Tuning of Standing Postural Responses to Instability and Cost Function

Journal Pre-proofs Research Article Tuning of standing postural responses to instability and cost function Matteo Bertucco, Amber Dunning, Terence D. Sanger PII: DOI: Reference:

S0306-4522(19)30898-X https://doi.org/10.1016/j.neuroscience.2019.12.043 NSC 19453

To appear in:

Neuroscience

Received Date: Revised Date: Accepted Date:

27 August 2019 23 December 2019 27 December 2019

Please cite this article as: M. Bertucco, A. Dunning, T.D. Sanger, Tuning of standing postural responses to instability and cost function, Neuroscience (2019), doi: https://doi.org/10.1016/j.neuroscience.2019.12.043

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Tuning of standing postural responses to instability and cost function Matteo Bertucco1*, Amber Dunning2†, Terence D. Sanger3 1

Department of Neurosciences, Biomedicine and Movement Sciences, University of Verona, Verona, Italy; 2

Department of Biomedical Engineering, University of Southern California, Los Angeles, CA, USA

3 Departments

of Biomedical Engineering, Child Neurology, and Biokinesiology, University of

Southern California, and Children’s Hospital of Los Angeles, Los Angeles, CA, USA

*Corresponding author at: Matteo Bertucco Department of Neurosciences, Biomedicine and Movement Sciences. University of Verona Via Felice Casorati 43, 37131 Verona, Italy Tel.: +39 045 8425112, Fax: +39 045 8425131 E-mail address: [email protected] †

Amber Dunning is currently with Exponent, Management Consulting, Los Angeles, CA, USA.

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Abstract Whole-body movements are performed daily, and humans must constantly take into account the inherent instability of a standing posture. At times these movements may be performed in risky environments and when facing different costs of failure. The aim of the study was to test the hypothesis that in upright stance participants continuously estimate both probability of failure and cost of failure such that their postural responses will be based on these estimates. We designed a snowboard riding simulation experiment where participants were asked to control the position of a moving snowboard within a snow track in a risky environment. Cost functions were provided by modifying the penalty of riding in the area adjacent to the snow track. Uncertainty was modified by changing the gain of postural responses while participants were standing on a rocker board. We demonstrated that participants continually evaluated the environmental cost function and compensated for additional risk with feedback-based postural changes, even when probability of failure was negligible. Results showed also that the participants’ estimates of the probability of failure accounted for their own inherent instability. Moreover, participants showed a tendency to overweight large probabilities of failure with more biomechanically constrained standing postures that results in suboptimal estimates of risky environments. Overall, our results suggest that participants tune their standing postural responses by empirically estimating the cost of failure and the uncertainty level in order to minimize the risk of falling when cost is high.

Keywords: Postural control, standing posture, risk, cost function, decision making, uncertainty. 2

Introduction Human upright stance is inherently unstable. When participants are asked to stand quietly in an upright position, their body shows small postural oscillations. Specifically, in order to maintain a balanced upstanding position, the destabilizing torque due to gravity must be counterbalanced by a corrective torque exerted by the feet against the support surface (Winter, 1995). These torques cause a continuous body fluctuation around the upright position achieved by constant feedback-based postural motor responses (Peterka, 2002, 2018). When these postural oscillations are exacerbated due to pathological circumstances (Factor et al., 2011; Saxena et al., 2014; Wang et al., 2017) or when standing on unstable surfaces (Silva et al., 2018), participants experience an increased likelihood of falls that requires more prudent strategies to ensure that all movements are well within stability limits, such as steeping at lower perturbation level or increasing agonist-antagonist muscle coactivation (Schulz et al., 2006; Hasson et al., 2009, Lang et al., 2019). Human postural responses are constantly performed in risky environments. Avoiding risk is so fundamental to natural movements that is not surprising that behaviors change in different risk settings. When, for instance, we stand near the edge of a cliff or in an aisle of a glassware store, there is a tendency to make smaller, slower and more cautious movements. We define the term “risk” to be the expected cost of behavior. Risk is therefore the product of the probability of error and the cost of error (Sanger, 2014). For instance, standing on a very narrow wooden board suspended just few centimeters above the floor, or standing within an enclosed bridge hundreds of meters above a canyon are both low-risk. It is only when high likelihood of error is combined with high cost of error that we face high-risk actions. In recent years, planning and control of movements have been described within the framework of decision-making under risk. In typical decision-making tasks, participants have to take into account not only the uncertainty of motor outcome after selecting the plan, but also the rewards or costs of any potential outcomes that may occur (Todorov and Jordan, 2002; Todorov, 2004; Trommershäuser et al., 2008; Wolpert and Landy, 2012; Dunning et al., 2015). For instance, when reward is inversely proportional to movement endpoint variance, participants tend to vary the movement speed in order to make more accurate movements (Nagengast et al., 2011; Bertucco et al., 2015; Bertucco and Sanger, 2018). Some other studies have shown that when participants performed rapid aiming movements to a target with adjacent penalty region(s), they shifted their 3

