1Departments of Neurology, 2Neurobiology and Anatomy, 3Brain and Cognitive Science, 4Physical Medicine and Rehabilitation, 5The Center for Visual Science, and 6The Brain Injury Rehabilitation Program at St. Mary's Hospital, University of Rochester School of Medicine and Dentistry, Rochester, New York, 14642
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ABSTRACT |
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Poliakov, Andrew V. and Marc H. Schieber. Limited Functional Grouping of Neurons in the Motor Cortex Hand Area During Individuated Finger Movements: A Cluster Analysis. J. Neurophysiol. 82: 3488-3505, 1999. Primary motor cortex (M1) hand area neurons show patterns of discharge across a set of individuated finger and wrist movements so diverse as to preclude classifying the neurons into functional groups on the basis of simple inspection. We therefore applied methods of cluster analysis to search M1 neuronal populations for groups of neurons with similar patterns of discharge across the set of movements. Populations from each of three monkeys showed a large group of neurons the discharge of which increased for many or all of the movements and a second small group the discharge of which decreased for many or all movements. Two to three other small groups of neurons that discharged more specifically for one or two movements also were found in each monkey, but these groups were less consistent than the groups with broad movement fields. The limited functional grouping of M1 hand area neurons suggests that M1 neurons act as a network of highly diverse elements in controlling individuated finger movements.
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INTRODUCTION |
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Classification of neurons into groups based on
similar patterns of discharge is a traditional approach to analysis of
neuronal populations. Classification schemes may be suggested by
externally observable features. Neurons of the primary motor cortex
(M1) hand area, for example, might be classified into different groups apparently controlling different digits of the hand, as suggested by
the iconic motor homunculus and simiusculus (Penfield and
Rasmussen 1950; Woolsey et al. 1951
).
Alternatively, M1 neurons might be grouped according to which muscles
or which movements they seem to control (Humphrey 1986
;
Phillips 1975
). Recent evidence indicates, however, that
single M1 neurons discharge during movements of several different
fingers (Schieber and Hibbard 1993
) and that the outputs
of many single corticospinal neurons diverge to innervate multiple
spinal motoneuron pools (Buys et al. 1986
; Fetz
and Cheney 1980
; Kasser and Cheney 1985
;
Lemon et al. 1986
; Mantel and Lemon 1987
;
Porter and Lemon 1993
; Shinoda et al. 1979
,
1981
). These findings call into question whether or not groups
of M1 neurons control particular digits, movements, muscles, or
combinations thereof.
Other schemes for grouping neurons might be based on more abstract
constructs. A number of recent theoretical considerations have raised
the possibility that neural control of finger movements could rely on
constructs that would reduce the high number of mechanical degrees of
freedom inherent in the fingers. For example, much of the human hand's
movement and posture can be represented by a small number of principle
components (PCs), where each PC represents simultaneous changes in the
angles of all joints in the hand (Santello and Soechting
1997; Soechting and Flanders 1997
). Others have
raised the possibility that the CNS might use movement primitives
(Giszter et al. 1993
) or virtual fingers (Arbib et al. 1985
; Iberall and Fagg 1996
) to combine
the motion of multiple joints or fingers into a single controlled unit.
Groups of neurons with similar discharge patterns might represent
constructs such as PCs, movement primitives or virtual fingers, but
such groups would not necessarily be apparent if M1 neurons were
classified into groups based on simply observed features like body
part, muscle, or movement.
Yet another possibility, however, is that the discharge of a given
motor cortex neuron represents multiple features of movement and/or
multiple body parts, with the relative weighting of different movement
features and/or body parts varying from neuron to neuron (Ashe
and Georgopoulos 1994; Fu et al. 1995
;
McKiernan et al. 1998
; Schieber and Hibbard
1993
). In this case, M1 neurons would form a highly diverse
population, without distinct groups of M1 neurons representing
particular body parts, movements, muscles, PCs, primitives or virtual
fingers. Such diversity of the M1 neuronal population might be
relatively inapparent when examined during behavioral tasks involving
only a small number of reciprocal movements (e.g., flexion/extension
about a single joint) or a family of similar natural movements (e.g.,
reaching in different directions). Diversity might be much more
apparent during performance of highly skilled behaviors that require M1
activity to individuate more sophisticated movements from more
rudimentary, fundamental movements (Schieber 1990
;
Schieber and Poliakov 1998
). Diversity of the M1
neuronal population might contribute to an extensive repertoire of
skilled movements.
In the present work, we recorded the activity of single M1 neurons as highly trained monkeys performed a set of skilled, individuated finger movements. Because the M1 neurons appeared quite diverse, we applied methods of cluster analysis to objectively examine M1 populations for groups of neurons with similar patterns of discharge across the set of individuated finger movements. In this application, cluster analysis had the important advantage of requiring no a priori assumptions about the nature of the groups to be identified. Such groups in theory could represent anything from concrete, externally observable features such as particular digits to more abstract constructs such as movement primitives. We also used clustering algorithms that made no a priori assumptions about the number of groups to be identified.
Cluster analysis revealed only two functional groups that were present
consistently in the neuronal populations recorded from each of three
monkeys: one large group of neurons that discharged for many or all
finger movements and a second smaller group of neurons the tonic
discharge of which paused during many or all movements. Although a few
small groups of relatively movement-specific neurons were found in each
monkey, these groups were less robust than the two groups with broad
movement fields, differed from monkey to monkey, and failed to account
for all the movements performed by each monkey. Many task-related
neurons did not fall into any definable group. Our findings suggest
that M1 neurons do not form large functional groups representing either
concrete features or abstract constructs. Instead, we suggest that in
controlling individuated finger movements M1 neurons act as a network
of highly diverse elements. A preliminary report of this work has
appeared in abstract form (Poliakov and Schieber 1998).
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METHODS |
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All procedures for the care and use of these purpose-bred monkeys complied with the United States Public Health Service Policy on Humane Care and Use of Laboratory Animals, followed the Public Health Service Guide for the Care and Use of Laboratory Animals, and were approved by the appropriate Institutional Animal Care and Use Committee.
