The fMRI environment may alter the very phenomena researchers aim to study. This concern has motivated diverse research groups to test how posture and cognition interact (e.g., Lundström et al., 2008; Harmon-Jones and Peterson, 2009). Replication experiments, however, remain sparse, likely because posture receives more attention as a procedural caveat than a research field in its own right. Beyond posture, neuroimagers must also address several other procedural and statistical concerns before obtaining meaningful results (e.g., Eklund et al., 2016). All in all, these studies highlight the importance of considering posture across all cognitive and imaging research.

### POSTURE INFLUENCES PHYSIOLOGY

Heart rate, respiratory volume, oxygen consumption, core body temperature, cortisol secretion, and other indicators of physiological arousal stabilize at higher levels when upright compared to supine (**Figure 1**; Cole, 1989; Kräuchi et al., 1997; Hennig et al., 2000; Badr et al., 2002; Jones and Dean, 2004). These physiological differences may influence the fMRI derived blood-oxygen-level dependent (BOLD) signal, regardless of whether or not brain processes actually change (Kastrup et al., 1999; Di et al., 2013). fMRI measures neuronal activity indirectly (see Shmuel, 2015); the BOLD signal stems from the hemodynamic properties of neural populations and remains

#### TABLE 1 | Each body posture raises particular considerations in terms of brain imaging modalities and cognitive experiments.

*To conduct fMRI beyond a horizontal body posture requires specialized scanners, which are extremely uncommon. Researchers can conduct EEG and fNIRS in any posture, but must care for occipital sensors in the supine position. Humans execute most physical and cognitive actions when sitting or standing. To better depict the posture assumed in fMRI, this photo shows a participant before entering the bore. During scanning, the head and upper body remain inside the bore, which measures about 60 cm in diameter for standard scanners.*

highly sensitive to cardiopulmonary variables (Chang and Glover, 2009; Chang et al., 2009; Di et al., 2013; Weinberger and Radulescu, 2016). Thus, demonstrating that posture affects the BOLD signal falls short of confirming a change in neural activity; cardiopulmonary variables remain yoked to body position and also weigh heavily on BOLD activity.

 A few experiments employ a stance-adjustable positron emission tomography (PET) gantry and report greater blood flow to both visual and cerebellar cortices when standing erect compared to lying supine (Ouchi et al., 1999, 2001). Using fNIRS, researchers document decreases in both oxygenated and deoxygenated cortical hemoglobin volume when participants move from lying supine to sitting upright (Edlow et al., 2010; Ozgoren et al., 2012). Due to a paucity of upright MRI scanners capable of functional sequences, researchers have yet to replicate postural fNIRS experiments with fMRI. Because fNIRS and fMRI measure similar signals (Cui et al., 2011), we can only presume that postural discrepancies would also influence fMRI data.

Beyond cardiovascular measures, posture exerts a quantifiable and direct impact on neural activity. A few EEG experiments demonstrate that, compared to lying horizontally, lying headup on an incline between 30–45◦ (Cole, 1989; Vaitl and Gruppe, 1992) and sitting upright (Chang et al., 2011; Spironelli et al., 2016) increase high-frequency neural activity, associated with alertness and sensory processing, and dampen down lowfrequency oscillations associated with relaxed or drowsy states. More recent studies leverage high-density EEG systems and reveal greater high-frequency power across the cortex in more upright postures (Thibault et al., 2014) as well as an 80% increase in occipital gamma power when supine compared to prone (Rice et al., 2013). Posture further alters event related potentials (ERPs) in response to standard visual paradigms (Rice et al., 2013), painful stimuli (Spironelli and Angrilli, 2011; Fardo et al., 2013), and emotional processing (Price et al., 2012; Messerotti Benvenuti et al., 2013). In contrast to these findings, a recent sensor-level MEG study revealed greater high-frequency power over common language areas only, rather than the entire cortex, when sitting upright compared to when supine or reclined (Thibault et al., 2015). Sensorlevel MEG results, however, may represent only the strongest postural effects and source-level analyses of such data may reveal more widespread changes reminiscent of previous EEG findings (Lifshitz et al., under review). Whereas, the majority of these studies employ healthy young adults, posture may exert a particularly strong influence on brain function in the elderly and specific patient groups (e.g., cardiovascular disease or tramautic brain injury: Ouchi et al., 2005; Thompson et al., 2005). In this regard, converging evidence from cognitive, medical, and neuroscientific research supports the "embodied brain" hypothesis and underscores the importance of postural variables in modern imaging experiments.

### UNDERLYING MECHANISMS BY WHICH POSTURE OPERATES

At least two physiological and one cognitive mechanism contribute to the influence of posture on brain data: (1) changes in noradrenalin output, (2) altered CSF thickness, and (3) a preparatory cognitive state based on the subset of interactions possible with the environment.

visual field (Kano, 1991), or to socially and physically interact with our environment (Hari and Kujala, 2009). Motor plans depend on ongoing limb configuration (de Lange et al., 2006), the excitability of motor cortex increases in freestanding compared to supported postures (Tokuno et al., 2009), and when sitting, compared to supine, people react more quickly to moving visual fields (Kano, 1991) and are more likely to perceive themselves as moving when exposed to a moving visual field (Guterman et al., 2012). Moreover, the supine posture decreases social behaviors (Harmon-Jones and Peterson, 2009; Price et al., 2012) and hardly invites typical social interactions known to modulate brain activity, such as eye contact (Ferri et al., 2014). These posturedependent cognitive states may manifest in both resting-state brain oscillations (Chang et al., 2011; Thibault et al., 2014; Spironelli et al., 2016) and neural responses to stimuli (i.e., ERPs: Spironelli and Angrilli, 2011; Price et al., 2012; Fardo et al., 2013). The causality of interactions between cognition and brain activity may always remain elusive; cognitive states propel physiological change (i.e., top-down processes) and physiological parameters also weigh on cognitive states (i.e., bottom-up effects).

Taken together, physiological cascades, cranial fluids, and cognitive set all exert varying influences on brain imaging data across postures. Whereas, noradrenergic output and cognitive processing may directly influence cortical activity measured at the neuronal level, CSF shunts the transmission of electromagnetic activity from neurons to sensors and exerts little influence on neuronal activity itself. Adopting experimental designs that evaluate and integrate these three mechanisms can only help to better understand ecological human functioning.

### CORRECTING AND ACCOUNTING FOR THE EFFECTS OF POSTURE

Two paths emerge to overcome postural caveats in neuroimaging. First, we can rework standard experimental designs to minimize the influence of posture on brain activity; and second, we can embrace new imaging technologies conducive to everyday human behavior.

Accounting for the three aforementioned postural mechanisms would require a combination of innovative experimental designs, computational expertise, and a new body of research to draw upon. For example, to maintain cortical excitability in the supine posture, researchers could entertain the possibility of applying pressure to the body via anti-shock trousers to maintain baroreceptor firing (Cole, 1989), pharmacologically sustaining noradrenalin levels, or providing periodic stimulation via conversation or sensory input to sustain participant alertness. Overcoming variation in CSF thickness may require anatomical brain scans from each participant plus compensatory algorithms to calculate the standard redistribution of CSF as a function of posture. Such algorithms do not yet exist and would demand further head modeling research that taps into a database of posture-induced CSF perturbations across individuals (e.g., see Rice et al., 2013). Novel research on posture and cognition, moreover, could help future experimental designs minimize variations in cognitive state among postures. For example, research already demonstrates that poor sleep impedes working memory when supine compared to sitting (Muehlhan et al., 2014) and hampers psychomotor performance when sitting compared to standing (Caldwell et al., 2003). These findings suggest that weeding out sleep-deprived participants from supine imaging experiments could help researchers collect brain data that better reflect upright human functioning. Neuroimagers could further benefit from extending similar screening procedures to participants with mood and hormonal disturbances in response to MRI environments (Muehlhan et al., 2011) and mental performance problems in response to scanner noise (Pripfl et al., 2006). With diligence, neuroimagers can improve current research paradigms to account for a number of these postural discrepancies.

Imaging the human brain increasingly relies on smaller, lighter, and more mobile hardware. These devices hold the potential to thrust brain imaging toward investigating everyday interactive and social cognition. With the use of overhead gantries, participants undergoing EEG and fNIRS can now move and interact in a laboratory environment (Gramann et al., 2011; Mahoney et al., 2016). Recent developments, moreover, permit individuals to connect EEG electrodes to their smartphone and record brain activity in everyday contexts (Stopczynski et al., 2014). Moving while recording EEG, however, comes with caveats.  One potential concern is that researchers who are not careful may mistake these artifacts for brain oscillations themselves. The fNIRS signal also

### REFERENCES

Alperin, N., Hushek, S. G., Lee, S. H., Sivaramakrishnan, A., and Lichtor, T. (2005). MRI study of cerebral blood flow and CSF flow dynamics in an upright posture: the effect of posture on the intracranial compliance and pressure. Acta Neurochir. Suppl. 95, 177–181. doi: 10.1007/3-211-32318-X\_38

remains sensitive to motion artifacts, but responds less to muscle contamination. These portable devices sacrifice signal quality for ecological human functioning. The use of these technologies, however, is not an "either-or" dilemma. In a single experiment, we can combine data from the more precise and static imaging modalities with data from ecological yet coarser devices. Similar to how portable devices revolutionized the field of eye-tracking (Hayhoe and Ballard, 2005), wearable neuroimaging technologies hold promise to revolutionize how we study the living human brain.

### CONCLUSION

Across numerous experiments, posture reliably influences brain data, core physiology, and cognitive performance. This reality rings alarm bells in a field that rarely considers postural constraints. Whereas, ecological comportments such as standing and moving recruit a host of additional brain processes and represent the base from which we perform our largest diversity of interactions, few brain imaging studies ask participants to stand or move. A pillar of neuroimaging, MRI, confines participants to a supine position seldom assumed during common wakefulness. This state of affairs brings into question the practice of using neuroimaging findings to inform our ecological behavior of everyday life. Bridging the lacuna between imaging context and ecological posture would further unveil the neural processes giving rise to the living human brain.

### AUTHOR CONTRIBUTIONS

RT reviewed the literature, consulted with experts, and prepared the initial draft. RT and AR prepared the final draft together. AR provided comments throughout manuscript preparation.

### FUNDING

AR acknowledges funding from the Canada Research Chair program, Discovery and Discovery Acceleration Supplement grants from the Natural Sciences and Engineering Research Council of Canada (NSERC), Canadian Institutes of Health Research, and the Bial Foundation. RT, also a Bial recipient, acknowledges an Alexander Graham Bell Canada Graduate Scholarship from NSERC. The funding sources had no involvement in reviewing the literature, writing the manuscript, or deciding to submit the paper for publication.

### ACKNOWLEDGMENTS

We thank Lu Zhou for help with graphics and Drs. Xu Cui and Joseph Baker for providing the photo of fNIRS.

**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2016 Thibault and Raz. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Corrigendum: Imaging Posture Veils Neural Signals

#### Robert T. Thibault 1 and Amir Raz 1, 2, 3 \*

*1 Integrated Program in Neuroscience, Department of Neurology and Neurosurgery, McGill University, Montreal, QC, Canada, 2 The Lady Davis Institute for Medical Research at the Jewish General Hospital, Montreal, QC, Canada, 3 Department of Psychiatry, Institute for Community and Family Psychiatry, McGill University, Montreal, QC, Canada*

Keywords: posture, neuroimaging, EEG, fMRI, upright, supine, cognition, perception

### **A corrigendum on**

### **Imaging Posture Veils Neural Signals**

by Thibault, R. T., and Raz, A. (2016). Front. Hum. Neurosci. 10:520. doi: 10.3389/fnhum.2016.00520

Reason for Corrigendum:

In the original article, there was an error. A correction has been made to the Introduction, section 'Imaging Methods and Imaging Postures', first paragraph.

#### Edited and reviewed by:

*Eric Yiou, University of Paris-Sud, France*

#### \*Correspondence:

*Amir Raz<EMAIL_ADDRESS>
Received: *10 January 2017* Accepted: *20 January 2017* Published: *01 February 2017*

#### Citation:

*Thibault RT and Raz A (2017) Corrigendum: Imaging Posture Veils Neural Signals. Front. Hum. Neurosci. 11:45. doi: 10.3389/fnhum.2017.00045*

The sentence "MEG outperforms EEG in terms of signal-to-noise ratio when accessing deeper brain regions (Goldenholz et al., 2009)" should read "MEG outperforms EEG in terms of signal-tonoise ratio when accessing **superficial** brain regions (Goldenholz et al., 2009)."

The authors apologize for this error and state that this does not change the scientific conclusions of the article in any way.

