Figure 1 shows the profiles for grip and load force, grip and load force rate, and box height for the right (red) and left (blue) hands for a representative control participant and an individual with stroke. Left plots show unweighted box condition and right plots show the weighted condition. For the control participant, force and force rate profiles are similar between the two arms, following smooth, single-peaked trajectories. Additionally, peak force and force rates are higher for the weighted condition as compared to the unweighted box condition, with max force rates peaking before box lift. The participant with stroke (RCVA) shows deficiencies in measures of anticipation and execution for the paretic (left) arm compared to the nonparetic (right) arm, particularly in the evolution of load force and load force rate prior to box lift.

Left (blue) and right hand (red) profiles for grip force (solid) and load force (dotted), grip force rate (solid) and load force rate (dotted), and box height as a function of time for a representative neurotypical control participant and an individual with stroke (RCVA; paretic arm = left). Plots on the left show the unweighted box condition. Plots on the right show the weighted box condition. The dashed vertical line indicates the time of box lift

To confirm that force rates peaked before box lift onset, and thus can be assessed as indices of planning, we performed separate analyses testing for differences between box lift onset time and the time of peak GFR and LFR. The analyses verified that box lift onset (M = 2.82 s) occurred significantly later in time than peak GFR (M = 2.55 s), χ2(1) = 33.57, p < .001, and peak LFR (M = 2.63 s), χ2(1) = 16.98, p < .001.

The analysis for peak GFR and LFR tested the hypothesis that participants with LCVA would show deficient scaling of force rate across box weight conditions as compared to controls and RCVA. We also predicted that differences would emerge between the paretic arm in the stroke groups (right arm for LCVA, left for RCVA) and the nonparetic arm. To examine these effects, we analyzed LFR and GFR with linear mixed effects models including terms for Group, Weight Condition, Hand, and their interaction, as well as a random effect term for Subject.

Peak GFR. The analysis of peak GFR revealed a significant Group by Weight Condition interaction, χ2(2) = 53.67, p < .001. Controls showed the greatest increase in GFR across weight conditions, followed by the LCVA group, and the RCVA group showed the smallest difference between conditions (Fig. 2). Tukey’s adjusted post-hoc contrasts examining group differences within the unweighted and weighted box conditions revealed differences between the control and RCVA groups for the weighted box condition, p = .02, with no other significant between-group differences. There were no additional significant two- or three-way interactions in the analysis, and thus no effects involving Hand (all p’s > 0.05). The analysis also yielded a significant main effect of Condition, χ2(1) = 17.54, p < .001, and no main effect of Group, χ2(1) = 5.56, p = .06.

Peak GFR as a function of weight condition for the control, LCVA, and RCVA group. Solid lines show individual subject means. Dotted lines show group means. Error bars show the standard error of the mean

As shown in Fig. 2, participants with stroke showed considerable variability in the scaling of peak GFR across weight conditions. In secondary analyses, we examined predictors of individual variation in the scaling of peak GFR using backward stepwise regression. The best fitting model, R2 = 0.30, F [3, 21] = 4.54, p = .01, included participants’ hemisphere of lesion (ß = − 0.35, p = .054), paretic arm ARAT score (ß =0.32, p = .09), and paretic side monofilament test score (ß =-0.26, p = .15). Importantly, the LCVA and RCVA groups did not differ across any predictors of motor or sensory function (all p’s > 0.05). The inclusion of hemisphere accords with the results for the analysis of GFR suggesting that the RCVA group was more impaired, relative to controls, than the LCVA group, for the scaling of GFR.

Peak LFR. The analysis of peak LFR revealed a significant Group by Weight Condition interaction, χ2(2) = 38.45, p < .001. As shown in Fig. 3, LFR increased more steeply across weight conditions for controls as compared to the LCVA and RCVA groups. Tukey’s adjusted post-hoc contrasts examining group differences within each box weight condition revealed differences between controls and the LCVA group (p = .03) and the RCVA group (p < .001) within the weighted box condition and no other group differences. There was also a significant Hand by Group interaction, χ2(2) = 71.87, p < .001. For controls, LFR values were higher for the left hand than the right hand, while the LCVA and RCVA groups produced higher LFR with the nonparetic (left in LCVA, right in RCVA) as compared to the paretic hand (right in LCVA, right in LCVA). The interaction between Weight Condition and Hand was not significant, p = .38, nor was the three-way interaction between Group, Weight Condition, and Hand, p = .14. There were significant main effects of Hand, χ2(1) = 7.73, p < .01, Weight Condition, χ2(1) = 29.99, p < .001, and Group, χ2(1) = 14.72, p < .001.

