TIMING VARIABILITY OF REACH TRAJECTORIES IN LEFT VERSUS RIGHT HEMISPHERE STROKE

Abstract

This study investigated trajectory timing variability in right and left stroke survivors and healthy controls when reaching to a centrally located target under a fixed target condition or when the target could suddenly change position after reach onset. Trajectory timing variability was investigated with a novel method based on dynamic programming that identifies the steps required to time warp one trial’s acceleration time series to match that of a reference trial. Greater trajectory timing variability of both hand and joint motions was found for the paretic arm of stroke survivors compared to their non-paretic arm or either arm of controls. Overall, the non-paretic left arm of the LCVA group and the left arm of controls had higher timing variability than the non-paretic right arm of the RCVA group and right arm of controls. The shoulder and elbow joint warping costs were consistent predictors of the hand’s warping cost for both left and right arms only in the LCVA group, whereas the relationship between joint and hand warping costs was relatively weak in control subjects and less consistent across arms in the RCVA group. These results suggest that the left hemisphere may be more involved in trajectory timing, although the results may be confounded by skill differences between the arms in these right hand dominant participants. On the other hand, arm differences did not appear to be related to differences in targeting error. The paretic left arm of the RCVA exhibited greater trajectory timing variability than the paretic right arm of the LCVA group. This difference was highly correlated with the level of impairment of the arms. Generally, the effect of target uncertainty resulted in slightly greater trajectory timing variability for all participants. The results are discussed in light of previous studies of hemispheric differences in the control of reaching, in particular, left hemisphere specialization for temporal control of reaching movements.

1. Introduction

Individuals recovering from a cerebrovascular accident (CVA) frequently exhibit motor impairments of the paretic arm that limit their performance of activities of daily living, such as reaching to grasp an object. Movements of the paretic limb typically are slow and less smooth than those of healthy individuals, with increased variability of hand trajectories (Archambault et al., 1999; Levin, 1996). These characteristics of upper limb movements result from larger and less coordinated joint variations compared to healthy control individuals (Levin, 1996; Reisman and Scholz, 2006).

Many studies also have reported motor deficits of the non-paretic arm (Haaland et al., 2004; Kwon et al., 2007; Schaefer et al., 2007; Winstein and Pohl, 1995) that frequently affect motor timing. For example, in a tapping task, individuals with a left-sided stroke showed higher variability of the inter-tap interval with their left arm compared to the corresponding control individuals (Kwon et al., 2007). In contrast, persons with a right hemisphere stroke did not show this deficit when performing with their right arm, suggesting that the left hemisphere may play a bigger role in the control of movement timing. Schaefer and collaborators (2007) reported that persons with a right CVA had reduced modulation of acceleration duration and substantial errors in final position when performing targeted single joint elbow movements with their non-paretic limb. In contrast, left CVA survivors showed reduced modulation of acceleration amplitude but had fewer final position errors. Robertson and Roby-Brami (2011) reported differences between stroke victims with right and left hemisphere lesions in the coordination of trunk and arm movements during reaching. The above findings reinforce previously reported hemispheric specializations for controlling different aspects of movements (Elliott, 1985; Haaland and Delaney, 1981; Harrington and Haaland, 1991; Lavrysen et al., 2003; Todor and Doane, 1978).

Most studies of hemispheric differences have investigated tasks in which only a small number of joints were involved. Only a few studies have examined reaching movements that involved a large number of degrees of freedom of joint motion (Cirstea and Levin, 2007; Levin, 1996; Levin et al., 2002; Michaelsen et al., 2001; Reisman and Scholz, 2003; Reisman and Scholz, 2006). For example, Levin’s group (Cirstea et al., 2003) was one of the first groups to quantitatively study coordination deficits among arm joints in persons following a stroke. Reisman and Scholz (2003) investigated differences between mildly paretic, left hemisphere stroke survivors and healthy persons in their joint coordination for reaching, using the Uncontrolled Manifold (UCM; Scholz and Schöner, 1999) approach to partition joint variance into ‘good’ variance (flexible combinations of joints across repetitions that led to a stable hand path) and ‘bad’ variance, which leads to hand path variability. They reported that stroke survivors actually exhibited more ‘good’ variance than did healthy controls when reaching to targets. However, the stroke survivors also showed less effective decoupling of joint space such that ‘bad’ joint configuration variance was significantly larger than for control subjects, leading to more hand path variability. These studies were limited to the study of persons with left hemisphere lesions, however.

Freitas and Scholz (2009) recently reported in young healthy individuals that the use of flexible patterns of joint coordination to produce a consistent hand path increased when the target of reaching could suddenly change location after reach onset compared to reaching to a fixed target, suggesting that movement planning can affect the use of motor abundance. The question of how movement planning affects the use of motor abundance in persons who have suffered a stroke currently is under investigation by our group. Preliminary results indicate that, as with healthy individuals, stroke survivors show more ‘good’ variance than bad variance related to the reach trajectories although they have higher bad variance than healthy controls. Therefore, they have higher overall task variable variability. However, this typical UCM variance analysis is based on positional variability at each point in a movement trajectory and does not address directly movement timing. Thus, a question that has not been investigated previously in multi-joint reaching is whether and to what extent the timing of reaches is affected when the target position is uncertain and whether lesions to different hemispheres affects movement timing under conditions of uncertainty. Haaland et al. (2004) studied the effect of target uncertainty on temporal events of reaching in person post stroke using the double-step paradigm. The authors observed longer reaction time and movement time for individuals that suffered a left hemisphere stroke compared to healthy adults whether the target location was certain or uncertain. However, when stroke survivors had to change direction with their left hand to acquire a target that had jumped, their movement was slower than for controls reaching with the same arm. In contrast, comparisons of temporal measures between healthy individuals and right hemisphere stroke survivors revealed non-significant differences related to target conditions.

It has been suggested that the brain is lateralized for the organization of time-domain characteristics of sequential action, but not for the metrical scaling of parameters of force production (Walter and Swinnen, 1990). Studies comparing movement timing characteristics between individuals with left and right brain lesions suggested a right hemisphere specialization for the timing of discrete, distal limb movements (Harrington et al., 1998) or left hemisphere specialization for sequential movements related to whole limb tapping (Winstein and Pohl, 1995). In addition, one study of movements involving trunk motion suggested that both hemispheres contribute to the temporal coordination of the body segments (Esparza et al., 2003). Uncertainty about hemispheric specialization in the literature is likely due to the different tasks used to evaluate movement timing as well as the different events investigated and the involvement of a different number of degrees of freedom.

Most studies that have investigated deficits of movement timing after brain lesions have focused on the temporal characteristics of individual events such as reaction time, movement time or time to peak velocity (Chang et al., 2008; Dipietro et al., 2007; Dipietro et al., 2009; Haaland et al., 2004; Harrington et al., 1998). However, such events are often difficult to identify in individual joint movements of persons with stroke due to the large number of movement subunits they exhibit (Dipietro et al., 2007; Dipietro et al., 2009). Thies and collaborators (2009) proposed a new method to quantify movement timing variability that includes the entire trajectory rather than individual timing events. This method has been used recently to compute timing characteristics of the upper limb motion during two functional tasks (drinking and moving a plate) in healthy individuals and stroke survivors. Overall, the authors found greater trajectory timing variability for the stroke group compared to control individuals, and these differences were larger for the unilateral task. That study only investigated the paretic limb, however, and did not report on performance differences between left and right hemisphere strokes (Thies et al., 2009).