Visually cued individuated finger movement task
Three juvenile (~4-6 yr old) male rhesus monkeys
(Macaca mulatta; K, 6 kg; A, 5 kg; and
C, 7 kg) were trained to perform visually cued individuated
finger movements. The behavioral paradigm, and the finger movements
made by monkey K, have been described in detail previously
(Schieber 1991). The monkey's elbow was restrained in a
molded cast, and the right hand was placed in a pistol-grip manipulandum that separated each finger into a different slot. At the
end of each slot, each fingertip lay between two microswitches. By
flexing or extending a digit a few millimeters, the monkey closed the
ventral or dorsal switch, respectively. This pistol-grip manipulandum
was mounted, in turn, on an axis permitting flexion and extension wrist
movements. A potentiometer coupled to the axis transduced wrist motion,
and the output of this potentiometer was fed to level-crossing circuits
that simulated flexion and extension switches for the wrist.
The monkey viewed a display on which each digit (and the wrist) was represented by a row of five light-emitting diodes (LEDs). The middle, yellow LED in a row was illuminated when neither the flexion or extension switch for that digit was closed. One of two green LEDs on either side of the middle yellow LED was lit whenever the flexion (leftward green LED) or extension (rightward green LED) switch was closed. When the monkey flexed or extended a digit, closing a microswitch, the middle yellow LED went out and the leftward or rightward green LED came on. The yellow and green LEDs thus informed the monkey which switches were open and which were closed. Red LEDs at either end of the row were illuminated as cues instructing the monkey to close either the flexion (leftward red LED) or extension (rightward red LED) switch.
The monkey initiated each trial by placing all digits and the wrist in their middle positions, so that no switches were closed and the middle yellow LED in each row was illuminated. After a pseudorandomly varied initial hold period of 500-750 ms, one red LED was illuminated under microprocessor control, instructing the monkey which switch to close (or to move the wrist). If the monkey closed the instructed switch within the 700-ms allowed response time after illumination of the red LED and held it closed for a final hold period (500 ms for monkeys K and C; 300 ms for monkey A) without closing any other switches, then the trial had been performed correctly and the monkey received a water reward. After each rewarded trial, the finger movement to be instructed for the next trial was rotated in a pseudorandom order. Consecutive rewarded (correctly performed) trials of a given instructed movement therefore did not occur immediately after one another but instead were separated by trials of other instructed movements. In contrast, if the monkey failed to perform correctly-either by failing to close the instructed switch within the allowed 700-ms response time or by closing another switch before or after the instructed switch-no reward was delivered, and the same instruction was presented again for the next trial. (This protocol ensured that the monkey could not intentionally fail trials of difficult movements and earn rewards only on trials of easier movements.) After each trial, a minimum intertrial interval (1000 ms for monkey K; 500 ms for monkeys A and C) was required before the monkey could initiate the next trial. Because the monkey had to initiate each trial by actively placing all digits and the wrist in their middle positions, the actual intertrial interval was variable, determined in part by the monkey.
Examination of the finger movements generated by monkeys performing
this task showed that in each rewarded trial, the digit the monkey had
been instructed to move underwent more movement than any other digit
(Schieber 1991). Moreover, each digit had its greatest
excursion when it was the instructed digit. In some movements,
particularly when the monkey was instructed to flex the thumb or wrist,
other digits remained stationary. In other movements, however,
noninstructed digits moved to a greater or lesser degree. Each movement
is therefore referred to as an instructed movement of a
given digit in a given direction, recognizing that there was often some
movement of noninstructed digits. For brevity, each instructed movement
is denoted by the number of the instructed digit (1 for the thumb
through 5 for the little finger, W for the wrist), and the first letter
of the instructed direction (f for flexion, e for extension). Thus
"2f" denotes instructed flexion of the index finger.
Monkeys K and C were trained to perform 12 different finger and wrist movements. Monkey A, in contrast,
was trained to perform only six movements
1f, 2f, 3f, 4f, 2e and
3e
all with the wrist axis fixed.
Neuron recording
Trained monkeys were prepared for single-unit recording by
surgically implanting both a head-holding device and a rectangular Lucite recording chamber that permitted access to an area encompassing M1 contralateral to the trained hand. A few days after this procedure, daily 2- to 3-h recording sessions began. In each session, as the
monkey performed the individuated finger movement task, a Trent-Wells
hydraulic microdrive mounted on a custom XYZ micropositioner was used
to advance a Pt/Ir microelectrode (0.5-1.5 M impedance) into the
cortex. Signals from the microelectrode were filtered (300 Hz to 3 kHz), amplified 10,000 times, and monitored continuously on an
oscilloscope and audiomonitor headphones. Single neuron action
potentials were discriminated with a dual time/amplitude window and
monitored by overlapping waveforms on a storage oscilloscope. Times of
discriminated potentials were collected and stored to computer disk
along with behavioral event marker codes.
In many microelectrode penetrations, intracortical microstimulation
(ICMS) was used to confirm the location of the M1 hand area. The
connections of the microelectrode were switched from the recording
preamplifier to a stimulus isolator (BAK BSI-1) and trains of 12, biphasic, 200-µs, 5- to 40-µA constant current pulses at 330 Hz
were delivered as the awake monkey performed the finger movement task.
ICMS was triggered under computer control as the monkey waited in the
task's initial hold period for a instruction cue or by the
investigator as the monkey rested quietly between trials. Responses to
ICMS were identified in monkey K by observing evoked
movements of the fingers or wrist and by palpating contractions of
forearm muscles. In monkeys A and C, ICMS
responses also were identified in averages of rectified electromyograms
(EMG) recorded through percutaneously implanted electrodes using both
conventional trains and single-pulses of ICMS (Cheney and Fetz
1985; Cheney et al. 1985
). Placement of
electrodes in each muscle was confirmed by observing that movement
appropriate for the muscle was produced by tetanic electrical
stimulation (trains of 12 biphasic, 0.2-ms, 50- to 6,000-µA, pulses
at 100 Hz) delivered between the bipolar electrode pair implanted in
that muscle. In each of the three monkeys, the cortical territory from
which ICMS evoked visible finger movements or EMG responses was
coextensive with the region containing task-related neurons.
