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First published online August 17, 2007
Journal of Experimental Biology 210, 2949-2960 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.005801

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Unsteady locomotion: integrating muscle function with whole body dynamics and neuromuscular control

Andrew A. Biewener^1,*, and Monica A. Daley^2,*

¹ Concord Field Station, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 01238, USA
² Department of Movement Science, Division of Kinesiology, University of Michigan, Ann Arbor, MI 48109, USA

View larger version (26K): [in this window] [in a new window]   Fig. 1. (A) Spring-mass model (or `spring-loaded inverted pendulum', SLIP) for the dynamics of legged terrestrial locomotion. The body is represented by a point mass m, located at the body center of mass (CoM; black circle), and the leg by a linear compression spring with leg stiffness kleg and contact angle o. (B) Despite its simplicity, the spring-mass model accurately describes the fluctuations in mechanical energy of the body during running (PEg, gravitational potential energy; KEv and KEh, vertical and horizontal kinetic energy, respectively; Ecom, center of mass energy) (Daley and Biewener, 2006; Daley et al., 2006). (C) Furthermore, all terrestrial animals appear to exhibit spring-mass dynamics, whether they run on two, four, six or eight legs. Multiple legs act in concert to produce the effective `leg-spring' dynamics (Holmes et al., 2006). (D) Similarly, a lateral spring-mass model describes well the medio-lateral dynamics of cockroach locomotion, in which three legs operate as a single effective `leg-spring' in the medio-lateral plane (Full et al., 2002).

View larger version (16K): [in this window] [in a new window]   Fig. 2. Gastrocnemius muscle performance in a human (A) and guinea fowl (B) during running. Traces are scaled to align the stance periods of the running stride (broken lines). EMG traces in A and B are rectified and averaged over many stride cycles. (A) Average human gastrocnemius activity (EMG) relative to ground reaction force (Dietz et al., 1979), along with gastrocnemius fascicle length measured from ultrasound recordings [traced from fig. 3 in Lichtwark and Wilson (Lichtwark and Wilson, 2006)]. (B) Average guinea fowl gastrocnemus activity (EMG), muscle–tendon force and fascicle length [thin lines indicate s.e.m. (Daley, 2006)]. Note that the muscle is activated with similar timing and undergoes a similar strain pattern during stance in both the human and guinea fowl (as well as other animals). The muscle is activated in anticipation of stance, with increases in activity during stance suggestive of reflex feedback (e.g. Dietz et al., 1979).

View larger version (32K): [in this window] [in a new window]   Fig. 3. Proximo-distal differences in muscle architecture within the hindlimb of a cursorial animal (similar patterns occur in the forelimb and in the limbs of other running birds and mammals). Representative fascicle strain (red) and myoelectric (EMG) patterns (black) recorded in vivo from muscles of various animals are shown in relation to proximo-distal differences in muscle–tendon architecture. For fascicle strain traces, the tick on the scale bar indicates zero strain (the estimated resting length of the fascicles, based on the average length during quiet standing). In vivo forces (gray) are also shown for the two distal muscles. Fascicle strain and time scales are the same for all muscle recordings shown. Duration of stance phase is shaded gray.

View larger version (22K): [in this window] [in a new window]   Fig. 4. (A) Schematic representation of regional patterns of joint work over the course of stance summarizing patterns observed for muscle groups of various animals during running. Curved arrows indicate the rotational motion of the distal segment of each joint (clockwise versus counterclockwise). Arrow color shows whether net energy is produced (red) or absorbed (blue) or zero (gray) at that joint during stance. These joint patterns are shown in relation to muscle work patterns in B and C. Muscle path arrows indicate hypothesized contraction of muscle groups, undergoing net shortening and positive work (red), lengthening and negative work (blue), or no net length change (gray). In this example, the hip extends, doing positive work mainly during the second half of stance (C); the knee flexes, doing negative work (energy absorption) mainly during the first half of stance (B); the ankle initially flexes during the first half of stance (B) and then extends during the second half of stance (C), doing net positive work; and the TMP (tarsometatarsal–phalangeal) joint dorsiflexes doing negative work throughout stance, though shown in B only (overall limb work is zero, characteristic of steady level locomotion assuming no work is done by other pelvic and trunk muscles). In comparison, the hamstrings (biceps) shorten while active, performing positive work (second half of stance, C); the quadriceps (vastus) undergo net lengthening while active doing negative work (first half of stance, B); the triceps surae [gastrocnemius (soleus, not shown) and plantaris] contract isometrically doing zero net work throughout stance, whereas the digital flexors are stretched and absorb energy initially (B) and then remain isometric during the second half of stance (not shown). As a result of their biarticular organization, the gastrocnemius, plantaris and digital flexor act as force links and, although they do no significant net work as a group, act to transfer energy from the hip and knee joints (via the hamstrings and/or quadriceps) to the ankle joint. This pattern is observed during steady level locomotion as well as during jumping in several species. See text for additional details.

View larger version (39K): [in this window] [in a new window]   Fig. 5. Distal-limb muscle performance during running on a slope in guinea fowl (A,B) and turkeys (C). (A) Fascicle strain (via sonomicrometry), EMG and muscle–tendon force in the lateral gastrocnemius (LG) of guinea fowl during running on the level versus the incline. Although LG work output increases by increased fascicle shortening and force development on an incline, (B) total and mass-specific work performance of the LG (and digital flexors) is less than if each hindlimb muscle contributed work in proportion to its mass, and small compared to the whole-body work demand (see Daley and Biewener, 2003). (C) Patterns of fascicle strain, force and muscle work for the LG and peroneus longus (PL) of turkeys running on the level, incline and decline show that these muscles also modulate their mechanical work output largely by changes in lengthening versus shortening strain [part C was originally published in Gabaldón et al. (Gabaldón et al., 2004)]. In C, negative strain and velocity indicate lengthening, filled circles are averages over stance, and open circles are averages over the period of force production within stance.