### REFERENCES

Goldenholz, D. M., Ahlfors, S. P., Haemaelaeinen, M. S., Sharon, D., Ishitobi, M., Vaina, L. M., et al. (2009). Mapping the signal-to-noise-ratios of cortical sources in magnetoencephalography and electroencephalography. Hum. Brain Mapp. 30, 1077–1086. doi: 10.1002/hbm.20571

**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2017 Thibault and Raz. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# The Neuro-Mechanical Processes That Underlie Goal-Directed Medio-Lateral APA during Gait Initiation

Jean-Louis Honeine1 \*, Marco Schieppati 1,2 , Oscar Crisafulli 1 and Manh-Cuong Do3

1 Department of Public Health, Experimental and Forensic Medicine, University of Pavia, Pavia, Italy, 2 Centro Studi Attività Motorie (CSAM), Fondazione Salvatore Maugeri (IRCSS), Scientific Institute of Pavia, Pavia, Italy, 3 Faculty of Sport Science, Complexité, Innovations, Activités Motrices et Sportives (CIAMS), Université Paris-Saclay, Orsay, France

Gait initiation (GI) involves passing from bipedal to unipedal stance. It requires a rapid movement of the center of foot pressure (CoP) towards the future swing foot and of the center of mass (CoM) in the direction of the stance foot prior to the incoming step. This anticipatory postural adjustment (APA) allows disengaging the swing leg from the ground and establishing favorable conditions for stepping. This study aimed to describe the neuro-mechanical process that underlies the goal-directed medio-lateral (ML) APA. We hypothesized that controlled knee flexion of the stance leg contributes to the initial ML displacement of the CoP and to the calibration of the first step. Fourteen subjects initiated gait starting from three different initial stance widths of 15 cm (Small), 30 cm (Medium), and 45 cm (Large). Optoelectronic, force platform and electromyogram (EMG) measurements were performed. During APA, soleus activity diminished bilaterally, while tibialis anterior (TA) activity increased, more so in the stance leg than in the swing leg, and to a larger extent with increasing initial stance width. Knee flexion of the stance leg was observed during APA and correlated with the ML CoP displacement towards the swing leg. ML CoP and CoM displacements during APA increased with increasing stance width. The activity of stance-leg TA was correlated with the degree of knee flexion. Swing-leg tensor fasciae latae (TFL) was also active during APA. Across subjects, when stance-leg tibialis activity was low, TFL activity was large and vice versa. The modulation of the ML CoP position during APA allowed the gravity-driven torque to place the CoM just lateral to the stance foot during step execution. Accordingly, the gravity-driven torque, the ML CoM velocity during step execution, and the step width at foot contact (FC) were lower in the Small and greater in the Large condition. Consequently, the position of the stepping foot at FC remained close to the sagittal plane in all three conditions. Conclusively, coordinated activation of hip abductors and ankle dorsiflexors during APA displaces the CoP towards the swing leg, and sets the contact position for the swing foot.

Keywords: gait initiation, center of pressure, center of mass, frontal plane, knee flexion, ankle dorsiflexor muscles, hip abductor muscles

#### Edited by:

Gilles Allali, Geneva University Hospitals, Switzerland

#### Reviewed by:

Mariangela Dipaola, Polytechnic University of Milan, Italy Romain Tisserand, Claude Bernard University Lyon 1, France

> \*Correspondence: Jean-Louis Honeine<EMAIL_ADDRESS>
Received: 15 June 2016 Accepted: 19 August 2016 Published: 31 August 2016

#### Citation:

Honeine J-L, Schieppati M, Crisafulli O and Do M-C (2016) The Neuro-Mechanical Processes That Underlie Goal-Directed Medio-Lateral APA during Gait Initiation. Front. Hum. Neurosci. 10:445. doi: 10.3389/fnhum.2016.00445

## INTRODUCTION

Gait initiation (GI) is a critical task because it involves transiting from stable bipedal stance to unstable unipedal stance. It requires anticipatory postural adjustments (APA) that reconfigure the position of the center of mass (CoM) with respect to the center of foot pressure (CoP) in order to take advantage of gravity and progress forward (Carlsöö, 1966; Brenière and Do, 1986, 1991; Brenière et al., 1987; Brenière, 2001).

It is well established that the displacement of CoM during APA is achieved by shifting the CoP backwards and in the direction of the swing leg (Jian et al., 1993; Elble et al., 1994; Lepers and Brenière, 1995). The backward shift of the CoP is caused by a reduction in soleus activity and activation of the tibialis anterior (TA; Crenna and Frigo, 1991). During APA, modulation of the antero-posterior distance between the vertical projections to the ground of the CoM and CoP positions generates a torque driven by gravity (henceforth termed disequilibrium torque) that propels the body forward (Lepers and Brenière, 1995; Michel and Do, 2002; Honeine et al., 2013, 2014). In the frontal plane, the initial CoP excursion in the direction of the future swing leg during APA causes gravity to move the CoM closer to the stance leg (Jian et al., 1993; Elble et al., 1994; Lepers and Brenière, 1995; McIlroy and Maki, 1999). By doing so, the nervous system disengages the swing leg from the ground. During the single-support phase of the first step, the distance between CoM and CoP in the frontal plane and the mediolateral (ML) fall of the CoM shape the positioning of the stepping foot at the moment of its contact with the ground (Lyon and Day, 1997, 2005; Caderby et al., 2014).

Carlsöö (1966) and later Winter (1995) stated that the initial displacement of the CoP in the direction of the swing leg is caused by unloading the stance leg and loading the swing leg, which they argued is produced by the hip abductor activity from the swing side. However, this may not be the sole mechanisms underpinning the disengagement of the future swing limb. When standing, the knee joint is extended due to the backward pull of the soleus on the tibia and to the action of gravity (Woodhull et al., 1985) connected with the anterior position of the CoM with respect to the knee. Therefore, the knee acts as a loadbearing joint (Walker and Erkman, 1975; Freeman et al., 1980). Notably, flexion of the knee of the stance leg during singlesupport is known to occur during gait (Segal et al., 2006; Shamaei et al., 2013). Hence, it may be appropriate to examine whether flexion of the knee also occurs during the APA in order to unload the stance leg during the preparation phase of GI. In this study, we tested the hypothesis that the central nervous system (CNS) employs stance-leg knee flexion as a complementary strategy to swing-leg hip abduction in order to unload the stance leg and displace the CoP in the direction of the swing leg during APA. Furthermore, we postulated that the modulation of the CoP displacement during APA also determines the disequilibrium torque and the lateral fall of the body towards the swing leg during step execution, with the purpose of positioning the stepping foot close to the sagittal plane at its foot contact (FC).

We asked volunteers to start walking from different initial stance widths at their spontaneous forward velocities. Increasing the stance widths prior to step execution has been shown to produce larger CoM and CoP displacements, in order to modulate the distance between CoM and CoP in the frontal plane and consequently the gravity-driven torque during step execution (Lyon and Day, 1997). If our hypothesis is correct, flexion of the knee of the stance leg should occur in the APA phase. The finding of a greater knee flexion of the stance leg accompanied by larger CoM and CoP displacement with a larger initial stance width would corroborate the proposition.

We also expected the ampler CoP displacement, which should occur the larger the initial stance width, to produce a greater gravity-driven torque during step execution. This would in turn increase the velocity of the CoM fall in the frontal plane prompting the stepping foot to land close to the subjects' sagittal plane.

### MATERIALS AND METHODS

### Participants

Fourteen (11 F) healthy young adults participated in the study. Their mean age, mass and height were 29 years (ranging from 21 to 41), 61 kg (47–80) and 1.68 m (1.58–1.80), respectively. As conformed to the Declaration of Helsinki, subjects provided written informed consent to the experiment, which was approved by the ethics committee of Fondazione Salvatore Maugeri (No. 2056CE).

### Tasks and Procedures

Subjects stood with each foot on a distinct force platform (Kistler 9286BA, Winterthur, Switzerland). The position of each heel was equidistant to the border of each platform. Following the start of the acquisition, subjects were instructed to initiate walking in a self-paced mode. This was done to avoid the startle effect on GI, which occurs when subjects are asked to start walking following an acoustic command (Queralt et al., 2010). Subjects were not given any instruction about the speed at which to initiate walking and were left to execute GI at their preferred velocity. They performed three sets of conditions of GI, in which they started from predefined initial stancewidths of 15, 30 and 45 cm, termed Small, Medium and Large, respectively, in the text. There was no explicit instruction about the positioning of the first or successive footsteps. The order of the trials was randomized across subjects. Following GI, subjects were instructed to continue walking for at least six steps. Subjects were not specifically told to execute GI starting from a given leg (Hiraoka et al., 2014), even if in most of the trials subjects initiated gait with the same leg. Subjects performed as many trials as needed in order to achieve at least 12–15 trials per condition, all performed with the same leg. The distribution of the weight over each leg was checked during the experiment so that if the difference exceeded 1 kg before the CoP started moving, the trial was repeated in order to prevent the effects of anticipation on the GI features.

### Data Acquisition

Twenty-three reflective markers were positioned on the subjects' body in the following anatomical locations: vertex, acromion, C7, L5 and bilaterally on lateral head, medial epicondyle of the elbow, head of the ulna, anterior superior iliac spine, greater trochanter, lateral epicondyle of the femur (knee), lateral malleolus, heel and 1st metatarsus-phalangeal joint. The Smart-D optoelectronic system (BTS Bioengineering, Italy) employed 12 infrared cameras that measured the position of the body markers with respect to the laboratory global reference. Anthropometric measurements of the segments of the body were made manually. This allowed for the computation of the three-dimensional position of the body's CoM (Winter, 1993). Bipolar electrodes (Freeemg, BTS Bioengineering, Italy) were employed to wirelessly record bilaterally the electromyogram (EMG) of TA, soleus, gastrocnemius medialis, biceps femoris (BF), semitendinosus (ST), semimembranosus (SM), tensor fasciae latae (TFL) and gluteus medius (nine subjects). Skin preparation and electrode placement were performed according to the SENIAM protocol (Merletti and Hermens, 2000). Optoelectronic, force platform and EMG data were recorded synchronously at acquisition frequencies of 140, 560, 1000 Hz, respectively. Data were stored in a computer for off-line analysis using a custommade program written using Matlab (Mathworks, Natick, MA, USA).

### Analysis of Biomechanical Variables

The global ML CoP position was calculated from the output of both force platforms according to Equation 1:

$$\text{CoP}\_{\text{global}} = \left[ (\text{F}\_1 \ast \text{CoP}\_1) \right. \\ \left. + (\text{F}\_2 \ast \text{CoP}\_2) \right] / (\text{F}\_1 \to \text{F}\_2) \tag{1}$$

where F1 and F2 are the vertical ground reaction forces under each leg, and CoP1 is the ML position of CoP under one leg while CoP2 is the ML position of the CoP under the other. The coordinates of CoP1, CoP2, CoPglobal and the positions of each marker were referred to the same laboratory reference system.

The instant at which GI effectively started (t0) was set as the instant at which the ML CoP position exceeded the baseline by three standard deviations. The instant of the first heel-off (HO) was determined when the vertical position of the heel marker of the swing leg exceeded the value at baseline by 1 mm. The instant when the heel marker of the swing-leg reached its lowest vertical position signaled the instant of the successive FC (see **Figure 1**). Both instants were referred to t0. APA was defined as the time-period spanning from t0 to HO. The step execution phase extended from HO until swing foot landing (FC). The velocity of the CoM in the frontal plane was obtained by the derivation of the ML component of CoM position in time. Step length at FC was measured as the distance between the position of the heel of the stepping foot at t0 and at FC in the sagittal plane. Step width at FC was the distance in the frontal plane between the stance-foot heel marker at t0 and stepping-foot heel marker at its FC. The greater trochanter, knee and malleolus markers on both sides were used to calculate the knee angles in the sagittal plane.

FIGURE 1 | Detection of t0, heel-off (HO) and foot-contact (FC). Panel (A) depicts the time-course of the mediolateral (ML) center of foot pressure (CoP) position. Panel (B) shows the time-course of the vertical position of the heel marker of the swing leg. Both plots were obtained from a single trial of one subject in the Medium stance-width condition. The dots on the curves indicate the time of initiation of CoP movement (t0), HO and FC. Anticipatory postural adjustment (APA) was defined as the time-period between t0 and HO, and step execution as the time-period between HO and FC.

The unloading of the stance leg was measured as the reduction of vertical ground reaction force at the instant of maximum CoP displacement during APA with respect to that measured at t0. The loading of the swing leg during APA was measured as the amount of increase in vertical ground reaction force at the instant of maximum CoP displacement during APA with respect to that measured prior to t0.

