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Neural population partitioning and a concurrent brain-machine interface for sequential motor function.
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PMID:  23143511     Owner:  NLM     Status:  MEDLINE    
Although brain-machine interfaces (BMIs) have focused largely on performing single-targeted movements, many natural tasks involve planning a complete sequence of such movements before execution. For these tasks, a BMI that can concurrently decode the full planned sequence before its execution may also consider the higher-level goal of the task to reformulate and perform it more effectively. Using population-wide modeling, we discovered two distinct subpopulations of neurons in the rhesus monkey premotor cortex that allow two planned targets of a sequential movement to be simultaneously held in working memory without degradation. Such marked stability occurred because each subpopulation encoded either only currently held or only newly added target information irrespective of the exact sequence. On the basis of these findings, we developed a BMI that concurrently decodes a full motor sequence in advance of movement and can then accurately execute it as desired.
Maryam M Shanechi; Rollin C Hu; Marissa Powers; Gregory W Wornell; Emery N Brown; Ziv M Williams
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Type:  Journal Article; Research Support, N.I.H., Extramural; Research Support, Non-U.S. Gov't     Date:  2012-11-11
Journal Detail:
Title:  Nature neuroscience     Volume:  15     ISSN:  1546-1726     ISO Abbreviation:  Nat. Neurosci.     Publication Date:  2012 Dec 
Date Detail:
Created Date:  2012-11-28     Completed Date:  2013-01-29     Revised Date:  2013-07-11    
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Nlm Unique ID:  9809671     Medline TA:  Nat Neurosci     Country:  United States    
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Languages:  eng     Pagination:  1715-22     Citation Subset:  IM    
Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA.
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MeSH Terms
Action Potentials / physiology*
Brain-Computer Interfaces*
Macaca mulatta
Motor Cortex / cytology*,  physiology*
Neurons / cytology,  physiology*
Photic Stimulation / methods
Psychomotor Performance / physiology*
Random Allocation
Reaction Time / physiology*
Grant Support
5R01-HD059852/HD/NICHD NIH HHS; DP1 OD003646/OD/NIH HHS; DP1 OD003646/OD/NIH HHS

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Journal ID (nlm-journal-id): 9809671
Journal ID (pubmed-jr-id): 21092
Journal ID (nlm-ta): Nat Neurosci
Journal ID (iso-abbrev): Nat. Neurosci.
ISSN: 1097-6256
ISSN: 1546-1726
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nihms-submitted publication date: Day: 1 Month: 11 Year: 2012
Electronic publication date: Day: 11 Month: 11 Year: 2012
Print publication date: Month: 12 Year: 2012
pmc-release publication date: Day: 01 Month: 6 Year: 2013
Volume: 15 Issue: 12
First Page: 1715 Last Page: 1722
PubMed Id: 23143511
ID: 3509235
DOI: 10.1038/nn.3250
ID: NIHMS412030

Neural population partitioning and a concurrent brain-machine interface for sequential motor function
Maryam M. Shanechi123
Rollin C. Hu23
Marissa Powers2
Gregory W. Wornell1
Emery N. Brown34
Ziv M. Williams23
1Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA
2Department of Neurosurgery, Massachusetts General Hospital, Boston, MA, USA
3Harvard Medical School, Boston, MA, USA
4Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, MA, USA
Correspondence: Correspondence should be addressed to Z.M.W. (

An important motivation for the design of brain-machine interfaces (BMIs) to date has been their potential ability to restore lost motor function in individuals with neurological injury or disease (e.g., due to motor paralysis or stroke). In such cases, the envisioned role of the BMI is to decode the intended movement from neural activity in the relevant areas of the brain, and use this information to control an affected limb, prosthetic, or other device.

The design of such BMIs has received considerable attention in recent years1-18. Work to date has principally focused on achieving the motor goal in tasks that involve single-targeted movements, such as the task of moving a cursor on a display to an individual target location. These BMIs can decode the continuous trajectory of one- to three-dimensional movement (including a grasp in some studies)1-14, the intended target location15, 16, or both the target and trajectory jointly using approaches such as optimal feedback control17, 18. However, in many natural tasks—such as playing a succession of notes on a piano—the goal is more complex, and the motor plan for achieving it can be viewed as a complete sequence of such simpler plan elements to be executed in order.

Our focus is on the design of BMIs that can achieve the goal of these sequential motor plans. Planned sequential behavior is a fundamental motor process in which all targets of a movement sequence are planned ahead of its initiation. Hence a BMI for performing such behavior would allow a person to plan a full motor sequence ahead of execution. For example, when picking up a cup and bringing it to one’s lips, a person normally formulates the complete motor plan prior to its execution as opposed to planning and performing each of its elements individually and separately. Therefore, the objective of such a BMI would be to perform the sequential behavior by decoding all elements of the sequence concurrently and in advance of movement – thus requiring the consideration of a concurrent architecture. This BMI functionality is distinct from that in prior BMIs that decode and execute individual single-targeted movements one by one, and hence have a sequential BMI architecture1-18.

