Integrative and Comparative Biology Integrative and Comparative Biology, volume 54, number 6, pp. 1109–1121 doi:10.1093/icb/icu058 Society for Integrative and Comparative Biology

SYMPOSIUM

Compensations during Unsteady Locomotion Mu Qiao* and Devin L. Jindrich1,† *Kinesiology Program, School of Nutrition and Health Promotion, Arizona State University, Phoenix, AZ, USA; † Department of Kinesiology, California State University, San Marcos, CA 92096, USA From the symposium ‘‘Terrestrial Locomotion: Where Do We Stand, Where Are We Going?’’ presented at the annual meeting of the Society for Integrative and Comparative Biology, January 3–7, 2014 at Austin, Texas. 1

E-mail: [email protected]

Introduction Locomotion is a complex task that involves dynamic interactions between animals and their environment. The passive dynamics of segmented systems can show unpredictable or chaotic behavior (Blickhan et al. 2007). Joints are actuated by many redundant muscles, and forces from uniarticular muscles alone can cause movements of many segments (Zajac and Gordon 1989). Muscles, and the many neurons that innervate them, are heterogeneous and have nonlinear, time-dependent behavior (Edman 1996; Huijing 1998). Therefore, understanding locomotion

requires parallel investigation of mechanics and physiology at many levels of organization. Reduced-parameter models can be useful for describing constant–average–velocity locomotion Despite its complexity, research on legged locomotion has revealed general mechanical principles that apply to a diversity of animals (Farley et al. 1993; Griffin et al. 2004). Terrestrial animals, including humans, show remarkable similarities in the mechanics of locomotion after controlling for body size

Advanced Access publication June 19, 2014 ß The Author 2014. Published by Oxford University Press on behalf of the Society for Integrative and Comparative Biology. All rights reserved. For permissions please email: [email protected].

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Synopsis Locomotion in a complex environment is often not steady, but the mechanisms used by animals to power and control unsteady locomotion (stability and maneuverability) are not well understood. We use behavioral, morphological, and impulsive perturbations to determine the compensations used during unsteady locomotion. At the level both of the whole-body and of joints, quasi-stiffness models are useful for describing adjustments to the functioning of legs and joints during maneuvers. However, alterations to the mechanics of legs and joints often are distinct for different phases of the step cycle or for specific joints. For example, negotiating steps involves independent changes of leg stiffness during compression and thrust phases of stance. Unsteady locomotion also involves parameters that are not part of the simplest reduced-parameter models of locomotion (e.g., the spring-loaded inverted pendulum) such as moments of the hip joint. Extensive coupling among translational and rotational parameters must be taken into account to stabilize locomotion or maneuver. For example, maneuvers with morphological perturbations (increased rotational inertial turns) involve changes to several aspects of movement, including the initial conditions of rotation and ground-reaction forces. Coupled changes to several parameters may be employed to control maneuvers on a trial-by-trial basis. Compensating for increased rotational inertia of the body during turns is facilitated by the opposing effects of several mechanical and behavioral parameters. However, the specific rules used by animals to control translation and rotation of the body to maintain stability or maneuver have not been fully characterized. We initiated direct-perturbation experiments to investigate the strategies used by humans to maintain stability following center-of-mass (COM) perturbations. When walking, humans showed more resistance to medio-lateral perturbations (lower COM displacement). However, when running, humans could recover from the point of maximum COM displacement faster than when walking. Consequently, the total time necessary for recovery was not significantly different between walking and running. Future experiments will determine the mechanisms used for compensations during unsteady locomotion at the behavioral, joint, and muscle levels. Using reduced-parameter models will allow common experimental and analytical frameworks for the study of both stability and maneuverability and the determination of general control strategies for unsteady locomotion.