The current study extends the work of Thies et al. (2009) by considering trajectory timing differences of the non-paretic as well as paretic arm, differences between individuals with right and left hemisphere strokes, the influence of planning for differences in task requirements, and by extending the analysis to joint trajectories. Stroke survivors and healthy, age-matched adults performed reaching towards either certain (fixed) and uncertain targets. Based on the Thies’ (2009) study of trajectory timing variability of hand accelerations, we hypothesized to find greater timing variability for stroke survivors compared to the control group, but for the non-paretic as well as paretic arms. We also hypothesized that trajectory timing variability would be larger for persons with left-hemisphere lesions. A set of different combinations of arm joint accelerations could lead to same resultant hand acceleration. Thus, in the present study, the timing variability analysis was applied to the hand paths as well as joint motions. By examining timing variability of each joint, it was possible to investigate how the temporal involvement of each joint (across time) was affected by the brain lesion.

2. Results

Fig. 1 presents the time series of twenty resultant hand acceleration profiles from a representative participant from each group (RCVA, LCVA and control), reaching with the left and right arm [respectively, left and right panels of Fig. 1a-c; in the case of the stroke survivors, the panels are also represented as the arm ipsilateral (non-paretic) or contralateral (paretic) to the lesion]. These trajectories were time-normalized to 100% only for purposes of illustration. However, the trajectories for the warping cost analysis were not time-normalized prior to the analysis (see methods for more details). Movements performed with the contralateral limb were, as expected, less smooth than those with the ipsilateral limb and both limbs of participants from control group.

Fig. 1.

Twenty profiles of hand acceleration of one representative participant of each group (in a, LCVA; b, RCVA; and, c, control) for the reaching movements under single-step (certain condition, top panels) and double-step (uncertainty target condition, bottom panels) trials to the center target using their left arm or right arm (left and right panels, respectively). PA = paretic arm; NP = non-paretic arm.

For statistical analyses three comparisons were run between groups: each brain side lesion (RCVA and LCVA) versus control group and RCVA vs. LCVA. The right (left) arm of control group was always compared with the right (left) arm of CVA groups, regardless if it was paretic or not. Repeated measures analyses of variance (ANOVA) were used for the dependent variables related to movement time (average and variability) and warping cost of hand acceleration, with factors arm and condition (certain vs. uncertain) treated as repeated measures. Multivariate ANOVA (RM-MANOVA) were run for the warping cost of joint accelerations, with all ten joint motions as dependent variables. Paired comparisons with Bonferroni adjustments were used in the case of main effects in post-hoc analyses of individual joints.

2.1. Movement Time

Movement time (MT) results are presented in Fig. 2a. For the control group, MT was significantly shorter than for either the LCVA (F(1,23)=6.7, p<0.05) or the RCVA (F(1,21)=12.4, p<0.01) groups. There also was a significant arm by group interaction for the comparisons of control subjects with both LCVA (F(1,23)=6.9, p<0.05) and RCVA (F(1,21)=7.7, p<0.05) groups (Fig. 2). Only the reaches with the paretic right arm of the LCVA were significantly slower than the right arm of controls (F(1,23)=7.5, p<0.05; Fig. 2a). For the RCVA group, in contrast, differences between the groups reached significance for both the non-paretic right arm (F(1,21)=9.5, p<0.01) and paretic left arm (F(1,21)=10.9, p<0.01). Overall, MT did not differ between the LCVA and RCVA groups (p=0.33) and there was no interaction between group and arm. The only significant difference was, as expected, between the paretic and non-paretic limb. MT for the paretic limb was longer than for the non-paretic limb regardless of the side of lesion or condition (F(1,20)=12.2, p<0.01).

Fig. 2.

Average (A) and standard deviation (B) across-participants of movement time for each group when reaching to the center target. Data are averaged across certain and uncertain conditions due to a lack of condition effect. Error bars depict standard errors of the mean. PA = paretic arm; NP = non-paretic arm.

MT variability (standard deviation) results were similar to those for MT (Fig. 2b). MT variability was significantly higher for both the LCVA (F(1,23)=42.1, p<0.0001) and RCVA (F(1,21)=21.5, p<0.0001) groups compared to the control group. In addition, both LCVA (F(1,23)=17.6, p<0.0001) and RCVA (F(1,21)=26.3, p<0.0001) individuals showed a significant interaction of group and arm for the comparisons with control group. MT variability for the LCVA group was significantly higher than for control individuals both for the non-paretic left arm (F(1,23)=9.2, p<0.01) and the paretic right arm (F(1,23)=37.8, p<0.0001). MT of the paretic left arm of the RCVA group was significantly more variable than the left arm of control subjects (F(1,21)=24.1, p<0.0001).

Comparison of MT variability between the LCVA and RCVA groups revealed only a significant group by arm interaction (F(1,20)=5.0, p<0.05). MT variability was greater for the non-paretic limb of the LCVA compared to the RCVA group, while the paretic limb of the RCVA group had higher MT variability than the paretic limb of the LCVA group (Fig. 2b).

2.2. Warping cost

The warping cost analysis was performed separately on 3D hand acceleration and 10 DOF joint motion accelerations as described in methods section. The results of these two analyses will be reported separately.

2.2.1 3D Hand Acceleration

A summary of statistical results is presented in Table 1. Comparing LCVA to the control group, the warping cost was significantly higher for the LCVA group. The effect of group depended, however, on the arm used to reach as revealed by the arm by group interaction. Warping cost was significantly higher only for the paretic, right arm of the LCVA group compared to right arm of controls (F(1,23)=21.79; p<0.001). In addition, warping cost of the hand acceleration trajectories was also higher for the uncertain target condition compared to the certain condition, independent of the arm or group (Fig. 3).

Table 1. Summary of statistical analysis of warping cost of 3D hand acceleration.

	Group Comparisons
	LCVA vs. Control		RCVA vs. Control		LCVA vs. RCVA
Effects	F	p	F	p	F	p
Group	16.01	0.01*	23.68	0.01*	1.49	0.24
Arm	4.05	0.056	35.96	0.01*	36.89	0.01*
Condition	7.54	0.05*	0.11	0.75	0.98	0.34
Arm by Condition	0.01	0.94	1.25	0.27	0.92	0.35
Arm by Group	23.03	0.001*	17.50	0.01*	5.71	0.05*
Condition by Group	1.29	0.27	0.95	0.34	2.25	0.15
Arm by Condition by Group	2.73	0.11	5.62	0.05*	4.83	0.05*

Fig. 3.

Average across-participants warping cost of 3D hand accelerations for each group (white bars, LCVA; gray bars, RCVA; and, black bars, CONTROL). Bars on left (right) hand-side of each subplot are for the certain and uncertain target conditions, all when reaching to the center target. Error bars depict standard errors. PA = paretic arm; NP = non-paretic arm. The overlying hatched bars represent the differences obtained when LCVA subjects with near or perfect Modified Fugl-Meyer upper extremity scores were eliminated from the analysis to make the average scores between the groups more comparable.

