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. Author manuscript; available in PMC: 2025 Apr 1.
Published in final edited form as: Hum Mov Sci. 2024 Feb 24;94:103196. doi: 10.1016/j.humov.2024.103196

Goal conceptualization has distinct effects on spatial and temporal bimanual coordination after left- and right- hemisphere stroke

Masahiro Yamada 1,2, Joshua Jacob 1, Jessica Hesling 1, Tessa Johnson 1,3, George Wittenberg 4, Shailesh Kantak 1,5
PMCID: PMC10939720  NIHMSID: NIHMS1970031  PMID: 38402657

Abstract

Perception of task goal influences motor performance and coordination. In bimanual actions, it is unclear how one’s perception of task goals influences bimanual coordination and performance in individuals with unilateral stroke. We characterized inter-limb coordination differences in individuals with chronic right- and left-hemisphere damaged (RCVA: n = 24, LCVA: n = 24) stroke and age-matched neurotypical controls (n = 24) as they completed bimanual reaching tasks under distinct goal conditions. In the dual-goal condition, participants reached to move two virtual bricks (cursors) assigned to each hand toward independent targets. In the common-goal condition, they moved a central common virtual brick representing both hands to a single, central target. Spatial and temporal coordination (cross-correlation coefficients of hand velocity and their time-lag), the redundant axis deviations (the hand deviations in the axis orthogonal to the axis along the cursor-target direction), and the contribution ratio of the paretic hand were measured. Compared to the dual-goal condition, reaching actions to the common-goal demonstrated better spatial bimanual coordination in all three participant groups. Temporal coordination was better during common-goal than dual-goal actions only for the LCVA group. Additionally, and novel to this field, sex, as a biological variable, differently influenced movement time and redundant axis deviation in participants with stroke under the common-goal condition. Specifically, female stroke survivors showed larger movements in the redundant axes and, consequently, longer movement times, which was more prominent in the LCVA group. Our results indicate that perception of task goals influences bimanual coordination, with common goal improving spatial coordination in neurotypical individuals and individuals with unilateral stroke and providing additional advantage for temporal coordination in those with LCVA. Sex influences bimanual performance in stroke survivors and needs to be considered in future investigations.

Keywords: cerebrovascular accident, hemiparesis, bimanual coordination, task goal

1. Introduction

Most daily activities are bimanual in nature, engaging the two hands in a task-dependent spatiotemporal manner (Kilbreath & Heard, 2005). Despite the complexity of bimanual coordination, task-oriented actions are highly coordinated such that common elements are tightly controlled in neurologically intact individuals. However, efficient bimanual coordination becomes challenging to individuals with unilateral stroke as they typically demonstrate profound strength and motor impairments of the paretic limb as well as higher-level cognitive and perceptual deficits that affect both limbs (Cauraugh & Summers, 2005; Faria-Fortini et al., 2011; Schaechter, 2004). Thus, determining the factors that can facilitate bimanual coordination is crucial in stroke rehabilitation.

One factor understudied in bimanual coordination research after stroke is the effect of perception on bimanual coordination. Traditionally, research in bimanual coordination has focused on understanding the task (e.g., unimanual versus bimanual) and environmental (e.g., movement speed, direction, and patterns) constraints that drive changes in coordination patterns (e.g., the in-/out-phase transition, velocity profiles) (Cunningham et al., 2002; Dickstein et al., 1993; Haken et al., 1985; Howard et al., 2009, 2009; G. N. Lewis & Byblow, 2004; Rice & Newell, 2004; Rose & Winstein, 2005; Schöner & Kelso, 1988; Sethi et al., 2023). Beyond these factors, more contemporary theoretical models of motor control (e.g., optimal feedback control theory) suggest that perception driven by goal conceptualization and performance feedback has a significant influence on bimanual coordination (Diedrichsen et al., 2010). At a perceptual level, the two hands may move to accomplish two independent goals (e.g., holding a cup in one hand while scrolling on a website with a computer mouse with the other hand; hereafter, referred to as a dual-goal task) or a unified common goal (e.g., carrying a tray with two hands; hereafter, referred to as common-goal task) (Figure 1B) (Liao et al., 2018). Historically, bimanual coordination research has almost exclusively examined the coordination of dual-goal tasks relative to unimanual tasks (e.g., Cunningham et al., 2002; Dickstein et al., 1993; Rice & Newell, 2004; Sethi et al., 2023). However, there is an increasing awareness that bimanual coordination tasks can be subdivided into different categories based on goal perception (e.g., dual-goal or common-goal) and motor constraints (e.g., symmetric and asymmetric hand movements) (Kantak et al., 2017).

Figure 1. The experimental setting and conditions.

Figure 1.

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Note. (A) Participants were strapped onto the chair. The horizontal gray line = the visual occlusion of arms. The two black square dots on the hands = electromagnetic markers for motion capture. (B) Bimanual conditions: (left) participants moved two blocks corresponding to each hand toward corresponding targets = dual-goal tasks; (right) participants moved a common-cursor, adjusted in the middle of the two hand markers, toward a unified target = common-goal tasks.

Distinct mechanisms are operational during common-goal and dual-goal bimanual actions (Altermatt et al., 2023; Liao et al., 2018). In neurotypical individuals, perturbations applied to one hand during dual-goal conditions did not affect the control of the other non-perturbed hand (Mutha & Sainburg, 2009). In contrast, perturbations imposed on one hand during common-goal condition required compensations by the other unperturbed hand, suggesting distinct goal-driven control strategies between common- and dual-goal actions (Diedrichsen et al., 2010; Diedrichsen & Dowling, 2009; Kazennikov et al., 2002). Liao et al. (2018) demonstrated different pattern of force variability of each hand during dual-goal (each hand exerts an assigned force) compared to common-goal tasks (two hands cooperatively generate a resultant force). Relatively fewer studies have directly compared common- and dual-goal actions in individuals with stroke. Johnson et al. (2022) reported faster movements during common-goal compared to dual-goal reach-to-grasp actions, suggesting that performance in stroke survivors can be immediately modulated by simply altering the perceptual presentation of task goals. It is plausible that greater interdependence of the two hands during common-goal actions may influence bimanual coordination in individuals with unilateral stroke. However, research thus far comparing bimanual coordination between common- and dual-goal actions in small samples of stroke survivors has yielded contradictory findings. For example, Kantak et al. (2016, n = 11) reported poor temporal coordination during common-goal reaching tasks compared to dual-goal reaching tasks. In contrast, Johnson et al. (2022, n = 30) reported no difference in bimanual coordination between common-goal compared to dual-goal bimanual reach-to-grasp actions, despite faster movements under the common-goal condition. Thus, it is unclear how the conceptualization of goal (i.e., dual-goal and common-goal) influences bimanual coordination in individuals with and without stroke.

