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Probing the limits to muscle-powered accelerations: lessons from jumping bullfrogs

Thomas J. Roberts^* and Richard L. Marsh

Biology Department, Northeastern University, 414 Mugar, 360 Huntington Ave, Boston, MA 02115, USA

View larger version (8K): [in a new window]   Fig. 1. A diagram of the model for muscle-powered accelerations at rest (A) and during a contraction (B). To simulate a muscle–lever–load system (inset) with an effective mechanical advantage that could vary during the contraction, the muscle–tendon unit operated across a gearing system that included a controllable gearbox to accelerate a load. The muscle consisted of several actuators acting in parallel to produce muscle force–velocity, length–tension and activation properties. The movement was subject to inertial and gravitational forces. The properties and dimensions of the muscle and the load were chosen to approximate the entire hindlimb and body of a jumping frog.

View larger version (16K): [in a new window]   Fig. 2. The velocity, force and power of the center of mass of four frog jumps, as determined from high-speed video analysis. Time zero on the graphs was taken as the time of the beginning of electromyographic activity in the plantaris muscle. Takeoff angles for all four jumps were between 20° and 40° from the horizontal.

View larger version (23K): [in a new window]   Fig. 3. Fascicle velocities, lengths and electromyographic activity of the plantaris muscle for six jumps of differing lengths: (A,B) 80 cm, (C) 75 cm, (D,E) 50 cm, (F) 40 cm. Longer jumps are characterized by a bimodal pattern of shortening velocity, with the fastest velocities occurring early and late in the jump.

View larger version (24K): [in a new window]   Fig. 4. A comparison of the movement of the body (thick black lines) with the shortening of the plantaris muscle fascicles (thin red lines) in two frog jumps (frog 1 and frog 6). The velocity of shortening in the plantaris is independent of the velocity of the body (A,C). Panels B and D contrast the shortening of the plantaris muscle fascicles with the displacement of the body. At the point where half of the muscle fascicle shortening has occurred (vertical broken line), the body has undergone very little displacement. EMG, electromyographic activity.

View larger version (147K): [in a new window]   Fig. 5. Four frames from a high-speed video sequence of a frog jump. Frame 2 depicts the point where half of the plantaris muscle fascicle shortening has occurred.

View larger version (27K): [in a new window]   Fig. 6. A comparison of the movement of the modeled load (thick red line) with the movement of the body in the two longer frog jumps shown in Fig. 2 (thin blue and black lines). Each column of graphs presents the velocity, force and power of the load/body for a single contraction under one of four model configurations: (A) no series elastic element, constant effective mechanical advantage (EMA), (B) no series elastic element, decreasing EMA, (C) compliant series elastic element, constant EMA and (D) compliant series elastic element, increasing EMA. The shape of the force, velocity and power curves during jumping in frogs most closely resembles the model configuration shown in D, where the muscle actuator contracts through a series elastic element and a continuously increasing EMA. All model contractions occurred over the same total muscle strain and same total load displacement. Power is expressed in W kg-1 body mass.

View larger version (18K): [in a new window]   Fig. 7. Velocity, force and power output of the simulated muscle contractile element (thin red line), tendon (green line) and muscle–tendon unit (thick black line) for simulated jumps under the same four configurations as for Fig. 6: (A) no series elastic element, constant effective mechanical advantage (EMA), (B) no series elastic element, decreasing EMA, (C) compliant series elastic element, constant EMA and (D) compliant series elastic element, increasing EMA. All values are expressed relative to the maximum for the modeled muscle. When the muscle operates with a series elastic element (tendon), muscle velocity peaks early in the contraction due to stretch of the elastic element (top panels, C,D). Muscle–tendon power output can exceed peak isotonic power late in the jump due to high power outputs of the recoiling spring (bottom panels, C,D). When EMA is varied to maintain a constant muscle shortening velocity (B), power output is maintained at peak isotonic power until a small decline in force due to length–tension effects.

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