In addition to simultaneously decoding a motor sequence in advance, a concurrent architecture could also allow the BMI to consider the overall motor goal of the task at a higher-level. This is a result of the BMI having information about all the motor plan elements at once and in advance of execution. Hence one prospective BMI capability would be to consider all elements of the sequence concurrently, prior to action, in order to determine ways to perform the task more effectively. For example, the BMI might determine a way to accomplish the task more quickly, or more efficiently (to within any physical constraints that might exist). Alternatively, based on additional sensor inputs, the BMI might determine that the planned sequence of movements would result in an accident with an obstacle, and thus modify the execution of the task to avoid such an accident.

The realization of BMIs that can perform and potentially execute sequential motor function more effectively in this way will obviously require significant technological innovations. But as a key initial step, it requires considering a concurrent BMI architecture in which the elements of a planned motor task are decoded in parallel (i.e., at once), in contrast to the serial process of a sequential BMI. Hence, the feasibility of such BMIs hinges on the degree to which the elements of a motor plan sequence can, in fact, be decoded concurrently. This is the starting point for our research.

Prior work has demonstrated that individual neurons in the premotor cortex of primates display selective responses to planned single-targeted movements before their initiation, and that such responses often remain sustained during working memory until movement execution19-26. Such responses have been successfully exploited in the design of BMIs for single-target tasks15, 16. In comparison, the neural encoding of tasks requiring a full sequence of planned targeted movements to be formulated prior to execution is less well understood, and the design of real-time BMIs that can concurrently decode and then execute such sequential motor plans remains unexplored. Prior work has shown that an individual neuron can display a response that is selective to one or more elements of a sequential motor plan27-41 (see also Discussion). However, little is known regarding how information about multiple elements of a sequential motor plan (e.g., the planned targets of a sequential movement) is simultaneously distributed across the whole premotor population during working memory, and whether these plan elements can be accurately decoded from the neural population in a concurrent manner. More importantly, it is necessary to determine whether adding information about the elements of the motor plan, in sequence, to working memory affects the integrity of information about the plan elements that are already held, and how it affects their neural encoding. Finally, it is necessary to assess robustness—whether a BMI limited to recording from relatively small numbers of neurons is able to achieve sufficient and consistent decoding accuracy.

Here, we find that sequential motor plans can be decoded simultaneously, accurately, robustly, and in advance of movement from the neural activity in the premotor cortex of monkeys. Additionally our study reveals a surprisingly structured encoding mechanism that is used by the premotor populations for these sequential plans and that, in turn, allows for their accurate and concurrent decoding. Based on these findings, we develop and implement a real-time BMI that can concurrently decode a dual sequence of motor targets and then execute them as desired.


In the study, two adult male rhesus monkeys were trained to perform a task in which two targets were presented, in sequence, on a computer display. Each of the targets could randomly take on one of four possible spatial locations (“up”, “down”, “left”, or “right”). Repeated locations were precluded, so there were a total of 12 possible combinations (sequences) of two consecutive distinct target locations. After a blank-screen variable delay, a “go” cue appeared directing the monkeys to sequentially move a cursor from the center of the screen to each of the two remembered targets, in order (Dual-target task; Fig. 1a, b). We define the working memory period as the 500 ms blank-screen interval following presentation of the second target and before the earliest possible “go” cue. Therefore, the task here was a working-memory task in which the monkeys were required to serially add to working memory two randomly selected target locations in each trial and then simultaneously retain them in working memory prior to execution.

Multiple-unit responses were recorded from the premotor cortex as the primates performed this task. We recorded 281 well-isolated single neurons from the supplementary motor area (SMA) and dorsal premotor cortex (PMd) over 11 sessions, for an average of 26 ± 6 cells (mean ± s.d.) per recording session (note that some of these cells may not be distinct across the different sessions). Inhomogeneous Poisson models were fitted to each neuron’s spiking activity using an expectation-maximization algorithm42 (see Methods and Supplementary Modeling). Using these models, we employed a maximum-likelihood decoder to quantify the probabilities that groups of neurons could correctly identify the first and second targets on a trial-by-trial basis during the working memory period (leave-one-out cross-validation; see Methods). We used decoding accuracy as our measure of the amount of information encoded by a population of neurons about each target. Specifically, for an individual (first or second) target, we measured the percentage of trials in which the maximum-likelihood decoder correctly predicted the respective target from that population’s activity. Likewise, we measured the amount of information encoded about the full sequence as the percentage of trials in which both targets were correctly decoded.

