 |
INTRODUCTION |
Recently, studies of multijoint arm movement have
shown that a set of spike trains recorded from motor cortex can be used to predict the direction and speed of movement (Moran and
Schwartz 1999
; Schwartz 1992
). In fact, the
arm's trajectory is well represented in this activity when considered
as a population during reaching (Georgopoulos et al.
1988
; Moran and Schwartz 1999
) and drawing (Schwartz 1993
; Schwartz and Moran 1999
),
suggesting that this technique can provide a detailed prediction of the
behavior to take place in the immediate future. Drawing is
characterized by a linkage between the kinematics of the movement and
the shape of the figure to be drawn. In general, as the curvature of a
figure increases, the speed of the hand decreases. Specifically,
angular velocity is proportional to curvature raised to the
power; a relation known as the "
power law" (Lacquaniti et al. 1983
), or, alternatively, that speed
is proportional to curvature to the 
power. We examined
spiral drawing because the radius of curvature (
) changes linearly
with the extent or arc length of the figure. With the aim of
elucidating the predictive behavior of the cortical-movement system, we
used this linear relation to examine the timing of the directional signal as it changed within the task. To measure the temporal characteristics of this process we calculated a "prediction
interval" (PI) as the time interval between the cortical
representation of a direction and the occurrence of that direction in
the movement. This interval increased throughout the spiral as it was
drawn from outside
in and decreased when drawn inside
out.
Curvature (1/
) increases or decreases depending on the direction of
drawing and the PI changed consistently when plotted against curvature for spirals drawn in either direction, suggesting that curvature is the
primary determinant of the prediction interval.
The ability to use population activity to visualize accurately the
shape of the figure to be drawn suggests a movement plan in motor
cortex. By examining the timing between the directions specified in
this plan and their appearance in the movement, it is possible to infer
some of the dynamic principles used in the control of this type of arm
movement. A short report of these results has been published
(Schwartz 1994
).
 |
METHODS |
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 the Assessment and
Accreditation of Laboratory Animal Care and the Society for Neuroscience were followed.
Behavioral task
Monkeys were trained using operant conditioning to draw various
figures with a single finger on a touchscreen (Moran and
Schwartz 1999
). Each monkey performed a sequence of tasks after
each cell was isolated. A center
out task was followed sequentially
by sinusoidal, spiral, and figure-eight drawing tasks. Drawing tasks
began with a circle (10-11 mm radius) displayed on the screen to
indicate the starting location of the task. The animal placed and held its finger in this circle for 100-300 ms (hold period). At the end of
this interval, the entire figure to be traced was displayed, and the
animated circle was moved a small increment along the figure away from
the animal's finger. The animal was required to keep its finger on the
screen surface and move to the newly displaced circle. As soon as the
finger touched the target circle, the circle moved again, following the
outline of the spiral. Repeating this process resulted in an animated
sequence with the circle continuously just ahead of the smoothly moving
finger. The surface of the touchscreen was lubricated daily with
mineral oil to minimize friction with the sliding finger of the monkey.
If the animal lifted its finger from the screen or did not move its
finger to the newly displaced target circle within a 300 ms increment,
the trial was aborted. The rate of the movement was determined by the
animal because the constrained time increment was generous enough to
allow very slow movements. After several weeks of training, smooth
continuous movements were made with this approach. Spirals were
presented as two classes in five randomized blocks. In the first class,
the spiral was traced from outside
in; in the second class, it was
traced from inside
out. Each spiral consisted of three circuits: the
outer radius was 7.5 cm, and the innermost radius was 1.5 cm. A liquid
reward was administered at the end of a successful trial (a complete
tracing of the figure). This sequence of tasks was repeated with each
isolated cell.
Cortical and electromyographic recording (EMG) technique
Glass-coated platinum-iridium electrodes were used to record
single motor cortical units extracellularly. Both intramuscular or
epimysial electrodes were used to record electromyographic data from
various shoulder/elbow muscles. These techniques are described in the
preceding paper (Moran and Schwartz 1999
).
Kinematic recording technique
With the use of three-dimensional (3-D) positional data recorded
from various points on the arm during a trial, shoulder and elbow joint
angles were calculated as a function of time. The monkey's arm was
fitted with a lightweight hinged orthosis that was strapped to both the
upper and lower arm with the hinge centered over the elbow joint. Three
infrared emitters were attached to the orthosis: one on each end of the
device (wrist and shoulder marker) and the third close to the hinge on
the forearm segment. An Optotrak 3010 motion analysis system (Northern
Digital, Waterloo, Ontario) sampled the 3-D position of the three
markers at 100 Hz during the drawing tasks. The movement data were
digitally filtered using a phase-symmetrical, natural B-spline (quintic order) with a low-pass cutoff frequency of 10 Hz (Woltring
1986
). The distance between the center marker and the hinge
(elbow) was measured with a caliper at the beginning of each experiment.
To generate joint angles, attitude matrices were calculated for both
the upper and lower arm segments. With the use of the distance from the
center marker to the elbow and the vector connecting the center marker
to the wrist marker, the 3-D location of the elbow joint was
calculated. The vectors from the wrist marker to the elbow joint and
the elbow joint to the shoulder marker defined the long axes
(y) of the two segments. Assuming a single degree of freedom
(DOF) for the elbow joint, the medial/lateral (z) axes for
each segment are equal and were calculated by a vector cross product of
the two long (y) axes vectors. Finally, the
posterior/anterior (x) axes of the segments were calculated
from vector cross products of their z- and
y-axes. The axes vectors were normalized to generate 3 × 3 attitude matrices for both the forearm and upper arm. The torso of
the monkey was assumed fixed and aligned with the global reference
frame such that its attitude matrix equaled the identity matrix.
