Publications

2008
Berg AM, Biewener AA. Kinematics and power requirements of ascending and descending flight in the pigeon (Columba livia). J Exp BiolJ Exp BiolJ Exp Biol. 2008;211 :1120-30.Abstract
Ascending or descending locomotion involves a change in potential energy (PE) and a corresponding change in power requirement. We sought to test whether the mechanical power required for steady ascending or descending flight is a simple sum of the power required for level flight and the power necessary for potential energy change. Pigeons (Columba livia) were trained to fly at varying angles of ascent and descent (60 degrees , 30 degrees , 0 degrees , -30 degrees , -60 degrees ), and were recorded using high-speed video. Detailed three-dimensional kinematics were obtained from the recordings, allowing analysis of wing movement. Aerodynamic forces and power requirements were then estimated from kinematic data. As expected, ;PE flight power' increased significantly with angle of flight (0.234 W deg.(-1)), though there appeared to be a limit on the amount of PE that the birds could gain or dissipate per wingbeat. We found that the total power output for flight at various angles was not different from the sum of power required for level flight and the PE rate of change for a given angle, except for the steep -60 degrees descent. The total power for steep descent was higher than this sum because of a higher induced power due to the bird's deceleration and slower flight velocity. Aerodynamic force estimates during mid-downstroke did not differ significantly in magnitude or orientation among flight angles. Pigeons flew fastest during -30 degrees flights (4.9+/-0.1 m s(-1)) and slowest at 60 degrees (2.9+/-0.1 m s(-1)). Although wingbeat frequency ranged from 6.1 to 9.6 Hz across trials, the variation was not significant across flight angles. Stroke plane angle was more horizontal, and the wing more protracted, for both +60 degrees and -60 degrees flights, compared with other flight path angles.
2007
Tobalske BW, Warrick DR, Clark CJ, Powers DR, Hedrick TL, Hyder GA, Biewener AA. Three-dimensional kinematics of hummingbird flight. J Exp BiolJ Exp BiolJ Exp Biol. 2007;210 :2368-82.Abstract
Hummingbirds are specialized for hovering flight, and substantial research has explored this behavior. Forward flight is also important to hummingbirds, but the manner in which they perform forward flight is not well documented. Previous research suggests that hummingbirds increase flight velocity by simultaneously tilting their body angle and stroke-plane angle of the wings, without varying wingbeat frequency and upstroke: downstroke span ratio. We hypothesized that other wing kinematics besides stroke-plane angle would vary in hummingbirds. To test this, we used synchronized high-speed (500 Hz) video cameras and measured the three-dimensional wing and body kinematics of rufous hummingbirds (Selasphorus rufus, 3 g, N=5) as they flew at velocities of 0-12 m s(-1) in a wind tunnel. Consistent with earlier research, the angles of the body and the stroke plane changed with velocity, and the effect of velocity on wingbeat frequency was not significant. However, hummingbirds significantly altered other wing kinematics including chord angle, angle of attack, anatomical stroke-plane angle relative to their body, percent of wingbeat in downstroke, wingbeat amplitude, angular velocity of the wing, wingspan at mid-downstroke, and span ratio of the wingtips and wrists. This variation in bird-centered kinematics led to significant effects of flight velocity on the angle of attack of the wing and the area and angles of the global stroke planes during downstroke and upstroke. We provide new evidence that the paths of the wingtips and wrists change gradually but consistently with velocity, as in other bird species that possess pointed wings. Although hummingbirds flex their wings slightly at the wrist during upstroke, their average wingtip-span ratio of 93% revealed that they have kinematically ;rigid' wings compared with other avian species.
Richards CT, Biewener AA. Modulation of in vivo muscle power output during swimming in the African clawed frog (Xenopus laevis). J Exp BiolJ Exp BiolJ Exp Biol. 2007;210 :3147-59.Abstract
The goal of this study is to explore how swimming animals produce the wide range of performance that is seen across their natural behaviors. In vivo recordings of plantaris longus muscle length change were obtained by sonomicrometry. Simultaneous with muscle length data, force measurements were obtained using a novel tendon buckle force transducer placed on the Achilles tendon of Xenopus laevis frogs during brief accelerating bursts of swimming. In vivo work loops revealed that the plantaris generates a variable amount of positive muscle work over a range of swimming cycle durations (from 0.23 to 0.76 s), resulting in a large range of cycle power output (from 2.32 to 74.17 W kg(-1) muscle). Cycle duration correlated negatively with cycle power, and cycle work correlated positively (varying as a function of peak cycle stress and, to a much lesser extent, fascicle strain amplitude). However, variation in cycle duration only contributed to 12% of variation in power, with cycle work accounting for the remaining 88%. Peak cycle stress and strain amplitude were also highly variable, yet peak stress was a much stronger predictor of cycle work than strain amplitude. Additionally, EMG intensity correlated positively with peak muscle stress (r(2)=0.53). Although the timing of muscle recruitment (EMG phase and EMG duty cycle) varied considerably within and among frogs, neither parameter correlated strongly with cycle power, cycle work, peak cycle stress or strain amplitude. These results suggest that relatively few parameters (cycle duration, peak cycle stress and strain amplitude) vary to permit a wide range of muscle power output, which allows anurans to swim over a large range of velocities and accelerations.