Histology
After the completion of all experiments on monkeys K
and A, electrolytic lesions were made by passing DC current
(40 µA for 40 s) through a microelectrode at selected locations.
Several days later, the monkey was tranquilized with Ketamine (10 mg/kg im), killed by lethal injection of thiopental (300 mg/kg iv), and
perfused transcardially with phosphate-buffered saline followed by
phosphate-buffered 4% paraformaldehyde. Before removing the brain from
the cranium and photographing the cortical surfaces, marking ink tracks
were placed at selected locations around the recording sites via a
needle mounted on the same microdrive. Frozen sections of both
hemispheres were cut in the coronal plane at 30 µm, and every fourth
section was mounted and stained for Nissl substance. The location of
microelectrode penetrations was reconstructed based on examination of
these sections. When particular penetration tracks could not be
identified in the histological material, their locations were
interpolated based on the locations of identified tracks, electrolytic
lesions, and postmortem inked tracks. Histological confirmation of
penetration locations in monkey C are unavailable at present
because monkey C continues to be a subject in other studies.
Nevertheless, the use of ICMS gives us a high degree of confidence that
neurons recorded from monkey C were located in the M1 hand
area (Widener and Cheney 1997).
Data analysis
To determine whether each recorded M1 neuron was related to the
individuated finger movements performed by the monkey, we tested the
null hypothesis that the neuron's firing rate modulation during the
1 s preceding the end of the movement (switch closure) could have
occurred by chance alone. For each instructed movement, we compiled a
histogram (20-ms binwidth) of the neuron's spike discharge during all
correctly performed trials, aligning the data at the time of switch
closure in each trial (e.g., Fig. 2). We then averaged the neuron's
firing rate across the entire 1-s period preceding switch closure. If
variation in the neuron's firing rate from bin to bin had been
unrelated to performance of the instructed movement, then deviations
from the average rate for the entire 1 s would have resulted from
chance alone. We therefore used a two-tailed Kolmogorov-Smirnov test to
compare nonparametrically the neuron's firing rate in the bins of the
histogram with hypothetical constant firing at the average rate for the
1 s preceding switch closure. To apply this test, the maximal
deviation (D) between the cumulative sums for the neuron's
histogram and the hypothetical constant average firing rate was found.
The null hypothesis for a given instructed movement was rejected at
P = 0.05 when D exceeded the critical value
of 1.36/n where n is the number of spikes contributing to the neuron's histogram during the 1 s preceding switch closure. Given that several movements were tested, however, a
Bonferroni correction for multiple tests was applied. To test the
hypothesis that a neuron was related to at least one of several instructed movements at the P = 0.05 confidence level,
the P value for at least one of the m movements
performed by the monkey should reach 0.05/m. For
monkeys K and C that performed 12 movement, we
therefore used a critical P value of 0.05/12 = 0.004167. For monkey A, which performed six movements, we
used 0.05/6 = 0.008333. The corresponding critical value for the
cumulative sum deviation, D, was interpolated from tabulated
critical values for the Kolmogorov-Smirnov test. Only neurons found in
this way to be related to at least one of the instructed movements
performed by each monkey were included in the populations used for
cluster analysis.
For purposes of cluster analysis, we characterized each neuron's firing rate modulation during each instructed movement with a single numeric discharge measure. Initially, we used the change (CH) in firing for each movement, calculated by subtracting the average firing rate during a 200-ms baseline period (1,000-800 ms before switch closure) from the average firing rate during the 100 ms immediately before switch closure. Subsequently we repeated the cluster analyses with two additional discharge measures. For a second discharge measure, we used a baseline period from 1,000 to 700 ms before switch closure and thereafter computed the cumulative sum, using the sum at the time of switch closure as a discharge measure (CU), thus integrating the discharge over the preceding 700 ms. For a third measure, we computed the average firing rate during the 100 ms immediately before switch closure without subtracting a baseline value (FR). Note that unlike the first two methods, FR values can only be positive or zero; this would fail to reflect that neurons with tonic, baseline discharge might have shown a decrease in firing rate during a particular movement. The cluster analyses described below thus were repeated on the neuronal population from each monkey using three different discharge measures: CH, CU, and FR.
Each neuron's discharge across the instructed movements then could be characterized by a 12-dimensional vector consisting of the neuron's discharge measures during each of the twelve movements. For monkey A, discharge measures for the six movements not performed were set to zero. To search for neurons with similar relative patterns of discharge across the movements rather than similar absolute discharge, we normalized each neuron's vector to unit length by dividing each discharge measure by the sum of the root mean squares of the 12 values. The unit vectors of all neurons thus were normalized to lie on the surface of an imaginary 12-dimensional sphere.
To apply a cluster analysis procedure to our neuronal populations, a
measure of similarity between any two neurons had to be established.
Because a 12-dimensional unit vector was assigned to every neuron based
on its relative discharge across the 12 movements, we defined the
similarity of two neurons, Sij, as the Euclidean distance in 12-dimensional space between their unit vectors
vi and vj,
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Agglomerative, hierarchical techniques were implemented for clustering
(Johnson and Wichern 1992). To apply these techniques to
N neurons, we started with N clusters, each
containing a single neuron. An N × N symmetric matrix
of similarities, S, then was calculated, and the pair of
clusters closest to each other was identified. These were merged to
form a new cluster. Then the similarity matrix was updated, and the
next step of clustering was performed, etc., until all neurons were
merged into one cluster. To ensure that the results of clustering were
not critically dependent on the clustering method, we repeated the
cluster analyses on the neuronal population from each monkey using two
alternative methods: single linkage and average linkage. These methods
differ in how the distance between two clusters is defined. In the
single-linkage method, the distance between two clusters was defined as
the minimum distance between any two individual neurons from the two
clusters. In the average-linkage method, the unit vectors of all
members of each cluster were averaged, and the distance between two
clusters was defined as the distance between their average vectors. The average-linkage method thus agglomerates nearby members of the population around their common mean until the space near the mean is
devoid of nearby members, whereas the single-linkage method links an
existing cluster to whatever member of the population is close to any
member of the existing cluster. Consequently, the single-linkage method
tends to create somewhat smaller groupings than the average-linkage method.
