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First published online March 8, 2005
Journal of Experimental Biology 208, 939-949 (2005)
Published by The Company of Biologists 2005
doi: 10.1242/jeb.01472

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Human hopping on very soft elastic surfaces: implications for muscle pre-stretch and elastic energy storage in locomotion

Chet T. Moritz^1,2,* and Claire T. Farley¹

¹ Locomotion Laboratory, Department of Integrative Physiology, University of Colorado, Boulder, CO 80309-0354 USA
² Department of Integrative Biology, University of California, Berkeley, CA 94720-3140 USA

View larger version (16K): [in a new window]   Fig. 1. (A,B) Peak downward center of mass displacement during stance (COM), peak `leg' compression and peak `surface' compression vs surface stiffness for hopping at (A) 2.2 Hz and (B) 3.0 Hz. Positive leg compression values indicate shorter legs at midstance than at landing, and positive values for COM displacement and surface compression indicate downward movement. (C) Combined vertical stiffness of the leg and surface (Kvert) vs surface stiffness during hopping at 2.2 and 3.0 Hz. Values are means and S.E.M.s for all subjects, lines are least squares regressions and many error bars are hidden by symbols. The arrows indicate when the surface stiffness equals the preferred vertical stiffness at 2.2 Hz (filled arrows) and 3.0 Hz (open arrows). At this surface stiffness, center of mass displacement equals surface displacement. The dashed line in (C) indicates equal vertical stiffness and surface stiffness over the entire range. Vertical stiffness exceeded surface stiffness on the softest surfaces because the legs extended while the surface simultaneously compressed in the first half of stance.

View larger version (31K): [in a new window]   Fig. 2. Examples of displacements, powers, joint angles and vertical ground reaction force vs time for hopping at 2.2 Hz on the 81, 15 and 11 kN m-1 surfaces. All traces begin at landing and end at takeoff. Stick figures show body posture and surface position at instants of landing, peak force and takeoff on each surface. On the stiffest surface (81 kN m-1), the legs first compressed and then extended, leading to in-phase kinematics and power of the leg, center of mass (COM) and surface. Also, the joints flexed and then extended. On the 15 kN m-1 surface, the legs barely changed length and the center of mass followed the surface motion and power. On the softest surface (11 kN m-1), the legs first extended and then compressed, resulting in out-of-phase leg and surface power. The transient changes in leg length on the 15 and 11 kN m-1 surfaces are likely due to the fact that small changes in muscle force result in large changes in surface compression and thus leg length, on the softest surfaces.

View larger version (23K): [in a new window]   Fig. 3. Example leg force vs leg length change for the same subject as in Fig. 2 hopping at (A) 2.2 Hz and (B) 3.0 Hz on a range of surfaces. Surface stiffness values are above each curve. Thick lines represent early stance and thin lines represent late stance. On the stiffest surface, the spring-like legs compressed as force rose to its peak at midstance (thick line) and then extended as force fell until takeoff (thin line). In contrast, on the softest surface, legs extended as force rose to its peak and then compressed as force fell to zero at takeoff. The slight increase in area of the leg force–displacement work loops on softer surfaces offset the slightly greater energy dissipated by the surface when it compressed further. The increase in stiffness at peak force on the softest surfaces in A was observed in four of the eight subjects.

View larger version (17K): [in a new window]   Fig. 4. Mechanical work by the legs during the landing (circles) and takeoff (squares) parts of the stance phase vs surface stiffness for hopping at (A) 2.2 Hz and (B) 3.0 Hz. Values are means and S.E.M.s for all subjects, lines are least squares regressions and error bars are hidden by symbols. Arrows indicate when the surface stiffness equals the preferred vertical stiffness at 2.2 Hz (filled arrow) and 3.0 Hz (open arrow). On all surfaces, the magnitudes of the positive and negative work were equal because the surfaces dissipated negligible energy. On stiffer surfaces, the legs absorbed mechanical energy (i.e. performed negative work) during landing and then performed positive mechanical work during takeoff. In contrast, on softer surfaces, this sequence was reversed. The legs performed positive work during landing and then absorbed mechanical energy during takeoff. Leg work was not minimized when surface stiffness and vertical stiffness were equal due to small transient changes in leg length in early and late stance (see Fig. 2B) that were not reflected in the values for leg compression between touchdown and midstance in Fig. 1.

View larger version (35K): [in a new window]   Fig. 5. Example rectified EMG vs time during hopping at 2.2 Hz on the 81, 27 and 11 kN m-1 surfaces for the (A–C) soleus (SOL), (D–F) vastus medialis (VM), (G–I) vastus lateralis (VL) and (J–L) rectus femoris (RF). All traces begin at touchdown and end at the following touchdown. First and second dashed lines indicate the times of peak force and takeoff, respectively. Hoppers had the least extensor muscle activity on a moderately stiff surface (27 kN m-1) and more activity on the softer and stiffer surfaces.

View larger version (10K): [in a new window]   Fig. 6. Extensor muscle mean EMG during the stance phase (mean ± S.E.M.) vs surface stiffness for hopping at (A) 2.2 Hz and (B) 3.0 Hz. Extensor muscles are SOL, MG, LG, VM, VL, RF and ST. Mean EMG values are expressed as a percent of the mean EMG during stance phase on the 81 kN m-1 surface during 2.2 Hz hopping. Solid lines are least squared regressions. Arrows indicate when the surface stiffness equals the preferred vertical stiffness at 2.2 Hz (filled arrows) and 3.0 Hz (open arrows). Extensor muscle activation was minimized on the 27 kN m-1 surface when hopping at 2.2 Hz, whereas absolute leg work was minimized on the 17 kN m-1 surface (see Fig. 4).

View larger version (32K): [in a new window]   Fig. 7. Individual extensor muscle mean EMG during the stance phase (mean ± S.E.M.) vs surface stiffness for hopping at (A, C and E) 2.2 Hz and (B, D and F) 3.0 Hz. Muscles are grouped by those that extend the angle (A and B), knee (C and D) and hip (E and F). All values are expressed as a percent of the mean EMG for that particular muscle during stance phase on the 81 kN m-1 surface during 2.2 Hz hopping. Notice that vertical axis scale differs to accommodate the large increase in RF EMG during hopping at 3.0 Hz. Muscles extending the same joint exhibit similar trends in EMG across the range of surface stiffness, possibly as a result of series elastic stiffness of the shared distal tendons.