Nishikawa K, Biewener AA, Aerts P, Ahn AN, Chiel HJ, Daley MA, Daniel TL, Full RJ, Hale ME, Hedrick TL, et al. Neuromechanics: an integrative approach for understanding motor control. Integr Comp BiolIntegr Comp BiolIntegr Comp Biol. 2007;47 :16-54.Abstract
Neuromechanics seeks to understand how muscles, sense organs, motor pattern generators, and brain interact to produce coordinated movement, not only in complex terrain but also when confronted with unexpected perturbations. Applications of neuromechanics include ameliorating human health problems (including prosthesis design and restoration of movement following brain or spinal cord injury), as well as the design, actuation and control of mobile robots. In animals, coordinated movement emerges from the interplay among descending output from the central nervous system, sensory input from body and environment, muscle dynamics, and the emergent dynamics of the whole animal. The inevitable coupling between neural information processing and the emergent mechanical behavior of animals is a central theme of neuromechanics. Fundamentally, motor control involves a series of transformations of information, from brain and spinal cord to muscles to body, and back to brain. The control problem revolves around the specific transfer functions that describe each transformation. The transfer functions depend on the rules of organization and operation that determine the dynamic behavior of each subsystem (i.e., central processing, force generation, emergent dynamics, and sensory processing). In this review, we (1) consider the contributions of muscles, (2) sensory processing, and (3) central networks to motor control, (4) provide examples to illustrate the interplay among brain, muscles, sense organs and the environment in the control of movement, and (5) describe advances in both robotics and neuromechanics that have emerged from application of biological principles in robotic design. Taken together, these studies demonstrate that (1) intrinsic properties of muscle contribute to dynamic stability and control of movement, particularly immediately after perturbations; (2) proprioceptive feedback reinforces these intrinsic self-stabilizing properties of muscle; (3) control systems must contend with inevitable time delays that can simplify or complicate control; and (4) like most animals under a variety of circumstances, some robots use a trial and error process to tune central feedforward control to emergent body dynamics.
McGowan CP, Baudinette RV, Biewener AA. Modulation of proximal muscle function during level versus incline hopping in tammar wallabies (Macropus eugenii). J Exp BiolJ Exp BiolJ Exp Biol. 2007;210 :1255-65.Abstract
We examined the functional role of two major proximal leg extensor muscles of tammar wallabies during level and inclined hopping (12 degrees, 21.3% grade). Previous in vivo studies of hopping wallabies have revealed that, unlike certain avian bipeds, distal hindlimb muscles do not alter their force-length behavior to contribute positive work during incline hopping. This suggests that proximal muscles produce the increased mechanical work associated with moving up an incline. Based on relative size and architectural anatomy, we hypothesized that the biceps femoris (BF), primarily a hip extensor, and the vastus lateralis (VL), the main knee extensor, would exhibit changes in muscle strain and activation patterns consistent with increased work production during incline versus level hopping. Our results clearly support this hypothesis. The BF experienced similar activation patterns during level and incline hopping but net fascicle shortening increased (-0.5% for level hopping versus -4.2% for incline hopping) during stance when the muscle likely generated force. Unlike the BF, the VL experienced active net lengthening during stance, indicating that it absorbs energy during both level and incline hopping. However, during incline hopping, net lengthening was reduced (8.3% for level hopping versus 3.9% for incline hopping), suggesting that the amount of energy absorbed by the VL was reduced. Consequently, the changes in contractile behavior of these two muscles are consistent with a net production of work by the whole limb. A subsidiary aim of our study was to explore possible regional variation within the VL. Although there was slightly higher fascicle strain in the proximal VL compared with the distal VL, regional differences in strain were not significant, suggesting that the overall pattern of in vivo strain is fairly uniform throughout the muscle. Estimates of muscle work based on inverse dynamics calculations support the conclusion that both the BF and VL contribute to the additional work required for incline hopping. However, on a muscle mass-specific basis, these two muscles appear to contribute less than their share. This indicates that other hindlimb muscles, or possibly trunk and back muscles, must contribute substantial work during incline hopping.