mean endpoint based on the value and location of the penalty (Trommershäuser et al., 2003, 2005; Wu et al., 2006). Recently a theory of “Risk-Aware Control” has proposed a new mathematical formulation that integrates theories of optimal feedback control with concepts of risk behavior in humans (Sanger, 2014). According to this theory, humans have the ability to continuously estimate values of the probability and cost of failure for all the states that could possibly result from movement errors, and moreover, that they can estimate risk even without experiencing failure. In support of the theory, a recent study investigated how participants respond to uncertainties and cost of failure during movement execution in a dynamic simulation environment. Risk was imposed by artificially manipulating motor uncertainty under different penalties for failure (Dunning et al., 2015). Participants showed their ability to tune their statistical motor behavior based on cost, by accounting for possible outcomes in response to environmental uncertainty. Similarly, recent studies have shown that participants take into account risk also in standing postural control (Manista and Ahmed, 2012; O’Brien and Ahmed, 2013, 2014, 2015). Specifically, in one of these studies, participants were asked to perform a swift out-and-back movement of the center of pressure, projected as a cursor on a screen, as close to the edge of a penalty area as possible without falling into it and rapidly return to their starting position. Increasing the penalty and adding gaussian noise to the position of the center of pressure affected the endpoint variability and resulted in participants staying farther from the edge of the penalty area (O’Brien and Ahmed, 2013). All these experiments were performed investigating whole-body movements with discrete tasks. Whole-body, goal-directed aiming movements performed by standing participants are usually anticipated by feedforward postural activity of trunk and lower limb muscles to minimize perturbations to vertical posture (Massion, 1998; Leonard et al., 2009; Bertucco and Cesari, 2010; Trivedi et al., 2010; Bertucco et al., 2013). Moreover, it has been shown that when participants are asked to perform a reaching movement in standing position, anticipatory postural control is modulated in response to the margin for error defined by their stability limits (Manista and Ahmed, 2012). Therefore, it is suggested that participants rely mainly on motor planning processes for whole-body, goal-directed aiming tasks to compensate for risk (Maloney et al., 2007). Even though it is well known that standing postural control emerges from a constant interplay between feedforward and sensory feedback control strategies (Massion, 1998; Forbes et

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al., 2018; Peterka, 2018), it is still poorly understood how perceived risk would affect postural corrective responses during ongoing continuous movements in dynamic risky environments. Therefore, according to Risk-Aware Control theory, we predicted that participants would also take into account probabilities of outcomes in response to intrinsic motor uncertainty such as the inherent instability of human upright stance. We hypothesized that participants would continuously regulate upright postural responses in dynamic risky environments. We also hypothesized that they would be able to estimate the cost and probability of failure that they have not specifically experienced in this environment as well. When the probability and cost of failure vary throughout the workspace, Risk-Aware Control theory states that individuals must maintain estimates of these values for all states that could possibly result in movement errors. Therefore, we also anticipated that this will lead to a selection of postural response strategies that would reduce risk even when the probability of failure was negligible. To test our hypothesis, we designed a riding simulation experiment, similar to a previous study using finger movements (Dunning et al., 2015). In the riding experiment, participants were asked to control the position of a snowboard within a path of snow in a risky environment, i.e. an environment where cost and reward were varied based on positional location. Specifically, cost functions were provided by modifying the penalty of riding outside of a snow path, whereas probability of failure was controlled by modifying the gain of postural responses while participants were standing on a rocker board that controlled the position of the snowboard on the screen. Indeed, the rocker board provides a simple environmental manipulation which results in instability that forces participants to constantly synchronize the ankle and hip strategies to stabilize the stance (Horak and Nashner, 1986; Chagdes et al., 2013; Mani et al., 2016). If participants continuously maintain estimates of both probability and cost of failure, then their postural responses would depend on the specific form of cost function. We further anticipated that changes in postural behavior would not require participants to experience failure by deviating from the path of snow, but that they would instead estimate the cost of failure based on knowledge of the task. Experimental procedures Study participants

