a , 3D best direction of each unit versus their locations in deltoid, for each subject. The best direction is given by the direction of the unit vector from the origin. The color of the vector codes for location. As location changes from posterior to anterior (and color changes from the blue to the red end of the spectrum), best direction changes from down – out–backward to up–out–forward. b , Pooled 3D best directions of all units versus their normalized locations in deltoid, for all subjects. Best directions are coded for location as in a . 

Contexts in source publication

Context 1

... the down–backward direction. In the horizontal and frontal planes, the threshold line yielded a best direction of out–back- ward and out–downward, respectively. The orientation of the threshold plane in the bottom row illustrates that the 3D best direction of unit 10.1 was in the out–back–downward direction. Unit 10.2 was found in a recording location 6.5 cm anterior to that of unit 10.1 (i.e., in the medial deltoid). Its best direction in the sagittal plane was in the up–forward direction, comparable to that of unit 9.2. Considering only the sagittal plane, one might thus conclude that the best directions for units 10.1 and 10.2 differed by 180°. The threshold lines for the horizontal and frontal planes, however, show that the best directions for unit 10.2 in these planes differed from those of unit 10.1 by only 60 and 15°, respectively. With respect to the lines for unit 10.1, the threshold lines for unit 10.2 were slightly rotated counterclockwise, such that the best direction was out–forward for the horizontal plane and straight outward for the frontal plane. Accordingly, the plane fit to the 3D data yielded a best direction for unit 10.2 that was oriented out–forward and slightly up. Of the three units in Figure 10, unit 10.3 was found in the most anterior recording location. Considering only the sagittal plane, this unit appeared to have approximately the same best direction as unit 10.2; however, the threshold lines for the other two planes were rotated counterclockwise with respect to those of unit 10.2 (by 30 and 35° for the horizontal and frontal planes, respectively). The best directions for these planes are thus forward– out (with a greater forward component than that of unit 10.2) in the hori- zontal plane and out–up in the frontal plane. The orientation of the threshold plane in 3D confirms that the best direction of this unit is up – out–forward. It follows from these results that the very large (or very small) differences found between the best directions of deltoid units for forces in the sagittal plane are deceptive. Units with apparently opposite best directions in the sagittal plane (such as units 10.1 and 10.2) might in fact have threshold planes that differ only relatively little in their orientations. Thus, in 3D space the dif- ference between the best directions of units 10.1 and 10.2 was only 53°. On the other hand, units with approximately the same best direction in the sagittal plane might show significant differ- ences between their best directions in 3D. Thus, the difference between the 3D orientation of the planes of units 10.2 and 10.3 was 48°, although their threshold lines in the sagittal plane dif- fered by only 6°. Analogous to the bimodal units described above for biceps (e.g., unit 6.3) we also found evidence for multiple directional inputs on deltoid SMUs (19%, n ϭ 14 in the 2D experiment (Fig. 9), 7%, n ϭ 5 in the 3D experiments). The 3D recruitment data for a bidirectional deltoid unit are shown in Figure 11. From the sagittal plane data, which are best fit by two approximately par- allel threshold lines, one cannot discern whether the threshold planes in 3D would be parallel, yielding two best directions opposite to each other or whether the two planes would have a line of intersection. However, two parallel threshold planes would intersect all three experimental planes with two parallel lines, and the two-line fits to the horizontal and frontal plane data clearly show that this is not the case. The two lines in these plots are not parallel but instead intersect at an angle of 90° in the horizontal and 125° in the frontal plane. Accordingly, the two threshold planes fit to the 3D data have a line of intersection. The best directions for this unit are up – out–forward and down – out–back- ward and differ by 93° in 3D. None of the threshold data of bidirectional units found in the second set of experiments were fit by two parallel planes, meaning that all bidirectional units exhib- ited intersecting threshold planes. The differences between the two best directions of such units ranged from 58 to 96° in 3D space with an average value of 77°. In Figure 12, each deltoid SMU is represented by a unit vector radiating (from the origin) in the best direction of the unit. The color of the vector codes for the anterior–posterior location of the unit in the muscle. In general, as unit location changed from posterior (blue end of spectrum) to anterior (red end), best direction gradually changed from down –backward to up– forward. A similar pattern was found in all three subjects (Fig. 12 a ). Regressing recording location on the x , y , z coordinate of the tip of the unit vector