Main RP, Biewener AA. Skeletal strain patterns and growth in the emu hindlimb during ontogeny. J Exp BiolJ Exp BiolJ Exp Biol. 2007;210 :2676-90.Abstract
Most studies examining changes in mechanical performance in animals across size have typically focused on inter-specific comparisons across large size ranges. Scale effects, however, can also have important consequences in vertebrates as they increase in size and mass during ontogeny. The goal of this study was to examine how growth and development in the emu (Dromaius novaehollandiae) hindlimb skeleton reflects the demands placed upon it by ontogenetic changes in locomotor mechanics and body mass. Bone strain patterns in the femur and tibiotarsus (TBT) were related to ontogenetic changes in limb kinematics, ground reaction forces, and ontogenetic scaling patterns of the cross-sectional bone geometry, curvature and mineral ash content over a 4.4-fold increase in leg length and 65-fold increase in mass. Although the distribution of principal and axial strains remained similar in both bones over the ontogenetic size range examined, principal strains on the cranial femur and caudal femur and TBT increased significantly during growth. The ontogenetic increase in principal strains in these bones was likely caused by isometry or only slight positive allometry in bone cross-sectional geometry during growth, while relative limb loading remained similar. The growth-related increase in bone strain magnitude was likely mitigated by increased bone mineralization and decreased curvature. Throughout most of ontogeny, shear strains dominated loading in both bones. This was reflected in the nearly circular cross-sectional geometry of the femur and TBT, suggesting selection for resistance to high torsional loads, as opposed to the more eccentric cross-sectional geometries often associated with the bending common to tetrapods with parasagittal limb orientations, for which in vivo bone strains have typically been measured to date.
Hedrick TL, Biewener AA. Low speed maneuvering flight of the rose-breasted cockatoo (Eolophus roseicapillus). I. Kinematic and neuromuscular control of turning. J Exp BiolJ Exp BiolJ Exp Biol. 2007;210 :1897-911.Abstract
Maneuvering flight has long been recognized as an important component of the natural behavior of many bird species, but has been the subject of little experimental work. Here we examine the kinematics and neuromuscular control of turning flight in the rose-breasted cockatoo Eolophus roseicapillus (N=6), testing predictions of maneuvering flight and control based on aerodynamic theory and prior kinematic and neuromuscular studies. Six cockatoos were trained to navigate between two perches placed in an L-shaped flight corridor, making a 90 degrees turn midway through each flight. Flights were recorded with three synchronized high-speed video cameras placed outside the corridor, allowing a three-dimensional reconstruction of wing and body kinematics through the turn. We simultaneously collected electromyography recordings from bilateral implants in the pectoralis, supracoracoideus, biceps brachii and extensor metacarpi radialis muscles. The cockatoos maneuvered using flapping, banked turns with an average turn radius of 0.92 m. The mean rate of change in heading during a complete wingbeat varied through the turn and was significantly correlated to roll angle at mid-downstroke. Changes in roll angle were found to include both within-wingbeat and among-wingbeat components that bear no direct relationship to one another. Within-wingbeat changes in roll were dominated by the inertial effects while among-wingbeat changes in roll were likely the result of both inertial and aerodynamic effects.
Hedrick TL, Usherwood JR, Biewener AA. Low speed maneuvering flight of the rose-breasted cockatoo (Eolophus roseicapillus). II. Inertial and aerodynamic reorientation. J Exp BiolJ Exp BiolJ Exp Biol. 2007;210 :1912-24.Abstract
The reconfigurable, flapping wings of birds allow for both inertial and aerodynamic modes of reorientation. We found evidence that both these modes play important roles in the low speed turning flight of the rose-breasted cockatoo Eolophus roseicapillus. Using three-dimensional kinematics recorded from six cockatoos making a 90 degrees turn in a flight corridor, we developed predictions of inertial and aerodynamic reorientation from estimates of wing moments of inertia and flapping arcs, and a blade-element aerodynamic model. The blade-element model successfully predicted weight support (predicted was 88+/-17% of observed, N=6) and centripetal force (predicted was 79+/-29% of observed, N=6) for the maneuvering cockatoos and provided a reasonable estimate of mechanical power. The estimated torque from the model was a significant predictor of roll acceleration (r(2)=0.55, P<0.00001), but greatly overestimated roll magnitude when applied with no roll damping. Non-dimensional roll damping coefficients of approximately -1.5, 2-6 times greater than those typical of airplane flight dynamics (approximately -0.45), were required to bring our estimates of reorientation due to aerodynamic torque back into conjunction with the measured changes in orientation. Our estimates of inertial reorientation were statistically significant predictors of the measured reorientation within wingbeats (r(2) from 0.2 to 0.37, P<0.0005). Components of both our inertial reorientation and aerodynamic torque estimates correlated, significantly, with asymmetries in the activation profile of four flight muscles: the pectoralis, supracoracoideus, biceps brachii and extensor metacarpi radialis (r(2) from 0.27 to 0.45, P<0.005). Thus, avian flight maneuvers rely on production of asymmetries throughout the flight apparatus rather than in a specific set of control or turning muscles.
