A trade-off between kinematic and dynamic control of bimanual reaching in virtual reality

Abstract

Bimanual coordination is an essential component of human movement. Cooperative bimanual reaching tasks are widely used to assess the optimal control of goal-directed reaching. However, little is known about the neuromuscular mechanisms governing these tasks. Twelve healthy, right-handed participants performed a bimanual reaching task in a three-dimensional virtual reality environment. They controlled a shared cursor, located at the midpoint between the hands, and reached targets located at 80% of full arm extension. Following a baseline of normal reaches, we placed a wrist weight on one arm and measured the change in coordination. Relative contribution (RC) was computed as the displacement of the right hand divided by the sum of displacements of both hands. We used surface electromyography placed over the anterior deltoid and biceps brachii to compute muscle contribution (MC) from root mean squared muscle activity data. We found RC was no different than 50% during baseline, indicating participants reached equal displacements when no weights were applied. Participants systematically altered limb coordination in response to altered limb dynamics. RC increased by 0.91% and MC decreased by 5.3% relative to baseline when the weight was applied to the left arm; RC decreased by 0.94% and MC increased by 6.3% when the weight was applied to the right arm. Participants adopted an optimal control strategy that attempted to minimize both kinematic and muscular asymmetries between limbs. What emerged was a trade-off between these two parameters, and we propose this trade-off as a potential neuromuscular mechanism of cooperative bimanual reaching.

NEW & NOTEWORTHY This study is the first to propose a trade-off between kinematic and dynamic control parameters governing goal-directed reaching. We propose a straightforward tool to assess this trade-off without the need for computational modeling. The technologies and techniques developed in this study are discussed in the context of upper extremity rehabilitation.

INTRODUCTION

Bimanual coordination is a hallmark of the human motor control system. One hand “knowing” what the other is doing affords us the ability to perform complex movements necessary for activities of daily living such as opening a jar or tying shoelaces. The simplicity with which most of us perform these tasks is belied by the complexities encountered when designing movement tasks to make testable predictions regarding bimanual control. For example, it is often difficult to predict when control of two effectors, say the upper extremities, should remain independent or if coupling the limbs leads to better control. Recently, optimal feedback control theory (OFCT) has provided researchers with a framework to test predictions relating to bimanual coordination (1). This theory posits that the motor system generates an optimal control strategy that attempts to minimize the costs associated with movement. Diedrichsen et al. (2) elegantly describe a two-part cost function that when minimized approaches the optimal solution. The first term encodes the cost associated with the task-specific nature of movement. For example, when reaching a target, a person tries to minimize the distance between the target and the hand. This cost penalizes nonrewarding states, such as being “far” from the target, and rewards states that achieve the external goal of the movement. Alone, this cost fails to provide a converging solution as there exists motor redundancy that allows for an infinite number of trajectories, velocity profiles, etc. that would satisfy the goal of the task (3). Therefore, a regularization term functions to constrain the solution to minimize the costs associated with superfluous motor commands. In our reaching example, this would yield reaches that are mostly straight and not excessively fast, as this would reduce accuracy and lead to more energetically costly movements. In bimanual tasks, this naturally leads to cooperation between the limbs (4); however, the nature of this cooperation is highly task-specific. For example, when participants perform bimanual center-out reaching when one hand is exposed to a dynamic perturbation, the nature of bimanual coordination is modulated to fit the task constraints (5). In a two-cursor condition, where each hand controls its own cursor, only the hand receiving the perturbation corrects for movement error. When the two hands share control of a single cursor, both hands counter the perturbation. This cooperation in the shared-cursor condition is predicted by OFCT because the visual manipulation induces coupling between the limbs. Therefore, the overall muscle activation should be minimized when both limbs produce nominal outputs, as the regularization term follows the sum of squares of motor commands sent to the muscles (2, 6).

The first purpose of this study was to test a specific prediction stemming from OFCT regarding the extent to which each limb contributes to shared cursor control when the force demands for reaching are manipulated. To this end, we designed a center-out reaching task using a virtual reality (VR) system, which allowed participants to control a virtual cursor located at the midpoint between the hands (5). We systematically increased the force demands for reaching by placing wrist weights on one arm to drive a change in bimanual coordination. This change in coordination is predicted by OFCT in that the wrist weights serve to increase the cost associated with using the weighted limb. As the regularization of motor commands takes the form of a sum of squares, and the torque due to gravity on the arm increases with reaching displacement, this cost can be minimized by reducing the reaching displacement of the weighted limb relative to the nonweighted limb. Specifically, we hypothesized that if participants optimized control of a shared cursor during center-out reaching, introducing an asymmetry in the force demands for reaching would increase the displacement of the nonweighted limb compared with the weighted limb.