Rotation matrices for both the shoulder and elbow joint were generated
from the segmental attitude matrices. Finally, Cardanic angles (Euler
permutation x, y', z") were calculated from the direction
cosines of the rotation matrices resulting in three shoulder joint
angles (adduction[+]/abduction[
], internal[+]/external[
] rotation and flexion[+]/extension[
]) and a single elbow angle (flexion[+]/extension[
]). The anatomic position (i.e., hands hanging down at sides) represented the posture in which all joint angles were zero.
Single-cell analysis
Each trial for a particular class was divided into 100 bins over
the movement time. In addition, 10 "prebins" were calculated for
the period just before movement onset. Every prebin had the same time
width as a movement bin, and fractional intervals (Richmond et
al. 1987
; Schwartz 1993
) were calculated
throughout all 110 bins. These values were averaged across trials
within classes, binwise. The resulting average firing rates were
low-pass filtered (ccsmh, IMSL, Visual Numerics, Houston, TX) and
square-root transformed (Moran and Schwartz 1999
).
Average trajectories were calculated using the finger displacement data
that had been collected simultaneously. Using the same low-pass filter
function (ccsmh, IMSL), the x and y finger
coordinates were temporally normalized to 101 instants encompassing the
100 movement bins. For each trial and in every bin, the velocity of the
finger was calculated. These velocities were either averaged across the
five trials recorded in a single experiment or across all experiments
for comparison to population vectors.
To test the directional sensitivity of these individual cell responses
across time within a single task, it was necessary to transform
movement directions into firing rates. We used the instantaneous
direction of the movement in each bin of the spiral task and the tuning
parameters of the cell derived from the center
out task (Eq.
3 of the previous paper, Moran and Schwartz 1999
)
to generate a simulated discharge rate in each bin of the drawing task
(Schwartz 1992
). The resulting time series of simulated
discharge rates for an entire trial was compared with the actual
discharge rates of that cell using cross-correlation. The time lag of
the peak-positive correlation was used as an indication of the average interval (AI) between a direction predicted by a single cell's activity and the movement of the finger in that direction. This not
only tested the directional sensitivity of the neuron within the task
but also showed whether the tuning function was robust and valid across
different types of tasks.
Population vector analysis
The method used to construct population vectors has been
described in detail in previous papers (Moran and Schwartz
1999
; Schwartz 1993
). Population vectors were
calculated in each of the 110 bins for both classes. The preferred
direction of each cell included in the study was calculated from the
center
out task; the assumption is made that the cell's preferred
direction is constant between different tasks (center
out, spiral,
etc.) and within a given movement. Both the movement vectors
and population vectors were converted from a cartesian coordinate
system (x, y) to a polar system (
, r) where
direction and magnitude were independently smoothed using a cubic
spline function ("ccsmh," IMSL). "Neural trajectories" were
generated by integrating the time series of population vectors
(Moran and Schwartz 1999
) as a movement path
representation in the cortical activity.
To investigate the time relation between the isomorphic representation
of the spiral shape present in the cortical population activity and the
movement of the hand along that path, it was necessary to match
individual population directions to movement directions. Because spiral
drawing essentially consists of contiguous circular movements, the
directional component (
) of movement velocity is a monotonic
function of time; it increases continually for outside
in
(counterclockwise) movements and decreases for inside
out (clockwise)
movements. When direction crossed the 2
-0 radian transition, 2
was added to the remaining directions to eliminate discontinuities in
the directional profile; the reverse was done for clockwise movements.
The directional components of both neural population and movement
velocity vectors were fit with a third-order polynomial ("rcurv,"
IMSL) to assure that direction changed monotonically. The population
vector directions were applied as abscissa data (time being the
ordinate) to a cubic spline routine ("csakm," IMSL). (Note: spline
routines require that abscissa data (knots of the spline) be either
steadily increasing or decreasing (i.e., monotonic) so that the
ordinate data are a function of the abscissa data. The validity of
these operations can be assessed by comparing the processed directions
to the raw unsmoothed directions presented in RESULTS. The
movement direction data were fitted with the same spline routine but in
the reverse order of the population data (i.e., time was the abscissa,
and direction was the ordinate). For any instant of movement time, the
corresponding movement direction could then be interpolated from the
movement spline. This direction was then applied to the spline of
population vector directions, and its corresponding interpolated time
was subtracted from the movement time instant. We refer to this time
interval as the "prediction interval" (PI). This differs from the
average interval derived from the cross-correlation of simulated and
actual discharge rates of individual cells described above. There is
only one AI for each trial in contrast to a continuum of values for the
PI. The PI is a descriptor of the timing between population vector
direction and movement velocity direction; the AI refers to the average lag between simulated and actual discharge rates in an individual cell.
 |
RESULTS |
The activity patterns of 318 cells from 4 hemispheres of 2 monkeys
were included in this study. The recordings sites as determined by the
location of electrode penetrations were shown in the previous paper
(Moran and Schwartz 1999
). Of these cells, 77 were
recorded in the same dorsal premotor area. The remainder were in the
primary motor cortex. Cells were included in this study if they were
directionally tuned (r > 0.84 for the cosine fit in
the center
out task), fired during the task, and were passively
driven by movements of the shoulder and/or elbow joints. The cells
included in this study are a subset of those analyzed in the previous
reaching paper (Moran and Schwartz 1999
). Initially we
will consider the results of the primary motor cortical cells (3 hemispheres). Later we will compare the behavior of premotor to primary
motor cortical cells in a single animal.