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Body control may involve feedback control strategies to modify SLIP behavior SLIP mechanics may afford animals a degree of intrinsic dynamic stability, that is, the ability to maintain re-entrant patterns of locomotion despite small perturbations (Seyfarth et al. 2002). Both passive muscle and/or tissue properties and active control can contribute to stabilizing locomotion after perturbations (Nishikawa et al. 2007). Viscoelastic properties of muscles and tendons could contribute to opposing perturbations faster than can the active reflexive or compensatory control (Wilson et al. 2001; Jindrich and Full 2002). Intrinsic stability may be augmented by modifications to SLIP behavior such as protraction of the leg before stance (Grimmer et al. 2008) or the retraction speed of the stance leg before touch down (Seyfarth et al. 2003). However, depending on the task and perturbation, compensations based on feedback may also be necessary (Ristroph et al. 2010). Multiple steps may be necessary to stabilize SLIP systems (Carver et al. 2009). During walking, humans respond to mediolateral (ML) perturbations by adjusting lateral placement of the foot, potentially involving algorithmic control of foot-placement based on predictions of an inverted-pendulum model (Hof 2008; O’Connor and Kuo 2009; Hof et al. 2010). The relatively simple, algorithmic control of foot-placement is reminiscent of rules used to successfully control dynamicallystable robots in three dimensions based on SLIP mechanics (Raibert et al. 1984; Raibert and Hodgins 1993). The controller used for the robots employed three relatively simple feedback rules to maintain running height (measured as the vertical apex of the COM during flight), speed, and body orientation. The rules were effective for monopedal, bipedal, and quadrupedal bouncing gaits (Raibert 1990). The control rules developed for legged robots represent a successful solution to the problem of movement control of several degrees of freedom (DOFs) in three dimensions for bouncing movement. Therefore, these rules could be useful as testable hypotheses for the strategies used by humans during running (Qiao and Jindrich 2012). We used maneuvering tasks to test hypotheses that humans use body-control strategies consistent with those used by Raibert’s robots. Specifically, we tested whether (1) running height is related to leg force, and not the alternative strategy of increasing the duration of stance; (2) incremental changes to speed are linearly correlated to placement of the foot, that is, the distance from the center of pressure (COP) to a ‘‘Neutral Point’’ (NP) associated with running at

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and for speed (Heglund et al. 1982; Blickhan and Full 1993). The mechanics of locomotion in bipedal humans, quadrupedal vertebrates, and even arthropods’ gaits can be described by a ‘‘spring-loaded inverted pendulum’’ (SLIP) model (Lee and Farley 1998; Srinivasan and Ruina 2006; Lamoth et al. 2009; Whittington and Thelen 2009). Approaches such as SLIP models seek to represent locomotion with the fewest parameters possible; therefore, they can be termed ‘‘task-level’’ approaches. Simplified models such as the SLIP can be useful. For example, relationships among SLIP parameters are consistent across animals, allowing for functional predictions (Blickhan and Full 1993). When running, faster speeds are primarily associated with increased angle swept by stance leg instead of changes in the leg’s stiffness (Farley et al. 1993). Describing tasklevel behavior with models such as SLIP can facilitate studies of musculoskeletal and neural function (Full and Koditschek 1999). For example, when changes in the leg’s stiffness are required, they can be achieved both by changes in the stiffness of the ankle and in the angle of the knee (Farley and Morgenroth 1999). The SLIP model therefore represents a useful, consistent framework that can be used to characterize constant–average–velocity (CAV) locomotion. However, the locomotion of humans and animals is often unsteady. Animals must maneuver to move in a complex environment (Jindrich and Qiao 2009). Maneuvering involves changes to the direction of movement and/or in orientation of the body. Successful locomotion also requires stability. Stability can be defined as maintaining patterns of movement that do not diverge over time and attenuate the effects of perturbations (Guckenheimer and Holmes 1983; Full et al. 2002; Hasan 2005; Segal et al. 2008). Natural variability of motor output can act as internal perturbations to movement and require corrections (Stergiou and Decker 2011). Compensating for external (environmental) perturbations can also require stabilization (Oates et al. 2005, 2008; Rogers et al. 2011). For animals, both maneuverability and stability can affect fitness, and for humans instability can lead to injury (Howland 1974; Rogers and Mille 2003). Therefore, determining the mechanisms used by animals and humans to maneuver and maintain stability is critical for understanding locomotion in an ecologically-relevant context. An outstanding question is whether describing the mechanics and control of unsteady locomotion will require substantial departures from task-level approaches such as SLIP.

M. Qiao and D. L. Jindrich

Unsteady locomotion

Perturbation experiments can reveal potential locomotion parameters and strategies for effective unsteady locomotion Humans and other animals may also exhibit SLIP dynamics in the horizontal plane (Jindrich and