As the asymmetric reaching trajectories predicted in our task are a direct result of the motor system’s attempt to minimize movement costs by evenly distributing motor output to the two limbs, we assayed the muscle activity in each limb using surface electromyography (EMG). Surface EMG has long been used as a proxy for the motor output from the central nervous system (7, 8). When humans reach for objects in three-dimensional space, the shoulder is the primary contributor to movement (9). Moreover, as the height of the required reach increases, participants increasingly engage elbow flexion. In this study, we asked participants to make bimanual reaches, starting with their hand resting in their lap, to targets at eye and shoulder level. We measured the three-dimensional position and EMG for both arms during the reach out and back (lap-to-lap). During such movements, muscle activity in the anterior deltoid and biceps brachii, measured by the root mean square (RMS) of EMG time series data, increases as participants reach out to the target and decreases for the return to lap. Therefore, we used RMS of the anterior deltoid and biceps brachii EMG signals as a measure of motor output in our shared cursor-reaching task. It is natural to assume that increasing the weight of one limb relative to the other will increase the muscle activity needed to move the weighted limb. However, as the motor system tries to minimize the costs associated with movement, participants should decrease the use (i.e., displacement) of the weighting limb, thereby minimizing muscle activity asymmetries between limbs. One outstanding question is to what extent the participants will minimize muscle activity asymmetries versus their attempts to minimize spatiotemporal asymmetries between limbs (10, 11). The second purpose of this study was to test the relationship between bimanual coordination and muscle output asymmetries in a redundant motor task. We predicted that if we were to observe changes in RMS muscle activity in the anterior deltoid and biceps brachii this would coincide with changes in the relative contribution of each limb to the overall reach. Establishing this relationship will provide evidence for a trade-off in neuromuscular control of bimanual-coordinated reaching. We discuss the results in the context of the motor system tuning the sensitivity of feedback gains to emphasize kinematic versus dynamic information used for sensorimotor integration.

MATERIALS AND METHODS

Participants

We recruited 13 healthy young adults from the Catholic University of America’s undergraduate and graduate school population. One participant was removed from the study for not scoring above +75 on the Edinburg handedness questionnaire–short-form (12, 13), leaving a final study population of 12 right-handed individuals (age = 23.6 ± 4.3 yr, 5 female). Participants gave written informed consent before engaging in the study and all procedures were approved by the Catholic University of America’s Institutional Review Board. Participants received a $25 gift card for each testing session.

Experimental Setup

Participants were seated comfortably in an armless desk chair in a space that allowed for free movement of both upper extremities. The chair was located 1.5 m in front of two Oculus Rift virtual reality (VR) infrared cameras (Facebook, Inc.). Participants then donned a Rift head-mounted display and were handed two Rift Touch controllers. These controllers were used to interact with virtual objects projected into a custom three-dimensional virtual reality environment programmed in the Unity video game engine (Unity Technologies). Three-dimensional position of both Touch controllers was recorded using LabStreamingLayer (UC San Diego, GitHub: https://github.com/sccn/liblsl) and sampled at 50 Hz. We then secured, using medical adhesive, four Trigno Wireless EMG sensors (Delsys, Inc., Natick, MA) to the anterior deltoid and short head of the biceps brachii, bilaterally. These sensors measured surface EMG activity at 2,000 Hz.

Virtual Reality Task

Participants performed a bimanual, center-out reaching task to cube-shaped targets located at 80% of their maximum reach. Targets appeared one at a time, at one of six locations: +15° from midline, midline, and −15° from midline, both at eye-level and shoulder-level (see Fig. 1A for schematic). Participants controlled a single spherical cursor, located at the midpoint between the Rift Touch controllers; vision of the hands was not provided. Therefore, the only visual objects projected into the VR space were a single cursor, a single target, and the default wire grid room (four walls and a floor). Once a target cube appeared, participants were instructed to reach with both hands to place the cursor inside the target. Once the cursor collided with the target and remained in the target for 0.5 s, the target disappeared, and the participant returned their hands to their lap. Therefore, one trial consisted of the full out-and-back reach. We began the experiment with a practice block where we instructed participants to reach to the targets using only one hand at a time, followed by reaches using both hands. This gave participants explicit knowledge that each hand contributed equally to cursor control and that the most efficient strategy was to use both hands. They were verbally instructed to use both hands while reaching for the targets but that they could use as much or as little of one hand as they liked. We then emphasized that while reaching for the targets, they should “reach however feels most comfortable.” Participants made self-paced reaches.

Figure 1.

Experimental design. A: schematic of testing setup. Targets were located at shoulder and eye level at 80% of full arm extension. Each of the six targets appeared with equal frequency within each block. B: exemplar task sequence of within-subjects, repeated-measure design. Both experimental factors, initial limb weighting (left vs. right wrist) and load level (30% vs. 60%), were counterbalanced across blocks and days.

