Mechanical Effects of Canes on Postural Control: Beyond Perceptual Information

1 Background: Numerous studies showed that postural balance improves through light touch on a 2 stable surface highlighting the importance of haptic information, seemingly downplaying the 3 mechanical contributions of the support. The present study examined the mechanical effects of 4 canes for assisting balance in healthy individuals challenged by standing on a beam. 5 Methods: Sixteen participants supported themselves with two canes, one in each hand, and applied 6 minimal, preferred, or maximum force onto the canes. They positioned the canes in the frontal 7 plane or in a tripod configuration. 8 Results: Results showed that canes significantly reduced the variability of the center of pressure and 9 center of mass to the same level as when standing on the ground. In the preferred condition, 10 participants exploited the altered mechanics by resting their arms on the canes and, in the tripod 11 configuration, allowing for larger CoP motions in the task-irrelevant dimension. Increasing the 12 exerted force beyond the preferred level yielded no further benefits, in fact had a destabilizing 13 effect on the canes: the displacement of the hand on the cane handle increased with the force. 14 Conclusions: Despite the challenge of a statically unstable system, these results show that, in 15 addition to augmenting perceptual information, using canes can provide mechanical benefits and 16 challenges. First, the controller minimizes effort channeling noise in the task-irrelevant dimensions 17 and, second, resting the arms on the canes but avoiding large forces that would have destabilizing 18 effects. However, if maximal force is applied to the canes, the instability of the support needs to be 19 counteracted, possibly by arm and shoulder stiffness. 20


⑵
Beam-CoP = Ground-CoP + ℎ 1 where h is the height of the beam and = [F x g , F y g , F z g ] is the ground reaction forces recorded by 2 the force plate. The x-axis corresponded to the ML direction, the y-axis to the AP direction, and the 3 z-axis to the vertical direction, as illustrated in Fig. 1.  4 As , gg z x y FF  , the additional term on the right side of equation (1) and (2)  5 Error! Reference source not found.was negligible. Thus, in the following only the Ground-CoP was 6 considered. For the sake of clarity, the CoP on the ground was referred to as the  When two canes touched the floor, the participant had three regions of contact with the ground: 8 the feet on the beam, and the tips of the two canes. The feet were on the beam, which was located 9 on the force platform, thus measuring the ground reaction force and the center of pressure. 10 Information about the force applied on the canes was provided by the load cells at the tip of the 11 canes. The center of pressure of each cane was computed by the ratio between the moments, x m 12 and y m , and the forces, z f , measured by the load cells.
The spatial positions of the tips of the canes were determined from the markers attached to the 16 canes. With all variables in the laboratory coordinate frame, the total center of pressure (Total-CoP) 17 was computed as the ratio of the total moments, were calculated separately, because of the anisotropic constraints of the beam, i.e., the base of 1 support on the beam was larger in the AP direction than in ML. Another measure of postural sway 2 was defined as the area of the 95% tolerance ellipse. The same metrics were computed for both 3 Feet-CoP and Total-CoP. In addition, the fluctuations of the center of mass (CoM) were quantified 4 by the area of the 95% tolerance ellipse. This area was calculated in the horizontal (x-y) plane to 5 make it comparable to the areas of the CoPs. Note that movements in the vertical (z) direction were 6 negligible. To quantify movements of the hand at the tip of the cane, the path length of the hand 7 movement was calculated as the integral of the root mean squared sum of the derivatives of the x-, 8 y-and z-components. 9 Statistical Analysis 12 A linear mixed model was used to evaluate the differences in the variability of the center of mass 13 and the center of pressure between the three levels of force applied to the canes and the two cane 14 configurations. The mixed model compared the experimental conditions (fixed effects), i.e., beam, 15 force and cane configuration conditions, which were consistent across participants, and accounted 16 for the effects of normally distributed variability between participants (random effects). In equation 17 (10) Y is the latent response variable for each participant i and each trial j, B is the beam condition 18 (On the Beam or On the Ground); F is the force condition (three levels: Min, Pref, Max), C is the arm 19 configuration (two levels: Planar and Tripod),  are the fixed-effects coefficients, S are the random-20 effects coefficients. 21 ⑽ = 0 + 0 + + ( + ) + + 22 To better compare the force conditions in which participants were standing on the beam with the 1 canes on the ground, a second model (see equation 11) was tested on a subset of the data, excluding 2 trials in the control conditions. 3 Additional multiple comparisons were conducted across experimental conditions by pairwise t-tests 5 with Bonferroni correction. 6 All statistical analyses were carried out in R, with packages stats, lme4 and lmerTest (21). 7