Peak LFR for the control, LCVA, and RCVA groups by Hand and Weight Condition. As indicated the right hand is the paretic hand for the LCVA group, while the left hand is the paretic hand for the RCVA group. Black points and dashed lines show group means with bars for standard error. Colored lines and points show individual participant means, with individual participants represented by a different color

In secondary analyses we examined individual variation among participants with stroke in the scaling of peak LFR across weight conditions (weighted – unweighted) in a stepwise regression. The final regression model was not significant (R2 = 0.19, p = .19).

The analysis of measures of execution, peak GF and LF, tested the hypothesis that individuals with RCVA would be impaired in the scaling of force across weight conditions as compared to controls and LCVA, and that these deficits may be more pronounced for the paretic arm in participants with stroke. To assess these effects, we fitted LME models with terms for Group, Weight Condition, Hand, the interactions between these factors, and a random effect for Subject.

Peak GF. A main effect of Weight Condition emerged, χ2(1) = 42.4, p < .001, with no other main effects or interactions. Peak GF was higher for the weighted (36.29 ± 9.76 N) compared to the unweighted (23.13 ± 8.22 N) box condition.

Peak LF. The analysis for peak LF revealed a significant three-way interaction between Group, Weight Condition, and Hand, χ2(2) = 12.33, p < .001. As shown in Fig. 4, control participants showed the largest change in peak LF across weight conditions as compared to either stroke group, and the magnitude of scaling was greater for the nondominant arm as compared to the dominant arm in controls and in the nonparetic as compared to the paretic arm for the LCVA and RCVA groups. Accordingly, there was also a significant interaction between Group and Hand, χ2(2) = 387.58, p < .001, a main effect of Hand, χ2(1) = 6.18, p < .05, and a main effect of Weight Condition, χ2(1) = 658.03, p < .001.

Peak LF plotted across Weight Condition by Group (Control, LCVA, RCVA) and Hand. Paretic hands are denoted for the LCVA and RCVA groups. Black points and dashed lines show group data with standard error. Colored lines and points show individual participant data

We predicted that participants with stroke would show deficient coordination as compared to controls with increasing task demand, and that these effects may be more pronounced in the RCVA group based on prior work showing deficiencies in coordination with disruptions to right hemisphere structures. To examine differences in the coordination of force within either hand, we analyzed GF-LF correlation coefficients using a model with terms for Group, Weight Condition, and Hand.

GF-LF correlation. Figure 5 shows GF and LF as a function of time (left panels) and GF against LF (right panels) for a representative control participant (Fig. 5A and B) and a participant with stroke (LCVA; Fig. 5C and D). For control participants, increases between GF and LF were approximately linear. Participants with stroke, however, showed significant variation in the coordination of these forces. As demonstrated in Fig. 5C and D, some individuals with stroke show marked impairments in LF production particularly with the paretic arm (i.e., the right hand in Fig. 5C and D).

Each pair of plots shows GF (solid) and LF (dashed) as a function of time and GF plotted against LF for a single trial for a representative control participant (top) and a participant with stroke (bottom) in the unweighted (left column) and weighted (right column) condition. Blue lines show the left hand. Red lines show the right hand. Note that the participant with stroke has left CVA, thus the right hand (red) is paretic. LF onset and max are denoted using vertical dashed lines. Box liftoff is shown in the vertical dotted line

The analysis of grip-load force correlation coefficients revealed significant interactions between Group and Condition, χ2(2) = 6.15, p < .05, and Group and Hand, χ2(2) = 138.28, p < .001, with no three-way interaction between Group, Weight Condition, and Hand or Hand by Weight Condition interaction (p > .05). These interactive effects are shown in Fig. 6. For the Group by Weight Condition interaction, both the LCVA and RCVA groups showed larger differences in grip-load coordination across weight conditions as compared to controls. The interaction between Group and Hand was driven by the higher grip-load correlation coefficients for the nonparetic left hand as compared to the paretic right hand in the LCVA group and the nonparetic right hand as compared to the paretic left hand in the RCVA group, while the two hands were similar for controls. There were also significant main effects of Hand, χ2(1) = 5.73, p < .05, Group, χ2(2) = 9.17, p < .05, and Weight Condition, χ2(1) = 21.10, p < .001.