For comparisons of the RCVA and control groups, warping cost was also significantly larger overall for the RCVA group (Table 1). There also was a significant interaction among arm, condition and group. Warping cost was significantly higher for the RCVA persons than for controls regardless of whether they reached with their non-paretic right arm (F(1,21)=10.9, p<0.01) or paretic left arm (F(1,21)=23.2, p<0.001). The non-dominant left arm of control subjects exhibited a significantly higher warping cost than the dominant right arm, when reaching under the uncertain (F(1,12)=20.1, p<0.01) but not the certain (p=0.093) target condition. The paretic left arm of the RCVA group had a higher warping cost than the non-paretic right arm for both the certain (F(1,9)=21.3, p<0.01) and uncertain (F(1,9)=18.1, p<0.01) conditions.

Warping cost was higher overall for the paretic than the non-paretic arm of both LCVA and RCVA groups (F(1,20)=36.9, p<0.001), as expected. There was a significant interaction among arm, condition and group when comparing the LCVA to RCVA participants. Simple interaction effects performed with each arm revealed significantly larger warping cost for the uncertain compared to the certain condition when considering the non-paretic arm (F(1,20)=4.8, p<0.05). However, for the paretic arm, there was no significant difference in warping cost between the certain and uncertain conditions (p>0.82; Fig. 3), and no interaction with group (p>0.06).

Overall, the relationship between the warping cost for hand acceleration and the stroke survivors’ level of impairment, indicated by their Modified Fugl-Meyer (MFM) scores, was quite strong. For the paretic arm, a linear regression of warping cost on the MFM score revealed a significant relationship (F(1, 42)= 45.7, p<0.001, R² = 0.52) across both targeting conditions. This relationship was higher for the uncertain (F(1, 20)= 36.1, p<0.001, R²=0.64) than for the certain condition (F(1, 20)= 14.8, p<0.01, R²=0.42). However, when performing the analysis separately for LCVA and RCVA groups on the combined conditions, the RCVA group’s MFM score was strongly related to the paretic left arm’s warping cost (F(1,8)= 44.0, p<0.0001, R²=0.85), whereas the LCVA group’s MFM score was less strongly related to the paretic right arm’s warping cost (F(1,10)= 8.9, p<0.05, R²=0.47).

The relationship between warping cost and impairment level was much weaker for the non-paretic limb, accounting for only 22% of the variance (F(1,42)= 12.0, p<0.01) overall. This finding is not surprising, however, because the MFM score is obtained for the paretic, not the non-paretic limb.

The hatched bar extensions in Fig. 3 depict changes in the effects that occurred when participants with the highest upper extremity MFM scores, which has a maximum of 57, were eliminated from statistical analyses. This was done because there were a larger number of individuals in the LCVA group with near- or perfect MFM scores (Table 3) and we wanted to see what differences persisted when the groups were more equivalent on average in impairment levels. Thus, data for participants LCVA1, LCVA8, LCVA9 and LCVA11 were eliminated from this additional analysis, resulting in an average MFM score of 43.6 ± 13.4 for the reduced LCVA group and compared to 43.9 ± 9.1 for the RCVA group.

Table 3. Constant and variable error of targeting.

		LCVA		RCVA		CTRL
CONSTANT ERROR		Mean	SEM	Mean	SEM	Mean	SEM
Left Arm	Certain	4.70	1.12	7.25	1.51	3.69	0.54
	Uncertain	4.30	1.10	8.29	1.42	3.80	0.68
Right Arm	Certain	6.43	1.78	4.19	0.94	3.58	0.58
	Uncertain	5.87	1.74	5.37	0.90	3.47	0.49
VARIABLE ERROR
Left Arm	Certain	8.00	1.36	10.15	1.16	6.00	0.30
	Uncertain	7.78	0.96	10.21	1.11	6.76	0.39
Right Arm	Certain	8.83	1.30	7.28	1.21	6.95	0.52
	Uncertain	10.80	1.25	8.18	0.86	6.45	0.29

Differences in the statistical comparisons with and without removal of these participants were limited, however. For the comparison of the LCVA with the control group, there now was a significant arm by condition by group interaction (F(1,19)=5.6, p<0.05) present with the less impaired subjects removed. Considering the left, non-paretic arms, the uncertain condition led to higher warping cost than the certain condition regardless of group (F(1,19)=8.4, p<0.01). There was no interaction between condition and group (p>0.72). For the right arm, which was paretic for the LCVA group, there was a significant interaction between group and condition (F(1,19)=7.76, p<0.05), with no difference between certain and uncertain conditions for the control subjects but higher warping cost for the uncertain compared to certain condition for the LCVA participants (Figure 3).

For the LCVA vs. RCVA comparison, the statistical results were similar as when all subjects were included. There was still a significant three-way interaction (F(1,16)=6.32, p<0.05). As with the full group, the uncertain condition (5.81 ± 0.43) resulted in higher warping cost than the certain condition (5.16 ± 0.36) for the non-paretic arm (F(1,16)=4.76, p<0.05). However, although there was still no main effect of condition (p>0.37) for the paretic arm, there was now a significant group by condition interaction (F(1,16)=17.63, p<0.05). This resulted from the LCVA group exhibiting larger warping cost when reaching in the uncertain (9.87 ± 1.38) versus certain (7.93 ± 1.12) condition (F(1,7)=6.62, p<0.05), while the RCVA group had no-significant difference in warping cost between the certain (11.23 ± 1.42) uncertain (10.41 ± 1.29) conditions (p>0.32).

2.2.2 Joints’ Accelerations

A summary of the multivariate statistical results is presented on Table 2. The RM-MANOVA comparing LCVA and control groups revealed significant effect of group, with warping cost being significantly higher for the LCVA group than for control subjects. This was true for all joint accelerations (minimum F(1,23)>4.6, p<0.05), except adduction (p=0.08) and internal rotation (p=0.48) of the shoulder and elbow extension (p=0.052). However, there was also a significant arm by group interaction. Univariate statistics revealed this effect for most joint motions (minimum F(1,23)>4.6; p<0.05), except for scapular/clavicular abduction (p=0.06), shoulder adduction (p=0.08), forearm pronation (p=0.06) and wrist abduction (p=0.43). As can be seen from Fig. 4, the interaction was due to paretic right arm joints of LCVA individuals having consistently higher warping cost than the left arm, whereas control subjects had consistently higher warping cost for the non-dominant left arm than for the right arm.

Table 2. Summary of multivariate statistical analysis of warping cost of joint accelerations.

	Group Comparisons
	LCVA vs. Control		RCVA vs. Control		LCVA vs. RCVA
Effects	F	p	F	p	F	p
Group	3.63	0.05*	7.56	0.01*	4.04	0.05*
Arm	0.68	0.73	3.55	0.05*	2.80	0.053
Condition	2.72	0.05*	2.32	0.08	2.80	0.06
Arm by Condition	1.16	0.39	1.25	0.27	1.82	0.17
Arm by Group	2.90	0.05*	2.25	0.09	2.30	0.09
Condition by Group	1.23	0.35	1.11	0.43	1.42	0.29
Arm by Condition by Group	0.75	0.67	2.33	0.08	1.31	0.33

Fig. 4.

