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.
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.
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.
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.
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.
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.
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.
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.
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).
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.
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.
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.
Measurements of joint work and power were determined using inverse dynamics analysis based on ground reaction force and high-speed video recordings of tammar wallabies as they decelerated and accelerated while hopping over a force platform on level ground. Measurements were obtained over a range of accelerations ranging from -6 m s(-2) to 8 m s(-2). The goal of our study was to determine which joints are used to modulate mechanical power when tammar wallabies change speed. From these measurements, we also sought to determine which hind limb muscle groups are the most important for producing changes in mechanical work. Because our previous in vivo analyses of wallaby distal muscle function indicated that these muscle-tendon units favor elastic energy savings and perform little work during steady level and incline hopping, we hypothesized that proximal muscle groups operating at the hip and knee joint are most important for the modulation of mechanical work and power. Of the four hind limb joints examined, the ankle joint had the greatest influence on the total limb work, accounting for 89% of the variation observed with changing speed. The hip and metatarsophalageal (MP) joints also contributed to modulating whole limb work, but to a lesser degree than the ankle, accounting for 28% (energy production) and -24% (energy absorption) of the change in whole limb work versus acceleration, respectively. In contrast, the work produced at the knee joint was independent of acceleration. Based on the results of our previous in vivo studies and given that the magnitude of power produced at the ankle exceeds that which these muscles alone could produce, we conclude that the majority of power produced at the ankle joint is likely transferred from the hip and knee joints via proximal bi-articular muscles, operating in tandem with bi-articular ankle extensors, to power changes in hopping speed of tammar wallabies. Additionally, over the observed range of performance, peak joint moments at the ankle (and resulting tendon strains) did not increase significantly with acceleration, indicating that having thin tendons favoring elastic energy storage does not necessarily limit a tammar wallaby's ability to accelerate or decelerate.
The activity of muscles can be concentric (shortening), eccentric (lengthening) or isometric (constant length). When studying muscle function it is important to know what the muscle fascicles are actually doing because the performance of muscle is strongly influenced by the type of activity: force decreases as a function of shortening velocity during concentric contractions; force produced during eccentric contractions can be stronger than maximum isometric force, and force production is enhanced if a concentric contraction follows an eccentric phase. It is well known that length changes of muscle fascicles may be different from length changes of the overall muscle-tendon unit because of the compliance of the series elasticity. Consequently, fascicles of joint extensor muscles may not undergo eccentric activity even when the joint flexes, but the extent to which this occurs may vary with the compliance of the series elasticity and may differ between species: the vastus lateralis, a knee extensor, shortens when active during trotting in dogs and lengthens in rats. Previous studies of kinematics of trotting in horses have shown that during stance, the elbow extends nearly continuously with a brief period of flexion near mid-stance and the knee exhibits two phases of flexion followed by extension. The lateral triceps (an elbow extensor) has no external tendon but the vastus lateralis has a relatively long external tendon and the fascicles insert on an aponeurosis. Thus, one might expect the relation between fascicle strain and overall length change of the muscle-tendon units to be quite different in these two muscles. In the present study in horses, fascicle length changes of the lateral triceps and vastus lateralis were measured with sonomicrometry and length changes of the muscle-tendon units were estimated from muscle architecture and joint kinematics for four horses trotting on a treadmill at nine speeds. Because the focus of this study was the relation between length changes of the muscle-tendon unit (estimated from kinematics) and length changes in the muscle fascicles, we divided the stance-phase sonomicrometry records into phases that corresponded to the alternating flexion and extension of the joint as indicated by the kinematic records. During its one eccentric phase, the triceps shortened by 0.7+/-0.4% despite a predicted lengthening of 1%. Similarly, the vastus shortened by 3.7+/-1.9% when kinematics predicted 3.2% lengthening. During their concentric phases the triceps shortened by 10.6% and the vastus shortened by 8.1%. Strain in the triceps did not change with speed but it did in the vastus. Strain rate increased with speed in both muscles as did the integrated EMG, indicating an increase in the volume of muscle recruited. Thus, despite differences in their architecture and the kinematic patterns of the associated joints, these two joint extensors exhibited similar activity.