The experiment had two independent variables to assess what effect altering limb dynamics would have on bimanual coordination. The first variable was the hand (left vs. right) on which we placed a wrist weight; the second variable was the load (30% vs. 60%) applied to the wrist, tailored to each participants’ body mass. This required participants to attend two testing sessions on two different days; the number of days between testing sessions was not controlled for and ranged between 1 and 34 days. A single session consisted of 5 blocks of 96 trials, for a total of 480 trials on day 1 and an additional 480 trials on day 2. The first, third, and fifth blocks were baseline blocks where no weights were applied to the wrists. In the second and fourth blocks, we attached one wrist weight to either the left or right wrist. The order of hand (right vs. left) and load (30% vs. 60%) was counterbalanced across blocks and days. See Fig. 1B for an exemplar task sequence. The wrist weights (Gymenist Adjustable Ankle/Wrist Weights, Gymenist) were adjusted to provide either a 30% or 60% increase in the torque due to gravity at the shoulder of a fully outstretched arm. Specifically, we tuned the mass of the wrist weight according to each participants’ body mass, using the following equation:

$$\mathit{wrist}\mathit{weight}\mathit{mass}=\mathit{percent }\times 0.05 \times \mathit{ body}\mathit{mass }\times 0.53$$

where “percent” refers to either 30% or 60%. The 0.05 converts body mass into arm mass, and the 0.53 value defines the center of mass of the arm as a percentage of the distance from the acromion to the ulnar styloid process. These constants were taken from Table 3.2 in McGinnis (14). For example, a 70 kg person would experience approximately a 10 Nm torque due to gravity at the shoulder joint when fully extending their upper arm parallel to the ground. To increase this by an additional 3 Nm (30% loading condition), we would add 0.556 kg to the wrist. The wrist weights allowed for a mass resolution of 31 g.

Data Analysis

The central purpose of this study is to show that participants optimize reaching in our VR task. We hypothesized that this would be reflected in an increase in use of the nonweighted limb relative to the weighted limb. To quantify a change in limb use, we used as our primary outcome measure relative contribution (RC). We computed this value as the displacement of the right hand divided by the sum of displacements for the right and left hands, multiplied by 100. Therefore, a value equal to 50 would signify a perfectly equal contribution by both hands to the overall reach, whereas any value greater than 50 would signify increased right limb use. RC values less than 50 would signify increased left limb use. Critically, RC was calculated for only the outward reach. That is, the displacement for each hand was defined as the change in three-dimensional position from the trial starting position (hands resting in lap) to the cursor-target collision.

We performed two bias corrections on RC. First, we performed a baseline correction by subtracting from each value the mean of RC during block 1. That is, each day’s 480 trials were corrected relative to the mean of that day’s first 96 trials. This corrected for any potential a priori laterality bias that might cause participants to favor using their dominant hand (15). The second correction adjusted for baseline differences in RC based on target location. The Unity program draws targets relative to a coordinate frame origin located at the midpoint between the Oculus infrared cameras. Although the testing chair was placed in the same location relative to this origin for all data collections, this correction allowed us to remove any potential lateral bias due to participant positioning or postural differences between subjects. Positioning biases were on the order of less than 5 cm. Moreover, we performed a one-way ANOVA on RC during the first baseline block with within-subjects factor target location. We found a significant effect of target location (F_1.6,18.1 = 9.7, P = 0.002, ges = 0.47; Greenhouse-Geisser correction) and visual inspection of the data suggested that when reaching for lateral targets, the hand required to cross the body’s midline moved farther than the other hand. To correct for these two sources of bias, we added “Target” as a grouping variable in our baseline correction. Simply, these two bias corrections had the effect of subtracting from each target’s RC value the mean during baseline of all 16 reaches to that specific target. We then repeated the one-way ANOVA and found no difference in RC between target locations (P = 0.14).

Optimal control during reaching with a shared cursor manifests as a minimization of the sum of squares of motor output (2). As each muscle contributes to the regularization term (see introduction) as the square of outputs, the minimum cost solution would be one where the two limbs produce the same output. To quantify this, we approximated muscle output as the root mean square (RMS) of the surface EMG signal for the full out and back reach. Before calculating RMS, we detrended and zero-offset the full time series recording and applied a 5–250 Hz bandpass filter (16). After signal conditioning, we then computed muscle contribution (MC), as we did for RC, for each homologous muscle pair. That is, we divided RMS for the right muscle by the sum of RMS values for both right and left muscles. Finally, we applied the same bias corrections (baseline and target location corrections) as was done for RC.

One possible outcome is for RC and MC to covary in response to limb loading. For example, as the wrist weight increases the force demands for reaching in the weighted limb, participants should decrease the relative contribution of that arm to the overall reach. Therefore, MC would increase, and RC would decrease in response to the right-hand (RH) weighted condition; vice versa for the left-hand (LH) weighted condition. We performed a descriptive analysis of this trade-off by scatter-plotting the change in RC, relative to baseline, versus the change in MC. We then evaluated the slope of a line connecting the points clustered by hand (RH vs. LH) for each muscle pair.

