Modeling muscle function using experimentally determined subject-specific muscle properties.

Muscle models are commonly based on intrinsic properties pooled across a number of individuals, often from a different species, and rarely validated against directly measured muscle forces. Here we use a rich data set of rat medial gastrocnemius muscle forces recorded during in-situ and in-vivo isometric, isotonic, and cyclic contractions to test the accuracy of forces predicted using Hill-type muscle models. We identified force-length and force-velocity parameters for each individual, and used either these subject-specific intrinsic properties, or population-averaged properties within the models. The modeled forces for cyclic in-vivo and in-situ contractions matched with measured muscle-tendon forces with r2 between 0.70 and 0.86, and root-mean square errors (RMSE) of 0.10 to 0.13 (values normalized to the maximum isometric force). The modeled forces were least accurate at the highest movement and cycle frequencies and did not show an improvement in r2 when subject-specific intrinsic properties were used; however, there was a reduction in the RMSE with fewer predictions having higher errors. We additionally recorded and tested muscle models specific to proximal and distal regions of the muscle and compared them to measures and models from the whole muscle belly: there was no improvement in model performance when using data from specific anatomical regions. These results show that Hill-type muscle models can yield very good performance for cyclic contractions typical of locomotion, with small reductions in errors when subject-specific intrinsic properties are used.

Different Segments within Vertebrate Muscles Can Operate on Different Regions of Their Force-Length Relationships.

To relate in vivo behavior of fascicle segments within a muscle to their in vitro force-length relationships, we examined the strain behavior of paired segments within each of three vertebrate muscles. After determining in vivo muscle activity patterns and length changes of in-series segments within the semimembranosus muscle (SM) in the American Toad (Bufo americanus) during hopping and within the sternohyoid (SH) muscle in the rat (Rattus rattus) during swallowing, and of spatially separated fascicles within the medial gastrocnemius (MG) muscle in the rat during trotting, we measured their corresponding in vitro (toad) or in situ (rat) force-length relationships (FLRs). For all three muscles, in vivo strain heterogeneity lasted for about 36-57% of the behavior cycle, during which one segment or fascicle shortened while the other segment or fascicle simultaneously lengthened. In the toad SM, the proximal segment shortened from the descending limb across the plateau of its FLR from 1.12 to 0.91 of its optimal length (Lo), while the distal segment lengthened (by 0.04 ± 0.04 Lo) before shortening down the ascending limb from 0.94 to 0.83 Lo. In the rat SH muscle, the proximal segment tended to shorten on its ascending limb from 0.90 to 0.85 Lo while the distal segment tended to lengthen across Lo (0.96-1.12 Lo). In the rat MG muscle, in vivo strains of proximal fascicles ranged from 0.72 to 1.02 Lo, while the distal fascicles ranged from 0.88 to 1.11 Lo. Even though the timing of muscle activation patterns were similar between segments, the heterogeneous strain patterns of fascicle segments measured in vivo coincided with different operating ranges across their FLRs simultaneously, implying differences in force-velocity behavior as well. The three vertebrate skeletal muscles represent a diversity of fiber architectures and functions and suggest that patterns of in vivo contractile strain and the operating range over the FLR in one muscle region does not necessarily represent other regions within the same muscle.

The effect of fast and slow motor unit activation on whole-muscle mechanical performance: the size principle may not pose a mechanical paradox.

The output of skeletal muscle can be varied by selectively recruiting different motor units. However, our knowledge of muscle function is largely derived from muscle in which all motor units are activated. This discrepancy may limit our understanding of in vivo muscle function. Hence, this study aimed to characterize the mechanical properties of muscle with different motor unit activation. We determined the isometric properties and isotonic force-velocity relationship of rat plantaris muscles in situ with all of the muscle active, 30% of the muscle containing predominately slower motor units active or 20% of the muscle containing predominately faster motor units active. There was a significant effect of active motor unit type on isometric force rise time (p < 0.001) and the force-velocity relationship (p < 0.001). Surprisingly, force rise time was longer and maximum shortening velocity higher when all motor units were active than when either fast or slow motor units were selectively activated. We propose this is due to the greater relative effects of factors such as series compliance and muscle resistance to shortening during sub-maximal contractions. The findings presented here suggest that recruitment according to the size principle, where slow motor units are activated first and faster ones recruited as demand increases, may not pose a mechanical paradox, as has been previously suggested.

