Edited by: Renée Morris, University of New South Wales, Australia
Reviewed by: Benzi Kluger, University of Colorado Denver, USA; Ian Q. Whishaw, University of Lethbridge, Canada
This article was submitted to Movement Disorders, a section of the journal Frontiers in Neurology.
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The joints of the hand provide 24 mechanical degrees of freedom. Yet 2–7 principal components (PCs) account for 80–95% of the variance in hand joint motion during tasks that vary from grasping to finger spelling. Such findings have led to the hypothesis that the brain may simplify operation of the hand by preferentially controlling PCs. We tested this hypothesis using data recorded from the primary motor cortex (M1) during individuated finger and wrist movements. Principal component analysis (PCA) of the simultaneous position of the five digits and the wrist showed relatively consistent kinematic synergies across recording sessions in two monkeys. The first three PCs typically accounted for 85% of the variance. Cross-correlations then were calculated between the firing rate of single neurons and the simultaneous flexion/extension motion of each of the five digits and the wrist, as well as with each of their six PCs. For each neuron, we then compared the maximal absolute value of the cross-correlations (MAXC) achieved with the motion of any digit or the wrist to the MAXC achieved with motion along any PC axis. The MAXC with a digit and the MAXC with a PC were themselves highly correlated across neurons. A minority of neurons correlated more strongly with a PC than with any digit. But for the populations of neurons sampled from each of two subjects, MAXCs with digits were slightly but significantly higher than those with PCs. We therefore reject the hypothesis that M1 neurons preferentially control PCs of hand motion. We cannot exclude the possibility that M1 neurons might control kinematic synergies identified using linear or non-linear methods other than PCA. We consider it more likely, however, that neurons in other centers of the motor system – such as the pontomedullary reticular formation and the spinal gray matter – drive synergies of movement and/or muscles, which M1 neurons act to fractionate in producing individuated finger and wrist movements.
The digits of the hand commonly have been thought to move independently of one another. But kinematic analysis has shown that simultaneous motion of multiple fingers occurs in virtually all human hand and finger movements. These include not only activities of daily living such as grasping and haptic exploration (
When simultaneous variation occurs in many independent elements – whether joint angles, muscles, or neurons – a limited variety of fixed patterns, or synergies, potentially can account for much of the simultaneous variation. The concept of synergies is useful, simplifying the problem of controlling all the original elements, primarily if the number of synergies needed to account for most of the variation in the data is substantially less than the number of original elements. Several different mathematical approaches, both linear and non-linear, might be used to identify such synergies, and which approach is most likely to capture synergies potentially used by the nervous system cannot be predicted.
Almost all prior studies of the kinematic synergies involved in hand movements have used a comparatively straightforward, linear approach – principal component analysis (PCA) (
These observations have led to the hypothesis that, at some level, the central nervous system (CNS) may simplify the computational burden of controlling the hand by driving PCs of hand kinematics. Patterns of simultaneous correlated movement kinematics, isometric forces, or muscle activity have been attributed variously to the spinal gray matter (
Many of the methods used in the present study for behavioral training, data collection, and initial analyses have been described in previous reports, and are summarized here as needed.
All care and use of these purpose-bred monkeys complied with the U.S.P.H.S. Policy on Humane Care and Use of Laboratory Animals, and was approved by the University Committee on Animal Resources at the University of Rochester. Each monkey was trained to perform visually cued individuated flexion and extension movements of the right hand fingers and/or wrist (
While behavioral performance depended only on the closing of the microswitches for the fingers and the level crossings for the wrist, a continuous analog signal representing the flexion/extension position of each digit was generated using a semiconductor strain gage (BLH SPB3-20-35) mounted on the lever-arm of each microswitch (
After training, aseptic surgery under isoflurane anesthesia was used to open a craniotomy over the left central sulcus at the level of the hand representation, and to implant both a rectangular Lucite recording chamber over the craniotomy and two head-holding posts. Once the monkey had recovered from this procedure and had become accustomed to performing the finger movement task with its head held stationary, EMG electrodes made of 32 gage, Teflon-insulated, multi-stranded stainless steel wire (Cooner AS632, Chatsworth, CA, USA) were implanted percutaneously using aseptic technique in 8–16 forearm and hand muscles under Ketamine anesthesia, using techniques adapted from those of Cheney and colleagues (
Thereafter in daily recording sessions, conventional techniques were used to record a single M1 neurons simultaneously with the analog signals representing the flexion/extension position of each digit and the wrist (sampled at 1 kHz) and with EMG activity from the implanted forearm and hand muscles (EMG amplification 2,000–100,000×, bandpass 0.3–3 kHz, sampling frequency ~4 kHz per channel) as the monkey performed individuated finger and wrist movements. During each recording session, two data acquisition interfaces were used to store data to disk on two host PCs, which also provided scrolling displays of all neuron, kinematic and EMG recordings (Power1401 interface, Spike2 software, Cambridge Electronic Design, UK). The same neuron data and behavioral event marker codes were stored in parallel in these two data streams, while the six kinematic signals were stored together on one system along with four EMG channels, and the remaining EMGs were stored on the other system. A third data acquisition interface and host PC running AVE software (courtesy Shupe, Fetz, and Cheney) were used concurrently to form initial on-line averages of rectified EMG for each channel using data segments extending ±50 ms from the time of all neuron spikes.
