Cortical Representation of Speed & Direction in Reaching: Motor Activity & Muscle Dynamics, Papers of Computer Science

Download Cortical Representation of Speed & Direction in Reaching: Motor Activity & Muscle Dynamics and more Papers Computer Science in PDF only on Docsity! Motor Cortical Representation of Speed and Direction During Reaching DANIEL W. MORAN AND ANDREW B. SCHWARTZ The Neurosciences Institute, San Diego, California 92121 Moran, Daniel W. and Andrew B. Schwartz. Motor cortical repre- sentation of speed and direction during reaching. J. Neurophysiol. 82: 2676–2692, 1999. The motor cortical substrate associated with reach- ing 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) com- ponents, 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. I N T R O D U C T I O N 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 him- self did not believe in a discrete somatotopic representation in the cortex, others (Fritsch and Hitzig 1870; Leyton and Sher- rington 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 cor- tical activity and arm movement by developing a model of single-cell activity. As the distributed nature of motor representations is becom- ing 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 Georgopou- los 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 repre- sentation 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 spi- ral drawing. In the last paper, both parameters varied harmon- ically 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 center3out task in which subjects made arm movements from a central location to eight targets separated by equal angles. Single-cell activity, charac- terized by a rate averaged over the reaction (RT) and move- ment 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 mod- ulated 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; Mo- rasso 1981; Soechting 1984). This is true of the center3out task; profiles to each target were bell-shaped and almost iden- tical. Three experimental conditions (movements encompass- ing all directions, constant directions within each movement, and similar speed profiles across different movements) made it possible to remove the directional component from the re- corded activity pattern while preserving the time-varying non- directional component. We used these characteristics to con- struct an equation relating single-cell discharge rate to movement direction and speed. The ensemble activity of motor cortical cells has been com- bined using the population vector algorithm (Georgopoulos et 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. 2676 0022-3077/99 $5.00 Copyright © 1999 The American Physiological Society al. 1983, 1988). These population vectors encode both instan- taneous speed and direction within a movement (Schwartz 1993, 1994a). Although it is clear that the directional contri- butions 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 com- ponent 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, suggest- ing 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 facili- tate electromyographic (EMG) activity (Fetz and Cheney 1978; Fetz and Finnochio 1975; Mantel and Lemon 1987). To com- pare the features of this cortical activity to muscle activity patterns, we recorded EMG activity of the proximal arm mus- cles 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 show- ing 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 para- digms 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. M E T H O D S The behavioral paradigm, surgical procedures and general animal care were approved by the Institutional Animal Care and Use Com- mittee. The outlines put forth by the Association for Assessment and Accreditation of Laboratory Animal Care and the Society for Neuro- science 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 mm horizontally and 17.5 mm 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 center3out 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 re- corded 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 center3out 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 mi- croelectrodes (10-mm tips). Standard criteria for single-unit identifi- cation 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 mA for 3–5 s) were occasionally placed along a pene- tration 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; clavic- ular pectoralis; triceps; biceps; and brachialis) were performed in a subset of the recorded trials. Two different types of EMG electrodes/ 2677CORTICAL REPRESENTATION OF SPEED AND DIRECTION DURING REACHING 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 6 5 (SE) ms for 41,560 trials. In addition, 15 prebins, having the same width as the movement bins, were calculated just before move- ment 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 move- ment directions. The outer perimeter of Fig. 3 shows the raw (i.e., unsmoothed and untransformed) firing rates during move- ments to each target for an example cell. During the hold-A period the rates were very similar across targets. In the subse- quent reaction and movement times, the activity was graded with movement direction. These histograms were smoothed and square-root trans- formed. 