Accurate and concurrent encoding of the motor sequence

We find that neural population activity within the premotor cortex accurately encoded the location of both targets during the working memory period. During this period, the population correctly encoded the first and second targets on 85% and 82% of the trials in the best session, respectively. When considering all 12 possible target combinations, the population encoded both targets correctly on 72% of the trials in this session (Fig. 2a; 285 dual-target trials were performed in this session). Across all tested sessions, the population correctly encoded the first and second targets on average on 76 ± 11% and 56 ± 17% of trials, respectively, both of which were significantly above chance (one-sided Z-test, P < 10−15; Supplementary Fig. 1a). Also, the population encoded both targets correctly on average on 45 ± 12% of the trials across all sessions, which was also far higher than chance at 1/12≈8% (one-sided Z-test, P < 10−15). These results were consistent across the two monkeys (P < 10−15 for both; Supplementary Fig. 2).

Robustness of the encoding

Only a small number of cells were needed to decode the target sequence with high accuracy. When performing the decoding analysis over all trials, which employed all 12 possible target combinations, only 29% of the population (7.5 cells) was needed, on average, to achieve higher than 90% of the population sequence accuracy (Fig. 2b; see Methods). When performing the decoding analysis over subsets of all trials that employed only 4 or 8 target combinations, population sequence accuracies in the best session were as high as 93% and 80%, respectively. In these cases, decoding from only 2 and 4 cells, respectively, was sufficient to achieve higher than 90% of these sequence accuracies.

Real-time concurrent BMI for sequential movement execution

Motivated by the observation that both targets can be concurrently and accurately decoded from the responses of relatively few neurons in the premotor cortex, we developed a real-time BMI capable of predicting both targets simultaneously prior to monkey’s motor response and then executing the targeted movements. In the associated experiments, we recorded a mean of 20 ± 2 cells per session from the premotor cortex of the same monkeys. Here Poisson models were first fitted to the neural population activity during the working memory period prior to the “go” cue (see Methods and Supplementary Fig. 1b) as the primates rehearsed a subset of target combinations that included either 4 or 8 possible sequences over an average of 26 ± 2 training trials per sequence (Fig. 1b). We chose to use either four or eight sequences in the BMI experiments to obtain sufficient training and real-time trials per session.

Using the Poisson models, sequence decoding accuracies for the set of 4 and 8 sequences in these training sessions (found using leave-one-out cross-validation) were 79 ± 2% and 80 ± 3% (mean ± s.e.m.; one-sided Z-test, P < 10−15), respectively. Following training, the primates performed the same task as before, but with the cursor now being sequentially positioned by the BMI on the targets decoded from the recorded neuronal activity during the single preceding working memory period (Fig. 1c; see Methods). Here, BMI-generated cursor movements were set to occur immediately following the presentation of the “go” cue and the added delays were selected to match the reaction times that the monkeys normally experienced when moving the cursor themselves following the “go” cue (obviously, cursor movements could be generated without the added delays if desired).

Both monkeys performed a total of 459 trials on the four-sequence set, and one monkey performed 110 trials on the eight-sequence set using the real-time BMI. Sequence accuracies for the set of four and eight sequences were 72 ± 2% and 71 ± 4%, respectively, both of which were significantly above chance (mean ± s.e.m., one-sided Z-test, P < 10−15). Both training and real-time BMI accuracies were similar and significantly above chance across the two monkeys (one-sided Z-test, P < 10−15 for both; For the four sequence sets, the first monkey had a BMI accuracy of 69 ± 3% and a training session accuracy of 77 ± 2% and the second monkey had a BMI accuracy of 75 ± 3% and a training session accuracy of 82 ± 2%). Sequence accuracies using the BMI were also close to the cross-validated sequence accuracies during the training sessions when taking into account the primates’ natural error rates during the standard task (Fig. 3). In fact the 95% confidence bounds for the two accuracies were overlapping (72 ± 4% vs. 73 ± 3% and 71 ± 8% vs. 66 ± 6%, for the sets of four and eight sequences, respectively; see Methods). These results established that two planned elements, i.e., the two intended sequential targets of movement, could be simultaneously predicted in advance of movement and then executed by a real-time BMI with high accuracy.

We also examined the time required by the concurrent decoder to decode the sequence. We find that the sequence decoding accuracy for the set of four, eight, and twelve sequences reached 90% of the maximum asymptotic accuracy possible, on average, after 488 ± 135 ms, 561 ± 119 ms, and 641 ± 121 ms from the initial presentation of the second target, respectively (Fig. 4). When performing the motor sequence, the minimum total time it took for the monkeys to both react to the two “go” cues and reach the two targets was on average 791 ± 93 ms (this is the sum of the two reaction times plus the two center-to-target movement times; Fig. 4).