The animals were well trained before data collection began. The top of
Fig. 1 shows the trajectories averaged
over all the recorded trials for both directions of tracing. The
largest radius of the trajectories was 7.7 cm, and the smallest, in the
center of the spiral, was 1.2 cm. An example tracing obtained for a
single motor cortical cell can be seen in the bottom of Fig. 1, whereas the rest of the data recorded for the example are shown in Fig. 2. The top row of the figure shows spike
activity raster plots for the outside
in and inside
out spiral. The
corresponding histograms in the second row exemplify the harmonic
firing rates typically seen during this task. As expected, this
activity is well correlated with the cosine of movement direction (3rd
row). In contrast, the movement speed (4th row) is not well modulated
in this task. There is, however, a tendency for the hand to slow in the
more curved part of the figure. As the monkey's finger slows down in the inner, highly curved portion of the spiral, the peak amplitudes of
cortical modulation also declined. Shoulder and elbow joint angles
(rows 5-8) are also harmonic, showing that intrinsic kinematic variables covary with extrinsic finger direction and, hence, cortical activity. Finally, the last five rows of Fig. 2 show that muscle activity is also harmonic. This cell, and indeed many of the cells we
studied, had an activity pattern that was correlated with finger direction, joint angles, and muscle activity. Many movement parameters are interrelated during these drawing tasks.

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Fig. 1.
Average (n = 1,590) finger trajectories during the
2 classes of spiral drawing. In the 1st class (A) the
animal traced the figure from outside in. The same template was
traced from inside out in the 2nd class (B). Finger
trajectories for a single example cell (n = 5) can
be seen in C and D.
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Fig. 2.
Typical data set recorded for a single cell. Top row:
5-trial rasters for a motor cortical cell during both an outside in
(left) and inside out tracing. Second
row: histograms were made by converting the raster data into
firing rates (spikes/s) and averaging across the 5 trials. The cosine
of finger direction (row 3), shows a harmonic relation
to the neural activity. There is a weak tendency for higher finger
speeds (row 4) on the outside of the spiral and for
slower speeds in the interior of the spiral. Four joint angles
(rows 5-8) were calculated for the shoulder and elbow
joints. Finally, rows 9-13 show the average muscle
activity (electromyographic, EMG) recorded during the trials.
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Single-cell responses
PRIMARY MOTOR.
Trial movement times were divided into 100 bins, and the average
discharge rate and movement velocity (direction and speed) were
calculated for each bin. On average, the monkeys performed the spiral
tasks in 2.5 s, yielding binwidths of ~25 ms (outside
in = 24.3 ± 2.6 ms, mean ± SE; inside
out = 25.2 ± 3.5 ms). In addition, 10 prebins were calculated for the
neural activity occurring just before movement onset (~250 ms). Using
the center
out tuning equation for each cell, simulated discharge
activity was calculated using the movement direction in each bin.
Figure 3 compares the simulated and
actual discharge activity for an example cell during both classes of
spirals. Like the actual activity, the simulated activity is harmonic;
as the movement direction crosses the preferred direction, the
discharge activity is maximal; when the movement direction is in the
anti-preferred direction, the activity is minimal. An important feature
in both the outside
in and inside
out spirals is the relative
timing between the actual and simulated discharge rates. The time
difference between the two profiles can be considered as the interval
between the representation of direction in the activity of the cell and
the occurrence of that direction in the movement. The average
correlation between the actual and predicted discharge rates over the
entire movement can be measured with conventional cross-correlation.
The two sets of profiles were highly correlated (A:
r = 0.79, B: r = 0.95) with lags of 77 and 94 ms, respectively. The same comparison was
made for each of the primary motor cells (for both classes of drawing).
A histogram of their peak correlation coefficients for the 241 primary
motor cells in this study is shown in Fig.
4A. This distribution is unimodal with a mean of 0.57 (n = 482). The time
interval that would best align the predicted and actual discharge rates
was also calculated for those cells with significant correlations (p < 0.01). Over 88% of the cells had significant
correlations for both classes of drawing. A histogram of these time
lags (for values lying between 350 ms before and 250 ms after the
movement) is plotted in Fig. 4B. The mean of this
distribution (n = 404) shows that on average, the
directional information contained in the discharge activity of these
cells predicts the movement of the finger by 90 ms.

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Fig. 3.
Simulated and actual discharge rates for an example cell. Tuning
information from the center out task was used to calculate a
predicted discharge rate for the cell using finger direction. The
neural activity was found to be highly correlated (A:
r = 0.79 at 77 ms; B:
r = 0.95 at 94 ms) to the simulated discharge
rates.
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Fig. 4.
A: histogram of peak correlation coefficients between
the actual and predicted firing rates of 241 primary motor cortical
cells (3 hemispheres). The drawing task consisted of 2 opposite spiral
movements yielding a total histogram count of 482. B:
histogram of movement lags between actual and predicted firing rates as
determined from cross-correlation. Only correlations from
A that were significant (p < 0.01)
are shown (n = 404). The figure illustrates that
the majority of motor cortical cells lead the movement.
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COMPARISON OF PRIMARY MOTOR AND PREMOTOR CELL RESPONSES.
To compare primary and premotor cortical activity in the same animal, a
subset of the total data were used. Correlation analysis was applied to
the cortical activity of 77 cells from the left dorsal premotor and 71 cells from the right primary motor cortex of the same animal.
Correlation coefficients from the analysis of the predicted and actual
discharge rates for each of these cells are shown in Fig.