Contradictory findings in stroke survivors may be partly due to the hemisphere of lesion after unilateral stroke. Previous research has indicated hemisphere-specific deficits in bimanual coordination and performance (Johnson et al., 2022; Schaffer et al., 2020; Varghese et al., 2023). Deficits in interlimb coordination and planning of symmetrical bimanual reach-to-grasp actions, particularly in dual-goal actions, have been associated with left cerebrovascular accident (LCVA) compared to right hemisphere cerebrovascular accident (RCVA) (Johnson et al., 2022). Moreover, Schaffer et al. (2020) demonstrated that the LCVA group showed smaller amplitudes along the redundant axes compared to the RCVA and control groups during a common-goal reaching task. In contrast, lesions to the right hemisphere are associated with greater deficits in adaptive control of bimanual reaching actions in the presence of task errors (Varghese et al., 2023). The hemisphere-specific bimanual deficits may reflect hemispheric specialization, which is well-documented for unimanual actions. Individuals with LCVA show profound deficits in praxis and planning of multi-joint actions (Mani et al., 2013; Schaefer et al., 2007, 2009), while those with RCVA show preferential deficits in visuospatial perception and adaptive control for end-point accuracy (Mani et al., 2013). In summary, the extent to which lesion of hemisphere influences bimanual coordination during bimanual reaching actions to common- vs. dual-goals is less known.

Besides coordination between the two hands, the extent and nature of engagement of the two hands may also differ between common- and dual-goal reaching actions. The optimal feedback control theory (OFCT) provides distinct predictions for how the two hands may engage under dual and common-goal conditions. Under dual-goal conditions where each hand is moving its own cursor to respective targets, each hand employs a two-step cost function (Diedrichsen et al., 2010). The first cost function aims to minimize the end-point error while the second minimizes inefficient motor commands thus yielding relatively straight reach paths with minimal movement along the redundant axes. In contrast, under common-goal conditions where the two hands are moving one common cursor, the two hands may compensate for each other and move along redundant axes. Unilateral stroke results in a more asymmetric system with the contralesional paretic arm having more motor deficits compared to the ipsilesional nonparetic arm. Such augmented motor asymmetry secondary to a unilateral stroke provides a unique opportunity to test the predictions of the OFCT. Capitalizing on this opportunity, we designed a common-goal task where participants moved a virtual rectangular brick from a midline start to a midline target position by moving the two arms forward (Figure 1B). In this common-goal task, movement along the long axis of the brick (i.e., the x-axis deviations in Figure 1A) is redundant to the task of moving the brick forward (i.e., along the y-axis), such that the brick remains in the center of and parallel to an imaginary line connecting each hand. This means that to keep the brick in the midline, movement of one arm closer or away from the midline requires simultaneous homologous movement with the other arm. In contrast, during the dual-goal task (Figure 1B), each hand moved its own virtual rectangular brick from a start position on each side of the midline to a target straight ahead of it.

In this study, we aimed to determine how individuals with LCVA, RCVA, and age-matched neurotypical controls coordinate and engage their arms during reaching actions under common vs. dual-goal conditions. We measured spatial and temporal coordination, and the deviations along the redundant axes between the two hands as participants reached forward to move a virtual horizontal brick to a target position. Also, we measured contribution ratio of two hands during the common-goal condition. Based on the findings of Schaffer et al. (2020), and Johnson e. al. (2022), we hypothesized that compared to the RCVA and control groups, the LCVA group will show significantly poor spatial and temporal coordination during common-goal and dual-goal conditions. Two predictions emerge from the tenets of the OFCT for arm contribution and redundant axis deviations under the two goal conditions. One, because each arm can compensate for the other in common-goal actions, we hypothesized that control participants will contribute less with their nondominant arm while individuals with LCVA and RCVA will contribute less with their paretic arm. Two, redundancy in the common-goal condition will allow more movement along the redundant axes compared to the dual-goal condition. Based on the findings of Schaffer et al., we hypothesized that the LCVA group will show smaller amplitudes of movement along the redundant axes during the common-goal condition compared to RCVA and control groups.

2. Methods

2.1. Participants

Study participants were recruited from the Moss Rehabilitation Research Institute (MRRI) Research Registry (Schwartz et al., 2005). Ninety-three potential participants were screened for study eligibility; seventy-two met the inclusion and exclusion criteria and participated in the study. We included participants with chronic (at least 6 months post) stroke aged between 21 and 80 with 1) unilateral ischemic or hemorrhagic anterior circulation stroke affecting cortical and/or subcortical white matter, 2) ability to reach at least 80 % of their arm length while fully supported on a frictionless surface and trunk constrained, 3) a Mini-mental scale score > 26 or score of 4 or above on auditory verbal comprehension part of the Western Aphasia Battery to ensure that participants could comprehend and follow instructions, 4) no evidence of hemispatial neglect, and 5) no pain or musculoskeletal problems in arms that might impede task performance. Exclusion criteria for stroke patients were 1) bilateral stroke, 2) complete paralyses, 3) basal ganglia/cerebellar stroke, 4) pain or stiffness in the upper extremity that will interfere with the task performance, 5) inability to follow task instructions, 6) presence of a pacemaker or similar medical implant, or 7) active medical, neurological, or psychiatric condition that would interfere with the ability to perform upper extremity motor tasks. Participants in the control group were age-matched individuals without neurological disorders or impairments. One LCVA participant participated but could not complete the task. The final sample included individuals with chronic hemispheric stroke affecting the left hemisphere (LCVA; n = 23), right hemisphere (RCVA; n = 24), and 24 neurotypical controls (CON). Table 1 summarizes the demographic and clinical characteristics of all groups. Participants received monetary compensation for their participation.