Average across-participants warping cost of joints’ accelerations of each group (LCVA, RCVA and control). Data represent the average between the two conditions. Results of each joint motion are presented as stacked bars and the labels of each bar represent, in a bottom to top order, scapula abduction (SCP_ABD), elevation (SCP_ELEV) and external rotation (SCP_ROT), shoulder abduction (SHO_ABD), flexion (SHO_FLEX) and internal rotation (SHO_IR), elbow extension (ELB_EXT) and pronation-supination (ELB_PRO), and wrist flexion-extension (WRS_FLEX) and abduction-adduction (WRS_ABD). All joint comparisons for stroke groups were significantly different from controls except where indicated (n.s.).

The RCVA group had higher overall warping costs compared to control subjects. This was true for all joints’ accelerations (minimum F(1,23)>4.6, p<0.05). Moreover, independent of group, the left arm (paretic limb for RCVA group) had higher warping costs than the right arm. This effect was present for most joints (minimum F(1,23)>4.4, p<0.05), except for adduction (p=0.07) and internal rotation (p=0.21) of shoulder and elbow extension (p=0.10).

The only significant main effect found in the RM-MANOVA when comparing LCVA to RCVA individuals was the group effect, indicating that persons with a RCVA had higher warping cost than those with a LCVA, independent of the arm used to reach and condition (Fig. 4). Although this group effect was present overall, no individual joint showed significant differences between stroke groups in the univariate analyses (all p>0.07).

2.2.3 Relationship between warping costs for joint and 3D hand accelerations

Multiple linear regression analyses were performed for each arm of each group to investigate the relationship between the warping costs of joint motions and the warping cost of 3D hand motion. The results showed that the warping cost of only few joints were significantly related to the warping cost of 3D hand acceleration (Fig. 5). The adjusted R²_adjusted values (R²_adj) for all regressions are presented in Fig. 5. The specific joints’ whose warping cost was related to the hand motion’s warping cost differed between arms and groups. For the control group (lower panels, Fig. 5), regardless of the arm used to reach, the hand’s trajectory timing variability appears to be related primarily to a few proximal joint motions, scapular rotation for the left arm, scapular abduction and shoulder flexion for the right arm. The standardized values, which indicate how many standard deviation units of increase occurs in the 3D hand warping cost for a 1.0 standard deviation change in the joint warping cost, were relatively small, as were the R²_adj values.

Fig. 5.

Scatter plots of Hand 3D vs. Joint warping cost for significant joint contributions to the multiple linear regression. ABD=abduction, ADD=adduction, EXT=extension, FLEX=flexion, ER=external rotation, PRO=pronation, ELEV=elevation. Standardized beta values for all significant joints from the multiple regressions are indicated in parentheses and represent the standard deviation increase in hand warping cost for a 1.0 standard deviation increases in the joint’s warping cost.

The warping costs of the non-paretic arms of both stroke groups were more strongly related to the joint warping cost (higher standardized and R²_adj values compared to controls; upper left and middle right panels, Fig. 5). For the RCVA group, shoulder internal-external rotation, forearm pronation and wrist abduction warping costs were significant predictors of the warping cost of 3D hand acceleration, with moderate sized values and R². In contrast, for the LCVA group, shoulder flexion, elbow extension and wrist abduction were significant predictors of the warping cost for 3D hand acceleration, with larger values and R² compared to the RCVA group.

For the paretic arms of both stroke groups, the R²_adj values for the relationship between joint warping costs and 3D hand warping costs were quite high, ≥ 0.90. Only the warping cost for wrist flexion was a significant predictor of the 3D hand warping cost for the RCVA group, however (Fig. 5, middle left panel). In contrast, warping costs of scapular abduction, shoulder adduction and flexion, and elbow extension were all significant predictors of the 3D hand acceleration warping cost for the LCVA group, with the proximal joints having relatively high values. The LCVA group showed the most consistent contribution of joint warping costs to hand warping cost across the paretic and non-paretic arms (shoulder flexion and elbow extension).

3. Discussion

In the current study, a novel method for examining the temporal variability of movement trajectories of arm reaching by computing the warping cost (Thies et al., 2009) was used to identify differences among persons with right and left hemisphere lesions and age-matched control subjects. This method provides the advantage of evaluating the correspondence of the entire reach trajectory across multiple reaches, not only the timing of individual events during the movement (e.g., time to reach the hand peak velocity). Such individual events are often difficult to determine when investigating the paretic limb of stroke victims, especially at the joint level. A low warping cost indicates that repeated trajectories of the hand or joints’ motions are relatively similar in their timing structure. High warping cost indicates large trial-to-trial timing variability. In the current study, trajectory timing variability for hand acceleration was substantially larger for the paretic limb compared to the non-paretic limb of stroke survivors and when compared to the same limb of control subjects. This finding was, of course, expected but supports the ability of the method to differentiate between different levels of trajectory control. Stroke survivors showed greater timing variability regardless of the side of the brain lesion compared to healthy, age-matched adults. This was true for the non-paretic as well as the paretic limb, particularly when considering the most impaired stroke survivors. Overall, these results corroborate the findings of Thies and colleagues (2009), which showed that stroke survivors had large warping costs of hand movement when performing functional tasks with the paretic limb. The current study extended that work, however, by considering trajectory timing differences of the non-paretic as well as paretic arm, differences between individuals with right and left hemisphere strokes, the influence of movement planning when the final target was uncertain, and by extending the analysis to joint trajectories.

Our hypothesis that differences in trajectory timing among stroke survivors and healthy adults would be greater when reaching under an uncertain target condition was partially confirmed. Trajectory timing variability was slightly larger in the uncertain condition compared to the certain condition for the non-paretic arms of all stroke survivors and for the paretic right arm of the LCVA group when reanalyzing using the more impaired stroke survivors. This was also the case for the non-dominant left arm of control adults (Fig. 3), but not for the dominant right arm. In these cases, uncertainty about the ultimate target location led to higher trajectory timing variability when reaching to the centrally located target. These results indicate that the approach is sensitive to small changes in task parameters related to motor planning and may be useful in future studies of planning. However, because the analysis included the entire movement trajectory, the warping cost measure was also influenced by adjustments in the trajectory occurring after the time of peak velocity and cannot be attributed to planning alone. In fact, Haaland and collaborators (2004) reported that target uncertainty led to decreased movement speed in persons with a left hemisphere stroke when reaching with their non-paretic left arm to a new target location compared to healthy controls reaching with the same arm.

