The Neurosciences Institute, San Diego, California 92121
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ABSTRACT |
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Moran, Daniel W. and Andrew B. Schwartz. Motor Cortical Representation of Speed and Direction During Reaching. J. Neurophysiol. 82: 2676-2692, 1999. The motor cortical substrate associated with reaching was studied as monkeys moved their hands from a central position to one of eight targets spaced around a circle. Single-cell activity patterns were recorded in the proximal arm area of motor cortex during the task. In addition to the well-studied average directional selectivity ("preferred direction") of single-cell activity, we also found the time-varying speed of movement to be represented in the cortical activity. A single equation relating motor cortical discharge rate to these two parameters was developed. This equation, which has both independent (speed only) and interactive (speed and direction) components, described a large portion of the time-varying motor cortical activity during the task. Electromyographic activity from a number of upper arm muscles was recorded during this task. Muscle activity was also found to be directionally tuned; however, the distributions of preferred directions were found to be significantly different from cortical activity. In addition, the effect of speed on cortical and muscle activity was also found to be significantly different.
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INTRODUCTION |
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How movement is represented in the brain is a
central problem in motor physiology. Jackson (1875),
based on his observations of epileptic seizures, helped establish the
idea of an anatomic correlate for movement. Although Jackson himself
did not believe in a discrete somatotopic representation in the cortex,
others (Fritsch and Hitzig 1870
; Leyton and
Sherrington 1917
; Schafer 1900
), using
electrical stimuli applied to the cerebrum to elicit muscle
contraction, developed the idea that different locations in the motor
cortex were responsible for movement of specific body parts. To date,
this issue is still controversial, which may in part be due to static
descriptions of movement-related activity. In the present set of
studies, we examined the dynamic time-varying correlations between
cortical activity and arm movement by developing a model of single-cell activity.
As the distributed nature of motor representations is becoming more
clear (Kalaska and Crammond 1992), it has been shown
that multiple parameters can be contained in the activity of single cells, that the same movement parameter can be found in multiple areas
and that representations within a structure are labile
(Alexander and Crutcher 1990a
,b
; Ashe and
Georgopoulos 1994
; Crutcher and Alexander 1990
;
Fritsch and Hitzig 1870
; Fu et al. 1993
,
1995
; Sanes et al. 1990
,
1992
). With this in mind, we studied neuronal activity
in two distinct cortical areas during three different tasks while
examining the representation of two movement parameters as they were
encoded throughout the duration of each task. This paper is the first
of three in which we examine the dynamic activity of motor cortical
cells during movement. Because movement can be characterized with
velocity vectors that in turn are described by direction and magnitude
(speed), we designed three types of experiments to examine these
parameters. In the first study, described here, direction is constant
and speed varied in each movement. In the second set of experiments,
speed changed monotonically, and direction changed harmonically during
spiral drawing. In the last paper, both parameters varied harmonically
as monkeys drew figure-eights.
One of the most clearly represented parameters correlated with motor
cortical activity is that of movement direction. Georgopoulos and
colleagues (Georgopoulos et al. 1982; Schwartz et
al. 1988
) have used a center
out task in which subjects made
arm movements from a central location to eight targets separated by
equal angles. Single-cell activity, characterized by a rate averaged
over the reaction (RT) and movement time (MT) to each target, varied in a regular way with direction. The rates, when plotted against movement
direction, can be fit with a cosine function. Each cell has a peak
discharge rate in a different "preferred direction," yet the tuning
function spans all directions, showing that each cell's activity is
modulated with all movements.
In the original observation of cosine directional tuning of motor
cortical activity, a single average (calculated over the reaction and
movement time of the task) discharge rate was compared with the angle
of the peripheral target from the center (Georgopoulos et al.
1982). Using the average rate in the comparison to direction was valid because these point-to-point movements were fairly straight. Although direction is almost constant during an individual movement, the speed of the arm is not. Typically, point-to-point movements are
made with bell-shaped velocity profiles (Georgopoulos et al. 1981
; Morasso 1981
; Soechting
1984
). This is true of the center
out task; profiles to each
target were bell-shaped and almost identical. Three experimental
conditions (movements encompassing all directions, constant directions
within each movement, and similar speed profiles across different
movements) made it possible to remove the directional component from
the recorded activity pattern while preserving the time-varying
nondirectional component. We used these characteristics to construct an
equation relating single-cell discharge rate to movement direction and speed.
The ensemble activity of motor cortical cells has been combined using
the population vector algorithm (Georgopoulos et al. 1983, 1988
). These population vectors encode
both instantaneous speed and direction within a movement
(Schwartz 1993
, 1994a
). Although it is
clear that the directional contributions of individual cells can sum to
generate a population vector that points in the movement direction, the
way these contributions combine so that the resultant vector magnitude
reflects speed is more elusive. This was one of the issues we were able
to address with our model of single-cell activity.
Motor cortical activity is considered to play an important role in
regulating skeletal muscle contraction because a component of
corticospinal fibers from this region project directly to motoneuronal pools and electrical currents applied to the precentral gyrus cause
muscle contraction (Asanuma and Rosen 1972;
Fritsch and Hitzig 1870
; Landgren et al.
1962
; Lemon et al. 1987
; Woolsey 1958
). Many reports have found motor cortical activity to be
related to the force generated against imposed loads during behavioral experiments, suggesting again that motor cortical activity was facilitating muscle contraction (Dettmers et al. 1996
;
Evarts 1968
; Georgopoulos et al. 1992
;
Humphrey et al. 1970
; Kalaska et al.
1989
; Maier et al. 1993
; Schmidt et al.
1975
; Thach 1978
). Correlation techniques have
shown that motor cortical activity can facilitate electromyographic
(EMG) activity (Fetz and Cheney 1978
; Fetz and
Finnochio 1975
; Mantel and Lemon 1987
). To
compare the features of this cortical activity to muscle activity
patterns, we recorded EMG activity of the proximal arm muscles and
subjected this activity to the same analyses that were applied to the
single-cell activity patterns. Although cortical cell and muscle
activity shared common features with respect to direction and speed,
there were also clear differences showing that muscle activity was not simply related to firing patterns of individual motor cortical cells.