Qiao 2009). However, horizontal plane SLIP models require modification to account for rotational dynamics (Holmes et al. 2006). Coupling among DOFs can result in complex three-dimensional movement. For example, forces used for translation can result in rotation about several axes (Full et al. 2002). For many maneuvers such as turning, both rotation and translation are important task requirements, but the strategies used by animals to control both translation and rotation are not well known. Therefore, understanding how movements of many coupled DOFs are simultaneously coordinated is an important question. Although not based on a mechanical analog like the SLIP, a relatively simple task-level model can relate morphological, behavioral, and task requirements for maneuvers in the horizontal plane (i.e., turning) that involve coupled translational and rotational movement (Fig. 2; Jindrich and Full 1999; Jindrich et al. 2006). The model is based on the hypothesis that maintaining orientation of the body relative to the direction of movement (i.e., facing the way you are going) is an important requirement for turning, and was derived by analytically integrating the approximate equations of motion when turning with a single, massless leg. The objective of the model is therefore to describe the coupling between translation and rotation of the body in the horizontal plane during legged turning maneuvers. Based on body shape and other morphological and behavioral parameters, the model suggested that if humans turn simply by generating the lateral forces necessary to change the direction of movement, considerable over-rotation of the body would result. However, fore-aft forces could be used to prevent inappropriate rotation of the body (Jindrich and Full 1999; Jindrich et al. 2006, 2007; Jindrich and Qiao 2009). The possibility that fore-aft forces prevent over-rotation is supported by the 7- to 20-fold increases in fore-aft (braking) forces during turns relative to CAV running, and the approximate doubling of average braking forces with an increase in the magnitude of the turn from 288 to 428 in humans. However, similarly-sized bipeds (ostriches) when executing sidestep turns of similar magnitudes (308 for humans versus 208 for ostriches), at the same velocity during the turn (2.6 m s1), generate fore-aft forces of significantly lower magnitude than do humans (6% body weight for ostriches versus 22% for humans). This presents the question of the morphological and behavioral differences that affect maneuvering strategies in different animals.

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constant speed; and (3) a proportional-derivative (PD) function can describe the relationship of hip moments to trunk pitch. Measurements of kinematics and dynamics supported the hypothesis that humans use strategies that are consistent with Raibert’s rules to maneuver. Running height was related to leg force and not to duration of stance (Qiao and Jindrich 2012). Interestingly, changes to running height appeared to be associated with independent changes to leg stiffness during the compression (first half) and thrust (second half) phases of stance (Fig. 1B). Increased leg force relative to constant-speed running was associated with decreased stiffness of the leg during thrust for stepping up and during compression for stepping down (Fig. 1B; Qiao and Jindrich 2012). This supports the hypothesis that leg force, coupled with changes in stiffness, is associated with changing running height. Body translation (acceleration and deceleration) was directly correlated to foot placement during running (Fig. 1C; Qiao and Jindrich 2012). Average leg placement in front of the NP is associated with deceleration, whereas placement behind the NP is associated with acceleration (Fig. 1C). Moreover, the distance between the COP position and the NP was significantly correlated to change in velocity during stance, both within tasks and for pooled data (Fig. 1C). These findings support the hypothesis that foot placement is used to control body translation (Hof 2008; Hof et al. 2010). The alternative of changing speed using hip moments was not supported (Qiao and Jindrich 2012). Foot placement alone could potentially result in acceleration or deceleration due to impulse re-direction (Birn-Jeffery and Daley 2012). Finally, a PD function explained the relationship between hip moments and trunk pitch (Fig. 1D). Overall, these results suggest that humans may use body-control strategies consistent with that of bouncing robots. Although some changes associated with unsteady locomotion (leg stiffness and foot placement) could be readily described with the SLIP template, some modifications to the template were also necessary. Specifically, feedback control of foot placement and hip moments may be necessary to maintain translational speed and upright orientation of the body.

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M. Qiao and D. L. Jindrich

Modest changes to several opposing parameters may afford robustness and behavioral options for unsteady locomotion To determine how maneuvering strategies may depend on morphology and/or behavior, humans

were compared with ostriches performing cutting turns at approximately the same running speed (2.6 m s1). Both humans and ostriches showed strong linear correlations between weight-specific measured fore-aft forces and the fore-aft forces

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Fig. 1 Using maneuvers in the sagittal-plane to determine the strategies used for body control in humans. (A) Movement-parameters investigated. A ‘‘virtual leg’’ was defined to connect the COM and COP. The NP position is defined as one-half of the product of touchdown velocity and stance duration, or approximately mid-stance for CAV running. As the human foot does not make a point contact with the ground, the average COP position was considered the foot placement position. (B) Axial virtual leg-force versus virtual leglength for Step-Down, CAV, and Step-Up conditions. Compression (first half of stance) and thrust (second half of stance) phases are separately identified. The nearly-linear relationships between force and length suggest that legs are functionally analogous to linear springs during running maneuvers. (C) Relationship of inter-step change in speed to NP position for three tasks. (D) Hip torque predicted from three potential models tuned for best fits. A ‘‘Proportional’’ model (P) represents a linear relationship between hip torque () and the difference between body angle () and a ‘‘desired’’ body angle ðd Þ;  ¼ kp ð  d Þ. A ‘‘Derivative’’ model (D) _ A ‘‘PD’’ model represents a linear _ of the body;  ¼ kv . represents a linear relationship between hip torque and angular velocity () _ Data represent averages of 400 relationship between torque, angle of the body, and angular velocity of the body;  ¼ kp ð  d Þ þ kv . trials from 16 participants.