The instantaneous disequilibrium torque acting in the frontal plane was calculated as the product of the vertical ground reaction force and the distance between the ground vertical projection of CoM and CoP in the frontal plane (Equation 2). To calculate the torque, the CoP position and the vertical force were down-sampled to 140 Hz. Due to friction between the foot and the floor, the disequilibrium torque is converted to shear force. In order to calculate the shear component of the ground reaction force generated by the torque, the latter was divided by the instantaneous height of CoM with respect to CoP (Equation 3):

$$\text{Torque } = \text{ d} \,(\text{CoM} - \text{CoP}) \ast \text{F} \tag{2}$$

$$\text{Shear force} = \text{Torque/h} \tag{3}$$

where d(CoM−CoP) is the distance between CoM and CoP in the frontal plane, F is the vertical force acting on the CoM and h is the vertical position of CoM with respect to the ground. The impulse during APA and during step execution was measured as the product of the average shear force during APA or during step execution and the respective time periods in which the force was applied (Equation 4). The impulse was then normalized by dividing it by the corresponding subject's mass.

$$\text{Impulse} = \text{Shear force}\_{\text{Avg}} \* \Delta t \tag{4}$$

### Analysis of EMG Activity

To calculate the start and end of EMG activities, the synchrosqueezed wavelet transforms of the raw EMG traces were calculated using the Morlet wavelet (Daubechies et al., 2011; Iatsenko et al., 2015). The final wavelet transform was composed of 125 frequency bins with a bandwidth of about 1.64 Hz ranging from 40 to 244.8 Hz for each time frame. A control-wavelet-coefficient matrix (154 × 1) was then created by averaging the coefficients that were found in the 25th percentile of the coefficient distribution. Multiple single-tailed Student's t-test was then used to compare each time-frame of the wavelet transform with the control-wavelet-coefficient matrix. Onset of muscle activation was considered the instant when p-value exceeded 0.05 for 50 consecutive time-frames. Offset was considered the instant when p-value was inferior to 0.05 for 50 consecutive time-frames (see **Figure 2**). The amplitude of EMG activity was calculated by rectifying the EMG raw traces, low-pass filtering the signal with a second order Butterworth no-lag filter with a cut-off frequency of 25 Hz, and calculating the area under the curve. Maximal EMG isometric activity of all muscles was measured by blocking the pertinent body segment against a rigid frame and asking the subject to exert a maximal isometric contraction against it for about 3–4 s. The peak activity of EMG was detected. The amplitude of the EMG activity during a timewindow of 1 s centered around the peak activity was then calculated.

### Statistics

We verified the distribution of each parameter by performing a Shapiro-Wilk test. Parameters that did not show a normal distribution were tested using non-parametric methods. Separate repeated-measures ANOVAs were used to test the effect of initial stance-width on the following variables: duration of APA; duration of step execution; anteroposterior (AP) instantaneous velocity of CoM at HO and at FC; maximum distance between CoP and CoM during APA and during step execution; EMG activities of stance-leg soleus, gastrocnemius,

TFL and gluteus medius during step execution; position of the swing-leg heel marker at FC; position of the swingleg hallux marker at FC. Separate 2 (swing − stance) × 3 (Small − Normal − Large) repeated-measures ANOVAs were used to test the statistical difference of the following variables: forward displacement of knee joints during APA; knees flexion during APA. Separate one-way Friedman repeated-measures analyses were used to test, during APA, differences in the amplitude of the swing- and stance leg TA EMG activity; effect of initial stance-width on the activity of the swing-leg TA activity; effect of initial stance-width on the activity of stance-leg tibialis activity; effect of initial stance-width on the activity of the swing-leg TFL. Pearson's method was used to test the linear relationship between the following variables: unloading and loading of the stance and swing legs, respectively, and the maximum displacement of CoP during APA; stanceleg knee forward displacement and stance-leg knee flexion; stance-leg knee flexion and maximum displacement of CoP during APA; amplitude of TA activity and knee flexion of the stance leg during APA; normalized impulse calculated during APA and normalized impulse during step execution; normalized impulse during step execution and ML CoM velocity at FC; normalized impulse during step execution and step width at FC. Hyperbolic fitting was used to determine the relationship between the TFL and TA activity in each of the three conditions. Linear and hyperbolic relationship were done using Sigmaplot (Systat software Inc., San Jose, CA, USA). Post hoc analyses of variables following a normal distribution were made by the Fischer's LSD test. The Wilcoxon signed-rank test was used to test non-normally distributed variables. The level of significance in all tests was set at p < 0.05. The software Statistica (StatSoft, Tulsa, OK, USA) was used.

### RESULTS

### Global Kinematics

As expected, prior to stepping, CoP was initially displaced in the direction of the swing leg while CoM moved in the opposite direction. **Figure 3A** shows the time-course of the mean curves of the ML CoP and CoM positions in the three stance-width conditions of a single subject (mean curves were obtained by averaging 15 trials). The instant t = 0 s, which is referred to as t0 in the text, indicates the instant at which the ML CoP position starts moving towards the swing leg. As can be seen in the Figure, prior to HO, the CoP is displaced towards the swing leg and the CoM is moved, with a delay, in the direction of the stance leg. Then, the CoP starts moving towards the stance leg. Next, around mid-stance, the CoM lateral excursion peaks and starts moving towards the future stance leg in anticipation of the second step.

The distance between CoP and CoM in the frontal plane was measured at two distinct moments: the instant when CoP lateral excursion peaks during APA and the instant when CoM reaches its maximum displacement during step execution (as indicated by the arrows in **Figure 3A**). Their grand means and standard deviations are shown in **Figures 3B,C**. The ANOVA showed a significant effect of the initial stance-width on the maximal distance between CoP and CoM during APA (F(2,26) = 156.6, p < 0.001), and on the maximal distance between CoP and CoM during step execution (F(2,26) = 153, p < 0.001). Post hoc analyses showed that the maximal distance between CoP and CoM during APA and during step execution were the lowest in the Small and the greatest in the Large stance-width condition (p < 0.001 for all comparisons). The CoP displacement during APA was not significantly correlated with the subjects' height

TABLE 1 | Global gait initiation (GI) variables.

∗ Indicates significant difference, p < 0.05.

**Table 1** contains the grand mean and standard deviation of the duration of APA, the duration of step execution, the instantaneous forward velocity of the CoM at the time instant of HO, and the forward velocity of CoM at the time instant of FC. Repeated-measures ANOVA showed no effect of initial stance width on the duration of APA (F(2,26) = 2.5, p = 0.1). The instantaneous forward velocity of CoM measured at the instant of HO was also comparable between the three conditions (F(2,26) = 1.1, p = 0.35). The ANOVA showed an effect of initial stance width on the duration of step execution (F(2,26) = 11, p < 0.001) and the instantaneous forward CoM velocity measured at the instant of FC (F(2,26) = 14.7, p < 0.001). Post hoc analysis showed that both duration of step execution and forward velocity of CoM at FC were smaller in the Large stance-width condition with respect to the Small and Medium conditions (p < 0.001).

### CoP ML Displacement and Flexion of the Knee of the Stance Leg

**Figure 4** shows the time-course of the ML CoP position (panel **A**) and the vertical ground reaction force (Panel **B**) under each foot. The traces represent a single trial obtained in each of the three stance-width conditions (Small, Medium and Large). The dots on the curves represent the moment at which the CoP displacement peaked. The loading of the swing and the unloading of the stance leg were accompanied by the displacement of CoP in the direction of the swing leg. **Figure 4C** shows a scatter plot of the maximum displacement of CoP as a function of the sum of the unloading and loading of the stance and swing leg (measured peak to peak). Three distinct linear relationships were obtained between the unloading of the stance leg and the maximum displacement of CoP during APA (Small: r 2 = 0.66, Medium: r 2 = 0.49, and Large: r 2 = 0.59). The relationships diverge because the position of the CoP in the frontal plane is not only caused by the amplitude of the vertical ground reaction force under each leg, but is also dependent on the initial stance width (see Equation 1).

**Figure 5A** shows a stick diagram of the lower limbs taken at different time-intervals in the sagittal plane. The trial seen in this Figure is the same Medium stance-width trial used in **Figure 4**. **Figures 5B,C** show the time-course of the knee AP position of the stance and swing leg, respectively. **Figures 5D,E** show the time-course of the knee angle of the stance leg and swing leg, respectively. The dots on the curves represent the moment of maximal CoP displacement. As can be seen in the Figure, at t0, i.e., while still standing, both knees are positioned behind the vertical position of CoM, a circumstance that lets gravity extend the knees. Following t0, the stance-leg knee is displaced forward so that it moves anteriorly to the CoM, favoring gravity to flex the knee. Meanwhile, the swing-leg knee is more or less stationary. The stance-leg knee remains anterior to the CoM during APA. Following foot-off of the swing leg, the CoM advancement places the CoM in front of the stance-leg knee so that the action of gravity halts the knee flexion or in some cases extends it slightly.

The grand mean and standard deviation of the AP displacements and flexion angles of the knees at the moment of maximal CoP displacement, relative to the initial position (at t0), are provided in **Figures 5F,G**. The ANOVA showed a difference in the forward displacement between the knees of the stance leg and the swing leg (F(1,13) = 57, p < 0.001). Knee forward displacement differed across the three conditions (F(2,26) = 66.2, p < 0.001). A significant interaction between swing- and stance-leg knee forward displacement and initial stance width was also found (F(2,26) = 14.15, p < 0.001). The knee angle of the swing leg was significantly different from that of the stance leg (F(1,13) = 210.4, p < 0.001). There was a general effect of condition on knee angle (F(2,26) = 104.2, p < 0.001). A significant interaction between swing and stance knee angle and initial stance width was also found (F(2,26) = 42.3, p < 0.001).

Post hoc analysis showed that both forward displacement and the flexion angle of the stance-leg knee were significantly different across conditions (p < 0.001). Amplitudes of forward displacement and flexion of the stance-leg were lower for the Small condition and greater for the Large condition compared to Medium (p < 0.001). A linear relationship was found between the forward displacement and the flexion angle of the stance-leg knee (r 2 = 0.52, **Figure 5H**). Finally, a linear relationship was found between the maximum displacement of CoP and the knee flexion of the stance leg (r 2 = 0.64, **Figure 5I**).

### EMG Activity During Gait Initiation

**Figure 6A** shows the time-course of the average traces of the TA, soleus, gastrocnemius medialis, BF, ST, semimenbranosus, TFL and gluteus medius from both legs obtained from one subject during the Medium stance-width condition. The grand mean and standard deviations of the onset and offset of the same muscles (across conditions) are shown by the horizontal bars in **Figure 6B**. When standing, both soleus and BF were

active. About 40 ms prior to t0 both soleus and BF were silenced in both legs while TA was activated bilaterally, concurrently with the swing-leg TFL. The offset of the EMG activity in the stance-leg TA and swing-leg TFL roughly coincided with the moment of HO. Triceps surae and hamstring muscles of the stance leg remained silent throughout the APA phase. The swingleg TA showed two distinct bursts during the step execution phase that lasted until about 100 ms following FC. A brief increase in EMG activity of the triceps surae, hamstrings and TFL of the swing leg was detected about 100 ms prior to HO and ended around the same time as foot-off. During step execution, the beginning of triceps surae activity of the stance leg was recorded slightly prior to HO and ended about 100 ms following FC. The stance-leg TFL was activated about 150 ms prior to HO and was silenced slightly prior to FC. Finally, hamstrings of the stance leg showed a small burst about 100 ms long following HO that usually ended at about mid-singlestance.

Since hamstrings and gastrocnemius muscles are silent during APA, the only candidate responsible for bringing the stance knee forward and initiate knee flexion is the TA muscle that is active during APA. The time-course of the average traces of TA EMG activity of the swing and stance leg of a single subject is provided in the three upper panels of **Figure 7A**. **Figure 7B** shows the medians and the 25th and 75th percentiles of the amplitude of the EMG activity of the TA activity (with respect to maximum isometric contraction) of the swing leg and stance leg during APA. The Friedman repeated-measures test showed that the activity of TA was in general significantly lower in the swing- than stance-leg during APA (χ 2 = 24.4, p < 0.001). The activity of the TA muscle of the swing leg did not differ across the three conditions (χ 2 = 1.28, p = 0.53). However, starting to walk

FIGURE 5 | Knee flexion and CoP displacement during APA. Panel (A) shows stick diagrams of the swing leg (top) and stance leg (bottom) taken at nine discrete instants in the sagittal plane. The stick diagrams represent the same Medium-condition trial as in Figure 4. The dashed lines represent the direction of the CoP-CoM vector. The instants comprise t0, instant of peak ML CoP during APA, HO, foot-off, FC and instants in between. As can be seen at t0, both knees are positioned behind the center of gravity. During APA, the swing-leg knee remains fixed while the ankle joint starts flexing and the stance-leg knee advances ahead of the center of gravity. The time-course of the stance knee position and swing knee position for the three single trials in each condition are found in panels (B,C) respectively. Panels (D,E) show the time-course of the stance-leg and swing-leg knee angle, respectively. The curves in panels (B–E) belong to the same trial. The small circles on the curves indicate the instant at which the maximum displacement of CoP in the direction of the swing leg was reached during APA. Panels (F,G) show the grand means and standard deviations of the forward displacement and flexion of the knee of the swing and stance leg, respectively, measured at the instant at which CoP displacement peaked. Panels (H,I) portray the linear relationship between the forward displacement of CoP and stance knee flexion, and between the stance-knee flexion and ML CoP displacement, respectively.

from different initial stance width had an effect on the activity of the stance-leg TA muscle (χ 2 = 28, p < 0.001). The Wilcoxon matched pair test indicated that the lowest activity of the stanceleg TA muscle was obtained in the Small condition (p < 0.05 for both comparisons) while the greatest activity was achieved in the Large condition (p < 0.05 for both comparisons).

