficient of determination of the spatio-temporal regression of Equation (5), R², describes the fraction of the variance in the binned spike-count that is linearly related to variations in the spatio-temporal velocity profile in the surrounding window. Expressed as a percentage, R² is referred to as the percent velocity-related modulation, or PVM.

Percent Kinematics Modulation (PKM)

The above analysis was further extended to include other kinematics variables that may modulate the neural activity, including the position and magnitude of acceleration:
(6)
Where P_x and P_y are the x- and y-components of the position, and is the magnitude of the acceleration vector whose x-component is given by A_x(l) = V_x(l)−V_x(l−1) = P_x(l)−2P(l−1)+P_x(l−2) and y-component given by the corresponding expression. Note that the velocity and acceleration vectors are implicitly included in Equation (6) as the first and second order differences between the positions in consecutive lags.

The coefficient of determination of the spatio-temporal regression in Equation (6) was expressed as a percentage and referred to as the percent kinematics modulation, or PKM.

Variations in percent modulations

In order to evaluate the variations in the percent modulations (i.e., POM, PVM or PKM) within and across different control modes and training sessions, we estimated their values for each neuron in 2-minute non-overlapping intervals. Within each control mode, the POM, PVM and PKM of individual neurons were determined by averaging across all the relevant 2-minute intervals. The ensemble-POM, ensemble-PVM and ensemble-PKM in a specific 2-minute interval were determined by averaging across all the significantly modulated neurons. Comparisons between control modes and training sessions were based on the mean-POM, mean-PVM and mean-PKM, which were computed by averaging the corresponding ensemble values across all the intervals in the same control mode.

Principal Component Analysis

Principal component analysis (PCA) is a standard technique for discovering the dimensionality of a data set and decomposing it into uncorrelated components [27], [28]. The sequences of spike-counts from N_n neurons is transformed linearly (with unit norm weight vectors) into N_n principal components, which are uncorrelated with each other and have extreme variance values. Since the principal components in this application are weighted sums of the recorded spike-counts they may be referred to as “principal-neurons”.

Specifically, we computed the N_n×N_n sample-correlation matrix of the normalized spike-counts of the N_n neurons, whose i-j element is the sample-correlation between the normalized spike-counts N_i and N_j of the i-th and j-th neurons, recorded during the relevant part of the experiment. The variance of the principal-neurons was determined by the eigen-values of the sample-correlation matrix. In particular, λ₁ is the maximum variance of any weighted-combination of the recorded spike-counts with a unit norm weight vector. The normalized eigen-value describes the fraction of the variance in the original data that is captured by the i-th principal-neuron. Expressed as a percentage, it defines the percent of the total variance in the neural ensemble carried by the i-th principal-neuron.

Results

The neural activity of most of the cortical neurons was more variable during brain control than during pole control. Generally, rate variability was higher than would be predicted by a homogeneous Poisson process, as indicated by variance that exceeded the mean (Figure 2, top panels). The variance of the binned spike-count (in 100-ms bins) exceeded the mean spike-count for most of the N_n = 183 neurons recorded in this session, (83%, 88% and 92% during pole control, BCWH and BCWOH, respectively). This excess variability was also evident in the ratio of the variance to the mean (the Fano factor), which was found to be mostly above 1.0 (Figure 2, bottom panels). Most importantly, the transition to brain control resulted in even higher excess variability and larger Fano factor for most of the neurons (78% and 87% of the recorded cortical neurons during BCWH and BCWOH, respectively) as evident from the scatter plots of Figure 2.

Figure 2. Firing rate statistics for N_n = 183 units recorded in one session.

Mean-variance relationship computed based on 100-ms bins (top panels); and scatter plots of Fano factor in brain versus pole control (bottom panels). BCWH–Brain control with hand movements, BCWOH–Brain control without hand movements.

doi:10.1371/journal.pone.0000619.g002

Percent Overall Modulation

The percent overall modulation (POM), defined in Equation (1), represents the percentage of the variance of the binned spike-count that is attributed to rate modulations (Figure 1, Methods). The pie-plots in Figure 3 illustrate the distribution of the variance in the spike-counts recorded from two M1 neurons in different control modes, based on the POM computed using Equation (2) (Methods). During pole control (Figure 3, top pies), rate modulations accounted for only 7% for the typical neuron depicted on the right and 36% for a highly modulated neuron depicted on the left. The contribution of rate-modulations to the variance of the neural activity was more significant in brain control with and without hand movements, accounting, respectively, for 13% and 34% of the variance for the typical neuron (Figure 3, right middle and bottom pies) and 37% and 58% for the highly modulated neuron (Figure 3, left middle and bottom pies). These examples indicate that POM was higher in brain control than in pole control.