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). Av- eraging 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 5 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. 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 dis- charge 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 5 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. Nondirec- tional EMG activity was also correlated to the speed profile (R2 5 0.96, lag 5 65 ms). Directional response Figure 6 shows the response of a motor cortical cell (same cell as Fig. 3) during the center3out task. The firing rate FIG. 2. Average movement kinematics for the center3out task. A: the monkey placed its finger in the center start circle (dark gray circle) and made a planar movement to one of the 8 peripheral targets (light gray circles). The thick black line shows the average of 5,195 movements to each target. The thin lines represent the standard deviation of the mean. B: average velocity profiles to each of 8 peripheral targets are shown by the 8 thick black lines. The overall standard deviation (across all target directions) is repre- sented by the thin lines. FIG. 3. Speed representation in a motor cortical cell. Firing rates for move- ments to each of the 8 center3out targets were aligned to movement onset (V . 0.15Vmax), divided into 25 bins (26-ms binwidth) and averaged over 5 trials. The resulting histograms, located radially around the figure, represent the average cortical activity recorded for movements in each of the respective directions. The vertical calibration bar on the left of the figures represents 100 spikes/s. The timing marks under each histogram are 440 ms [average reaction time (RT) 1 movement time (MT)] apart and represent the portion of the histogram that was used to generate the central figure. These firing rates were then smoothed using a 10-Hz low-pass digital filter and square-root trans- formed. The tonic firing rate occurring during the hold-A period (i.e., the activity before the 1st timing mark in the histograms) was subtracted from the record. The firing rates were then summed over the 8 movement directions to cancel the directional component. The resulting nondirectional profile (left middle) is highly correlated to the average movement speed (right middle profile). 2680 D. W. MORAN AND A. B. SCHWARTZ 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]). 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 re- sulted in a test statistic of z 5 0.45, which corresponds to a p value 5 0.64. The null hypothesis of a uniformity cannot be rejected, and there is little uncertainty that this distribution is uniform. FIG. 4. A: histogram of maximum r2 values between actual movement speed and neural nondirectional component from 897 M1 cells. A sliding time window equal to the RT 1 MT was used to find the maximum r2 for each cell. B: lags between M1 cells’ nondirectional components and the actual movement speeds as determined from peak correlations of the sliding window analysis (A). C and D: same analyses applied to the 142 dorsal premotor (Pmd) cells. FIG. 5. Average representation of nondirectional components in muscles and cortical cells. The finger speeds (n 5 41,560) of all recorded trials were averaged over reaction and movement times (rightmost profile). Ensemble nondirectional components for Pmd (n 5 5,680), M1 (n 5 35,880), and electromyographic recordings (EMG; n 5 8,800) were correlated to movement speed using a sliding window analysis. FIG. 6. Directional tuning in a motor cortical cell. The outer raster data show the spike activity occurring between the beginning of reaction time (1st long hash mark) and the end of the movement (last long hash mark). The firing rates for movements to each target were temporally aligned to central target exit time (center long hash mark) and square-root transformed. The center polar plot shows the resulting average firing rates for each target (●) regressed to a cosine function (—). The units on the polar plot are in [rad]spikes/s. FIG. 7. A: histogram of directional tuning r2 values for 1,039 cortical (M1 and Pmd) cells. B: distribution of preferred directions in the tested work space. A circular histogram composed of 30° bins shows a maximum count of 101 in the 0° bin and a minimum count of 70 in the 240° bin. 2681CORTICAL REPRESENTATION OF SPEED AND DIRECTION DURING REACHING 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. Begin- ning with the top row, a systematic rotation in preferred direc- tions 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. How- ever, 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). EMG activity from 14 left arm muscles of 2 different mon- keys was recorded. The number of trials recorded for each muscle varied. Table 1 shows the total number of trials re- corded 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, graph- ically compares the average preferred directions among the muscles recorded and shows that almost all of them are orien- tated upward and within 45° of the vertical axis. The Rayleigh test yields a statistical value of 8.70, which corresponds to a p FIG. 8. Directional tuning in shoulder/elbow muscles. The temporal activities to each of the eight targets are positioned accordingly in each figure with the muscles’ “preferred directions” shown in the center of each figure. The 5-trial histograms were aligned by central target exit. The range of reaction time onsets (●) and the range of movement terminations (vertical bars) are shown beneath each histogram. All muscles with the exception of “S2-Pectoralis” were recorded from the same arm. 2682 D. W. MORAN AND A. B. SCHWARTZ 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. 