A constitutive description of the anisotropic response of the fascia lata.

In this paper we propose a constitutive model to analyze in-plane extension of goat fascia lata. We first perform a histological analysis of the fascia that shows a well-organized bi-layered arrangement of undulated collagen fascicles oriented along two well defined directions. To develop a model consistent with the tissue structure we identify the absolute and relative thickness of each layer and the orientation of the preferred directions. New data are presented showing the mechanical response in uniaxial and planar biaxial extension. The paper proposes a constitutive relation to describe the mechanical response. We provide a summary of the main ingredients of the nonlinear theory of elasticity and introduce a suitable strain-energy function to describe the anisotropic response of the fascia. We validate the model by showing good fit of the numerical results and the experimental data. Comments are included about differences and analogies between goat fascia lata and the human iliotibial band.

Hind limb scaling of kangaroos and wallabies (superfamily Macropodoidea): implications for hopping performance, safety factor and elastic savings.

The aim of this study was to examine hind limb scaling of the musculoskeletal system in the Macropodoidea, the superfamily containing wallabies and kangaroos, to re-examine the effect of size on the locomotor mechanics and physiology of marsupial hopping. Morphometric musculoskeletal analyses were conducted of 15 species and skeletal specimens of 21 species spanning a size range from 0.8 to 80 kg that included representatives of 12 of the 16 extant genera of macropodoids. We found that unlike other groups, macropodoids are able to match force demands associated with increasing body size primarily through a combination of positive allometry in muscle area and muscle moment arms. Isometric scaling of primary hind limb bones suggests, however, that larger species experience relatively greater bone stresses. Muscle to tendon area ratios of the ankle extensors scale with strong positive allometry, indicating that peak tendon stresses also increase with increasing body size but to a lesser degree than previously reported. Consistent with previous morphological and experimental studies, large macropodoids are therefore better suited for elastic strain energy recovery but operate at lower safety factors, which likely poses an upper limit to body size. Scaling patterns for extant macropodoids suggest that extinct giant kangaroos (approximately 250 kg) were likely limited in locomotor capacity.

Differential design for hopping in two species of wallabies.

Hindlimb musculoskeletal anatomy and steady speed over ground hopping mechanics were compared in two species of macropod marsupials, tammar wallabies and yellow-footed rock wallabies (YFRW). These two species are relatively closely related and are of similar size and general body plan, yet they inhabit different environments with presumably different musculoskeletal demands. Tammar wallabies live in relatively flat, open habitat whereas yellow-footed rock wallabies inhabit steep cliff faces. The goal of this study was to explore musculoskeletal differences between tammar wallabies and yellow-footed rock wallabies and determine how these differences influence each species' hopping mechanics. We found the cross-sectional area of the combined ankle extensor tendons of yellow-footed rock wallabies was 13% greater than that of tammar wallabies. Both species experienced similar ankle joint moments during steady-speed hopping, however due to a lower mechanical advantage at this joint, tammar wallabies produced 26% more muscle force. Thus, during moderate speed hopping, yellow-footed rock wallabies operated with 38% higher tendon safety factors, while tammar wallabies were able to store 73% more elastic strain energy (2.18 J per leg vs. 1.26 J in YFRW). This likely reflects the differing demands of the environments inhabited by these two species, where selection for non-steady locomotor performance in rocky terrain likely requires trade-offs in locomotor economy.

Low speed maneuvering flight of the rose-breasted cockatoo (Eolophus roseicapillus). I. Kinematic and neuromuscular control of turning.

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.

Low speed maneuvering flight of the rose-breasted cockatoo (Eolophus roseicapillus). II. Inertial and aerodynamic reorientation.

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.