Population encoding reveals a novel partitioning mechanism

Observing that both target locations could be accurately and concurrently predicted from the neural population responses, we further examined the spatial and temporal structure of their encoding. In particular, we investigated how neurons within the premotor cortex were able to add new information about the second target to working memory without compromising the integrity of information about the first target that was already being held. To do so, we used the decoding approach that measures the amount of information held about the identity of each planned target in the sequence by considering all sequence combinations collectively.

We find that most cells encoded significant information about only the first (currently held) or only the second (newly added) target during the working memory period. Moreover, this partitioning was present across all target locations/sequences (i.e., responses were not sequence specific) and remained stable throughout recordings per day. Of the 281 neurons recorded in all sessions, 46% had a target accuracy significantly higher than chance for at least one of the two targets during the working memory period (one-sided Z-test, P < 0.01). Of these, 68% encoded significant information about only the first currently held target (Supplementary Fig. 3), and 23% encoded significant information about only the second added target (one-sided Z-test; P < 0.01; Fig. 5). The percentage of cells that encoded significant information about both targets was only 9% (one-sided Z-test; P < 0.01; note that a Bonferroni correction for multiple comparisons was done for all comparisons; Supplementary Fig. 4) and, even among these, most had target accuracies much closer to one of the two subpopulations of cells that significantly encoded only one target (Fig. 6; Supplementary Fig. 5). These results revealed a highly significant divergence in the amount of information encoded by the two subpopulations of neurons about the two targets (random permutation test, P < 10−15; see Supplementary Modeling; Supplementary Fig. 6). Moreover, we examined the relation between the activity of each of the two subpopulations to upcoming motor behavior and found that each subpopulation was only predictive of whether the respective first or second upcoming movement would be performed correctly or incorrectly (i.e., resulting in a behavioral error) by the primates following the “go” cue (one-sided Z-test, P < 10−15).

These results demonstrate that during the working memory period, most neurons were not selective to a specific sequence or simply to a spatial location. Rather, they were partitioned into two disjoint subpopulation, one encoding only the identity of the currently held (first) target and one encoding only the identity of the newly added (second) target within the sequence, regardless of the specific sequence (see Supplementary Fig. 7 for comparison to sequence specific selectivity found in prior work28-31, 41, 43).

The observed partitioning during working memory was not related to limb movement or simple visual related responses. No visual cues were presented during the working memory period and any movement before the “go” cue terminated the trial. This was also suggested by the partitioning mechanism itself since if the activity was due to targeted limb movement, then all cells would only reflect the direction of this single target. Finally the electromyography (EMG) activity during the working memory period was not predictive of the first movement direction (one-sided Z-test, P = 0.14), but was predictive of it during the first movement period after the “go” cue (one-sided Z-test, P = 0.01). In an additional set of analyses, we also found that encoding of the second target was not conditioned on the location of the first target, and vice versa (Supplementary Fig. 8).

Effect of adding information to working memory

In order to further examine how adding a new target to working memory affected the integrity of the currently held target, we disambiguated the process of holding information in working memory from that of adding information to it. The results were obtained from sessions in which the monkeys performed the standard dual-target trials (as before), but also performed single-target trials in randomly interleaved fashion (see Methods). Unlike dual-target trials, on single-target trials only the first target was presented and the second target presentation period was replaced with a blank-screen period of the same duration. The task timing was otherwise unchanged compared to the dual-target task.

We find that adding information about the second target location to working memory did not incur loss of information about the first target location. Of the cells that encoded significant information about the first target during working memory in single-target trials (one-sided Z-test, P < 0.01), most (74%) provided the same level of accuracy in decoding the first target during working memory in dual-target trials, despite the addition of a second target (χ2 test, P > 0.05). Moreover, for the whole population, there was also no significant difference in the first target accuracy during the working memory period when comparing dual-target and single-target trials across sessions (Wilcoxon’s signed-rank test, P = 0.69; Fig. 7). These results demonstrate that the subpopulation encoding the first target and their responses remained largely unchanged when the second target was added to working memory and, therefore, the addition of information about the second target did not comprise the integrity of information already held about the first target. It is important to emphasize here that the task involved serially adding to working memory two randomly selected target locations in each trial and then simultaneously holding them in working memory prior to execution. Such a task is distinct from memory-guided tasks in which the same motor sequence is repeatedly performed from memory after learning, or visually-guided tasks in which movements are serially cued and executed one-by-one29-31, 41, 43.

In a control analysis, we also examined whether neuronal encoding of the first target was affected by the number of targets presented per trial in a single session (i.e., one target versus two sequentially presented targets) by having one monkey perform only single-target trials. Comparing these single-target only sessions with sessions in which single-target trials were interleaved with dual-target trials on the same day, we found no significant difference between the population decoding accuracies of the first target on single-target trials between the two session types (χ2 test; P > 0.15; Supplementary Fig. 9).