Table 1.

Mean (SD) of the demographics and clinical assessment

CON LCVA RCVA p-value
Male Female Male Female Male Female Group Sex
N 12 12 10 14 7 16 NA NA
Age (years) 63.42 (11.54) 60.08 (10.77) 57.5 (10.97) 59.86 (10.55) 63.43 (6.21) 62.06 (7.85) 0.372 0.750
Hand dominance (R n : L n) R 12: L 0 R 12: L 0 R 9 : L 1 R 13: L 1 R 7 : L 0 R 14: L 2 NA NA
Yrs since stroke NA NA 11.1 (3.81) 9.57 (5.69) 9.14 (4.88) 7.31 (5.04) 0.115 0.164
UEFM NA NA 52.2 (14.82) 53.43 (14.22) 47.71 (18.52) 49.69 (10.97) 0.220 0.799
ARAT_NP NA NA 56.8 (0.42) 56.64 (0.84) 56.43 (0.79) 56.94 (0.25) 0.727 0.744
ARAT_ PA NA NA 43.6 (18.4) 47.21 (17.8) 40.86 (22.5) 46.31 (116) 1.000 1.000
Box and Block_NP (s) NA NA 18.4 (43.1) 17.8 (50.07) 22.5 (48.71) 11.6 (49.56) 0.508 0.312
Box and Block_PA (s) NA NA 35.2 (19.05) 39.5 (20.59) 27.29 (21.54) 26.88 (15.22) 0.081 0.736
Trail Making (B-A) (s) 29.69 (12.36) 48.26 (54.29) 82.82 (54.45) 135.64 (156.25) 80.3 (56.49) 64.3 (55.39) 0.263 0.844
Proprioception NA NA 5.85 (2.16) 8.54 (7.25) 9.86 (6.61) 13.13 (16.07) 0.115 0.847
Visual Perception 98.33 (12.53) 97.08 (14.11) 92.3 (10.09) 96.07 (10.03) 93.29 (7.5) 94.56 (9.07) 0.427 0.638
Grip Strength_NP NA NA 69.32 (16.38) 41.6 (11.53) 64.08 (18.9) 35.33 (13.59) 0.251 < 0.001
Grip Strength_PA NA NA 55.44 (30.73) 26.87 (23.04) 37.86 (27.69) 19.67 (17.16) 0.150 0.008
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Note. N = the number of participants in each group, CON = neurotypical controls, LCVA = Left cerebrovascular accident patients, RCVA = right cerebrovascular accident patients, Yrs = years, UEFM = Upper Extremity Fugl-Myer score, NP = nonparetic, PA = paretic, Box & Block test in seconds, Trail Making test is the section B – Section A results. Grip strength, Visual perception, Age, and years since stroke were analyzed with group x sex ANOVA with the anova_test() function within the rstatix package. Other variables were non-normally distributed. Thus, the raov() function within Rfit package was used with group x sex factorial rank-based nonparametric analysis. None of the variables showed a significant interaction with alpha < 0.05.

Prior to the experiment, participants with stroke underwent an assessment battery that included measures of motor capacity (Upper Extremity Fugl-Meyer (UEFM), grip strength), motor performance (Action Research Arm Test (ARAT), Box and Block test), executive function (Trail-making test B-A), and proprioception and visual perception. Proprioceptive ability was determined using an elbow position matching task with a greater discrepancy between the passively positioned paretic arm and the actively matched non-paretic arm, indicating greater proprioceptive deficits (Iandolo et al. 2014). Visual perception was measured using the Motor-Free Visual Perception Test-4 (MVPT-4).

2.2. Task and apparatus

The present study is part of a larger-scale study; here, we report motor behavior data. Participants were seated in a chair facing a computer monitor (a diagonal distance of 68.58 cm, LG co., Korea) with their trunks constrained to the chair. Their arms were supported on a low-friction tabletop and free to move in the horizontal (X-Y) plane with minimal resistance. An electromagnetic tracking system, 3D Guidance trakSTAR NDI (3D Guidance trakSTAR, NDI, Waterloo, Ontario), was used to track the end point position of the two arms. Magnetic sensors secured to dorsum of each wrist collected position data at a sampling frequency of 500 Hz and provided real-time feedback for interaction with a MATLAB-based customized graphical user interface (GUI). Participants wore elbow-length gloves to allow low-friction movements and direct view of the arms was blocked with a horizontal screen. Position data were stored for offline analyses. While participants moved their hands on the horizontal table surface, task presentation and concurrent feedback were displayed on the computer screen.

The motor task was a bilateral reaching task with the goal to move a virtual brick(s) to a virtual target on the computer screen as fast and accurately as possible. On the computer monitor (white background), a green rectangle was displayed (1.52 × 4.06 cm) near the bottom of the monitor, serving as the start position. Once the participant assumed the start position, the virtual brick(s) (1.27 × 3.81 cm) were presented visually but could not be felt haptically. There were two experimental conditions: dual-goal and common-goal. During the dual-goal condition, two virtual bricks, each representing the corresponding hand, were displayed on the computer screen (Figure 1B left) in front of the shoulder at 10% of their maximum arm reach. The goal was to move each brick to its respective target placed at 90% of their maximum arm reach as shown in Figure 1A, by moving the two arms forward on the table. Under the common-goal condition, a single common virtual brick was displayed in the midline (Figure 1B) with its movement representing the unweighted average of the two hands along the X and Y axes. Thus, forward movement of the brick (i.e., along the Y axis) could be accomplished through different contributions of right and left arm movements in the Y-axis. Movement along the long axis of the brick (X axis) was redundant to the task, such that the brick remained parallel to an imaginary line connecting the two hands. To maintain the midline position of the brick, movement of one hand along the X axis (closer to or away from the center) required simultaneous and similar movement of the other hand along the X axis. Direct visual feedback of the limbs was occluded throughout the experiment (Figure 1A), but the visual feedback of the virtual brick(s) was provided in real-time during movements.