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RESULTS |
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We recorded 133 task-related M1 neurons in the left hemisphere of
monkey K, 241 in monkey A, and 177 in
monkey C. Whereas the neurons from monkeys A and
C have not been described in other reports, 115 of the
neurons from monkey K have been included in a previous
analysis of the spatial distribution of neuronal activity in M1 during
individuated finger movements (Schieber and Hibbard 1993) and in a study using population vector analysis to show that the instructed movement performed is encoded in the discharge of
the M1 neuronal population (Georgopoulos et al. 1999
).
Eighteen more neurons from monkey K are included in the
present analysis because we used a slightly less stringent criterion
for selecting task-related neurons. The 61 neurons from monkey
S included in these previous studies were not included in the
present analysis because we felt this population was too small to
provide meaningful results with cluster analysis. Figure
1 shows the locations of the
microelectrode penetrations in which the present neuronal populations
were recorded in monkeys K and A. (Reconstruction of microelectrode penetrations in monkey C is unavailable,
as this monkey is currently the subject of additional studies.) Most of
these M1 neurons were located in the anterior bank and lip of the
central sulcus, rather than on the convexity of the precentral gyrus.
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Diversity of discharge patterns
A striking feature of neurons in the population from each monkey
was the wide variety of discharge patterns observed across the
different individuated finger and wrist movements. As illustrated in
Fig. 2, some neurons discharged in
relation to only one or two instructed movements. K13409,
for example, discharged bursts consistently during trials of movement
2e, discharged a few sporadic spikes during trials of 3e, 4e, or We,
and remained silent during other movements. The firing rate of most M1
neurons, however, varied significantly in relation to several movements
(Schieber and Hibbard 1993). The discharge of some
contained a broadly tuned component that varied systematically in
relation to the spatial geometry of the hand. Neuron K19801,
for example, generally discharged more for flexion movements than for
extensions and also discharged for thumb extension (1e), while
discharging little for extension of the index, middle, or ring finger
(2e, 3e, or 4e) and showing a slight increase in firing during
extension of the little finger or wrist (5e or We). But the discharge
of many other neurons did not vary in an orderly fashion.
K23505, for example, discharged bursts during trials of 3f
and 4f, and smaller bursts during 1f and 1e, but did not discharge
during trials of 2f. The discharge of such neurons could not be
described fully as varying continuously in relation to the spatial
geometry of the hand.
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Figure 3 illustrates the diversity of
discharge patterns across the different instructed movements observed
for all task-related M1 neurons in monkeys K, A, and
C. Here, each neuron is represented by a column; the columns
are arranged according to the order in which the neurons were recorded,
from left to right. Each of the 12 instructed movements is represented
by a row. The columns and rows define cells in which the normalized
firing rate change (CH) of that neuron (column) during that instructed
movement (row) is displayed using a color scale from +1 (dark red) to
1 (dark blue). The 12 cells in the column for each neuron thus
summarize the neuron's discharge pattern across the 12 instructed
movements by displaying the values of the 12-dimensional unit vector
representing that neuron's normalized increase (yellow to red) or
decrease (light to dark blue) in discharge during each movement, from
1f (bottom) to We (top). The diversity of these discharge patterns precluded our using inspection to classify the neurons into categories such as "thumb-related" or "flexion-related" neurons.
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Cluster analysis of EMG activity
For comparison with M1 neuronal activity, and to test our clustering methods, we performed a cluster analysis of EMG activity recorded from nine forearm muscles: flexor digitorum profundus, radial region (FDPr); flexor digitorum profundus, ulnar region (FDPu); flexor digitorum superficialis (FDS); palmaris longus (PL); extensor digiti secundi et tertii (ED23); extensor digitorum communis (EDC); extensor digiti quarti et quinti (ED45); extensor carpi radialis (ECR); and extensor carpi ulnaris (ECU). EMG recordings from these nine muscles were made simultaneously with the recordings of 10 neurons included in the population from monkey C as the monkey performed the individuated finger movement task. The raw activity from the intracortical microelectrode (ME) also was recorded in these 10 sessions, and we included these continuous waveform recordings in the cluster analysis with the EMG recordings. The change (CH) in activity for each of these 10 recordings (9 EMGs + 1 ME) from each of 10 sessions was computed from histograms of rectified waveforms averaged over all correctly performed trials of each instructed movement, parallel to the analysis of single neuron activity (see METHODS). The bottom display of Fig. 3 shows the 12-dimensional unit vectors for each of these recordings, again in the order in which they were recorded. Although at first glance these recordings may appear to be as diverse as the neuron recordings, because the monkey performed the finger movement task in a relatively stereotyped fashion each day, we anticipated that the EMG activity of a given muscle would show a similar pattern each day. Indeed, scanning the EMG unit vector display in Fig. 3 from left to right suggests a pattern repeating every 10 columns.
Figure 4 shows the results of single linkage clustering applied to this population of 100 EMG and ME recordings. In Fig. 4B, the order of the recordings shown in Fig. 3 EMGs, has been rearranged by the clustering process. The process began with each recording treated as a cluster. In reiterative steps, the most similar two clusters were identified and merged, creating progressively larger and larger clusters, until finally all the recordings were merged into a single cluster. As each step merged two clusters, the columns representing the recordings of one cluster were taken out of their position along the horizontal axis and placed next to the columns representing recordings of the other cluster. (Consequently, the position of groups at the end of the process depended in part on where similar members of the population were located before clustering, and in part on which members were most similar, i.e., clustered first.) The column representing each recording in Fig. 3 EMGs, therefore has been moved next to the columns representing other recordings with similar activity patterns across the 12 instructed movements (i.e., close on the 12-dimensional sphere) in Fig. 4B.