The lack of a difference between target conditions in healthy adults when reaching with the dominant right arm could suggest that skill level also plays a role in determining the effect of target uncertainty (see below). In addition, trajectory timing variability was actually greater for the certain compared to the uncertain condition when persons with a RCVA reached with their paretic left limb (Fig. 3). Because there were no differences in movement time between the two target conditions, and both involved reaching to the same central target, this finding is difficult to explain. Although the participants with a stroke in this study had no documented perceptual problems or spatial neglect, persons with a right hemisphere stroke are known to have greater perceptual and spatial deficits than persons with a left hemisphere stroke (Mack and Levine, 1981; Newcombe and Russell, 1969; van Ravensberg et al., 1984). One hypothesis to account for this result, therefore, is that these individuals had a greater focus of attention on the task when the final target location was uncertain compared to the certain target condition. If so, this may have resulted in subtle spatial/perceptual deficits becoming more of a factor in the certain condition.

The overall results of the warping cost analysis did not depend on whether the approach was applied to hand acceleration or individual joint accelerations. Similar trends in the results were observed whether focusing on the underlying components of the reaches (i.e., individual joint motions) or movement outcome (i.e., hand motion). Although only small differences between the LCVA and RCVA groups were found when comparing the non-paretic limbs, participants with a right hemisphere lesion had significantly higher warping costs for both the hand and joints for the paretic arm than did persons with a left hemisphere lesion.

Results of the present study may shed light on previously reported hemispheric differences related to the control of reaching. Results of previous studies (Haaland et al., 2004; Sainburg and Kalakanis, 2000; Sainburg and Wang, 2002) have led to the suggestion that the right hemisphere, reflected in left arm performance, is specialized for the control of limb impedance, and particularly the terminal position of reaching. In contrast, the left hemisphere is considered to be more involved in controlling dynamic features of reaching, such as trajectory formation. For example, reaches with the non-dominant left arm of right-handed individuals have been shown to be more sensitive to interaction torques and show greater hand path curvature compared to the dominant right arm (Bagesteiro and Sainburg, 2002). On the other hand, these authors have reported that reaches with the non-dominant left arm exhibit less error in final position during rapid reaches than does the dominant right arm. These findings have been corroborated in studies of reaching with the non-paretic limb in persons with stroke (Haaland and Harrington, 1996; Schaefer et al., 2007), leading to the suggestion that the left hemisphere is more specialized than the right hemisphere for trajectory formation related to reaching (Haaland and Harrington, 1996). Consistent with this finding, persons with a left CVA have been shown to have deficits in trajectory control as evidenced by greater deviations in their hand path, but intact final position accuracy when reaching with the left (non-dominant limb pre-stroke) arm (Schaefer et al., 2007). The later finding is consistent with the suggestion that closed-loop processes, dependent on sensory feedback, tend to be intact after a left-hemisphere stroke (Haaland and Harrington, 1996). In contrast, Schaefer and colleagues (Schaefer et al., 2007) found that right brain stroke survivors had positional deficits when reaching with the non-paretic right arm but had relatively normal hand trajectories. It should be noted, however, that the latter work examined planar reaching with a 2-DOF arm, allowing only shoulder and elbow joint movement. Whether these differences hold for more natural movements requires further study. For example, when a right hand-dominant individual attempts to thread a needle, they do much better holding the needle with the non-dominant left arm and performing the movement with the dominant right arm, consistent with the proposed hemispheric specialization. However, the level of precision required to insert the thread into the eye of the needle, which involves a relatively small and slow movement, suggests that final position control is also an important feature of the left hemisphere control.

An earlier study by Winstein and Pohl (1995) of a whole limb reciprocal tapping task generally supports the conclusions of Sainburg and colleagues. They reported that persons with a left-hemisphere stroke had greater deficits in the ballistic component of the movement, e.g., trajectory formation. Of relevance to the current study, these patients also were reported to have difficulty in the timing of sequential movements related to tapping. In contrast, persons with a right-hemisphere stoke were reported to have more difficulty with rapid on-line adjustments in tapping near the target. Further confirmation of these hemispheric differences were provided in mildly impaired stroke survivors by Pohl et al. (2000).

Some studies have revealed less clear differences between roles of the two hemispheres, however. For example, Haaland and Harrington (1989) did not find differences in reaction time, movement time or movement accuracy between healthy individuals and the non-paretic right arm of persons with right-hemisphere damage. In contrast, individuals with a left-hemisphere stroke showed slower reaction time and were less accurate when reaching with their non-paretic arm than healthy participants. In addition, a recent imaging study suggests that reported differences between the two hemispheres might be due partly to effects of reaching with the less skilled, non-dominant arm rather than pure hemispheric differences. For example, results of Falk et al. (1996) suggest that activation of the left hemisphere when performing ipsilateral movements may reflect, at least partially, simultaneous mirror movements performed by the right hand, limiting conclusions about hemispheric differences.

The current investigation appears to provide some support for the left hemisphere’s dominance in trajectory formation of reaching, at least with respect to movement timing. For healthy adults, the warping cost measure was significantly higher when participants reached with their left arm (right hemisphere) than when reaching with the right arm. This result was true for both the hand’s acceleration (Fig. 3) and the joints’ accelerations (Fig. 4). The results of this analysis for the non-paretic arm of the stroke survivors were in the same direction as for the control subjects. The non-paretic left arm of LCVA group, controlled primarily by the right hemisphere, exhibited greater trajectory timing variability than did the non-paretic right arm of the RCVA group. Though significant, these differences were small and were present only for the hand’s trajectory, not the joints’ trajectories. Caution in interpretation is required, however, because these differences could be due to differences in skill level between the arms due to differences in use that are a least partly related to lower-level neural processes. This is also true for interpretation of the effect of target uncertainty between the non-paretic arms of right and left strokes and between the dominant and non-dominant arms of control subjects.

In an attempt to disambiguate the arm differences in warping cost from the skill level, the constant error (CE) and variable error (VE) of targeting were analyzed (Table 3). As expected, both CE (F(1,16)=5.66, p<0.05) and VE (F(1,16)=7.77, p<0.05) were higher for the paretic versus the non-paretic arm of stroke participants. However, neither CE (p>0.83) nor VE (p>0.92) differed between the left non-paretic arm of the LCVA group and the right non-paretic arm of the RCVA group. Nor was there an interaction with the target condition. Also, as can be seen in Table 3, both CE and VE were higher for both arms of the stroke individuals compared to control subjects. However, there was no significant difference between the dominant and non-dominant arms of control subjects for either CE (p>0.75) or VE (p>0.37). There also was no significant interaction with the target condition. Although this is a limited measure of skill, it provides some indication that the arm differences in trajectory timing error, estimated by the warping cost measure, may not be due solely to skill differences.

The relationship between warping costs based on joint accelerations and the warping cost based on 3D hand acceleration provides some support for the greater role of left hemisphere in trajectory timing. The LCVA group was the only group for which this relationship was relatively similar across paretic and non-paretic arms. Both shoulder flexion and elbow extension warping costs were significant predictors of the hand’s warping cost for both paretic and non-paretic arms, in addition to the contribution of several other joints. Moreover, the R²_adjusted values were relatively high for both arms of the LCVA group (Fig. 5, upper panels), as were many of the values for the significant joint predictors. For the RCVA group, both the R²_adjusted value and values of contributing joints were more moderate for the non-paretic arm. As with the LCVA group, there was a strong relationship between joint warping cost and hand warping cost for the paretic arm of the RCVA group (Fig. 5, left middle panel). However, only wrist flexion warping cost was a significant predictor of the 3D hand warping cost. Thus, these results suggest that greater variability of the hand’s trajectory timing in left hemisphere strokes compared to controls is due to poor timing of both proximal (e.g., shoulder) and more distal (elbow) joints. In contrast, hand trajectory timing variability of the right brain strokes appears to be more related to distal joints (forearm and wrist), with some contribution by shoulder internal-external rotation. Of course, these initial observations need to be investigated in greater detail and with a greater number of patients.