2.3. Procedure

At the beginning of the experiment, maximum arm reach was recorded for the paretic arm in participants with stroke and for the nondominant arm in age-matched controls. Targets for the bilateral reaching task were positioned at 90% of each participant’s maximum arm reach to ensure that relative task difficulty was comparable across groups. At the beginning of each trial, participants positioned their hands at the start position right in front of their shoulder at 10% of their maximum arm reach. When the cursor remained within the start position for longer than 2000 ms, the virtual brick(s) appeared. Following a 2000 ms delay, the target position appeared green, signaling “Go”, whereby participants were instructed to move forward with their hands on the table, moving the virtual brick to the green target position as fast as possible. During the entire movement, continuous feedback about the virtual brick(s) was available in real time. After each trial, knowledge of results (KR) in the form of movement time (MT in ms) was displayed on the monitor. If the trial was longer than 1000 ms, the experimenter encouraged participants to move faster. If the cursor did not enter the target for a long duration (i.e., MT > 4000 ms), that trial was not included in the analysis. To ensure that participants understood the task, conditions, movement time requirements and feedback, they completed up to 15 trials at the beginning of the experiment. At the beginning of each condition, two exposure trials were given to allow participants to familiarize themselves to the new condition, following which 10 experimental trials were collected per condition (common- and dual-goal). The order of the two condition blocks was randomized across participants.

2.4. Data Analysis

The collected data were processed with MATLAB. Data of the right- and left-hand cursors and the common cursor were first interpolated into equal intervals and then filtered with the 3rd-order low-pass Butterworth filter (both directions) with the cutoff frequency of 8Hz. Then, the tangential velocity of the marker displacement was obtained. The movement onset was defined as the point at which velocity exceeded 8% of the peak velocity of each trial. This threshold detection was conducted by examining the data backward (i.e., the first time that velocity went below the threshold from the peak velocity to the go signal). The movement offset was defined as the first time the velocity profile went below the threshold between the peak velocity to the end of the trial. The dependent variables were calculated based on the velocity profiles of the cursor between the onset and offset.

The primary dependent variables of interest were (1) spatial and (2) temporal coordination of the hands, (3) redundant axis displacement, and (4) contribution of each hand. Cross-correlation between tangential velocity profiles of the two hands was used to index spatial and temporal coordination between hands (Kantak et al., 2016; Lodha et al., 2012; Nelson-Wong et al., 2009). Cross-correlation measures similarities of two distinct time series as a function of the displacement of one relative to the other. Repeated correlations between the two hand velocity profiles were obtained as the velocity profile of one hand was successively lagged. The maximum cross correlation coefficient obtained gave a measure of similarity between the two profiles, indexing spatial coordination. Cross-correlation coefficients were transformed by Fisher’s z-transformation prior to analyses (Kantak et al., 2016). A lower cross-correlation coefficient indicates that the two velocity profiles are spatially dissimilar. The time-lag associated with the maximum cross correlation is an index of temporal coordination and is indicative of how much one hand lagged the other. In the current study, for the CON group, a positive value can indicate that the dominant hand leads the non-dominant hand, whereas a negative value indicates the non-dominant hand leads the dominant hand. For the stroke group, a positive time-lag value can indicate that the nonparetic hand leads the paretic hand, whereas a negative value indicates the paretic hand leads the nonparetic hand.

For redundant axis displacement, we measured the displacement (in cm) of each hand’s cursor orthogonal to the imaginary movement axis between target and start cursor position (the x-axis in Figure 1A). The maximum displacement in the redundant axes between onset and offset was averaged by block. For contribution, the resultant displacement of both hands during the common-goal condition was calculated. Then, the displacement percentage of the ‘weaker’ hand (i.e., non-dominant hand for the CON and paretic limb for the stroke patients) was obtained by calculating: [Displacement of the paretic limb / (Displacement of the non-paretic limb + paretic limb)] × 100 (%). Thus, the contribution variable indicates the contribution of the paretic hand for the LCVA/RCVA groups or the non-dominant hand for the CON group. For performance, MT was defined as the time from the onset to the offset in ms and was an a priori supplemental variable of performance outcome.

2.5. Statistical Analysis

All statistical analyses were conducted with R. Our planned fixed factors were the group (CON, LCVA, and RCVA) and task condition (dual-goal and common-goal). Sex (males, females) was also included as a fixed factor in all analyses. We supplementarily analyzed MTs to show an overall performance. For MT and redundant axis displacement, while hand was included as a factor, we did not observe a main or interaction effect of the hand. Hence, the data for MT and redundant axis displacement was collapsed across hands. Thus, the hand was an additional fixed factor. Outliers were assessed with median absolute deviation (MAD) (Leys et al., 2013) after visual inspections. We adopted a linear mixed effect model using the lmerTest package (Kuznetsova et al., 2017). The individual intercept was considered random effects. All models were fitted with a restricted maximum likelihood estimation. Significance of fixed effects was determined by the F-value provided by the lmerTest package with Kenward-Roger degrees of freedom correction. Significant interactions were followed up with post-hoc analyses between-condition differences within each group. Post hoc contrast analyses were conducted with the emmeans R package. The contribution variable only pertained to the common-goal condition. This variable was analyzed with a 3 (group) × 2 (sex) factorial design.

We conducted two additional analyses. First, given the complexity of the mechanism of bimanual coordination after stroke, we consulted our demographic and clinical assessment data (see Table 1) to identify potential factors that uniquely explain the types of bimanual coordination for each group. We examined the best subsets of a linear regression that maximizes the model fit using the rFSA package. The rFSA randomly chooses variables, and the iteration is automatically repeated until the function finds a best-fit model (Lambert et al., 2018). This approach is more appropriate than a bottom-up/top-down process of model selection as the order of adding/removing terms affects the degrees of freedom in each step, and thus affects the results. We separately selected best subsets for spatial and temporal coordination for each group. For CON, available data were age, visual perception, and Trail Making tests. For RCVA and LCVA groups, additional assessments were available (Table 1). However, we dropped grip strength, Box & Block, and ARAT (Action Research Arm Test) as they were highly correlated with the UEFM scores. Accordingly, we included age, sex, visual perception, Trail Making (B-A), time-since-stroke (in months), UEFM, and proprioception. As all models were not multi-level factors, we fit all models with a linear model (i.e., lm() in R). If the best subsets included clinical assessment, the clinical assessment variable was standardized (but not centered) prior to analysis. Our second additional analysis was simple correlation analyses (Spearman’s rho, ρ) between spatial/temporal coordination and the redundant axis displacement (of the paretic hand) to examine whether the outcome of bimanual coordination would be related to the increased degrees of freedom during the common-goal task in the redundant axis.