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The clustering process successfully grouped all the 10 recordings made
from each of seven musclesFDPr, ED23, ECR, FDS, FDPu, EDC, and
PL
which appear in Fig. 4B as bands with horizontal rows of
similar color 10 columns wide. For example, the 10 recordings from FDPr
(Fig. 4B, far left) all had greatest EMG activity during instructed movement Wf, which appears as a horizontal red band in the
6th row from the bottom (arrowhead); each FDPr
recording also had substantial activity during 2f and 5e; this appears
as yellow-orange bands in the 2nd and 11th rows, respectively. In contrast, the 10 recordings from ED23 all had greatest EMG activity during instructed movement 5f as well as substantial activity during
1e, 2e and 3e. ED23 recordings therefore appear as a group 10 columns
wide, with a red horizontal band in the fifth row from the
bottom (5f), and yellow-orange horizontal bands in the
seventh-ninth rows (1e, 2e, 3e). [Note that
during individuated finger and wrist movements performed by
monkey C, as described in detail previously for other
monkeys (Schieber 1995
), a given muscle was not
necessarily most active as a prime mover of the digits it serves. FDPr
was most active as a wrist flexor. ED23 was most active in limiting flexion of digits 2 and 3 during 5f. And similarly, FDPu was most active in limiting extension of digit 5 during 4e.] The EMG recordings from ED45 and ECU were so similar that the cluster analysis did not
separate them, and recordings from these two muscles are intermingled in the 20 columns in Fig. 4B, far right. Of the 10 microelectrode recordings, 6 showed increased activity during most of
the movements and were grouped together by the clustering process
(ME*); the other 4 each showed a different pattern and were left as
isolated columns (*).
Figure 4A shows the corresponding dendrogram. Here the
recordings are represented by vertical lines rising from the abscissa in the same left-to-right order as in Fig. 4B. Horizontal
lines join the vertical lines for two recordings at the ordinate value representing the distance between the two recordings in the
12-dimensional space. As additional recordings are agglomerated onto
existing clusters of two or more, horizontal lines join the vertical
line representing each newly added recording to a vertical line
extending upwards from the existing cluster. The ordinate value of this horizontal line represents the distance from the newly added recording to the closest member of the existing cluster. To help identify major
groups, the blue lines have been replaced with red lines when the two
clusters being merged each already included 3% of the entire
population. The dendrogram thus provides a more quantitative view of
the groupings formed by the clustering process: the more the members of
a group are similar to one another, the lower along the ordinate are
the horizontal lines joining them; the more distinct the group's
members are from other members of the population, the longer the next
vertical line segment above joining that group to other members of the
population. The dendrogram of the clustered EMG recordings indicates
that the recordings obtained from a given muscle in different sessions
generally were very similar to one another-being joined at low
ordinate values
and that the recordings from different muscles (except
for ED45 and ECU) were relatively distinct
with long vertical lines
joining the group of recordings from one muscle to the group from another.
Figure 4C shows the corresponding similarity (or distance) matrix. Here, each recording is represented in the same order as in B along both the abscissa and the ordinate. The distance in the normalized 12-dimensional space between each possible pair of recordings is displayed in the appropriate cell using a color scale to represent values from 0 (dark blue) to 2 (dark red). Note that this color scale for the similarity matrix (C) has an entirely different meaning than the color scale for the unit vector display (B). Similarity matrix cells representing the distance between two similar recordings are dark blue because the distance between the two recordings in the 12-dimensional space is close to the minimum possible distance of 0. Similarity matrix cells representing the distance between two dissimilar recordings are yellow, orange, or red because the distance between the two recordings is closer to the maximum possible distance of 2. Because the similarity matrix is symmetric about its main diagonal and because the values along the main diagonal all are 0, only the cells above the main diagonal are shown. In the similarity matrix, groups of similar recordings appear as blue triangles with hypotenuses along the main diagonal. The distances between the contiguous recordings in these groups are low (blue), indicating that the unit vectors of these recordings are close on the 12-dimensional sphere, i.e., the recordings are similar. The degree to which the edges of these blue triangles are sharply defined (vs. blending gradually into green, yellow, orange, and red) provides another indicator of the degree to which the clustered recordings are distinct from other somewhat similar recordings. The larger squares of warmer colors away from the main diagonal provide an indication of the distance between each grouping represented along the main diagonal. For example, the large yellow-orange square at the intersection of the FDPr columns and the ED23 rows indicates that the FDPr and ED23 recordings were relatively dissimilar, whereas the large light-blue square at the intersection of the EDC columns and PL rows indicate that the EDC and PL recordings were relatively similar.
The dendrogram (A), unit vector display (B), and similarity matrix (C) thus provide complementary information on groups of recordings with similar activity patterns across the 12 instructed movements. The dendrogram provides a linear picture of the distance between members of a group and the distance between groups. The unit vector display provides a picture of the features of activity across the 12 instructed movement that render the members of a group similar. The similarity matrix provides a picture of the degree of similarity or dissimilarity between each group. Overall, the EMG recordings from each muscle were highly similar, clustering into a group, which in turn was relatively distinct from the groups of recordings from other muscles as well as being distinct from the ME recordings, which did not all cluster into a single group. These results indicate that the monkey used a stereotyped pattern of EMG activity to perform the task from session to session, while at the same time demonstrating that groups of similar recordings were formed by the clustering process. Such clear groupings were not produced, however, when the same clustering methods were applied to populations of single M1 neurons.
