Rigid Foot Soles Improve Balance in Beam Walking

Maintaining balance while walking on a narrow beam is a challenging motor task. This is presumably because the foot’s ability to exert torque on the support surface is limited by the beam width. Still, the feet serve as a critical interface between the body and the external environment, and it is unclear how the mechanical properties of the feet affect balance. Here we examined how restricting the degrees of freedom of the feet influenced balance behavior during beam walking. We recorded whole-body joint kinematics of subjects with varying skill levels as they walked on a narrow beam with and without wearing flat, rigid soles on their feet. We computed changes in whole-body motion and angular momentum across these conditions. Results showed that wearing rigid soles improved balance in the beam walking task, but that practice with rigid soles did not affect or transfer to task performance with bare feet. The absence of any after-effect suggested that the improved balance from constraining the foot was the result of a mechanical effect rather than a change in neural strategy. Though wearing rigid soles can be used to assist balance, there appear to be limited training or rehabilitation benefits from wearing rigid soles.


INTRODUCTION 1
Whether walking over rocks or across logs, humans have remarkable ability to maintain balance while 2 navigating difficult terrain 1,2 . In fact, healthy humans are so proficient in their ability to balance that some 3 turn to walking along a thin wire to truly challenge their skills. While there has been prolific research on 4 the control of postural balance over the past decades, this work has largely focused on understanding 5 how humans maintain balance during quiet standing 3-8 . Despite many insights into the limits of postural 6 balance, it is still an open question how the central nervous system controls the highly redundant and 7 extremely complex architecture of the body to maintain balance during more realistic locomotion, 8 especially in challenging environments. 9 10 A paradox of human motor control is that while the human body is vastly complex (e.g., large number of 11 degrees of freedom, long time delays, sensorimotor noise 9 , nonlinear muscle properties, intersegmental 12 dynamics), the overt behavior is often surprisingly simple in structure. Thus, low-dimensional models, 13 derived by compressing the number of degrees of freedom in the body, can be used to competently 14 describe human balance. For example, an inverted pendulum can adequately capture much of the 15 behavior that humans exhibit during quiet stance 8,10 . When the base of support is reduced, such as in the 16 case of standing on a narrow beam, adding a second linkage to make a double-inverted pendulum model 17 has proven sufficient 8,10,11 . In a recent study, Chiovetto et al. 12  walking on a beam, Chiovetto et al. 12 allowed participants to freely move their arms during the experiment 23 with the goal to look at the full complexity of the realistic behavior. How does the nervous system control 1 the high-dimensional architecture of the entire body to generate such low-dimensional patterns? 2 3 A critical aspect of maintaining balance is managing the physical interaction between the body and its 4 external environment. Because the feet serve as interfaces through which the body and ground 5 simultaneously act upon each other, they play a pivotal role in maintaining balance. As seen in the 6 development of prosthetics, the mechanical properties of the foot can significantly influence balance 7 behavior [13][14][15] . And yet, how the complex architecture of the human feet contributes to balance is still 8 poorly understood. Each foot consists of many articulated, rigid segments which are surrounded by 9 compliant, heterogeneous tissue, making it difficult to accurately measure and model the subtle 10 coordinated behavior of the foot [16][17][18] . Paradoxically, most models of human balance drastically simplify 11 the foot. In the inverted pendulum models of standing balance, the foot is typically reduced to a static, 12 rigid segment attached to the ground acted upon by an ideal torque source at the ankle. Thus, the foot's 13 influence on human balance, particularly during walking, remains understudied. 14 15 The aim of this study was to understand how the degrees of freedom of the foot and the ankle contribute 16 to maintaining mediolateral (ML) balance when walking on a narrow beam (Figure 1a). Both feet were 17 constrained by attaching a flat, rigid sole to the bottom of each foot (Figure 1b). The rigid sole prevented 18 any motion of the foot joints distal to the ankle, namely bending at the midfoot and torsion on the long 19 axis of the foot. Importantly, plantarflexion/dorsiflexion and inversion/eversion ankle motion was not 20 affected. 21