Alpha was set at 0.05 for all analyses, and type I error during post hoc analyses was controlled with Bonferroni correction at an alpha of 0.05.

3. Results

One RCVA participant was removed from overall analyses as they had a high proportion of unusable data due to inability to comply with the instructions (i.e., MT were too long; the cursor consistently stopped outside the target). This resulted in n = 24, 23, and 23 for the CON, RCVA, and LCVA groups. In a separate supplement file, the descriptive statistics of all dependent variables (Mean, SD, SE, 95% CI, and sample size used for each variable, as Part I) and estimated marginal means calculated from the model (Part II) are summarized.

3.1. Bimanual coordination: Spatial coordination

Two participants from the RCVA (n = 1) and LCVA (n = 1) groups were removed, and no outliers were detected from the remaining dataset, resulting in n = 24 for the CON group and n = 23 for the LCVA and RCVA groups. The results showed the main effects of group, F(2,64.796) = 14.80, p < 0.001, and condition, F(1,63.393) = 32.482, p < 0.001, with no other significant effects of: sex (p = 0.376), sex by group (p = 0.501), sex by condition (p = 0.895), group by condition (p = 0.464), or sex by group by condition (p = 0.991). Spatial coordination was better during the common-goal task (Estimated marginal mean, or EM = 2.78, SE = 0.06) than the dual-goal task (EM = 2.51, SE = 0.06). Post hoc tests for the group factor showed that coordination was better for the CON group than both LCVA and RCVA groups (p < 0.001), with no difference between the stroke groups (p = 0.864) (Figure 2-A).

Figure 2. Spatial and temporal coordination was better for the common-goal compared to the dual-goal condition for all groups.

Figure 2.

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Note. Gray dots are individual data points. Bars are standard error. Legend: Cond = condition; Common = common-goal, Dual = dual-goal. The x-axes: CON = control, LCVA = Left Cerebrovascular Accident patients, RCVA= Right Cerebrovascular Accident patients. Figure 2A: The y-axis is Fisher’s z-transformed correlation coefficients. A higher value indicates greater spatial coordination. Figure 2B: The y-axis is the time lag of the maximum correlation coefficients between hands. Zero indicates no time lag; positive value indicates that nonparetic/dominant hand led the paretic/non-dominant hand for stroke and control groups, respectively. Note that the post hoc tests showed the significant difference between tasks were found only in the LCVA group (*).

3.2. Bimanual coordination: Temporal coordination

One participant from the CON group was identified as outlier and was removed. The results showed a main effect of group, F(2,64.376) = 3.556, p = 0.043, which was superseded by the interaction between group and condition, F(2,63.319) = 4.217, p = 0.019. No difference was found in sex (p = 0.487) or other interactions of sex by group (p = 0.577), sex by condition (p = 0.135), and a three-way interaction (p = 0.197). Post hoc tests revealed that during the common-goal condition, no group difference was observed (p = 1.00). However, in the dual-goal condition, both CON and RCVA groups had positive values while the LCVA group had negative values, p = 0.0003 and 0.0001, respectively, indicating that the dominant hand/nonparetic hand led the non-dominant/paretic hand for the CON and RCVA groups but for the LCVA group, the paretic hand led the nonparetic hand. There was no difference between the CON and RCVA groups, p = 1.00 (Figure 2-B). Further, post-hoc analyses revealed no difference between the common- and dual-condition in the CON (t63.5 = − 0.675, p = 0.5022, Estimated marginal mean difference, EMdiff = − 6.21, SE = 9.2) and RCVA groups (t62.3 = − 1.525, p = 0.132, EMdiff = − 15.33, SE = 10.1). In the LCVA group, time-lags were significantly longer during dual-goal condition compared to common-goal condition (t64.2 = 2.383, p = 0.020, EMdiff = 22.39, SE = 9.4).

3.3. Performance outcomes: Movement time

Outliers were detected with MAD with a threshold of 4. For the CON group, participants were excluded from the common-goal condition with the dominant hand (n = 1), the common-goal condition with the non-dominant hand (n = 1), and the dual-goal condition with the dominant hand (n = 2). In the LCVA group, participants were excluded during the common-goal condition of the paretic (n = 1) and nonparetic hand (n = 1). No outliers were detected in the RCVA group.

Main effects were found to be significant on sex, F(1,64.82) = 5.757, p = 0.0193, condition, F(1,185.83) = 25.215, p < 0.001, group, F(2,64.83) = 11.605, p < 0.0001, but not on hand, F(1,185.27) = 0.813, p = 0.368. Although the interaction between sex and condition, F(1,185.83) = 0.215, p = 0.643, and group and condition, F(2,185.85) = 2.704, p = 0.070, did not reach significance, the main effects of sex and group were superseded by the interaction between sex and group, F(2,64.83) = 3.9995, p = 0.0230. For condition, MT was faster during the common-goal task (EM = 637.84 ms, SE = 35.97) than the dual-goal task (EM = 721.65, SE = 35.91). For the interaction, although there was no difference between sex in the CON (p = 0.4883) and RCVA (p = 0.8858) groups, a sex difference was evident in the LCVA group (p = 0.0004). Females in the LCVA group were slower (EM = 1056.16, SE = 89.81) than males (EM = 615.46, SE = 76.19). Within females, there was a significant difference between the CON and LCVA groups (p = 0.0001) but not between the CON and RCVA (p = 0.2235) or RCVA and LCVA (p = 0.082). Within males, a significant difference was observed between the CON and RCVA (p = 0.0068) but not between the CON and LCVA (p = 0.2274) or RCVA and LCVA groups (p = 0.5225) (Figure 3-A). None of the interactions between other factors and hand, three-way interactions, or four-way interaction were found to be significant, p > 0.05.

Figure 3. Movement time (MT) and redundant axis displacement.

Figure 3

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Note. For MT and redundant axis displacement, the hand (paretic/nonparetic or non-dominant/dominant) factor was added in the analysis; with no significant differences observed between hands.