Figure 3. Percent Overall Modulation (POM) in pole control, BCWH and BCWOH for two representative M1 units.

doi:10.1371/journal.pone.0000619.g003

Figure 4 demonstrates the same trend for all the significantly modulated neurons. Insignificantly modulated neurons, i.e., neurons with little or no rate modulation in all the control modes (Methods), were considered irrelevant for task performance, and were excluded from further analysis. During the session analyzed in Figure 4, 87% of the 183 recorded neurons exhibited significant modulations in at least one control mode. Most of the significantly modulated neurons exhibited higher POM during brain control than during pole control, as evident in the top panels of Figure 4 (78% and 91% of the significantly modulated neurons in BCWH and BCWOH, respectively, Table 1). For few neurons the estimated POM during pole control was even negative (possibly due to the finite length of the spike-train, see Methods) and became positive only during BCWH or BCWOH. Thus, the top panels in Figure 4 depict the changes in the firing rate statistics expressed in Figure 2 in terms of the POM.

Figure 4. Percent Overall Modulation (POM) for N_sig = 160 significantly modulated units recorded in the same session analyzed in Figure 2.

Top: Scatter plot of POM in brain versus pole control. Bottom: distribution of POM of all significantly modulated units (left) and those in M1 (right upper, N_sig = 56) and PMd (right lower, N_sig = 55).

doi:10.1371/journal.pone.0000619.g004

Table 1. Number of neurons with increasing POM (POM_inc) and increasing variance (Var_inc), during the sessions depicted in Figure 4, and 5, out of the N_sig significantly modulate neurons.

doi:10.1371/journal.pone.0000619.t001

The distributions of the POM of the significantly modulated neurons during brain control (BCWH and BCWOH) differed significantly from the distribution of the POM during pole control (Wilcoxon rank sum test, p = 1.2% and p = 10⁻¹⁰% for BCWH and BCWOH, respectively) as shown in the bottom left panel of Figure 4. The mean POM (±std) in the different modes were 8.8%±10.7%, 12.2%±11.7%, and 18.8%±14.4% for pole control, BCWH, and BCWOH, respectively. The corresponding distributions for M1 and PMd neurons are shown in the right bottom panels of Figure 4.

Variations in POM during that session are shown in Figure 5 for the ensemble-mean (top left) and for a typical PMd neuron (top right). The ensemble-POM is the average POM over all the significantly modulated neurons (Methods). The figure indicates that the ensemble-POM remained relatively stable in each mode of operation, but changed abruptly after the transition to brain control and especially after the transition to brain control without hand movements.

Figure 5. Variations in POM (top) and spike-count statistics (bottom) during the same experimental session analyzed in Figure 4 (ensemble-average–left panels; single PMd unit–right panels).

The POM and spike-count statistics were computed in 2-minute non-overlapping intervals and averaged across all the N_sig = 160 significantly modulated neurons to obtain the ensemble-average.

doi:10.1371/journal.pone.0000619.g005

POM and firing rate statistics

The underlying changes in the spike-count statistics (bottom panels of Figure 5) indicate that the ensemble-POM increased mainly due to an increase in the variance of the spike-count, which was not matched by the change in the mean spike-count. Indeed, most of the neurons (78%) whose POM was higher in BCWH than in pole control, exhibited also a larger variance, especially neurons in PMd (92%) and M1 (94%), as summarized in Table 1.

The transition from BCWH to BCWOH resulted in further increase in POM for most of the significantly modulated neurons (87%). This increase resulted from a combination of increasing variance and decreasing mean rate. Increasing POM from BCWH to BCWOH was usually associated with increasing variance, especially for PMd neurons (85%, Table 1), as shown for a typical PMd neuron in Figure 5 (bottom right). Furthermore, considering the overall transition from pole control to BCWOH, increasing POM was associated with increasing variance for most of the neurons (72%); especially among PMd (98%) and M1 (74%) neurons (Table 1). Thus, the overall increase in POM from pole control to BCWOH is attributed mainly to increasing variance.

Direct transition from pole control to BCWOH was tested in later sessions in which the joystick was removed immediately after the pole control epoch. The changes in the POM and the firing rate statistics during such a session are depicted in Figure 6. The large increase in the POM after the transition to BCWOH (top panels, ensemble average–left, a typical PMd neuron–right) is related mainly to increasing variance (bottom panels, respectively). Indeed, most (75%) of the neurons whose POM was higher in BCWOH than in pole control, exhibited also a larger variance, especially neurons in PMd (93%), and M1 (72%) (Table 1).