Results 8
This study examined the mechanical effect of cane support for maintaining standing balance. 9 Specifically, the experiment aimed to identify the mechanical effects of two canes on the control of 10 balance when standing on a narrow beam. Participants supported themselves by holding two canes 11 placed either on their side or in a tripod configuration (Figure 1). In the latter placement, the arms 12 formed a 45 deg angle and the canes were in front of the body, forming a triangle with the feet. 13 Participants were asked to exert three levels of force onto the canes: minimum (Min), preferred 14 (Pref), and maximum (Max). We measured the displacements of the center of pressure on the beam, 15 the forces on the canes, the body's center of mass, and the displacements of the hands at the cane. 16 To provide a baseline measure, both the center of pressure and the center of mass were quantified 17 when participants stood on the ground, in the same tandem foot position as on the beam. Another 18 reference measure was obtained when participants stood on the beam without cane support. The 19 overarching question of this study was how the different forces applied to the canes and two arms 20 configurations affected the mechanics and, hence, the control of postural balance. 21

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Forces Applied on the Canes. The first test verified that participants indeed followed instructions 1 and applied different forces on the canes. Table 1 shows the summed vertical forces applied on the 2 two canes averaged over the duration of the trial. For the three force instructions and for the two 3 cane placements the applied forces ranged between 4 and 50 N for each cane. The linear mixed 4 model confirmed the difference between the three force instructions with a significant main effect 5 (β = 10.1±2.6, p < 0.001). All three force conditions were larger than those examined in previous 6 studies and the preferred force differed from both the maximum and the minimum forces. The two 7 cane configurations did not elicit different forces in the three force conditions (β = -0.7±4.3, p = 8 0.86). Forces were averaged across the duration of the trial. 12 The preferred force applied on both canes was reliably around 33 N in both arm configurations, 13 corresponding to the weight of a 3.36 kg mass. Assuming the weight of one arm is 5% of the total 14 body weight, this force approximated the weight of the arm for an average body mass of 67 kg (3.35 15 kg) (5, 28). As each cane supported approximately the weight of half of the arm as the weight of the 16 arm was distributed across hand and shoulder, this preferred force offset the need to hold the arms 17 against gravity. To further probe into this effect, we estimated the weight of each participant's arm 18 as the 5% of total body mass. Figure 2 shows these values against the sum of the forces applied on 1 both canes; this value was calculated as the average across time and divided by gravity. This led to 2 the same units as the x axis. The estimated arm weight correlated with the preferred force applied 3 on the canes as indicated by the significant Pearson correlation coefficient (R = 0.64, p < 0.001). The 4 data cluster very closely around the identiy line, indicating that the preferred force is determined 5 by the weight of the participants arms. (colored lines), Total-CoP (grey lines) and also of the center of mass CoM (black lines) for each 9 experimental condition (yellow shading represents the beam width). When standing on the ground 10 ( Figure 3A), the fluctuations of CoM and CoP were considerably reduced compared to standing on 11 the beam without canes; this is especially pronounced in the AP direction ( Figure 3B), which was 12 not surprising. When standing on the beam without canes, both CoP and CoM showed visibly larger 13 excursions, both in the AP and ML directions, again as expected. 14 The six panels in Figure 3C show exemplary data from the same participant standing on the beam 15 with the canes on the ground. The excursions of both CoPs and CoM were significantly reduced 16 compared to those when standing on the beam without cane support and were similar to those 17 measured when standing on the ground ( Figure 3A,B). The planar cane configuration led to visibly 18 smaller variability in the AP direction than the tripod configuration, especially in the maximum force 19 condition. In the minimum force condition, ML variability was similar in both Feet-CoP and Total-20 CoP, in both cane configurations. With increasing forces applied on the canes, the Feet-CoP 21 decreased its ML amplitude. In contrast, the Total-CoP went beyond the width of the beam, 22 indicating that the participants were moving their weight away from the feet and actively relying on 23 the canes. Lastly, the fluctuations of the CoM, shown by the black lines, followed the changes of the 1 Total-CoP across different forces and cane placements and presented additional evidence that 2 participants shifted their weight beyond the base of support on the beam towards that provided by 3 the canes. 4 The CoP location along the beam changed between trials, even within the same participant. This 5 effect resulted from changing the distribution of body weight between the front and the back foot, 6 even without stepping off the beam between trials. 7 Insert Figure 3 about here 8