3.4. Redundant axis movement

Four outliers were detected and removed from the analysis (all from the CON group, n = 2 from the common-goal, n = 2 from the dual-goal condition). The results showed main effects on group, F(2,65.59) = 4.6896, p = 0.01254, and condition, F(1,190.54) = 276.03, p < 0.0001 (Figure 3-B), which were superseded by the group and condition, p < 0.001, and the three-way interaction between group, condition, and sex, F(2,190.61) = 8.76, p = 0.00023. No difference was found in hands (p > 0.05). The source of interaction is evident in Figure 3B. A follow-up analysis separated by sex (group by condition for each sex) revealed that for males, the movement along the redundant axis was significantly higher during the common-goal condition compared to the dual-goal condition, F(1,121.235) = 145.696, p < 0.0001. For females, there was a significant group by condition interaction, F(2,81.517) = 147.05, p < 0.0001, with main effects of both group and condition, p = 0.0025 and < 0.0001, respectively. For females, there was no significant difference between the three groups under the dual-goal condition. In contrast, the redundant axis displacement was larger for the RCVA (p = 0.0025) and LCVA (p < 0.001) group relative to the CON group during the common goal condition. There were no differences between the two female stroke groups (p = 0.1639). Within each group, comparison between common- and dual-goal conditions were significantly different (CON: t85.1 = 2.92, p = 0.045; LCVA: t80.1 = 11.384, p < 0.001; RCVA: t80.1 = 6.768, p < 0.001), with different magnitude, given by the t-value and SE (CON: EMdiff = 1.58 cm, SE = 0.541; LCVA: EMdiff = 6.27, SE = 0.551; RCVA: EMdiff = 4.45, SE = 0.658).

3.5. Contribution ratio of the paretic and non-paretic arm

No outliers were detected. The results showed the group difference, F(2,64) = 4.869, p = 0.011, partial eta squared (η2p) = 0.132, but not between sex, F(1,64) = 0.0005, p = 0.982, η2p ώ 0.01, or group by sex interaction, F(2,64) = 0.402, p = 0.671, η2p = 0.012. Post hoc tests on the group factor indicated that, in both RCVA and LCVA groups, the contribution of the paretic arm was lower than the contribution of the nondominant arm of the CON group (RCVA, p = 0.0352, and LCVA, p = 0.021) (Figure 4).

Figure 4. Contribution ratio.

Figure 4

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Note. Contribution ratio = [Displacement of the paretic/nondominant arm / (Displacement of the non-paretic arm + paretic arm]] × 100 (%).

3.6. Correlation between the redundant axis displacement and coordination

All correlations between the redundant axis and spatial/temporal coordination were non-significant (p = 1.00) after adjusting multiple comparisons (i.e., 2 (dual/common) × 3 (group) × 2 (spatial/temporal coordination) = 12 analyses) with Bonferroni correction. Albeit non-significant, for the RCVA group during the dual-task condition was trending to be significant relationship between the redundant axis and spatial coordination (ρ = − 0.57, p = 0.0540), suggesting that an increased displacement in the redundant axis was tending to correlate with poorer spatial coordination. A non-significant trend was also qualitatively observed for the LCVA group (ρ = − 0.48, p = 0.2348). It was interesting to note that this relationship was qualitatively weaker during the common-goal condition for both RCVA (ρ = − 0.25, p = 1.00) and LCVA (ρ = − 0.34, p = 1.00) groups, respectively. All correlations for temporal coordination were negligible and all correlation coefficients in the CON group was less than 0.2.

3.7. Regressing spatial coordination difference on clinical assessment

For temporal coordination, none of the variables resulted in a significant overall model for the CON, LCVA, and RCVA groups. For spatial coordination, UEFM was a significant predictor (t = 3.44, p = 0.0025 and t = 3.253, p = 0.0042 for LCVA and RCVA, respectively). Although the rFSA returned some clinical assessment as a part of the best subset, they were not significant contributors of the model performance. Besides, factors detected by the rFSA functions were highly influenced by high-leveraging outliers (i.e., outliers were not related to age, time since stroke, or UEFM). Collectively, our findings were (1) spatial coordination performance was primarily explained by UEFM and (2) none of the demographic or clinical assessments was related to temporal coordination (see Supplemental Material Part III for detail).

4. Discussion

The present study examined how individuals with LCVA, RCVA, and age-matched neurotypical controls coordinate and engage their arms during reaching actions under common-goal vs. dual-goal conditions. It was hypothesized that (1) compared to the RCVA and CON groups, the LCVA group would show significantly poor spatial and temporal coordination during common-goal condition and dual-goal condition; (2) the CON group would contribute less with their nondominant arm while individuals with LCVA and RCVA would show lesser contribution of the paretic arm; and (3) the LCVA group would show smaller amplitudes of movement along the redundant axes during common goal condition compared to RCVA and CON all the while having no between-group differences during the dual-goal condition.

Our first hypothesis was not fully supported. All groups showed better spatial coordination during common-goal compared to dual-goal conditions. The commonality of goal significantly influenced temporal coordination in the LCVA group, but not in the CON or RCVA groups. The LCVA group showed significantly longer time lag between arms under dual-goal, compared to common-goal condition. In the LCVA group, the paretic arm led the nonparetic arm; while for RCVA and CON groups, the nonparetic/dominant arm led the paretic/nondominant arm. Next, our second hypothesis was partially supported. Both LCVA and RCVA groups contributed less with their paretic hand during the common-goal condition, but the CON group did not show between-arm differences. Finally, consistent with the tenets of OFCT, all groups showed greater redundant axis movement in the common-goal condition compared to the dual-goal condition. Our third hypothesis that the LCVA group would show smaller amplitudes along the redundant axes during common goal actions was not supported. Instead, we observed that the effect of group on redundant axes was distinct for males and females. While this study was not powered to test sex differences, we found that females who had LCVA and RCVA had significantly larger redundant axes compared to females in the CON group; in contrast, there was no difference between males in the three groups. To our knowledge, this is the first study to report sex differences in bimanual performance after stroke.