Unsteady locomotion

caused the rotation due to fore-aft forces to decrease, but even four-fold changes in I could be completely offset by 34–49% decreases in !i, facilitated by the concurrent decrease of rotations due to the sinusoidal fore-aft forces normally observed during running (and also present during turns). Rotation due to fore-aft forces are normally equal and opposite rotation due to !i. Although the fore-aft forces themselves were unchanged, when turning with increased I, their contribution to the body’s rotation decreased, allowing for decreases to !i to maintain appropriate body-rotation without decreased braking forces. However, !i was not the only parameter that changed, and changes to !i were partially offset by changes in lateral placement of the foot. Overall, these alterations in initial conditions for stance resulted in the maintenance of unchanged average fore-aft forces during the turning step among different conditions of mass and inertia. Consequently, increasing I led to three main observations: (1) humans modify locomotion to maintain consistent average fore-aft (braking) forces during turns (Fig. 2D); (2) a parameter (!i) differed among inertia conditions and could have been used to maintain consistent fore-aft forces (Fig. 2C); and (3) the opposing effects of several turning parameters (i.e., !i, initial angle of the body, fore-aft forces, and lateral placement of the foot) result in a system that is robust to changes in inertia and affords several behavioral options for compensation (Fig. 2C). The robustness and stability gained from maintaining a balance of opposing factors may be analogous to the increased co-activation of muscles with the increasing demand for accuracy of movement (Gribble et al. 2003). Accounting these factors in the model restored its ability to predict braking across inertial conditions (Fig. 2D). Several issues remain un-resolved. First, although average fore-aft forces did not change among inertial conditions, trial fore-aft forces (and other parameters) continued to show a large variance (Fig. 2D). However, many parameters maintained the relationships expressed by the model. The large variance in braking force suggests that braking force by itself may not be the most directly task-relevant parameter, but may instead co-vary with other parameters to achieve an overall task goal (Scholz and Scho¨ner 1999). This observation is similar to the observations of relationships among joint coordination parameters that are maintained despite large variance in values of the parameters themselves (Scholz and Scho¨ner 1999; Auyang et al. 2009; Yen and Chang 2010). However, in the case of turning, the underlying reasons (potentially noise for some parameters and

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predicted from the equations in Fig. 2D (humans: slope ¼ 0.97; ostriches: slope ¼ 0.97; Fig. 2D) (Jindrich et al. 2006, 2007). These correlations support the hypothesis that morphological and behavioral parameters are related in a predictable way during running turns (Jindrich and Qiao 2009). However, ostriches also showed differences from humans. Importantly, lateral forces for ostriches were estimated to result in appropriate rotation of the body. Braking was not as necessary for ostriches to turn, and ostriches used smaller braking forces than humans (Fig. 2D). Instead of large differences in a single factor, several morphological and behavioral parameters resulted in reduced braking forces in ostriches. The ratio of mass-to-rotational inertia (M/I) for ostriches was 94% of that for humans. Ostriches also placed their feet more caudally (PAEP,imd for ostriches was 79% that for humans), and had shorter durations of stance ( for ostriches was 82% of that for humans). These changes to several morphological and behavioral parameters present the question of whether coupled changes to several parameters are also used to compensate for perturbations that may affect maneuvering performance in a single animal. To test the hypothesis that humans compensated for morphological perturbations with modest changes to several parameters, we experimentally manipulated body mass (M) and body rotational inertia (I) (Qiao et al. 2014). We constructed a rotational inertia-increasing apparatus from a rigid backpack frame with steel poles to which weights could be attached, based on previous designs (Carrier et al. 2001; Lee et al. 2001) (Fig. 2B and C). We used five different conditions: M0%I1 (control), 15% mass and three-fold increase in body rotational inertia: M15%I3, M15%I3.5, M17%I3.5, and M17%I4. Surprisingly, most measured aspects of turning performance, including the angle turned, average forces, peak braking forces, and force profiles were not significantly different among different levels of rotational inertia, even though I increased as much as four-fold. The pack resulted in minor changes to the duration of stance, which increased by 12% and were likely associated with an increase in mass (Farley and Taylor 1991). Similar to the comparison between ostriches and humans, compensating for increased M and I did not involve large changes to a single parameter (Qiao et al. 2014). Importantly, measured fore-aft forces did not differ among different conditions of rotational inertia. The lack of decreases in fore-aft forces was primarily due to significant decreases in initial rotational speed (!i; Fig. 2C). Increased I

