Realistic overground gait transitions are not sharp but involve gradually changing walk-run mixtures
as per energy optimality

Nicholas S. Baker¹, Leroy Long², and Manoj Srinivasan³
^1,3Mechanical and Aerospace Engineering, The Ohio State University, OH 43210
³Program in Biophysics, The Ohio State University, OH 43210
²Mechanical Engineering, Sinclair College, FL 32114
³Email: [email protected]

Abstract

Humans use two qualitatively different gaits for locomotion, namely, walking and running — usually using walking at lower speeds and running at higher speeds. Researchers have examined when humans switch between walking and running on treadmills and have noted hystereses in these gait transition speeds. Here, we consider an ecologically realistic overground locomotion task, one requiring traveling a given long distance (800 meters or 2400 meters) in a prescribed time duration. Unlike on a treadmill, this task allows the human to change speed or gait during the trial to reach the destination on time: this task is akin to traveling to an appointment at a particular time from your office to another office, arriving neither early or late. We find that gait transition is not sharp, but instead involves a “gait transition regime” in which humans use a mixture of walking and running, using mostly walking at around 1.9 m/s and mostly running around 3.0 m/s — supporting earlier results over short distances (120 m). The presence of this gradually changing walk-run mixture is predicted by energy optimality. We hypothesize that this energy optimal behavior in this realistic overground conditions accounts for the hysteretic behavior in treadmill experiments, apparently switching earlier than predicted by energy optimality.

1 Introduction

Humans and many other terrestrial animals exhibit a number of different gaits [1, 2, 3, 4, 5]. Humans walk, run, and much more occasionally, skip [6, 7]. Horses walk, trot, canter, and gallop, and more occasionally, use other gaits [3, 8, 9]. Such gait transitions have most commonly been studied using treadmills (Figure 1). In these treadmill gait transition experiments, the treadmill speed is changed slowly, either in a continuous fashion with some fixed acceleration, or in a series of acceleration phases alternating with constant speed phases [10, 11, 12, 13, 14, 15, 16, 17, 18]. These experiments found that people switch between walking and running around 2 m/s, but sometimes, the walk to run transition speed was different from — and higher than — the run to walk transition speed [18, 11, 12] and the transition speeds were different from that predicted by energy optimality [10]. In such treadmill experiments, the gait transition is ‘sharp’, that is, happens at a particular speed where there is a preference of running over walking, or vice versa. Most humans do not spend their lives on treadmills, so their behavior may not already be energy optimal for such gait transition tasks without considerable learning [19, 20, 21]. Here, in contrast to these treadmill gait transition experiments, we show that overground gait transitions in realistic overground locomotion is more gradual and provide some clues for why there might exist distinct walk-to-run and run-to-walk speeds on a treadmill.

Imagine you need to travel on foot from your home to an important appointment a kilometer away at a particular time (Figure 1). Unlike on a treadmill, where the speed is constrained, in this overground experiment, you can change speed or change gait. What might you do? If you start very early and have plenty of time, you might prefer to walk all the way. If you have very little time, you might need to run all the way. But if you had an intermediate amount of time, what might you do? Here, we perform this experiment for two long distances over 800 meters, and show that humans systematically use a mixture of walking and running when there is an intermediate amount of time. That is, we show that for such overground tasks, there is not a sharp gait transition speed below which walking is preferred and above which running is preferred. Having this mixture of walking and running instead of a sharp gait transition speed is energy optimal [1, 22, 23], and was earlier observed over short distance tasks in humans [1], so the primary experimental contribution of the current study is its demonstration over much longer distances.

Refer to caption — Figure 1: Experimental protocol. a) The classic treadmill-bound gait transition used in prior studies experiment does not provide any instantaneous choice in speed to the human, constraining speed at every moment, so that subjects are just asked to choose the gait they prefer at a given speed. b) Overground gait transition experiment used in the current study. Human subjects are asked to cover a given distance $D_{\mathrm{total}}$ in a fixed amount of time $T_{\mathrm{total}}$ , as if they have to travel on foot to make an appointment, exactly arriving on time. Subjects carry a stop-watch counting down time remaining to prescribed duration and are free to choose and change their gait or speed whenever during each trial. Trials are repeated for different prescribed durations so as to achieve different average speeds.