yielded significant correlations for subject A ( p Ͻ 0.001, r ϭ 0.79) and subject B ( p Ͻ 0.05, r ϭ 0.71) but a nonsignificant correlation for subject D ( p ϭ 0.066, r ϭ 0.66). Because all subjects exhibited a qualitatively similar relation between best direction and location, we then pooled the data (Fig. 12 b ). Pooling data from all subjects by normalizing the unit location (across the width of each subject’s deltoid, see Fig. 13 b ) yielded a highly significant relation between the 3D best direction and location ( p Ͻ 0.001, r ϭ 0.64). When regressing the 2D best directions for the horizontal and frontal planes on unit location, highly significant correlations ( p Ͻ 0.001) were obtained for all three subjects in both planes, with r 2 -values ranging from 0.6 to 0.8 (plots not shown). Units located in the posterior part of the muscle were best activated for out–backward (horizontal plane) and out– downward (frontal plane) forces. As unit location changed to the more anterior part of the muscle, best directions gradually changed to the out–forward and out–upward directions, with no suggestion of discontinuity at posterior–medial or medi- al–anterior compartmental boundaries. The range of threshold magnitudes in our sample of BI and deltoid units extended from 0.2 to 28 N, and ϳ 50% of the units had threshold forces of Ͼ 12 N. Thus, a substantial number of units in both muscles were recruited at relatively high force levels and could be assumed to contract quickly enough to be involved in the generation of fast-rising forces or movements. Moreover, as will be explained below, we found that units with threshold magnitudes as low as 2 N were involved in the generation of fast pulses of isometric force. Figure 13 illustrates the results from an experiment in which subject D produced isometric pulses to different targets in the frontal plane. (This figure is also representative of the results of the second dynamic experiment.) Simultaneous recordings from two different electrodes are shown. The threshold lines and preferred directions (in the frontal plane) of two units found on the two different electrodes are shown in Figure 13 a . The best direction of unit MD (found in the center of deltoid, Fig. 13 b ) was almost straight outward with only a slight upward component. On the other hand, unit M/AD (found in a recording location ϳ 3 cm anterior to unit MD) had an up–forward best direction. Consider now the relative timing of the multiunit bursts on the two recording electrodes during dynamic pulses (with a 250 msec time to peak) in the three different directions (Fig. 13 c , d ). As the direction of the pulse changed from upward ( top lines ) to up–out ( bottom lines ), the bursts in the two recordings reversed their order. For the upward direction (closer to best direction of unit M/AD), the burst in the recording at the more anterior site was earlier. For the outward direction (closer to best direction of unit MD), the burst in the recording at the more posterior site was earlier. Because we have ascertained that units M/AD and MD are involved in those bursts (as marked in the three-trial unit rasters), it appears that the recruitment order of these individual units also changed depending on the direction of the dynamic force. We found that threshold data for 93% of our biceps and deltoid motor units could be fit with lines in 2D and /or planes in 3D, consistent with a model in which activation levels are tuned as a cosine f unction of force direction (Fig. 2) and in consonance with the well established idea that the descending inputs to spinal motoneuronal –interneuronal pools may have cosine-tuned activ- ity (Georgopoulos et al., 1982, 1988; Fortier et al., 1993). Using the orientation of the line or plane as a measure of the best direction of a unit, we showed that SMUs of the same muscle were not activated homogeneously but instead different units had different best directions. The best directions of units changed continuously with their locations in the muscle and did not cluster into distinct groups. For deltoid, the gradual change in best directions may echo the gradual change in the mechanical actions of the muscle fibers (Buneo et al., 1996). As discussed below, the gradual change of best directions in biceps might be understood by considering that during the time course of a movement, biceps units may act in synergy with various deltoid units. Thus, the directional specificity of the recruitment order may act in con- junction with the phenomenon of size-ordered recruitment, to enable smooth and fatigue-resistant muscle contractions. But before developing these ideas, we will consider several technical issues that influence the interpretation of our data. Using only a 2 df force transducer in the first set of experiments raised the concern that any significant differences between 2D best directions of different BI units might be caused by day-to-day variability in the levels of force outside the sagittal plane. This possibility was ruled out by the fact that unit recordings obtained under identical force conditions (on the same electrode and/or in the same recording session) yielded significantly different best directions (Fig. 5, Table 1). Moreover, we were often able to identify two ...