Stability of the neural encoding structure

While implicit in the preceding results, it should be emphasized that as the pair of presented target locations varied over the hundreds of trials typical of a given day’s session, most neurons remained dedicated to encoding only the first (currently held) or only the second (added) target. For the two subpopulations of cells that encoded significant information about the respective first and second targets alone, most (89%) provided substantially the same level of accuracy in decoding their respective targets in the first and second halves of the recording session (χ2 test, P > 0.05; sessions included 263 ± 36 dual-target trials on average). Also, the sequence decoding accuracy (across all 12 sequences) of the entire population did not change over time between the first and second halves of the sessions (Wilcoxon’s signed-rank test, P = 0.37). Therefore, the partitioned premotor subpopulations appeared to be physiologically dedicated to encoding either the first or the second target added to working memory. Inherently, the neural decoding in our BMI exploited this stability of the two constituent subpopulations to achieve sustainable performance.


The purpose of the present study was to examine how multiple planned targets of sequential movement are concurrently encoded as a population by premotor neurons during working memory, and to determine whether the activity recorded simultaneously from multiple single-neurons can be used to concurrently and accurately decode the complete motor plan sequence in advance of movement and in real-time. Three methodological approaches were used to investigate these questions. First, we simultaneously recorded the activity of multiple cells across the whole premotor population. Second, we used an interleaved dual-target/single-target task in order to dissociate the dynamic process of maintaining target-related information in working memory from that of adding new information to it. Finally, we employed a maximum-likelihood decoding approach that allowed us to (i) define an accuracy measure for the amount of information that is concurrently encoded about planned motor sequences and, (ii) examine the spatiotemporal distribution of information across the whole population.

A neural partitioning mechanism

Our results reveal a novel functional structure within the premotor cortex that allowed for accurate and concurrent decoding of two planned motor targets across multiple spatial locations. We find that during working memory, premotor populations are largely partitioned into two fundamentally disjoint subpopulations of cells – one dedicated to encoding only the currently held (first) target and one dedicated to encoding only the newly added (second) target, irrespective of the specific sequence. Moreover, while the two target locations changed from trial to trial, the two encoding subpopulations did not. Notably, the subpopulation dedicated to encoding the first target and their responses remained largely unchanged when the second target was added to working memory, so that the process of adding information did not compromise the integrity of existing information (across all target locations). Also, only a small number of neurons were sufficient to accurately predict the location of both targets, making the decoding of such information highly robust.

Prior work has shown that individual premotor neurons display selective responses to single-targeted movements before their initiation19-26. It has also been shown that PMd neurons can be selective to the location of multiple target choices for a single-targeted movement before a final selection is made44, or can represent combined information about the target and the body-part to be used for a single-targeted movement45-47. When performing a planned sequential movement, prior studies have demonstrated that individual neurons within areas such as the parietal, premotor and prefrontal cortex can display selective responses to a sequential motor plan27-40, 43, 48. Some neurons (often a relatively small fraction) display increased activity for a specific combination of movements (for example a push followed by a pull of a manipulandum) during a preceding delay, suggesting that they encode information about more than one motor plan element at a time28-31, 37, 41, 43. Other cells have also been found to display selective responses during movement itself with increased activity prior to performing a particular movement (e.g., a push) only when it follows another specific movement (e.g., a pull) in sequence29, 31, 43, or prior to a movement only if it has a particular order in the sequence31, 43. What has remained unclear, however, is how information about individual elements of such sequential plans is simultaneously distributed across the whole population during working memory, and whether and how the process of adding new information about an element to working memory affects the integrity of information already held and its neural encoding.

While a major focus of this study was to investigate the encoding structure of premotor populations during the working memory period, we find that, consistent with prior studies29, 31, 43, neurons often altered the degree to which they encoded information about the two targets across different time-points during the task. Some cells, for example, encoded no information about the second target during the working memory period, but then encoded significant information about the second target during the second movement itself (Supplementary Fig. 5a). Such shifts in activity may reflect the dynamic role premotor neurons play in processing, maintaining, and then executing motor plans in combination with other motor cortical areas.

Another question arising from the study is how information encoded by premotor neurons is related to the later execution of the sequential task. Here, we find that the subpopulation of cells that predominantly encoded information about the first target was only predictive of whether the primates would perform the first upcoming movement correctly or incorrectly, and this was similarly true for the second subpopulation. This thus suggests that the ‘partitioning strategy’ revealed here was ultimately used to direct upcoming sequential motor behavior. In terms of the small number of cells that encoded information about both targets, it is interesting to speculate whether they may provide an important ‘bridge’ between distinct motor plan elements or a higher conceptual representation of specific motor combinations not provided by the other subpopulations of neurons.