In contrast to the stroke subjects, controls exhibited a weak relationship between joint warping costs and the 3D hand warping cost (Fig. 5, lower panels). Moreover, hand timing variability was related to only proximal joint timing variability, i.e., scapular and shoulder. The weak relationships between joint warping costs and the hand warping cost in control subjects seem puzzling on the surface. This finding may be a reflection of the fact that the warping cost is low overall compared to stroke subjects, and that the joints are better coordinated to minimize any effect of individual joint timing variability on the timing of the hand’s motion. Such a strategy would be consistent with the UCM hypothesis, although that is a posture-based hypothesis (Scholz and Schöner, 1999; Schöner and Scholz, 2007). The fact that the stroke subjects, and particularly their paretic arm, show a strong relationship between several joint warping costs and the 3D hand acceleration warping cost may reflect the more fixed hemiparetic synergies often described for such individuals, although not specifically with respect to movement timing (Beer et al., 2000; Beer et al., 2004; Brunnstrom, 1970). The fact that such deficits in stroke are related to abnormal joint dynamics is consistent with this suggestion (Beer et al., 2000).

Most studies have implied a primary role of the cerebellum in event timing (Ivry and Spencer, 2004), both in terms of perceptual judgment and movement production tasks (but see Harrington et al., 2004), with evidence for (Diedrichsen et al., 2003) and against (Aparicio et al., 2005) a role for the basal ganglia. It is well known, for example, that patients with cerebellar lesions exhibit a breakdown of the timing between movement components, e.g., the coordination between opening of the hand and associated arm movements (McNaughton et al., 2004), and show increased variability of tapping tasks (Spencer et al., 2003) (but see Harrington et al., 2004; McNaughton et al., 2004; Spencer et al., 2003). Much less direct evidence exists for the role of the cerebral hemispheres in event timing, particularly for movement tasks. Kagerer et al. (2002) provided evidence from a stimulus duration reproduction task that individuals with lesions of the right but not the left hemisphere are impaired in reproducing intervals longer than 2-3 seconds. Neither right or left hemisphere lesions affected reproductions < 2-3 seconds, suggesting that the disruption may be related more to memory than time perception per se. An earlier study by Harrington and colleagues (1998) revealed similar deficits in the time perception of non-linguistic acoustic stimuli in persons with right but not left hemisphere strokes that involved similar neural structures (e.g., premotor and prefrontal cortex). Neuroimaging studies also have revealed a possible role of the cerebral hemispheres in temporal perception tasks (Lewis and Miall, 2003; Smith et al., 2003), although the interpretation of specific brain activations during performance of laboratory tasks always requires caution. We could find few studies that have studied directly the role of the hemispheres in the timing of movements. Some imaging studies have suggested such a role in tasks that require complex timing, but the exact role played by the activated areas, which usually involve the cerebellum as well, in the required movement timing is difficult to determine (e.g., Mayville et al., 2002; Ullen et al., 2003). Thus, to the extent that the measured differences in warping cost between the arms can be attributed to hemispheric differences rather than skill, the current results provide novel evidence for a more dominant role of the left hemisphere in specifying the time course of the entire movement trajectory. In reality, different aspects of timing are likely distributed across many neural structures such that a single neural “time keeper” is unlikely.

Although the direction of arm differences when comparing the left paretic arm of RCVAs to the right paretic arm of LCVAs is consistent with the above reported arm differences for control adults and the non-paretic arm of stroke individuals (i.e., left arm having greater trajectory timing variability), one might expect greater timing variability of the paretic right arm when the left hemisphere is damaged if it plays a more important role in trajectory timing. Related to this issue is the relationship between the participants’ impairment level based on their Modified Fugl-Meyer scores (Lindmark and Hamrin, 1988) and their warping cost. The finding is interesting in itself because discovering relationships between clinical measures of impairment and more quantitative measures of performance have not been easy, especially when relating such measures to the outcome of training (Denti et al., 2008). Specific to the current issue is the fact that the relationship between arm impairments and warping cost was particularly strong in the RCVA group, the warping cost accounting for 85% of the variance of the participants’ MFM score. Because the items of the upper extremity MFM score do not reflect timing in any fundamental way, this suggests that the larger trajectory timing variability of the paretic left arm of this group was due to greater overall limb impairment, possibly related to the less skilled nature of the non-dominant arm pre-morbidity. Although the LCVA group also showed a significant correlation between the warping cost of their paretic right arm and their MFM scores, this relationship was weaker both with and without the least impaired participants’ data excluded. Here, the warping cost accounted for only 47% of the variance of the MFM scores. Thus, the lesion differences in warping cost of the paretic arm, being greater for the RCVA group, appears to be due to impairment level, possibly tied to less skilled arm use pre-stroke.

Generally speaking, then, the results from healthy adults and the non-paretic limbs of stroke survivors in this investigation tentatively support the idea that the left hemisphere is more involved in specifying trajectory timing than is the right hemisphere. However, the possibility that the differences are due to arm dominance effects cannot be ruled out completely. Further study with premorbid left hand dominant stroke survivors may shed further light on this issue. Of course, these results are specific to trajectory timing and do not address the presumed greater role of the right hemisphere in impedance and position control (Sainburg, 2005).

4. Experimental Procedures

4.1. Participants

Twenty-two individuals, 40-85 years old, twelve participants with a single left-brain stroke (LCVA) and ten participants with a single right-brain stroke (RCVA) more than 3 months prior to the study, participated. All stroke survivors performed the task with their paretic limb first, followed by their non-paretic limb. A summary of the stroke participant’s characteristics is presented on Table 3. Thirteen age-matched control adults (9 females; 64 ± 5.77 years old) without brain damage also participated in the experiment. Six right-handed, control subjects performed the task first with their left non-dominant arm and seven performed first with their right dominant arm. All participants were right-hand dominant (stroke survivors prior to their stroke) as determined by the Edinburgh handedness questionnaire (Oldfield, 1971). All participants gave informed consent consistent with the Declaration of Helsinki, and approved by the University’s Human Subjects Review Board.