Comparison of Postural Sway On and Off the Beam.
To first evaluate the difference between 9 balancing on the beam supported by canes with the two control conditions, the area of the CoM 10 served as a collective measure of balance performance. Figure 4A shows the CoM in the two control 11 conditions on and off the beam (white) next to the three force conditions on the beam (colored); 12 the data combined the two cane configurations to focus on the comparison with the two control 13 conditions. The figure makes it evident that standing on the beam without canes had the highest 14 degree of variability (β = 1682.1±290.2, p < 0.001). More notable is that when on the beam with 15 canes the variability of the CoM declined to levels similar to the variability on the ground. 16 Additionally, when comparing to the different force conditions with pairwise post-hoc comparisons, 17 the two higher forces did not differ from standing on the ground (Pref: p = 0.08, Max: p = 0.1). Only 18 the minimum force condition showed a small but significant elevation compared to standing on the 19 ground (Min: p = 0.02). Interestingly, when applying increasing force on the canes, the variability of 20 the CoM did not change (p = 1). 21 Figure 4B shows participant averages of the 95% confidence interval of the CoP for the two control 22 conditions without cane support (white bars) next to the three force conditions (colored). To take 23

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into account the different nature of Total-CoP and Feet-CoP when participants used canes, the 1 results were separated. Again, the data were pooled for the two cane configurations to facilitate 2 comparison. As expected, standing on the beam without cane support significantly increased the 3 CoP excursions with respect to standing on the ground by a factor of 10 (β = 2953.6±236.2, p < 4 0.001). However, when participants used the canes for support, the Total-CoP returned to values 5 similar to standing on the ground, as confirmed by the pairwise post-hoc comparisons (p = 1). The 6 Feet-CoP showed even smaller values than the Total-CoP with canes and the CoP on the ground 7 without canes (p < 0.001). While surprising at first, participants had three points of contact with the 8 floor that allowed them to rely less on foot-beam interaction and more on canes. 9 Taken together, these findings confirmed expectations that standing on the beam increased CoP 10 and CoM motions. However, both CoM and CoP variabilities approached the same level of variability 11 on the beam with canes and standing still on the ground. Given the instability when balancing on 12 the beam without canes, this gives first evidence of the significant mechanical effect of the canes. The main metric is variability in the ML direction, computed as the standard deviation of the CoP 17 motion, as it is the most relevant direction for maintaining balance on a beam. Figure 5A shows the 18 ML variability of the Total-CoP against the average forces applied on the canes; the data points 19 represent all individual trials of all participants with force condition differentiated by color. Figure  20 5B shows the same data averaged across the different force and arm conditions and pooled over all 21 participants. There was no evidence of any change with increasing force (β = -0.000015±0.0001, p = 22 0.87). While different from what expected in Hypothesis 1, this finding was consistent with previous 23 results: ML variability was significantly attenuated with small forces at the support, and increasing 1 force levels did not further affect the Total-CoP (10, 11). However, the Total-CoP was affected by 2 the canes placement showing a slightly larger ML variability in the tripod condition 3 (β=0.0006±0.0002, p < 0.001). The effect of arm configuration was counter to Hypothesis 3. 4 Insert Figure 5 about here 5 In contrast, the ML standard deviation of the Feet-CoP decreased with the average force for each 6 trial, as shown in Figure 5C. Figure 5D shows the pooled data of all participants for each 7 experimental condition. For both cane configurations the same trend was observed: applying a force 8 larger than minimum force reduced Feet-CoP variability (β = -0.0008±0.00015, p < 0.001). This 9 indicates that increasing force applied on the canes let participants rely less on foot-beam 10 interaction and more on canes. The variability in the ML direction for the Feet-CoP was not affected 11 by cane configuration (β = -0.00016±0.0002, p = 0.45), indicating that the spatial configuration of 12 the arms was not relevant for the ML direction of the Feet-CoP. This set of results on Feet-CoP is in 13 line with Hypothesis 1 and 3. 14