A concurrent BMI for planned sequential motor behavior

We exploited the simultaneous encoding and the neural partitioning mechanism observed in these experiments to develop a novel BMI functionality for performance of planned sequential motor behavior. This is a fundamental behavior in which all targets of a movement sequence are planned ahead of its initiation, and is largely distinct from behaviors involving the performance of independent single-targeted movements. The BMI functionality takes advantage of the concurrent encoding of a sequential motor plan in the premotor cortex, allowing it to determine all elements of the sequence simultaneously, upfront, and in advance of movement.

In addition, because the full motor plan is simultaneously decoded upfront and in advance of movement, the higher-level goal of the task can, in principle, also be analyzed before execution, and the motor plan reformulated accordingly. This could allow the prospective design of BMIs that can improve the performance of a sequential motor task, for example perform the task more quickly, more flexibly, or more efficiently than originally conceived. Such a BMI may, for example, alter the order in which the elements of the motor sequence are executed depending on rapid or unpredictable changes in the environment (e.g., to avoid unanticipated obstacles), or correct the original sequence based on the performance metrics of the task (e.g., proactively change a sequence of letters based on spelling rules). As a simple but illustrative example of such a prospective capability (in the context of our experiments and using a relatively small number of recorded neurons), we demonstrate that we could accurately decode the full sequence of two targets in a very short time period after target presentation (Figs. 3, 4). Taken together, we demonstrate a concurrent BMI that allows the performance of a sequential motor behavior in line with how we naturally plan and execute it. Moreover, since information about all elements of the sequence is known ahead of execution, considering such concurrent decoding provides the future prospect of designing BMIs that can perform such tasks more effectively.

Behavioral task

Two adult rhesus monkeys (Macaca Mulatta) were trained to perform a working memory sequential delayed motor task. Monkeys were first sequentially presented with two distinct target locations on a screen, which were randomly selected in each trial, and then had to move a cursor to each in order by using a joystick (Dual-target task; Fig. 1a). After initial presentation of a blank screen, two targets were sequentially presented each of which could randomly take on one of four possible spatial locations: “up” (U), “down” (D), “right” (R) or “left” (L). To ensure that the two target locations were distinct, the motor sequence was chosen at random from a total of 12 possible sequences, i.e., all possible combinations of the two target locations excluding the ones with repeated locations. Targets were displayed for 500 ms each and were interleaved by a 300 ms interval during which a blank screen was shown. Following the end of second target presentation, there was an additional blank screen variable delay of 550– 850 ms (the working memory period) following which the first “go” cue signal appeared. After this, the monkeys were required to move a cursor from the center of the screen to the first remembered target. After reaching the target, they were required to return the joystick to the center and then wait for a second “go” cue to appear after an additional 500 ms delay interval. Once the second “go” cue appeared, they were allowed to move the cursor from the center of the screen to the second remembered target. The monkeys received a juice reward if they correctly moved to the two instructed targets.

Dual-target vs. single-target task

To examine the effect of adding information about a new target to working memory, it was necessary to disambiguate the process of holding information in working memory from that of adding information to it. To do this, primates performed randomly interleaved dual-target and single-target trials in a subset of sessions. On dual-target trials, described above, the primates were sequentially presented with two targets and then a blank screen delay. The time delay from the end of the first target presentation to the first “go” cue was therefore 1350–1650 ms. On single-target trials, in comparison, the primates were presented by only the first target, and had to keep this single target in working memory for the same total 1350–1650 ms time duration as in dual-target trials. However, here, they were not presented by a second target and were only shown a blank screen until the “go” cue.

Neurophysiologic recordings

All procedures were performed under IACUC-approved guidelines and were approved by the Massachusetts General Hospital institutional review board. Prior to recordings, multiple (up to six) planar silicone multi-electrode arrays (NeuroNexus Technologies Inc., MI) were surgically implanted in each monkey. Each of the implanted arrays contained four shanks horizontally spaced 400 μm apart. Every shank was 4 mm long and, in turn, contained 8 electrode contacts each vertically spaced 200 μm apart for a total of 32 contacts per electrode array. Hence the electrode contacts themselves spanned the bottom 1.6 mm of the shank. We advanced the electrodes approximately 2mm in depth. The electrode arrays were inserted into the cortex manually using microscope magnification. A craniotomy was placed over the premotor cortex under stereotactic guidance (David Kopf Instruments, CA). The multi-electrode arrays were separately implanted into the dorsal premotor (PMd) and the supplementary motor (SMA) areas (Supplementary Fig. 10). The electrode lead of each array was secured to the skull and attached to female connectors with the aid of titanium miniscrews and dental acrylic. Confirmation of electrode positions was done in both monkeys by direct visual inspection of the sulci and gyral pattern through the craniotomy. Additional post-mortem confirmation of electrode positions was made in one monkey (the second monkey is still performing experiments). Recordings began two weeks following surgical recovery. A Plexon multichannel acquisition processor was used to amplify and band-pass filter the neuronal signals (150 Hz – 8 kHz; 1 pole low-cut and 3 pole high-cut with 1000x gain; Plexon Inc., TX).