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M. Qiao and D. L. Jindrich

or Bo ie d nt y at io n

Initial movement ent vem on direction (imd) o M cti dire ωi θr

θd

Fimd

Pp

Dec/Acc Fore-aft force Braking force Lateral foot placement Stance Period

A

Fp

COP

PAEP,imd

COM Perpendicular to movement direction (p)

Turn direction

Increased M,I Ostriches Humans

0.3 0.1 -0.5

-0.3

-0.1 -0.1

0.1

-0.3

ε=

-0.5

0.3

MVτ 2I

0.5

(

PAEP,imd

Fhmax = -0.7

-

4Vτ π2

πI(1 - ε)θd τ 2 Pp

Deflecting force Initial rotational Velocity Initial body angle

-0.7

0.5

)

Weight-Specific Measured Fore-aft Force

Fig. 2 Using horizontal-plane maneuvers to understand the coupling between translational and rotational movement. (A) Primary movement parameters used for horizontal-plane turning model. The model assumes that a biped of mass M and moment of inertia about the vertical axis I, traveling at velocity V, changes the direction of movement (of the COM velocity vector) by some angle d during a single step of duration . PAEP,imd is the initial movement direction of anterior extreme position, and Pp the average lateral, placement of the foot, calculated as the distance from COM to the COP under the foot. (B) Apparatus to experimentally increase rotational inertia in humans. (C) Compensations associated with increased-inertia turns relative to CAV running. Left figure represents CAV running. Each arrow represents a parameter value normalized to the same length. Arrows pointing upward represent positive contribution to rotating the body in the net direction of turn over the step. Arrows pointing downward indicate rotation opposite the direction of the trial turn. Right figure represents average change in parameters over different conditions of inertia. Lateral foot placement of the foot and initial rotational velocities both showed significant decreases, but values of other parameters did not change significantly. (D) Comparison of measured half-sine component of fore-aft forces to predictions from the turning model, Fhmax. Fhmax can be calculated in two steps. First, the ‘‘leg effectiveness number’’ (") can be determined for the leg. " predicts the amount of body rotation expected if a leg generates only the forces perpendicular to the initial movement direction (Fp) necessary to change the movement direction by a desired angle (d). Second Fhmax can be predicted based on " and lateral foot placement. Data from humans without loads (Jindrich et al. 2006; Qiao et al. 2014) are displayed as circles. Data from ostriches (Jindrich et al. 2007) are displayed as squares. Data from humans with increased inertia (Qiao et al. 2014) are displayed as triangles. Some predicted values are from equations including more parameters than those shown in the figure (Qiao et al. 2014). Large symbols represent mean values for each group.

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D

C

Weight-Specific Predicted Fore-aft Force (Fhmax)

B

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Unsteady locomotion

compensatory strategies for others) for high levels of variance despite controlled experimental conditions remain unclear. Direct perturbation experiments have the potential to reveal the relationships between proactive maneuvers and reactive strategies for stabilization

Materials and methods Participants and tasks Three participants (age ¼ 24.6  7.9 years; body mass ¼ 71.2  8.1 kg; height ¼ 1.74  0.02 m, mean  SD, 2M, 1F) walked (1.15 m s1) and ran (1.57 m s1) on a treadmill (Fig. 3). Impulsive 250 ms, 0.5 m s2 perturbations to the COM were generated using a linear stage motor (LDL-Series Ironless Linear Servo Motor, Rockwell Automation, Milwaukee, WI, USA). ML perturbations were used, based on past studies and because there may be less opportunity for passive ML stabilization than for antero-posterior stabilization (Bauby and Kuo 2000; Hof et al. 2010). A carbon fiber rod connected the motor to the participant (Fig. 3A). For each participant, three 3-min trials under each gait were collected. The instant and the direction of the perturbation were both randomized, resulting in five perturbations for each trial. Perturbations were applied by pulling and pushing in both left and right directions. All experimental procedures were approved by the institutional review board of the Arizona State University. Data collection A 10 camera 3-D motion capture system (VICONÕ , version 612, Oxford Metrics, Oxford, UK) recorded whole-body kinematics (Plug-In-Gait marker set, 14 mm diameter markers) at 120 Hz while participants walked and ran on a custom-built instrumental split-belt treadmill (Fig. 3A). Data analysis Joint angles were calculated from the locations of markers using inverse kinematics (Qiao and Jindrich 2012). Anthropometric data were determined by allometric scaling based on a reference model (Huston