Data Reduction and Statistical Analysis

Exploratory analysis of our data indicated that neither RC nor MC changed over time within a block (see results for more detail). This is an important check, for if a measure changed over time, we would include “time” as a factor in our analyses. Alternatively, if a measure remained constant throughout a block (as was seen for these data), we would assess performance in each block in aggregate. For RC, we calculated the mean-by-block grouping by participant, hand (LH weighted, RH weighted), and load (30%, 60%). Visual inspection of MC data showed several potential outlier values. Further analysis suggested these values were the result of sensor malfunction such as movement artifacts, likely caused by their interaction with clothing. To correct for these artifacts, we removed any MC value that fell outside of the median ±1.5 × IQR, where IQR is the interquartile range (removed 12.7% of observations). Following outlier removal, we calculated the mean-by-block of MC grouping by participant, hand, load, and muscle pair (biceps, deltoid).

For RC, we performed a repeated-measures ANOVA with within-subjects factors hand (LH weighted vs. RH weighted) and load (30% vs. 60%). For MC, we performed a repeated-measures ANOVA with within-subjects factors hand (LH weighted vs. RH weighted), load (30% vs. 60%), and muscle (deltoid vs. biceps). For the RC-MC trade-off analysis, we report 95% confidence intervals (CI) for the slope of the connector lines between hand clusters. Omnibus ANOVAs were computed in R (version 4.0.3) using the aov_ez() function from the afex package. Significant main effects and interactions were further analyzed using the emmeans package with model pairwise comparisons performed using the Tukey method; pooled degrees of freedom and adjusted test statistics are reported. Violations to sphericity were corrected using the Greenhouse-Geisser correction. Statistical significance was set to P < 0.05; we report ANOVA omnibus effect sizes as generalized eta-squared (17) and post hoc effect sizes using the Cohen’s d measure.

RESULTS

Figure 2 illustrates how coordination and muscle activity change throughout the reach for one participant who responded strongly to limb weighting. In Fig. 2A, we show the displacement of each hand throughout movement extent (from lap-to-target) in the 16 reaches to the midline, eye-level target. In both the RH and LH weighted conditions, the nonweighted limb displaced farther than the weighted limb, especially near the target collision. In Fig. 2B, we show that the RMS muscle activity of each deltoid muscle throughout movement extent (lap-to-lap) was greater in the weighted limb than in the nonweighted limb. Displacement time series data were resampled to 100 samples before averaging. RMS values were calculated using 50 nonoverlapping windows on resampled (5,000 samples per trial) time series data before averaging.

Figure 2.

Hand displacement (A) and deltoid muscle activity (B) throughout movement extent. Data from all 16 reaches within a block (LH weighted and RH weighted) to the midline, eye-level target were averaged for one 31-yr-old male participant who responded strongly to limb weighting. Displacement data from lap-to-target were resampled to 100 samples before averaging. RMS muscle activity values from lap-to-lap were computed using 50 nonoverlapping windows on resampled data before averaging (5000 samples/trial). Thick lines represent the mean; clouds represent SE. LH, left hand; RH, right hand; RMS, root mean square.

Block-Timeseries Analysis

RC did not change over time within each of the 96 trial blocks. To verify this, we reduced each 96 trial block into 6 trial bins, for a total of 16 bins per block. Importantly, each six trial bin contained one reach to each of the six target locations. We then performed a hand (RH weighted vs. LH weighted) × bin (bin 1 vs. bin 16) within-subjects ANOVA and found no main effect for bin (F_1,11 = 0.04, P = 0.85, ges = 0.001), nor a hand × bin interaction (F_1.7,18.6 = 0.10, P = 0.87, ges = 0.001). Further analysis of the time series data showed RC in the first baseline block hovered around 50% on both testing days (30% and 60% loading conditions were tested on different days) indicating that participants did not favor one hand over the other while reaching without load (Fig. 3, top). This was supported by one-sample t tests failing to reject the null hypothesis that RC values did not differ from 50 for either load level (30%: t₁₁ = 0.26, P = 0.8, d = 0.07, 60%: t₁₁ = 0.63, P = 0.54, d = 0.18). Time series analysis of MC showed that muscle activity, expressed as a percent change from baseline, did not change over time within a block. A repeated-measures ANOVA using hand, muscle, and bin as within-subjects factors failed to detect a significant main effect for bin (F_1,7 = 0.00, P = 0.98, ges = 0.001), nor a hand × bin interaction (F_{1.1, 7.8} = 0.31, P = 0.62, ges = 0.04) or muscle × bin interaction (F_1,7 = 2.11, P = 0.19, ges = 0.03). Figure 3 (bottom) illustrates the point that for each hand, muscle, and load, there is no change in MC over time (bin). Taken together, the lack of a change in time in either outcome measure motivated our approach to analyze these data within blocks in aggregate.