Unlike homologous muscles in many vertebrates, which appear to function similarly during a particular mode of locomotion (e.g. red muscle in swimming fish, pectoralis muscle in flying birds, limb extensors in jumping and swimming frogs), a major knee extensor in mammalian quadrupeds, the vastus lateralis, appears to operate differently in different species studied to date. In rats, the vastus undergoes more stretching early in stance than shortening in later stance. In dogs, the reverse is true; more substantial shortening follows small amounts of initial stretching. And in horses, while the vastus strain trajectory is complex, it is characterized mainly by shortening during stance. In this study, we use sonomicrometry and electromyography to study the vastus lateralis and biceps femoris of goats, with three goals in mind: (1) to see how these muscles work in comparison to homologous muscles studied previously in other taxa; (2) to address how speed and gait impact muscle actions and (3) to test whether fascicles in different parts of the same muscle undergo similar length changes. Results indicate that the biceps femoris undergoes substantial shortening through much of stance, with higher strains in walking and trotting [32-33% resting length (L0)] than galloping (22% L0). These length changes occur with increasing biceps EMG intensities as animals increase speed from walking to galloping. The vastus undergoes a stretch-shorten cycle during stance. Stretching strains are higher during galloping (15% L0) than walking and trotting (9% L0). Shortening strains follow a reverse pattern and are greatest in walking (24% L0), intermediate in trotting (20% L0) and lowest during galloping (17% L0). As a result, the ratio of stretching to shortening increases from below 0.5 in walking and trotting to near 1.0 during galloping. This increasing ratio suggests that the vastus does relatively more positive work than energy absorption at the slower speeds compared with galloping, although an understanding of the timing and magnitude of force production is required to confirm this. Length-change regimes in proximal, middle and distal sites of the vastus are generally comparable, suggesting strain homogeneity through the muscle. When strain rates are compared across taxa, vastus shortening velocities exhibit the scaling pattern predicted by theoretical and empirical work: fascicles shorten relatively faster in smaller animals than larger animals (strain rates near 2 L s-1 have been reported for trotting dogs and were found here for goats, versus 0.6-0.8 L s-1 reported in horses). Interestingly, biceps shortening strain rates are very similar in both goats and rats during walking (1-1.5 L s-1) and trotting (1.5-2.5 L s-1, depending on speed of trot), suggesting that the ratio of in vivo shortening velocities (V) to maximum shortening velocities (Vmax) is smaller in small animals (because of their higher V(max)).
To function over a lifetime of use, materials and structures must be designed to have sufficient factors of safety to avoid failure. Vertebrates are generally built from materials having similar properties. Safety factors are most commonly calculated based on the ratio of a structure's failure stress to its peak operating stress. However, yield stress is a more likely limit, and work of fracture relative to energy absorption is likely the most relevant measure of a structure's safety factor, particularly under impact loading conditions characteristic of locomotion. Yet, it is also the most difficult to obtain. For repeated loading, fatigue damage and eventual failure may be critical to the design of biological structures and will result in lower safety factors. Although area:volume scaling predicts that stresses will increase with size, interspecific comparisons of mammals and birds show that skeletal allometry is modest, with most groups scaling (l proportional, variant d0.89) closer to geometric similarity (isometry: l proportional, variant d1.0) than to elastic similarity (l proportional, variant d0.67) or stress similarity (l proportional, variant d0.5). To maintain similar peak bone and muscle stresses, terrestrial mammals change posture when running, with larger mammals becoming more erect. More erect limbs increases their limb muscle mechanical advantage (EMA) or ratio of ground impulse to muscle impulse (r/R= integral G/integral Fm). The increase in limb EMA with body weight (proportional, variant W0.25) allows larger mammals to match changes in bone and muscle area (proportional, variant W0.72-0.80) to changes in muscle force generating requirements (proportional, variantW0.75), keeping bone and muscle stresses fairly constant across a size range 0.04-300 kg. Above this size, extremely large mammals exhibit more pronounced skeletal allometry and reduced locomotor ability. Patterns of ontogenetic scaling during skeletal growth need not follow broader interspecific scaling patterns. Instead, negative allometric growth (becoming more slender) is often observed and may relate to maturation of the skeleton's properties or the need for younger animals to move at faster speeds compared with adults. In contrast to bone and muscle stress patterns, selection for uniform safety factors in tendons does not appear to occur. In addition to providing elastic energy savings, tendons transmit force for control of motion of more distal limb segments. Their role in elastic savings requires that some tendons operate at high stresses (and strains), which compromises their safety factor. Other 'low stress' tendons have larger safety factors, indicating that their primary design is for stiffness to reduce the amount of stretch that their muscles must overcome when contracting to control movement.