Most of the previous studies examining the relation between speed and
motor cortical discharge rates have been in paradigms based on isolated
elbow or wrist displacements with passive (Flament and Hore
1988; Lucier et al. 1975
) or active
(Bauswein et al. 1991
; Burbaud et al.
1991
; Butler et al. 1992
; Hamada
1981
) movement. These studies, which were designed to examine
putative muscle spindle contributions to motor cortical activity,
typically found a subpopulation of cells where mean firing rate was
related to average angular velocity with a single movement direction.
However, motor cortical activity was interpreted as not contributing to the generation of rapid single joint or oscillatory movement because cortical cells tended to be modulated in such a way that they lagged
EMG (Butler et al. 1992
) or fired after the movement
began (Hamada 1981
). In the present study with
two-dimensional multijoint movements, we show that cell activity is
modulated with speed in a way that depends on the cell's preferred
direction, a parameter that cannot be determined in a single-joint
task. Furthermore, in the present reaching task, the cortical activity
pattern clearly precedes each increment of the movement in a continuous
way throughout the task.
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METHODS |
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The behavioral paradigm, surgical procedures and general animal care were approved by the Institutional Animal Care and Use Committee. The outlines put forth by the Association for Assessment and Accreditation of Laboratory Animal Care and the Society for Neuroscience were followed.
Behavioral task
Rhesus monkeys (Maccaca mullata) were trained using operant conditioning to perform point-to-point movements and draw various figures with a single finger. All movements were performed by the animal moving its finger along the planar surface of a vertically oriented glass touchscreen covering a computer graphics monitor. The surface of the touchscreen was lubricated daily with mineral oil to minimize finger friction. The finger position was digitized at 50 Hz with a resolution of 22 µm horizontally and 17.5 µm vertically. A sequence of tasks was performed after each cell was isolated.
The first task performed (the results of which are the subject of this
paper) was a centerout task. The finger was moved from a center
position to one of eight peripherally arranged targets equally spaced
about a circle with a radius of 6.0 cm. Initially, a start target in
the form of a circle with a radius of 1.0 cm appeared at the center of
the touchscreen. As soon as the monkey placed its finger in the target,
spike occurrence times began to be logged. After a brief hold time
(hold-A) of 280-780 ms, the start circle disappeared as one of the
eight target circles appeared. X-Y coordinates of the finger
were measured from the touchscreen and recorded at this point. The
animal was given 300 ms to move its finger from the center to the
peripheral target while maintaining contact with the touchscreen. As
soon as the monkey's finger crossed the outer border of the target
circle, the sampling of movement data ceased. Spike data, however, were recorded until a second hold time (hold-B) of 50-170 ms was satisfied in the target circle. A liquid reward was given to the animal after
each movement. The monkey made five movements to each of the eight
targets in a random block design. After completing all 40 trials of the
center
out task, the monkey performed drawing tasks in which it
traced spirals and figure-eights, the results of which are discussed in
the two subsequent papers. This sequence was repeated with each
isolated unit.
Cortical recording technique
A 19-mm-diam stainless steel recording chamber was implanted in
the skull over the proximal arm region of primary motor cortex. Each
day a Chubbuck microdrive (Mountcastle et al. 1975) was
mounted on the chamber, which was sealed hydraulically. An electrode, held by the microdrive, was placed over a particular cortical location
with an x-y stage. Trans-dural penetrations were
used, and every attempt was made to record cell activity in all layers of the cortex. Single cells were isolated extracellularly with glass-coated platinum-iridium microelectrodes (10-µm tips). Standard criteria for single-unit identification based on wave shape, its stability, and the absence of doublets or triplets were used
(Georgopoulos et al. 1982
; Mountcastle et al.
1969
) as an indication of a well-isolated, healthy unit. In
addition to its activity pattern during the task, the cell's activity
was monitored as the joints of the arm were passively manipulated.
Small electrolytic lesions (2-3 µA for 3-5 s) were occasionally
placed along a penetration to mark the location of the electrode track
for later use during histological identification. Spikes were
transduced with a window discriminator to a transistor-transistor logic
(TTL) pulse. A clock in the laboratory interface (CED 1401) was used to
label the occurrence time of each spike (1-ms resolution) relative to
the beginning of the hold-A period. The interface transferred the data
to a laboratory microcomputer that controlled the touchscreen display
and recorded the finger's position every 20 ms. These data were
written to disk between trials.
EMG recording technique
EMGs of various shoulder and upper-arm muscles (latissimus
dorsi; infraspinatus; posterior, middle, and anterior
deltoids; clavicular pectoralis; triceps; biceps; and
brachialis) were performed in a subset of the recorded
trials. Two different types of EMG electrodes/methods were used in this
study. The first involved daily placement of fine wire intramuscular
electrodes (40 AWG stranded stainless steel) into the five muscles
chosen for that day. Each muscle was implanted with two wires (1 cm
separation) for bipolar recording. In a different monkey, chronic
epimysial patch electrodes (Loeb and Gans 1986) were
used. Two stainless steel wires were stripped of their last 5 mm of
insulation, threaded through a 7 × 10-mm piece of reinforced
Silastic sheeting (spaced 3 mm apart), and bonded to the sheeting using
Silastic cement. The epimysial electrodes were surgically implanted
under the skin and over the desired muscle belly. The leads to each
electrode were routed under the skin to the back of the head where they were attached to a connector and glued to the skull. The raw EMG signals were differentially amplified, band-pass filtered, rectified, and smoothed using a Paynter filter (
= 50 ms) (Gottlieb
and Agarwal 1970
) before being sampled at 100 Hz by the
laboratory interface (CED 1401). Cross-correlation between a raw
rectified EMG and a Paynter filtered EMG showed that the filtered
relative to the unfiltered data were delayed by 18 ms. The timing of
the Paynter-filtered EMG data used in this study was adjusted accordingly.
Cortical activity model
Although cortical activity is related to several movement
parameters, in this study only two of these parameters will be
investigated: movement speed and direction. The proposed temporal model
of single-cell activity in motor cortex is
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(1) |
Speed analysis I
The first step in the data analysis was to identify movement
onset in each trial of the centerout task. The position data sampled
from the touchscreen were digitally filtered using a phase-symmetric natural B-spline (quintic order) with a low-pass cutoff frequency of 10 Hz (Woltring 1986
). Velocity profiles were generated
directly from the spline coefficients. Movement onset was defined as
the point in time at which the velocity profile rose above 15% of maximum. Because positional data collection ceased as the finger crossed the outer boundary of the target, a portion of the descending velocity profile was truncated. Movement time was then defined as the
period between movement onset and subsequent entry into the outer
perimeter of the target circle. Reaction time was defined as the period
between target circle appearance and movement onset.