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... Ͻ 0.01 level. The values of the correlation coefficient r for the x , y , and z coordinates of the threshold force levels ranged from 0.40 to 0.95. These results illustrate that in consonance with the line fit to the 2D data, threshold data in 3D can be fit by a plane. In Figure 10, the threshold line for unit 10.1 in the sagittal plane was oriented much like that for unit 9.1, with a best direction in the down–backward direction. In the horizontal and frontal planes, the threshold line yielded a best direction of out–back- ward and out–downward, respectively. The orientation of the threshold plane in the bottom row illustrates that the 3D best direction of unit 10.1 was in the out–back–downward direction. Unit 10.2 was found in a recording location 6.5 cm anterior to that of unit 10.1 (i.e., in the medial deltoid). Its best direction in the sagittal plane was in the up–forward direction, comparable to that of unit 9.2. Considering only the sagittal plane, one might thus conclude that the best directions for units 10.1 and 10.2 differed by 180°. The threshold lines for the horizontal and frontal planes, however, show that the best directions for unit 10.2 in these planes differed from those of unit 10.1 by only 60 and 15°, respectively. With respect to the lines for unit 10.1, the threshold lines for unit 10.2 were slightly rotated counterclockwise, such that the best direction was out–forward for the horizontal plane and straight outward for the frontal plane. Accordingly, the plane fit to the 3D data yielded a best direction for unit 10.2 that was oriented out–forward and slightly up. Of the three units in Figure 10, unit 10.3 was found in the most anterior recording location. Considering only the sagittal plane, this unit appeared to have approximately the same best direction as unit 10.2; however, the threshold lines for the other two planes were rotated counterclockwise with respect to those of unit 10.2 (by 30 and 35° for the horizontal and frontal planes, respectively). The best directions for these planes are thus forward– out (with a greater forward component than that of unit 10.2) in the hori- zontal plane and out–up in the frontal plane. The orientation of the threshold plane in 3D confirms that the best direction of this unit is up – out–forward. It follows from these results that the very large (or very small) differences found between the best directions of deltoid units for forces in the sagittal plane are deceptive. Units with apparently opposite best directions in the sagittal plane (such as units 10.1 and 10.2) might in fact have threshold planes that differ only relatively little in their orientations. Thus, in 3D space the dif- ference between the best directions of units 10.1 and 10.2 was only 53°. On the other hand, units with approximately the same best direction in the sagittal plane might show significant differ- ences between their best directions in 3D. Thus, the difference between the 3D orientation of the planes of units 10.2 and 10.3 was 48°, although their threshold lines in the sagittal plane dif- fered by only 6°. Analogous to the bimodal units described above for biceps (e.g., unit 6.3) we also found evidence for multiple directional inputs on deltoid SMUs (19%, n ϭ 14 in the 2D experiment (Fig. 9), 7%, n ϭ 5 in the 3D experiments). The 3D recruitment data for a bidirectional deltoid unit are shown in Figure 11. From the sagittal plane data, which are best fit by two approximately par- allel threshold lines, one cannot discern whether the threshold planes in 3D would be parallel, yielding two best directions opposite to each other or whether the two planes would have a line of intersection. However, two parallel threshold planes would intersect all three experimental planes with two parallel lines, and the two-line fits to the horizontal and frontal plane data clearly show that this is not the case. The two lines in these plots are not parallel but instead intersect at an angle of 90° in the horizontal and 125° in the frontal plane. Accordingly, the two threshold planes fit to the 3D data have a line of intersection. The best directions for this unit are up – out–forward and down – out–back- ward and differ by 93° in 3D. None of the threshold data of bidirectional units found in the second set of experiments were fit by two parallel planes, meaning that all bidirectional units exhib- ited intersecting threshold planes. The differences between the two best directions of such units ranged from 58 to 96° in 3D space with an average value of 77°. In Figure 12, each deltoid SMU is represented by a unit vector radiating (from the origin) in the best direction of the unit. The color of the vector codes for the anterior–posterior location of the unit in the muscle. In general, as unit location changed from posterior (blue end of spectrum) to anterior (red end), best direction gradually changed from down –backward to up– forward. A similar pattern