4.2. Apparatus and Data Acquisition

The three-dimensional (3D) kinematics of the arm and scapula were recorded at 120-Hz using a eight-camera VICON motion measurement system. Rigid bodies with 4 markers each were placed on the hand, lower arm, upper arm, and on the superior aspect of the upper trunk, two-thirds of the distance between the neck and the acromion process to capture clavicle/scapula motion. Individual markers were placed below the notch of the sternum and on the tip of a pointer attached to a molded splint worn by the participant. The sternum marker served as the basis of the coordinate system used to compute various experimental measures. One static arm calibration trial was recorded prior to the experiment as a reference zero position for computing joint angles (see below). Additional markers recorded during this trial were placed on the radial and ulnar styloid processes of the wrist and on the medial and lateral epicondyles of the elbow, the average position of which were used to estimate the joint centers of the wrist and elbow, respectively. Another marker lateral and just inferior to the acromion process was used to estimate the shoulder joint location. In this trial, the arm was facing forward from the shoulder, with the upper arm, forearm and hand aligned and held parallel to the floor, the thumb pointing upward. In this position, the arm was parallel to the global y-axis and all joint angles were defined as zero. For the reference trial, the x-axis of each joint pointed laterally, the y-axis pointed along the long axis of the upper arm, forearm and hand, and the z-axis pointed upward.

4.3. Experimental Procedure

Fig. 6a provides a schematic of the experimental set-up (right arm view). Participants were seated in an adjustable-height chair to ensure that their forearm rested on the table in pronation, with the upper arm nearly vertical and the elbow flexed to approximately 90. Trunk motion was restrained by strapping it to the chair in such a way to ensure that scapular motion was not restricted. Participants began each trial from the same initial position. To ensure that this position was consistent across trials and conditions, a radiological vacuum bag was fitted around the lateral and medial aspect of the participants’ arm. Then the air was extracted from the bag, leaving the arm in a trough with rigid sides. From this position, participants were instructed to reach and touch a target displayed on the touch-screen computer monitor so the contact location of the pointer-tip could be recorded; and, then immediately to return to the initial position. The pointer was adjusted relative to the hand rigid body so that its tip was set at a distance equal to the index finger’s length when it was extended. Initially, the target height was 70% of the participant’s eye height from the tabletop and the target distance (i.e., the distance of the screen of the monitor from the participant) was of approximately 95% of the functional arm length. Functional arm length was measured by asking participants to actively extend their arm forward as much as they could and the distance from the acromion process of the shoulder to the tip of the index finger of the arm used to reach was noted. Then, participants were asked to reach the target and small adjustments were made to the target distance and height if participants could not reach the target comfortably. A green 1.5-cm diameter circular target was displayed on the video monitor at the beginning of all trials, centered on the participant’s midline.

Fig. 6.

Experimental set-up when the participants performed the movements with right arm (A) and target position (B) presented at the beginning of the trial and immediately after the participants’ hand started to move for single-step (top panels) and double-step trials (lower panels). The presented set-up was similar for left arm.

Each participant performed 160 trials of reaching with each arm. For all trials, participants were instructed to reach “as fast and as accurately as possible” to a target displayed at the center of the video monitor (certain center target; Fig. 6b). During the first block of 40 trials, the target location remained fixed throughout the trials. For the remaining 120 trials, the “double-step” paradigm was employed to create target location uncertainty (U). A target was always displayed initially at the central location, as for certain trials. When the participants’ hand moved from the initial position, a switch was released that could either have no effect on the central target location (uncertain center target) or could result in the target jumping, with a delay of approximately 16-ms, by 13-cm ipsilateral or contralaterally to the participant’s arm, which corresponded to a 16.5° deviation of the vector pointing from the initial position to the center of the central target (Fig. 6b). Forty trials of each target condition were randomized in the uncertain block using a customized LabView program. A ten-minute break was allowed between the block of certain trials and the double-step trials. Before the beginning of each condition, participants practiced less than 10 trials for each condition to familiarize with the task. Fatigue was never reported by the participants.

At the beginning of all trials, participants were told to fix their eyes on the centrally located target and start the movement as soon as they felt ready following an auditory signal. There was no reaction time requirement. The instruction during double-step trials was to initiate one smooth movement toward the central target, at the same movement speed as for the single-step trials. Then, if the target jumped, they were told to adjust their reach trajectory as quickly as possible toward the new target location but not to try to anticipate a target jump.

4.4. Data Analysis

Kinematic data were low-pass filtered at 5-Hz using a bi-directional, second-order Butterworth filter before further processing. The marker data during dynamic trials were referenced back to the arm calibration trial to compute the 10 rotational DOFs of the arm: three DOFs each at the clavicle/scapula and shoulder joints and two DOFs each at the elbow (flexion-extension and pronation-supination) and wrist (flexion-extension and abduction-adduction) joints. Joint angles were calculated using the algorithm proposed by Söderkvist and Wedin (1993).

The coordinates of the center target and the initial hand position were used to form a local coordinate system into which all marker data were rotated for further analyses. The x-axis of this local coordinate system was aligned with a vector from the hand’s starting position to the target’s center (corresponding to movement extent), and the y- and z-axes were formed orthogonal to this vector, following the right-hand rule (corresponding to two components of movement direction).

Movement onsets and terminations were defined, respectively, using 3% and 5% of the peak pointer-tip velocity. A larger cutoff for movement termination was used to eliminate final corrections used to stabilize the pointer-tip contact with the touch-screen. The determination of these instants of time were done automatically with a Matlab routine (Mathworks, Version 7.0) and visually checked for accuracy. The average and standard deviation of movement time, defined as the time from movement onset until movement termination, were used to describe the temporal characteristics of the participants’ performance.

4.4.1. Timing Variability Analysis

Continuous timing variability was computed using the method proposed by Thies et al. (2009) involving dynamic programming for curve-registration. The approach considers two aspects of the variability of any given signal separately: 1) variability in the timing of the signal, e.g., whether a characteristic feature at a specific instance of time in a reference trial occurs at the same instance in time as in a target trial, and 2) variability in the signal’s magnitude, e.g., the extent to which the maximum value of the characteristic feature is reproduced from trial-to-trial. The software algorithm, programmed in Matlab™, uses a two-stage process to quantify both aspects of movement variability separately. The current report focuses only on timing variability.

The algorithm first addresses timing errors between trials before calculating differences in signal magnitude. Therefore, for each trial-to-trial comparison a reference trial is defined to which a target trial is “time-warped”. The variability in timing is then quantified by the amount of warping that was necessary to align the two trials. For each data point, an acceleration vector in 3D space, $\ddot{\mathrm{p}}\left(\mathrm{t}\right)=[\ddot{\mathrm{x}}\left(\mathrm{t}\right),\ddot{\mathrm{y}}\left(\mathrm{t}\right),\ddot{\mathrm{z}}\left(\mathrm{t}\right)]$ of the reference trial, the algorithm defines the ‘error’ between it and a given data point, ${\ddot{\mathrm{p}}}^{\prime }\left({\mathrm{t}}^{\prime }\right)=[{\ddot{\mathrm{x}}}^{\prime }\left({\mathrm{t}}^{\prime }\right),{\ddot{\mathrm{y}}}^{\prime }\left({\mathrm{t}}^{\prime }\right),{\ddot{\mathrm{z}}}^{\prime }\left({\mathrm{t}}^{\prime }\right)]$ in the target trial as the Euclidean distance between the two points:

$$\mathrm{d}\left(\ddot{\mathrm{p}}\left(\mathrm{t}\right),{\ddot{\mathrm{p}}}^{\prime }\left({\mathrm{t}}^{\prime }\right)\right)=\sqrt{{\left(\ddot{\mathrm{x}}\left(\mathrm{t}\right)-{\ddot{\mathrm{x}}}^{\prime }\left({\mathrm{t}}^{\prime }\right)\right)}^2+{\left(\ddot{\mathrm{y}}\left(\mathrm{t}\right)-{\ddot{\mathrm{y}}}^{\prime }\left({\mathrm{t}}^{\prime }\right)\right)}^2+{\left(\ddot{\mathrm{z}}\left(\mathrm{t}\right)-{\ddot{\mathrm{z}}}^{\prime }\left({\mathrm{t}}^{\prime }\right)\right)}^2}$$