Figure 3.

Relative contribution and muscle contribution block-timeseries. Top: relative contribution (RC) of the right hand relative to the left during the first baseline (red), left-hand weighted (green), and right-hand weighted (blue) conditions. Each data point represents the mean and standard error of 6 consecutive trials (bins) throughout each testing block. RC did not change over time, indicating participants were not fatigued by weight application, nor did they adapt to the altered limb dynamics. However, placing the wrist weight on one arm increased the contribution of the contralateral limb. In addition, this altered coordination pattern was enhanced by increasing the mass of the wrist weight. Bottom: the change in muscle contribution (ΔMC) relative to the first baseline (red) increased in the weighted limb compared with the nonweighted limb in both the biceps brachii and anterior deltoid muscles. Like RC, ΔMC did not change over time within each block but was systematically altered by the wrist weights. For both muscle pairs, MC increased in the weighted arm compared with the nonweighted arm in a dose-response fashion, but this response was greater in the biceps compared with the deltoid. Study population comprised 12, right-handed young adults (age: 23.6 ± 4.3 yr, 5 female). LH, left hand; RH, right hand.

Coordination Analysis

We found that RC was altered by the location and mass of the wrist weights. There was a main effect for hand (F_1,11 = 42.6, P = 4.3e-05, ges = 0.56); since the placement of the wrist weights drove the coordination in opposite directions (Fig. 4), we failed to show a main effect for load (F_1,11 = 0.42, P = 0.53, ges = 0.12). However, we did find a hand × load interaction (F_1,11 = 13.6, P = 0.004, ges = 0.13). Post hoc analysis revealed that as the mass of the wrist weights increased from 30% to 60%, the change in coordination increased by an additional 0.8% for the LH weighted condition (t_18.4= 2.5, P = 0.022, d = 0.76) but only 0.5% for the RH weighted condition (t_18.4= 1.4, P = 0.18, d = 0.38). These results demonstrate a systematic change in bimanual coordination when weights are applied to the wrists during our shared cursor task, and this effect increases with an increase in wrist weight mass.

Figure 4.

The change in relative contribution (ΔRC) of the right hand relative to the first baseline block. Values above zero indicate an increase in the displacement of the right hand compared with the left hand. Participants increased the use of their nonweighted limb compared with their weighted limb (F_1,11 = 42.6, P = 4.3e-05, ges = 0.56). When we placed a wrist weight on the left hand, increasing the mass of the weight from 30% to 60% of arm torque increased RC of the right hand by an additional 0.8% (t_18.4= 2.5, P < 0.022, d = 0.76). Here, we show a systematic change in bimanual coordination in response to altered limb dynamics. Study population comprised 12, right-handed young adults (age: 23.6 ± 4.3 yr, 5 female). LH, left hand; RH, right hand.

Placing wrist weights on the arms of participants had a substantial influence on muscle activity during reaching. Figure 5 shows that muscle activity increased in the limb wearing the wrist weight relative to the contralateral limb. This was confirmed by the hand × load × muscle ANOVA reporting a main effect for hand (F_1,8 = 143.0, P = 2.2e-06, ges = 0.53). This finding is further supported by examination of a significant hand × load interaction (F_1,8 = 33.91, P = 3.9e-04, ges = 0.12). Post hoc analysis on this interaction shows a dose-response in the LH weighted condition such that increasing the load from 30% to 60% increased muscle activity by an additional 5.6% (t_9.96 = 2.5, P = 0.03, d = 0.79) in the left limb relative to the right. We did not see the dose-response in the RH weighted condition (t_9.96 = 1.3, P = 0.21, d = 0.4). We note that these changes are aggregated over muscle, as there was no muscle × load interaction (F_1,8 = 0.1, P = 0.771, ges = 0.003). We did not find significant hand × muscle (F_1,8 = 1.62, P = 0.24, ges = 0.02) or hand × load × muscle interactions (F_1,8 = 1.46, P = 0.26, ges = 0.005). Overall, these results demonstrate that when we place a wrist weight on one of the arms, participants increase muscle activation in the limb wearing the wrist weight relative to the contralateral limb. We also show a dose-response such that increasing the mass of the wrist weight increases muscle activation.

Figure 5.