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 di- rection (Table 2). The mean peak speed in this analysis was ;30 cm/s with a standard deviation of 610 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. 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 pat- terns 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 de- creases activity when the arm moves downward (270°). For faster movement speeds in the anti-preferred direction (down- ward), 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). FIG. 12. Results of a multiple regression analysis of Eq. 1 on single cell data. A: histogram of r2 values for all cells (n 5 1,039) recorded in this study. B: a similar analysis performed on nontransformed firing rates resulted in a slightly poorer median. C: using a constant lag of 145 ms, a reduced median r2 value was found for the transformed data. FIG. 11. Cortical and EMG tuning functions for different finger speeds. These functions were constructed from the results of regressing finger speed with normalized activity (Tables 2 and 3). In all figures, the thick black curve represents normalized activity during movements made with a peak speed of 35 cm/s. The thinner line corresponds to a peak speed of 25 cm/s. For the cortical figures (A and B), the center of the tuning curve for the mean speed (30 cm/s) is represented by an ordinate value of 1.0. For the muscular data, an ordinate value of 0.0 represents tonic activity during hold-A period, and 1.0 represents muscular activity when moving at mean speed in the muscle’s preferred direction. A: M1 cortical activity is always higher for faster speeds regardless of direction. B: Pmd cortical activity is also positively correlated with speed. C: anterior deltoid activity increases for higher speeds when moving in the muscle’s preferred (agonistic) direction; however, this muscle’s activity decreases during increasing speed for movements in the anti-preferred (antagonistic) direction. D: speed effects infraspinatus activity only when moving near the preferred direction. 2685CORTICAL REPRESENTATION OF SPEED AND DIRECTION DURING REACHING Multiple regression Equation 1 was validated using a multiple regression anal- ysis (rcov 2 IMSL). The form of Eq. 1 used in the multiple linear regression is D~t 2 t! 5 b0 1 \VW ~t!\bn 1 \VW ~t!\by sin @u~t!# 1 \VW ~t!\bx cos @u~t!# (5) The discharge rate, finger velocity, and direction as a function of time were the known parameters of the regression. The time lag (t) was varied from 250 to 2125 ms in single bin incre- ments. Two separate regressions were performed on each cell; one in which the firing rates were square-root transformed and the other in which they were not. Figure 12 shows the histo- grams of r2 values for all cells recorded (n 5 1,039) under three different conditions. Because this is a temporal analysis, the degrees of freedom (DOF) in the regression of Eq. 1 is much higher (78 DOF) than the time-averaged regression of Eq. 3 (6 DOF). As a result, an r2 . 0.08 is statistically significant at the p 5 1% level. In Fig. 12A, the time lag that yielded the best fit to the model (i.e., highest r2) for each cell using square-root transformed data were used to build a histo- gram of r2 values. Figure 12B is a similar analysis performed on nontransformed data. Finally, Fig. 12C shows the histogram for square-root transformed data using a fixed lag of 145 ms. The median r2 values in Fig. 12, A–C, are 0.68, 0.65, and 0.54, respectively. The results in Fig. 12, A and B, are very similar; the square-root transform slightly reduces the variance without changing the shape of the distribution. 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 cal- culated 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 5 arctan by/bx). Less than 20% of the cells had preferred directions that varied by .30° between the two models. 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 vec- tors. 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- FIG. 13. A and B: histograms of time lags found from the multiple regres- sion analysis of Eq. 1 on the primary motor cortical cells (A) and dorsal premotor cells (B). The distributions of lags are very similar to those shown in Fig. 4. The dynamic data from the regression shown in Fig. 12A (Eq. 1) were used to calculate preferred directions, and these were compared with the conventional, time-averaged calculation of preferred direction (Eq. 3) in C and D. The 2 methods gave similar results with .80% of both the primary motor (C) and premotor (D) cortical cells falling within a difference angle of ,30°. FIG. 14. Population vectors and trajectories. The outer octagonal figures contain vectorgrams of the velocity (thin) and population (thick) vectors for movements to each of the 8 targets of the center3out task. A: generated using 897 M1 cells. B: composed of 142 Pmd cells. Each set of vectors represents a time series (time advances in a counterclockwise direction) composed of 17 total vectors: 7 during the reaction period and 10 during the movement period. On average, the length of each vector corresponds to ;25 ms of time. The 10 population vectors that correlated best to the velocity vectors occurring over the movement period were integrated in time. The results of this integration can be seen in the center of each figure. The thin lines represent finger trajectory, whereas the thick lines represent the population trajectory. 