2 Methods

Experimental methods.

Experiments were approved by the Ohio State Institutional Review Board and human subjects participated with informed consent. We had $N=14$ subjects (11 male, 3 female) with age 21.3 $\pm$ 2.9 years (mean $\pm$ s.d.), mass 70.35 $\pm$ 13.99 kg, height 1.80 $\pm$ 0.10 m, and leg length 0.91 $\pm$ 0.26 m. Subjects were instructed to travel one of two distances on foot, $D_{\mathrm{total}}=$ 800 m or 2400 m, in a pre-determined amount of time, $T_{\mathrm{total}}$ , arriving exactly as allowed time expired, arriving neither early nor late (Figure 1b and Table 1). A stop-watch that counted down from $T_{\mathrm{total}}$ to zero was provided to the subject for reference throughout the trial. The $T_{\mathrm{total}}$ was not revealed to the subjects until just moments before starting a trial to eliminate as much prior planning as possible. The subjects received no additional instructions. The total distance and time constraints constrained only the average speed $v_{\mathrm{avg}}=D_{\mathrm{total}}/T_{\mathrm{total}}$ , but not the instantaneous speeds throughout the trial, in contrast to a classic treadmill gait transition experiment (Figure 1a).

For each total distance $D_{\mathrm{total}}$ , we used four different $T_{\mathrm{total}}$ corresponding to four different average speeds: 1.92, 2.24, 2.62, and 2.98 ms^-1. These speeds were chosen to be roughly in the treadmill gait transition regime [5, 24, 10, 11], as well as the regime in which humans used a mixture of walking and running in our earlier study where we examined this protocol for vastly shorter distances [1]. Because of the large distances involved here, each subject either performed two trials both at the 2400 m distance, or three trials, two at 800 m and one at 2400 m. In all, we performed $N_{\mathrm{trial}}=$ 42 total trials across the 14 subjects, with at least 9 trials per average speed. The trial assignment and trial order were randomized for each subject and across subjects. The total duration was not revealed to the subjects until a few moments before starting to eliminate as much pace planning as possible. All trials were performed on a 400 m outdoor track. Locomotion speeds were measured using GPS (10 Hz, VBOX Mini, Racelogic). Trials were video recorded and used to determine durations of walking and running during each trial, as visually classified by the investigators. The investigators classified the trial as running if there was a flight phase or if the hip moved downward and upward on a compliant-looking leg during stance phase, even if there did not seem to be a flight phase (jogging or grounded running); walking bouts are the complements of these running bouts [25, 26].

Trial ID	1	2	3	4	5	6	7	8
Distance $D_{\mathrm{total}}$ (m)	800	800	800	800	2400	2400	2400	2400
Duration $T_{\mathrm{total}}$ (min)	14.00	12.00	10.25	9.00	14.00	12.00	10.25	9.00
Average speed $V_{\mathrm{avg}}$ (m/s)	1.92	2.24	2.62	2.98	1.92	2.24	2.62	2.98

Table 1: Trials were drawn from these eight possibilities, two different distances at four different average speeds, constrained by choosing .

3 Results

Humans can achieve different average speeds with great precision over long distances.

Subjects typically completed the trials in exactly the prescribed amount of time, arriving neither too early nor too late, using walking and/or running, appropriately adjusting their speeds as needed. Only in 3 trials out of 42 trials did the subjects travelled so quickly initially that they had to be at virtually zero velocity for more than 10 sec, out of a typical trial duration of at least 540 seconds.

The subjects’ GPS-computed average speed was only 0.03 ms^-1 different from the prescribed speed on average. The GPS-computed average speed and prescribed average speed were fit by the linear regression $v_{\mathrm{computed}}=0.99V_{\mathrm{avg}}+0.043$ ( $p=10^{-37}$ , $R^{2}=0.991$ ), which simultaneously demonstrates human ability to achieve different average speeds with high precision and the GPS-computed speed’s reliability (see acknowledgment regarding GPS accuracy).

Humans mostly used a walk-run mixture for the intermediate average speeds.