Grip-load correlation coefficients across weight condition by Group and Hand

In secondary analyses, we examined predictors of individual variability in GF-LF coordination among participants with stroke using backward stepwise regression with the absolute difference in GF-LF correlation between the two arms (nonparetic-paretic) as the outcome measure and hemisphere of lesion, paretic arm ARAT score, monofilament test score, age, and sex as predictors. The best-fitting model, R2 = 0.62, F(5, 20) = 9.1, p < .001, retained participants’ paretic arm ARAT score (ß = − 0.99, p < .001), sex (ß = − 0.35, p = .02), paretic side monofilament score (ß = − 0.23, p = .10), age (ß = 0.21, p = .14), and proprioception difference (ß = 0.19, p = .17).

Bimanual coordination of force: Cross-correlation and time lag. To examine the bimanual coordination of force, we analyzed GFR and LFR cross correlation and time lags in separate models with terms for Group, Weight Condition, and their interaction.

The analysis of between-hand cross correlations of LFR yielded a significant Group by Weight Condition interaction, χ2(2) = 17.17, p < .001 (Fig. 7). The RCVA group showed the largest difference in cross-correlation values across weight conditions (Unweighted: r = .71 ± .45; Weighted: r = .84 ± .24), followed by the LCVA group (Unweighted: r = .79 ± .34; Weighted: r = .87 ± .15) and then controls (Unweighted: r = .95 ± .07; Weighted: r = .97 ± .03). There was also a significant main effect of Weight Condition, χ2(1) = 76.35, p < .001. No significant effects emerged for the analyses involving LFR time lag, GFR cross-correlation coefficients, or GFR time lag values.

LFR cross-correlation coefficients across Weight Condition by Group

To examine predictors of bimanual coordination among participants with stroke, we analyzed mean LFR cross-correlation coefficient values in a backward stepwise regression with the same predictors as our previous analyses. The best fitting model, R2 = 0.62, F(3, 22) = 14.83, p < .001, included participants’ paretic arm ARAT score (ß = 0.83, p < .001), sex (ß =0.39, p = .006), and hemisphere of lesion (ß = 0.20, p = .09).

The analyses of box tilt and hand position tested whether the between-group differences in measures of anticipation, execution, or coordination might be attributed to differences in the placement of the hands or how the box was lifted between groups.

Tilt at Lift. A one-sample t-test revealed that tilt at lift values differed from zero (no tilt), indicating significant box tilt at the time of lift, t [34] = -3.62, p < .001. We examined potential effects of Group and Weight Condition using linear mixed effects modeling. The analysis yielded a significant effect of Weight Condition, χ2(1) = 5.30, p = .02. Tilt at lift values were greater for the weighted box condition (-0.22 ± 0.76 cm) than the unweighted box condition (-0.09 ± 0.25 cm). Numerically, mean tilt at lift values suggested minimal leftward tilt for the control (-0.07 ± 0.44 cm), LCVA (-0.35 ± 0.87 cm) and RCVA (-0.10 ± 0.46 cm) groups. Importantly, there were no effects of Group (p = .26) or Group by Weight Condition interaction (p = .92).

Tilt at Max Height. Tilt at max height values did not differ significantly from zero, suggesting minimal tilt (p = .16). LME analysis revealed a significant effect of Weight Condition, χ2(1) = 6.29, p = .01, with no effect of Group (p = .62) or Group by Weight Condition interaction (p = .67). Mean tilt was greater for the weighted (0.51 ± 2.96 cm) as compared to the unweighted (0.07 ± 0.51 cm) box condition. In terms of the direction of tilt by group, controls showed positive mean tilt (0.14 ± 3.25 cm), suggesting rightward tilt toward the dominant arm, while participants with stroke showed tilt toward the non-paretic arm. Participants with LCVA showed negative (leftward) tilt (-0.06 ± 1.67 cm), while participants with RCVA showed positive (rightward) tilt (0.77 ± 2.42 cm). As demonstrated by the large standard deviations, however, there was considerable individual variation in box the direction and magnitude of tilt.

Hand Position Differences at Box Lift. To examine whether the tilt at box lift emerged from differences in hand placement on the box, we examined differences in left- and right-hand Z-position at box lift. Differences in left and right-hand Z-positions did not differ significantly from zero (p = .71). LME yielded no significant effects for Group (p = .64), Weight Condition (p = .93), or Group by Weight Condition interaction (p = .86). Mean hand difference values, while highly variable, suggested a tendency to grasp lower with the left than the right for the control (-0.36 ± 0.99 cm) and LCVA (-0.64 ± 1.32 cm) groups, while the mean for the RCVA group suggested lower right-hand position relative to the left (0.31 ± 2.37 cm).