**Figure 7C** shows the time-course of the average traces of the TFL of the swing- and stance-leg during GI in a single subject. The medians and the 25 and 75 percentiles of the amplitude of EMG activity (with respect to maximum isometric contraction) of the swing-leg TFL muscle during APA are shown in **Figure 7D**. The Friedman repeated-measures test showed no effect of initial stance width on the amplitude of EMG activity of the swing-leg TFL (χ 2 = 4.43, p = 0.11) and gluteus medius (χ 2 = 2.6, p = 0.09) during APA. Furthermore, ANOVA showed no difference across conditions in the amplitude of EMG activity during the step execution phase of soleus (F(2,26) = 0.36, p = 0.70), gastrocnemius (F(2,26) = 1.02, p = 0.37), TFL (F(2,26) = 1.97, p = 0.16) and gluteus medius (F(2,16) = 1.53, p = 0.25) of the stance leg.

We also investigated the complementary contribution of hip abduction of the swing side and of knee flexion of the stance side during APA. **Figure 8** shows the TA activity of the stance leg plotted against that of the swing-leg TFL (both normalized to maximum activity during isometric contraction) during APA in the three conditions. A hyperbolic relationship interpolated the data points in the Small (r 2 = 0.25), Medium (r 2 = 0.23) and Large condition (r 2 = 0.24). By looking closely into **Figure 8**, one can also see that the hyperbolic relationship is partly due to the fact that some subjects preferred the hip abductor activity more than stance-knee flexion and vice versa. **Figure 9** shows a scatter plot of the amplitude of the stance-leg TA activity from onset until the peak of CoP displacement and the stanceleg knee flexion at the peak of CoP displacement. A linear relationship was obtained between tibialis activity and knee flexion (r 2 = 0.55).

### Disequilibrium Torque During Gait Initiation

**Figure 10A** shows the average time-course of the shear force calculated by dividing the disequilibrium torque by the instantaneous height of the CoM (black line). For comparison, the gray line indicates the average time-course of the shear force measured by the platform. During APA, the shear force produced by the distance between CoP and CoM in the frontal plane displaced the CoM in the direction of the stance leg (negative values in the Figure). Following HO of the swing leg, the torque started acting in the opposite direction.

The impulse theorem allows to quantify the amount of force generated during a certain time interval. Therefore, the impulse derived from the shear force calculated from the disequilibrium torque (see ''Materials and Methods: Analysis of Biomechanical Variables'' Section) has been used to describe the effect of the torque during APA and step execution on the kinematics of GI in the frontal plane. A linear relationship was obtained between the impulse values calculated from the shear force during APA and those calculated during step execution (r 2 = 0.59; **Figure 10B**). In addition, the impulse calculated during step execution was correlated with the instantaneous velocity of CoM (r 2 = 0.4; **Figure 10C**) and step width at FC (r 2 = 0.46; see **Figure 10D**).

**Figure 10E** shows the grand mean and standard deviation of the AP and ML position of the heel and hallux markers at the instants of t0 and FC. The AP position of the markers has been calculated relative to the position of the heel markers at t0 (both feet on ground). The ML position of the markers was computed with respect to the subjects' sagittal plane, calculated as the plane passing between the two anterior superior iliac spines slightly prior to t0. The position of the heel and the hallux markers at FC with respect to the medial line were not different across the three conditions (F(2,26) = 2.27, p = 0.12 and F(2,26) = 0.33, p = 0.72, respectively). Step length was also comparable across the three conditions (F(2,26) = 0.21, p = 0.81).

### DISCUSSION

Human gait is a state of controlled disequilibrium, in which anticipating the position of the body with respect to the ground is critical to avoid destabilizing torques (Bauby and Kuo, 2000). It is fragile, because it can be disturbed by many bodily conditions, including even minor degradations of the sensory information or motor output or both (Mazzaro et al., 2005; Nardone et al., 2014), as well as by cognitive tasks (Lajoie et al., 1993). Further, unlike the hopping gait of kangaroos that is characterized by symmetrical leg jumping action, human bipedal gait is asymmetrical and involves alternate single-support and double-support phases. Hence, the asymmetry of human gait requires substantial balance control in the frontal plane in order to prevent lateral falls (Thorstensson et al., 1984; MacKinnon and Winter, 1993; Orendurff et al., 2004; Sozzi et al., 2013; Wang and Srinivasan, 2014).

During GI, the CNS is confronted with the difficult task of transiting between a symmetrical quasi-static state to an asymmetrical dynamic state (Delafontaine et al., 2015). Indeed, to start walking appropriately, the CoM is moved to a position favorable to gait prior to lifting the future swing leg (Carlsöö, 1966; Brenière and Do, 1986; Brenière et al., 1987; Brenière and Do, 1991; Jian et al., 1993; Elble et al., 1994). On the one hand, the backward shift of CoP, which is responsible for the forward movement of the CoM, is caused mainly by activation of TA and decrease in soleus activity (Crenna and Frigo, 1991; Lepers and Brenière, 1995; Brenière, 2001; Honeine et al., 2013, 2014). On the other hand, the initial lateral shift of CoP in the direction of the swing leg causes the CoM to move toward the stance leg. Carlsöö (1966) and Winter (1995) argued that swing-leg abductor activity during APA unloads the stance leg and loads the other which in turn produces a lateral displacement of the CoP. However, flexing the knee of the stance leg during APA can also help unloading the swing leg. It has been already shown that the knee is moderately flexed in the stance leg during walking. This knee flexion prevents higher rate of loading during gait, and translates to attenuated rates of loading and peak vertical ground reaction force in healthy adults (Riskowski et al., 2005; Riskowski,

EMG activity. Panel (A) shows the average time-course of one subject (Medium condition) of the rectified and low-pass filtered EMG traces (Fcut = 25 Hz) of the tibialis anterior (TA), soleus (Sol), gastrocnemius medialis (Gas), biceps femoris (BF), semitendinosus (ST), semimembranosus (SM), tensor fasciae latae (TFL) and gluteus medius muscles of the swing side (blue, left) and stance side (orange, right). t0, HO and FC are indicated by the dashed lines. Panel (B) shows the grand means and standard deviations of all subjects of the onset and offset across the three conditions of the same muscles' activity calculated with respect to t0.

FIGURE 7 | EMG activity of TA and TFL. This figure contains information about the activity of tibialis activity and TFL muscles of both sides during GI. Panels (A,C) show the average envelope traces of TA and TFL, respectively, of a single subject in the three conditions (from top to bottom: Small, Medium and Large) of the swing leg (dashed line) and the stance leg (solid line). Panels (B,D) show the medians along with the 25th and 75th percentiles of the amplitudes of TA activity of the swing and stance legs and of TFL activity of the swing leg during APA, respectively (values are normalized to maximum isometric contraction). TA activity of the swing leg during APA was not affected by the initial stance width. However, TA activity of the stance leg was larger the greater the initial stance-width. The amplitude of TFL EMG activity was only moderately affected by the initial stance width.

2010). Hence, we hypothesized that the stance-leg knee flexion, which is part of the normal motor program for walking, could also be exploited in order to unload the stance leg during the preparation of GI.

### Knee Flexion of the Stance Limb During APA

In line with Lyon and Day (1997), initiating gait at increasing stance widths causes greater displacement of the CoP in the direction of the swing leg and CoM in the opposite direction during APA. Our results also confirm the findings of Carlsöö (1966) and Winter (1995) in that the CoP displacement during APA is caused by unloading and loading the stance and swing legs, respectively (see **Figure 4**). In our hands, the greater excursions of CoP and CoM occurred without significant modifications of the global kinematic variables of GI (see **Table 1**) and most notably the duration of APA. This facilitates the comparisons across conditions without the need to normalize in time.

As can be seen in **Figure 5**, at t0 both knees are placed behind the vertical projection of CoM. However, during APA, the stance knee is displaced forward, placing the joint anterior to the CoM vertical projection in the sagittal plane allowing gravity to participate in flexing the knee. Meanwhile, the swingleg knee position and angle remain more or less constant. The stance-leg knee forward advancement and flexion augmented with increasing stance width. The amplitude of the flexion of the stance-leg knee was also correlated with the lateral displacement of CoP. The linear relationship between stanceleg knee flexion and lateral displacement of CoP is in line with our hypothesis that stance knee flexion unloads the stance leg and thus participates in shifting the CoP in the direction of the swing leg.

Hamstrings and gastrocnemius activity are associated to knee flexion during the double stance phase of gait (Goldberg et al., 2004). However, none of those muscles were active during flexion of the stance-leg knee in early APA. Moreover, BF that shows tonic activity while standing becomes silent during APA (see **Figure 6**). The reason might be that hamstrings also extend the hip. Hip extension during GI should potentially slightly restrict forward movement and is therefore undesirable. Conversely, the ankle plantarflexion produced by gastrocnemius activation would impede the backward CoP displacement required for generating forward motion. Slightly prior to t0, soleus and BF muscles are silenced bilaterally followed by TA activation (**Figure 6**). As more appropriately stated by Zajac and Gordon (1989), ''at times, such as in standing, muscles crossing the ankle extend (soleus) or flex (TA) the knee much more that they flex and extend the ankle''. In this study, the amplitude of the TA muscle of the stance leg is greater than that of the swing leg. Furthermore, the amplitude of the stance-leg TA activity increases with larger stance-widths (see **Figure 7**). This result suggests that the reduction in soleus tonic activity and the activation of the TA of the stance leg move the stance-leg knee forward with respect to the CoM position in the sagittal plane, thereby favoring gravity to flex the stance knee. Indeed, a linear relation between the amplitude of EMG activity of TA of the stance leg and flexion of the stance-leg knee is found here (**Figure 9**), strengthening the hypothesis that the stanceleg TA participates in displacing the CoP in the direction of the swing leg during the preparation phase of GI. It is to be noted that feet plantar afferents can influence the activity of TA and soleus during APA when raising one leg quickly (Do and Gilles, 1992). Cutaneous afferents can sense the augmentation in the shear force under the feet (Abbruzzese et al., 1996; Choi et al., 2016) that occurs with increasing stance width (Carmines and MacMahon, 1992). The changes of the cutaneous afferent input, in the different conditions, could have contributed to the modulation of stance-leg TA activity that participates in the lateral displacement of CoP during APA.

Following lift-off of the swing foot, the forward momentum of CoM places the latter anterior to the stance-leg knee, as occurs during the single-support phase of steady-state gait (Liu et al., 2008). This causes gravity to extend the stance knee thereby halting the flexion that occurred during APA. Furthermore, the activity of triceps surae and the hamstring muscles, increases during step execution. Those muscles could also be implicated in checking the knee flexion during single support.

### The Complementary Action of Hip Abduction and Stance Knee Flexion

Starting gait with different stance widths has no significant effect on the amplitude of hip abductor EMG activity of the swing leg during APA, albeit a slight tendency of some subjects (9 out of 14) to decrease hip abductor activity was observed when starting gait from a large stance width. Remarkably, a hyperbolic relationship binds the amplitude of stance-leg TA activity with that of the hip abductor muscles of the stance leg in each of the three conditions (see **Figure 8**). Some subjects relied more on swing-leg hip abductor activity and others on stance-leg dorsiflexor activity, while most relied on both rather equally. It is to be noted that the decrease in hip abductor activity in the Large condition of the nine subjects mentioned above is accompanied by a systematic increase in stance-leg knee flexion. A possible explanation is that due to biomechanical constraints, the hip abduction strategy is less efficient when starting from a large stance width. Conclusively, the actions of stance-knee flexion and swing-leg hip abduction appear to be complementary and synergistic in unloading the stance leg and loading the swing leg during APA. The coordination of the two strategies would result in more efficient and flexible ML displacement of the CoP in the direction of the swing leg.

### The Effects of Modulation of ML CoP Displacement During APA on the Execution of the First Step

By modulating hip abduction and stance-leg knee flexion during APA, the CNS efficiently controls the distance between CoP and

FIGURE 9 | Relationship between stance-leg TA EMG activity and knee flexion. This shows a scatter plot of the stance-leg knee flexion angle plotted against the amplitude of stance-leg TA activity during APA (normalized to maximum isometric contraction). A linear relationship was found to bind the two variables (y = 0.07x + 1.34) suggesting that stance-leg knee flexion might be modulated through TA activity of the same leg.