Daley MA, Felix G, Biewener AA. Running stability is enhanced by a proximo-distal gradient in joint neuromechanical control. J Exp BiolJ Exp BiolJ Exp Biol. 2007;210 :383-94.Abstract
We currently know little about how animals achieve dynamic stability when running over uneven and unpredictable terrain, often characteristic of their natural environment. Here we investigate how limb and joint mechanics of an avian biped, the helmeted guinea fowl Numida meleagris, respond to an unexpected drop in terrain during running. In particular, we address how joint mechanics are coordinated to achieve whole limb dynamics. Based on muscle-tendon architecture and previous studies of steady and incline locomotion, we hypothesize a proximo-distal gradient in joint neuromechanical control. In this motor control strategy, (1) proximal muscles at the hip and knee joints are controlled primarily in a feedforward manner and exhibit load-insensitive mechanical performance, and (2) distal muscles at the ankle and tarsometatarso-phalangeal (TMP) joints are highly load-sensitive, due to intrinsic mechanical effects and rapid, higher gain proprioceptive feedback. Limb kinematics and kinetics during the unexpected perturbation reveal that limb retraction, controlled largely by the hip, remains similar to level running throughout the perturbed step, despite altered limb loading. Individual joints produce or absorb energy during both level and perturbed running steps, such that the net limb work depends on the balance of energy among the joints. The hip maintains the same mechanical role regardless of limb loading, whereas the ankle and TMP switch between spring-like or damping function depending on limb posture at ground contact. Initial knee angle sets limb posture and alters the balance of work among the joints, although the knee contributes little work itself. This distribution of joint function results in posture-dependent changes in work performance of the limb, which allow guinea fowl to rapidly produce or absorb energy in response to the perturbation. The results support the hypothesis that a proximo-distal gradient exists in limb neuromuscular performance and motor control. This control strategy allows limb cycling to remain constant, whereas limb posture, loading and energy performance are interdependent. We propose that this control strategy provides simple, rapid mechanisms for managing energy and controlling velocity when running over rough terrain.
Biewener AA, Daley MA. Unsteady locomotion: integrating muscle function with whole body dynamics and neuromuscular control. J Exp BiolJ Exp BiolJ Exp Biol. 2007;210 :2949-60.Abstract
By integrating studies of muscle function with analysis of whole body and limb dynamics, broader appreciation of neuromuscular function can be achieved. Ultimately, such studies need to address non-steady locomotor behaviors relevant to animals in their natural environments. When animals move slowly they likely rely on voluntary coordination of movement involving higher brain centers. However, when moving fast, their movements depend more strongly on responses controlled at more local levels. Our focus here is on control of fast-running locomotion. A key observation emerging from studies of steady level locomotion is that simple spring-mass dynamics, which help to economize energy expenditure, also apply to stabilization of unsteady running. Spring-mass dynamics apply to conditions that involve lateral impulsive perturbations, sudden changes in terrain height, and sudden changes in substrate stiffness or damping. Experimental investigation of unsteady locomotion is challenging, however, due to the variability inherent in such behaviors. Another emerging principle is that initial conditions associated with postural changes following a perturbation define different context-dependent stabilization responses. Distinct stabilization modes following a perturbation likely result from proximo-distal differences in limb muscle architecture, function and control strategy. Proximal muscles may be less sensitive to sudden perturbations and appear to operate, in such circumstances, under feed-forward control. In contrast, multiarticular distal muscles operate, via their tendons, to distribute energy among limb joints in a manner that also depends on the initial conditions of limb contact with the ground. Intrinsic properties of these distal muscle-tendon elements, in combination with limb and body dynamics, appear to provide rapid initial stabilizing mechanisms that are often consistent with spring-mass dynamics. These intrinsic mechanisms likely help to simplify the neural control task, in addition to compensating for delays inherent to subsequent force- and length-dependent neural feedback. Future work will benefit from integrative biomechanical approaches that employ a combination of modeling and experimental techniques to understand how the elegant interplay of intrinsic muscle properties, body dynamics and neural control allows animals to achieve stability and agility over a variety of conditions.