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Fifteen healthy adults (29.1 years old  3.5 SD), 10 males and 5 females, participated in the experiment. The participants were not professional or experienced snowboard or skateboard athletes. They had no previous history of traumas or neuropathies to the lower limbs. The University of Southern California Institutional Review Board approved the study protocol (IRB# UP-09-00263). All participants gave informed written consent for participation and received compensation in proportion to their final score plus a base sum. Authorization for analysis, storage, and publication of protected health information was obtained according to the Health Information Portability and Accountability Act (HIPAA). The study protocol was performed in accordance with the Declaration of Helsinki. Experimental protocol The experiment was performed on a rectangular wood rocker board (38.1 x 35.6 x 8.9 cm). It allowed tilting movement about one axis up to 35° of slant (Fig. 1A). An iPad® (2nd generation, iOS 6.0, resolution of 1024x740 pixels, Apple Inc., Cupertino, California, USA) was attached to the short edge of the rocker board with a custom-made wooden frame in landscape orientation (Fig. 1A). A custom application was created using Corona SDK (Version 2012.11.15, Corona Labs Inc., Palo Alto, California, USA). The update rate of the screen and rate of data acquisition was 30 fps. The custom application was also displayed in real time on a 24” computer monitor positioned at a height of 1.7 m from the floor (Fig. 1B). The experiment took approximately one hour to complete. Participants were asked to stand upright on the rocker board facing to the monitor with their feet parallel to each other, between 20 and 25 cm apart, and parallel to the short edge of the rocker board. Instructions for the experiment were verbally specified by the experimenter and presented again on the iPad® screen for the participants to read once they were on the rocker board and ready to start (Fig. 1B). The snow track was 700 pixels wide, and the center dashed line was 15 pixels wide, and the snowboard width was 40 pixels. The curves of the snow track were generated using Bezier curves (Farin, 1996). In the experiment, participants maintained one-dimensional steering control of a snowboard on the screen, i.e. they could only move the snowboard to the left and right. Eleven out of fifteen participants chose to perform the experiment with their left foot placed forward, while the rest chose to place their right foot forward (Fig. 1B). Participants stood on the rocker board with the monitor positioned about 1 m away from either their left side or right side (Fig. 6

1B), depending on their personal stance preference. The goal of the game was to complete each trial as quickly as possible, where the speed of the snowboard was determined solely by the position on a two-lane snow track. While in a snow track, snowboarding within the area between the center dashed black line and the edge of the track produced acceleration to a maximum velocity of 1100 pixels/sec along the direction of the movement, snowboarding on the center dashed black line

caused

the

snowboard

to

decelerate

to

550

pixels/sec

with

a

constant

acceleration/deacceleration equal to 275 pixels/s2 (see Fig. 2). Participants were able to control the position of the snowboard by tilting the rocker board in the sagittal plane, which yielded the tilting of the iPad® in the left/right directions resulting with a change in position of the snowboard on the custom application (Fig. 1B). When the rocker board was not tilted the snowboard maintained its current position. Each trial was 30,000 pixels in length and took approximately 30 to 60 seconds to complete. Points were awarded inversely proportional to the time taken to complete each trial. Participants could achieve a maximum score of 100 points for each trial if they maintained the snowboard in the maximum velocity space along the entire length of the snow track. There was also a penalty associated with exiting the snow track altogether. Each side of the snow track was depicted by either green colored grass or dark grey colored rocks. Hitting the grass along the side of the snow track slowed the snowboard to 2 pixels/sec within 2-3 frames of the update rate of the screen, which will be referred to as “stopped”. Running into the rocks resulted in the snowboard immediately stopping and then subsequently being moved to the center of the snow track (the timer was stopped so that this was equivalent to running into the grass) but with an additional 500-point penalty (Pen) that was subtracted from the total score at the end of the experiment (see below for details). Applying the cost function in this manner effectively reinforced the cost, since more successful trials were related not only to increased points and therefore increased monetary reward (see below), but also decreased experiment time. Figure 2 contains representative screenshots of the iPad® application. To amplify the inherent motor variability of standing postural sway, uncertainty was artificially enhanced by increasing the sensitivity of iPad®’s gyroscope within the custom application when tilting the rocker board, and thus the iPad® (Fig. 1A-B). This had the effect to augment the gain of postural responses while steering the snowboard in horizontal direction, and 7

therefore simulate an enhancement of inherent variability of postural sway. Within the context of this study, we will define this imposed variability as instability. There were three different imposed instability conditions: Low, Middle and High instability where the snowboard horizontally steered at 10, 25 and 40 pixels/sec respectively for one degree of inclination of the iPad® (see Fig. 2). The first 10,000 pixel of each trial were practice, giving the participant enough time to get up to the speed and adjust to the instability level. During this practice phase, no points were accumulated or lost. The snowboard always started the trial where it ended the previous trial, unless it was the first trial of a block, in which case the snowboard started in the middle of the snow track. During the experiment, participants’ responses were tested under four cost functions: 1) symmetric low-cost, grass on both sides of the snow track (GG), 2) symmetric high-cost, rocks on both sides of the snow track (RR), 3) asymmetric high-cost ventral, rocks on the ventral side of participant’s stance and grass on the dorsal side (Rv), and 4) asymmetric high-cost dorsal, rocks on the dorsal side of participant’s stance and grass on the ventral side (Rd). Participants performed 36 total trials, which were divided in 6 blocks (two for each instability level) presented in random order. Within each block, participants performed six trials in random order, consisting of two trials for each symmetric cost condition (GG and RR) and one trial for each asymmetric cost condition (Rd and Rv). Overall, this means that participant s performed each symmetric cost condition four times at each instability, and they performed each asymmetric cost condition twice at each instability. A minimum of 20 seconds of rest was given to the participants at the end of each trial. Each participant performed a practice block before the experiment within the symmetric low-cost environment to familiarize themselves with the snowboard control, experiencing each instability level twice. Participants were informed that riding the snowboard within the bounds of the snow track (white region) would yield maximum velocity, while touching the black dashed center lane would cause the snowboard to slow down and hitting the side of the snow track would bring the snowboard to stop. Participants were also told that they could earn a maximum of 100 points per trial and were encouraged to explore the snow track during the practice block during which points earned or lost would count for their monetary reward. The points earned and time taken to complete the trial were displayed on the screen of the custom application both during the trial and at the end of each trial in order to provide the participant with feedback. A total score (Ts)