5A. The means are 0.42 (n = 154) for the premotor cells and 0.52 (n = 142) for the primary motor cortical cells. Only
64% of premotor cell trials showed significant correlations for both
classes of spirals, whereas over 86% of the primary motor cell trials
were significant. The timing of the two sets of cells is shown by their
significant correlation lags in Fig. 5B. The average primary
motor lag was 80 ms. Interestingly, the premotor cell responses had a
bimodal distribution with peaks at 0 and 250 ms.

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Fig. 5.
A: comparison of peak correlation coefficients from
premotor and primary motor areas in a single monkey. In the motor
cortex (right hemisphere), 71 units were recorded. Recordings were made
from 77 premotor cortical cells in the contralateral hemisphere.
Overall, the firing rates from primary motor cortical cells have higher
correlation with predicted rates than premotor cells. B:
histogram of time lags found from significant premotor correlations
(n = 103) and a similarly sized population of
primary motor (n = 103) correlations. As in Fig.
4B the primary motor cortical cells have a unimodal
distribution with an average lead time of 100 ms. The premotor cortical
cells show a bimodal distribution with lead times of 250 and 0 ms.
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Population responses
DIRECTION COMPARISON.
Population vectors were constructed from the total sample of primary
motor cortical cells (n = 241) for both movement
classes. The 110 bins of each trial were used to create 110 population vectors for each class. Finger displacement data were used to calculate
100 movement velocity vectors. The 110 population and 100 movement
vectors for each class are shown in Fig.
6. Visual inspection suggests that the
population and movement vectors are very similar for each class.
Indeed, using vector field analysis (Shadmehr and Mussa-Ivaldi
1994
), the correlation between the 100 movement vectors and 100 population vectors yields a coefficient of 0.97 for the outside
in
spiral and 0.96 for the inside
out spiral. (Note: the 100 population
vectors chosen consisted of the last 4 prebins and the 1st 96 task
bins. This corresponds to average shift of 100 ms, which is in
agreement with Fig. 4B.)

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Fig. 6.
Vectograms of both movement (A and C) and
population (B and D) vectors for the 2 classes of spiral movement. The population vectograms were generated
using the primary motor cortical cells from all 3 hemispheres
(n = 241). The population vectograms are composed
of 110 vectors, the 1st 10 of which occur before movement onset.
Movement vectograms each contain 100 vectors occurring during the
movement. On average, each vector accounts for 25 ms of movement time
yielding a total movement time of 2.5 s. The 10 "prebins"
vectors for the population vectograms represent neural activity
occurring 250 ms before movement onset ( ).
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The directions of the population and movement vectors are compared in
Fig. 7. Population vector direction is
shown as the thick line, whereas the movement direction is the thin
line. The unfiltered population vector directions are also included in
Fig. 7 (
) to illustrate the raw data. There is a very good match of population vector and movement vector direction as represented by the
slope and shape of these curvilinear traces. In the outside
in task,
the two directions are coincident initially, and then diverge slightly.
The opposite description applies to the inside
out task, where the
two directions are disparate initially and then converge toward the end
of the task. The instantaneous interval (prediction interval) between
the two traces in each class was measured along the horizontal. Because
the spirals were drawn outwardly and inwardly, the
convergence-divergence of the direction traces is related to the
position of the finger on the spiral.

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Fig. 7.
Directional comparison between the movement (thin line) and population
(thick line) vectors for both an outside in (left ordinate) and
inside out (right ordinate) spiral. In both cases, the interior of
the spiral is represented by high directional values (20-23 radians),
whereas the outside of the spiral corresponds to small directions (2-5
radians). The same curvilinear relation of direction to time is present
in both the population and movement vectors for both classes. The
neural and movement directions are coincident in the outer portion of
the spiral, but the neural directions lead those of the movement more
as when the finger is moving in the inner portion of the spiral. The
population directions ( ), before smoothing and polynomial
fitting, of every 5th population vector are shown to illustrate the
nature of the raw data.
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TIMING CHARACTERISTICS.
The spirals were constructed so that the radius of curvature changed
linearly with position along the figure; the radius of curvature is
correlated with position that, in turn, is related to prediction
interval. In addition, finger speed is tightly coupled to curvature
(Lacquaniti et al. 1983
) and is also related to the prediction interval. Both curvature and speed as a function of time are
plotted in Fig. 8. In general, curvature
and speed are inversely related. The prediction intervals were plotted
against curvature, radius of curvature, and speed for both classes
(Fig. 9). Although both parameters show a
relationship to prediction interval, the curvature-PI relation (Fig. 9,
A and B) appears more consistent
(r = 0.98, 0.98) than the speed-PI relation (Fig. 9C, r = 0.92). At small curvatures, the
prediction interval is small. When the curvature is 0.18-0.20
cm
1, the prediction interval rises rapidly. The
curves approach an asymptote around 0.4 cm
1 and
thereafter have an approximately constant value of 100 ms. When PI is
plotted against the radius of curvature (inverse of curvature), the
relation is strikingly linear (O
I, r = 0.98; I
O,
r = 0.98), and the data from both classes overlap. The
prediction interval is a direct function of the instantaneous radius of
the figure. In the straightest portions of the spiral, the direction signal occurs 40 ms before the movement and when the path is curved, this interval rises to 100 ms.

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Fig. 8.
Curvature and speed as a function of time for both classes of spirals.
Curvature was low on the outside of the spiral and increased as the
finger moved to the interior of the spiral (A and
B). Although the finger speed profile was not consistent
between the 2 classes, there was a tendency for finger speed to be high
on the outside of the spiral and low in the interior (C
and D) showing the inverse relationship between speed
and curvature.
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Fig. 9.