The change in muscle contribution of the right limb (ΔMC) relative to the left compared with the first baseline block. Values greater than zero indicate increased muscle activity in the right muscle (biceps or deltoid) compared with the left muscle. Muscle activity in the weighted limb was higher than in the nonweighted limb (F_1,8 = 143.0, P = 2.2e-06, ges = 0.53), regardless of load and muscle pair. When the wrist weight was placed on the left arm, increasing the load from 30% to 60% increased muscle activity in the left arm by an additional 5.6% (t_9.96= 2.5, P = 0.03, d = 0.79). Here, we show that placing a wrist weight on one arm produces an asymmetry in activity in the muscles controlling the upper extremities. Study population comprised 12, right-handed young adults (age: 23.6 ± 4.3 yr, 5 female). LH, left hand; RH, right hand.

Compensation Analysis

These results clearly show a change in bilateral coordination, both in terms of hand kinematics and muscle activity in response to altered limb dynamics. However, both measures (RC and MC) quantify the relative difference between the limbs. A critical prediction from OFCT is that during shared cursor control, the unperturbed limb compensates for the perturbation in the contralateral limb. To examine this, we compared reaches in the nonweighted limb during contralateral limb-weighting (i.e., right limb performance during LH weighting) to its performance during the first baseline in two ways. Our first kinematic assessment of compensation was to determine the change in final endpoint position measured relative to a fixed location directly below the participant. We found that when the 60% load was applied to the right wrist, the left hand reached 0.9 cm farther than it did during baseline (t_42.7= 2.9, P = 0.018, d = 1.22); when the load was applied to the left wrist, the right hand reached 1.0 cm farther than it did during baseline (t_42.7 = 3.3, P = 0.006, d = 1.08). This effect was not seen in the 30% loading condition (RH weighted: t₁₁ = 0.48, P = 0.64, d = 0.14; LH weighted: t₁₁ = 0.02, P = 0.98, d = 0.01). Our second electrophysiological assessment of compensation was to compare the RMS muscle activity of the nonweighted limb during contralateral limb weighting compared with baseline. Our analyses failed to detect a change in muscle activity for either load or for either muscle (all P > 0.3). Taken together, these results show that the nonweighted limb compensates for the load applied to the contralateral limb, but that this effect is expressed via a change in kinematic control rather than muscle output.

Trade-off Analysis

Our coordination analysis clearly shows that placing weight on one wrist increases muscle activity and decreases displacement of that limb compared with the nonweighted limb. To analyze this further, we plotted the change in RC versus the change in MC for each muscle pair for the 60% load condition (Fig. 6), where each participant contributes two points, one for each condition (LH weight and RH weighted). We then computed the slope of a line connecting the two points for each participant. In the 30% load condition, the mean slope for the biceps was −0.01 (95% CI: [−1.3, 2.1]), and the mean slope for the deltoid was −0.12 (95% CI: [−0.61, 0.39]). In the 60% load condition, the mean slope for the biceps was −0.13 (95% CI: [−0.24, -0.02]), and the mean slope for the deltoid was −0.35 (95% CI: [−0.88, −0.03]). What emerges is a trade-off between RC and MC. Due to the way RC and MC were calculated, this trade-off manifests as negative slopes, with the RH-weighted clusters located in the 4th quadrant and LH-weighted clusters located in the 2nd quadrant.

Figure 6.

The average change in relative contribution and the average change in muscle contribution is plotted for each participant in both the LH weighted and RH weighted blocks. Each participant contributes two points, which are connected by a solid black line. The average of slopes for the bicep (top) was −0.13 (95% CI: [−0.24, −0.02]), and the average of slopes for the deltoid (bottom) was −0.35 (95% CI: [−0.88, −0.03]). These negative slopes and the clustering of LH weighted points in the 2nd quadrant and RH weighted points in the 4th quadrant indicate that a tradeoff emerges between kinematic and dynamic control of reaching during our shared cursor task. Study population comprised 12, right-handed young adults (age: 23.6 ± 4.3 yr, 5 female). LH, left hand; RH, right hand.

DISCUSSION

Our goal in this study was to determine whether altering upper limb dynamics would systematically change bilateral coordination during reaching in a three-dimensional virtual environment. We had participants reach for targets while controlling a single cursor displayed at the midpoint between the hands. When we applied wrist weights to one of the arms, participants adopted a coordination strategy that favored use of the nonweighted arm and were reaching with a pronounced asymmetry in muscle activity between limbs. Specifically, we found that increasing the mass of the wrist weight progressively increased RC of the nonweighted limb. Although this change in coordination was expected, we found evidence to support the prediction that participants adopted an optimal control strategy that resulted in their compensating with the nonweighted limb. However, this optimization was likely incomplete since participants increased muscle activity in the weighted limb compared with the nonweighted limb. What emerged was an inverse relationship between the change in coordination and the change in muscle activity of the arms, suggesting a trade-off arising in the neuromuscular control of bimanual reaching.