2006
McGowan CP, Duarte HA, Main JB, Biewener AA. Effects of load carrying on metabolic cost and hindlimb muscle dynamics in guinea fowl (Numida meleagris). J Appl Physiol (1985)J Appl Physiol (1985)J Appl Physiol (1985). 2006;101 :1060-9.Abstract
The goal of this study was to test whether the contractile patterns of two major hindlimb extensors of guinea fowl are altered by load-carrying exercise. We hypothesized that changes in contractile pattern, specifically a decrease in muscle shortening velocity or enhanced stretch activation, would result in a reduction in locomotor energy cost relative to the load carried. We also anticipated that changes in kinematics would reflect underlying changes in muscle strain. Oxygen consumption, muscle activation intensity, and fascicle strain rate were measured over a range of speeds while animals ran unloaded vs. when they carried a trunk load equal to 22% of their body mass. Our results showed that loading produced no significant (P > 0.05) changes in kinematic patterns at any speed. In vivo muscle contractile strain patterns in the iliotibialis lateralis pars postacetabularis and the medial head of the gastrocnemius showed a significant increase in active stretch early in stance (P < 0.01), but muscle fascicle shortening velocity was not significantly affected by load carrying. The rate of oxygen consumption increased by 17% (P < 0.01) during loaded conditions, equivalent to 77% of the relative increase in mass. Additionally, relative increases in EMG intensity (quantified as mean spike amplitude) indicated less than proportional recruitment, consistent with force enhancement via stretch activation, in the proximal iliotibialis lateralis pars postacetabularis; however, a greater than proportional increase in the medial gastrocnemius was observed. As a result, when averaged for the two muscles, EMG intensity increased in direct proportion to the fractional increase in load carried.
Main RP, Biewener AA. In vivo bone strain and ontogenetic growth patterns in relation to life-history strategies and performance in two vertebrate taxa: goats and emu. Physiol Biochem ZoolPhysiol Biochem ZoolPhysiol Biochem Zool. 2006;79 :57-72.Abstract
This study examined ontogenetic patterns of limb loading, bone strains, and relative changes in bone geometry to explore the relationship between in vivo mechanics and size-related changes in the limb skeleton of two vertebrate taxa. Despite maintaining similar relative limb loads during ontogeny, bone strain magnitudes in the goat radius and emu tibiotarsus generally increased. However, while the strain increases in the emu tibiotarsus were mostly insignificant, strains within the radii of adult goats were two to four times greater than in young goats. The disparity between ontogenetic strain increases in these taxa resulted from differences in ontogenetic scaling patterns of the cross-sectional bone geometry. While the cross-sectional and second moments of area scaled with negative allometry in the goat radius, these measures were not significantly different from isometry in the emu tibiotarsus. Although the juveniles of both taxa exhibited lower strains and higher safety factors than the adults, the radii of the young goats were more robust relative to the adult goats than were the tibiotarsi of the young compared with adult emu. Differences in ontogenetic growth and strain patterns in the limb bones examined likely result from different threat avoidance strategies and selection pressures in the juveniles of these two taxa.
Daley MA, Usherwood JR, Felix G, Biewener AA. Running over rough terrain: guinea fowl maintain dynamic stability despite a large unexpected change in substrate height. J Exp BiolJ Exp BiolJ Exp Biol. 2006;209 :171-87.Abstract
In the natural world, animals must routinely negotiate varied and unpredictable terrain. Yet, we know little about the locomotor strategies used by animals to accomplish this while maintaining dynamic stability. In this paper, we perturb the running of guinea fowl with an unexpected drop in substrate height (DeltaH). The drop is camouflaged to remove any visual cue about the upcoming change in terrain that would allow an anticipatory response. To maintain stability upon a sudden drop in substrate height and prevent a fall, the bird must compensate by dissipating energy or converting it to another form. The aim of this paper is to investigate the control strategies used by birds in this task. In particular, we assess the extent to which guinea fowl maintain body weight support and conservative spring-like body dynamics in the perturbed step. This will yield insight into how animals integrate mechanics and control to maintain dynamic stability in the face of real-world perturbations. Our results show that, despite altered body dynamics and a great deal of variability in the response, guinea fowl are quite successful in maintaining dynamic stability, as they stumbled only once (without falling) in the 19 unexpected perturbations. In contrast, when the birds could see the upcoming drop in terrain, they stumbled in 4 of 20 trials (20%, falling twice), and came to a complete stop in an additional 6 cases (30%). The bird's response to the unexpected perturbation fell into three general categories: (1) conversion of vertical energy (EV=EP+EKv) to horizontal kinetic energy (EKh), (2) absorption of EV through negative muscular work (-DeltaEcom), or (3) converting EP to vertical kinetic energy (EKv), effectively continuing the ballistic path of the animal's center of mass (COM) from the prior aerial phase. However, the mechanics that distinguish these categories actually occur along a continuum with varying degrees of body weight support and actuation by the limb, related to the magnitude and direction of the ground reaction force (GRF) impulse, respectively. In most cases, the muscles of the limb either produced or absorbed energy during the response, as indicated by net changes in COM energy (Ecom). The limb likely begins stance in a more retracted, extended position due to the 26 ms delay in ground contact relative to that anticipated by the bird. This could explain the diminished decelerating force during the first half of stance and the exchange between EP and EK during stance as the body vaults over the limb. The varying degree of weight support and energy absorption in the perturbed step suggests that variation in the initial limb configuration leads to different intrinsic dynamics and reflex action. Future investigation into the limb and muscle mechanics underlying these responses could yield further insight into the control mechanisms that allow such robust dynamic stability of running in the face of large, unexpected perturbations.