The movement time for each trial of the centerout task was divided
into 10 bins. In addition, 15 "prebins" were defined in the period
just before movement onset. The prebins were used to encompass the
neural activity occurring during the hold-A and reaction times. Each
prebin had the same time width as a movement bin, and fractional
intervals (Richmond et al. 1987
; Schwartz 1993
) were calculated throughout all 25 bins. The firing rates in each bin were averaged across the five repetitions and square-root transformed (Ashe and Georgopolous 1994
). The
square-root transform is useful in making the variance of a Poisson
distribution (typically found in binned data) independent of its mean
(Sokal and Rohlf 1995
). (Note: all references to
cortical activity in the text and equations assumes the square-root
transform has been applied.)
The same 10-Hz low-pass digital filter used for the movement data was
applied to the neural data. The firing rate averaged over the last five
prebins of the hold-A period (before beginning of reaction period) was
calculated and subtracted from each of the 25 bins to remove the tonic
background component. Processed firing rates for a single cell were
added bin-by-bin across all eight targets to reveal the nondirectional
component of the discharge rate profile. This technique is summarized
in Eq. 2
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(2) |
To generate an ensemble representation of speed, the nondirectional components of all recorded cells were averaged together binwise. An overall lag was calculated from the ensemble representation using the sliding window correlation method described above. As a comparison to neural activity, a similar ensemble analysis was carried out on the EMG data.
Directional analysis
Initially, a single, mean firing rate was calculated over the
reaction and movement times for each trial, averaged over the five
repetitions to each target, and square-root transformed. The finger
location at the end of movement time was subtracted from its location
at movement onset, yielding a movement displacement vector that was
averaged over the five repetitions to each target. The directional
components of the averaged displacement vectors and the cortical
activity were regressed to the cosine tuning function model
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(3) |
Once the nondirectional component of the cell's activity was found, it
was subtracted from the total discharge pattern along with the tonic
activity to get an estimate of the time-varying directional component
to each target. According to Eq. 1, the directional
component of a cell's firing rate for the centerout task
(by and bx
terms when multiplied by
V(t)
) should be a
series of bell-shaped curves in time. Movements to the target closest to the cell's preferred direction should generate the largest positive
curve. Conversely, the directional component of discharge for movements
opposite the preferred direction should be a negative curve whose
magnitude is equal to that seen in movements in the preferred
direction. Movements to the remaining targets should generate
directional components with magnitudes that vary systematically between
those in the preferred and anti-preferred direction. The directional
components to each of the eight targets were categorized according to
the angle between the movement direction and the cell's preferred
direction. The data in each category (0, ±45, ±90, ±135, 180) were
averaged over all cells to obtain ensemble temporal representations of
the directional components.
Speed analysis II
Whereas Eq. 1 will give a firing rate profile in time, it is also informative to examine the effect of speed on the directional tuning function (discharge rate vs. direction). For this analysis we used average discharge rates during trials in which the movements were of different durations. The behavioral paradigm did not completely constrain the speed used by the monkey to reach each target; it was rewarded for movement durations <300 ms. Because of the extensive amount of training before recording data and because our analysis is based on five-repetition averages, ensemble intertarget variations in speed were not significant. However, by analyzing individual repetitions, enough variation in intratarget speed was found to make some statistically significant observations. This allowed us to construct directional tuning functions for different movement speeds.
To compensate for the latency between cortical activity and finger
speed, the average time lag, , found previously was used to select
the 10 bins of cortical activity that corresponded to finger movement.
Because there is significant variation in firing rate magnitudes across
different cells, the individual firing rates (n = 40)
for each cell were normalized by their overall mean. Each of the
targets for a particular cell were labeled according to its direction
relative to the cell's preferred direction. The normalized firing
rates for movements in the cells' preferred directions were regressed
to peak finger speeds. This provided a measure of the change in overall
firing rate due to changes in speed when moving in the average cell's
preferred direction. This was repeated for movements ±45, ±90, ±135,
and 180° from the preferred direction. Combining these results, the
variation in the "average" tuning curve as a function of speed was found.
The same analysis was applied to the EMG data to calculate the effect of finger speed on the muscle tuning curves. To combine multi-day data for the same muscle, the baseline voltage from each experiment was subtracted before analysis.
Population vector analysis
The population vector algorithm (Georgopoulos et al.
1983) uses each cell's preferred direction to define a vector
that is subsequently weighted by its current activity and summed with vectors similarly derived from other cells recorded during the same
task. The resultant vector, termed the "population vector," tends
to point in the direction of movement. A time series of these vectors
can be generated throughout the movement, and they match the
instantaneous velocity of the hand as it moves (Georgopoulos et
al. 1988
; Schwartz 1993
). This algorithm can be
expressed in equation form as
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(4) |
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RESULTS |
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A total of 1,066 cells were recorded from eight hemispheres of four monkeys. Figure 1 illustrates the locations of the 218 penetrations from which these cells were recorded. In seven of the eight hemispheres, recordings were made in the primary motor cortical area; in one hemisphere dorsal premotor activity was recorded exclusively. The criterion used to select cells for further analysis was that good single-unit isolation was maintained during all five repetitions to each of the eight targets (40 trials). Each unit was examined during passive manipulation of the shoulder, elbow, wrist, and hand. Cells that were responsive exclusively to manipulation of the hand or fingers were excluded from further analysis. These criteria were met for 1,039 of the units, 142 of which were recorded in dorsal premotor cortex. The major purpose of this analysis was to study primary motor (M1) cortical activity. However, as a comparison, a limited number of dorsal premotor (Pmd) cortical cells were similarly analyzed.