Modulation of proximal muscle function during level versus incline hopping in tammar wallabies (Macropus eugenii).

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.

Running stability is enhanced by a proximo-distal gradient in joint neuromechanical control.

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.

Effects of load carrying on metabolic cost and hindlimb muscle dynamics in guinea fowl (Numida meleagris).

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.

The mechanics of jumping versus steady hopping in yellow-footed rock wallabies.

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.

Joint work and power associated with acceleration and deceleration in tammar wallabies (Macropus eugenii).

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.

Walking and running in the red-legged running frog, Kassina maculata.

Although most frog species are specialized for jumping or swimming, Kassina maculata (red-legged running frog) primarily uses a third type of locomotion during which the hindlimbs alternate. In the present study, we examined Kassina's distinct locomotory mode to determine whether these frogs walk or run and how their gait may change with speed. We used multiple methods to distinguish between terrestrial gaits: the existence or absence of an aerial phase, duty factor, relative footfall patterns and the mechanics of the animal's center of mass (COM). To measure kinematic and kinetic variables, we recorded digital video as the animals moved over a miniature force platform (N=12 individuals). With respect to footfall patterns, the frogs used a single gait and walked at all speeds examined. Duty factor always exceeded 0.59. Based on COM mechanics, however, the frogs used both walking and running gaits. At slower speeds, the fluctuations in the horizontal kinetic energy (E(k)) and gravitational potential energy (E(p)) of the COM were largely out of phase, indicating a vaulting or walking gait. In most of the trials, Kassina used a combined gait at intermediate speeds, unlike cursorial animals with distinct gait transitions. This combined gait, much like a mammalian gallop, exhibited the mechanics of both vaulting and bouncing gaits. At faster speeds, the E(k) and E(p) of Kassina's COM were more in phase, indicating the use of a bouncing or running gait. Depending on the definition used to distinguish between walking and running, Kassina either only used a walking gait at all speeds or used a walking gait at slower speeds but then switched to a running gait as speed increased.

Dynamics of leg muscle function in tammar wallabies (M. eugenii) during level versus incline hopping.

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.

In vivo and in vitro heterogeneity of segment length changes in the semimembranosus muscle of the toad.

Many studies examine sarcomere dynamics in single fibres or length-tension dynamics in whole muscles in vivo or in vitro, but few studies link the various levels of organisation. To relate data addressing in vitro muscle segment behaviour with in vivo whole muscle behaviour during locomotion, we measured in vivo strain patterns of muscle segments using three sonomicrometry crystals implanted along a fascicle of the semimembranosus muscle in the American toad (Bufo americanus; n = 6) during hopping. The centre crystal emitted an ultrasonic signal, while the outer crystals received the signal allowing the instantaneous measurement of lengths from two adjacent muscle segments. On the first day, we recorded from the central and distal segments. On the second day of recordings, the most distal crystal was moved to a proximal position to record from a proximal segment and the same central segment. When the toads hopped a distance of two body lengths, the proximal and central segments strained -15.1 +/- 6.1 and -14.0 +/- 4.9 % (i.e. shortening), respectively. Strain of the distal segment, however, was significantly lower and more variable in pattern, often lengthening before shortening during a hop. From rest length, the distal segment initially lengthened by 2.6 +/- 2.0 % before shortening by 6.5 +/- 3.2 % at the same hop distance. Under in vitro conditions, the central segment always shortened more than the distal segment, except when passively cycled, during which the segments strained similarly. When the whole muscle was cycled sinusoidally and stimulated phasically in vitro, the two adjacent segments strained in opposite directions over much (up to 34 %) of the cycle. These differences in strain amplitude and direction imply that two adjacent segments can not only produce and/or absorb varying amounts of mechanical energy, but can also operate on different regions of their force-length and force-velocity relationships when activated by the same neural signal. Understanding regional differences in contractile dynamics within muscles is therefore important to linking our understanding of sarcomere behaviour with whole muscle behaviour during locomotion.

Comparative power curves in bird flight.