If we consider each original element (here the motion of each of the five digits and of the wrist) as a dimension in an abstract Euclidean space with orthogonal axes, we can consider our data (here the simultaneous positions of the five digits and the wrist at each time step) as a cloud of points in the six-dimensional space. If some of the original elements are correlated, then there will be a direction in this space that accounts for their simultaneous, correlated variation. PCA can be thought of as a translation of the origin and a rotation of the orthogonal axes such that as much of variance in the data points as possible lies along a single axis, which then is defined as that of the first PC (PC1) (
Two important differences exist, however, between the original axes and the PC axes: first, whereas projections of the data along the original dimensions may be correlated, projections of the data in the directions of the PC eigenvectors are uncorrelated. And second, whereas the original elements may each have any amount of variance, the PCs are rank-ordered according to the fraction of the total variance accounted for by each, with PC1 accounting for the most variance and progressively higher-order PCs accounting for progressively less variance. For purposes of identifying synergies and thereby reducing dimensions, low-order PCs are most likely to represent meaningful synergies while high-order PCs that account for little variance can be considered to be “noise” and disregarded.
For the present study, the kinematic data representing the flexion/extension position of each digit and of the wrist was normalized from −1 (greatest extension achieved by that digit) to +1 (greatest flexion achieved by that digit) across each recording session, and downsampled to 200 Hz. PCA performed on these normalized, six-dimensional kinematic data from each recording session then resulted in six PC eigenvectors (the translated and rotated basis of orthonormal unit vectors) rank-ordered according to the variance accounted for by each, and the temporal weighting of each eigenvector as a function of time throughout the recording session.
To enable cross-correlation of neuron firing rate with kinematic variables, each neuron’s spike train was converted to an analog representation of firing rate as a function of time as:
We then performed cross-correlation of each neuron’s instantaneous firing rate against each of the kinematic variables – both the six original digit and wrist positions and their six PCs – for leads and lags up to ±500 ms. Prior to cross-correlation, each signal was mean-zeroed and normalized such that the auto-covariance at zero lag was 1. Each cross-correlation was performed using data over the entire duration of the recording, which in monkey C averaged 777 ± 228 s (mean ± SD; range: 370–1550 s) and in monkey G averaged 690 ± 273 s (range: 178–1515 s).
The present data include 49 single-neuron recording sessions made during 38 daily microelectrode penetrations in monkey C, and 155 single-neuron recording sessions made during 83 microelectrode penetrations in monkey G (
Principal component analysis was performed on the kinematic data from each recording separately. Figure
The six eigenvectors derived by PCA are illustrated for four selected sessions from each monkey in Figure
To examine the consistency of the patterns identified by PCA across all recording sessions more objectively, we performed average-linkage cluster analysis on all six eigenvectors from all sessions, using 1 minus the absolute value of the dot product between eigenvectors as a distance measure. Because the dot product between two unit vectors will be 1 if they point in the same direction and −1 if they point in exactly opposite directions, two eigenvectors that point along the same line in the six-dimensional space will have a distance measure of 0, and two eigenvectors that are orthogonal to one another (dot product of 0) will have a distance measure of 1.
Initially, this cluster analysis was performed on all the sessions from each monkey separately. Figure
We therefore defined six kinematic synergies in each monkey by dividing the clustered eigenvectors into six groups of equal size, as illustrated by lines drawn on each distance matrix to create an evenly spaced, 6 × 6 square grid. If the eigenvectors had clustered into six perfectly distinct groups, with one eigenvector from each session in each group, then the six large dark regions along the main diagonal would have been perfectly delimited by these lines. While less than perfect, we felt that the borders of the dark regions were close enough to the squares delimited along the main diagonal for us to consider that the lines delimited six different kinematic synergies that were relatively consistent in each monkey. We refer to these six kinematic synergies as S1–S6.