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The average trajectories to each of the eight targets over all trials are shown in Fig. 2A. The circle sizes (1 cm radius) representing the targets, excursion lengths, (6 cm) and trajectories are drawn to scale. The thick lines are average trajectories comprised of 5,195 movements to each target. Standard deviations are represented by the thin lines. Movement recording was initiated at the beginning of the reaction time (interval between peripheral target presentation and movement initiation) and ended when the outer perimeter of the target circle was crossed. The average velocity profiles to each of the eight targets (thick lines), and the overall standard deviation (thin lines) across all recorded trials are shown in Fig. 2B. An ANOVA (IMSL, Visual Numerics) on the peak speeds grouped by targets found that these speeds were not significantly different across targets (p < 1%).
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Speed response I
The neuronal firing rates during each trial's movement time were divided into 10 bins to normalize binwidths among all trials. Across all cells, the average binwidth was 24 ± 5 (SE) ms for 41,560 trials. In addition, 15 prebins, having the same width as the movement bins, were calculated just before movement onset. On average, the first eight bins corresponded to the later part of the hold-A period, and the next seven bins covered the reaction time. Five-trial averages were made over all movement directions. The outer perimeter of Fig. 3 shows the raw (i.e., unsmoothed and untransformed) firing rates during movements to each target for an example cell. During the hold-A period the rates were very similar across targets. In the subsequent reaction and movement times, the activity was graded with movement direction.
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These histograms were smoothed and square-root transformed. The average firing rate in the five bins before reaction time was subtracted from the reaction and movement time bins, eliminating the tonic component of cortical activity (b0). Averaging the resulting profiles across the eight targets removed the directional component (bx and by terms) of the discharge profile. Finally, the 17-bin window of neural activity that best correlated with finger speed over the reaction and movement time was found. The result is the left profile in the center of Fig. 3. This nondirectional profile is very similar to the speed of the hand averaged across the eight targets (right profile in the center of Fig. 3). For this cell, the two waveforms were highly correlated (r2 = 0.96) at a lag of 155 ms. In general, this was true for cells throughout the motor cortical population as shown in Fig. 4A. A histogram of the corresponding time lags between the nondirectional discharge and velocity profile for all M1 cells in the population can be seen in Fig. 4B. The time lag distribution peaked at a mode of 125 ms with a median value of 75 ms.
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A similar analysis was performed on the recorded responses of 142 premotor cortical cells. Figure 4C shows the results of correlating the nondirectional portions of Pmd cortical discharge with speed. Lags between Pmd cortical activity and finger speed had a median value of 100 ms, but the mode of the distribution was 175 ms (Fig. 4D).
An ensemble nondirectional activity profile was generated by averaging all 897 M1 profiles bin-by-bin. The result (Fig. 5) is highly correlated (R2 = 0.99) with the speed profile, and leads it by 145 ms. This M1 profile was compared with those derived from Pmd and muscle activity. Each curve in Fig. 5 is composed of the 17 bins that best correlate with finger speed. Pmd activity had an r2 of 0.68 at a lag of 190 ms. Nondirectional EMG activity was also correlated to the speed profile (R2 = 0.96, lag = 65 ms).
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Directional response
Figure 6 shows the response of a
motor cortical cell (same cell as Fig. 3) during the centerout task.
The firing rate during the reaction and movement times to each target
was averaged temporally over the trial and across repetitions. The
eight resulting firing rates were square-root transformed and regressed
against direction (Eq. 3) to generate a directional tuning
function. The filled circles in the polar plot of Fig. 6 represent the
processed firing rates for the cell, and the solid black line is the
cosine tuning function. The tuning function explains well the
dispersion of these points. The r2 for
the directional tuning of this cell is 0.96 with a preferred direction
of 180°
(arctan[By/Bx]).
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All cells used in this study were analyzed this way. A histogram of
r2 values for the 1,039 cells is shown
in Fig. 7A. (Note: due to their similarities in directional tuning, both Pmd and M1 responses were included in Fig. 7.) The average
r2 was 0.71 with 75% having values
greater than or equal to 0.7. The distributions of preferred directions
can be seen in the circular histogram of Fig. 7B. Preferred
directions were well distributed throughout the workspace with a very
slight skewing. The 0° bin (rightward) of preferred directions
contained the highest number of cells (101). The direction with the
least number of cells (70) was down and to the left (240°). All other
directions contained counts between 70 and 101 cells. A Rayleigh test
(Batschelet 1981) performed on the preferred directions
resulted in a test statistic of z = 0.45, which
corresponds to a p value = 0.64. The null hypothesis of
a uniformity cannot be rejected, and there is little uncertainty that
this distribution is uniform.
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Similarly, the average EMG activity of each muscle was directionally
analyzed. Figure 8 shows the temporal
activity of nine of the left arm muscles recorded in this study. Except
for the "S2 Pectoralis," all the examples shown in Fig. 8 were from
a single monkey (S1) using intramuscular electrodes. Beginning with the
top row, a systematic rotation in preferred directions can be seen in the shoulder muscles whose origins vary systematically from
posterior to anterior. Note the similarity in preferred directions between the two pectoralis muscles shown in Fig. 8, suggesting that the
two monkeys used very similar strategies in controlling this muscle.
Another interesting result in Fig. 8 is the similarity in preferred
directions among the biceps and triceps from the same arm. Classically
considered antagonists to one another, these two muscles appear to be
co-contracting during movements up and to the right. However, on closer
inspection it can be seen that the biceps activity precedes the triceps
activity. The biceps crosses the shoulder, and the short head acts as a
shoulder flexor in addition to its contribution to elbow flexion. The
early activity in this muscle may be acting to flex the shoulder. The
subsequent uniarticular triceps activity (short and lateral heads)
counteracts elbow flexion and allows the biceps to continue flexing the
shoulder. Although the triceps long head does cross the shoulder, its
primary function is stabilization of the shoulder joint, and it
contributes insignificantly to shoulder flexion/extension
(Gray's Anatomy 1980).
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EMG activity from 14 left arm muscles of 2 different monkeys was recorded. The number of trials recorded for each muscle varied. Table 1 shows the total number of trials recorded for each muscle, those trials with significant directional tuning and the average preferred direction across tuned trials. A histogram of r2 values for directional tuning in muscles (Fig. 9A) shows that the EMG activity was as well tuned as that of the neurons during this task. However, Fig. 9, B and C, graphically compares the average preferred directions among the muscles recorded and shows that almost all of them are orientated upward and within 45° of the vertical axis. The Rayleigh test yields a statistical value of 8.70, which corresponds to a p value of 0.00017. The null hypothesis of uniformity is clearly rejected. This differs from the distribution of cortical cell preferred directions, which were found to be uniform (Fig. 7B).