22
On the one hand, a highly flexible foot may be critical for actively sensing and controlling the physical 23 interaction between the foot and the beam. Sawers et al. 19 found that dancers have an increased set of available whole-body actions (i.e., more muscle synergies) to maintain balance when walking on a beam 1 compared to novices. This underscores that limiting degrees of freedom reduces the number of 2 movements available to withstand perturbations and maintain upright balance. Thus, constraining the set 3 of motor actions of the feet could impair balance and worsen performance in the beam walking task 4 (Hypothesis 1a). An alternative argument, however, is equally plausible. Constraining the foot to act as a 5 rigid, flat segment could increase contact stability between the foot and the flat surface of the beam and 6 thereby improve performance 20 . For example, Robbins et al. 21 found that elderly men improved beam 7 walking when they wore shoes with hard, thin soles. They stepped off the beam less frequently compared 8 to performing the task with bare feet or shoes with softer soles. Hence, an alternative expectation is that 9 rigid soles positively affect balancing performance (Hypothesis 1b). 10 11 Changing the mechanics of the feet could also cause subjects to adapt their control strategy for 12 maintaining balance with practice. When the rigid soles are removed, this altered strategy could 13 subsequently influence balance performance. For instance, if the rigid soles led to worse performance 14 when the rigid soles were removed, we would expect subjects to quickly return to their original control 15 strategy (Hypothesis 2a). This scenario corresponds many adaptation studies where, for example, the 16 adaptation to a perturbing force field only persists as short-term after-effects as they are not functional 17 when the perturbation is removed. If the adapted strategy leads to improved balance behavior after 18 removing the soles, however, we would expect that this acquired strategy and its positive impact on 19 performance would persist (Hypothesis 2b). This scenario would indicate that the soles acted as a teaching 20 aid that could accelerate learning to balance. A third feasible scenario is that humans do not even alter 21 their control policy when the rigid soles are attached to their feet. For example, if it is only the change in 22 the foot mechanics that altered performance, we would not expect subjects to change their control policy 23 (Hypothesis 2c). If this was the case, we would expect practice with constrained feet to have no influence on subsequent performance with bare feet. By assessing how practice of the beam-walking task with 1 constrained feet influences subsequent balance behavior with bare feet, we gain insight not only into how 2 the complex architecture of the foot influences the neural control of balance, but also whether this may 3 be a suitable intervention for either assisting or rehabilitating impaired balance behavior. 4 5 This study investigated how constraining the foot affected mediolateral (ML) balance in beam walking for 6 young individuals with varying levels of prior balance training. We tested whether constraining the feet 7 influenced ML-balance during beam walking compared to performing the task with bare feet. Previous 8 work has shown that the velocity of the center of mass (COM-V) in the ML-direction is a good indicator of 9 skilled balance 12 . Hence, impaired balance is indicated by an increased velocity of the center of mass 10 (COM-V) in the ML-direction and increased whole-body angular momentum (WB-AM) about the beam 11 axis; improved balance would show the opposite trend. To evaluate whether practice with constrained 12 feet affected performance after removing the rigid soles, we tested subjects walking with bare feet before 13 and after walking with rigid soles. In addition to testing the hypotheses, further analyses of whole-body 14 coordination were conducted to shed light on how constraining the foot influenced ML-balance during 15 beam walking. 16