To visualize each kinematic synergy, we vector-averaged all the eigenvectors assigned to a given synergy. Figures
The first synergy, S1, was characterized by motion of digits 3, 4, and 5 in the same direction, with d3 moving the most. In monkey C, S1 also included some motion of d2 and d6 in the same direction. S2 was dominated by movement of the wrist, d6. S3 was dominated by movement of the thumb, d1, with slight movement of d5 in the opposite direction. In monkey C, S3 also included some motion of d2 and d3 in the same direction as d1. S4 consisted primarily of motion of d2, in monkey C also including lesser motion of d4 and d5 in the opposite direction. S5 can be characterized as motion of d3 and d5 in opposite directions, in monkey G including motion of d4 in the same direction as d5. S6 comprises motion of d4 in one direction with motion of d3 and d5 in the opposite direction. The six average kinematic synergies found in the two monkeys thus were similar.
For each M1 neuron, we preformed cross-correlation of its firing rate separately against the simultaneously recorded position of each digit and of the wrist, as well as against the temporal weighting of each of the six PCs derived from that simultaneous position data. Figure
We reasoned that if an M1 neuron represented one of the kinematic synergies identified by PCA, then the cross-correlation of its firing rate with that synergy should be stronger than its cross-correlation with any of the individual digits or the wrist. For each monkey, we therefore plotted each M1 neuron’s MAXC with any of the digits against its MAXC with any of the average synergies. The resulting scatterplots are shown separately for the two monkeys in Figure
Because some M1 neurons correlated most strongly with a kinematic synergy (points above the line of unity slope) whereas others correlated most strongly with an original DoF (points below the line), we also considered the possibility that the transformation from synergies to the muscle activation needed to drive them might occur at least in part within M1. More specifically, M1 neurons with relatively direct output to spinal motoneuron pools, particularly groups of cortico-motoneuronal (CM) cells with output to a similar subset of muscles, might produce patterns of activation in multiple muscles that would facilitate a given synergy (
Each of the present neurons had been tested for such outputs with spike-triggered averaging of rectified EMG activity (
We also examined the distribution of MAXCs over the digits and kinematic synergies. The upper marginal histograms of Figure
Previous studies have identified kinematic synergies of human hand motion by applying PCA to joint angles monitored during various activities, including grasping (
The studies cited above generally have found that: (i) a small number of the lowest order PCs account for a substantial majority of the variance in the motion of multiple joints; (ii) the synergies identified by PCA generally were similar from one subject to another; and (iii) the lowest order PCs represent a fundamental opening and closing of the hand involving similar motion in the thumb and all four fingers. In the present study, we likewise found that (i) the first PC accounted for ~50% of the variance, and the first three PCs for ~85%; (ii) the synergies identified by PCA were relatively consistent across sessions and between monkeys, and (iii) the first synergy (typically PC1) represented motion of the fingers in the same direction, albeit to different degrees in the two monkeys. In these three respects, the synergies identified here with PCA are similar to those identified in previous studies, although the present monkeys were instructed to move only one finger at a time insofar as possible.
We examined the structure of the kinematic synergies identified by PCA (Figure
These features of the synergies identified with PCA may be related to findings on the relative independence of the digits and the structure of muscles in the macaque hand. Our previous studies of the individuated finger and wrist movement task performed by different monkeys demonstrated that the thumb, index finger, and wrist moved with more independence than the more ulnar digits – the middle, ring, and little fingers (
None of the kinematic synergies identified with PCA appeared to correspond to the activation of a particular muscle, however. Although S1 might be thought to reflect the action of the extrinsic multitendoned finger muscles – FDP, FDS, and EDC – in macaques FDP consists of two major compartments: FDPr, which exerts the most tension on d2, less on d3, and still less on d4; and FDPu, which exerts the most tension on d5 and d4 and less on d3 (
To some extent, the kinematic synergies identified here may reflect the particular mechanical constraints of the present individuated finger and wrist movement task (Figure
Overall, M1 neurons that had progressively stronger correlations with finger and wrist kinematics had stronger MAXCs with both synergies (or PCs) and original DoFs. If an M1 neuron specifically represented one of the kinematic synergies identified by PCA, then its firing rate would be expected to correlate more strongly with some synergy than with the motion of any of the individual digits or wrist. A minority of M1 neurons in each monkey – those represented by points lying above the line of unity slope in Figure
Although we found little evidence that kinematic synergies are represented by M1 neurons more strongly than the original digit and wrist DoFs, our findings do not exclude a number of other possible ways in which synergies might be used by the CNS in controlling movement of the wrist, hand and fingers. First, methods other than PCA, either linear (e.g., independent component analysis), or non-linear (e.g., Isomap), may be necessary to identify kinematic synergies used by the nervous system. Second, although here we used digit and wrist positions as the original DoFs, synergies of other kinematic, and/or dynamic DoFs – such as velocity (
Much of the basic generation of such muscle synergies might occur at subcortical levels, including the PMRF and the spinal gray matter. Neurons in the intermediate zone of the lumbar spinal gray of the spinalized frog provide premotor drive for a limited number of muscular synergies (
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
This work was funded by National Institutes of Health R01s EB010100 and NS065902. The authors thank Marsha Hayles for editorial comments.