The relationship between mechanical power output and forward velocity in bird flight is controversial, bearing on the comparative physiology and ecology of locomotion. Applied to flying birds, aerodynamic theory predicts that mechanical power should vary as a function of forward velocity in a U-shaped curve. The only empirical test of this theory, using the black-billed magpie (Pica pica), suggests that the mechanical power curve is relatively flat over intermediate velocities. Here, by integrating in vivo measurements of pectoralis force and length change with quasi-steady aerodynamic models developed using data on wing and body movement, we present mechanical power curves for cockatiels (Nymphicus hollandicus) and ringed turtle-doves (Streptopelia risoria). In contrast to the curve reported for magpies, the power curve for cockatiels is acutely concave, whereas that for doves is intermediate in shape and shows higher mass-specific power output at most speeds. We also find that wing-beat frequency and mechanical power output do not necessarily share minima in flying birds. Thus, aspects of morphology, wing kinematics and overall style of flight can greatly affect the magnitude and shape of a species' power curve.

Hindlimb muscle function in relation to speed and gait: in vivo patterns of strain and activation in a hip and knee extensor of the rat (Rattus norvegicus).

Understanding how animals actually use their muscles during locomotion is an important goal in the fields of locomotor physiology and biomechanics. Active muscles in vivo can shorten, lengthen or remain isometric, and their mechanical performance depends on the relative magnitude and timing of these patterns of fascicle strain and activation. It has recently been suggested that terrestrial animals may conserve metabolic energy during locomotion by minimizing limb extensor muscle strain during stance, when the muscle is active, facilitating more economical force generation and elastic energy recovery from limb muscle-tendon units. However, whereas the ankle extensors of running turkeys and hopping wallabies have been shown to generate force with little length change (<6% strain), similar muscles in cats appear to change length more substantially while active. Because previous work has tended to focus on the mechanical behavior of ankle extensors during animal movements, the actions of more proximal limb muscles are less well understood. To explore further the hypothesis of force economy and isometric behavior of limb muscles during terrestrial locomotion, we measured patterns of electromyographic (EMG) activity and fascicle strain (using sonomicrometry) in two of the largest muscles of the rat hindlimb, the biceps femoris (a hip extensor) and vastus lateralis (a knee extensor) during walking, trotting and galloping. Our results show that the biceps and vastus exhibit largely overlapping bursts of electrical activity during the stance phase of each step cycle in all gaits. During walking and trotting, this activity typically commences shortly before the hindlimb touches the ground, but during galloping the onset of activity depends on whether the limb is trailing (first limb down) or leading (second limb down), particularly in the vastus. In the trailing limb, the timing of the onset of vastus activity is slightly earlier than that observed during walking and trotting, but in the leading limb, this activity begins much later, well after the foot makes ground contact (mean 7% of the step cycle). In both muscles, EMG activity typically ceases approximately two-thirds of the way through the stance phase. While electrically active during stance, biceps fascicles shorten, although the extent of shortening differs significantly among gaits (P<0.01). Total average fascicle shortening strain in the biceps is greater during walking (23+/-3%) and trotting (27+/-5%) than during galloping (12+/-5% and 19+/-6% in the trailing and leading limbs, respectively). In contrast, vastus fascicles typically lengthen (by 8-16%, depending on gait) over the first half of stance, when the muscle is electrically active, before shortening slightly or remaining nearly isometric over much of the second half of stance. Interestingly, in the leading limb during galloping, vastus fascicles lengthen prior to muscle activation and exhibit substantial shortening (10+/-2%) during the period when EMG activity is recorded. Thus, patterns of muscle activation and/or muscle strain differ among gaits, between muscles and even within the same muscle of contralateral hindlimbs (as during galloping). In contrast to the minimal strain predicted by the force economy hypothesis, our results suggest that proximal limb muscles in rats operate over substantial length ranges during stance over various speeds and gaits and exhibit complex and changing activation and strain regimes, exemplifying the variable mechanical roles that muscles can play, even during level, steady-speed locomotion.