17
The results showed that constraining the feet improved ML-balance in the beam walking task (Hypothesis 18 1b). Moreover, task performance with bare feet was unaffected by practice with rigid soles (Hypothesis 19 2c). Together, these findings indicate that the improvement in balance from constraining the foot was the 20 result of a mechanical effect rather than a change in neural strategy. Additional analyses showed that the 21 angular momentum of most individual segments was reduced when wearing the rigid soles. Moreover, 22 the contribution of ankle torque relative to hip torque was increased when the feet were constrained. We 23 propose that constraining the feet improved performance because of an increase in contact stability 1 between the foot and the beam 20 . 2 3 RESULTS 4 Seven healthy subjects took part in the experiment. Their prior balance training ranged from none to 5 several years in competitive gymnastics. In each trial, subjects were instructed to walk the length of a 6 narrow beam (3.4cm wide and 5m long) without stepping off the beam (Figure 1a). A trial was deemed 7 successful if the subject did not step off before reaching the end of the beam; otherwise the trial was 8 declared a failed trial. Subjects had to complete 20 successful trials in each of the following three blocks: 9 The first block consisted of 20 successful trials with bare feet (BF-Pre block), followed by 20 successful 10 trials with constrained feet (CF block), and another 20 successful trials with bare feet (BF-Post block) 11 (Figure 1c). 12 13

Number of Failed Trials 14
To gauge if constraining subjects' feet affected their ability to accomplish the beam-walking task, we 15 examined its influence on the number of failed trials in each of the three blocks. A one-way within-subject 16 analysis of variance (ANOVA) revealed that foot condition (BF-Pre, CF, BF-Post) did not have a significant 17 effect on the number of failed trials (F2,12 = 0.38, p = 0.69) (Figure 2). On average, subjects failed in 18 approximately 4-5 trials in each block. As expected, performance across subjects varied along a continuum 19 determined in part by their prior balance training. Subjects who exhibited the best performance (shown 20 in red and orange in Figure 2) were trained gymnasts. As the results below show, the cohort presented a 21 sufficient spectrum of balance abilities that allowed more general conclusions. 22

Example Data
Even though constraining the subjects' feet did not require more attempts to accomplish the overall task 1 goal, analysis of more fine-grained measures revealed that it did significantly influence their balance 2 proficiency as they performed the task. Figure 3a-c displays the series of body postures of two 3 representative subjects during a typical trial in each of the three conditions. For reference, data from 4 Example Subject 1 is shown in light blue in other results figures; Example Subject 2, who was trained in 5 gymnastics, is shown in dark red. Subjects displayed not only large trunk movements, but also large and 6 variable movements of both arms. Importantly, these body movements were visibly reduced in the CF 7 block.

Center of Mass Velocity (COM-V) 14
As demonstrated in prior work 12 (Figure 5a). Thus, practice with constrained feet did not influence subjects' balance performance 8 with bare feet (Hypothesis 2c). 9 10

Whole-Body Angular Momentum (WB-AM) 11
We also examined how performing the balance beam task with rigid soles influenced subjects' whole-12 body angular momentum (WB-AM) about the axis of the beam. The measure of WB-AM quantified the 13 angular momentum of a subject's body with respect to the beam. In the beam walking task, the body was 14 subject to ground reaction forces acting on the feet. These external forces induced considerable changes 15 in the body's WB-AM. We quantified WB-AM with respect to the beam axis, rather than the body's center 16 of mass or head position for two reasons: First, the beam was fixed and thus provided an inertial reference 17 frame. Second, our prior work revealed that the structure of AM was less complex when quantified about 18 the beam axis 12 . 19 20 The same one-way ANOVA rendered a significant effect of block on the RMS of WB-AM (F2,12 = 21.73, p < 21 0.001) (Figure 6a-b). Planned comparisons revealed that constraining the foot had a similar effect on RMS 22 of WB-AM as it did on COM-V. The RMS of WB-AM significantly decreased from the BF-Pre block (M = 23 5.07kg·m 2 /s, SD = 2.40kg·m 2 /s) to the CF block (M = 3.17kg·m 2 /s, SD = 1.52kg·m 2 /s) (t6 = 4.69, p = 0.0034), and then significantly increased from the CF block to the BF-Post block (M = 4.75kg·m 2 /s, SD = 2.21kg·m 2 /s) 1 (t6 = -5.33, p = 0.0018) (Figure 6b). There was no difference in RMS of WB-AM between the BF-Pre block 2 and the BF-Post block (t6 = 1.71, p = 0.14) (Figure 6b), nor between the last successful trial of the BF-Pre 3 block (M = 4.01kg·m 2 /s, SD = 2.08kg·m 2 /s) and the first successful trial of the BF-Post block (M = 4 4.67kg·m 2 /s, SD = 2.158kg·m 2 /s) (t6 = -0.86, p = 0.42), (Figure 6a). Again, these results indicate that 5 constraining subjects' feet significantly improved their ML balance (Hypothesis 1b), but the improved 6 performance with constrained feet did not transfer or influence subjects' subsequent performance with 7 bare feet (Hypothesis 1c). Each segment's AM significantly decreased from the BF-Pre block to the CF block (ps > 0.014) and then 23 subsequently increased from the CF block to the BF-Post block (ps < 0.024) (Figures 7-8). There were no significant differences between AM in the BF-Pre and BF-Post blocks (ps > 0.14). Hence, the reduction in 1 WB-AM when wearing rigid soles was due in large part to a reduction in each segment's contribution to 2 WB-AM. It was not the result of reduced AM from a single large segment, for example. 3 4