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Starting with the activity profiles of individual cortical cells, directional (corresponding to the bx and by terms in Eq. 1) and nondirectional (the bn term) activity patterns were separated by subtracting both the tonic and nondirectional activity to each target. These profiles were then categorized by preferred direction and averaged across cells to give the average directional components to each target (relative to preferred direction) across the population. The average nondirectional response (same as Fig. 5) is shown together with the directional profiles in Fig. 10A. When moving in the preferred direction, the M1 directional component is much larger than the nondirectional term. In contrast, when moving perpendicular to the preferred direction, the time-varying directional component is very small, suggesting that the observed activity of a cell is dominated by the nondirectional component when moving in this relative direction. With the exception of ±90°, the directional and nondirectional components have similar bell-shaped profiles, suggesting that both terms could contain instantaneous speed information. This is the rationale for setting the speed term in Eq. 1 as a multiplier to both the directional and nondirectional terms.
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The directional interprofile amplitudes shown in Fig. 10A
begin following the cosine tuning model ~50 ms into the reaction time. From that point on, the correlation with the tuning model remains
high (r2 > 0.98) throughout the rest
of the movement. However, the profile amplitude for movements in the
preferred direction (top curve) has a larger overall
magnitude than in the anti-preferred direction (bottom
curve). Because these curves were derived by subtracting the same
nondirectional component from the response to each target, this may
indicate that the speed component varies (interacts) with movement
direction. In fact, previous work (Schwartz 1992) has
shown that speed is better represented in motor cortical activity patterns when movements are near the cell's preferred direction. Subtracting a constant contribution from each profile would then tend
to underestimate the speed component for the profiles near the
preferred direction, making the resulting direction profile too large.
The nondirectional response in the premotor population appears to have a much faster temporal profile than both the finger speed (Fig. 5) and the directional responses (Fig. 10B). The directional interprofile magnitudes from the premotor ensemble show excellent cosine tuning (r2 > 0.99) throughout the movement illustrating that premotor cell activity can represent direction very well.
Speed response II
Average speed profiles for movements to each of the eight targets were statistically similar across targets. However, magnitudes of individual profiles vary in repeated movements to the same target. Trials were sorted by movement direction (relative to the preferred direction), and the average discharge rate in each trial was regressed to peak speed. EMG activity was regressed to speed the same way. The regression results that were found to be significant in at least two or more directions are shown in Tables 2 and 3.
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The motor cortical regression analysis shows that discharge rate increases with increasing finger speed regardless of finger direction. However, the amount of change in discharge (i.e., slope) is dependent on direction. The discharge rate increases more in the preferred direction than in the anti-preferred direction (Table 2). The mean peak speed in this analysis was ~30 cm/s with a standard deviation of ±10 cm/s. The mean rate and slopes for each direction were used to construct ensemble tuning curves for trials with peak speeds of 25 and 35 cm/s (Fig. 11A). The difference in firing rate between the two curves is greater in the preferred direction than in the anti-preferred direction, suggesting that speed does not simply shift the tuning curve. The ratios (last column of Table 2), consisting of the differences between fast and slow firing rates divided by their mean, were similar across directions, suggesting that the speed effect was multiplicative on the directional tuning curve.
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The premotor cortical cells also showed an overall increase in discharge rate with increasing finger speed, which was significant throughout all directions. However, the change in discharge rate was twice as large as that for the M1 cells in the preferred direction and substantially less in the anti-preferred direction (Fig. 11B).
Of the 14 muscles analyzed, only two showed significant changes in activity with increasing speed in two or more target directions (Table 3). EMG patterns for anterior deltoid and infraspinatus were positively correlated with finger speed when moving in the muscle's preferred direction. As movements were made further away from the muscle's preferred direction, the slope between EMG and speed either became insignificant or negative. (Although statistically insignificant, similar patterns were seen in all recorded muscles). The anterior deltoid activity shown in Fig. 11C is greater with faster movements when moving upwards (90°). However, because this muscle is active during the hold-A period to counteract gravity, it decreases activity when the arm moves downward (270°). For faster movement speeds in the anti-preferred direction (downward), there is a decrease in anterior deltoid activity instead of an increase. This is opposite the effect seen in motor cortical cells for movements made in the anti-preferred direction (Fig. 11, A and B). The direction response of infraspinatus was only modulated by speed when moving in the muscle's preferred direction (Fig. 11D).
Multiple regression
Equation 1 was validated using a multiple regression
analysis (rcov IMSL). The form of Eq. 1 used in the
multiple linear regression is
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(5) |
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The individual cortical lags that provided the best fits to Eq. 1 can be seen in Fig. 13, A and B. The figure is divided into primary and premotor cortical subpopulations to compare with the lags shown in Fig. 4, C and D. The distributions in Figs. 4, C and D, and 13, A and B, have identical modes and very similar shapes showing that the two methods for calculating cortical time lags provide similar results. Figure 13, C and D, show a distribution of differences in preferred directions calculated from regressing the mean rates of Eq. 3 and the dynamic rates of Eq. 1 to cortical activity. The preferred direction is determined by the regression coefficients by and bx (preferred direction = arctan by/bx). Less than 20% of the cells had preferred directions that varied by >30° between the two models.
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An average representation of cortical discharge rate was generated by categorizing cell activity by preferred direction and averaging across all cells. Using Eq. 1 to regress the eight temporal firing rates to the corresponding finger velocities, an overall r2 of 0.99 was found at a lag of 145 ms. None of the individual cells had r2 values >0.95, yet over 99% of the variance in the average motor cortical activity can be explained by Eq. 1.
Population response
We used the responses of individual cells in the cortical
population to provide a measure of how their combination might lead to
a representation of speed and direction during reaching. Responses from
all directionally tuned (r2 > 0.7) M1 cells were combined to form a time series of population vectors. The results are shown in the perimeter of Fig.