Daley MA, Biewener AA. Running over rough terrain reveals limb control for intrinsic stability. Proc Natl Acad Sci U S AProc Natl Acad Sci U S AProc Natl Acad Sci U S A. 2006;103 :15681-6.Abstract
Legged animals routinely negotiate rough, unpredictable terrain with agility and stability that outmatches any human-built machine. Yet, we know surprisingly little about how animals accomplish this. Current knowledge is largely limited to studies of steady movement. These studies have revealed fundamental mechanisms used by terrestrial animals for steady locomotion. However, it is unclear whether these models provide an appropriate framework for the neuromuscular and mechanical strategies used to achieve dynamic stability over rough terrain. Perturbation experiments shed light on this issue, revealing the interplay between mechanics and neuromuscular control. We measured limb mechanics of helmeted guinea fowl (Numida meleagris) running over an unexpected drop in terrain, comparing their response to predictions of the mass-spring running model. Adjustment of limb contact angle explains 80% of the variation in stance-phase limb loading following the perturbation. Surprisingly, although limb stiffness varies dramatically, it does not influence the response. This result agrees with a mass-spring model, although it differs from previous findings on humans running over surfaces of varying compliance. However, guinea fowl sometimes deviate from mass-spring dynamics through posture-dependent work performance of the limb, leading to substantial energy absorption following the perturbation. This posture-dependent actuation allows the animal to absorb energy and maintain desired velocity on a sudden substrate drop. Thus, posture-dependent work performance of the limb provides inherent velocity control over rough terrain. These findings highlight how simple mechanical models extend to unsteady conditions, providing fundamental insights into neuromuscular control of movement and the design of dynamically stable legged robots and prosthetic devices.
Biewener AA. Patterns of mechanical energy change in tetrapod gait: pendula, springs and work. J Exp Zool A Comp Exp BiolJ Exp Zool A Comp Exp BiolJ Exp Zool A Comp Exp Biol. 2006;305 :899-911.Abstract
Kinematic and center of mass (CoM) mechanical variables used to define terrestrial gaits are compared for various tetrapod species. Kinematic variables (limb phase, duty factor) provide important timing information regarding the neural control and limb coordination of various gaits. Whereas, mechanical variables (potential and kinetic energy relative phase, %Recovery, %Congruity) provide insight into the underlying mechanisms that minimize muscle work and the metabolic cost of locomotion, and also influence neural control strategies. Two basic mechanisms identified by Cavagna et al. (1977. Am J Physiol 233:R243-R261) are used broadly by various bipedal and quadrupedal species. During walking, animals exchange CoM potential energy (PE) with kinetic energy (KE) via an inverted pendulum mechanism to reduce muscle work. During the stance period of running (including trotting, hopping and galloping) gaits, animals convert PE and KE into elastic strain energy in spring elements of the limbs and trunk and regain this energy later during limb support. The bouncing motion of the body on the support limb(s) is well represented by a simple mass-spring system. Limb spring compliance allows the storage and return of elastic energy to reduce muscle work. These two distinct patterns of CoM mechanical energy exchange are fairly well correlated with kinematic distinctions of limb movement patterns associated with gait change. However, in some cases such correlations can be misleading. When running (or trotting) at low speeds many animals lack an aerial period and have limb duty factors that exceed 0.5. Rather than interpreting this as a change of gait, the underlying mechanics of the body's CoM motion indicate no fundamental change in limb movement pattern or CoM dynamics has occurred. Nevertheless, the idealized, distinctive patterns of CoM energy fluctuation predicted by an inverted pendulum for walking and a bouncing mass spring for running are often not clear cut, especially for less cursorial species. When the kinematic and mechanical patterns of a broader diversity of quadrupeds and bipeds are compared, more complex patterns emerge, indicating that some animals may combine walking and running mechanics at intermediate speeds or at very large size. These models also ignore energy costs that are likely associated with the opposing action of limbs that have overlapping support times during walking. A recent model of terrestrial gait (Ruina et al., 2005. J Theor Biol, in press) that treats limb contact with the ground in terms of collisional energy loss indicates that considerable CoM energy can be conserved simply by matching the path of CoM motion perpendicular to limb ground force. This model, coupled with the earlier ones of pendular exchange during walking and mass-spring elastic energy savings during running, provides compelling argument for the view that the legged locomotion of quadrupeds and other terrestrial animals has generally evolved to minimize muscle work during steady level movement.