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The locomotion parameters modulated and the control rules used for unsteady locomotion are largely unknown (Biewener and Daley 2007; Jindrich and Qiao 2009). Our experiments on sagittal-plane maneuvers identified potential feedback-control strategies for running. Morphological perturbations of maneuvers identified compensations and constraints associated with coupling translational and rotational movements. However, many questions remain. For example, it is not known whether the proactive strategies used during maneuvers are similar to the reactive strategies used to compensate for de-stabilizing perturbations. There are reasons to hypothesize that maneuverability and stability involve similar movement strategies. For example, both result in similar outcomes: forces and moments to change the direction of movement and rotation of the body. However, anticipation may allow for different movement strategies than for reactive compensations. For example, more time may be available to plan and execute proactive compensations than for reactive compensations. Moreover, other factors, such as speed and gait, could also affect the compensations used differently for maneuverability and for stability. We consider studies involving direct perturbations, both of translation and rotation, to be a critical next step for better understanding of legged locomotion. We have therefore initiated experiments to investigate the compensation strategies employed for stability. Our long-term goals are to determine the parameters used, and control strategies employed, to stabilize locomotory perturbations that include both translational and rotational components. We expect that several factors, including gait, speed, and when perturbations occur within the step cycle, have the potential to affect the compensations used. One important question is the relative importance of within-step compensation strategies and compensation strategies that require leg placement. For example, within a step, humans push off with the trailing limb to reduce energy loss due to collisions (Kuo et al. 2005). Between steps, humans can adjust initial leg orientation and swing speed to improve stability (Seyfarth et al. 2003). Based on our maneuverability studies that revealed that initial stance conditions are important for both sagittal-plane and

horizontal-plane maneuvers, we hypothesized that step transitions are important for compensating for de-stabilizing perturbations. As a first step toward this goal, we have initiated a novel set of experiments to directly perturb humans both when walking and when running (Qiao et al. 2012). We applied impulsive ML perturbations to determine the compensatory responses of humans both during walking and running on an instrumental split-belt treadmill. We hypothesized that (1) the time necessary to reject perturbations will be different for walking and running and (2) responses to perturbations would differ depending on whether the foot ipsi-lateral or contra-lateral to the perturbation was in stance at the time of onset of the perturbation.

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M. Qiao and D. L. Jindrich

A Cameras

safety gantry

Carbon fiber rod

linear stage motor

z y 0.7 m

instrumental split-belt treadmill

Right Left (m)

B

time to reversal (TTR) maximum speed

maximum displacement

TTI

recovery duration

perturbation inflection onset

reversal point

recovery

time (s)

perturbation inflection reversal recover

COM 0.5 m right

left

Fig. 3 Direct perturbations to investigate the compensations associated with stability. (A) Experimental apparatus. Participants walked on a treadmill, attached to a linear motor, and secured to a gantry for safety. (B) Definition of primary temporal parameters: inflection point (maximum COM speed in ML direction), reversal point (maximal deflection of ML COM), and recovery. The dashed gray lines represent the range of the COM trajectory in the ML direction without perturbation. (C) Body-response from a representative trial at the onset of perturbation, instant of inflection, reversal point, and instant of recovery.

and Passerello 1982; Pandy and Andriacchi 2010). Foot touchdown was determined as when the COM of the leading foot reached a local maximal AP value. The instantaneous COM of the whole body was calculated using instantaneous locations of segments. The whole-body COM time-series were smoothed using a fourth-order-zero-lag-low-pass Butterworth digital filters at 4 Hz. COM position was differentiated using a first-order 3-point central difference algorithm to obtain velocity (Qiao et al. 2014). The velocity was then Butterworth filtered at 5 Hz and differentiated again to obtain acceleration. We defined one stride as the time between two consecutive anterior extreme positions from the COM of the same foot. We assumed that responses were the same in both directions of perturbations, and inverted all