14A, where movements to each
target are represented by 17 population vectors (7 for RT and 10 for
MT) as well as the corresponding movement velocity vectors. Vectors
corresponding to each movement are centered at their corresponding
target location in the diagram with the time series advancing in a
counter-clockwise direction. The movement vectors (thin lines) are
short and point in random directions during the RT, whereas the
population vectors (thick lines) generally are initially short but
quickly elongate during the middle of RT before movement begins. Vector
field correlations (Shadmehr and Mussa-Ivaldi 1994)
between the movement and population vectors were performed at varying
lags to find the highest correlation. The M1 population vectors had a
maximum correlation of 0.97 at a lag of 145 ms, whereas the Pmd
population vectors had a maximum correlation of 0.87 at a lag of 170 ms.
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Neural trajectories can be formed by integrating the population vectors (multiplying by the average binwidth and adding them tip-to-tail). Using the lag information from the vector field correlations above, the 10 population vectors that temporally corresponded to the movement period were integrated into the trajectories shown in the center of Fig. 14A. The M1 neural trajectories match the hand trajectories. Figure 14B shows the population vectors and trajectories generated from the premotor cortical data. Like the M1 cells, the Pmd cells provide a good overall representation of the movement trajectory.
The population vector magnitudes were regressed to finger speed across all eight targets and for each of the 10 movement bins. Figure 15A shows the results of this regression for the M1 cells. A correlation coefficient of 0.94 was found at a lag of 145 ms. Figure 15B shows the regression results for the premotor data. In this case, a correlation coefficient of 0.83 was found at a lag of 166 ms, which is a shorter lag than the 190-ms lag found from cross-correlating the nondirectional component with finger speed (Fig. 5).
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Averaging the magnitudes of the population vectors across all eight directions yields a population vector "velocity" profile that can be directly compared with the ensemble nondirectional profiles shown in Fig. 5. Based on M1 activity, both methods produce an accurate representation of the actual speed (Fig. 15C). Figure 15D shows the results of a similar procedure performed on the premotor activity. The two curves have very different temporal profiles. The Pmd nondirectional component peaks during the portion of the movement where the population magnitude is changing the most. This Pmd component is better correlated to acceleration, whereas the population vector magnitudes are well related to speed in this portion of the movement. The method used to generate population vectors removes additive factors that are common across all targets. Thus the nondirectional component (bn), derived as a common effect across all targets, is not pertinent to the construction of population vectors. Consequently, the effect of speed on population vector length is due solely to the interaction between speed and direction (bx and by terms; see APPENDIX).
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DISCUSSION |
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The directional sensitivity of motor cortical cells has been described primarily with a single estimated firing rate for each reach. To demonstrate a continuous relation between movement parameters and cortical activity, it is necessary to examine those components that vary in time. During reaching, the arm's trajectory is fairly straight; movement direction is approximately constant. In contrast, the speed of the arm varies with a bell-shaped velocity profile, making it useful to compare this parameter to firing rate over time. The design of this reaching paradigm with constant movement direction and time-varying speed allowed us to separate the effects of these two parameters on discharge rate. Our analysis revealed that speed acts both independently and interactively with direction to modulate discharge activity. This was the motivation for including both nondirectional (bn) and directional (bx, by) terms in Eq. 1.
The idea that speed and direction information is combined in the activity of single cells in the form of Eq. 1 was addressed and supported with four different approaches. The directional cancellation procedure showed that single-cell activity could be separated into nondirectional and directional components. A regression between peak speed and firing rate in individual trials showed that there was an interaction between speed and discharge rate so that speed was acting as gain factor on the directional tuning curve. The validity of Eq. 1 was tested directly with multiple regression. And, finally the magnitudes of the population vectors calculated during this task were shown to be directly proportional to speed in a way that depended on the form of Eq. 1.
Initially we removed the directional component of activity by adding
movements in opposite directions. Because the directional responses of
these cells are symmetrical (cosine tuned), the directional modulation
is equal and opposite about some mean value. After removing the
directional component, the residual (nondirectional) pattern was found
to be highly correlated with the speed profile. Speed also acts as a
multiplier of the directional modulation in single cells after the
nondirectional effect was subtracted from the discharge profile (Fig.
10). One way to visualize how discharge activity is affected by the
combination of speed and direction is with the tuning functions in Fig.
11. Speed tends to modulate cortical discharge rate primarily when
moving in the preferred direction, suggesting that speed
acts as a gain factor of the directional tuning function. Previously, a
gain factor was used to describe the receptive field of posterior
parietal cells because the angle of the eyes in the head potentiated or attenuated the retinotopic tuning function (Andersen et al.
1985). This type of interaction differs from the effect static
loads have on the directional tuning in motor cortical cells
(Kalaska et al. 1989
). Loads tended to shift the tuning
function of these cells as an additive offset. This is similar to the
effect of movement amplitude on the tuning functions of pallidal cells
(Turner and Anderson 1997
).
Continuous control of reaching
Our results show that direction and speed are represented
continuously in the discharge activity of single cells during reaching. Point-to-point movements have been considered classically as discrete events. Reaching movements consist of an initial ballistic transport component characterized by a stereotypic force pulse and velocity profile. The shape of the force pulse remains the same, but its magnitude is graded with different amplitudes of movement
(Hollerbach and Flash 1982; Morasso
1981
). During this phase of movement, the effect of sensory
input may be delayed until the terminal phase of the reach as the hand
approaches the target (Brooks 1974
; Massey et al.
1986
; Megaw 1974
; Paillard 1982
;
Paillard and Brouchon 1974
). The terminal phase of
reaching is under visual control, and it is here that accuracy
constraints come into play (Fitts and Peterson 1964
;
Meyer et al. 1982
; Soechting 1984
;
Woodworth 1899
). Because most of the distance covered
during the reach is in the initial transport phase and this is
unaffected by ongoing sensation or the absence of it (Bossom
1974
; Taub et al. 1975
), it was suggested that
the control of this movement was completely specified before it began
(Ghez and Vicario 1978
; Kelso and Holt 1980
).
The concept of open-loop control during reaching led to the idea that
only the endpoint or target need be specified by the nervous system and
that the springlike properties of the arm would ensure the proper
delivery of the hand to the preset target location (Polit and
Bizzi 1979). Although soon abandoned (Bizzi et al. 1982
, 1984
), this idea was replaced with similar
theories using equilibrium points that shifted during the movement
(Bizzi et al. 1984
; Flash 1987
;
Hatsopoulos 1994
; Won and Hogan 1995
).