Effect of Forces on Postural Balance in the AP Direction. The standard deviations of both Feet-CoP 15
and Total-CoP were also compared in the AP direction, i.e., along the beam length. Figure 6 shows 16 that applying different levels of force did not affect AP variability neither in Feet-CoP (β = 17 0.0003±0.0002, p = 0.29) nor Total-CoP (β = 0.0002±0.0002, p = 0.37). However, AP variability was 18 larger in the tripod condition than the planar condition, both for Feet-CoP and Total-CoP (Feet-CoP: 19 β = 0.002±0.0007, p < 0.01; Total-CoP: β = 0.002±0.0004, p < 0.001). This confirmed that the tripod 20 cane condition allowed for more variability along the length of the beam and that participants 21 actually exploited this extended base of support by channeling noise in this task-irrelevant direction 22 (Hypothesis 3). 23 Insert Figure 6 about here 1 Effect of Forces on Variability of Cane Motion. Even though participants were instructed to stand 2 still, some small movements in the body, arms, and hands were always present (7). This noise 3 inevitably transferred from the hand to the cane handle, deflecting the cane from the vertical 4 position. As a cane is an inverted pendulum, small lateral deflections destabilize the vertical cane. 5 To quantify these deflections, the path length of the hand on the cane handle was computed for 6 each trial. Figure 7A shows the paths traveled by the right and left hands of one participant over the 7 course of one trial in each force condition (marked by color). The path length of the hand increased 8 when more force was applied (right cane: β = 0.006±0.001, p < 0.001; left cane: β = 0.006±0.001, p 9 < 0.001). Figure 7B shows path lengths of all participants, plotted against the average force applied 10 on the respective cane; each point represents the path length traveled by the right or left hand 11 during one trial. It shows that the path length increased with the amount of force applied. Path 12 length in the minimum force condition was significantly different from the maximum force condition 13 for both hands (right hand: p < 0.001, left hand: p < 0.001). The preferred force condition was not 14 significantly different from the minimum condition for the right hand (p = 0.09) and only slightly 15 significant for the left hand (p < 0.05). These results suggest that higher forces indeed had a 16 destabilizing side-effects as expected (Hypothesis 2). This reduction in postural sway was observed for all force levels, even for relatively small forces 2 applied to the two canes. However, applying more force on the canes did not affect the medio-3 lateral component of the Total-CoP, but only the Feet-CoP, i.e., measured directly under the feet on 4 the beam. The preferred force level on the canes corresponded to resting the arms' weight on the 5 canes, suggesting that participants exploited the mechanical support. However, when exerting 6 higher forces showed signs of destabilization, as the inverted pendulum of the canes was susceptible 7 to small excursions at the handle. In addition, having the canes in front rather than on the sides 8 allowed to channel variability in the antero-posterior direction, while the task-relevant, i.e., medio-9 lateral direction remained relatively unaffected by this cane placement. 10

Perceptual Benefits of Canes. Numerous previous studies investigated the effect of light touch on 11
postural control and showed that increasing forces applied on a support surface did not provide 12 further benefit to reduce CoP motion (9-12, 15, 27). However, some of the touch condition in 13 previous studies by Jeka and colleagues required subjects to apply a very small target force of 1 N 14 to 5N. Instructing participants to apply such a small force might create an additional goal beyond 15 maintaining balance: matching the touch force to the target level. Trying to accurately achieve the 16 target force may have introduced additional control processes in balance control. To avoid this 17 possibility, we did not provide participants with feedback of their applied force, but left them free 18 to choose the amount of force, as long as they chose three different levels. As the present study 19 also wanted to probe into the mechanical effects of canes on control, our study tested forces from 20 5 N to 100 N that extended well above the previously tested force conditions. 21 Our results on variability of the Total-CoP and the CoM showed again that, while canes were 22 generally helpful for balance, exerting the maximum level of force on the canes did not provide any 23 further stabilizing effect. In addition, when free to use their preferred force, participants did not 24