General results of cluster analysis of M1 neuronal populations
Because we could not classify M1 hand area neurons by simple inspection and because many neurons could not be treated as broadly tuned, we applied cluster analysis to examine the neuronal population in each monkey for groups of neurons the discharges of which varied similarly across instructed movements. The results of single linkage clustering of the M1 neuronal populations recorded from monkeys K, A, and C are shown in Figs. 5-7, respectively. The general results of clustering were consistent across all three monkeys. The largest group always consisted of neurons the discharges of which increased for many or all of the instructed movements performed by the monkey. This group appears in the neuronal unit vector displays (B in Figs. 5-7) as a broad band of columns containing predominantly yellow, orange, and red cells located toward the right of the display. In the similarity matrix (C in Figs. 5-7), this group appears as a large blue triangle toward the right of the matrix. The borders of the blue triangle are not necessarily sharply defined, indicating that this group of neurons was not necessarily distinctly isolated from other members of the population. The dendrograms (A in Figs. 5-7) show that members of this group were relatively close to one another, agglomerating at distances from ~0.2 to 0.5. The absence of long vertical lines leading upward from this group in the dendrogram again indicates that the group was not sharply isolated from other members of the population. Defining the movement field of a given neuron as the set of instructed movements in relation to which that neuron discharged, this large group can be described as consisting of neurons with broad field excitation (BFE).
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A second, smaller group also appeared in each monkey. This group was composed of neurons the discharges of which decreased for most or all instructed movements, which we describe as broad field inhibition (BFI). The BFI group appears as several contiguous columns of light blue to dark blue cells toward the left end of each neuronal unit vector display (Figs. 5B-7B), with a corresponding blue triangle against the main diagonal of the similarity matrix below (Figs. 5C-7C). The column of red cells rising above the BFI group's blue triangle in each similarity matrix indicates that most other neurons of the population were quite unlike neurons of the BFI group. Nevertheless, like the BFE group, the BFI group was not necessarily sharply isolated from other members of the population. Compared with the BFE group, members of the BFI group were less similar, agglomerating at larger distances of ~0.3-0.9 (Figs. 5A-7A).
Other small groups in each monkey were characterized by more specific movement fields. The nature of these small groups varied from monkey to monkey, however. For example, whereas monkey K had one group of neurons that discharged almost exclusively for movement 1f, monkey C had no 1f group but rather had a 5f group that was not found in monkey K. The members of these other small groups generally were separated by distances intermediate between the BFE and BFI groups. Like the BFE and BFI groups, these other small groups were not necessarily sharply isolated from other members of the neuronal population in each monkey. Many other neurons did not fall into any sizable group. Such neurons can be viewed as lying in the interstices between groups. As the clustering process proceeded from closest neurons to most distant (from lowest to highest horizontal lines of the dendrograms in Figs. 5A-7A), the BFE group formed a core onto which the smaller groups and the interstitial neurons gradually were agglomerated.
Nonrandom features of the M1 population
The diversity of the neuronal population in each monkey, the limited number of groups apparent in the cluster analysis, and the fact that the groups were not sharply demarcated from other members of the population, all raised the possibility that the observed groupings could have arisen by chance alone. To examine this possibility, we performed cluster analyses on two imaginary neuronal populations.
First, we created a population of 177 neurons (equal to the number of
neurons in the population from monkey C) in which the discharge measure for each neuron during each instructed movement was
chosen randomly with an even distribution from 1 to +1. These values
were normalized to unit vectors for each neuron and then clustered
using the single-linkage algorithm (Fig.
8). In comparison with the real neuronal
populations, this randomized population lacked neurons that discharged
much more intensely for one instructed movement than for any others
(Fig. 8B). Such movement-specific neurons appeared as
columns with one dark red cell in the unit vector displays of the real
populations (Figs. 5B-7B).
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Clustering of this randomized population showed that its most similar neurons were separated by distances >0.4, whereas in each of the real populations several small groups started to form at distances <0.4. Furthermore clustering of this random population produced no BFE, BFI, or other groupings like those seen in the real populations. The dendrogram revealed no clusters of short vertical lines; the unit vector display showed no columns of similar neurons; and the similarity matrix showed no dark blue triangles against the main diagonal. This randomized population thus was much more evenly distributed in the 12-dimensional clustering space than any of the three real neuronal populations. These observations suggest that the real neuronal populations did contain groups of neurons the similarity of which was not the result of random variation in neuronal discharge from one instructed movement to the next.
An important difference between this random population and the real neuronal populations, however, lies in the distributions of their discharge measures. Whereas discharge in the randomized population varied evenly from negative to positive and was symmetric about zero, the discharge distribution of a real population of cortical neurons is neither even from maximum to minimum nor symmetric about zero discharge. We therefore generated a second imaginary population in which the discharge measures from the real population of monkey C were reshuffled randomly. This process maintained the same distribution of discharge measures for the imaginary population as a whole (Fig. 9D), while eliminating any association of particular discharge values during particular instructed movements in single neurons.
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Figure 9 shows the results of clustering this randomly reshuffled population. Most striking again was the absence of groups characterized by BFE and BFI. In place of these BFE and BFI neurons, however, the randomly reshuffled population had many neurons that discharged much more intensely for one instructed movement than for any others, appearing as columns with single dark red cells in the unit vector display (Fig. 9B). Indeed, whereas only a few groups of neurons so selective for a particular instructed movement appeared in the real population from each monkey, such groups appeared for many instructed movements in the randomly reshuffled population. The occurrence of these groups reflects the fact that the distribution of real discharge measures included many small positive values and only a few large positive values (Fig. 9D). One large value thus frequently was associated with 11 much smaller values by chance alone. Unlike these groups of neurons that discharged selectively for a particular movement in the real neuronal populations, however, the minimum distance separating these similar neurons in the randomly reshuffled population was >0.4.
The occurrence of a large number of BFE neurons in each monkey therefore did not result simply from chance association of increased discharge during multiple instructed movements in a single neurons. Likewise, the groups of BFI neurons did not result from chance association of decreased discharge during multiple movements. Such results suggest that neurons in the BFE and BFI groups are likely to have functional importance in cortical control of individuated finger movements.