Our main finding is that participants increase the relative contribution of their nonweighted hand when reaching to targets under shared cursor control and that this is a direct result of their adopting an optimal control strategy. In our shared-cursor task, participants are free to use either hand as much or as little as they want, so long as the cursor hits the target. This uncontrolled degree of freedom allows participants to capitalize on redundancy in the motor system (3). Using the motor redundancy framework, RC values can vary widely and are only constrained by task goals and the biomechanical features of the movement. We show that during baseline trials where no weights were applied to either hand, participants reached with an RC value no different from 50%. Then, when wrist weights were applied to the left limb, RC increased to favor the right limb and this effect increased with increasing mass and vice versa. Using a redundancy framework alone falls short in fully explaining these two results. There is no explicit rationale for why RC values would be centered around 50%. It has been shown that variability in multiple effector systems is uncontrolled along a task-irrelevant dimension (4), which in our study would allow for a distribution of relative limb contributions. However, there is no assumption that there exists a fixed set-point giving rise to a preferred coordination pattern or that the distribution be centered at 50%, as was seen in our study. Moreover, motor redundancy alone cannot explain why participants in our experiment shift their coordination pattern in response to altered limb dynamics or why they compensate by reaching farther with their nonweighted limb. This tendency for participants to adopt a coordination pattern that centers RC around 50%, to shift this set-point in response to altered limb dynamics, and to compensate with the nonweighted limb implies participants are adopting an optimized control strategy.

In the OFCT framework, the nervous system attempts to minimize the sum of squares of the motor output to all effectors involved in the movement (2). Our result showing participants’ reach with an RC of 50% during baseline trials implies nearly identical motor outputs in the two arms, which gives rise to a set-point in coordination representing the optimal solution. When we place a wrist weight on one arm, participants require greater motor output to that limb to counter the increased inertia and increased torque due to gravity. To minimize the difference in motor output between the limbs, participants shift RC in a direction that favors the nonweighted limb. This compensation is a common feature of shared-cursor tasks. Previous research has shown compensation of the unperturbed limb in rapid perturbation adaptation tasks (18–20), force-field adaptation tasks (5), and visual-gain adaptation tasks (21). Importantly, movement features were complementary such that the nonperturbed hand acts to reduce the amount of adaptation needed in the perturbed hand. We found a similar response, namely that participants reached ∼1 cm farther with the nonweighted limb during contralateral limb weighting. However, we failed to detect an associated increase in RMS muscle activity. This may be due to limitations in surface EMG recording such as skin-electrode interface and motion artifact limitations (22). In addition, our RMS measures were computed throughout the entire lap-to-lap reach, and transient spikes in activity could have been attenuated by averaging.

A key observation in shared-cursor tasks is that compensation is smaller in magnitude in the nonperturbed limb compared with the perturbed limb and is likely due to incomplete optimization (2, 5, 21, 23). We found incomplete optimization in our experiment as well. Specifically, we found MC increased in the weighted limb relative to the nonweighted limb. A fully optimized reach would maintain perfect motor output matching between the limbs, which would result in MC values being unchanged from baseline. However, movements can never be fully optimized because there exists significant noise in the neuromuscular system (24, 25). Moreover, the cost function governing the optimization problem of reaching assumes weighting factors are applied to different aspects of movement (5, 26). In our task, one aspect is the minimization of the sum of squares of motor output while another is the minimization of kinematic asymmetries between the limbs. It is possible that participants in our task are attempting to minimize the discrepancy between motor outputs to the limbs, but that the weighting factor applied to limb dynamics is relatively low (of lesser importance). Participants could also be trying to maintain a tight spatiotemporal coupling between the limbs, which is a robust feature of the human motor system (10), resulting in a relatively large weighting factor (of greater importance). This helps to explain our findings that participants show modest changes in bilateral coordination with relatively large changes in motor output. Our interpretation is that the optimal control strategy adopted by participants gives rise to a trade-off between the changes in muscle activity and coordination.