A: comparison of curvature to prediction intervals.
During low curvature drawing there appears to be only about a 30-ms lag
between motor cortical activity and arm movement. This lag rapidly
increases with curvature until reaching an asymptotic value of ~100
ms. B: same data as A with abscissa
inverted showing a strong, consistent relation between the prediction
intervals and radius of curvature. C: although not as
consistent as curvature, an inverse relationship between finger speed
and direction lag can be seen in the 2 classes of spirals.
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This finding differs from point-to-point reaching movements which have
average intervals of 125-150 ms (Moran and Schwartz 1999
). One reason for this difference may be the parameters
used to calculate the lags. The lags calculated in the point-to-point reaching data were based on finger speed, whereas in this study they
are based on finger direction. The time lags pertaining to these two
parameters may be independent (Schwartz and Moran 1999
). It should also be noted that we are comparing time lags throughout the
movement, not just at the beginning. In fact, the neuronal processing
associated with movement initiation may differ from those associated
with ongoing control. To examine the transient activity responsible for
time lags at movement onset, we used data that had not been smoothed.
Population vector directions were calculated from 250 ms before through
400 ms after movement onset and compared with velocity vectors that
began at movement onset. (Note: the hand was moving at a near-maximal
speed as it exited the start circle border at "movement onset".)
Lags were calculated from the directions using the same algorithm
outlined above, and the result can be seen in Fig.
10.

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Fig. 10.
Transient lags occurring during movement onset. During the movement
initiation portion of the tracing task, both the outside in and
inside out spiral have higher lags than would be expected during
"steady-state" tracing. From 225 ms on, both spirals have lags
matching those predicted by Fig. 9.
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Both the outside
in and inside
out spirals in Fig. 10 show rapidly
decaying lags occurring during movement onset. In the case of the
outside
in spiral, the transiently decaying lag lasts 225 ms. The
inside
out spiral also has a fast decaying lag at movement onset
lasting ~125 ms, which levels off and is followed by a much slower
decaying lag. The initial lags (100-150 ms) are comparable with those
found in the center
out task. After 250 ms, these transient lags are
gone, and the lags follow the pattern apparent in Fig. 7. Figure 10
suggests that there are two separate processes taking place. The first
is a transient process that occurs during movement initiation where,
regardless of the curvature, a high lag between the movement and the
neural representation of movement exists. The second consists of
shorter lags correlated with movement curvature.
NEURAL IMAGE.
An image of the trajectory represented by the population vectors can be
formed by adding the vectors tip-to-tail. These neural trajectories are
shown in Fig. 11. As expected with the
high correlations between the movement and population vectors, the
neural trajectories match closely the figures drawn with the finger.
Due to the variable lags illustrated in Fig. 9, the highest fidelity
outside
in spiral encompassed 97 bins of data (population vectors
from 1 prebin and 96 task bins). On the other hand, the best matching
inside
out spiral spanned 103 bins of data (4 prebins and 99 task
bins). At the beginning of the outside
in task, the PI was small
(~30 ms or 1 bin) and at the end of the movement, the PI was ~100
ms (4 bins). The prediction began only 1 bin ahead but ended 4 bins before the end of the actual movement for a total of 97 bins. In
contrast, more bins are needed in the inside
out task, which started
with a PI of 100 ms (~4 bins) and ended with a small PI of 30 ms (1 bin) for a net addition of three bins more than the movement.

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Fig. 11.
Population trajectories for both an outside in (A) and
an inside out (B) spiral movement. The trajectories
were constructed by adding the individual vectors of Fig. 6 tip-to-tail
(integrating).
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COMPARISON OF PREMOTOR AND PRIMARY MOTOR CORTICAL POPULATION
RESPONSE.
The response of the premotor and primary motor cortical populations
differ when compared with the vector algorithm. Our sample of premotor
cortical cells was relatively small (n = 77) and
because a few cells with responses not consistent with directional
tuning can skew the population vector with small sample sizes
(Georgopoulos et al. 1986
), we applied an additional
selection criterion to the premotor-primary motor cortical analysis.
Only those cells that had at least 10% of their discharge rate during
the spiral task explained by the directional tuning function
(r > 0.3) were selected for this analysis. This
resulted in a population of 50 premotor cells. A population of 50 primary motor cortical units (r > 0.3) from the same
animal was compared with the same sized population of premotor cortical
cells. A vectogram consisting of population responses from the two
cortical areas is shown in Fig. 12. The
motor cortical population still yields vectors that change directions
smoothly through the movement. These are comparable to those in Fig. 6,
which were composed of cells from three hemispheres. Vector
correlations between the primary motor population vectors and the
movement vectors yielded coefficients of 0.94 and 0.90 for the
outside
in and inside
out spirals, respectively. In contrast, the
premotor vectors change direction erratically yielding movement correlations of 0.62 (outside
in) and 0.82 (inside
out). This is
evident in the neural trajectories derived from the vectors. In Fig.
13, A and B, the
neural trajectories derived from primary motor data still show
representations recognizable as spirals. However, the premotor neural
trajectories in Fig. 13, C and D, have little
resemblance to the drawn figure.

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Fig. 12.
Vectograms of population vectors generated from both primary
(A and B) and premotor (C
and D) cortical cells for both spiral tasks
(A and C, outside in; B
and D, inside out). The 100 vectors were generated
from 50 cells in each cortical area of a single monkey during the
spiral. With an equal number of cortical cells, the primary motor area
contains a more consistent representation of the movement than does the
premotor area.
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Fig. 13.