Figure 6. Variations in POM (top) and spike-count statistics (bottom) during an experimental session with direct transition form pole control to BCWOH (ensemble-average–left panels; single PMd unit–right panels).

The POM and spike-count statistics were computed in 2-minute non-overlapping intervals and averaged across all the N_sig = 169 significantly modulated neurons to obtain the ensemble-average.

doi:10.1371/journal.pone.0000619.g006

POM in different cortical areas

The mean-POM, computed as the mean of the ensemble-POM across each control mode (Methods), was higher in brain control than in pole control for all cortical areas examined from both monkeys (Figure 7, Table 2). The standard deviation of the ensemble-POM during each control mode is marked by an error bar (reflecting variations in the ensemble-POM across time). The change in the mean-POM from pole control to either BCWH or BCWOH was higher than the respective standard deviations in most of the recorded cortical areas (except for the limited group of SMA neurons).

Figure 7. Mean-POM of the N_sig significantly modulated units in different cortical regions during different control modes in a single session with each monkey.

Full bars mark the mean values across all the 2-minute intervals in the same control mode, and error bars represent the standard deviation. M1–primary motor cortex, PMd–dorsal premotor cortex, S1–primary somatosensory cortex, SMA–supplementary motor area, PP–Posterior Parietal Cortex (medial intraparietal).

doi:10.1371/journal.pone.0000619.g007

Table 2. Mean-POM and Mean-PVM of neurons in different brain regions during each control mode. The standard deviations reflect variations in the ensemble-statistics across time.

doi:10.1371/journal.pone.0000619.t002

Variance distribution in principal neurons

The POM analysis decomposed the variance of the spike-counts of individual neurons into the variance associated with rate modulations and the variance associated with neural noise (Figure 3). At the ensemble level, principal component analysis (PCA, Methods) was used to decompose the total variance of the neural activity into uncorrelated principal components, or “principal neurons”. Figure 8 depicts the percent variance carried by the different principal neurons during the same session analyzed in Figures 4, 5 and 7. The percent variance dropped sharply for the first few principal neurons and remained relatively constant thereafter. In an ideal case, when the noise is generated from independent identically distributed random processes, the percent variance of the background noise is constant. Thus, the relatively constant variance level beyond the initial 5–15 principal neurons can be attributed mainly to the neural noise. In contrast, the excess variance of the initial principal neurons above the background level reflects correlated activity among the different neurons and can be attributed mainly to rate-modulations by common modulating signals.

Figure 8. Percent variance carried by the different principal neurons during the same session analyzed in Figure 5.

The analysis decomposed the variance carried by the ensemble of the significantly modulated neurons recorded from all brain regions. Inset: zoomed-in version of the same plot for the initial 20 principle neurons.

doi:10.1371/journal.pone.0000619.g008

The decomposition of the variance of the ensemble activity into principal neurons extends the single-neuron based POM analysis, and suggests that the modulating signals responsible for the POM were highly correlated. Indeed, the accumulated excess variance in the initial principal neurons (Figure 8) was comparable to the average POM indicated in Figure 5, and small compared with the accumulated variance of the background noise level. Furthermore, as seen from Figure 8, the variance of the first principal neuron, i.e., the maximum variance of any weighted sum of the neural activity (with unit norm weight vector), was higher during brain control than during pole control. This indicates that the variance of the modulating signals, which contributed to correlated neural activity, was higher during brain control than during pole control.

Percent velocity modulation

The contribution of the velocity of movement (both the velocity-vector and the speed) to the variability in the neural activity, was evaluated using the regression between the spike counts in 100-ms bins and the velocity profile during the surrounding 1900-ms window (Methods, Equation (5)). Spike trains evoked during pole control were related to the hand velocity, while spike trains evoked during BCWOH were related to the cursor velocity. The analysis for BCWH accounted for the correlation with both the hand and cursor velocities. The coefficient of determination, R², of the regression quantifies the fraction of variance in binned spike-counts that is attributed to the velocity profile. Expressed as a percentage, the coefficient of determination is referred to as the percent velocity-related modulation (PVM, Methods).

We also extended the analysis to include all the kinematics variables, i.e., the time course of the position (which implicitly includes the time course of the velocity and acceleration), speed and magnitude of the acceleration, in the surrounding 1900-ms window, as described by Equation (6) (Methods). The resulting coefficient of determination was expressed as a percentage and referred to as percent kinematics modulation (PKM, see Methods). Overall, the results for the PKM were similar to the PVM, and are stated only briefly for completeness.