Russo et al. Mechanical Effects of Canes on Postural Control 20
choose a high level of force to maintain balance, presumably because there was no further benefit. 1 Rather, they stayed within a force level that reduced the need to hold their arms against gravity. 2 Taken together, these findings corroborated the widely accepted conclusion that even very light 3 touch provides perceptual information that enhances balance performance, similar to how visual 4 information stabilizes postural control (20). Hence, at first blush, these results seem to support the 5 conclusion that the mechanical effect of the support was negligible. 6 Mechanical Benefits of Canes on Postural Control. Intuitively, canes should facilitate balance, as 7 canes on the ground increase the base of support and that inherently changes the mechanics of the 8 system. But what are these mechanical effects and how do they affect demands on postural control? 9 Our data gave several indications that cane support went beyond being purely perceptual support 10 and also afforded mechanical benefits. First, as the additional contacts with the floor enlarged the 11 base of support, CoP and CoM went outside the beam width, which limits the base of support 12 without the canes. Therefore, humans indeed used the available larger base of support. Second, 13 while the extent of the fluctuations in CoP and CoM did not depend on the magnitude of forces 14 applied to the canes, they did depend on the placement of the canes. The standard deviations of 15 the Total-CoP and Feet-CoP in the tripod condition were significantly larger than in the planar 16 configuration. In particular, the tripod placement affected predominantly the antero-posterior 17 direction, channeling more variability in the task-irrelevant dimension. Third, the Feet-CoP motion 18 significantly decreased with increasing force on the canes, indicating that the more force applied on 19 the canes, the more control relied on their support to balance. Fourth, the preferred force 20 corresponded to 5% of average body weight, approximately equivalent to the weight of the 21 participant's arm (5). Hence, this choice of support reduced the effort required to hold one's arms, 22 while exploiting the new mechanical support provided by the additional devices. 23 Mechanical Challenge due to Instability of the Canes. Applying forces on the vertical canes is an 1 isometric task with potential instability. Unlike in previous studies that tested forces applied on a 2 fixed surface, the canes were not inherently stable; rather, mechanically they presented an inverted 3 pendulum at its unstable equilibrium point. Hence, the inherent noise in the human sensorimotor 4 system introduces displacements. Assuming that noise increases with force, this destabilizing effect 5 increases with higher forces. On the other hand, as previously shown in the context of pushing a 6 stick against a wall, a downward compression force component on the cane increases the instability 7 of the inverted pendulum and any small excursion will destabilize the canes (22-24). Human joint 8 stiffness also increases with increasing force and may have counteracted this perturbing effect to 9 maintain postural balance (14). However, given the straight arms in our experiment, the stiffness at 10 the shoulder joint may have been limited as the increased displacements of the hands and canes 11 with higher forces showed. Interestingly, the variability of the CoM and the Total-CoP did not vary 12 with increasing force, indicating that the larger displacements at the hand may have been 13 compensated at the torso. Hence, these findings reveal that the cane support not only facilitated 14 balance, but also created complex control demands across the multi-segmented body. 15 Underlying Control Mechanisms. All together, these results present an intricate picture of how the 16 canes affected the control of postural stability, with some effects cancelling each other. What are 17 the potential control mechanisms underlying these observations? To begin, when standing on the 18 beam with canes, the variability of the CoM and Total-CoP in the ML or task-relevant direction were 19 essentially identical to those when standing on the ground. If the measured fluctuations when 20 standing on the ground are regarded as a floor effect determined by the noise level (as participants 21 were asked to stand as still as possible), then the use of canes enabled participants to minimize CoM 22 and Total-CoP variability to this lower bound. That could also be the reason why the different force 23 levels did not lead to further reductions. Second, when the canes formed a tripod, the fluctuations 24

Russo et al. Mechanical Effects of Canes on Postural Control 22
of the CoP were larger than in the planar condition, making use of the larger base of support. 1 Especially, the higher variability in the AP direction suggested that the controller did not constrain 2 fluctuations, i.e., allowing more variability in this task-irrelevant direction. Allowing variability in 3 directions orthogonal to what affects the task is usually interpreted as a reduction of control effort 4 (1, 6). Third, control took advantage of the additional devices, evidenced in the preferred force level 5 that just off-set the weight of the arms while staying away from higher forces that potentially 6 introduced destabilizing effects. In summary, we speculate that the controller avoids high forces not 7 only because they require more effort without any obvious benefit, but also because they introduce 8 additional demands on neuro-muscular stiffness to counteract destabilizing forces. The controller 9 also allows fluctuations as long as the CoP stays within a certain region, whose limits are defined by 10 the margin of the base of support and by the noise of the system. 11 Limitations and Outlook. In the present study participants used canes to balance on a narrow beam 12 holding them with the arms extended. While this presented a clean geometric body configuration, 13 different mechanisms might be manifest if the canes were held with flexed arms or when walking 14 with one or two canes. Our metrics, ML and AP standard deviations and the total area of CoM and 15 CoP, could capture interesting features of the task, but they were scalar measures of data 16 distributions. Additional analyses could characterize the temporal evolution of the forces and their 17 relative centers of pressure. Further, recent work went beyond analyzing the point of application of 18 the force vector, and examined the orientation of the ground reaction force with respect to the 19 center of mass. This analysis revealed interesting information about the relative role of 20 biomechanics and control (2, 26). Applying these methods to the more challenging task of standing 21 on a narrow beam with canes could provide further information about the strategy adopted by the 22 controller when using canes. 23

