Journal of Applied Physiology
Vol. 82, No. 1, pp. 13-14, January 1997

Invited Editorial on "Interaction of leg stiffness and surface stiffness during human hopping"

R. McN. Alexander

Department of Biology, University of Leeds, Leeds LS2 9JT, United Kingdom

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ACKNOWLEDGEMENTS

REFERENCES

ARTICLE

WHEN A HUMAN RUNS or a kangaroo hops, the center of mass of the body rises and falls like a bouncing ball. The analogy has proved helpful in several studies of running and hopping (e.g., Ref. 9) and is used again by Ferris and Farley in an article (6) in this issue of the Journal. They ask whether we modify the springlike properties of our legs to suit the elastic properties of the floor or ground on which we are moving. They have found it convenient to study hopping in place rather than forward running.

If a spring obeys Hooke's law, its changes of length are directly proportional to changes in the force acting on it. There are two ways of describing this property. The stiffness of a spring is (force change/length change), and the compliance is the reciprocal of that, i.e., (length change/force change). In this editorial, I use compliance, because the compliance of two springs connected in series is simply the sum of the compliances of the individual springs. When a person hops or runs on a springy floor, the compliance of the floor is added to the compliance of her or his legs.

Observations of humans and animals running on rigid floors have shown that the legs behave approximately as Hookean springs (9) and that leg compliance is independent of running speed. This is not inevitable; in an earlier study (4), Farley and her colleagues asked subjects to hop at different frequencies or to different heights and showed that leg stiffness could be varied at will. (Higher frequencies for constant height and greater heights at constant frequency require less compliant legs.) Also, changes of stride frequency when subjects run at constant speed are made possible by changed leg compliance (5).

In the new study, Ferris and Farley (6) had subjects hop at constant frequency on a platform of variable compliance. At its most compliant setting, the platform was depressed 70 mm by the peak force. They found that leg compliance was reduced as platform compliance increased, keeping the total compliance constant.

The leg may behave like a physical spring, but its properties depend only in part on elastic compliance. A spring absorbs energy (does negative work) as it is stretched and does positive work as it shortens, and a muscle does not need elastic properties to do the same. Like other solids, muscle has true elastic compliance, but this allows its fibers to be stretched by only ~1.3% when the muscle contracts isometrically. Consequently, muscle compliance is unimportant in running, compared with tendon compliance (1). Humans have two important springs in their legs, leg tendons and the ligaments of the arch of the foot (8). Together, these account for about one-half of the apparent compliance of the leg. Inelastic lengthening and shortening of the muscles account for the rest.

In a study of kangaroo hopping (3), a distinction was made between the elastic compliance that resides mainly in the tendons and the inelastic pseudocompliance represented by muscles that do negative followed by positive work, as if they were springs. In kangaroos, as in people, the compliance and the pseudocompliance each account for roughly one-half of the (negative and positive) work done in each stride (3, 7).

A fully activated muscle contracting isometrically uses metabolic energy at a predictable rate. It uses energy faster when doing positive work and less fast when doing negative work (12). Also, it exerts less force when shortening and more when lengthening. Together, the metabolic rate-velocity and force-velocity relationships (Eqs. 2 and 5 in Ref. 11) imply that a muscle that does negative followed by positive work uses more metabolic energy than one that contracts isometrically while exerting the same forces. From this follows the principle of energy saving by elastic mechanisms in running; by doing some of the required (negative and positive) work, tendon compliance enables the muscles to work more nearly isometrically, and so saves metabolic energy (3). Ferris and Farley (6) explain this point by treating the metabolic cost of hopping as the sum of a cost of force production and a cost of work performance, an approach that may seem conceptually helpful but does not reflect the underlying physiological processes.

It is not clear to what extent the reduction of leg compliance, when hopping on compliant surfaces, is a reduction of true elastic compliance, and to what extent it is reduction of pseudocompliance. It is only by reducing the pseudocompliance that metabolic energy can be saved.

For vertical hopping, the overall compliance of the leg (its length change divided by the force) is identical to the vertical compliance (the vertical displacement of the hip, divided by the force), but for running, the overall compliance is much greater than the vertical compliance (9). It is the overall compliance that is kept constant in running at different speeds and that determines the (potential plus kinetic) energy changes at each footfall. Ferris and Farley (6) compare running-surface stiffnesses with the vertical stiffness of a runner's leg. However, the overall compliance (~0.1 mm/N; Ref. 9) is much greater than the compliance of the Harvard-tuned track (0.004 mm/N; Ref. 10) or of the soles of training shoes (~0.005 mm/N; Ref. 2). We should not expect runners to make substantial changes of overall compliance, to suit different tracks or shoes.

ACKNOWLEDGEMENTS

Dr. R. F. Ker made valuable comments on a draft of this editorial.

REFERENCES