Dynamics of mallard (Anas platyrynchos) gastrocnemius function during swimming versus terrestrial locomotion.

This study investigates how the contractile function of a muscle may be modulated to accommodate changes in locomotor mode and differences in the physical environment. In vivo recordings of lateral gastrocnemius (LG) activation, force development (measured using tendon buckle transducers) and length change (measured using sonomicrometry) were obtained from mallard ducks (Anas platyrhynchos) as they swam at steady speeds in a water tank and walked or ran on land. LG force recordings were compared with combined lateral and medial gastrocnemius (MG) muscle-tendon force recordings obtained from the contralateral limb, allowing force development by the MG to be estimated relative to that of the LG. Although similar stresses were calculated to act in the LG and MG muscles during terrestrial locomotion (126 and 115 kPa, respectively), stresses were considerably greater in the LG compared with the MG during swimming (62 versus 34 kPa, respectively). During both steady swimming and terrestrial locomotion, the LG developed force while shortening over a considerable range of its length (swimming 23.6 % versus terrestrial 37.4 %). Activation of the muscle occurred near the end of passive lengthening during the recovery stroke, just prior to muscle shortening. As a result, the muscle generated broad positive work loops during both locomotor modes. LG work during swimming (4.8 J x kg(-1)) averaged 37 % of the work performed during terrestrial locomotion (13.1 J x kg(-1)), consistent with the twofold greater force and 58 % greater strain of the muscle during walking and running. Because limb cycle frequency was similar for the two locomotor modes (swimming 2.65 versus terrestrial 2.61 Hz), differences in power output (swimming 12.6 W x kg(-1 )versus terrestrial 32.4 W x kg(-1)) largely reflected difference in work per cycle. Tendon elastic energy savings was a small fraction (<5 %) of the work performed by the muscle, consistent with a fiber-tendon design of these two muscles that favors muscle work to produce limb movement with little tendon strain. These results are consistent with a higher cost of terrestrial locomotion in ducks compared with other, more cursorial birds that may operate their muscles more economically and achieve greater tendon elastic savings.

Mechanics of limb bone loading during terrestrial locomotion in the green iguana (Iguana iguana) and American alligator (Alligator mississippiensis).

In vivo measurements of strain in the femur and tibia of Iguana iguana (Linnaeus) and Alligator mississippiensis (Daudin) have indicated three ways in which limb bone loading in these species differs from patterns observed in most birds and mammals: (i) the limb bones of I. iguana and A. mississippiensis experience substantial torsion, (ii) the limb bones of I. iguana and A. mississippiensis have higher safety factors than those of birds or mammals, and (iii) load magnitudes in the limb bones of A. mississippiensis do not decrease uniformly with the use of a more upright posture. To verify these patterns, and to evaluate the ground and muscle forces that produce them, we collected three-dimensional kinematic and ground reaction force data from subadult I. iguana and A. mississippiensis using a force platform and high-speed video. The results of these force/kinematic studies generally confirm the loading regimes inferred from in vivo strain measurements. The ground reaction force applies a torsional moment to the femur and tibia in both species; for the femur, this moment augments the moment applied by the caudofemoralis muscle, suggesting large torsional stresses. In most cases, safety factors in bending calculated from force/video data are lower than those determined from strain data, but are as high or higher than the safety factors of bird and mammal limb bones in bending. Finally, correlations between limb posture and calculated stress magnitudes in the femur of I. iguana confirm patterns observed during direct bone strain recordings from A. mississippiensis: in more upright steps, tensile stresses on the anterior cortex decrease, but peak compressive stresses on the dorsal cortex increase. Equilibrium analyses indicate that bone stress increases as posture becomes more upright in saurians because the ankle and knee extensor muscles exert greater forces during upright locomotion. If this pattern of increased bone stress with the use of a more upright posture is typical of taxa using non-parasagittal kinematics, then similar increases in load magnitudes were probably experienced by lineages that underwent evolutionary shifts to a non-sprawling posture. High limb bone safety factors and small body size in these lineages could have helped to accommodate such increases in limb bone stress.