was found in all three subjects (Fig. 12 a ). Regressing recording location on the x , y , z coordinate of the tip of the unit vector yielded significant correlations for subject A ( p Ͻ 0.001, r ϭ 0.79) and subject B ( p Ͻ 0.05, r ϭ 0.71) but a nonsignificant correlation for subject D ( p ϭ 0.066, r ϭ 0.66). Because all subjects exhibited a qualitatively similar relation between best direction and location, we then pooled the data (Fig. 12 b ). Pooling data from all subjects by normalizing the unit location (across the width of each subject’s deltoid, see Fig. 13 b ) yielded a highly significant relation between the 3D best direction and location ( p Ͻ 0.001, r ϭ 0.64). When regressing the 2D best directions for the horizontal and frontal planes on unit location, highly significant correlations ( p Ͻ 0.001) were obtained for all three subjects in both planes, with r 2 -values ranging from 0.6 to 0.8 (plots not shown). Units located in the posterior part of the muscle were best activated for out–backward (horizontal plane) and out– downward (frontal plane) forces. As unit location changed to the more anterior part of the muscle, best directions gradually changed to the out–forward and out–upward directions, with no suggestion of discontinuity at posterior–medial or medi- al–anterior compartmental boundaries. The range of threshold magnitudes in our sample of BI and deltoid units extended from 0.2 to 28 N, and ϳ 50% of the units had threshold forces of Ͼ 12 N. Thus, a substantial number of units in both muscles were recruited at relatively high force levels and could be assumed to contract quickly enough to be involved in the generation of fast-rising forces or movements. Moreover, as will be explained below, we found that units with threshold magnitudes as low as 2 N were involved in the generation of fast pulses of isometric force. Figure 13 illustrates the results from an experiment in which subject D produced isometric pulses to different targets in the frontal plane. (This figure is also representative of the results of the second dynamic experiment.) Simultaneous recordings from two different electrodes are shown. The threshold lines and preferred directions (in the frontal plane) of two units found on the two different electrodes are shown in Figure 13 a . The best direction of unit MD (found in the center of deltoid, Fig. 13 b ) was almost straight outward with only a slight upward component. On the other hand, unit M/AD (found in a recording location ϳ 3 cm anterior to unit MD) had an up–forward best direction. Consider now the relative timing of the multiunit bursts on the two recording electrodes during dynamic pulses (with a 250 msec time to peak) in the three different directions (Fig. 13 c , d ). As the direction of the pulse changed from upward ( top lines ) to up–out ( bottom lines ), the bursts in the two recordings reversed their order. For the upward direction (closer to best direction of unit M/AD), the burst in the recording at the more anterior site was earlier. For the outward direction (closer to best direction of unit MD), the burst in the recording at the more posterior site was earlier. Because we have ascertained that units M/AD and MD are involved in those bursts (as marked in the three-trial unit rasters), it appears that the recruitment order of these individual units also changed depending on the direction of the dynamic force. We found that threshold data for 93% of our biceps and deltoid motor units could be fit with lines in 2D and /or planes in 3D, consistent with a model in which activation levels are tuned as a cosine f unction of force direction (Fig. 2) and in consonance with the well established idea that the descending inputs to spinal motoneuronal –interneuronal pools may have cosine-tuned activ- ity (Georgopoulos et al., 1982, 1988; Fortier et al., 1993). Using the orientation of the line or plane as a measure of the best direction of a unit, we showed that SMUs of the same muscle were not activated homogeneously but instead different units had different best directions. The best directions of units changed continuously with their locations in the muscle and did not cluster into distinct groups. For deltoid, the gradual change in best directions may echo the gradual change in the mechanical actions of the muscle fibers (Buneo et al., 1996). As discussed below, the gradual change of best directions in biceps might be understood by considering that during the time course of a movement, biceps units may act in synergy with various deltoid units. Thus, the directional specificity of the recruitment order may act in con- junction with the phenomenon of size-ordered recruitment, to enable smooth and fatigue-resistant muscle contractions. But before developing these ideas, we will consider several technical issues that influence the interpretation of our data. Using only a 2 df force transducer in the first set of experiments raised the concern that any significant differences between 2D best ...