4.1. Reaching actions to a common goal led to better spatial coordination.

How the task was presented perceptually (i.e., as common vs. dual goals) influenced spatial coordination between the two hands during bimanual reaching, irrespective of the groups. Spatial coordination was better for all groups under the common goal condition. The current findings are in direct contrast to our previous preliminary findings (n = 11 stroke survivors; 10 neurotypical controls) that reported better bimanual coordination during dual-goal compared to common-goal reaching task (Kantak et al., 2016). These contrasting findings highlight the caution that needs to be exercised when making deterministic inferences from studies with small sample sizes. Our findings corroborate with those of Johnson et al. (2022), who demonstrated better performance during reach-to-grasp actions to common dowels compared to separate dowels. Collectively, these studies provide converging evidence across reaching as well as grasping movements to indicate that actions performed to accomplish a common-goal lead to better spatial bimanual coordination and performance compared to dual or separate goals.

What factors about common-goal afford better spatial coordination relative to dual-goal for bimanual actions? We hypothesized that one potential factor would be related to the level of redundancy afforded by common goal conditions. Under dual-goal conditions, each arm is relatively constrained to a fairly straight reach trajectory from the start to the target. In contrast, under the common-goal condition, the two arms can harness the available redundancy and choose the most economical solutions to move the common virtual brick to the target position. For example, while reaching to a common goal, one may choose to reach diagonally with bilateral elbow extension, rather than reaching straight forward using shoulder-elbow coordination. As evidenced by our data, actions to the common goal were accompanied by larger movements along the redundant axes compared to dual-goal actions. Thus, to determine if additional redundancy in the common goal condition is related to bimanual coordination, we assessed the correlation between the redundant axis deviation and spatial coordination. Although non-significant, the poor spatial coordination with increased redundant axes movement suggest that the additional redundancy afforded in the common goal condition may not improve bimanual coordination in the common-goal condition. One explanation of this result is that the exploitation of redundant space may not be a simple linear relationship with performance. Ranganathan et al. (2019) showed that variability of redundant axis deviation in the paretic hand decreased when the paretic hand was forced to contribute more than the nonparetic hand and increased when the paretic hand did not have to contribute more than the nonparetic hand. Thus, specific task demands imposed on each hand must be considered as another constraint in future research.

Another factor may relate to how attentional resources are allocated differently between the two task conditions. In the common goal condition, the participant needs to focus on how a single virtual brick is moved to its target. In contrast, during the dual-goal condition, the participant must focus on two distinct virtual bricks to ensure they reach their respective targets. This distributed attention may mimic a dual-task paradigm and attenuate bimanual coordination. Irrespective of the underlying mechanism, our current findings add to the growing body of literature highlighting how the perception of the action goal influences bimanual coordination in neurotypical adults (Diedrichsen et al., 2010; Diedrichsen & Dowling, 2009; Mechsner et al., 2001; Shea et al., 2016) and those with stroke (Johnson et al., 2022).

Spatial coordination deficits in participants with stroke were related to the severity of motor impairment (i.e., UEFM score). Impaired ability to individuate joints, a deficit quantified by UEFM, is associated with more curved reaching paths of the paretic arm that may contribute to poor spatial coordination. Further, the paretic arm also shows deficits in compensating for nonparetic arm movements under common-goal conditions, thus contributing to poor spatial coordination between hands. Thus, impairments in motor function as well as poor ability to adapt may underlie spatial coordination deficits after stroke.

4.2. Reaching under common-goal condition showed improved temporal bimanual coordination only in the LCVA group.

While temporal coordination was comparable between CON, LCVA and RCVA groups under the common-goal condition, dual-goal condition influenced the three groups differently. One, LCVA showed significantly better temporal coordination under common-goal compared to dual-goal condition, while between-condition differences were not significant for CON and RCVA group. Two, the paretic right arm led the nonparetic arm in the LCVA group while the nonparetic/dominant arm lead the paretic/nondominant arm in RCVA/CON group. Previous studies have reported a right, dominant arm lead in temporal dynamics of bimanual coordination (Byblow et al., 1994; Viviani et al., 1998). Neurophysiologic studies have shown an increase in cortical excitability and a decrease in intracortical inhibition (Short-Interval intracortical inhibition, SICI) during bimanual movements (Stinear & Byblow, 2004). Specifically, the primary motor cortex of the dominant hemisphere shows reliable reduction in SICI, indicating that hand dominance may play a role in the control of bimanual actions. Our findings provide further support to this notion and highlight the importance of considering the concordance of hand dominance and paresis in temporal bimanual coordination.

Impaired temporal coordination under dual-goal condition in LCVA may result from multiple interacting factors. One, leading with the paretic arm under dual-goal conditions may impair temporal dynamics such that the nonparetic arm may further trail behind increasing the time-lag. Greater attention required to control the paretic arm along a relatively straight trajectory may lead to greater delays in attending to and controlling the nonparetic arm, thus increasing the time lag between arms under the dual-goal condition. Second, and related factor may be the left hemisphere specialization for coupled bimanual actions. Multiple studies have demonstrated left-hemisphere-specific deficits in symmetric (in-phase) bimanual coordination, many of which were tested for separate goals (Blinch et al., 2019; Kilbreath et al., 2006; G. Lewis & Perreault, 2007; Serrien et al., 2003, 2012). Despite of longer time-lags under dual-goal conditions, the LCVA group was able to significantly improve temporal coordination between their arms under the common-goal condition. Improvements in time-lags were observed for the CON and RCVA groups, however, they did not reach statistical significance. Further, significant improvements in temporal coordination under common-goal condition in LCVA group was associated with a mean positive time-lag. This suggested that the common-goal condition, as a group, the LCVA participants led with their nonparetic arm. This finding is novel, and further highlights the critical role of task-goal perception on bimanual coordination.

Similar to previous findings (Kantak et al., 2016), temporal coordination was not significantly related to unimanual sensorimotor deficits of the paretic arm or cognitive deficits, indicating a distinct bimanual coordination deficit. Previous work has indicated that callosal connectivity between the two primary motor cortices is related to temporal coordination during bimanual tasks (Bortoletto et al., 2021; Wahl et al., 2016). Future studies that include imaging and neurophysiology are needed to highlight the neural substrates of temporal coordination after stroke affecting the left and right hemisphere.