Subjects used a mixture of walking and running in 90% of the trials at the two intermediate speeds (2.22 and 2.6 ms^-1). On average, walking dominates the walk-run mixture at the lower speeds and running dominates the walk-run mixture at the higher speeds (Figure 2a), so that the walk-run mixture gradually changes as speed is increased. The time fraction of walking decreases and the time fraction of running increases with average speed. Thus, for this overground gait transition task, there is no sharp gait transition speed but only a “gait transition regime”, which has substantial overlap with the speed range 2 m/s to 3 m/s. Despite the substantially greater distances involved (800 m and 2400 m), the overall trends in the walk-run fraction is similar to that observed for trials with much smaller distance (120 m) in the earlier study [1].

Walking at low speeds and running at higher speeds.

In each of the walk-run mixtures, walking generally happens at low speeds and running generally happens at higher speeds. Figure 2c shows the time spent at various walking and running speeds at each of the four average speeds. Each histogram shows two peaks, one at a walking speed and another at a running speed. Considering these histograms (Figure 2c) with the time fraction of walking versus running (Figure 2a) suggests that people accomplish the required average speed by averaging over a slow walking speed and a faster running speed, as qualitatively predicted by energy optimality [1]. As the average speed increases, the speed distribution changes so that there is more time spent at the higher running speeds, resulting in a larger peak at the higher speed. Speed 1.98 ms^-1 is dominated by walking and speed 2.96 ms^-1 is dominated by running.

Humans typically switch gait only a small number of times even for long distances lowering switching costs.

Pure energy optimality in the absence of fatigue or any uncertainty predicts that in the regime where a walk-run mixture is optimal, there should be exactly one switch between walking and running. Multiple switches between walking and running is not optimal. Here, we find that the median number of switches is one for three out of the four speeds we considered, with speed 2.62 m/s having two switches as median, with some variability around this median (Figure 2b). If we assume the cost of a single switch to be $m\left(V_{\mathrm{run}}^{2}-V_{\mathrm{walk}}^{2}\right)/2$ approximately [27, 28], we estimate about 3.4 J per unit body mass when the walking speed is 1.5 m/s and the running speed is 3 m/s. This gait and speed switch cost of 3.4 J/kg is negligible compared to about 2300 J/kg for walking 800 m at 1.5 m/s, using steady walking costs from [29, 30]. Despite this cost per switch being negligible, humans only switch gaits a small number of times, still keeping the switching cost negligible.

4 Discussion

We have performed overground gait transition experiments over much longer distances than earlier and shown that humans use remarkably similar behavior to short distance bouts. Specifically, we find a gradually morphing walk-run transition regime, that involves walk-run mixtures, dominated by walking at lower speeds and by running at higher average speeds. These overground walk-run mixtures necessarily involve transitions from walking at a low speed to running at a high speed and vice versa, so perhaps the hysteretic behavior on a treadmill is a reflection of the overground strategy deployed in an unfamiliar treadmill setting.

Aside from instantaneous energetics, gait transition from walking to running has been attributed to muscle force-velocity behavior [31], interlimb coordination variability [32], mechanical load or stress [33, 18], and cognitive or perceptual factors [34, 35]; see [36] for a review. However, none of these factors can show why there may be hystereses between the walk-to-run and the run-to-walk speeds on treadmills [37]. And importantly, we know it is unclear how any of these ‘instantaneous’ theories with the gradual walk-run-mixture-based gait transition regime behavior we have demonstrated in this manuscript. Predicting a walk-run mixture over a full bout as being optimal must necessarily require a theory that integrates some performance measure over the entire bout.

We have considered one kind of overground gait transition, in which the task is traveling a given distance at a desired average sub-maximal speed. Another kind of ecological overground gait transition that might have been common in our evolutionary past is to be walking normally and then having to accelerate to a higher running speed to either chase prey or evade a predator. Piers et al [38] considered such a gait-transition task, but this is a substantially different task from that considered here from an energy optimality perspective, as it will be dominated by the cost of changing speeds and the cost of switching gaits [27, 28] – so we do not a priori expect identical gait transition speeds.

Future work could involve understanding what factors mediate the triggering of transitions between walking and running, as well as speed changes within a gait, based on the task requirements.

Acknowledgment

This work was supported in part by NSF CMMI grant 1254842. Thanks to Mark Snartese and Max Donelan in suggesting the use of VBOX GPS over a less accurate GPS device, enabling the original study [1] as well as this current study.