Computing this error for every possible pairing of data points gives an error surface in which the axes represent time in the reference trial and target trial, respectively. More details can be found in Thies et al. (2009). Dynamic programming was then used to calculate the path of minimum error across the diagonal of the error surface, which defines the optimal time warping of the target trial onto the reference trial. The RMS error between this path of least error and an ideal 45° line (corresponding to a simple offset with no warping) represents the amount of time-warping done and is referred to as the warping cost. The dynamic programming approach enforces the constraint that the warping does not change the temporal order of the data points in the target trial.

The following formal steps were carried out to perform the timing variability analysis, computed in two different spaces: 3D hand acceleration and joint accelerations. In both spaces, the reference trial was selected based on the across-trials median time spent to complete the task, i.e., the time interval between the movement onset and the time to reach the target. For the analysis of 3D hand trajectory, the acceleration of each dimensional space (x, y, z) was calculated and the portion of the trajectory between movement onset and termination was selected. For the analysis of joint motion, the acceleration of each joint angle motion (i.e., 10 DOF) was calculated and the portion of the joint motion between movement onset and termination was selected. The amount of warping that was necessary to align a target trial with the reference trial was used as indication of trajectory timing variability. The warping cost was calculated for each dimension of 3D hand acceleration and the average across dimensions and trials was computed for statistical analyses. For joint motion, the averaged across-trials warping cost between the reference and each target trial for each joint was analyzed separately.

4.4.2. Constant Error (CE) and Variable Error (VE)

Although not of primary importance to this report, the constant and variable error of pointing to the target were also computed to help disambiguate arm dominance and hemispheric lesion differences in the warping cost measure. The terminal pointer tip position was obtained as the sample at which the difference between the pointer tip and the calibrated target position was smallest, before obvious adjustments in the pointer tip position. The difference between the pointer tip position and target for the entire reach was plotted in all three dimensions, as well as the resultant distance. Computations of CE and VE were based on resultant value of the differences in each dimension. In some cases, when the termination was difficult to obtain for stroke participants with low Modified Fugl-Meyer scores, a combination of the resultant error and error in the anterior-posterior dimension of the pointer tip were both used to determine the termination point. CE and VE were computed across trials using standard formulas (Schmidt and Lee, 2011).

4.5. Statistical Analyses

The goal of this study was to investigate differences between groups and arms when they were reaching to the same target, including the effect of target uncertainty. Therefore, only trials performed to the center target under certain and uncertain conditions were studied. Statistical analyses were performed in SPSS 16.0 (SPSS Inc., Chicago, USA). Repeated measures analyses of variance (ANOVA) were used to verify the effects of group/arm (LCVA, RCVA and control) and target condition (certain vs. uncertain) on the movement time (both averaged and standard deviation) and timing variability (warping cost) of the movements, with target condition as repeated measure factor. For the comparison between control and either LCVA or RCVA groups, the arm factor was defined as left and right arms. However, for the comparison between LCVA and RCVA groups, the arm factor was defined as paretic and non-paretic limbs. That is, the right, paretic limb of LCVA group was compared with the left, paretic limb, of RCVA group. A mixed design MANOVA was used to examine the effects of group, arm and target condition on the dependent variables relating to 10-DOF of warping cost for joint accelerations. The level of significance was set at p<0.05.

Finally, the relationship between the warping costs based on joint motion accelerations and the warping cost based on 3D hand acceleration was investigated separately for each arm and group using multiple linear regression analysis in SPSS. Regressions were performed with the backward elimination procedure; all variables were entered into the equation and then sequentially removed. The joint warping cost with the smallest partial correlation with the 3D hand warping cost was considered first for removal. If it met the criterion for elimination (probability of F-to-remove ≥ 0.1), it was removed. After the first variable was removed, the variable remaining in the equation with the smallest partial correlation was considered next for removal. The procedure stopped when there were no variables in the equation that satisfied the removal criteria. The values and R²_adjusted of the final equation were then assessed. Because of the small number of subjects, we accepted joint contributions with a p-value of < 0.10. This led to inclusion of two joint warping costs, shoulder internal-external rotation for the RCVA group’s non-paretic arm and shoulder adduction for the paretic arm of the LCVA group.

Highlights.

• Trajectory timing variability was studied in right and left brain strokes and healthy controls

• Stroke survivors showed higher timing variability of both paretic and non-paretic arms compared to controls

• The non-paretic arm of left hemisphere strokes and the left arm of controls had higher timing variability than the other arm

• Target uncertainty increased timing variability except for the dominant arm of controls

• Results were generally consistent with the left hemisphere’s presumed greater role in trajectory formation

Table 4. Summary of stroke survivor’s characteristics.

Group	Gender	Age (Yrs.)	UE Modified Fugl-Meyer	Years since stroke	Lesion
LCVA1	M	60	55	2.0	Scans not available
LCVA2	F	78	47	1.6	Internal capsule (IC), corona radiata
LCVA3	F	67	51	7.3	Pons
LCVA4	M	77	25	2.4	parietal cortex and basal ganglia
LCVA5	M	81	55	0.7	Left Putamen
LCVA6	M	71	54	0.3	Scans not available
LCVA7	M	44	51	0.3	Basal Ganglia, thalamus, sparing posterior limb of IC
LCVA8	M	74	57	4.0	Posterior aspect of left insula, frontal and temporal lobes
LCVA9	M	57	57	0.3	Antero medial aspect of left frontal lobe, superior-lateral aspect of the parietal lobe
LCVA10	M	48	46	0.3	Posterior limb of IC
LCVA11	F	66	57	2.0	Lateral thalamus, posterior limb of IC
LCVA12	M	62	20	1.0	Scans not available
		65.4 ±11.7	47.9 ± 12.5	1.9 ±2.1
RCVA1	F	77	47	0.3	Posterior limb of IC, amygdala, parahippocampal gyrus
RCVA2	F	59	45	1.0	Basal ganglia; hemorrhagic
RCVA3	M	50	49	1.0	Posterior limb of IC
RCVA4	M	78	25	2.0	Lateral basal ganglia, corona radiata
RCVA5	F	68	51	0.3	Parietal lobe, corona radiata
RCVA6	F	66	52	1.0	Frontal lobe operculum, white matter of the temporal-parietal region
RCVA7	M	44	35	0.3	Frontal lobe in a watershed distribution
RCVA8	M	56	50	1.3	Scans not available
RCVA9	M	66	50	3.0	Right pons
RCVA10	F	46	35	2.5	Anterior aspect of right lateral ventricle
		61.0 ±11.4	43.2 ± 9.4	1.3 ±0.9