The equilibrium trajectory hypothesis supposes that a time series of
muscle tensions is calculated before movement initiation. Each combination of terms can be represented by a point in space where the
arm would rest if those tensions were frozen at an instant in time.
In experiments where reaching was transiently perturbed with amplified
Coriolis forces, subjects in the dark initially made unusually curved
trajectories, missing the target (Lackner and Dizio
1994). Because Coriolis forces are absent at the end of the
movement when the arm is stationary, the hand should, under the
influence of the equilibrium trajectory, arrive at the correct target
location. Furthermore, subjects rapidly modified their abnormally
curved trajectories, making them straighter on subsequent trials. This
shows that the subjects were compensating for the unusual inertial
loads placed on the arm, an operation that would be unnecessary if the
equilibrium trajectory was effective. This also shows that there was a
continuous monitoring of afferent information during the movement that
was used to compensate for the abnormal trajectory.
One aspect of the equilibrium-point hypothesis is that the
equilibrium-point and actual trajectories should be similar. This will
happen only if the limb is sufficiently stiff during the movement
(Flash 1987). However, recent elegant measurements show the arm to be much less stiff in the middle of the trajectory than
predicted (Gomi and Kawato 1996
). The measured stiffness of the arm was used to construct equilibrium-point trajectories, and
from these, velocity profiles were calculated. These calculated profiles were multipeaked and quite different from those of the actual trajectory.
These behavioral studies show that there is a continuous process underlying the generation of reaching. This process is characterized by a temporal template and is not immediately affected by sensory feedback. Our neuronal results show that implementation of this process is incremental throughout the task. Reaching is controlled by an ongoing process that keeps the hand moving continuously along a specified trajectory.
Neural recordings
Neural activity in the motor cortex varies in a systematic way
during reaching movements. The centerout paradigm was originally designed to test the responses of motor cortical cells to movement direction. Integrated activity within these approximately straight reaches is characterized with a cosine tuning function (Caminiti et al. 1990b
; Georgopoulos et al. 1983
,
1988
). Time series of population vectors constructed
during a three-dimensional version of this task closely matched a
corresponding series of movement vectors (Georgopoulos et al.
1988
). During drawing movements where both the direction and
speed of the arm changes within the movement, the length and direction
of the population and movement vectors matched (Schwartz
1993
, 1994a
). These results showed that motor cortical activity, when considered as an ensemble, did predict the
arm's trajectory in a continuous manner.
Such a demonstration is more difficult using only the responses of
individual cells. In this study we developed a model that explains how
speed and direction can be encoded at the same time in the activity
pattern of a single cell. In an earlier study, Ashe and
Georgopoulos (1994) performed a multiple regression of target
direction, hand position, velocity, and acceleration to discharge rate.
This analysis showed that motor and parietal cortical cells had
activity that was correlated with all of these parameters. Direction
accounted for most of the variance in discharge followed by speed and
position of the hand. A very small part of the discharge activity was
related to acceleration. The mean best lag between motor cortical
activity and the movement parameters was
90 ms (cortical activity
before movement). For the parietal cells, the mean lag was +30 ms
(cortical activity after movement). Another analysis using multiple
regression (Fu et al. 1995
) found that the static
parameters of direction, target position, and movement amplitude
(respectively) were represented sequentially in single motor cortical
cell activity patterns. Our analysis is similar to that of Ashe and
Georgopoulos because of the use of time-varying parameters.
Equation 1 included one kinematic parameter (velocity) while
the model of Ashe and Georgopoulos included three kinematic parameters
(position, velocity, and acceleration) as well as a constant target
parameter (target direction). The explanatory power of our model was
generated by the use of both a direction-dependent (velocity) and a
direction-independent speed term.
Combining the activity of all the cells (categorizing targets by preferred direction) and regressing to Eq. 1 led to an "ensemble" or overall r2 of 0.99. This result is much larger than any of the of individual cell regressions used to create the average activity. Several factors could be responsible for this ensemble superiority. The effect of movement parameters that influence the discharge of individual cells in an inconsistent manner will be removed by averaging across cells, whereas those parameters that many cells have in common will be more apparent. In the same way, stochastic noise in cortical firing rates would also be reduced and would lead to a higher fidelity signal. This is the fundamental meaning of the population vector.
The interaction of speed and direction as factors in the modulation of
cortical activity can be an important consideration when studying
reaching movements. For instance, in the centerout task, if the
subject moves faster in some directions than others, the differences in
speed will lead to an errant measurement of preferred direction. This
may be a special problem when performing a task with different arm
orientations (Caminiti et al. 1991
; Scott and
Kalaska 1995
, 1997
). Nonuniform movement speeds
to different targets will appear to alter the preferred direction of
the cell; however, it will not alter population vector direction, only
its magnitude.
Premotor activity
Activity patterns of single premotor cortical cells are similar to
those of M1 cells in this task. The major difference between the two
cell types is in their nondirectional components. The premotor
nondirectional component peaks faster, and the overall width of this
profile is narrower than the velocity profile. Consistent with other
reports (Caminiti et al. 1991; Crammond and
Kalaska 1996
; Kurata and Tanji 1986
), this
suggests that the premotor contribution to reaching is earlier and more
transient than M1. When aligned with the beginning of movement (15%
maximum), the nondirectional activity corresponds better to the initial
acceleration profile of the hand rather than velocity. The
speed-direction interaction is expressed with greater sensitivity in
these cells when compared with M1, with a regression slope between
activity and speed that is twice as steep in the preferred direction
but half as steep in the anti-preferred direction. The observation that
these cells are speed and direction sensitive shows that the
representation of these parameters does not arise de novo in the
primary motor cortex. Direction, speed and amplitude sensitivity has
been found in the cellular activity of many areas linked anatomically to M1 (Crutcher and Alexander 1990
; Fortier et
al. 1989
; Ruiz et al. 1995
; Schwartz
1994b
; Turner and Anderson 1997
).
EMG
Using the centerout task we found our sample of proximal-arm
EMG activity levels to be cosine-tuned in the planar movement task.