CoM in the frontal plane and consequently the disequilibrium torque during APA. Moreover, due to friction between the floor and the stance foot, the torque is converted into shear force that in turn displaces the CoM and places it just medially with respect to the stance foot during the single-stance phase of the execution of the first step (see **Figure 3**). In line with Lyon and Day (2005), our results show that the subjects modulate the CoP displacement during APA across conditions in order to control the ML distance between CoM and CoP during the step-execution phase. More precisely, the small displacements of CoP during the Small stance-width condition produce a small ML CoM-CoP distance during step execution, while the ample displacements of CoP during the Large stance-width condition produce a greater ML CoM-CoP distance (see **Figure 3**). Consequently, the ML disequilibrium torque and the CoM velocity during step execution are greater when larger the initial stance-width. The greater velocities of the CoM during step execution measured under larger initial stance-width causes the stepping foot to land at a larger distance with respect to the stance foot (Caderby et al., 2014). This causes the foot to be placed close to the subjects' mid-sagittal plane at the FC in all three conditions, so that subjects subsequently progressed easily along their initial straight-ahead line (see **Figure 10**). This result is interesting, because it shows that, already at the first step, subjects tend to place the foot in the appropriate position for performing the next sets, regardless of the initial postural attitude. In Honeine et al. (2014) we showed that by modulating the CoM and CoP distance in the sagittal plane the CNS sets step length, the antero-posterior velocity of CoM and the duration of the first step. Here, we complete those results by showing that by controlling the disequilibrium torque in the frontal plane during APA, the CNS determines also the ML velocity of CoM and the ML position of the swing leg at the instant of first FC.

FIGURE 10 | ML disequilibrium torque and step execution parameters. The time-course of the shear force calculated from the disequilibrium torque (black trace) and measured from the platform (gray trace) are shown in panel (A) (average of 15 trials). The vertical dashed lines indicate HO and FC events. The negative values during APA indicate that the torque is pushing the body in the direction of the stance side. The positive values during step execution designate that the torque is acting in the direction of the swing leg. Panel (B) shows a scatter plot representing a linear relationship between the normalized (divided by mass) impulse calculated during APA and the normalized impulse computed during the step execution (y = −0.98x + 0.12). Panel (C) shows a scatter plot representing the linear relationship that was found between the normalized impulse during step execution and the instantaneous ML CoM velocity measured at FC (y = 0.37x + 0.05). Panel (D) shows a scatter plot representing the linear relationship found between the normalized impulse calculated during step execution and step width (y = 0.32x + 0.03). Panel (E) shows the grand means and standard deviations of the position, with respect to the sagittal plane (dotted line), of the heel and hallux markers in ML and anteroposterior (AP) direction at t0 and at FC in the three conditions. As can be seen, the subjects placed the foot at about the same position and with the same orientation close to the sagittal plane at FC in all three conditions.

### Limitations

The initial stance width for each condition (15, 30 and 45 cm) was fixed for all the subjects. Due to anthropometric differences between subjects, a same width of the base of support could provoke different biomechanical constraints on the CoP displacement. Nonetheless, possibly because of the large inter-subject variability, the maximum displacement of the CoP towards the swing leg during APA was not significantly correlated with height or width of the pelvis, measured as the distance between the two anterior superior iliac spines.

Furthermore, the results of this study do not permit to make a quantitative statement about which strategy (hip abduction or stance-leg knee flexion) is mechanically more effective in displacing the CoP towards the swing leg during APA. To do so, in our opinion, this would require the calculation the contribution of the hip abduction and knee flexion torques to the CoP displacement, which is beyond the scope of this current article. One would also consider that different initial stance widths can slightly modify the angle of the tendon insertion between the hip abductors and femur. Therefore, different abduction forces could be generated for the same level of EMG activity, so that comparing EMGs across condition should be done with care.

### Final Considerations

Our results support the hypothesis that both hip abduction and stance-leg knee flexion participate in unloading the stance leg and displacing the CoP in the direction of the swing leg during GI. On the one hand, hip abduction is caused by activation of the hip abductors of the swing leg (Carlsöö, 1966; Winter, 1995). On the other hand, stance-leg knee flexion is favored by the activation of TA and silencing of soleus of the same leg. The flexion of the knee during APA could be seen as an adaption of the CNS to facilitate and increase the robustness of the ML balance control process. Consequently, when ML balance control is examined in patients suffering from motor problems during GI, both hip abduction and stance knee flexion should be taken into account, in addition to initial stance width (Goodworth et al., 2014). Knee-flexion control in the frontal plane during APA

### REFERENCES

could be inadequate in patients suffering from gait problems such as cerebral palsy, Parkinson's disease (Hiraoka et al., 2006; Hiraoka and Abe, 2007; Okada et al., 2011a,b; Mazzone et al., 2014), stroke, amputees (Aruin, 2016).  Jacobs et al. (2009) found that during GI, knee trembling causes multiple APAs that are observable as a right-left leg loadingunloading cycles. Interestingly, the alternating unloading and loading of the legs was accompanied by similar alternating activation and deactivation of right-left TA (see Figure 2 in Jacobs et al., 2009). Therefore, knee trembling in Parkinson's disease patients might be preventing them from displacing CoM correctly towards the stance leg and thus not allowing them to initiate gait properly. Indeed, the smaller ML CoP displacement during APA and larger step width of the first step at GI have been observed in Parkinson's disease (Okada et al., 2011a,b). This could be in part associated with inappropriate knee flexion. Therefore, correcting the knee flexion angle of the stance leg during APA with a smart orthosis could possibly be an effective solution for enhancing GI and possibly steady-state gait in these patients.

### AUTHOR CONTRIBUTIONS

J-LH contributed with project creation, data collection, data analysis and drafted the manuscript. MS contributed with project creation, data analysis. OC contributed in data collection, data analysis. M-CD contributed with project creation and data analysis. All authors discussed the results and participated in the revision of the manuscript.

### FUNDING

This study was supported in part by the Ricerca Finalizzata grants (GR-2009-1471033 and RF-2011-02352379) from the Italian Ministry of Health and by the PRIN grants (2009JMMYFZ and 2010MEFNF7) from the Italian Ministry of University.

frontal plane. Clin. Neurophysiol. 124, 1175–1186. doi: 10.1016/j.clinph.2012. 12.001

**Conflict of Interest Statement**: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2016 Honeine, Schieppati, Crisafulli and Do. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution and reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# The Throw-and-Catch Model of Human Gait: Evidence from Coupling of Pre-Step Postural Activity and Step Location

Matthew J. Bancroft and Brian L. Day\*

Sobell Department of Motor Neuroscience and Movement Disorders, UCL Institute of Neurology, University College London, London, UK

Postural activity normally precedes the lift of a foot from the ground when taking a step, but its function is unclear. The throw-and-catch hypothesis of human gait proposes that the pre-step activity is organized to generate momentum for the body to fall ballistically along a specific trajectory during the step. The trajectory is appropriate for the stepping foot to land at its intended location while at the same time being optimally placed to catch the body and regain balance. The hypothesis therefore predicts a strong coupling between the pre-step activity and step location. Here we examine this coupling when stepping to visually-presented targets at different locations. Ten healthy, young subjects were instructed to step as accurately as possible onto targets placed in five locations that required either different step directions or different step lengths. In 75% of trials, the target location remained constant throughout the step. In the remaining 25% of trials, the intended step location was changed by making the target jump to a new location 96 ms ± 43 ms after initiation of the pre-step activity, long before foot lift. As predicted by the throw-and-catch hypothesis, when the target location remained constant, the pre-step activity led to body momentum at foot lift that was coupled to the intended step location. When the target location jumped, the pre-step activity was adjusted (median latency 223 ms) and prolonged (on average by 69 ms), which altered the body's momentum at foot lift according to where the target had moved. We conclude that whenever possible the coupling between the pre-step activity and the step location is maintained. This provides further support for the throw-and-catch hypothesis of human gait.

Keywords: postural balance, gait initiation, motor activity, humans, gait, biomechanical phenomena, locomotion, walking

### INTRODUCTION

When taking a step, postural activity usually precedes the lift of the stepping foot by around half a second. It modulates the force between the feet and ground to accelerate the body sideways and forwards, and is observed during single steps as well as during locomotion (Carlsöö, 1966; Mann et al., 1979; Crenna and Frigo, 1991; Jian et al., 1993; MacKinnon and Winter, 1993). What is the function of this pre-step activity? One possibility is that its job is to move the body mass directly over the upcoming stance foot, allowing the stepping

#### Edited by:

Eric Yiou, University of Paris-Sud, France

#### Reviewed by:

John Leonard Zettel, University of Guelph, Canada Thomas Robert, Université de Lyon, France

> \*Correspondence: Brian L. Day<EMAIL_ADDRESS>
Received: 16 August 2016 Accepted: 29 November 2016 Published: 22 December 2016

#### Citation:

Bancroft MJ and Day BL (2016) The Throw-and-Catch Model of Human Gait: Evidence from Coupling of Pre-Step Postural Activity and Step Location. Front. Hum. Neurosci. 10:635. doi: 10.3389/fnhum.2016.00635 foot to be lifted freely without compromising balance. However, this is not what is usually observed during single steps or locomotion. At the instant the stepping foot is lifted, the vertical projection of the body's center of mass (CoM) commonly lies outside and medial to the base of support formed by the stance foot (Jian et al., 1993; MacKinnon and Winter, 1993; Lyon and Day, 1997, 2005). This means that the body is not balanced, but is falling sideways under gravity during a step.

An alternative function of the pre-step activity has been proposed by the throw-and-catch model of human gait (Lyon and Day, 1997). This hypothesis states that the pre-step activity represents a ''throw'', which gives the body a specific position and momentum at the time of foot lift. At this point, the body enters a ballistic phase during the step where it falls under gravity along a trajectory determined by the pre-step activity, just as a ball would after being thrown. The direction and magnitude of the throw is finely tuned to take into account the initial state of the body and the intended final position of the stepping foot. Thus, during the step, the stepping foot swings towards its intended target while at the same time being optimally placed when it lands to ''catch'' the body and regain balance.

The throw-and-catch model predicts that the pre-step activity depends on both the body's initial conditions and the intended step location. In support of this are the findings that the resulting position and velocity of the body's CoM at the point of foot lift depend on both the initial stance width (Lyon and Day, 1997) and whether the step is to a forward or diagonal location (Lyon and Day, 1997, 2005), but are not influenced by the final position of the trailing foot (Lyon and Day, 2005). However, the predicted coupling between the pre-step activity and the intended step location has been shown to be breakable under certain circumstances. If the intended step location changes after the stepping foot leaves the ground, for example by shifting the position of a target, it is possible for the foot to land at a location different to that originally planned (Reynolds and Day, 2005, 2007; Kim and Brunt, 2009, 2013; Tseng et al., 2009; Nonnekes et al., 2010). This ability to de-couple the pre-step activity from the step location represents a challenge to the throw-and-catch hypothesis.

Here we investigate the strength of coupling between the pre-step activity and the step location under conditions previously unexplored. First, we study stepping onto five (for each foot) possible target locations, either demanding different step directions with the same step length, or demanding different step lengths with the same direction. The throw-and-catch hypothesis predicts that the pre-step activity will differ and be unique for each target location. Second, we occasionally make the central target jump to another location just after the pre-step activity has been initiated, but before the stepping foot has been lifted. This timing of target jump potentially allows the pre-step activity to be adjusted should it be advantageous to do so. The crucial question, therefore, is whether the pre-step activity is adjusted to take account of the new target location, or is unchanged such that all necessary adjustments are made later during the step, similar to that observed with later target jumps. Support for the throw-and-catch hypothesis would be obtained if: (1) the pre-step activity were modulated by the target jump; and (2) the modulation were dependent on the final location of the target.

### MATERIALS AND METHODS

Ten human subjects (7 male; 24 ± 2 years; 64 ± 7 kg; mean ± standard deviation (SD)) gave written informed consent to participate in the experiment and reported no known neurological, sensory, muscular or orthopedic disorders. The experiment was approved by the UCL Research Ethics Committee and conformed to the Declaration of Helsinki. Participants were provided a written information sheet detailing the experimental procedures. Further to this, the experimental procedures were explained verbally. All subjects were naïve to the purpose of the study.

### Protocol

Subjects performed a step onto a floor-bound target. Prior to the step, subjects stood barefoot and still with both feet parallel. The medial borders of the feet were separated by 15 cm. This starting position was chalk-marked to ensure a consistent starting location for all steps. The positions of the targets required a forwards movement, with five targets located on each of the left and right sides (**Figure 1**). Subjects were instructed to step as accurately as possible to the target, and bring the trailing foot alongside. An accurate step to each target was self-defined by all participants prior to the experiment. To achieve this, participants placed the appropriate foot over each of the 10 targets without time constraints in a manner they deemed accurate. For these accuracy trials, subjects were allowed to adjust their foot's position until they felt it represented an accurate step to a target. The step was redone if the subject or experimenter felt it necessary. Subjects were instructed to land their foot in this way for all subsequent steps and the position of their foot when it landed was compared to this ideal position. By instructing subjects to step accurately to the targets, rather than as quickly as possible, we sought to minimize variability in the placement of the stepping foot and thereby minimize variability in the step location.