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was calculated at the end of the experiment as the sum of the scores of each trial. Participants received a US dollar monetary reward (MR) based on Ts and penalties as following: MR =$20 + [(Ts-(n*Pen))/(max(S)] * $10

(1)

Where max(S) was the maximum possible score for all the trials (100 points x 36 = 3600 points), n was the number of times the participant run into the rocks and $10 was the reward for max(S). A $20 reward was added to avoid negative rewards in case of multiple penalties.

Data Analysis During the experiment, we recorded the position of the snowboard and the time it took to complete each trial. Points were recorded, but not used in the analysis as they were rounded, and therefore less accurate, and only piecewise proportional (participant could not earn less than 0 points from speed penalties). The analysis was performed in Matlab 8.3 software (Mathworks Inc., Natick, MA, USA, 2014) and RStudio software (RStudio Inc., Version 0.98.109, Boston, MA, USA). Position data for all participants were combined to represent average behavior of sample population and fit to Equation 2 using maximum likelihood estimation (Dunning et al., 2015). In these functions, zero is the center of the entire snow track and units are in pixels: 𝑦 = (𝑝)𝑓1(𝑥|𝜇1,𝜎𝑥1) + (1 ― 𝑝)𝑓2(𝑥|𝜇2,𝜎𝑥2)

𝑓(𝑥) =

1

𝑒

𝜎 2𝜋

―(𝑥 ― 𝜇)2 2𝜎𝑥2

(2)

(3)

The equation 2 represents the bimodal gaussian distribution fitting since participants could decide to ride the snowboard either on the left and right side of the center line of the snow track, where x is the horizontal position of the snowboard, 1 and 2 are the means of each Gaussian, x1 and x2 are the standard deviation of the respective Gaussians, f1 and f2 are the probability density

9

function of each Gaussian estimated with Equation 3, p is the weighting factor between the Gaussians, and y is the resulting probability of the position (Dunning et al., 2015). The position data for each participant, for each cost function at each instability level were fit to Equation 2 using maximum likelihood estimation. To quantify the average distance from the center of the snow track that participants attempted to maintain for each condition, the absolute value of 1 and 2 were weighted by the area under the Gaussian, p and p-1, and summed. Linear regressions were fitted to the means across participants of the three levels of instability conditions of each cost function. Statistical Analysis Statistical analysis was performed using RStudio (RStudio Inc., Version 0.98.109, Boston, MA). We performed a linear mixed effects model (lmer function, R-package ‘lme4’) on Position defined as the distance from the center of the snow track. As fixed effects, we entered Cost (4 levels: GG, RR, Rv, Rd) and Instability (3 levels: Low, Middle, High) into the model. As random effects, we had intercepts for participants, as well as by-participant slopes for the effect of Cost and Instability. 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛~𝐶𝑜𝑠𝑡 + 𝐼𝑛𝑠𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦 + (1 + 𝐶𝑜𝑠𝑡|𝑆𝑢𝑏𝑗𝑒𝑐𝑡 + 𝐼𝑛𝑠𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦|𝑆𝑢𝑏𝑗𝑒𝑐𝑡)

(4)

Similarly, we also performed a linear mixed effects analysis (lmer function, R-package ‘lme4’) on the Time to complete each trial between Cost and Instability: 𝑇𝑖𝑚𝑒~𝐶𝑜𝑠𝑡 + 𝐼𝑛𝑠𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦 + (1 + 𝐶𝑜𝑠𝑡|𝑆𝑢𝑏𝑗𝑒𝑐𝑡 + 𝐼𝑛𝑠𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦|𝑆𝑢𝑏𝑗𝑒𝑐𝑡)

(5)