This might be taken as support for the direct control of muscle
activity by the motor cortex because both single cortical cells and
muscle activity are directionally tuned. However, there are clear
differences between the two types of activity in this task. Perhaps the
most important distinction is that the preferred directions of the
sampled muscles were all oriented vertically, whereas the distribution
of motor cortical preferred directions were uniformly distributed. It
is likely that the preferred directions of the muscles in this task are
oriented to counteract gravity because this is an important torque
component for a vertically orientated center
out task
(Kakavand et al. 1996
). Previous studies involving EMG
activity in a horizontally oriented center
out task found that muscle
preferred directions were evenly distributed (Georgopoulos et
al. 1984
). Because the movements in that study were in a
near-horizontal plane and the monkey's arm was semi-supported by the
manipulandum, gravity would be expected to have a negligible role on
muscle dynamics.
Another interesting difference between the centerout results of
Georgopoulos et al. (1984)
and our results is the
difference in preferred directions of some muscles. For instance, the
latissiumus dorsi in the horizontal study had a preferred direction
that pulled the hand backward while in the vertical task, the preferred
direction was oriented superiorly and medially. Without joint angle
information from both tasks, it is difficult to speculate; however, the
primary functions of the latissiumus dorsi are shoulder extension,
which would result in a posterior preferred direction, and adduction, which would yield a medial preferred direction. Thus both preferred directions are a probable result of agonist activity in the two different tasks. It is likely that arm orientation can affect the
preferred direction of a muscle.
It is interesting that the nondirectional component of EMG activity is
well correlated with the velocity profile in contrast to the
expectation that agonist activity would look more like the initial
phase of the acceleration profile as found in typical single-joint
movements (Gottlieb et al. 1989). When multiple muscles are simultaneously active across the same joint in unconstrained arm
movements, the combination of activity, perhaps asynchronous, across
the other muscles as well as the nonmuscle derived forces acting on the
limb complicate the relation between the forces produced in individual
muscles and the actual torques generated across a joint
(Bernstein 1967
; Flanders et al. 1994
;
Gottlieb 1996
).
Another interesting feature is the relationship between speed and EMG activity during movements in different directions. As expected, EMG activity increases when moving faster in a muscle's preferred direction. This positive correlation with speed disappears or becomes negative when moving in other directions. Antagonistic bursts are often present if a movement is made fast enough; however, with our well-trained subjects moving at peak speeds <40 cm/s, antagonist bursts were not evident. The data in this study suggest that the way a muscle contributes to changes in movement speed in a particular direction differs from that of M1 cells, which showed positive correlation with speed throughout all directions.
Population activity
The representation of trajectory-related information present in
the population of recorded activity is easy to visualize using a simple
algorithm. Summing the activity patterns of many cells together
vectorially results in a time series of population vectors that
represents the instantaneous velocity of the finger as it moves to the
target in the centerout task. Our knowledge of the way direction and
speed are encoded by single cells can help explain why the population
vector, when integrated, is such a robust predictor of the finger's
trajectory. To construct a population vector of appreciable length,
there must be some asymmetry in the vector components used to derive
it. Because the distribution of preferred directions in the population
is uniform, the asymmetry stems from the uneven distribution of
individual firing rates at the instant when the population vector is
calculated. We have shown that both direction and speed will contribute
to the uneven distribution of firing intensities across the population.
Cells with preferred directions near the movement direction will fire
faster, and these larger contributions will make the population vector
point in the direction of movement. If all the cells in the population now increased their discharge rate by the same amount (e.g., adding 10 spikes/s to all cells), the resulting population vector would point in
the same direction and have the same magnitude. This is a consequence
of the normalization used in Eq. 4. In fact, any factor that
changed the activity of all cells in the population by an additive
constant would not change the magnitude or orientation of the
population vector (see APPENDIX). Interestingly, if the
effect of this additive factor is not constant in all directions when performing the center
out task, the preferred direction will appear to change when the experimental parameters are varied (e.g., presence or absence of external loads). Changes in preferred direction of
individual cells without changes in the population vector direction has
been reported in several studies (Caminiti et al.
1990a
,b
; Chen and Wise 1996
; Scott and
Kalaska 1995
). However, an increase or decrease in the firing
rate of all cells by the same ratio, as our results show
(Fig. 11), will change the length of the population vector by that
ratio (see APPENDIX). This is the basis for the robust relation between the population vector magnitude and speed. Speed acts
as a gain factor on the firing rates of individual cells, increasing
the amplitude of the tuning function. As a result, the speed effect is
emphasized in those cells firing fastest (i.e., those with preferred
directions near the movement direction), and they will have an
increased contribution to the population vector. This illustrates how
the multiple representation of parameters in the activity patterns of
single cells can be easily extracted using a population algorithm.
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APPENDIX |
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Here we derive the relation between time-varying parameters that
influence single-cell discharge rate and population vector magnitude.
The theoretical length of a population vector can be calculated by
combining the motor cortical cell model of Eq. 3 and the
population vector algorithm of Eq. 4. The formula for a
population vector using the average discharge rates from a population of cells collected over a movement to target 1 is
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(A1) |
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(A2) |
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(A3) |
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(A4) |
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(A5) |
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(A6) |
We have shown that population vector length is directly proportional to
finger speed; therefore calculating theoretical population vector
lengths for both a fast and slow movement should result in different
values. Now assuming speed affects discharge rate in the manner
proposed in Eq. 1, a ratio of population vector lengths in
the slow versus fast task can be calculated. Two forms of
Eq. A2 would be generated: one for the fast
trials and one for the slow trials. However, Eq.
A3 would be unchanged. Recalculating population vector
magnitudes for both populations yields
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(A7) |
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(A8) |
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(A9) |
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(A10) |
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ACKNOWLEDGMENTS |
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A. Kakavand trained the animals and assisted in the experiments, J. Adams provided support in EMG data collection, and E. Lumer provided mathematical assistance.
This work was supported by the Neurosciences Research Foundation, the Barrow Neurological Institute, and National Institute of Neurological Disorders and Stroke Grant NS-26375.
Address for repint requests: A. B. Schwartz, The Neurosciences Institute, 10640 John Jay Hopkins Dr., San Diego, CA 92121.
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FOOTNOTES |
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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 22 July 1996; accepted in final form 28 November 1997.
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REFERENCES |
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