Context 3

... data for one deltoid unit. The top three rows depict the threshold lines for each of the three planes. These were derived only from trials with force ramps within the respective plane. The bottom row shows the 3D plane fit to data from all trials. In 57 of the 59 units examined in this set of experiments the plane fit to the threshold data was significant ( p Ͻ 0.05). In 45 of these units the plane fit was significant at the p Ͻ 0.01 level. The values of the correlation coefficient r for the x , y , and z coordinates of the threshold force levels ranged from 0.40 to 0.95. These results illustrate that in consonance with the line fit to the 2D data, threshold data in 3D can be fit by a plane. In Figure 10, the threshold line for unit 10.1 in the sagittal plane was oriented much like that for unit 9.1, with a best direction in the down–backward direction. In the horizontal and frontal planes, the threshold line yielded a best direction of out–back- ward and out–downward, respectively. The orientation of the threshold plane in the bottom row illustrates that the 3D best direction of unit 10.1 was in the out–back–downward direction. Unit 10.2 was found in a recording location 6.5 cm anterior to that of unit 10.1 (i.e., in the medial deltoid). Its best direction in the sagittal plane was in the up–forward direction, comparable to that of unit 9.2. Considering only the sagittal plane, one might thus conclude that the best directions for units 10.1 and 10.2 differed by 180°. The threshold lines for the horizontal and frontal planes, however, show that the best directions for unit 10.2 in these planes differed from those of unit 10.1 by only 60 and 15°, respectively. With respect to the lines for unit 10.1, the threshold lines for unit 10.2 were slightly rotated counterclockwise, such that the best direction was out–forward for the horizontal plane and straight outward for the frontal plane. Accordingly, the plane fit to the 3D data yielded a best direction for unit 10.2 that was oriented out–forward and slightly up. Of the three units in Figure 10, unit 10.3 was found in the most anterior recording location. Considering only the sagittal plane, this unit appeared to have approximately the same best direction as unit 10.2; however, the threshold lines for the other two planes were rotated counterclockwise with respect to those of unit 10.2 (by 30 and 35° for the horizontal and frontal planes, respectively). The best directions for these planes are thus forward– out (with a greater forward component than that of unit 10.2) in the hori- zontal plane and out–up in the frontal plane. The orientation of the threshold plane in 3D confirms that the best direction of this unit is up – out–forward. It follows from these results that the very large (or very small) differences found between the best directions of deltoid units for forces in the sagittal plane are deceptive. Units with apparently opposite best directions in the sagittal plane (such as units 10.1 and 10.2) might in fact have threshold planes that differ only relatively little in their orientations. Thus, in 3D space the dif- ference between the best directions of units 10.1 and 10.2 was only 53°. On the other hand, units with approximately the same best direction in the sagittal plane might show significant differ- ences between their best directions in 3D. Thus, the difference between the 3D orientation of the planes of units 10.2 and 10.3 was 48°, although their threshold lines in the sagittal plane dif- fered by only 6°. Analogous to the bimodal units described above for biceps (e.g., unit 6.3) we also found evidence for multiple directional inputs on deltoid SMUs (19%, n ϭ 14 in the 2D experiment (Fig. 9), 7%, n ϭ 5 in the 3D experiments). The 3D recruitment data for a bidirectional deltoid unit are shown in Figure 11. From the sagittal plane data, which are best fit by two approximately par- allel threshold lines, one cannot discern whether the threshold planes in 3D would be parallel, yielding two best directions opposite to each other or whether the two planes would have a line of intersection. However, two parallel threshold planes would intersect all three experimental planes with two parallel lines, and the two-line fits to the horizontal and frontal plane data clearly show that this is not the case. The two lines in these plots are not parallel but instead intersect at an angle of 90° in the horizontal and 125° in the frontal plane. Accordingly, the two threshold planes fit to the 3D data have a line of intersection. The best directions for this unit are up – out–forward and down – out–back- ward