And for the standard deviation x of Gaussian distribution of Position data between Cost and Instability: 𝜎𝑥~𝐶𝑜𝑠𝑡 + 𝐼𝑛𝑠𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦 + (1 + 𝐶𝑜𝑠𝑡|𝑆𝑢𝑏𝑗𝑒𝑐𝑡 + 𝐼𝑛𝑠𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦|𝑆𝑢𝑏𝑗𝑒𝑐𝑡)

(6)

Once we had created the models, in order to test if the fixed effects significantly affected the dependent variable, we compared the model including all the factors (Full) against a reduced 10

model without the effect in question (Null), for each dependent variable and for each factor. Similarly, to test interaction, that is, interdependence between 2 fixed effects, we compared the model that takes into account the interaction between fixed effects (Full) against the model without the interaction (Null), for each dependent variable. For all comparisons, we used likelihood ratio test as a means to attain p-values and Akaike’s information criterion values (AIC) (Akaike, 1992). Likelihood is the probability of seeing the data given a model. The logic of the likelihood ratio test is to compare the likelihood of two models with each other. We performed the likelihood ratio test using ANOVA (anova in R) to compare the two models. In this analysis method, if the factor in question significantly affects the dependent variable, then the comparison will report a significant p-value (< 0.05) and an AIC value smaller than the Full model (AICFull) with respect to the Null model (AICNull). Similarly, a significant interaction between factors will result in a significant difference between the Full and the Null models (p value < 0.05), with the Full model characterized by a lower AIC. Least-squares means (predicted marginal means) for specified factors with Tukey's adjustment were used for pairwise comparisons (lsmeans function, R-package ‘lsmeans’). We were also interested in the role that failure played in forming the behavior during the task conditions. Therefore, the percentage of failed trials, trials in which the participant deviated from the snow track, were calculated for each level of instability and each cost function condition. Results No participant withdrew from the study and there were no complaints of fatigue. Position data of the snowboard resembled bimodal Gaussian distributions (Fig. 3). As the instability level increased, by the means of increasing the sensitivity of iPad®’s gyroscope, the two peaks of the distribution shifted towards each other, merging into a single Gaussian distribution at high instability level. Specifically, participants rode the snowboard between the center line and the edge of the track with low levels of instability and moved toward the centerline as the instability increased. This demonstrates a trade-off in which participants accepted the cost of riding on the midline in order to reduce to likelihood of riding off the snow track. This behavior was even more accentuated with cost RR condition as compared to GG cost condition. In the asymmetric risk environment, position data showed substantially disproportionate distributions, with peaks toward the cost environment with lower penalty. That is, participants had the tendency to ride the snowboard on the side of the snow track that was farthest from the rocks. However, as the 11

instability increased, participants rode the snowboard closer to the center dashed black line and thus closer to the rocks in order to balance the risk to falling on either side (Fig. 3). Over the four cost function environments, participants took on average 27.40 seconds  1.04 SD, 27.83 seconds  2.77 SD and 30.27 seconds  5.23 SD to complete the trial for the Low, Middle and High instability condition respectively. The likelihood ratio test reported a significant effect on Time for Instability (AICFull = 2827.50; AICNull = 2963.80; 2 = 142.297, p < 0.0001) and Cost (AICFull = 2827.50; AICNull = 2829.21; 2 = 9.710, p = 0.046) factors. A significant interaction between the 2 fixed effects was found (AICFull = 2823.01; AICNull = 2827.50; 2 = 16.491, p = 0.01). The performances during Rv cost environment with High instability took longer to complete a trial compared to the other cost environment conditions (p < 0.01). As it is shown in the box plot of Figure 4 the increased distribution with increased instability level demonstrates that some participants were more skilled than others at playing the game. The mean Position measured as the distance from the center of the snow track were fit to Equation 2 for each condition is shown in Figure 5. A significant effect on Position for Instability (AICFull = 1696.16; AICNull = 1760.38; 2 = 70.223, p < 0.0001) and Cost (AICFull = 1696.16; AICNull = 1771.76; 2 = 83.605, p < 0.0001) factors was found. On average, participants rode the snowboard 150.7 pixels  26.3 SD, 127.2 pixels  38.0 SD and 100.0 pixels  36.2 SD from the center of the snow track for Low, Middle and High instability respectively. As the instability level increased, participants moved the snowboard closer to the center line to reduce the probability of hitting the boundary of the snow track. Over the three level of instability, the Position of the snowboard was on average 137.0 pixels  29.1 SD, 95.1 pixels  31.2 SD, 129.9 pixels  33.3 SD and 148.9 pixels  37.4 SD from the center of the snow track for GG, RR, Rd and Rv cost function conditions respectively. A significant interaction between the 2 fixed effects was reported (AICFull = 1689.69; AICNull = 1696.16; 2 = 18.465, p = 0.005). Participants moved the snowboard farther from the center line during the Rv environment compared to the other cost conditions in Middle and High instability (Fig. 5). The symmetric high-cost condition caused participants to move the snowboard closer to the center line, accepting the higher penalty to decrease the likelihood of incurring the cost of running off the snow track, regardless of the instability level. Interestingly,