PVM was significantly correlated with POM (p<10⁻¹⁰), as shown in Figure 9, with coefficients of correlation of 0.72, 0.68 and 0.79 for pole control, BCWH and BCWOH, respectively (0.72, 0.71 and 0.81, respectively for PKM versus POM). This strong correlation implies that the activity of cortical neurons, which exhibited larger rate modulations, was, in general, better correlated with the velocity profile, and can thus contribute more to its prediction. In contrast, there was no significant correlation between POM, or the increase in POM, and the magnitude of the decoding weights used in the BMI filter.

Figure 9. Correlation between PVM and POM for all the N_sig = 160 significantly modulated neurons recorded in one session.

Coloured dashed lines mark the linear regression lines. Black dashed lines mark the diagonal unit-slope lines.

doi:10.1371/journal.pone.0000619.g009

While PVM was strongly correlated with POM, the slope of the linear relationship was only 0.31, 0.21 and 0.12, for pole control, BCWH and BCWOH, respectively (0.35, 0.23 and 0.14, respectively for PKM versus POM). The smaller than unit slopes indicate that only a small fraction of the modulations was correlated with the velocity profile. Most importantly, the slopes of the PVM-POM or PKM-POM relationships were smaller in brain control compared to pole control. This suggests that modulating signals, which were not correlated with the kinematics of the movement, had a larger effect on the POM during brain control than during pole control.

The mean-PVM in most cortical regions did not increase significantly after switching to brain control, as indicated in Figure 10. Thus the mean-PVM did not follow the significant and large increase in the mean-POM shown in Figure 7. While the mean-POM of M1 neurons, for example, increased from 17.5±0.7% in pole control to 20.0±1.1% in BCWH and 30.1±1.6 in BCWOH, the mean-PVM decreased from 7.2±0.5% to 6.4±0.5% and 5.1±1.1% (Table 2). The mean-PKM (Table 2) was at the most 0.8% higher than the mean-PVM, and decreased from 8.0±0.7% for M1 neurons during pole control to 7.1±0.5% and 5.8±1.2%, during BCWH and BCWOH, respectively. Since the increase in POM was not matched by increasing PVM or PKM, the higher neuronal rate modulations observed during brain control cannot be explained only by increased modulations due to the kinematics of the movement.

Figure 10. Mean-PVM of the N_sig significantly modulated units in different cortical regions during different control modes in the same sessions as Figure 7.

Full bars mark the mean values across all the 2-minute intervals in the same control mode, and error bars represent the standard deviation. M1–primary motor cortex, PMd–dorsal premotor cortex, S1–primary somatosensory cortex, SMA–supplementary motor area, PP–posterior parietal cortex (medial intraparietal).

doi:10.1371/journal.pone.0000619.g010

Effect of training

In all the experimental sessions, with both monkeys, the POM was always higher in brain control than in pole control, as demonstrated in Figure 11 (top panel). Furthermore, in all the control modes, the POM decreased gradually with training. These trends were statistically significant in pole control and BCWH (p<0.05). In contrast, the mean-PVM remained approximately the same, and even increased, with training (Figure 11, middle panel). The difference between the two, i.e., POM minus PVM, is depicted in the bottom panel of Figure 11, and exhibited statistically significant decreasing trends in all the control modes (p<0.02). Similar results were obtained when considering the mean-PKM, which accounts for modulations by the kinematics of the movement. Thus, the changes in POM during BMI training seem to reflect mainly changes in untagged modulations not correlated with the kinematics of the movement.

Figure 11. Effect of training: percent overall modulation POM, percent velocity modulation PVM and percent untagged modulation PUM of the N_sig significantly modulated neurons during all the 10 BMI sessions with monkey #1.

N_sig = 156, 130, 142, 142, 150, 140, 160, 166, 174 and 165. Initial sessions included BCWH while later sessions included only BCWOH.

doi:10.1371/journal.pone.0000619.g011

The observed trends in the mean-POM and in the percent untagged modulations mirrored the trend in task performance [7]. Behavioral performance, quantified by either the time to reach the target or the success-rate, deteriorated after switching to brain control, but improved gradually with training. Thus, in general, the POM and the percent untagged modulations increased as the behavioral performance degraded and decreased as the behavioral performance improved.

Discussion

Our analyses indicate that cortical neurons that are used to control a BMI modulate their activity more intensely during brain control than during pole control. The enhanced modulations were evident in increased variability of the binned spike-counts beyond the level expected from homogeneous Poisson processes. We quantified this excess variability using the POM, which described the overall contribution of modulating signals to the variance of the binned spike-counts of individual neurons. The method for estimating the POM was based on the assumption tha