and differ by 93° in 3D. None of the threshold data of bidirectional units found in the second set of experiments were fit by two parallel planes, meaning that all bidirectional units exhib- ited intersecting threshold planes. The differences between the two best directions of such units ranged from 58 to 96° in 3D space with an average value of 77°. In Figure 12, each deltoid SMU is represented by a unit vector radiating (from the origin) in the best direction of the unit. The color of the vector codes for the anterior–posterior location of the unit in the muscle. In general, as unit location changed from posterior (blue end of spectrum) to anterior (red end), best direction gradually changed from down –backward to up– forward. A similar pattern was found in all three subjects (Fig. 12 a ). Regressing recording location on the x , y , z coordinate of the tip of the unit vector yielded significant correlations for subject A ( p Ͻ 0.001, r ϭ 0.79) and subject B ( p Ͻ 0.05, r ϭ 0.71) but a nonsignificant correlation for subject D ( p ϭ 0.066, r ϭ 0.66). Because all subjects exhibited a qualitatively similar relation between best direction and location, we then pooled the data (Fig. 12 b ). Pooling data from all subjects by normalizing the unit location (across the width of each subject’s deltoid, see Fig. 13 b ) yielded a highly significant relation between the 3D best direction and location ( p Ͻ 0.001, r ϭ 0.64). When regressing the 2D best directions for the horizontal and frontal planes on unit location, highly significant correlations ( p Ͻ 0.001) were obtained for all three subjects in both planes, with r 2 -values ranging from 0.6 to 0.8 (plots not shown). Units located in the posterior part of the muscle were best activated for out–backward (horizontal plane) and out– downward (frontal plane) forces. As unit location changed to the more anterior part of the muscle, best directions gradually changed to the out–forward and out–upward directions, with no suggestion of discontinuity at posterior–medial or medi- al–anterior compartmental boundaries. The range of threshold magnitudes in our sample of BI and deltoid units extended from 0.2 to 28 N, and ϳ 50% of the units had threshold forces of Ͼ 12 N. Thus, a substantial number of units in both muscles were recruited at relatively high force levels and could be assumed to contract quickly enough to be involved in the generation of fast-rising forces or movements. Moreover, as will be explained below, we found that units with threshold magnitudes as low as 2 N were involved in the generation of fast pulses of isometric force. Figure 13 illustrates the results from an experiment in which subject D produced isometric pulses to different targets in the frontal plane. (This figure is also representative of the results of the second dynamic experiment.) Simultaneous recordings from two different electrodes are shown. The threshold lines and preferred directions (in the frontal plane) of two units found on the two different electrodes are shown in Figure 13 a . The best direction of unit MD (found in the center of deltoid, Fig. 13 b ) was almost straight outward with only a slight upward component. On the other hand, unit M/AD (found in a recording location ϳ 3 cm anterior to unit MD) had an up–forward best direction. Consider now the relative timing of the multiunit bursts on the two recording electrodes during dynamic pulses (with a 250 msec time to peak) in the three different directions (Fig. 13 c , d ). As the direction of the pulse changed from upward ( top lines ) to up–out ( bottom lines ), the bursts in the two recordings reversed their order. For the upward direction (closer to best direction of unit M/AD), the burst in the recording at the more anterior site was earlier. For the outward direction (closer to best direction of unit MD), the burst in the recording at the more posterior site was earlier. Because we have ascertained that units M/AD and MD are involved in those bursts (as marked in the three-trial unit rasters), it appears that the recruitment order of these individual units also changed depending on the direction of the dynamic force. We found that threshold data for 93% of our biceps and deltoid motor units could be fit with lines in 2D and /or planes in 3D, consistent with a model in which activation levels are tuned as a cosine f unction of force direction (Fig. 2) and in consonance with the well established idea that the descending inputs to spinal motoneuronal –interneuronal pools may have cosine-tuned activ- ity (Georgopoulos et al., 1982, 1988; Fortier et al., 1993). Using the