Shielded cabling carried the signals from the electrode array to a set of six 16-channel amplifiers. Signals were then digitized at 40 kHz and processed to extract action potentials in real time by the Plexon workstation. Classification of the action potential waveforms was performed using template matching and principle component analysis based on waveform parameters. Only single, well-isolated units with identifiable waveform shapes and adequate refractory periods (less than 1% of spikes within a 1 millisecond interval) were used for the online experiments and offline analysis. No multiunit activity was used.

Model construction

For the analysis of standard recording sessions, we model the activity of each neuron under any given sequence as an inhomogeneous Poisson process whose likelihood function is given by49, 50

[Formula ID: FD1]
where Δ is the time increment taken to be small enough to contain at most one spike, Nkc is the binary spike event of the c ’th neuron in the time interval [(k −1)Δ, kΔ], λc (k|Si) is its instantaneous firing rate in that interval, i S is the i ’th sequence, and K is the total number of bins in a duration KΔ . We take Δ = 5 ms as the bin width of the spikes. By building the neuronal models under each sequence separately in the dual-target task we avoid making any a priori assumptions about whether the cells encode individual targets or combined sequences. For each sequence and neuron, we need to estimate the firing rate λc (k|Si) using the neuronal data observed. To do so, we use a state-space approach using the expectation-maximization (EM) algorithm42, 51, 52 (see Supplementary Modeling). After fitting the models, we validated them using the χ2 goodness-of-fit test on the data42 and confirmed that they fitted the data well (P > 0.7 for all cells in all sessions).

Maximum-likelihood decoder

Once models are fitted, a maximum-likelihood decoder is used to decode the intended sequence based on the neuronal activity in any period of interest. A maximum-likelihood decoder is the optimal decoder in the sense of maximizing accuracy, i.e., the percentage of trials in which the combined sequence is decoded correctly, when the sequences are equally likely to be presented as is the case in our experiments. The decoder finds the likelihood of observing the population neuronal data under each sequence and selects the sequence with the highest likelihood as its prediction. Using the likelihood model in (1) and assuming that neurons are conditionally independent given the sequence, the population likelihood under any sequence is given by

[Formula ID: FD2]
where K is the total number of bins in any period of interest during the trial, C is the total number of neurons, and λc (k|Si) for k = 1,…,K and c = 1,…,C is the estimate of the firing rate. The predicted sequence, S^, is thus given by
[Formula ID: FD3]
To find the sequence decoding accuracy of a single cell, the maximum-likelihood decoder uses only that cell’s spiking activity to decode the sequence (Fig. 5 and Supplementary Fig. 5). The decoder also outputs the posterior probability of each sequence, which is the probability that it is the correct one after the neuronal observations, i.e.,
[Formula ID: FD4]

To dissociate the decoding accuracy of the first and second targets, denoted by T1 and T2, the decoder also outputs their predictions based on the neuronal activity. To do so, the decoder finds their posterior probabilities, i.e., p(T1=l1∣N1:K1:C) and p(T2=l2∣N1:K1:C), for all possible spatial locations, l1 and l2, by summing over the posterior probability of the sequences that have these spatial locations as their first or second targets. The decoder then picks the spatial location with the highest first target (second target) posterior, or equivalently likelihood in our design, as its first (second) target prediction.

Comparison of the first target decoding accuracies in the single-target and dual-target tasks

To find the first target decoding accuracy of the single-target task we modeled the activity of each neuron under any given single target location as an inhomogeneous Poisson process, which was fitted using the EM procedure. We then performed the maximum-likelihood decoding analysis using leave-one-out cross-validation on the single-target trials. To make the comparison, for the dual-target task we constructed two models one for the first target and one for the second target, and then performed the decoding analysis for each target separately.

Determining the number of cells required to achieve the population accuracy

We found the number of cells required to achieve a given percentage of the population accuracy by first sorting them in each session based on their single neuron sequence accuracies and then performing the decoding analysis in that session for different number of cells in descending order.