Motor cortical population trajectories generated from the vectograms of
Fig. 12. The outside in class is on the right
(A and C) and the inside out is the
left column (B and D). The
finger trajectory is well represented, even in this small population of
motor cortical cells (A and B). This is
not true of the premotor cortical population (C and
D).
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The horizontal speed components of the premotor neural and finger
trajectories for the inside
out spiral were compared to help
elucidate the distortion in the premotor neural trajectories. As shown
in Fig. 14, there are two local peaks
in the "neural" speed profile for every movement peak. One peak
corresponds to the finger speed extremum; the other precedes it by an
average of 250 ms. This, along with the timing of the individual neural responses of the premotor cortical cells shown in Fig. 5B,
suggests that this population of premotor cortical cells is composed of two subpopulations, each of which generates trajectory signals that
differ by ~250 ms. The timing of the premotor responses shown in Fig.
5B were used to separate the premotor cells into two groups. The activity patterns of those cells with an average lag >125 ms were
shifted back in time by 250 ms. The data of cells with lags <125 ms
were not shifted. The resulting neural trajectories are shown in Fig.
15. The distortions found in Fig. 13,
C and D, are absent, showing that they were due
to timing differences between the two subpopulations of cells in the
premotor cortex. The locations of the cells in the two subpopulations
were analyzed to determine whether they came from distinct regions or
layers within the dorsal premotor area, but there was no anatomic
distinction.

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Fig. 14.
Horizontal component of movement speed compared with that of the
premotor population vector magnitude during an inside out spiral. The
premotor population magnitude (thick line) shows 2 local peaks for
every movement peak (thin line), suggesting that the premotor area
consists of 2 sets of cells coding for the same movement but at
different points in time. One set of cells matches the movement ~250
ms beforehand, whereas the 2nd set is synchronous with the movement.
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Fig. 15.
Lag-adjusted premotor population trajectories. All cells having an
average interval >125 ms had their firing rates shifted back in time
by 250 ms. Those having average intervals <125 ms were not altered. A
new set of population vectors was constructed yielding a better match
to the movement (A: outside in, B:
inside out).
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Joint angles and angular velocity
Joint angle information was collected for the right arm of
subject 2. A total of 465 individual trials were recorded
and averaged. In Fig. 16, 4 DOF about
the shoulder and elbow joints are plotted for both tracing directions.
To demonstrate superimposition, the inside
out data were plotted in
reverse order from that of the outside
in task. The data were
superimposed and showed that the monkey had approximately the same
instantaneous arm posture for both tracing directions.

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Fig. 16.
Joint angles as a function of extent (position on the spiral) for both
classes of spirals. Elbow flexion, shoulder flexion, internal rotation,
and adduction were generated from direction cosines (Cardanic form) of
upper and forearm attitudes. The high degree of overlap between the 2 classes suggests that instantaneous arm postures for a given location
on the spiral were similar between the 2 tasks. Because movement
direction and single-cell activity also varied harmonically throughout
the task, joint angular velocity would be expected to covary with these
parameters as well. The anatomic position represents all joint angles
being zero.
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Arm posture and finger position were well correlated in these tasks.
Because instantaneous arm posture determines finger position, the
angular velocities of the joints are correlated with hand velocity.
This raises several possibilities; for instance, the latency between
cortical signal and shoulder/elbow displacement could be fixed so that
the curvature-related prediction intervals in the population analysis
resulted from a variable phase between finger velocity and joint
angular velocities of the proximal arm. Another possibility is that
finger and joint displacements were phase locked; then the variable lag
would lie between cortex and all kinematic variables. To address this
issue, the relative phases between the directional component of finger
velocity and the four joint angular velocities were analyzed. The first
maximum in a joint angular velocity for the outside
in task was used
to determine an offset or bias term for the joint angular velocity.
This allowed the finger velocity and a joint angular velocity to be
initially aligned so it would be easier to observe any variations in
phase. By plotting joint angular velocity and the cosine of finger
direction cos(
bias), the change
in phase between these two variables can be assessed.
Three of the four joint angles measured in this study were found to
have a constant phase relationship with finger velocity. Shoulder
adduction, the only joint angular velocity found to have a significant
variable phase relationship, is shown in Fig.
17. During the outside
in task, the
phase between these components is initially zero with a slight phase
advance (~25 ms) occurring at the end of the movement. Although
shorter than the 75-ms change in prediction interval found for the
cortical responses, this small phase advance is consistent with the
hypothesis that the variable prediction interval could be a property of
proximal-to-distal kinematic lags. However, the possibility that the
shoulder component is directly linked to cortical activity is
eliminated in the inside
out task because the phase between the two
velocity components increases by >150 ms during the outward
progression of the hand. This phase relation is opposite to the
decreasing prediction interval between cortical activity and hand
velocity. Hence none of the joint angles had a constant phase
relationship with cortical activity.

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Fig. 17.
Phase relation between a proximal arm intrinsic coordinate (shoulder
adduction velocity) and a distal arm extrinsic coordinate (finger
velocity). Shoulder adduction velocity (thick line) is plotted against
cosine of finger direction. In both classes the phase lag is initially
zero but increases (A: outside in lag = 25 ms;
B: inside out lag = 150 ms) as the task
progresses regardless of curvature, suggesting that the variable
cortical lags shown in Fig. 7 are not simply due to phase lag in
proximal-to-distal arm kinematics.