Results Walking and running achieved similar perturbationrejection performance in different ways Impulsive ML perturbations resulted in peak ML COM speed and acceleration that were not significantly different between running and walking (Table 1). However, TTI showed a non-significant trend to be shorter for walking than for running (Table 1). The possibility of shorter TTI during walking was supported by significantly smaller COM displacement during walking than during running (Fig. 4A and B and Table 1). Surprisingly, despite smaller effects of perturbations during walking, there was not a significant difference in the time or number of steps to recovery between walking and running (Table 1). One reason for the consistent absolute time to recovery was differences in the relative lengths of each stage of recovery. For walking, total time to recovery was dominated by the time from reversal to recovery (57%), whereas recovery time during running was

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C

x

data from right-side perturbations. Perturbations were classified as ipsi-lateral or contra-lateral based on whether the perturbation was in a medial direction (ipsi) or in a lateral direction (contra) relative to the stance foot. The COM inflection point was estimated as the instant when ML speed of COM started decelerating from toward the perturbation to opposing the perturbation (zero ML acceleration). The time from the perturbation to this inflection point was the time to inflection (TTI). The point of maximum deviation was the instant when the COM reached its maximum lateral position, and it was defined as the reversal point (zero ML speed). The time from the onset of the perturbation to the reversal point was defined as the time to reversal (TTR). In some trials, the perturbation was applied when the COM was moving in the same direction as the perturbations, and had inflection points before the onsets of perturbations. The recovery ended when the COM fell within the range of normal ML variation of the COM (Fig. 3B). We used a sine wave to fit the time course of the COM in the ML direction during the unperturbed periods, and the amplitude of that sine wave was considered the range of motion. We used repeated measures analysis of variance to determine the effect of gait (walk and run) and posture (ispi- and contra-lateral position of the foot) on the response to perturbations. All calculations were performed using Matlab (R2013b, Mathworks, Natick, MA, USA).

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Unsteady locomotion Table 1 Responses to perturbations both for walking and running Unit

Walk

Run

COM maximum acceleration

ms

0.42

1.22  0.19

1.56  0.49

COM maximum speed

m s1

0.11

0.19  0.02

0.22  0.00

COM maximum displacement

m

50.01

0.061  0.003

0.091  0.002

Time to inflection (TTI)

s

0.08

0.34  0.12

0.57  0.01

Time to reversal (TTR)

s

0.94

0.82  0.19

0.81  0.05

Time to recovery

s

0.12

1.92  0.32

1.46  0.004

Time from inflection to reversal

s

0.24

0.49  0.26

0.22  0.03

Time from reversal to recovery

s

Step # from perturbation to recovery

Fig. 5 The percentage of each stage during the recovery after perturbation. (A) Walking. (B) Running.

Table 2 Responses to perturbations depending on foot in stance Unit

p

Ipsi-

Contra-

m s2

0.63

1.46  0.49

1.02  0.465

50.05

1.10  0.13

0.65  0.06

COM maximum acceleration

0.71

0.22  0.06

0.17  0.07

2.52  0.79

3.60  0.15

COM maximum speed

m s1

0.1

COM maximum displacement

m

0.59

0.081  0.032

0.064  0.002

Time to inflection (TTI)

s

0.76

0.47  0.14

0.44  0.22

Time to reversal (TTR)

s

0.92

0.85  0.19

0.81  0.26

Time to recovery

s

0.79

1.68  0.37

1.72  0.21

Time from inflection reversal

s

0.84

0.39  0.32

0.34  0.009

Time from reversal to recovery

s

0.77

0.83  0.19

0.90  0.47

0.85

3.1  0.59

3.2  1.19

Note: Mean  SD.

Step # from perturbation to recovery Note: Mean  SD.

Direction of perturbation relative to the stance leg did not change the time-course of recovery

Fig. 4 ML position and velocity during perturbation trials. (A) Walking, (B) running, (C) speed during walking, and (D) speed during running. Mean position or velocity during ipsi-lateral perturbation trials is represented by solid lines, and contra-lateral trials by dashed lines. Data are averages over all trials from all subjects. Shaded areas represent  1SD.

dominated by TTR (55%; Table 1 and Fig. 5B). The differences in recovery could, in part, be due to differences in step frequency between gaits. Walking had a lower step frequency than running (walking 2 step s1, running 3.5 step s1).

Responses to perturbations applied ipsi-laterally (i.e., the perturbation laterally to the stance leg; a left perturbation with the left leg in stance) or contralaterally were not significantly different for any parameter measured (Table 2). The similarity of response in both directions relative to the stance leg does not support the hypothesis that compensations depend on stance leg, but instead supports the hypothesis that step-transitions may be associated with rejection of perturbation.