orientation of the line or plane as a measure of the best direction of a unit, we showed that SMUs of the same muscle were not activated homogeneously but instead different units had different best directions. The best directions of units changed continuously with their locations in the muscle and did not cluster into distinct groups. For deltoid, the gradual change in best directions may echo the gradual change in the mechanical actions of the muscle fibers (Buneo et al., 1996). As discussed below, the gradual change of best directions in biceps might be understood by considering that during the time course of a movement, biceps units may act in synergy with various deltoid units. Thus, the directional ...

Context 4

... subserves an activation of part of the parent muscle in synergy with various other muscles or motor units in the system. The force vectors produced by such units might be necessary to balance the ones generated by other synergistic muscles during the production of a desired force (Flanders, 1993). Thus, the bidirectional units found here might constitute subpopulations that are activated in synergy with other units in the system. This idea is consistent with findings by Jongen et al. (1989) who report intramuscular differences in activation during cocontraction of other muscles. If these bimodal SMUs receive input from only unimodally tuned neurons, the question arises as to how unimodal inputs can produce bimodal outputs. Summing two cosine f unctions always results in a third unimodal cosine f unction. Even when the two input f unctions have a threshold nonlinearity (see Materials and Methods section of this study and Flanders and Soechting, 1990) their addition results in a unimodal output f unction, unless the angular separation between the two input peaks is wide and/or the threshold is high. Thus, to reproduce the tuning pattern of bimodal units whose two best directions differ by Ͻ 90° (the norm in our study), some kind of nonlinear interaction has to occur between the two unimodal inputs. Using NEURON simulation software (Hines and Carnevale, 1997) we attempted to create the observed MN output solely from a specific pattern of convergence of unimodally tuned inputs at the dendritic arbor of the MN (Herrmann, 1998). Several combinations of inputs with different relative locations, weights, and preferred directions were simulated, but none of them re- sulted in the pattern of bimodal output observed experimentally. Thus, it seems that a solution at the level of the motoneurons would have to be a very specific one and that unimodal inputs do not tend to produce a bimodal output as a result of simple convergence patterns. An alternative model might contain a re- ciprocal inhibition between two unimodally tuned inputs. It is also possible that the bidirectional tuning of SMUs arises from bimodally tuned inputs. It has been suggested that a muscle is organized into smaller submodules such that the elements controlled by the CNS are neuromuscular compartments rather than whole muscles (Wind- horst et al., 1989; English et al., 1993). Such partitioned control might be functionally advantageous because individual muscles are nonuniform in their mechanical actions (Chanaud et al., 1991a; Carrasco and English, 1997) and/or their fiber type dis- tribution (Chanaud et al., 1991b). The existence of neuromuscu- lar compartments suggests the fractionation of the MN pool of a muscle into smaller, differently activated subpopulations. Presum- ably each subpopulation would then receive homogenous activa- tion such that recruitment order within each compartment is determined by MN size (Windhorst et al., 1989). For cat hindlimb muscle, the fibers innervated by MNs of the same subpopulation have been found to be largely restricted to a distinct muscular territory (English and Letbetter, 1982). According to these arguments we would have expected BI and deltoid units to fall into a limited number of groups, each group containing units with the same best direction and localized in a restricted muscle area. Instead we found a continuous distribu- tion of best directions with no convincing evidence for clustering. When grouping BI units with similar best directions together, their anatomical territories overlapped widely and spanned the whole width of the muscle (Fig. 8). Thus, the MN pool of these muscles appears not to be compartmentalized but to instead receive a more continuously distributed innervation. Georgopou- los et al. (1988) have shown that the 3D best directions of motor cortical cells uniformly cover the 3D space and do not appear to cluster into