The final position of the stepping foot was emphasized as being paramount and non-adjustable following foot landing. After the stepping foot landed subjects were required to step with the trailing foot and bring it alongside their stepping foot. The final position of the trailing foot does not affect the performance of the initial step (Lyon and Day, 2005) so no specific instruction was given as to where to place the trailing foot. However, subjects were encouraged to finish the step in a balanced state, similar to which they started. When a target illuminated to the left, a left-foot leading step was required and when a target illuminated to the right, a right-foot leading step was required. Multiple targets on both left and right sides were used to prevent prediction of target jump location or stepping side, thereby ensuring unbiased conditions at the time of target presentation and target jump.

A trial began with an audible beep, which was followed by a random delay and illumination of a step target. Illumination of the target acted as a cue for the subject to initiate a step

out of the page. Subjects were instructed to step to a visually-presented target (blue circles). In most trials a target illuminated on either the left or right side and its location did not change (B). In some trials the target jumped 15 cm from the central target to one of four peripheral targets (medial, lateral, distal or proximal) shortly after initiation of the pre-step activity (C). (D) Probability tree outlining the number of trials and probability per condition. A target jump occurred with a probability of 0.33 after illumination of the central target.

to its location in their own time. The stepping targets were oriented so that step length and direction could be independently manipulated (**Figure 1A**). That is, for medial, central and lateral targets, step length was constant (35 cm) but step direction was different (0◦ , 25◦ , 50◦ forward of the stepping foot respectively). Equally, for proximal, central and distal targets, step direction was constant (25◦ forward of the stepping foot) but step length was different (20 cm, 35 cm, 50 cm respectively).

### Experimental Conditions

In 75% of trials, one of the five targets on either the left or right side was selected pseudo-randomly and illuminated for the duration of the step (constant condition; **Figure 1B**). The central target was selected most frequently (probability = 0.67), whereas the peripheral targets were selected less often but each with equal frequency (probability = 0.083).

In 25% of trials, the central target was illuminated on either the left or right side and was made to unpredictably jump to one of its four peripheral targets selected pseudorandomly (jump condition; **Figure 1C**). The peripheral targets were selected with equal frequency when a target jumped to a new location (probability = 0.25). After illumination of the central target, the probability of it jumping was 0.33.

The target jump was achieved by simultaneously extinguishing the central target and illuminating one of the four peripheral targets. Target jumps were triggered when the difference in vertical force between the stepping and trailing foot sides exceeded 80 N. This related to a mean (SD) of 7.8 (0.9)% (range: 5.7%–8.8%) of total body weight. Due to inherent electrical transmission delays, the new target would emit light 16.5 ms after the trigger signal. This delay is accounted for in all reported data. The new target appeared shortly after the initiation of the pre-step activity (mean (SD) latency: 96 (43) ms), long before the stepping foot lifted. The locations of the new targets meant that the required magnitude of foot adjustment remained constant (15 cm) but either step direction (medialor lateral-jump) or length (distal- or proximal-jump) required modification.

A total of 160 trials were completed and performed in 10 blocks of 16 steps. The number of trials and its probability for each condition is summarized in **Figure 1D**.

### Apparatus

Targets were circular (2.5 cm diameter) and illuminated via electroluminescent paper (Light Tape UK Limited, Barnsley, Yorkshire, UK) within a low-profile display on the floor in front of the subject. Ambient light conditions were dim (<0.1 Lux; Isotech 1332A Digital Illuminance Meter, Southport, Merseyside, UK) to eliminate potential distractors and ensure that the target light was compelling. Three infrared-emitting diode markers were placed at the base of the first metatarsal and head of the first (hallux) and fifth metatarsals of each foot. Marker positions were tracked at 200 Hz by two motion capture units comprising six ''cameras'' (Codamotion cx-1, Charnwood Dynamics, Leicestershire, UK). At the start of a trial, subjects stood with each foot over separate force platforms (9281C1, Kistler, Winterthur, Switzerland) which were embedded in the floor. Force was acquired at 1000 Hz.

### Data Analysis

Both marker position and force data were digitally low-pass filtered using a zero-lag, second order Butterworth filter with 15 Hz and 30 Hz cut-off frequencies respectively. An anti-aliasing analog filter was used on force data prior to this.

The two force platforms were summed to evaluate the net force acting on the body in three-dimensions. From Newton's Second Law of Motion, the acceleration of the body's CoM was calculated by dividing net force by a subject's mass. The net acceleration of the body's CoM while the subject stood still (from the beginning of a trial until target illumination) was assumed to be zero and used as a baseline for the remainder of the trial. CoM velocity at foot lift, which has previously been shown to be an important variable in stepping (Lyon and Day, 1997, 2005), was then estimated by numerical integration of the CoM acceleration during the pre-step activity (trapezoidal method).

Typically, the center of pressure initially moves laterally towards the stepping side heel during the pre-step activity (Mann et al., 1979; Breniere et al., 1987). Therefore, the pre-step activity's initiation was calculated as the first point after target illumination that the medio-lateral (ML) center-of-pressure velocity towards the stepping foot exceeded 5 cm.s−1 for at least 50 ms. Stepping foot lift was the first point that the stepping side's vertical force went below 1% of total body weight. Pre-step activity duration was the time from its initiation to stepping foot lift. The time the stepping foot landed was the first point after foot lift that the ML, antero-posterior (AP) and vertical speed of the stepping foot hallux marker went below 2 cm.s−1 . Speed was calculated as the absolute value of the first derivative of marker position. The final position of the stepping foot was the mean position of the three foot markers upon landing.

To investigate whether the pre-step activity was modulated when the intended step location changed, the body's horizontal (AP and ML) motion in jump trials was compared to constantcentral (the initial target in a jump trial) steps over time after alignment. All trials were aligned to the initiation of the pre-step activity and CoM acceleration was differentiated to calculate jerk. Two-dimensional 95% confidence intervals (confidence ellipses) were then generated at each time point for the constant-central condition. **Figure 2** shows an example of this for one subject. The latency of any modulation was defined as the first time, at least 100 ms after a target jump, that a jump trial diverged from the constant-central confidence interval. The delay of 100 ms after a target jump was chosen as this relates to the shortest reported latencies to adjust lower limb trajectory or modulate ground reaction forces in visuomotor tasks (Reynolds and Day, 2005, 2007; Leonard et al., 2011). Modulation latency was measured for each jump condition and subject.

Sixteen jump trials (1% of total trials, 4% of jump trials) were excluded from the analysis due to the target jump being triggered

either before the initiation of the pre-step activity or shortly before the stepping foot lifted.

### Statistical Analysis

No bias was found between the left and right sides or dominant and non-dominant legs in the latency of the target jump from the pre-step activity's initiation, final position of the stepping foot, CoM velocity at foot lift, or duration of the pre-step activity (all P > 0.05). Therefore left-sided steps were reflected about the laboratory AP axis and combined with right-sided steps. All steps are reported as if they were right-sided.

Foot placement and CoM velocity at foot lift contained both ML and AP components and as such are multidimensional variables requiring analysis by multidimensional statistical methods. Ideally, a repeated-measures ANOVA capable of analyzing differences in multidimensional variables would be used to test whether the foot landed accurately or whether CoM velocity differed with target location. However, to the best of our knowledge, no such test exists. Therefore, paired t-tests for multidimensional variables (one-sample Hotelling's tests; Batschelet, 1981; Zar, 2010) were used to distinguish differences between conditions. Using multidimensional statistical methods, rather than examining the data in two dimensions separately, is advantageous as power is increased (Batschelet, 1981) and no a priori assumptions are required about which dimension of the data an effect is expected. CoM velocity at foot lift was paired within-subject by subtracting the mean of the constant-central condition from all other stepping conditions.

Unidimensional temporal variables (pre-step activity duration and modulation latency) were submitted to repeatedmeasures ANOVA with the within-subject factor of step location. ANOVAs were performed using SPSS statistical software (IBM Corporation, New York, NY, USA). Hotelling's tests and all other analyses were performed using custom written Matlab scripts (The Mathworks Inc., Natick, MA, USA). Statistical significance was set at an alpha level of 0.05 after Bonferroni correction for multiple comparisons. Greenhouse Geisser correction was used in ANOVAs when the assumption of sphericity was violated. Normality of data analyzed by Hotelling's tests was confirmed by Mardia's test of skewness and kurtosis (Mardia, 1970).

### RESULTS

### Steps When the Target Location Remained Constant

All subjects were able to land the stepping foot on or near the target when its location remained constant. On average, the final position of the foot was not different to each subject's self-defined ideal step, which was the case when stepping to all target locations (**Figure 3**, black symbols; all T 2 (2,8) < 5.3, P > 0.7). This indicated that a successful step was taken to all targets.

In order to land the foot in this position, all subjects produced pre-step activity that accelerated the body sideways, away from the stepping foot, and forwards. The mean (SD) time from the pre-step activity's initiation until foot lift was

561 (89) ms and was not consistently affected by the step location (F(4,36) = 0.8, P = 0.520). However, the pre-step activity that accelerated the CoM differed with target location (**Figure 4**). **Figures 4A,C** depict the mean CoM acceleration for one subject and shows activity before the lift of the stepping foot. **Figures 4B,D** show that for this subject the pre-step acceleration resulted in the body gaining velocity that was specific for each intended step location. For the group analysis, each subject's mean CoM velocity at foot lift for steps to the central target was subtracted from the mean value for steps to each peripheral target. The resulting two-dimensional (AP and ML) representation of relative CoM velocity at foot lift showed a target-specific organization that resembled the relative positions of the targets in Cartesian coordinates (**Figure 4E**). The confidence ellipses of CoM velocity at foot lift for steps to medial, lateral, distal and proximal locations were all significantly different from each other (all T 2 (2,8) > 82.5, P < 0.001), indicating that the pre-step activity was coupled to the planned step location.

### Steps When the Target Location Changed

All subjects adjusted their step when the target jumped to a new position shortly after initiation of the pre-step activity. This was demonstrated by the final position of the foot being different to that originally planned (constant-central steps) for steps to all target-jump locations (**Figure 3**, red symbols; all T 2 (2,8) > 1900, P < 0.001). Furthermore, the mean final position of the foot was not different to each subject's self-defined ideal step for any target jump location (all T 2 (2,8) < 8.0, P > 0.3), indicating

within-subject pairing by subtracting the constant-central mean. Filled circles are each subject's mean estimated CoM velocity at foot lift for each target. Ellipses are

Hotelling's 95% confidence ellipses of the group mean. As per the key, black= central; yellow= medial; green= lateral; blue= distal; magenta= proximal.

that the step adjustments were successful and accurate. The final position of the foot after a target jump was mostly the same as when stepping without a target jump (lateral, distal and proximal all T 2 (2,8) < 10.5, P > 0.18), however medial steps were modestly but significantly different from each other (mean vector distance = 1.1 cm; T 2 (2,8) = 49.2, P = 0.002).

To determine whether the pre-step activity was modulated in response to a change in step location, the CoM motion when subjects stepped to the constant-central target was compared with that when the target jumped (see **Figure 2** for details). An initial modulation could be reliably detected in 94% of all jump trials, with 6% of trials being excluded because their jerk trace lay outside the constant-central ellipse at the time of target jump. The first detectable modulation occurred before the foot lifted from the ground in the vast majority (93%) of the remaining trials, with a modulation after foot lift in 7% of trials (**Figure 5**). The median modulation latency was 223 ms (interquartile range = 158) and was not affected by the new target's location (F(3,27) = 1.0, P = 0.41). Subjects would also delay the lift of the stepping foot to elongate the pre-step activity in response to the change of target location. When compared with steps to the constant-central target, foot lift was significantly delayed by 69 (55) ms in jump trials (P = 0.003), but did not depend on target-jump location (F(3,27) = 1.8, P = 0.178). The stepping foot was also lifted later in jump trials than in steps to the same location without a target jump (F(1,9) = 10.9, P = 0.009). The mean (SD) pre-step activity duration of steps with a target jump was 629 (129) ms.

Typically, the initial response to a change in target location acted to reduce the forward acceleration of the body, as shown for a single subject in **Figure 6C**. This ''braking'' effect was apparent for all target jump locations even if an increase in

forward acceleration seemed more appropriate, for example during a jump that required an increased step length. The initial non-specific response was rapidly followed by a target-specific acceleration of the CoM (**Figures 6A,C**) leading to different CoM velocities at the point of foot lift (**Figures 6B,D**). For the group, the confidence ellipses of the change in CoM velocity at foot lift for steps with a medial, lateral, distal and proximal target jump were all significantly different from each other (**Figure 6E**; all T 2 (2,8) > 83.9, P < 0.001) demonstrating that the pre-step activity modulation was target-specific. The modulated CoM velocity at foot lift reflected the positions of the new stepping target, similar to that observed when the target position remained constant, suggesting that an attempt was made to re-couple the pre-step activity and step location.

### DISCUSSION

The experiments were designed to test the throw-and-catch hypothesis of human gait. This was achieved by measuring the coupling between the pre-step activity (the throw) and the final stepping-foot position (the catch). The hypothesis states that the two actions are intimately coupled such that the pre-step activity differs with the planned step location. This was verified in the experiment where the final location was known to the subject throughout the movement. For the experiment in which the final location changed just after the throw was initiated, which effectively de-coupled the two actions, the throw was found to be adjusted so that it was re-coupled to the new step location. Together these results provide support for the throw-and-catch hypothesis of human gait.