References

[1] L. L. Long and M. Srinivasan, “Walking, running, and resting under time, distance, and average speed constraints: optimality of walk–run–rest mixtures,” Journal of The Royal Society Interface, vol. 10, no. 81, p. 20120980, 2013.
[2] M. Srinivasan, “Fifteen observations on the structure of energy minimizing gaits in many simple biped models,” Journal of the Royal Society Interface, vol. 8, pp. 74–98, 2011.
[3] M. Hildebrand, “Analysis of tetrapod gaits: general considerations and symmetrical gaits,” in Neural control of locomotion, pp. 203–236, Springer, 1976.
[4] J. J. Collins and I. N. Stewart, “Coupled nonlinear oscillators and the symmetries of animal gaits,” Journal of Nonlinear Science, vol. 3, no. 1, pp. 349–392, 1993.
[5] R. Margaria, Biomechanics and Energetics of Muscular Exercise. Oxford, UK, Clarendon Press., 1976.
[6] A. E. Minetti, “The biomechanics of skipping gaits: a third locomotion paradigm?,” Proceedings of the Royal Society of London. Series B: Biological Sciences, vol. 265, no. 1402, pp. 1227–1233, 1998.
[7] M. Ackermann and A. van den Bogert, “Predictive simulation of gait at low gravity reveals skipping as the preferred locomotion strategy,” Journal of biomechanics, 2012.
[8] D. F. Hoyt and C. R. Taylor, “Gait and the energetics of locomotion in horses,” Nature, vol. 292, pp. 239–240, 1981.
[9] A. Ruina, , J. E. A. Bertram, and M. Srinivasan, “A collisional model of the energetic cost of support work qualitatively explains leg-sequencing in walking and galloping, pseudo-elastic leg behavior in running and the walk-to-run transition,” J. Theor. Biol., vol. 14, pp. 170–192, 2005.
[10] A. Hreljac, “Preferred and energetically optimal gait transition speeds in human locomotion.,” Med. Sci. Sports Exerc., vol. 25, pp. 1158–1162, 1993.
[11] A. Hreljac, R. T. Imamura, R. F. Escamilla, and W. B. Edwards, “When does a gait transition occur during human locomotion?,” Journal of Sports Science and Medicine, vol. 6, pp. 36–43, 2007.
[12] A. Hreljac, R. Imamura, R. F. Escamilla, and W. B. Edwards, “Effects of changing protocol, grade, and direction on the preferred gait transition speed during human locomotion,” Gait & Posture, vol. 25, pp. 419–424, 2007.
[13] G. L. Daniels and K. M. Newell, “Attentional focus influences the walk-run transition in human locomotion,” Biological Psychology, vol. 63, pp. 163–178, 2003.
[14] I. V. Caekenberghe, V. Segers, K. D. Smet, P. Aerts, and D. D. Clercq, “Influence of treadmill acceleration on actual walk-to-run transition,” Gait & Posture, vol. 31, pp. 52–56, 2010.
[15] V. Segers, M. Lenoir, P. Aerts, and D. D. Clercq, “Kinematics of the transition between walking and running when gradually changing speed,” Gait & Posture, vol. 26, pp. 349–361, 2007.
[16] A. J. Raynor, C. J. Yi, B. Abernethy, and Q. J. Jong, “Are transitions in human gait determined by mechanical, kinetic or energetic factors?,” Human Movement Science, vol. 21, pp. 785–805, 2002.
[17] M. T. Turvey, K. G. Holt, M. E. LaFiandra, and S. T. Fonseca, “Can the transitions to and from running and the metabolic cost of running be determined from the kinetic energy of running?,” Journal of Motor Behavior, vol. 31, pp. 265–278, 1999.
[18] F. J. Diedrich and J. W. H. Warren, “Why change gaits? dynamics of the walk-run transition,” Journal of Experimental Psychology: Human Perception and Performance, vol. 21, pp. 183–202, 1995.
[19] N. Seethapathi, B. C. Clark, and M. Srinivasan, “Exploration-based learning of a stabilizing controller predicts locomotor adaptation,” Nature Communications, vol. 15, no. 1, p. 9498, 2024.