Correlation of Upper-and Lower-Body Angular Momentum (CORR-AM) 5
As seen in Figure 9 the upper-body segments (head, thorax, upper arms, lower arms, and hands) 6 generated AM opposite in direction to the AM generated by the lower-body segments (pelvis, thighs, 7 shanks, and feet). To examine if the coordination of upper-body and lower-body AM contributions were 8 affected by constraining the foot, we computed correlation between the sum of AM of lower body 9 segments (LB-AM) and the sum of AM of upper-body segments (UB-AM) for each trial, which we refer to 10 as CORR-AM. Note that three outlier trials (0.7% of all trials) were omitted from the analysis as the CORR-11 AM values were uncharacteristically low. Consistent with the representative data shown in Figure 9, 12 upper-body AM and lower-body AM were highly anti-correlated as the overall mean of CORR-AM across 13 all conditions was -0.88 (SD = 0.05). As illustrated in Figure 10, rotation of the upper body segments (with 14 respect to the hip) was opposite to that of the lower body segments (with respect to the beam). This 15 suggests that subjects used a "hip-dominant" strategy to maintain balance. 22 16 17 A one-way within-subjects ANOVA found a significant effect of block on CORR-AM (F2,12 = 22.75, p = 18 0.000083) (Figure 11a-b). The CORR-AM significantly increased, i.e., became less correlated, from the BF-  (Figure 11b). There was no difference in CORR-AM between the BF-Pre 22 block and the BF-Post block (t6 = 0.85, p = 0.43) (Figure 11b), nor between the last successful trial of the 23 (t6 = 1.84, p = 0.12), (Figure 11a). Interestingly, the upper-body AM and lower-body AM became less 1 correlated when the foot was constrained, even though balance proficiency was improved. In fact, the 2 trained gymnasts (red and orange traces in Figure 11a-b) also had the least anti-correlation. 3 4 DISCUSSION 5 The goal of this study was to determine how reducing the complexity of the foot influenced whole-body 6 coordination to maintain balance in a challenging beam walking task. We found that constraining the feet 7 with rigid soles immediately improved balance as indicated by a reduction in the variability of COM-V and 8 WB-AM. However, we did not find evidence that subjects altered their control strategy in response to the 9 reduction in foot degrees of freedom. Practicing the task with rigid soles did not influence subsequent 10 behavior with bare feet. 11