### Steps When the Target Location Remained Constant

The throw-and-catch model predicts that the pre-step activity depends on the intended step location. This is because the direction and magnitude of the body throw would need to be tuned differently in order for the body to fall towards its target during steps to different locations. Previous research identified a coupling between the pre-step activity and step location for forwards and diagonal steps (Lyon and Day, 1997, 2005). We sought to investigate whether this finding, and the throw-and-catch model, generalized to steps of different lengths and directions. The resulting data therefore required that both ML and AP body motion was analyzed together using multidimensional statistics (Hotelling's tests and confidence ellipses). The results confirmed that the pre-step activity systematically differed with target location in steps of both different lengths and directions (**Figure 4**). The net result of these changes was such that when the stepping foot lifted from the ground, the body had gained velocity, and therefore momentum, that was specific to the intended step location. Lyon and Day (1997) demonstrated that the body's momentum at the point of foot lift is a key factor that predicts the body's trajectory during the step. The coupling between the body's momentum and step location in the present results suggests that this ballistic model generalizes and the throw is fine-tuned for steps of different lengths and directions.

In order to test the throw-and-catch model's generality, steps were initiated from an imposed initial posture which allowed both step length and direction to be precisely controlled. Although the initial posture may not have been a natural stance width or foot angle for all subjects, it is unlikely to have affected their behavior significantly. The step was otherwise natural for each subject as the initiation and duration of the step was unconstrained. This lack of temporal constraint is unlikely to have affected the use of a ballistic strategy, as it has been demonstrated both for temporally unconstrained steps (Lyon and Day, 1997, 2005) and when initiating gait as quickly as possible (Yiou et al., 2016). It is possible that differences in step duration may have influenced the throws to different targets (Zettel et al., 2002a,b; Yiou et al., 2016). However, this is unlikely to explain our data because although step duration changed with step length, it did not change with step direction (data not shown). In exploring the throw-and-catch in steps of different lengths and directions, subjects would often step beyond the force platforms. Subsequently, CoM position was unable to be reliably estimated (for a discussion of CoM position estimation from force data see Lyon and Day, 1997). The position from which the body initiates its fall is an important aspect of the throw (Lyon and Day, 1997, 2005) but, by demonstrating a step location-specific change in CoM velocity, the present results show that the pre-step activity is tuned to the future foot position.

The between-subject variability of the throw in this experiment (**Figure 4E**) and in Lyon and Day (1997) shows that there is no ''one-size-fits-all'' throw to achieve a successful step. Even for the same subject, different throws could successfully be caught by identical foot-landing positions. This likely reflects both the ability to make mid-step adjustments (Reynolds and Day, 2005, 2007; Kim and Brunt, 2009, 2013; Tseng et al., 2009; Nonnekes et al., 2010) and the numerous solutions that exist to catch the body without losing balance (Koolen et al., 2012). However, the present results show that there is pressure to maintain the throw within limits which differ for different step locations. This suggests there is some advantage in coupling the pre-step activity and step location.

### Steps When the Target Location Changed

The pre-step activity and the step location can be uncoupled, for example by changing the location of a target. In this scenario the body throw and step location become uncoupled if the pre-step activity remains unchanged while the foot position changes. Previous work has shown that if the target is made to jump after the foot leaves the ground, so that the pre-step activity cannot be changed, the final position of the stepping foot can still be altered, albeit with varying degrees of success depending on the extent and direction of the target jump (Reynolds and Day, 2005, 2007; Kim and Brunt, 2009, 2013; Tseng et al., 2009; Nonnekes et al., 2010). This de-coupling does not necessarily disprove the throw-and-catch hypothesis, but may be interpreted as there being some flexibility in the coupling which can be exploited under certain circumstances. A better test of the hypothesis is to measure whether there is an attempt to re-couple the pre-step activity with the new step location under conditions when the pre-step activity has an opportunity to be adjusted. Here we made the target change location during the pre-step activity, long before the stepping foot left the ground, thus allowing time for a re-coupling of the pre-step activity with the new target location. The target jump was unpredictable, as more often than not the target location did not change and could be to any one of four locations when it did. This procedure resulted in substantial uncertainty and rendered attempts at anticipating the target jump unlikely to be of value to the subject. We argue that an attempt to re-couple the pre-step activity with the new step location would provide support for the throw-and-catch hypothesis given that an adjustment could be initiated after the foot leaves the ground.

Previous research is conflicted on whether the pre-step activity can be modulated. Experiments that unpredictably perturbed the trajectory of the body during the pre-step activity via mechanical pulls have returned mixed results, with muscle activity being altered to correct the body's trajectory in response to resistive (Mouchnino et al., 2012; Mille et al., 2014) but not assistive perturbations (Mouchnino et al., 2012). Additionally, stimulation of proprioceptive (Ruget et al., 2008) and vestibular (Bent et al., 2002) afferents were found not to affect the pre-step activity, suggesting it may be immutable once it has been initiated. This was not found to be the case in the present experiment, since the pre-step activity was modulated in the vast majority of trials when prompted by a visual cue. Furthermore, the precise modulation of the pre-step activity depended on the new target location. This suggests that an attempt was made to re-couple the pre-step activity to the new target location and provides causal evidence that the pre-step activity is fine-tuned to take the final position of the foot into account. According to the throw-and-catch hypothesis, re-coupling the pre-step activity to the new target location would have promoted a more appropriate fall of the body towards its intended target after the lift of the stepping foot. This does not rule out the possibility that further adjustments were made during the step.

Although the net adjustment of the pre-step activity was different depending on where the target jumped, a non-specific initial response to the perturbation was evident that reduced the forward acceleration of the body. Similar ''braking'' responses to visual cues have been reported after the lift of the stepping foot during both single steps and locomotion (Kim and Brunt, 2013; Potocanac et al., 2016). In the present experiment, this braking was used irrespective of where the target moved. Although the braking could have been expected when the step length required shortening, it was surprising that it was also used when a longer step was required. This is because greater forward acceleration was observed for longer steps when the target did not move (**Figure 4**). The braking may have enabled a pause whilst the necessary actions for a successful step were reconsidered (Potocanac et al., 2016), which would explain the increase in pre-step duration that was observed when a target jumped. Mille et al. (2014) also report a similar delay in stepping after a mechanical pull to the body prior to a step. Presumably, in the current experiments, the extra time was needed to re-program and adjust the body throw so that it was re-coupled to the new final foot location.

### What Advantage Does the Throw-and-Catch Coupling Offer?

Stepping can be considered a ballistic action if, as we suggest, gravity drives the fall of the body during the step with its trajectory being controlled by the pre-step activity. The ballistic nature of stepping is sometimes misinterpreted as sensory information not being attended to or usable during the step. This interpretation is clearly false given that adjustments to the step are possible both before the lift of the stepping foot, as shown in this paper, and after foot lift when suitable sensory cues are provided (Reynolds and Day, 2005, 2007; Kim and Brunt, 2009, 2013; Tseng et al., 2009; Nonnekes et al., 2010). However, the magnitude and direction of mid-step adjustments are limited by the fall of the body and the subsequent balance constraints. For example, the size of medially-directed foot adjustments cannot be made as large as laterally-directed adjustments (Reynolds and Day, 2005). This limitation may underlie the incentive to maintain the coupling between the pre-step activity and final foot location demonstrated in the present experiment. At the same time, the ability to rapidly alter the intended foot

### REFERENCES

Batschelet, E. (1981). Circular Statistics in Biology. London: Academic Press.

position mid-step offers a degree of flexibility in the coupling, which would be essential for responding to an unexpected environmental threat or maintaining foot landing accuracy in the presence of error in the initial throw.

### CONCLUSION

We find that there is a close coupling between pre-step activity and final foot position during unperturbed steps of different lengths and directions. Furthermore, there is pressure to maintain this coupling when the demanded step location unpredictably changes shortly after initiation of the pre-step activity. We conclude that these results support the throw-andcatch hypothesis of human stepping.

### AUTHOR CONTRIBUTIONS

MJB and BLD conceptualized and designed the experiment, analyzed the data, drafted and revised the manuscript and approved its final version. MJB acquired the data.

### FUNDING

This work was funded by a University College London (UCL) Grand Challenge studentship.

### ACKNOWLEDGMENTS

We would like to thank Mr. Dan Voyce for technical assistance.

Zettel, J. L., McIlroy, W. E., and Maki, B. E. (2002b). Environmental constraints on foot trajectory reveal the capacity for modulation of anticipatory postural adjustments during rapid triggered stepping reactions. Exp. Brain Res. 146, 38–47. doi: 10.1007/s00221-002-1150-5

**Conflict of Interest Statement**: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2016 Bancroft and Day. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution and reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Anticipatory Postural Control of Stability during Gait Initiation Over Obstacles of Different Height and Distance Made Under Reaction-Time and Self-Initiated Instructions

Eric Yiou1,2\*, Romain Artico1,2 , Claudine A. Teyssedre1,2 , Ombeline Labaune1,2 and Paul Fourcade1,2

1 CIAMS, Université Paris Sud, Université Paris-Saclay, Orsay, France, 2 CIAMS, Université d'Orléans, Orléans, France

Despite the abundant literature on obstacle crossing in humans, the question of how the central nervous system (CNS) controls postural stability during gait initiation with the goal to clear an obstacle remains unclear. Stabilizing features of gait initiation include anticipatory postural adjustments (APAs) and lateral swing foot placement. To answer the above question, 14 participants initiated gait as fast as possible in three conditions of obstacle height, three conditions of obstacle distance and one obstacle-free (control) condition. Each of these conditions was performed with two levels of temporal pressure: reaction-time (high-pressure) and self-initiated (low-pressure) movements. A mechanical model of the body falling laterally under the influence of gravity and submitted to an elastic restoring force is proposed to assess the effect of initial (foot-off) center-of-mass position and velocity (or "initial center-of-mass set") on the stability at foot-contact. Results showed that the anticipatory peak of mediolateral (ML) center-of-pressure shift, the initial ML center-of-mass velocity and the duration of the swing phase, of gait initiation increased with obstacle height, but not with obstacle distance. These results suggest that ML APAs are scaled with swing duration in order to maintain an equivalent stability across experimental conditions. This statement is strengthened by the results obtained with the mechanical model, which showed how stability would be degraded if there was no adaptation of the initial center-of-mass set to swing duration. The anteroposterior (AP) component of APAs varied also according to obstacle height and distance, but in an opposite way to the ML component. Indeed, results showed that the anticipatory peak of backward center-of-pressure shift and the initial forward centerof-mass set decreased with obstacle height, probably in order to limit the risk to trip over the obstacle, while the forward center-of-mass velocity at foot-off increased with obstacle distance, allowing a further step to be taken. These effects of obstacle height and distance were globally similar under low and high-temporal pressure. Collectively, these findings imply that the CNS is able to predict the potential instability elicited by the obstacle clearance and that it scales the spatiotemporal parameters of APAs accordingly.

Keywords: stability, anticipatory postural adjustments, obstacle clearance, mechanical modeling, temporal pressure, gait initiation, motor coordination, human

#### Edited by:

Christopher J. Hasson, Northeastern University, USA

#### Reviewed by:

Arturo Forner-Cordero, University of São Paulo, Brazil Laurence Mouchnino, Aix-Marseille Université, France

> \*Correspondence: Eric Yiou<EMAIL_ADDRESS>
Received: 03 May 2016 Accepted: 25 August 2016 Published: 07 September 2016

#### Citation:

Yiou E, Artico R, Teyssedre CA, Labaune O and Fourcade P (2016) Anticipatory Postural Control of Stability during Gait Initiation Over Obstacles of Different Height and Distance Made Under Reaction-Time and Self-Initiated Instructions. Front. Hum. Neurosci. 10:449. doi: 10.3389/fnhum.2016.00449

### INTRODUCTION

The control of postural stability is crucial for the efficient performance of day-to-day motor tasks. Like all terrestrial species, humans move around in a gravity field that permanently induces postural destabilization through its attracting effect towards the center of the earth. Major questions in motor control relate to the way in which humans are able to maintain stability during motor tasks that involve whole body progression, such as locomotor tasks, and how they adapt to environmental constraints, e.g., when clearing an obstacle. Gait initiation, which corresponds to the transient period between quiet standing and swing foot contact with the ground, is a classical paradigm for studying balance control mechanisms during complex whole body movement (e.g., Brenière et al., 1987; Lyon and Day, 1997, 2005; McIlroy and Maki, 1999; Yiou et al., 2012a for a recent review; Caderby et al., 2014). The act of lifting the swing foot from the ground to step in the desired direction does indeed induce a reduction in the size of the mediolateral (ML) base of support, moving from a bipedal to a unipedal stance. If the center of mass is not repositioned above (or closer to) the limits of the new base of support -i.e., the stance foot–, the body will topple towards the swing leg side during the single stance phase (or ''swing phase'') of gait initiation under the effect of gravity, which may cause lateral instability at foot contact. This instability is invariably attenuated during volitional stepping by the development of dynamic postural phenomena that occur before the swing phase. These dynamic phenomena correspond to ''anticipatory postural adjustments'' (APAs). They include a center of pressure shift towards the swing leg side which serves to accelerate the center of mass in the opposite direction, i.e., towards the stance leg side (Do et al., 1991; Jian et al., 1993; McIlroy and Maki, 1999; Nouillot et al., 2000; Caderby et al., 2014; Yiou et al., 2016). If not enough APAs are generated in the ML direction, a strategy of base of support enlarging, associated with a more lateral swing foot placement, has been shown to be triggered to maintain stability (Zettel et al., 2002; Caderby et al., 2014). In addition to this putative stabilizing function, APAs have been shown to provide the dynamic conditions for whole body progression in the desired direction. For example, during gait initiation, APAs in the anteroposterior (AP) direction include a backwards center of pressure shift that promotes the forward propulsive forces necessary to reach the intended center of mass velocity and step length (Brenière et al., 1987; Lepers and Brenière, 1995; Michel and Chong, 2004).