Biewener AA, Ahn AN. Tired of fatigue? Factors affecting the force-length relationship of muscle. J Appl Physiol (1985)J Appl Physiol (1985)J Appl Physiol (1985). 2006;101 :5-6.
2005
Usherwood JR, Hedrick TL, McGowan CP, Biewener AA. Dynamic pressure maps for wings and tails of pigeons in slow, flapping flight, and their energetic implications. J Exp BiolJ Exp BiolJ Exp Biol. 2005;208 :355-69.Abstract
Differential pressure measurements offer a new approach for studying the aerodynamics of bird flight. Measurements from differential pressure sensors are combined to form a dynamic pressure map for eight sites along and across the wings, and for two sites across the tail, of pigeons flying between two perches. The confounding influence of acceleration on the pressure signals is shown to be small for both wings and tail. The mean differential pressure for the tail during steady, level flight was 25.6 Pa, which, given an angle of attack for the tail of 47.6 degrees , suggests the tail contributes 7.91% of the force required for weight support, and requires a muscle-mass specific power of 19.3 W kg(-1) for flight to overcome its drag at 4.46 m s(-1). Differential pressures during downstroke increase along the wing length, to 300-400 Pa during take-off and landing for distal sites. Taking the signals obtained from five sensors sited along the wing at feather bases as representative of the mean pressure for five spanwise elements at each point in time, and assuming aerodynamic forces act within the x-z plane (i.e. no forces in the direction of travel) and perpendicular to the wing during downstroke, we calculate that 74.5% of the force required to support weight was provided by the wings, and that the aerodynamic muscle-mass specific power required to flap the wings was 272.7 W kg(-1).
Wickler SJ, Hoyt DF, Biewener AA, Cogger EA, De La Paz KL. In vivo muscle function vs speed. II. Muscle function trotting up an incline. J Exp BiolJ Exp BiolJ Exp Biol. 2005;208 :1191-200.Abstract
Different locomotor tasks, such as moving up or down grades or changing speed, require that muscles adjust the amount of work they perform to raise or lower, accelerate or decelerate the animal's center of mass. During level trotting in the horse, the triceps had shortening strains of around 10.6% while the vastus shortened 8.1% during the stance phase. Because of the 250% increase in metabolic rate in horses trotting up a 10% incline which is, presumably, a result of the increased requirement for mechanical work, we hypothesized that muscle strain during trotting would be increased in both the triceps and the vastus over that observed when trotting on the level. Because times of contact are similar in level and incline trotting, we also hypothesized that strain rates of these muscles would be increased, accompanied by an increase in EMG activity. We examined the lateral head of the triceps and the vastus lateralis while trotting up a 10% incline (5.7 degrees) over a range of speeds. The triceps shortened by 18% compared with 10.6% shortening on the level, and the vastus shortened by 18.5% compared with 8.1% on the level. The increased shortening velocities that were observed in both muscles probably reduced the force that any given set of activated muscle fibers could produce. If this pattern held for other limb muscles that do work to elevate the horse's center of mass on an incline, then a greater volume of muscle would have to be recruited to generate an equivalent force for body support. This was reflected in significant increases in the EMG intensity (IEMG) of both muscles.