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there was not a significant effect on Position for the asymmetric high-cost when rocks were on the ventral side of participant’s stance (Rv) as stability level increased (Fig. 5). The likelihood ratio test reported a significant effect on x for Instability (AICFull = 1537.02; AICNull = 1673.07; 2 = 142.053, p < 0.0001) and Cost (AICFull = 1537.02; AICNull = 1548.24; 2 = 19.224, p = 0.0007). Over the four cost environments, x was on average 43.5 pixels  10.5 SD, 60.1 pixels  21.5 SD and 81.6 pixels  22.9 SD for Low, Middle and High Instability level respectively. A significant interaction between the 2 fixed effects was found (AICFull = 1535.44; AICNull = 1537.02; 2 = 13.583, p = 0.03). A larger  was noted for the Rv and GG cost functions compared the RR and Rd environments in the High Instability condition (Fig. 6). A successful trial was defined as a trial during which the participant never drove the snowboard off the snow track. As the instability level increased, failed trials occurred more often in the asymmetric high-cost conditions, particularly for Rv, compared to the symmetric high-cost and symmetric low-cost conditions at the High instability level. Participants opted to stay so far away from the Rocks, that they hit the Grass on the opposite side of the snow track more frequently. Participants reacted to the increased cost by riding the snowboard closer to the center line even if failure was not experienced for RR compared to the other cost conditions and RR compared to Rd in Low and Middle Instability levels respectively (Fig. 5 and Fig. 7). This represents a mechanism that estimates and predicts failure that has not yet occurred. Moreover, GG and Rv cost conditions showed a similar successful rate (about 90%) in Middle Instability despite the fact there was a significant difference of 30 pixels from the center line between these conditions (Fig. 5 and Fig. 7). In order to quantify any effect of learning within the course of the experiment we compared the failure of the first half of the blocks with the second half. There was not significant difference of failure between the two groups of blocks, therefore it indicates that after the initial practice trials, there was no observable learning effect. Discussion Risk is a ubiquitous characteristic of human movement, commonly due to unpredictable or unknown dynamics of the environments as well as the inherent features of the neuromuscular system. A recently proposed theory, “Risk-Aware Control”, has formulated a new mathematical framework in which movement planning and control are governed by estimates of risk based on 13

uncertainty about the current state and the knowledge of cost of errors (Sanger, 2014). This theory allows for safe behavior in an unpredictable environment, including in the presence of increased motor variability due to inherent instability of a system, such as an unstable upright stance in humans. A fascinating fundamental aspect of the theory is that motor behavior will be modified by the perceived risk even if failure has not yet been experienced (Sanger, 2014; Bertucco et al., 2015; Dunning et al., 2015). The aim of this study was to test the hypothesis that participants estimate both cost of failure and probability of failure in the framework of postural control, where uncertainty derives from the inherent instability of human upright stance, such that their standing postural responses will be continuously tuned based on these estimates. In our study, we designed a riding simulation in which participants controlled the position of a snowboard while standing on a rocker board within a dynamic environment with manipulated cost functions and uncertainty. Uncertainty was artificially increased by changing the gain of iPad®’s gyroscope response when tilting the rocker board. Changing the postural sway-reference gain setting varied the responsiveness of the support surface, resulting in greater and faster board rotation angle. By increasing the gain settings, it created greater mechanical instability in response to anterior-posterior sway. Thus, it affected the relative stability of the sensory environment and, therefore it had consequences for controlling the postural sway (Clark and Riley, 2007; Mani et al., 2016). It is worth noting that since the gain was not reported to the participants, they had to estimate the increased uncertainty from their immediate motor experience. At low instability, which denoted high controllability of the rocker board, participants maintained a tight bimodal Gaussian distribution of snowboard position between the center line and the edge of the snow track with symmetric low-cost environment (grass-grass). This showed that participants tuned their postural responses in order to optimize the expected cost of behavior. In the asymmetric environment participants rode the snowboard close to the low-cost condition, and therefore acting analogous to symmetric low-cost environment. During symmetric high-cost condition participants moved about 30 pixels close to the center line compared to low-cost condition at identical low instability level (Fig. 5). Interestingly, participants modified their postural behavior in the presence of risk even though riding off of the snow track was never experienced by any participant at this difficulty level (Fig. 7). As the instability level increased, participants moved the snowboard toward the center line (Fig. 3 and 5). The departure from the boundary of the snow track proportional to the instability 14