Discussion We initiated a series of experiments to investigate the compensation strategies used during unsteady locomotion. These first experiments involved direct ML perturbations to humans while walking and running

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Differences in dynamics of walking and running may account for differing compensation strategies It would be reasonable to expect walking and running to involve different strategies for controlling unsteady locomotion. Walking and running operate at different time-scales, and the role of different

levels of organization (i.e., musculoskeletal/spinal versus higher brain centers) may be speed-dependent (Full and Koditschek 1999; Biewener and Daley 2007). Walking may allow for different behavioral strategies than for running. For example, during walking turns, rotation in the direction of the stance foot has been termed a ‘‘spin’’ and separated from rotation away from the stance foot (‘‘step’’ turns) (Hase and Stein 1999; Taylor et al. 2005). The specific strategy used depends on the magnitude of the turn and when the maneuver is initiated (Patla et al. 1991). In contrast, cutting turns during running use opposite legs, but are similar in many respects and can be described by the same task-level model (Jindrich et al. 2006). Second, walking involves periods when both feet are on the ground, and force couples could contribute to forces and moments used for control (Hase and Stein 1999). Third, walking maneuvers and compensations are commonly executed over multiple steps (Fajen and Warren 2003). Our findings support the hypothesis that there are functionally important differences between walking and running. Walking may be more intrinsically able to reject perturbations using passive mechanisms, resulting in greater resistance to perturbations (Jindrich and Full 2002). We also cannot reject the hypothesis that neural feedback mechanisms also contributed to perturbance-rejection during walking. Perturbance-rejection commonly involved multiple steps both during walking and running Although COM displacements were lower in walking than in running, it was surprising that the absolute time to recovery was not different between these activities. This similarity was related to the slower recovery from the maximum perturbation position (the reversal point) during walking relative to running (Fig. 4 and Table 1). Compensation necessary to reject perturbations and return to a normal locomotor trajectory may be slower during walking relative to running. The speed at which compensations can act to recover from perturbations may, in part, reflect the importance of step transitions to recovery. Stride periods during walking are longer than during running, providing more time for compensations to act. Feedback from ankle muscles can therefore change the trajectory of COM during stance (Nielsen and Sinkjaer 2002). However, the ability of humans to plan and execute maneuvers or compensations based on feedback may be limited. For example, both gradual (308) and sharp (608) walking turns cannot be

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on a treadmill. Surprisingly, walking and running did not show significant differences in the total time to recovery. However, walking exhibited greater resistance to perturbations (smaller displacement of COM), whereas the greater step-frequency of running allowed more rapid recovery (shorter time from the beginning to recovery at reversal to full recovery). These observations suggest that withinstep mechanics may be important for limiting the kinematic effects of force perturbations, and step transitions may be important for stabilization after perturbation. Several limitations place our findings into a specific context. First, this study represents a first step and was not designed to provide detailed information about the mechanisms of stability, or compare compensations used for stability to those used for maneuvers. The limited numbers of participants and perturbations prevent us from addressing many interesting questions, including phase-dependence of compensations, the effects of perturbations of different magnitudes, in different directions or with a rotational component, or the joint-level or musclelevel adjustments underlying behavioral strategies. Moreover, some non-significant comparisons of Tables 1 and 2 (e.g., TTI in Table 1) may have been significant with more subjects. However, randomizing the position and direction of perturbations mitigated potential effects of phase, and allowed us to make the relatively simple comparisons of recovery between walking and running. Moreover, the time-course of recovery over multiple steps potentially decreases the impact of the phase of perturbation both for walking and for running (Oliveira et al. 2013). This possibility is supported by the absence of significant differences between ipsi-lateral and contra-lateral perturbations (Table 2). The significant differences we observed were relatively large (430%; Table 1). However, the possibility remains that additional effects of gait or speed remain to be discovered. Planned experiments involve testing larger samples of coupled rotational and translational perturbations of different magnitude and direction, and performing more sophisticated kinematic and dynamic analyses to reveal compensatory mechanisms.

M. Qiao and D. L. Jindrich

Unsteady locomotion

Acknowledgments We were deeply grateful to Prof. James Abbas for using the facilities in the gait laboratory in the Center for Adaptive Neural Systems at Arizona State University. We are grateful to Mark Hughes for help with assembling and programming the linear motor apparatus. Support for participation in this symposium was provided by the Company of Biologists, and the Society for Integrative and Comparative Biology (Divisions of Vertebrate Morphology, Comparative Biomechanics, Neurobiology, and Animal Behavior).

Funding This work was supported by the Kinesiology Program at Arizona State University.

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