We found that for both muscle pairs (biceps and deltoid), there was an inverse relationship between a change in RC and a change in MC. For example, when muscle activity in the right biceps increased relative to the left biceps, the left arm reached farther than the right arm and vice versa. Participants responded to the need for increased muscle activity in the weighted limb by using it less. As the shared-cursor task forces any reduction in displacement for one limb to be countered by an increase in displacement for the contralateral limb, participants increase RC in the direction of the nonweighted limb. This optimization is captured by the inverse relationship in our trade-off analyses. We propose that the slopes of the connecting lines in Fig. 6 represent a trade-off in the optimization of different terms in the cost function. In Diedrichsen’s original work, he models the cost function as containing three terms (5). The first term penalizes the distance between the shared cursor and target; the second term penalizes residual velocity at the end of movement; the final term penalizes large, asymmetric motor commands sent to each limb. The critical insight of OFCT is that the motor system can flexibly regulate feedback, which is modeled by applying scalar weighting factors to each term in the cost function. This flexible control over the costs associated with movement is reflected in the slopes of our trade-off analyses. If the slope is near zero, this would indicate the participants are insensitive to the asymmetry in motor commands (term 3) and impose tight regulation over spatiotemporal asymmetries between the limbs (term 1). However, the motor system is sensitive to changes in limb dynamics (27) and participants can increase their sensitivity to task dynamics through manipulations to visual feedback (23). If the slope’s magnitude is large (steep relationship), this would indicate participants upregulate sensitivity to motor output asymmetries and allow the limbs to reach with large differences in displacement. Recently, evidence in support of a “cost combination” hypothesis has extended our understanding of optimization (28). In this framework, there are at least two cost functions, one that minimizes the energy consumed during reaching and a second that ensures participants make smooth reaches, rather than one cost function with multiple terms. Moreover, the central nervous system likely organizes control over effort and smoothness by imposing hierarchical control over these multiple cost functions (29). Interestingly, Oguz et al. (29) found that this hierarchical control gives rise to a trade-off between the cost functions governing control over the dynamics (effort) and kinematics (smoothness) of movement. Therefore, our procedure for determining the trade-off between muscle activity and bimanual coordination may provide an accessible way to determine the mechanisms of hierarchical neuromuscular control without the need for computational modeling.

There are some limitations that should be considered when assessing this relationship. First, the slopes represent the relative weight between these two terms in the cost function. Absolute measures of each weighting factor would require computational modeling (30). However, our relative measure may have uses in comparing different groups within the same study such as comparing healthy controls to people with neurological injury. Second, it is unclear what effect residual velocities at the endpoint of movement (term 2) has on this relationship. We were unable to account for this variable due to the rather large cursor and target sizes. This results in movements with a low index of difficulty, allowing for fast movements with low accuracy requirements (31). Participants may have continued to move within the target and still achieve the task goals. Despite these limitations, this metric is simple to implement and interpret and can be used to quantify the relative importance of the costs associated with movement.

Our data suggest that when reaching for a virtual target with both hands, participants use an optimal control strategy that minimizes the costs associated with movement. When controlling a cursor located at the midpoint between the hands, participants compensate for the altered limb dynamics of the weighted arm by reaching farther with the contralateral, nonweighted arm. Despite the nonweighted arm moving farther, the weighted limb produced substantially more muscle activity. The relationship between these two factors (kinematic vs. muscle asymmetries) constitutes a trade-off in the assignment and control over disparate costs during movement. Our study provides an accessible tool for assessing the relative sensitivity to the costs associated with movement and helps to define the neuromuscular control parameters governing goal-directed reaching. A natural extension of this cost assignment analysis is to determine the control parameters associated with limb asymmetries due to neurological impairment. For example, learned non-use is a maladaptive response to lateralized brain injury, such as stroke, that leads to long-term disuse of a paretic limb (32). Constraint-induced therapies have been used to counter the effects of learned non-use by immobilizing the nonimpaired limb, thereby forcing patients to use their impaired limb (33). Constraint-induced therapies, when viewed in the OFCT framework, can be seen as imposing an infinite cost to the nonimpaired limb. However, recent results from animal models of stroke and experiments with human stroke survivors suggest bilateral training may be more beneficial than unilateral training alone (34, 35). Therefore, using shared-cursor tasks in conjunction with an ability to alter limb dynamics, such as using wrist weights or exoskeletons, may provide the task and environmental constraints needed to increase limb use in patients with paretic stroke. We propose that this approach may lead to therapies that allow for graded constraint. That is, instead of unilateral, all-or-nothing approaches used in constraint-induced therapies, researchers and clinicians can use bilateral training with titrated amounts of constraint based on the patient’s individual needs. Although VR feedback provides a precise, controlled method for coupling the limbs, in therapy environments, similar limb coupling might be achieved during bilateral manipulation of objects (16). This study demonstrates the feasibility of such an approach, and we provide an accessible tool for determining an individual’s sensitivity to constraint.

GRANTS

A.T.B. was supported by the National Center for Advancing Translational Sciences of the National Institutes of Health under Award No. TL1TR001431. A.T.B., P.S.L., and B.S.B. were supported by the National Institute on Disability, Independent Living, and Rehabilitation Award No. 90REGE0004. A.T.B. and B.S.B. were supported by the National Institute of Neurological Disorders and Stroke Award No. 1U24NS107222.

DISCLAIMERS

The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

A.T.B., A.W.D., B.S.B., and P.S.L. conceived and designed research; A.T.B. performed experiments; A.T.B. analyzed data; A.B.T. A.W.D., B.S.B., and P.S.L. interpreted results of experiments; A.T.B. prepared figures; A.T.B. drafted manuscript; A.T.B., B.S.B., and P.S.L. edited and revised manuscript; A.T.B., B.S.B., and P.S.L. approved final version of manuscript.