level was proportional to the lower controllability of the rocker board due to the amplification of the inherent motor variability of standing postural sway as demonstrated by an increase of position Gaussian distribution with instability level (Fig. 6). This result is in accordance with previous studies where participants remained farther from a penalty region when additional noise was added to the trajectory of their center of pressure (O’Brien and Ahmed, 2013) or to the motor output during a reaching task (Chu et al., 2013). Interestingly, while participants behaved analogously in the asymmetric low-cost environment to the symmetric low-cost task at low level of instability, participants adjusted their postural responses differently at higher instability levels. Participants did not ride the snowboard near the center of the snow track as much in the asymmetric high-cost ventral condition, in order to minimize the likelihood of riding on the center line and into the high cost region (rocks) on the opposite side. This occurred even though it caused participants to ride off the track into the low-cost region (grass) more often and resulted in participants taking longer to complete the trial (Fig. 7). Contrarily, postural responses were adjusted differently with the asymmetric high-cost dorsal condition at higher instability levels, that is, participants moved the snowboard toward the center line of the snow track similarly to symmetric low-cost (Fig. 5). A single inverted pendulum has been largely proposed as the underlying biomechanical model of human standing by pivoting around the ankle joint (Winter, 1995; Morasso et al., 2019). The implicit assumption is that the projection of the body center-of-mass on the standing surface is mainly regulated by feedback-based control of ankle dorsi- and plantar flexor muscles (Kouzaki and Shinohara, 2010). Because of the biomechanical arrangement of the ankle and foot, it has been shown a greater capability for forward excursion of the body over the foot than for backward excursion (Newton, 2001). Therefore, the different behavior between the two asymmetric cost environments can be attributed in part to smaller stability limits in the backward direction compared with the forward direction (King et al., 1994; Holbein-Jenny et al., 2007). Particularly, King et al. (1994) showed that functional base of support, namely maximal center of pressure excursion capacity, was lesser in the posterior direction, relative to functional base of support during quiet standing. In order to fairly compare the postural behavior associated with the highcost dorsal condition to the ventral cost condition, participants would have been required to control the rocker board predominantly with the ankle joint in plantarflexion, which resembled a control of the body center-of-mass during quiet standing mainly in backward position (Winter, 1995; Kouzaki and Shinohara, 2010). In addition, fear contributes to this decreased amount of leaning 15

backward as noted by a significant affect of fear, as measured by the Fear of Falling Index (Newton, 2001). Thus, the biomechanical constraint of the ankle joint and fear of falling could have reduced controllability of the board and therefore increasing the likelihood of failure by running into the high cost region. Moreover, the high failure rate in the asymmetric high-cost ventral condition with High Instability level would suggest that participants did not accurately estimate the probability of failure, since they had lower failure in the other cost conditions with High Instability, and therefore chose to ride closer to the grass, risking failure (Fig. 5 and Fig. 7). Overall, our results suggest that the estimate of probability function is, indeed, asymmetric itself and participants accurately estimate probability of failure by accounting not only for the inherent instability, but also for the biomechanical constraints due to stability limits of human upright standing posture. Moreover, participants tend to overweight large probabilities of failure due to more biomechanically constrained postures that results in suboptimal estimates of risky environments. It worthwhile to recognize that the concept of risk we described in this paper, “risk-awareness”, is derived from risk-aware control and a fundamentally different concept than the more ubiquitous “risk-sensitivity” originating from an economical decision-making perspective of motor control (Braun et al., 2011; Sanger, 2014). Risk-sensitivity is used to describe interindividual differences in response to risk, where risk is defined in terms of higher moments of reward. In this experiment, an explicit cost function was provided so there should not be much inter-individual difference. In the context of this paper we defined awareness of risk as continuous estimates of both the cost of failure and probability of failure in a task. Overall, our findings are similar to the results of a previous study in which participants tuned their motor responses to risk in a similar dynamic environment task where probability of failure was modified by the experimenters (Dunning et al., 2015). In that study, participants were instructed to maintain one-dimensional steering control of a vehicle on a two-lane road by using their hands to steer the vehicle in a driving simulation on an iPad®. The current study implemented an identical cost function as in our previous study, although the cost functions were represented by different images. Probability of failure was artificially enhanced by adding Gaussian noise to the responses of participants, thereby adding “motor noise”. The current study extends this result by demonstrating that not only are participants able to estimate instability due to external motor noise added to their movement by the environment, but that they are also able to estimate instability 16