12
In support of Hypothesis 1b our results showed that constraining the feet with rigid soles is an effective 13 method of assisting balance. This finding is in accordance with the conclusions of Robbins et al. 21 . By 14 further assessing the effect of practice with the rigid soles, however, we found that it may not be an 15 effective intervention for training or rehabilitating balance (Hypothesis 2c). In general, an intervention 16 meant to enhance the performance or learning of a motor skill and should change neural control such 17 that it results in improved task performance under normal conditions 23,24 . In our study, barefoot 18 performance was unaffected by practice with constrained feet. In fact, we did not even observe a short-19 lived after-effect, which further suggests that subjects did not change their neural control strategy. While 20 it is conceivable that subjects could alter their control strategy with long-term practice wearing rigid 21 soles 19 , it remains an open question whether that learned strategy would improve or impair subsequent 22 barefoot performance. It also cannot be ruled out that subjects might have learned a new control strategy, 23 but that strategy was entirely context-dependent such that it did not transfer 25 . Evidence for this would require testing the effect of longer practice with the rigid soles to seek improvements within one 1 condition. Without any further investigations, the results presented here suggest that constraining the 2 feet may not be an effective intervention for training or retraining balance. Understanding how this 3 manipulation improved balance performance can inform the development of future interventions. 4 5 When balancing on a narrow base of support, the ankle's ability to exert torque on the beam through the 6 foot is limited 10 . Thus, it is not surprising that numerous studies have reported that humans use a hip-7 dominant strategy to maintain balance when standing on a beam 3,4,8,10,22,26 . Consistent with these studies 8 of standing balance, we similarly observed that subjects used a hip strategy to maintain ML balance when 9 walking on a beam, as indicated by high anti-correlation between the AM generated by the upper-and 10 lower-body segments 22 . Importantly, this was observed even though the arms were allowed to move 11 freely, representative of real-world conditions. Even though subjects used a hip-dominant strategy during 12 beam walking, this did not mean that the influence of the foot and ankle was minimal as is often presumed 13 when balancing on a narrow beam. In fact, our finding that constraining the feet significantly altered 14 balance behavior showed otherwise. 15 16 Not only did constraining the feet decrease the overall AM magnitude of most individual segments, it also 17 resulted in less anti-correlation between the AM of the upper-and lower-body segments. Though the 18 change in anti-correlation was small, it was significant and observed in all subjects (Figure 11b). As 19 demonstrated in a prior simulation study of a double-inverted pendulum model 22 , the degree of anti-20 correlation decreases when the overall magnitude of ankle torque increases relative to the magnitude of 21 hip torque. These simulations assumed no change in signal-to-noise ratio. It is important to note that the 22 increase in relative ankle contribution observed with constrained feet could have resulted from increased 23 ankle torque, decreased hip torque, or a combination of the two. While we cannot definitively discern how the change in relative ankle contribution occurred, we do know that it can be attributed to altering 1 the physical interaction between the foot and beam. The fact that subjects did not appear to learn or 2 adopt a new control strategy during practice with constrained feet further supports the notion that the 3 improvement in balance was the result of a mechanical effect. 4 5 We speculate that constraining the feet improved balance because it increased the stability of contact 6 between the foot and the beam. Note that the width of the support surface was identical in the BF and 7 CF conditions, meaning that adding the flat, rigid soles did not increase the maximum torque that could 8 be applied at the ankle. However, constraining the feet may have increased the "effective" range of ankle 9 torque. While the multiple degrees of freedom in each foot may increase control and/or sensing abilities, 10 they also make the foot compliant. Without the soles, exerting large ankle torque onto the beam could 11 cause the compliant foot to rotate. If so, subjects possibly reduced the amount of torque applied at the 12 ankle to avoid this rotation. Future studies comparing the distribution of pressure under the feet in each 13 condition would shed further light on this possible explanation. 14 15 Wearing rigid soles may have increased the amount of torque that could be applied at the ankle without 16 resulting in foot rotation about the beam 20 , and thus improved performance. But note, this is only one 17 mechanism through which the "effective" range of ankle torque could have been increased. Interestingly, 18 the subjects who were most proficient at maintaining balance tended to have less anti-correlation of 19 upper and lower body momentum in the BF conditions. It is possible that these subjects were either able 20 to modulate the mechanical properties of their ankle and foot or they could better compensate for the 21 interaction dynamics at the foot-beam contact. This could explain why Sawers and Ting 19 observed more 22 muscle synergies in experienced balancers. For instance, reducing the interaction dynamics could require 23 finer control of the degrees of freedom in the feet (e.g., toes) that expert dancers and balancers might learn with training. This also underscores that simple structure in overt balance behavior is not necessarily 1 indicative of a "simple" controller in the neuromotor system. 2 3 While our results gave clear evidence that adding flat rigid soles can assist balance, this benefit to balance 4 may come at cost. For instance, Takahashi et al. 27 found that wearing shoes with stiff soles significantly 5 increased the metabolic cost of walking. Moreover, we observed that there was no transfer from 6 practicing beam walking with constrained feet to walking with bare feet. Ultimately, future work is needed 7 to further understand (1) the influence of the foot and ankle mechanical properties on balance, and (2) 8 how expert balancers modulate or compensate for its effects. We expect that addressing these open 9 questions will yield promising new insights for enhancing the assistance and rehabilitation of balance. 10 11

