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Journal of Experimental Biology partnership with Dryad

Eric Tytell

When people walk, they unconsciously choose a step length and frequency that minimizes the energy required – on average. But every step is actually a bit different. Sometimes the ground is uneven; sometimes the upper body posture is different; and besides, no one can swing their legs exactly the same way every time.

So how do people manage the variability in their steps? The variability isn't purely random, because it is correlated over time: one quick step is more likely to be followed by another quick step than by a slow step. These correlations could be important, because they tend to be highest in healthy people and lower in the elderly and in people with Huntington's disease.

To probe the neural control of cycle-bycycle changes in walking, Jonathan Dingwell at the University of Texas, Austin, and his colleagues Joby John and Joseph Cusumano at Penn State University, looked at healthy humans walking on a treadmill at a variety of different speeds. The subjects had a clear – if artificial – goal: don't drift off the ends of the treadmill. The authors hypothesized that the subjects used a simple strategy to achieve the goal – match the treadmill speed at each step.

The researchers looked at fluctuations in stride length, stride duration and instantaneous walking speed. Variations in length and duration tended to persist – one short or slow step was more likely to be followed by another short or slow one – a sign that the subjects' nervous systems weren't controlling stride length or duration very tightly. Walking speed had the opposite property, technically termed ‘anti-persistence’ – high speed steps tended to follow low speed steps and vice versa – which the researchers interpreted as a sign of tight neural control.

Dingwell and colleagues propose that the subjects were optimizing performance on what they called a ‘goal equivalent manifold’ or GEM. On the GEM are all the ways the subjects could walk so that their speed matched that of the treadmill. Variation along the GEM doesn't affect the strategy of matching the treadmill's speed. For example, short quick steps and long slow steps may match the speed equally well. But variation perpendicular to the GEM – short slow steps, for instance – leads rapidly to failure, like falling off the end of the treadmill. The nervous system aims to eliminate that sort of variation. Indeed, when they looked at variation perpendicular to the GEM, they saw statistically significant anti-persistence. In other words, the subjects were correcting themselves to stay on the GEM.

The strategy seems obvious but, in fact, there are ways to stay on a treadmill that don't require any information about the GEM. For example, the subjects could have simply tried to minimize variation in step length and duration independently of one another. But, in that case, the researchers wouldn't have seen any anti-persistence in speed and, indeed, statistical tests indicate that the subjects were not using that strategy.

But what about energy minimization? Short quick steps and long slow steps are energetically costly, even if they do meet the goal of staying on the treadmill. The researchers saw few of these extreme steps. So it appears that the subjects were striking a balance between low energy costs and the strategy of matching the treadmill speed.

The researchers conclude that the nervous system controls tasks in a smart way. It doesn't try to reduce variation that doesn't affect the goal – in this case, staying on the treadmill and simultaneously keeping energy costs low.