As tetrapods increase in size and weight through ontogeny, the limb skeleton must grow to accommodate the increases in body weight and the resulting locomotor forces placed upon the limbs. No study to date, however, has examined how morphological changes in the limb skeleton during growth reflect ontogenetic patterns of limb loading and the resulting stresses and strains produced in the limbs. The goal of this study was to relate forelimb loads to in vivo bone strains in the radius of the domestic goat (Capra hircus) across a range of gaits and speeds through ontogeny while observing how the growth patterns of the bone relate to the mechanics of the limb. In vivo bone strains in the radius were recorded from two groups of juvenile goats (4 kg, 6 weeks and 9 kg, 15 weeks) and compared with previously reported strain data for the radius of adult goats. Ontogenetic strain patterns were examined in relation to peak forelimb ground reaction forces, ontogenetic scaling patterns of cross-sectional geometry and bone curvature, and percentage mineral ash content. Peak principal longitudinal tensile strains on the cranial surface and compressive strains on the caudal surface of the radius increased during ontogeny but maintained a uniform distribution, resulting in the radius being loaded primarily in bending through ontogeny. The increase in strain occurred despite uniform loading (relative to body weight) of the forelimb through ontogeny. Instead, the increase in bone strain resulted from strong negative growth allometry of the cross-sectional area (proportional to M(0.53)) and medio-lateral and cranio-caudal second moments of area (I(ML) proportional to M(1.03), I(CC) proportional to M(0.84)) of the radius and only a small increase (+2.8%) in mineral ash content. Even though bone strains increased with growth and age, strains in the younger goats were small enough to suggest that they maintain safety factors at least comparable with adults when moving at similar absolute speeds. Increased variability of loading in juvenile animals may also favor the more robust dimensions of the radius, and possibly other limb bones, early in growth.
We used a combination of high-speed 3-D kinematics and three-axis accelerometer recordings obtained from cockatiels flying in a low-turbulence wind tunnel to characterize the instantaneous accelerations and, by extension, the net aerodynamic forces produced throughout the wingbeat cycle across a broad range of flight speeds (1-13 m s(-1)). Our goals were to investigate the variation in instantaneous aerodynamic force production during the wingbeat cycle of birds flying across a range of steady speeds, testing two predictions regarding aerodynamic force generation in upstroke and the commonly held assumption that all of the kinetic energy imparted to the wings of a bird in flapping flight is recovered as useful aerodynamic work. We found that cockatiels produce only a limited amount of lift during upstroke (14% of downstroke lift) at slower flight speeds (1-3 m s(-1)). Upstroke lift at intermediate flight speeds (7-11 m s(-1)) was moderate, averaging 39% of downstroke lift. Instantaneous aerodynamic forces were greatest near mid-downstroke. At the end of each half-stroke, during wing turnaround, aerodynamic forces were minimal, but inertial forces created by wing motion were large. However, we found that the inertial power requirements of downstroke (minimum of 0.29+/-0.10 W at 7 m s(-1) and maximum of 0.56+/-0.13 W at 1 m s(-1)) were consistent with the assumption that nearly all wing kinetic energy in downstroke was applied to the production of aerodynamic forces and therefore should not be added separately to the overall power cost of flight. The inertial power requirements of upstroke (minimum of 0.16+/-0.04 W at 7 m s(-1) and maximum of 0.35+/-0.11 W at 1 m s(-1)) cannot be recovered in a similar manner, but their magnitude was such that the power requirements for the upstroke musculature (minimum of 54+/-13 W kg(-1) at 7 m s(-1) and maximum of 122+/-35 W at 1 m s(-1)) fall within the established range for cockatiel flight muscle (<185 W kg(-1)).
The goal of our study was to examine whether the in vivo force-length behavior, work and elastic energy savings of distal muscle-tendon units in the legs of tammar wallabies (Macropus eugenii) change during level versus incline hopping. To address this question, we obtained measurements of muscle activation (via electromyography), fascicle strain (via sonomicrometry) and muscle-tendon force (via tendon buckles) from the lateral gastrocnemius (LG) and plantaris (PL) muscles of tammar wallabies trained to hop on a level and an inclined (10 degrees, 17.4% grade) treadmill at two speeds (3.3 m s(-1) and 4.2 m s(-1)). Similar patterns of muscle activation, force and fascicle strain were observed under both level and incline conditions. This also corresponded to similar patterns of limb timing and movement (duty factor, limb contact time and hopping frequency). During both level and incline hopping, the LG and PL exhibited patterns of fascicle stretch and shortening that yielded low levels of net fascicle strain [LG: level, -1.0+/-4.6% (mean +/- S.E.M.) vs incline, 0.6+/-4.5%; PL: level, 0.1+/-1.0% vs incline, 0.4+/-1.6%] and muscle work (LG: level, -8.4+/-8.4 J kg(-1) muscle vs incline, -6.8+/-7.5 J kg(-1) muscle; PL: level, -2.0+/-0.6 J kg(-1) muscle vs incline, -1.4+/-0.7 J kg(-1) muscle). Consequently, neither muscle significantly altered its contractile dynamics to do more work during incline hopping. Whereas electromyographic (EMG) phase, duration and intensity did not differ for the LG, the PL exhibited shorter but more intense periods of activation, together with reduced EMG phase (P<0.01), during incline versus level hopping. Our results indicate that design for spring-like tendon energy savings and economical muscle force generation is key for these two distal muscle-tendon units of the tammar wallaby, and the need to accommodate changes in work associated with level versus incline locomotion is achieved by more proximal muscles of the limb.