View larger version (29K): [in this window] [in a new window]   Fig. 6. Proximal muscle strain (bold lines) and EMG patterns (thin lines) recorded in vivo during level (red traces) versus incline (blue traces) locomotion for muscles of various animals (gait indicated in parentheses on right). Example patterns show increased shortening of the horse triceps and vastus (Wickler et al., 2005), the rat biceps (Gillis and Biewener, 2002) and wallaby biceps femoris (McGowan et al., 2007), as well as reduced net lengthening of the wallaby vastus, when moving on an incline. Stance duration is shown by the light red (level) and light blue (incline) shading. All muscles are displayed with the same fascicle strain and temporal scales. For fascicle strain traces, the tick on the scale bar indicates zero strain.

View larger version (37K): [in this window] [in a new window]   Fig. 7. Body CoM dynamics following perturbations in relation to spring-mass model dynamics. (A) Computer simulation of the spring-mass trajectory following a change from a soft to hard surface, with no change in leg stiffness (kleg), resulting in an asymmetrical CoM path and a steep trajectory during take-off at the end of support. (B) Actual CoM vertical displacement of a human runner encountering an abrupt but expected change from a soft to hard substrate. The runner maintains similar (symmetrical) CoM motion by anticipating the change and adjusting kleg within the first step (Ferris et al., 1999). (C) Computer simulation of the spring-mass trajectory following a sudden, unexpected drop in substrate height (40% of leg length). In the perturbed step, the only model value that differs from the level step is the limb contact angle (o), which is steeper due to the backward motion of the limb before it contacts the ground (see also Fig. 8B). The angle used in the simulation was that measured experimentally from guinea fowl. (D) Actual CoM trajectory and energy changes of running guinea fowl following an unexpected drop in substrate height equal to 40% of leg length (PEg, solid blue line; KEv and KEh, solid green and broken purple lines; Ecom, total center of mass energy, solid black line). The broken vertical gray line indicates when the foot contacted the tissue paper `false floor', and the gray box indicates the duration of stance. The bar graph (right) shows the net energy changes during the step (between the start and end of the traces on the left). Two response modes were observed: in most cases the body dynamics of the bird match the conservative spring-mass model (as shown in C), converting lost PEg to forward KE (D, top graphs). In some cases, however, the limb muscles absorb net energy, decreasing the total body mechanical energy (Ecom; D, bottom graphs). The different response modes are associated with different limb postures when the foot contacts the ground (Daley and Biewener, 2006; Daley et al., 2006).

View larger version (16K): [in this window] [in a new window]   Fig. 8. Postural influences on intrinsic limb dynamics following a perturbation. Intrinsic mechanical changes can simplify control and stabilization of running dynamics, because these mechanisms rely on the natural dynamics of the body and limb interacting with the environment, without the need for altered muscle activation through central or reflex neural pathways. (A) Following an unexpected change in substrate properties during hopping in place, humans exhibit an intrinsic decrease in limb stiffness (kleg) due to increased flexion of the knee in response to rapid limb loading (Moritz and Farley, 2004). (B) Upon encountering an unexpected drop in terrain height, guinea fowl exhibit an intrinsic increase in limb contact angle (o) due to the normal backward motion of the limb during late swing phase just prior to ground contact (to match foot and ground speed). If the limb acts as a simple compression spring, limb loading (and ground reaction force) depends on the angle between the limb and the bird's velocity (o). The backward motion of the limb in the drop step results in altered geometry as shown, which is associated with an intrinsic decrease in the ground reaction force impulse over stance (the time integral of force, Fg), due to decreased peak force and shorter contact duration. These dynamics are consistent with the spring-mass model (Daley and Biewener, 2006).

View larger version (29K): [in this window] [in a new window]   Fig. 9. The left panel schematically illustrates the hypothesized interplay between feed-forward muscle activation and intrinsic mechanical effects during running over a terrain drop (solid line) perturbation. Arrow color and direction conventions are the same as in Fig. 4. (A) Activation of muscles in anticipation of stance results in extension of the hip, ankle and TMP joints upon tissue paper (dotted line) contact. Depending on the balance among multiarticular muscles at the knee joint, the knee either flexes (A) or remains relatively extended (B). This alters limb posture and limb loading at ground contact. When the knee is flexed and o close to vertical (A), limb loading is low, and the distal joints act as springs (purple and blue cumulative work curves for the ankle and TMP joints absorb with low net work output). When the knee is relatively extended and o is lower (B), limb loading is greater, and the distal muscles undergo stretch, resulting in net energy absorption (blue arrows for distal muscles, and negative cumulative work for the ankle and TMP joints). In contrast the hip behaves uniformly, producing energy, as if the hip extensors are under feed-forward control and insensitive to perturbations. The knee does little net work under either condition. We hypothesize that variation in the breaking force of the tissue paper results in altered distal muscle contraction dynamics during the perturbation (on left, greater and lower distal muscle work production in A and B, respectively), leading to altered stance phase limb posture and dynamics