Soman A, Hedrick TL, Biewener AA. Regional patterns of pectoralis fascicle strain in the pigeon Columba livia during level flight. J Exp BiolJ Exp BiolJ Exp Biol. 2005;208 :771-86.Abstract
Regional fascicle strains were recorded in vivo from the pectoralis of carneau pigeons using sonomicrometry during level slow flight, together with regional electromyography (EMG) and deltopectoral crest (DPC) strain measurements of whole muscle force. Fascicle strain measurements were obtained at four sites within the pectoralis: the anterior (Ant), middle (Mid) and posterior (Post) sternobrachium (SB), and the smaller thoracobrachium (TB). Strains were also recorded along the intramuscular aponeurosis of the pectoralis to assess its 'in-series' compliance with respect to strains of Post SB and TB fascicles. In-series segment strains were also obtained along Ant SB and Mid SB fascicles, which insert directly on the DPC without attaching to the intramuscular aponeurosis. In-series segment strains differed from 2% to 17.2%, averaging differences of 6.1% at the Ant SB site and 1.4% at the Mid SB site. Temporal patterns of in-series fascicle segment strain were similar at both sites. Regional fascicle strains also exhibited similar temporal patterns of lengthening and shortening and were most uniform in magnitude at the Ant SB, Mid SB and TB sites (total strain: 33.7%, 35.9% and 33.2% respectively), but were smaller at the Post SB site (24.4%). Strains measured along the aponeurosis tracked the patterns of contractile fascicle strain but were significantly lower in magnitude (19.1%). Fascicle lengthening strains (+25.4%) greatly exceeded net shortening strains (-6.5%) at all sites. Much of the variation in regional fascicle strain patterns resulted from variation of in vivo recording sites among individual animals, despite attempts to define consistent regions for obtaining in vivo recordings. No significant variation in EMG activation onset was found, but deactivation of the Ant SB occurred before the other muscle sites. Even so, the range of variation was small, with all muscle regions being activated midway through lengthening (upstroke) and turned off midway through shortening (downstroke). While subtle differences in the timing and rate of fascicle strain may relate to differing functional roles of the pectoralis, regional patterns of fascicle strain and activation suggest a generally uniform role for the muscle as a whole throughout the wingbeat cycle. Shorter fascicles located in more posterior regions of the muscle underwent generally similar strains as longer fascicles located in more anterior SB regions. The resulting differences in fiber length were accommodated by strain in the intramuscular aponeurosis and rotation of the pectoralis insertion with respect to the origin. As a result, longer Ant and Mid SB fascicles were estimated to contribute substantially more work per unit mass than shorter Post SB and TB fascicles. When the mass fractions of these regions are accounted for, our regional fascicle strain measurements show that the anterior regions of the pectoralis likely contribute 76%, and the posterior regions 24%, of the muscle's total work output. When adjusted for mass fraction and regional fascicle strain, pectoralis work averaged 24.7+/-5.1 J kg(-1) (206.6+/-43.5 W kg(-1)) during level slow (approximately 4-5 m s(-1)) flight.
McGowan CP, Baudinette RV, Usherwood JR, Biewener AA. The mechanics of jumping versus steady hopping in yellow-footed rock wallabies. J Exp BiolJ Exp BiolJ Exp Biol. 2005;208 :2741-51.Abstract
The goal of our study was to explore the mechanical power requirements associated with jumping in yellow-footed rock wallabies and to determine how these requirements are achieved relative to steady-speed hopping mechanics. Whole body power output and limb mechanics were measured in yellow-footed rock wallabies during steady-speed hopping and moving jumps up to a landing ledge 1.0 m high (approximately 3 times the animals' hip height). High-speed video recordings and ground reaction force measurements from a runway-mounted force platform were used to calculate whole body power output and to construct a limb stiffness model to determine whole limb mechanics. The combined mass of the hind limb extensor muscles was used to estimate muscle mass-specific power output. Previous work suggested that a musculoskeletal design that favors elastic energy recovery, like that found in tammar wallabies and kangaroos, may impose constraints on mechanical power generation. Yet rock wallabies regularly make large jumps while maneuvering through their environment. As jumping often requires high power, we hypothesized that yellow-footed rock wallabies would be able to generate substantial amounts of mechanical power. This was confirmed, as we found net extensor muscle power outputs averaged 155 W kg(-1) during steady hopping and 495 W kg(-1) during jumping. The highest net power measured reached nearly 640 W kg(-1). As these values exceed the maximum power-producing capability of vertebrate skeletal muscle, we suggest that back, trunk and tail musculature likely play a substantial role in contributing power during jumping. Inclusion of this musculature yields a maximum power output estimate of 452 W kg(-1) muscle. Similar to human high-jumpers, rock wallabies use a moderate approach speed and relatively shallow leg angle of attack (45-55 degrees) during jumps. Additionally, initial leg stiffness increases nearly twofold from steady hopping to jumping, facilitating the transfer of horizontal kinetic energy into vertical kinetic energy. Time of contact is maintained during jumping by a substantial extension of the leg, which keeps the foot in contact with the ground.

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