due to their own biomechanical constraints and limits on the neuromuscular system’s ability to stabilize an unstable dynamic environment. It has been demonstrated that postural threats, such as an elevated platform or reduced base of support, have a critical role in the decision making process with consequences for generating postural control changes (Adkin et al., 2000, 2002; Carpenter et al., 2001; Huang and Ahmed, 2011; Adkin and Carpenter, 2018). This study further demonstrates that participants constantly tune their standing postural behavior by weighing the estimation of cost of failure and the uncertainty level in order to minimize the risk of undesirable motor responses. Perception of risk guides all of our actions, and this is essential for successful performance of motor actions in unpredictable environments. Only through constant awareness and avoidance of risk do we remain safe from potential unsafe situations. To our knowledge, it is still poorly understood to what extent risk behavior affects postural strategies at the neurophysiological level. Future studies that systematically measure changes in the EMG and cortical activity as cost of error and uncertainty are manipulated would give the possibility to distinguish between these possibilities. In particular, it would be worthwhile to investigate how awareness of risk contributes to different models of learning processes for standing postural control and whole-body movements. In conclusion, the framework of decision-making under risk may provide new insights for understanding the underlying neurophysiological mechanisms of injured central nervous system states in which the control of posture or the perception of risk are altered (Fasano et al., 2017; Cuevas-Trisan, 2019). Author Contributions MB, AD and TDS conceived and designed the study; MB performed the experiment; MB and AD analyzed the data; AD designed the custom application; MB wrote the manuscript; AD and TDS reviewed the manuscript. Acknowledgments We thank the anonymous reviewers whose comments helped to improve and clarify this manuscript.

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Funding We are grateful to the University of Southern California, Department of Biomedical Engineering and the Crowley Carter Foundation for financial support for this project.

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Figure captions Figure 1: Experimental set-up. A) Rocker board used for the experiment with iPad® embedded into a custom-made wooden frame in landscape orientation. B) The participant stood upright on the rocker board. The figure represents a participant in Regular stance. Rocking the board in the sagittal plane the board yielded the tilting of the iPad® in the left/right directions resulting with a change in position of the snowboard on the custom application. Figure 2: Exemplar screen view of iPad® custom application. Cost functions for a participant in “regular” stance: (GG) symmetric low-cost, grass (green colored in the application) on both sides of the snow track; (RR) symmetric high-cost, rocks (dark grey colored in the application) on both sides of the snow track; (Rv) asymmetric high-cost ventral, rocks on the ventral side of participant’s stance and grass on the dorsal side; and (Rd) asymmetric high-cost dorsal, rocks on the dorsal side of participant’s stance and grass on the ventral side. Region 1 produced acceleration to maximum speed of 1100 pixels/sec; region 2 decelerated the snowboard to 550 pixels/sec; region 3 immediately stopped the snowboard to 2 pixels/sec. Figure 3: Raw population position data. Plots are the histograms (light grey) of the pooled participant data for each cost condition (by row) and instability level [Low, Middle, High] (by column). The solid dark grey lines are the kernel densities of the data and the dashed black lines are the bimodal Gaussian fits. In the asymmetric cost task (Rv and Rd) it can be seen that participants maintained a position of the snowboard far away from the side with rocks. The x-axis represents the position of the center of the snowboard on the snow track in pixels. The snow track was 700 pixels wide and the snowboard was 40 pixels wide. Participants rode the snowboard off the track at  350 pixels. As the instability level increased participants moved toward the center of the snow track. GG: grass on both sides of the snow track; RR: rocks on both sides of the snow track; Rv: rocks on the ventral side of participant’s stance and grass on the dorsal side; Rd: rocks on the dorsal side of participant’s stance and grass on the ventral side. 22

Figure 4: Participants’ average time to complete a trial. The box plot shows the distribution of all participants’ times to complete a trial for each cost condition (GG, RR, Rv, Rd) and instability level (Low, Middle, High). Figure 5: Distance from the center of the snow track across cost and instability conditions. Points show the mean and standard error of the distance (in pixels) from the center of the snow track all participants maintained for each cost condition (⬤ GG, ⬤ RR,  Rv,  Rd) and instability level (Low, Middle, High). Distance values were derived from the peak of fitted probability density function within each participant for each cost condition and instability level. As instability level increased, participants moved the snowboard proportionally toward the center of the snow track (note that 0 and 350 pixels corresponded to the center and the edge of the snow track respectively). Figure 6: x of Gaussian distribution of position data across cost and instability conditions. Points show the mean and standard error of x values in pixels for each cost condition (⬤ GG, ⬤ RR,  Rv,  Rd) and instability level (Low, Middle, High). The distribution of Position data increased proportionally with the level of Instability. Figure 7: Percentage of successful trials. Points show total percentage of successful trials for all participants for each cost condition (⬤ GG, ⬤ RR,  Rv,  Rd) and instability level (Low, Middle, High). Successful trial was defined as a trial during which the participant never drove the snowboard off the snow track. As the instability level increased, failed trials occurred more often in asymmetric high-cost conditions, particularly for Rv, compared to symmetric high-cost and symmetric low-cost for High instability level. Participants preferred to stay away from the Rocks so that they hit the Grass on the opposite side of the snow track more frequently.

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Highlights Whole-body movements are performed daily in risky environments Humans continuously regulate postural responses in dynamic risky environments Postural responses are tuned by estimating the cost of failure and the uncertainty level

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