[20] J. C. Selinger, J. D. Wong, S. N. Simha, and J. M. Donelan, “How humans initiate energy optimization and converge on their optimal gaits,” Journal of Experimental Biology, vol. 222, no. 19, p. jeb198234, 2019.
[21] J. T. Choi and A. J. Bastian, “Adaptation reveals independent control networks for human walking,” Nature neuroscience, vol. 10, no. 8, pp. 1055–1062, 2007.
[22] R. M. Alexander, “Optimization and gaits in the locomotion of vertebrates.,” Physiol. Rev., vol. 69, pp. 1199–1227, 1989.
[23] A. Falisse, G. Serrancolí, C. L. Dembia, J. Gillis, I. Jonkers, and F. De Groote, “Rapid predictive simulations with complex musculoskeletal models suggest that diverse healthy and pathological human gaits can emerge from similar control strategies,” Journal of The Royal Society Interface, vol. 16, no. 157, p. 20190402, 2019.
[24] A. Thorstensson and H. Robertson, “Adaptations to changing speed in human locomotion: speed of transition between walking and running,” Acta. Physiol. Scand., vol. 131, pp. 211–214, 1987.
[25] M. A. Daley and A. Birn-Jeffery, “Scaling of avian bipedal locomotion reveals independent effects of body mass and leg posture on gait,” Journal of Experimental Biology, vol. 221, no. 10, p. jeb152538, 2018.
[26] R. Blickhan and R. J. Full, “Similarity in multilegged locomotion: bouncing like a monopode.,” J. Comp. Physiol. A., vol. 173, pp. 509–517, 1993.
[27] N. Seethapathi and M. Srinivasan, “The metabolic cost of changing walking speeds is significant, implies lower optimal speeds for shorter distances, and increases daily energy estimates,” Biology letters, vol. 11, no. 9, p. 20150486, 2015.
[28] J. R. Usherwood and J. E. A. Bertram, “Gait transition cost in humans,” Eur J. Appl. Physiol., vol. 90, pp. 647–650, 2003.
[29] A. C. Bobbert, “Energy expenditure in level and grade walking.,” J. Appl. Physiol, vol. 15, pp. 1015–1021, 1960.
[30] M. Srinivasan, “Optimal speeds for walking and running, and walking on a moving walkway,” CHAOS, vol. 19, p. 026112, 2009.
[31] D. J. Farris and G. S. Sawicki, “Human medial gastrocnemius force-velocity behavior shifts with locomotion speed and gait,” PNAS, vol. 109, pp. 977–982, 2012.
[32] J. C. Kao, S. D. Ringenbach, and P. E. Martin, “Gait transitions are not dependent on changes in intralimb coordination variability,” Journal of motor behavior, vol. 35, no. 3, pp. 211–214, 2003.
[33] C. T. Farley and C. R. Taylor, “A mechanical trigger for the trot-gallop transition in horses,” Science, vol. 253, no. 5017, pp. 306–308, 1991.
[34] B. J. Mohler, W. B. Thompson, S. H. Creem-Regehr, H. L. Pick, W. H. W. Jr., J. J. Rieser, and P. Willemsen., “Visual motion influences locomotion in a treadmill virtual environment,” in ACM SIGGRAPH Symposium on Applied Perception in Graphics and Visualization, pp. 19–22, 2004.
[35] P. Guerin and B. G. Bardy, “Optical modulation of locomotion and energy expenditure at preferred transition speed,” Experimental Brain Research, vol. 189, pp. 393–402, 2008.
[36] S. M. Kung, P. W. Fink, S. J. Legg, A. Ali, and S. P. Shultz, “What factors determine the preferred gait transition speed in humans? a review of the triggering mechanisms,” Human movement science, vol. 57, pp. 1–12, 2018.
[37] F. J. Diedrich and W. H. Warren Jr, “The dynamics of gait transitions: Effects of grade and load,” Journal of motor behavior, vol. 30, no. 1, pp. 60–78, 1998.
[38] N. J. Pires, B. S. Lay, and J. Rubenson, “Joint-level mechanics of the walk-to-run transition in humans,” Journal of Experimental Biology, vol. 217, no. 19, pp. 3519–3527, 2014.

Realistic overground gait transitions are not sharp but involve gradually changing walk-run mixtures as per energy optimality