METHODS 12
Subjects 13 Seven healthy subjects (gender: 2 females and 5 males, age: 28.7 ± 2.5 years, mass: 68.4 ± 10.9 kg, height: 14 1.74 ± 0.08 m) took part in the experiment. None had any prior experience with the specific experimental 15 task. The experiment conformed to the Declaration of Helsinki and written informed consent was 16 obtained from all participants according to the protocol approved by the ethical committee at the Medical 17 Department of the Eberhard-Karls-Universität of Tübingen, Germany. 18

Experimental Protocol 19
In each trial, the subject walked along a narrow beam (3.4 cm wide, 3.4 cm high, 4.75 m long) at a self-20 selected speed. Before the start of each trial, subjects stood with their left foot on the beam and their 21 right foot on the ground. After the experimenter gave the "go"-signal, they placed their right foot on the 22 beam and began walking. Upon reaching the end of the beam, subjects were instructed to step off, placing their feet on either side of the beam. Subjects did not receive any other instruction on how to walk or 1 how fast they should walk across the beam. They could use all body segments, including arms, as they 2 wished to maintain balance. For data processing, the placement of the right foot on beam indicated the 3 start of each trial; the last step before stepping off the beam marked the end of the trial. A trial was 4 deemed successful, if the subject remained on the beam for its entire length. If the subject lost balance 5 and had to step on the ground before reaching the end, the trial was labeled as unsuccessful. After each 6 trial, subjects were allowed to take a short rest if needed. 7 Each subject was instructed to complete 20 successful trials in each of the following three blocks: Bare 8 Feet-Pre (BF-Pre), Constrained Feet (CF), and Bare Feet-Post (BF-Post). In the BF-Pre and BF-Post blocks, 9 participants walked without shoes; in the CF block, participants performed trials with flat, rigid soles 10 attached to each foot. The solid soles were 3D printed and designed to be slightly larger than all subjects' 11 feet (width: 12cm at widest point, length: 31cm, depth: 1cm). All subject wore the same size soles. They 12 were secured to the subjects' feet with hook and loop straps and reinforced with duct tape as illustrated 13 in Figure 1b. These soles did not affect the plantar/dorsi-flexion and inversion/eversion motion of the 14 ankle. 15

3D Motion Capture Data Collection 16
Reflective markers were placed on the subjects' bodies following Vicon's Plug-In Gait marker set ( Figure  17 1). During each trial, 3D whole-body motion capture data was collected using a 10-camera motion capture 18 system (Vicon, Oxford, UK) at a sampling rate of 100Hz. As illustrated in Figure 1a, the origin of the lab 19 coordinate frame was set to the start end of the beam, with its y-axis aligned along the beam and its x-20 axis perpendicular to the beam. Commercial Vicon software was used to reconstruct and label the markers 21 to interpolate between short missing segments in the 3D marker trajectories. 22 Based on the subject's self-reported height and weight, subject-specific dynamic models (Plug-In Gait 1 model consisting of 15 rigid body segments, Table 1) were fit to the 3D marker trajectories using C-Motion 2 Visual3D software (Germantown, MD). The dependent measures for each trial were calculated using the 3 model-based data exported from Visual3D that were subsequently analyzed using custom scripts in 4 Matlab (The Mathworks, Natick, MA) as described in detail below.