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EMG response
The muscular activity in the left arms of both monkeys was
recorded in a subset of the total trials. Subject 1 had
chronic epimysial electrodes implanted on clavicular pectoralis,
middle deltoids, posterior deltoids, infraspinatus,
and brachialis muscles. A total of 75 individual trials were
recorded for both the outside
in and inside
out classes. Figure
18 shows the average activity in each
of these muscles over all recorded trials. Similarly, intramuscular activity was recorded from eight muscles of subject 2. The
average EMG activity recorded in clavicular pectoralis
(n = 95 experiments), anterior deltoids
(n = 35), middle deltoids (n = 165), posterior deltoids (n = 170),
latissimus dorsi (n = 40), biceps
brachii (n = 15), triceps brachii
(n = 145), and brachialis
(n = 50) can be seen in Fig.
19. With the exception of biceps
brachii, all of the muscles recorded have responses that are
temporally similar to both movement direction and cortical activity.
Because EMG activity covaries well with movement direction, the
variable lags seen in the population response could be due to earlier
activation of muscles during higher curvature. With the use of the
EMG's preferred direction information calculated from center
out
task, a predicted versus actual EMG activity plot was made. Because the
predicted EMG activity is generated from finger kinematics, the plots
essentially compare EMG activity with finger velocity. However, the
muscle activities behaved the same way as the angular velocities of the
joints. They either remained phase locked to the finger or like the
shoulder adductor infraspinatus (Fig.
20), the finger lagged the muscle more
later in the task.

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Fig. 18.
Average EMG activity for the left arm of Subject 1 for both classes of
spirals. Each histogram is generated from 75 trials recorded over
multiple days using epimysial electrodes. The left column corresponds
to the outside in class and the right to the inside out class. With
the exception of middle deltoids in the inside out
class, all the muscles show harmonic activity similar to cortical
activity.
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Fig. 19.
Average EMG activity for the left arm of subject 2 for
both classes of spirals. Like Fig. 18, EMG data were combined over
multiple days. Intramuscular fine wire electrodes, inserted daily, were
used to collect the data. The left column corresponds to
the outside in class and the right to the inside out
class. With the exception of biceps brachii, all the muscles
showed the same stereotypic response seen in Fig. 18. Biceps
brachii has approximately twice as many peaks in EMG as the other
muscles.
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Fig. 20.
Simulated and actual EMG activity for infraspinatus muscle of
subject 1. The simulated EMG was generated from the
center out tuning parameters of the muscle and finger velocity during
spiral tracing. The actual EMG activity (thick line) preceded and
matched well the simulated activity (thin line) by 75 ms on average.
The phase relationship between the peaks in activity was found to be
similar to the joint angular velocities (Fig. 17). In the outside in
case (A) the lag between the 2 representations was ~0
and increased to 75 ms at the end of the movement. In the inside out
case (B) the lag started out ~50 ms and increased to
100 ms.
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DISCUSSION |
The population vector algorithm shows that hand trajectory is well
represented in the activity of motor cortical cells
(Georgopoulos et al. 1988
; Moran and Schwartz
1999
; Schwartz 1993
, 1994
;
Schwartz and Moran 1999
). In this study we show not only
that the spatial attributes of a complex movement are encoded in this
activity, but that the timing of this isomorphic representation
relative to the movement changes in a characteristic way that is
determined by the shape of the figure. As a tool, the population vector
algorithm has proven to be useful in showing that movement direction is an important parameter encoded in many brain areas (Caminiti et al. 1990
; Fortier et al. 1989
;
Georgopoulos et al. 1984
; Kalaska et al.
1983
; Motter et al. 1987
; Ruiz et al.
1995
; Snowden et al. 1992
). Furthermore, this
algorithm has shown how populations of cells encode parameters that
single cells cannot. In this model, we make a tacit assumption that
contributions from individual cells are being summed at the same node
to form a population vector. Although the model succeeds as a predictor
of movement kinematics, there is no convincing evidence of such a node.
Even when the movement itself is considered as the convergence point,
our results show that the signals reaching it traversed pathways of
different durations as the task progressed.
The spiral drawn in this task consisted of three concentric circuits
with smoothly changing radii. Many movement parameters change in a
cyclic manner when this type of figure is drawn. Finger direction and
many of the joint angles changed harmonically during this task as did
single-cell and EMG activity. Within a given task, the correlation of
these parameters to each other makes it difficult to distinguish the
effect of cortical activity in generating these modulated patterns.
However, several points can be addressed by considering timing and
movements in both directions. The timing between the instantaneous
directional signal in the cortical population and finger direction
varies throughout each drawing task. This prediction interval is
position dependent; it is large where curvature is high and smaller on
the outside of the spiral regardless of drawing direction. Although the
prediction interval may be determined by the figural aspects of the
task, the neuronal activity at a given location along the spiral is very dependent on the direction of movement.
One possibility for variable lags is intersegment delays along the arm.
Variable lags were found between shoulder adduction and finger
movement. However, the variable lags were not position dependent. For
both tracing directions, the intersegment delays were low during the
initial part of the movement and increased as the movement progressed.
Another possible contribution to the observed lags may be the delays
between muscle activation and limb displacement. However, a comparison
of EMG modulation and hand direction showed the same pattern as that of
the joint angles, suggesting that proximal-arm muscle activity and
proximal-arm kinematics are phase locked. It is unlikely that the
variable lags found in this task can be better reconciled with an
intrinsic coordinate system. However, other reference frames, such as
the affine coordinate system initially used in vision research and more
recently in motor control (Pollick and Sapiro 1997
), may provide a constant lag relationship with cortical activity, suggesting that movements may be planned in a non-Euclidean reference frame.