distinct groups. Thus, the neural substrate to create a continuous, finely graded distribution of the best directions of SMUs is available at the supraspinal level. A similar lack of compartmentalization has been found in a bitendoned finger extensor (Schieber et al., 1997). Although one might logically expect to find two distinct compartments in this muscle (one for each tendon), most units contribute to force on both tendons, with selectivity for either tendon ranging on a continuum. Analogously, BI has two distinct anatomical subdivi- sions with different attachments and moment arms at the shoulder (Wood et al., 1989), but the organization of its MN pool reveals more of a continuum. In deltoid, on the other hand, it seems apparent that the pulling directions of the SMUs change contin- ually with location along the broad attachment of the muscle (Buneo et al., 1997), thus motivating the continuously changing directional innervation of different parts of the muscle. Accordingly, the best directions of deltoid SMUs varied continuously across a wide area of space (Fig. 12). The correlation between best direction and recording location might also be related to the topography of the spinal M N pool as suggested by Kernell (1989). A rostrocaudal topography has been described for M N pools of the two parts of deltoid muscle in the rat (Choi and Hoover, 1996). The considerable overlap found between these two pools may be consistent with our finding of continuous rather than compartmentalized preferred directions and multiple directional preferences for some units. Similar features of muscle activation are found in movements and dynamic isometric forces (Ghez and Gordon, 1987; Flanders et al., 1996; Pellegrini and Flanders, 1996). This suggests that similar control strategies are involved in these two tasks. In Figure 13 we show that the timing of the activity of a unit moved from an early to a progressively later point in the force pulse as the direction of the pulse moved away from the best direction of the unit. Given the parallels between the neural control of force pulses and movements, one can speculate that the relative timing of recruitment during a movement could potentially be predicted from the best directions of the units under static conditions and the directions of dynamic forces during movement. As arm muscles change their mechanical actions with arm posture, the directional tuning of whole muscles generally changes in parallel with the new pulling directions of the muscles (Flanders and Soechting, 1990). Although it remains to be determined whether the best directions of the motor units change with posture (or if whole muscle tuning changes via recruitment of different units), this suggests that the central control mechanism takes limb configuration into account when issuing motor commands. Muscles with different mechanical actions are activated at different times during a reaching movement (Flanders et al., 1996). Thus, a factor determining the timing of the activation of a muscle might be the degree of correspondence between its pulling direction and the direction of force currently required. If differences in mechanical action exist across units within a muscle, the population of units optimally fit to produce a required force vector will change with limb position and force direction during a movement. Based on this logic, we hypothesize that at different points in the movement, the various units are recruited according to their mechanical actions. The neuromuscular system could thereby gradually make use of the wide number of units available instead of activating a few discrete populations. This spatiotemporal recruitment rule would necessarily involve violations of the size principle (Henneman et al., 1965; see also DeL uca and Erim, 1994). However, reminiscent of the advantages of size-ordered recruitment, this strategy would minimize fatigue and increase efficiency because mainly those units ideally suited for the production of a required force vector would be active at any given time. Furthermore, because cosine-tuned units are active over a wide range of directions, the change in unit activation during a movement need not consist in the abrupt recruitment and derecruitment of distinct subpopulations but can instead proceed smoothly by gradual recruitment and derecruitment and differential modulation of the firing rates of different units. This smooth change in relative unit activity would agree with the postulate that in the execution of a motor act, the control mechanism strives to minimize abrupt changes in the motor commands (Dornay et al., ...