Reproducibility of functional groups
That most of the functional groups identified by the present cluster analysis were not sharply isolated from other members of the neuronal population, that the movement fields characterizing the more movement specific groups varied from monkey to monkey, and that such movement specific groups could arise by chance association of one large discharge value with eleven smaller values for a given neuron, all raised the possibility that the presence of these groups might have resulted from the particular method we chose to quantify neuronal discharge or from the algorithm we used for clustering. We therefore repeated the cluster analysis of each monkey's neuronal population using two other measures of neuronal discharge (CU and FR, see METHODS) and one other clustering algorithm (average linkage, see METHODS). This produced a total of six different cluster analyses of each monkey's neuronal population (3 discharge measures × 2 clustering algorithms). We used these six cluster analyses to examine the neuronal population in each monkey for groups that were stable across the discharge measures and clustering algorithms.
The large BFE group appeared in all six cluster analyses performed on the neuronal populations from each of the three monkeys. The smaller BFI group never appeared in analyses using the FR discharge measure because the spike frequency during the 100 ms preceding switch closure could never be negative. The BFI group did appear consistently, however, in the other four cluster analyses using either CH or CU with either single- or average-linkage clustering performed on the neuronal populations from each of the three monkeys. The large BFE and smaller BFI groups thus appeared consistently across discharge measures and clustering algorithms.
The remaining small groups of movement selective neurons were more difficult to identify across cluster analyses. To employ a consistent criterion, we therefore identified neuronal groups in which a minimum percentage of the total population had been clustered together before being joined to the remainder of the population. Because the single linkage clustering algorithm tends to form smaller groups than the average linkage algorithm (see METHODS), we used 3% of the population as the criterion for cluster analyses performed with the single linkage algorithm, and 5% for average linkage. In Figs. 5-7, these groups are identified in the dendrogram by red lines joining them to the rest of the population. Note that one or two of the small groups identified in this way typically were part of the larger BFE group. Table 1 shows the number of small groups identified using each of the six cluster analyses in each of the three monkeys.
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We then examined the small groups identified by the six cluster analyses to determine the degree to which the groups varied or remained stable. First we examined the movement field of each small group in one analysis and searched the other analyses for groups with the same movement field. Occasionally a group identified in several analyses appeared to have been subdivided in one analysis. The 4e,5e group in monkey C, for example, appeared subdivided into two groups in the analysis using the CH discharge measure and single-linkage algorithm (Fig. 7), though it appeared as a single group in the other five analyses. Table 2 lists the small groups in each monkey identified in at least four of the six cluster analyses along with the number of analyses in which each group was identified. These groups are denoted by black bars above the neuronal unit vector display (B) in Figs. 5-7.
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Besides appearing consistently across analyses, a stable group should include a core of neurons that remain part of the group whenever that group is identified. Each of the relatively stable small groups listed in Table 2 therefore was examined to determine how many neurons were present consistently across the different cluster analyses in which that group was identified. Table 3 illustrates this consistency for the 5f group in monkey C. The 5f group was identified in all six cluster analyses of monkey C's neuronal population. In the six different cluster analyses, from 6 to 22 neurons were included in the 5f group (counts at bottom). Of the 177 neurons in the population from monkey C, 29 were clustered in the 5f group by at least one of the six cluster analyses. Five of these 29 neurons were clustered in the 5f group by all six cluster analyses (counts at right). Although the 5f group thus was quite variable across the six cluster analyses, it contained a stable core of five neurons.
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For each relatively stable small group in each monkey, Table 2 lists
the number of core neurons consistently in the group whenever that
group was identified. For two of the relatively stable groups4e,5e in
monkey C and 3e,5e in monkey K
no such core
neurons were found. If we then count only those groups identified in at
least four of the six analyses containing a core of at least one neuron
consistently present whenever the group is identified, we find only two
to four such groups in each monkey, one being the BFI group in each monkey.
Spatial location of functional groups
We found previously that M1 neurons discharging in relation to any
given finger movement are distributed throughout the M1 hand area
(Schieber and Hibbard 1993). Nevertheless members of the
functional groups identified by the present cluster analyses might be
located close together in the M1 cortex, and different groups might be
spatially segregated. To examine this possibility, we plotted the
spatial location of the members of each identified group in each
monkey. Figure 10 shows such a plot for
each group identified in monkey A. Here, the members of each
group shown in Fig. 6-BFE, BFI, 2f, 2e and 3e-are plotted as spheres
in a separate three-dimensional lollipop diagram for each group. An additional plot shows the location of all neurons in the population. Although the number of neurons in most groups was too small for statistical testing, we observed no systematic tendency for members of
a group to be located close to one another, or for the members of one
group to be segregated from those of another in the physical space of
the M1 hand area.
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DISCUSSION |
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Functional groups in M1 identified by cluster analysis
In the M1 neuronal populations recorded from each of three monkeys, cluster analysis revealed only a limited number of groups of neurons with similar discharge patterns across the finger and wrist movements performed by each monkey. In all three monkeys, the largest group consisted of neurons the firing of which increased during many or all of the individuated movements performed by the monkey. Although this BFE group was not sharply isolated from other members of the neuronal population, the BFE group appeared consistently in the neuronal population from each of the three monkeys, no matter which measure of neuronal discharge or clustering algorithm was used. Furthermore the BFE group consistently formed a sizable fraction (roughly 20-25%) of the population.
A second group identified reliably in all three monkeys consisted of neurons with tonic discharge at rest whose firing decreased during many or all of the finger movements, a pattern to which we refer as BFI. Although much smaller than the BFE group, the BFI group was identified in each monkey using two measures of neuronal discharge (our FR measure could not identify inhibition) with either clustering algorithm.
Neither a BFE nor a BFI group appeared on clustering two imaginary
neuronal populations: one in which discharge measures were randomly
distributed from 1 to +1, another in which measures were drawn
randomly from a real distribution. Although BFI and BFE neurons may
appear relatively nonspecific for control of individuated finger
movements, their robust presence in all three monkeys and their absence
in the randomized populations suggest that the BFE and BFI groups both
represent types of neurons fundamentally important for M1's
contribution to control of individuated finger movements. The
physiology of these neurons was organized such that their discharge
either increased (BFE) or decreased (BFI) to a similar extent during
many or all individuated finger and wrist movements.