Another possibility is that the time-varying lags between cortical
activity and finger velocity could be explained by higher order terms
(e.g., acceleration), accounting for a higher percentage of cortical
discharge during higher curvatures. In the spiral tasks, as the
curvature increases, the tangential velocity decreases, whereas at the
same time both normal and tangential accelerations increase. Because
normal acceleration is always directed toward the center of the spiral,
it is position dependent. For the inside
out spiral, the normal
acceleration will lead the tangential velocity by 90°, but for the
outside
in spiral, it will lag tangential velocity by 90°. If the
normal acceleration did alter the lags, it would cause an increased
phase lag for higher curvatures in the outside
in spiral but a
decreased phase lag for higher curvatures for the inside
out spiral,
which is inconsistent with the observed prediction intervals.
Unlike normal acceleration, tangential acceleration always leads
tangential velocity by 90° phase shift. If it is assumed that the activity of a motor cortical cell were modulated by both tangential velocity and tangential acceleration, then the phase lag
(measured in degrees) would increase under higher curvatures. However,
because the cycle time or period decreases in the inner portion of the
spiral, the time lag (measured in ms) between tangential velocity and tangential acceleration decreases. Assuming the worse case
scenario (i.e., cortical activity is composed of 50% velocity coding
and 50% acceleration coding), the net affect of the increased tangential acceleration and decreased tangential velocity in high curvature areas would actually slightly reduce the time lag, making it
unlikely that acceleration (normal or tangential) contributes to the
observed time lags between cortical activity and movement.
The curvature-dependent lags differ from those observed at movement
initiation and suggests that the process of movement initiation is
distinct from that underlying intramovement control. At the beginning
of both tasks, there is a curvature-independent, transient lag of
~150 ms, similar to that found in point-to-point movements. This
initiation process subsides ~225 ms after the finger left the start
target, after which the lags become curvature dependent. The initial
portion of a reach is somewhat ballistic, and there may be a similar
lack of feedback control at the beginning of the drawing task. The
subsequent variable lags may be indicative of visual feedback that
becomes important in the ongoing tracing. A similar finding was made in
the oculomotor saccade control system (Munoz et al.
1991
). At the beginning of a saccade, superior colliculus output neurons fire at least 25 ms ahead of movement initiation, whereas within a saccade their activation results in an acceleration change within 10 ms.
The changes in PI were directly related to the instantaneous radius of
the figure. During straight drawing, the population vector directions
match that of the trajectory, and it is unlikely that the signal is
functioning in a predictive or causal manner because the PI is small.
Although both direction and speed are always represented accurately,
when the PI is small, the output of the motor cortex may reflect
corollary discharge generated in synchrony with the movement. For
straight paths, a "keep moving in the same direction" signal
transmitted once would be more efficient than continuous transmission
of the same direction. The timing lag between cortical signal and
movement may be related to the amount of intervening processing
required to generate the movement represented centrally by the
population vector. For regions of higher curvature, the motor cortical
PI is large, and the signal represented in this portion of the neural
trajectory may contribute to the underlying mechanism of trajectory
generation. Studies examining the representation of different movement
parameters (Ashe and Georgopoulos 1994
; Fu et al.
1995
; Kalaska et al. 1989
; Schwartz
1992
) find that direction is the predominant parameter represented in the discharge of motor cortical cells. If the motor cortex can be considered an important structure for the processing of
movement direction, it would be reasonable that within a continuous movement, this function comes into play only when direction changes rapidly, in regions where the path is curved. In this interpretation, more processing is required when direction changes rapidly over a short distance.
Timing considerations also have the potential to elucidate processing
between different neural structures. Our results show that premotor
cortical cells seem to be divided into two populations: those that
encode the direction synchronously during drawing and those that
predict it by ~250 ms. Because the PI in the primary motor cortex is
midway between the intervals of these two subpopulations and there is a
well-established reciprocal linkage between these cortical areas, these
results might be interpreted as evidence for a functional loop.
However, it is difficult to account for the long latency (125 ms)
between the appearance of corresponding direction signals in the
different populations. Even an indirect path through subcortical
structures would have a characteristic loop time that was much shorter
than this.
There are other possible explanations for these results. In a
circular task such as spiral drawing, the variables of interest typically have harmonic (i.e., sinusoidal) components. The derivative of a sinusoidal signal is another sinusoidal signal shifted by 90°.
The 250 ms seen between the two subpopulations of premotor cells
corresponds to a 90° phase shift in the spiral task (each circuit
takes ~1 s). Thus the subpopulation with a 250-ms direction lag could
actually be an acceleration signal and the later premotor subpopulation
a velocity representation.
The demonstration of an isomorphic representation of endpoint
trajectory in these cortical cells makes it possible to study the
instantaneous latencies between this representation and movement. There
are a number of explanations for the elastic nature of this latency.
Some of these are related to mechanics
time delays through a series of
joint rotations, and muscle excitation-displacement lags are examples
of these. Our data suggest that the timing relations of these factors
cannot account for the variable lags in both directions of tracing.
However, there are complex phase relations between many peripheral
motor elements that may contribute to these elastic lags. Directional
comparison of EMG activity and hand trajectory shows that the muscle
activity occasionally leads arm displacement by magnitudes as large as
those between neural activity and movement, suggesting a complex
relation between cortical output, muscle contraction, and arm
displacement. However, the clear, consistent relation between
prediction interval and curvature and the robust representation of
trajectory in these motor cortical areas suggests that
direction-related parameters such as curvature (change in
direction/distance) and angular velocity (change in direction/time) are
important in determining the way that the output of these areas
eventually contributes to the generation of movement.
A. Kakavand trained the animals and assisted in the experiments.
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 reprint requests: A. B. Schwartz, The Neurosciences
Institute, 10640 John Jay Hopkins Dr., San Diego, CA 92121.
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.