Postural stability during gait initiation might be further challenged by the presence of an obstacle that needs to be cleared. There has been extensive literature on the control of obstacle crossing during ongoing locomotion, especially in regards to the role of vision (e.g., Mohagheghi et al., 2004; Patla and Greig, 2006; Marigold et al., 2007). In comparison, the question how the postural and the focal components of gait initiation over an obstacle are coordinated to ensure safe body progression has received much less attention (e.g., Brunt et al., 1999; Yiou et al., 2016). Yet, it is known that gait initiation is among the motor activities associated with the highest proportion of falls in the elderly (Robinovitch et al., 2013). In addition, the most frequent cause of falling in this population is an incorrect weight transfer, which, as stated above, is one of the major functions of APAs. In addition to the risk of tripping over the obstacle, the presence of an obstacle gives rise to an increase in the duration of the swing phase and therefore an increase in the potential for lateral instability (Zettel et al., 2002; Yiou et al., 2016). Hence, it is surprising that previous studies on the influence of an obstacle on the lateral motion of the center of mass during ongoing walking have reported that lateral stability remained unchanged when the height of the obstacle was varied (Chou et al., 2001; Hahn and Chou, 2004). This result led the authors to suggest the existence of some forms of adaptive postural mechanisms aimed at compensating for the increased potential instability related to obstacle height. However, these mechanisms remain to be clarified. To date, the question of whether or not the stabilizing mechanisms of gait initiation can accommodate obstacle constraints has been investigated in only one study (Yiou et al., 2016). This study showed that the amplitude of ML APAs was larger in the obstacle condition than in the obstacle free (control) condition. It was suggested that this increase was responsible for the maintenance of postural stability at swing foot contact. Similar results were obtained by Zettel et al. (2002) during their comparison of reactive stepping over an obstacle in response to a brisk plate-form shift with the same reactive stepping in an obstacle-free condition. However, these studies are all limited by the fact that only one obstacle height and distance were tested. Thus, one can question the generalizability of these results and more specifically, the extent to which the central nervous system (CNS) is able to adjust the stabilizing features of gait initiation (including ML APAs and base of support enlargement) to match changes in obstacle height and distance and the related potential for instability. Moreover, subjects of these studies invariably increased ML APAs when stepping (voluntarily or reactively) over the obstacle; thus, it could not be established that the absence of such an increase would have necessarily led to instability at foot contact. Lyon and Day (1997, 2005) used a single-segment mechanical model in which the body falls freely under the influence of gravity to predict the magnitude of the lateral center of mass fall during the swing phase of step initiation. In the present study, we elaborated on a mechanical model that was based on these last two studies in order to investigate how changes in the parameters of ML APAs can impact on postural stability at foot contact. Such modeling may thus provide further insight into the adaptability of the postural system to environmental constraints.

This study aims to investigate how the CNS controls postural stability during gait initiation when clearing obstacles of different heights and distances. Changes in obstacle height and distance were expected to bring about modulation of the swing phase and give rise to instability. In addition, as daily motor tasks may be performed under various temporal pressure constraints, gait initiation trials were performed in reaction-time (high pressure) and self-initiated (low pressure) conditions. Our previous study (Yiou et al., 2016) showed that the duration of APAs associated with gait initiation when faced with an obstacle was shorter Yiou et al. Stability Control during Obstacle Clearance

under high pressure than under low pressure. This difference in duration was compensated by an increase in the amplitude of ML APAs. As only one obstacle height and distance were used (one 20 cm high obstacle, placed at a 20% body height distance from the participant), it can be questioned whether the CNS uses a similar anticipatory postural adaptation to temporal pressure when the obstacle constraints are manipulated. This is particularly the case when height and distance are increased, thereby placing a higher level of stress on the postural system.

This question might be addressed in regards to current theory on motor control, according to which our nervous system would possess neural structures (or internal models) that predict the future state of a system given the current state and the sensorimotor control signals (Wolpert and Flanagan, 2001). Such prediction would allow us to achieve rapid and accurate voluntary behavior despite the difficulties presented by motor noise, delayed sensory feedback, and a complex musculoskeletal apparatus. As stressed in Mille et al. (2012), it is clear that ''the anticipatory nature of the APAs involves a role for motor prediction''. Specifically, APAs structure would reflect the existence of internal models that predicts the destabilizing effect associated with the stepping (Lyon and Day, 1997, 2005). When stepping over an obstacle, it can therefore be expected that APAs will be scaled according to the potential destabilization associated with obstacle constraints. We thus hypothesize that the stabilizing features of gait initiation are scaled according to the changes in the swing phase duration that is associated with obstacle height and/or distance. More specifically, it is expected that a greater swing phase duration will be associated with larger ML APAs and eventually, a larger base of support in order to maintain unchanged postural stability at swing foot contact. Similar effects of obstacle constraints are expected under low and high temporal pressure conditions. However, APAs of larger amplitude and lower duration are expected in the high pressure condition compared with the low pressure condition. Mechanical modeling of the whole body during gait initiation is expected to reveal the extent to which postural stability at foot contact may be degraded in case ML APAs are not adequately scaled to modifications in swing duration induced by obstacle constraints.

### MATERIALS AND METHODS

### Participants

Fourteen subjects (eight males and six females, aged 23.2 ± 4 years [mean ± SD], height 173.4 ± 7.3 cm and weight 65.8 ± 8.7 kg) participated in the experiment. All were free of any known neuromuscular disorders. They gave written informed consent after being instructed as to the nature and purpose of the experiment, which was approved by the local ethics committee. The study conformed to the standards set by the Declaration of Helsinki.

### Experimental Protocol

Participants were requested to initiate gait as fast as possible with their preferred limb while clearing an obstacle placed in front of them (**Figure 1**). Three conditions of obstacle

height (2.5%, 5% and 10% of each subject's height), three conditions of obstacle distance (10%, 20% and 30% of each subject's height) and an obstacle-free control condition were used. The three obstacle distances corresponded to 21%, 42% and 63% of the step length obtained in the control condition, respectively. Each condition of obstacle height and distance was realized in two blocks, which differed in terms of their level of temporal pressure constraint: a reaction-time and a self-initiated block. In the reaction-time block (high temporal pressure), participants were instructed to initiate gait ''as soon as possible'' after an acoustic signal was given. In the selfinitiated block (low temporal pressure), they were instructed to initiate gait when they felt ready, after receiving an ''all set'' signal; it was made clear that the ''all set'' signal was not a ''go'' signal and that they could take as much time as they needed to prepare their movements. The order of conditions within one given block and the order of the blocks were randomized between participants. In each condition, subjects were allowed two familiarization trials. Five trials were then recorded. A 3-min rest was imposed between two successive conditions to avoid fatigue. In each condition, the participants initially stood upright with their feet hipwidth apart, their arms hanging loosely either side of their body and their body weight evenly distributed between their legs. The boundaries of their feet in the initial posture were outlined on the force plate, and participants were instructed to systematically reposition their feet within these marks under supervision. They were repeatedly reminded of the task instructions.

### Materials

Gait was initiated on a force plate (600 × 1200 mm, AMTI, Watertown, MA, USA) located at the beginning of a five-meter track (**Figure 1**). The force plate was embedded in the track and was large enough to allow the participant's swing foot to systematically land on it at the end of gait initiation. After crossing the obstacle, participants walked to the end of the track, then stood still for a few seconds before returning to their starting position. The obstacle consisted of a lightweight wooden rod (length: 65 cm; diameter: 1 cm) that rested on two adjustable upright standards. The participant's toes served as the reference point for positioning the obstacle at the various distances. Reflective skin markers (9 mm in diameter) were placed bilaterally at the hallux (toe marker), head of the fifth metatarsal (metatarsal marker), posterior calcaneus (heel marker) and at the middle of the top of the obstacle (obstacle marker). A V8i VICON eight-camera (Mcam2) motion capture system (Oxford Metrics Ltd., UK) with 64 analog channels was used to record the movement of the foot markers and to detect the position of the obstacle. Kinematic and kinetic data were collected simultaneously at a rate of 500 Hz. Data acquisition and stimulus display were controlled by a custommade program written in MatlabTM (R2009b, The MathWorks Inc., Natick, MA, USA).

### Data Analysis

Kinematic and force plate data were low-pass filtered using a Butterworth filter with a 15 Hz (Mickelborough et al., 2000) and a 10 Hz (Caderby et al., 2014) cut-off frequency, respectively. The ML (yP) and AP (xP) coordinates of the center of pressure were computed from force plate data as follows:

$$\text{yP} = \frac{M\mathbf{x} + \mathbf{F}\mathbf{y} \times dz}{\text{Fz}} \tag{1}$$

$$\text{xP} = \frac{-M\text{y} + \text{F}\mathbf{x} \times d\mathbf{z}}{\text{F}\mathbf{z}}\tag{2}$$

where Mx and My are the moments around the AP and ML axes, respectively; Fy, Fx and Fz are the ML, AP and vertical ground reaction forces, respectively; and dz is the distance between the surface of the force plate and its origin.

Instantaneous acceleration of the center of mass along the AP and ML axes was determined from the ground reaction force according to Newton's second law. Center of mass velocity and displacement were computed by successive numerical integrations of center of mass acceleration using integration constants equal to zero, i.e., initial velocity and displacement null (Brenière et al., 1987). The following instants were determined from biomechanical traces: gait initiation onset (t0), swing heel off, swing toe off and swing foot contact. T0 and foot contact were determined from force plate data, whereas heel off and toe off were determined from VICON data. Two t0 times were estimated, one for the ML axis and one for the AP axis. The t0 times corresponded to the instants when the ML or AP center of pressure trace deviated 2.5 standard deviations from its baseline value. Heel off and toe off corresponded to the instants when the vertical position of the swing heel marker and the anterior position of the swing toe marker increased by 3 mm from their position in the initial static posture. Foot contact corresponded to the instant when the ML and AP center of pressure traces shifted abruptly laterally towards the swing leg side, and forwardly, respectively (this abrupt shift occurred at the same instant in the two traces).

### Mechanical Model

In the present study, the human body was modeled during the swing phase of gait initiation (from toe off to foot contact) as

a single conic inverted pendulum which rotates about a fixed point 0 (**Figure 2**). This model was based on work carried out in earlier studies (Jian et al., 1993; MacKinnon and Winter, 1993; Lyon and Day, 1997, 2005). The displacement of this cone had five degrees of freedom on the absolute referential (0, x, y, z), i.e., three translations and two rotations. A new referential (0, x1, y1, z1) was considered after precession ψ around z and nutation θ around x1, in which the inertia momentum of the body was expressed with its eigenvalues (Winter et al., 1990). The proper rotation ψ around z1 with respect to ψ and θ was neglected. During the swing phase, we considered that the center of mass was falling laterally under the influence of two forces: the gravity force P = mg (where m is the mass of the solid, and g is the gravitational acceleration) and an elastic restoring force T that reflects active muscular control of the movement (Farley and Morgenroth, 1999; Morasso and Schieppati, 1999), with T = k|yM| (where k is the stiffness of the hip abductor muscles acting on the stance leg side during the swing phase (Winter, 1995) and |yM| is the absolute value of the ML center of mass shift, which was systematically oriented towards the swing leg side (positive values) during the swing phase). The initial position and velocity of the cone corresponded to the position and velocity of the subject's center of mass at toe off. The addition of a restoring force on the conic model was necessary in order to control the initial velocity at toe off. Without this supplementary force, the conic pendulum would fall towards the stance leg side in most trials.

The equation of motion in (0, x1, y1, z1) was:

$$\left(\left|\mathrm{OM}\times\left(m\mathrm{g}+k\,\left|\mathrm{yM}\right|\right)\right|=\frac{\mathrm{d}\sigma\_{/0}}{\mathrm{d}t}\right)\tag{3}$$