In each monkey we also found a few small groups of neurons characterized by discharge patterns that showed much more intense firing during one or two particular finger movements than during others. Using a criterion that the group be identified using four of our six combinations of discharge measure and clustering algorithm, we identified three such groups in monkey K, three in monkey A, and two in monkey C. Of these, only two groups in monkey K, three in monkey A, and one in monkey C, had core neurons that were included in the group across all the combinations of discharge measure and clustering algorithm with which the group was identified. These small, movement-specific groups differed from the BFE and BFI groups, however, in that the same groups were not found from monkey to monkey. Furthermore we found that such small, movement-specific groups could appear in an imaginary neuronal population the discharge measures of which were drawn randomly from a real distribution. Although we cannot exclude the possibility that the movement-specific groups in each monkey represented some important function unique to each monkey-such as assisting in movements the monkey found particularly difficult-the functional importance of these small, movement-specific groups thus remains less certain than that of the BFE and BFI groups.
Of course, the population of recorded neurons constituted only a small
sampling of the total number of neurons in each monkey's M1 hand area.
Groups consisting of large absolute numbers of neurons therefore might
have gone undetected. Nevertheless, because we sampled relatively
evenly through the M1 hand area and because our analysis would have
identified groups constituting 5% of the population, groups of this
size are unlikely to have gone undetected. Studies comparing the
postspike effects of single cortical neurons with the effects of
intracortical microstimulation at the same site have provided evidence
of local groups of M1 neurons with similar patterns of output
connections to spinal motoneuron pools (Cheney and Fetz
1985
; Cheney et al. 1985
). Our findings suggest
that these local groups each constitute <5% of the population or else
that in spite of their similar output connections the different members
of such local groups discharge differently across a set of individuated movements.
Comparison with other means of analyzing the neuronal population
Our application of cluster analysis to explore M1 neuronal
populations for functional groups of similar neurons differs from traditional approaches, which we felt might not incorporate the diverse
features displayed by different neurons during individuated finger
movements. One traditional approach would have been to classify M1
neurons into a number of predefined groups based on features of the
behavioral tasks studied. For example, ventral premotor cortex neurons
have been classified as discharging either during precision pinch or
else during power grasp (Rizzolatti et al. 1988). In the
present context, M1 neurons could have been classified as best-related
to a particular movement (e.g., 1f or 2f or 3f or ... 5e or We)
based on the neuron's maximal discharge. Alternatively, M1 neurons
could have been classified as best-related to a particular digit (1, 2, 3, 4, 5, or W) depending on the movements for which the neuron showed
the greatest flexion/extension discharge differential; a neuron
discharging most intensely during movement 3f and pausing entirely
during movement 3e then would be classified as a digit 3 neuron. With
any such classification, however, many of the present M1 neurons would
have been difficult to assign to one category or another.
A second traditional approach would have been to assume that each M1
neuron was tuned broadly for individuated finger movements with
discharge varying continuously in relation to the spatial geometry of
the hand (Georgopoulos et al. 1982). A population vector
then could be used to extract information about which finger movement
was performed from the discharge of the M1 neuronal population. The
population vector approach has been applied successfully to neuronal
populations carrying information on movement direction, movement force,
complex movement trajectories, and even facial features
(Georgopoulos et al. 1986
, 1989
, 1992
, 1993
;
Schwartz 1993
; Young and Yamane 1992
).
Indeed, many of the present M1 neurons show a component of broad tuning
in relation to individuated finger movements, and the population vector
computed from their discharge during different finger movements can
specify the instructed movement (Georgopoulos et al.
1999
). The population vector approach assumes, however, that
the discharge of a given neuron varies systematically across a finger
movement space. This assumption characterizes the discharge of many M1
neurons incompletely, especially neurons that discharged intensely for
movements of nonadjacent fingers while not discharging for movements of
the fingers in between (e.g., K23505 in Fig. 2).
Implications for the control of individuated finger movements
Whether M1 controls body parts, movements, or muscles has been a
topic of long-standing discussion and debate (Humphrey
1986; Lemon 1988
; Walshe 1948
).
If different groups of M1 neurons exerted control on particular
fingers, particular movements, or particular muscles, we would have
expected to find different groups of M1 neurons that discharged in
relation to particular sets of fingers, movements, or muscles. Enough
groups should have been present to account for all the movements
performed by each monkey, but such was not the case. Nor did the groups
we identified in each monkey appear to represent a set of more abstract
features-principle components, movement primitives, or virtual
fingers-the different combinations of which could represent the
movements performed. Our findings thus provide little evidence that
different groups of M1 neurons act to control different movement
features. An alternative hypothesis would be that M1 neurons are
broadly tuned such that each neuron's discharge varies systematically
in relation to the spatial geometry of the hand. Although this might be
an accurate description of many neurons in the present populations, it
fails to characterize many others.
How might M1 neurons control individuated finger movements using neither groups of neurons to control particular digits, movements, or muscles nor a population of broadly tuned neurons? We suggest that the different combinations of muscle activity needed to produce many different movements could be controlled by the output of a network composed of diverse neuronal elements. The elements of such a network would not necessarily be specific for any given digit or movement nor would their activity necessarily resemble that of any particular muscle. Furthermore the discharge of single neuronal elements would not need to be related systematically to the spatial geometry of the hand nor would the population of neurons necessarily contain groups with similar behavior. Rather, behavioral diversity of different neurons would increase the variety of different outputs the network could achieve, providing an extensive and flexible movement repertoire.
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ACKNOWLEDGMENTS |
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The authors thank J. Gardinier for technical assistance and M. Hayles for editorial comments.
This work was supported by Grant R01-NS-27686 from the National Institute of Neurological Disorders and Stroke.
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FOOTNOTES |
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Address for reprint requests: M. H. Schieber, Dept. of Neurology, University of Rochester Medical Center, 601 Elmwood Ave., Box 673, Rochester, NY 14642.
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 7 October 1998; accepted in final form 28 July 1999.
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