2686 D. W. MORAN AND A. B. SCHWARTZ 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. Neural trajectories can be formed by integrating the popu- lation 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 tempo- rally 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 trajec- tory. 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). 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 mag- nitudes are well related to speed in this portion of the move- ment. 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 popu- lation 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). D I S C U S S I O N 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 move- ment parameters and cortical activity, it is necessary to exam- ine those components that vary in time. During reaching, the arm’s trajectory is fairly straight; movement direction is ap- proximately 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 in- cluding 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 FIG. 15. A: regression between finger speed and population vector magni- tudes of M1 cells. B: similar regression performed on premotor population vector magnitudes resulted in a lower correlation. C: comparison of average population vector magnitudes (thick lines) and ensemble nondirectional com- ponents (thin lines). The nondirectional and population magnitude profiles for M1 cells are very similar (r2 5 0.96), and both represent well the average finger speed. D: Pmd cells generate very different results (r2 5 0.07) when comparing population vector magnitude to nondirectional activity. Time 0 represents movement onset. 2687CORTICAL REPRESENTATION OF SPEED AND DIRECTION DURING REACHING 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 center3out task. Our knowl- edge 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 move- ment 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 conse- quence 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 orienta- tion of the population vector (see APPENDIX). Interestingly, if the effect of this additive factor is not constant in all directions when performing the center3out 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. A P P E N D I X 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 PV1 5 O i51 num cells D# i,1 2 B0,i D# i,max z Bx,i D# i,max (A1) Equation A1 is for movements along the positive x-axis; thus there is no y component and PV# 1 is equal to the magnitude of the population vector. D# i,1 corresponds to the average firing rate of cell i to target 1 and D# i,max corresponds to the maximum depth of modulation for cell i across all targets. Movements in this direction correspond to a direction of zero degrees; therefore the average discharge of cell i during movements to target 1 can be written as D# i,1 5 B0,i 1 D# i,max cos ~upd! (A2) Likewise, the x component of cell i’s preferred direction can be written as Bx,i D# i,max 5 cos ~upd! (A3) Substituting Eqs. A2 and A3 into Eq. A1 yields PV1 5 O i51 num cells cos2 ~upd! (A4) Assuming a uniform directional distribution of N cells, Eq. A4 can be rewritten as PV1 5 N 2p E 0 2p cos2 ~u!du (A5) Solving: PV1 5 N 2p Fu2 1 sin ~2u!4 G u 0 2p 5 N 2 (A6) Thus for a population of cells with a uniform distribution of preferred directions with discharge rates described completely by cosine tuning, the lengths of the population vectors for a center3out task would be equal to one-half the number of cells in the population. We have shown that population vector length is directly propor- tional 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 PV1,HS 5 O i51 num cells D# i,max,HS cos 2 ~upd! 1 ~B0,i,HS 2 B0,i! cos ~upd! D# i,max,HS (A7) PV1,LS 5 O i51 num cells D# i,max,LS cos 2 ~upd! 1 ~B0,i,LS 2 B0,i! cos ~upd! D# i,max,HS (A8) where the subscripts HS and LS correspond to the high-speed and low-speed trials, respectively. (Both equations are normalized by the high-speed maximum discharge rate because it would be the larger overall firing rate.) Converting to integrals and solving yields PV1,HS 5 N 2 (A9) PV1,LS 5 N 2 D# max,LS D# max,HS (A10) The lengths of the population vectors are dependent only on the ratios of the depths of modulation of the cells for the two different trials. Although the B0 term could vary with speed, it would have no effect on the population vector lengths. The proof above was based on 2690 D. W. MORAN AND A. B. SCHWARTZ average population vectors (Eq. 3); however, the results would be the same for a multi-bin analysis. 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