4.3. Reduced contribution of the paretic arm

Consistent with previous findings in individuals with stroke, we observed that individuals with LCVA and RCVA demonstrate reduced contribution of their paretic arm during common-goal reaching actions (Kang & Cauraugh, 2015, 2017; Kantak et al., 2016). Previous work using reaching actions (Kantak et al., 2016) and force production tasks (Kang & Cauraugh, 2015, 2017; Lodha et al., 2012) have demonstrated reduced contribution/use of the paretic arm compared to the nonparetic arm. Multiple factors may influence the asymmetric contribution ratio during symmetric bimanual actions. One, paresis (or weakness) as measured using grip strength was significantly greater for the paretic arm compared to the nonparetic arm. Pollet et al. (2022) demonstrated that greater strength capacity was associated with greater contribution of the paretic hand during a common-goal force production task. Our results help generalize these findings to goal-directed reaching actions. More recent findings suggest that control deficits of the paretic arm may also contribute to contribution ratio. Kang et al. (2017) showed that variability (SD) of asymmetric contribution was higher in stroke patients than neurotypical individuals, and variability was correlated with control space exploitation strategies. Finally, recent work has also highlighted the role of effort on the choice of the weaker arm during unimanual actions (Schweighofer et al., 2015). Greater effort associated with selecting and moving the paretic arm may further bias greater contribution of the nonparetic arm during common-goal actions. While we did not measure effort in this study, future studies need to investigate the factors associated with reduced contribution of the paretic arm in bimanual actions.

4.4. Sex as a biological variable moderator of hemispheric differences in bimanual performance and movement along redundant axes.

We found that the effect of group on redundant axes displacement differed between males and females under common goal condition. While there were no group differences in males, females in the LCVA and RCVA groups showed larger displacements compared to controls in the common goal condition. These findings did not support our original hypothesis that LCVA group will show smaller displacements in the redundant axes and are different than the trends reported in the study by Schaffer et al., 2020. The difference in our findings may result from differences between the two studies including the experimental set up and sample size and characteristics. For example, the target distance was normalized to participants’ maximum reach instead of a fixed distance in the Schafer study. In addition, our participants with stroke (n= 47) had greater degree of motor impairments (UEFM: LCVA: 52.81+ 14.4; RCVA: 48.7 + 15.3) than the participants (n = 16) with stroke in the Schafer study (UEFM: LCVA: 62.0 ± 5.9; RCVA: 58.7 ± 5.9). Finally, and importantly, our results of significant sex by group by condition interaction suggest that the moderating effect of sex may influence group effects.

While the current study was not powered to detect sex differences in bimanual performance, our results yielded a significant interaction between sex and hemisphere of lesion, thus highlighting the role of sex as a crucial biological variable in bimanual performance and movement along redundant axis. Previous work has reported inconsistent findings on bimanual performance between men and women, with some studies reporting better performance in men (Shetty et al., 2014) (Mickevičienė et al., 2011), others reporting better performance in women (Khanjari & Arabameri, 2021), and others reporting no difference (Mickevičienė et al., 2011). While these disparate findings are likely due to differences in tasks and measures employed, these findings point to differences in bimanual performance between males and females. Sex differences in visuo-motor components such as visual perception (Hausinger & Pletzer, 2021; Voyer et al., 2020), curve tracing (Voyer & MacPherson, 2020), and visuo-motor tracking (Mathew et al., 2020) may contribute to bimanual performance differences between males and females. Given that there were grip force differences between males and females in our sample, it cannot be ruled out that differences in bimanual performance between the two sexes in stroke patients may be influenced by muscle strength differences, handedness and hemisphere-specific effects.

To the best of our knowledge, ours is the first study to show that bimanual performance differs for males and females with stroke dependent on the hemisphere of lesion. While the impact of sex on functional hemispheric asymmetries in visual processing, interhemispheric transfer of visual information, and visual perception has been reported (Hausinger & Pletzer, 2021; Hausman et. al., 2013), there is little known about how hemispheric asymmetry in motor control is impacted by sex. Neuroimaging studies have reported overlapping, yet distinct neural networks as well as corpus callosum characteristics that may influence bimanual coordination. For example, during symmetric (in-phase) actions, women reported greater functional connectivity between the right supramarginal gyrus and left anterior cingulate motor area as well as between vermis and left cerebellar crusI/II; while men show greater functional connectivity between the right supplementary motor area and left lingual gyrus (Rogojin et al., 2023). These sex-related differences in neural networks may underlie the sex differences observed between LCVA and RCVA groups. However, without detailed lesion-symptom mapping and connectivity data of the corpus callosum, it is difficult to delineate the neural basis of the sex and damaged hemisphere interaction observed here. Previously, a significant interaction between sex and side of hemisphere damage has been reported in functional outcomes after acute intravenous thrombolysis after stroke (Hametner et al., 2015). Future studies powered to detect behavioral and neural differences between males and females are needed to shed light on the hemispheric-specific differences in bimanual performance between males and females.

5. Conclusions and implications

Bimanual reaching actions to a common-goal, rather than dual-goals were associated with better spatial coordination in individuals with and without unilateral stroke. Further, common-goal actions benefitted temporal coordination in the LCVA groups. These results imply that bimanual coordination during reaching actions can be enhanced in stroke survivors by manipulating the perceptual nature of the task such that they work toward a common interactive task goal. The effects may be more robust in those with LCVA than RCVA and controls. While unimanual motor deficits of the paretic arm may influence spatial bimanual coordination, temporal coordination may be mediated by mechanisms specific to inter-limb coordination, rather than primary motor cortical output. Future studies are needed to identify the specific mechanisms that underlie temporal characteristics of bimanual coordination. Sex differences have not been considered until recently, but emerging evidence suggests that sex differences can affect motor control strategies. The present study provides preliminary evidence to support that sex and hemisphere of lesion may interact to influence bimanual performance under common-goal conditions, thus highlighting their role in motor control as well as rehabilitation.

Supplementary Material

1

Highlights:

  • Perception of task goals influences bimanual coordination.

  • Reaching to common-goal actions improves spatial coordination in individuals with stroke and neurotypical controls.

  • Compared to dual goals, reaching to common goal improves temporal coordination in those with left cerebrovascular accident.

  • Contribution of the paretic arm is reduced during common goal actions.

  • Sex as a biological variable influences bimanual performance after stroke.

Funding:

This work was supported by the Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health [R01HD092481].

Footnotes

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