BMI model training

In each BMI recording session, the monkeys first performed the dual-target task using a joystick (training session) during which models were constructed for the neuronal activity during an 800 ms time window prior to presentation of the “go” cue. This window length was chosen because in the standard dual-target sessions, it was sufficient to achieve better than 95% of the (maximum) sequence accuracy possible when using the entire window starting from second target presentation until the “go” cue (Supplementary Fig. 1b). We modeled the activity of each neuron in this window under any sequence as a homogeneous Poisson process (point process with constant rate), instead of an inhomogeneous one, to make the model construction faster for the BMI experiments. Hence using (1) the likelihood function for the spiking activity of neuron c under any of the sequences, Si, was modeled as49, 50

[Formula ID: FD5]
where λc(Si) denotes the fitted firing rate of that neuron in the 800 ms window for sequence Si and K = 800/ Δ is the total number of bins in this period with bin width Δ = 5ms. The firing rates were fitted using maximum likelihood parameter estimation. Here, the task involved either four (both monkeys) or eight (monkey P) sequences. The four-sequence task consisted of either “U-R”, “U-L”, “D-R”, “D-L” or “L-U”, “L-D”, “R-U”, “R-D”. The eight-sequence task consisted of the union of the sequences in the two four-sequence tasks.

The training sessions were followed by the real-time BMI sessions in which these trained Poisson models were used to predict the sequence using the maximum-likelihood decoder.

Concurrent online predictions and movement execution in the BMI

After the training sessions, the monkeys performed the same task as before. However, this time, cursor position was controlled by target predictions made by the maximum-likelihood decoder rather than the joystick. During the real-time BMI experiments, individual spike timings of all cells within the population were continuously recorded at a 40 kHz resolution by the Plexon multi-channel acquisition processor. Each recorded spike was then transmitted via an Ethernet port to a separate computer running a Matlab routine in real time. For each real-time trial, the Matlab routine then used the maximum-likelihood decoder to calculate the likelihood of the population spiking activity during the 800 ms time window prior to the “go” cue, i.e., N1:K1:C under each sequence, Si. This likelihood was calculated based on the trained Poisson models and assuming neurons were independent conditioned on the sequence. Hence the population likelihood for each sequence was found as

[Formula ID: FD6]
The maximum likelihood decoder then outputted the sequence under which the population likelihood was maximized as the decoded sequence.

Based on the sequence decoded, a second Matlab routine running on the same computer then activated an analog output channel on the NI DAQ I/O interface to go from 0V to either +5V or −5V for 500 ms. The voltage line was, in turn, connected to a second NI DAQ I/O input channel located on a third computer running the behavioral program. Depending on the voltage received, the cursor displayed in the middle of the screen moved in a straight line to one of the four possible target locations (e.g., +5V in I/O channel 1 corresponded to a cursor location within the top target). This process then repeated for the second decoded target after another artificially introduced time delay. Here, the time delays in the two generated movements were selected to be similar to those that the monkeys normally experienced when performing the standard task using a joystick. However, the NI DAQ could in principle generate the two movements in as little as a few milliseconds apart.

Behavior versus prediction errors

Since the primates did not perform the dual-target working-memory task with 100% behavioral accuracy, some of the BMI errors were due to behavioral errors (i.e., the monkey not remembering the correct sequence during working memory) as opposed to decoder errors. Hence a more relevant accuracy number for the performance of the BMI could be the sequence accuracy obtained during the training session using leave-one-out cross-validation. This is because in the cross-validation analysis we calculate the accuracy by comparing the decoded sequence with the sequence the monkeys actually select after the “go” cue. For the BMI sessions, however, we compare the decoded sequence to the instructed sequence to find the accuracy. We hence tested whether after taking into account the primates’ natural error rates, the accuracy during training sessions would be close to the BMI accuracy. Denoting the behavioral accuracy of the monkeys by Pb and the decoder accuracy found from the training session by Pt we can calculate what the accuracy of selecting the instructed sequence would be after taking into account the behavioral errors. Denoting the resulting accuracy by Pf we have that

[Formula ID: FD7]
In other words when the monkey and the decoder are both correct, the instructed sequence is selected. However, if the monkey is incorrect and the decoder is also incorrect in decoding the monkey’s intended sequence, the probability of the decoder selecting the correct instructed sequence by random chance is 1 / (S −1) . We can find the mean and s.e.m. of Pf from those of Pb and Pt assuming Pb and Pt are independent53 and then compare it with the BMI accuracy.


FN1Note: Supplementary information is available on the Nature Neuroscience website.

FN2AUTHOR CONTRIBUTIONS M.M.S. developed the real-time decoder, conceived and performed the computational analysis, assisted with animal recordings, and wrote the manuscript. R.C.H. and M.P. assisted with animal training and recordings. G.W.W. and E.N.B. were involved in the computational methodological development and edited the manuscript. Z.M.W. conceived and designed the study, developed the BMI system, performed the animal training and recordings and wrote the manuscript.

FN3COMPETING FINANCIAL INTERESTS The authors declare no competing financial interests.


R.C.U is funded by the NREF, E.N.B is funded by NIH DP1 OD003646, Z.M.W is funded by NIH 5R01-HD059852, PECASE and the Whitehall Foundation.

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