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Postural balance improves with light touch on a stable surface suggesting perceptual benefits of 1 additional support. Here, new insights on the mechanical benefits of inherently unstable devices -2 canesare presented. Participants adapted to the novel mechanical system by trading off the 3 benefits from the additional support with the instability introduced by pushing on the canes. 4 Fluctuations of ground reaction forces show a channeling of noise in the task-irrelevant dimensions. 5 Such mechanical benefits provide a better understanding of the role of support when balance is 6 challenged, allowing future work to explore tailored rehabilitation protocols and the development 7 of novel assistive devices. The study was approved by the Institutional Review Board of Northeastern University. 18

Consent for publication 19
Not applicable. 20 Experimental setup. Participants stood on a beam that was placed in a xed position on a force plate, holding a cane in each hand. A set of 43 light-re ective markers measured displacements of the full body and the canes in 3D. The canes were instrumented with two 6D torque sensors at the bottom of each cane. The sketch shows the planar cane con guration where the two canes were placed to be on one line with the feet. In the tripod con guration, the canes were placed at a 45° angle with the frontal plane to form a triangle with the feet.

Figure 2
Relation between estimated arm mass and force applied on the canes in the preferred force condition. Each data point represents the value for one trial (3 trials per participant). Arm mass has been estimated as 5% of total body mass of each participant. The force value on the y-axis was computed as the average force applied on one cane during one trial plus the average force applied on the other cane. Filled and empty points are trials in the Planar and Tripod arm con gurations, respectively. The Pearson correlation coe cient indicates a signi cant correlation graphically shown by the blue solid line; the solid black line is the identity line.

Figure 3
Representative paths of the center of pressure (CoP) and of the center of mass (CoM) in the horizontal plane. The two CoPs and CoM for one trial for each of the different force instructions and the two postures are shown in a top-down view. A. Exemplary trial when standing on the ground. The grey line represents the CoP and the black line the CoM. B. CoP and CoM of one trial of the same participant are shown when standing on the beam without canes. C. Each panel shows both the CoP at the feet (colored) and the total CoP (grey) for the three force conditions: minimum (green), preferred (blue), maximum (red); black lines show the center of mass (CoM). The two postures are identi ed by the drawings at the top of each panel. The beam is the light yellow area bounded by thin lines for visibility. For all conditions on and off the beam, the participant stood in tandem stance with the same foot in the front.

Figure 4
Variability metrics for the center of pressure (CoP) and center of mass (CoM) for all experimental conditions. The light yellow background indicates metrics for standing on the beam, while the white background on the left shows results for standing on the ground. The colored bars show the metrics when the participants used canes; green, blue and red differentiate the three force conditions. A: Area of the center of mass (CoM) quanti ed by the 95% tolerance ellipse. Each bar shows the mean and standard error (n=16) for the different experimental conditions, pooled over all participants. The white bars on the left show the CoM area when participants stood on the ground and on the beam, without canes; the green, blue and red bars represent the three force conditions. B: Area of the center of pressure (CoP, Total-CoP and Feet-CoP) quanti ed by the 95% tolerance ellipse. Each bar shows the mean and standard error (n=16) for the different experimental conditions, pooled over all participants. The two white bars show the CoP area when participants did not use canes. The lower value of CoP on the left represents the participants standing on the ground; the white bar shows the CoP area when participants stood on the beam. The colored bars show the Total-CoP and the Feet-CoP when the participants used canes. (signi cance levels: ***: p < 0.001; *: p < 0.05)  Paths and path lengths of the left and right hands for different force instructions differentiated by color.
A: Exemplary paths of the movements of the left and right hands from two point of view: x-y at the top, zy below. Each colored line shows one trial in the three force conditions. B: Path lengths for the left and right hands per trial are plotted against the average force applied to the cane.