Contractile properties of the pigeon supracoracoideus during different modes of flight

The supracoracoideus (SUPRA) is the second largest muscle of the avian wing. It is the major antagonist to the larger pectoralis (PECT), which is the primary downstroke muscle for bird flight(Dial, 1992a). The SUPRA is active in all modes and speeds of flight(Dial 1992a; Tobalske, 1995), yet, with practice, birds may take off without use of the muscle(Degernes and Feduccia, 2001; Sokoloff et al., 2001). Electromyographic (EMG) data suggest that the muscle decelerates the wing during late downstroke and reaccelerates the wing during the beginning of upstroke (Dial, 1992a). Regardless of its capacity to elevate the wing, an in situ study of the function of the SUPRA indicated that the principal role of the muscle is supination of the humerus during the transition from downstroke to upstroke(Poore et al., 1997). The need for supination explains the activation of the SUPRA during faster flight when lift should presumably function to elevate the wing independent of muscle activation (Rayner, 1985; Poore et al., 1997; Hedrick et al., 2002; Hedrick et al., 2004).

The mechanical properties of the SUPRA in vivo are, unfortunately,unknown. The vast majority of the variation observed in avian wingbeat kinematics occurs during upstroke(Scholey, 1983; Tobalske, 2000; Tobalske et al., 2003a) and this variation appears to correspond with changes in aerodynamic function(Rayner, 1995; Spedding et al., 2003). In contrast, considerable insight is now available on the contractile behavior of the PECT in flying birds.

The PECT is largely designed to generate work and power(Biewener, 1998; Biewener and Roberts, 2000). Power output in the PECT varies with flight mode and speed(Dial and Biewener, 1993; Hedrick et al., 2003; Tobalske et al., 2003b; Tobalske et al., 2005). The large size and complex architecture of the PECT(Sokoloff et al., 1998) is accompanied by significant heterogeneity in regional activation patterns(Boggs and Dial, 1993) and muscle strain (Biewener et al.,1998; Soman et al.,2005).

The anatomy of the SUPRA differs from that of the PECT(Baumel et al., 1993; Poore et al., 1997). Although both muscles are bipinnate, the SUPRA is narrow, with a long tendon of insertion. The PECT is broad, with a short tendon of insertion and a substantial region of parallel fibers in the anterior pars sternobrachialis. Interpreted in the light of muscle function during terrestrial locomotion, the anatomy of the SUPRA would suggest that the muscle is used to produce force rather than work and also to exploit elastic energy storage and recovery (Biewener and Baudinette, 1995; Roberts et al., 1997; Biewener,1998; Biewener and Roberts,2000). Release of stored energy reduces the metabolic cost of terrestrial locomotion (Alexander,1988; Biewener and Roberts,2000). Such storage has been identified as a potential function of the avian furcula (Jenkins et al.,1988), but it has not been documented for any muscles of the wing.

As power costs for flight are high(Harrison and Roberts, 2000),it is generally assumed that selective pressures in evolution optimized the avian wing for metabolic efficiency. A competing selective pressure is likely for wing control, particularly during maneuvers(Warrick et al., 2002). For maneuvering, it is thought that distal muscles of the wing are relatively more important than large proximal muscles such as the PECT and SUPRA(Dial, 1992a; Dial, 1992b). However, using EMG recordings and in situ rates of force development in the PECT and SUPRA, Poore et al. (Poore et al.,1997) hypothesized that there should be antagonistic force development in the PECT and SUPRA to facilitate control.

During slow flight in most birds, weight support and thrust are produced only during downstroke and upstroke appears to be aerodynamically inactive(Spedding et al., 1984; Tobalske, 2000; Hedrick et al., 2004; Usherwood et al., 2005). Therefore, in slow flight, we expect PECT power to match the aerodynamic requirement for flight while SUPRA power should match the inertial power required for upstroke. Inertial work produced by the PECT to accelerate the wing during downstroke is expected to be transformed into aerodynamic work at the end of downstroke (Van den Berg and Rayner, 1995; Hedrick et al.,2004).

Much of the information presently available about PECT function in flying birds is from the pigeon Columba livia (Gmelin 1789), so we selected this species for investigating SUPRA function. We began with four predictions from prior research. Given the expected role of the SUPRA in supination of the wing (Poore et al., 1997), we hypothesized (1) that peak force in the muscle would occur at the transition from downstroke to upstroke rather than at mid-upstroke. Anatomy led us to predict that (2) it would operate with little length change and store elastic energy it its tendon (Biewener,1998; Biewener and Roberts,2000). A need for control of the wing and joint stability would result in (3) overlap in force production with the PECT(Poore et al., 1997). Finally,given the present evidence that upstroke produces little or no lift during slow flight (Tobalske, 2000),we hypothesized that (4) power output in the SUPRA should equal inertial power in upstroke, whereas power output in the PECT should match aerodynamic power required for slow flight.

We obtained pigeons (N=7, including five white carneau and two king, body mass 561.9±94.9 g, means ± s.d., Table 1) from commercial suppliers. An additional three white carneau pigeons (562.3±8.2 g)(Soman et al., 2005) were used for 3-D kinematic analysis and estimation of inertial power(P_iner). The birds were housed in a 2 m × 8 m× 2 m outdoor aviary at the Concord Field Station, Harvard University(Bedford, MA, USA) and had access to food and water ad libitum. The Institutional Animal Care and Use Committee at Harvard University approved all housing and experimental protocols (accredited by the Association for Assessment and Accreditation of Laboratory Animal Care International). The birds were trained to fly between platforms (30 cm × 40 cm) and horizontal poles (diameter 2.5 cm) to accomplish one of three modes of flight:level, ascent and descent. Level flights (3.9±0.5 m s^–1) were between platforms supported 1.5 m above the floor and spaced 7–9 m apart. Ascending (1.4±0.5 m s^–1) and descending (1.8±0.3 m s^–1)flights were from a platform placed on the ground and a horizontal pole placed 1.2 m horizontally and 2 m vertically from the platform to effect flight paths∼60° relative to horizontal. Flight speeds varied from 0 m s^–1 (hovering, when the bird was unwilling to ascend) to 2 m s^–1. All training and experiments took place in a hallway 1.9 m × 4.2 m × 12 m.

Morphometric data (Table 1)were obtained after the completion of experiments. Mass (M) was obtained for single muscles, and 10 measurements of fascicle length(L) and fascicle angle (α) were obtained for each surface,superficial and deep. Muscle cross-sectional area (A) was calculated as M/ρL assuming a muscle density (ρ) of 1060 kg m^–3. Measurements of tendon length and mass from the SUPRA were used to estimate tendon cross-sectional area assuming a tendon density of 1120 kg m^–3 (Ker,1981).

Additional wing and body measurements were obtained with the wings spread as in mid-downstroke using standard techniques(Tobalske and Dial, 1996; Tobalske et al., 1999).

We obtained synchronized 2-D kinematic data during implanted flights(N=7 birds) to estimate the aerodynamic power requirements of the PECT during flight. To estimate the inertial power requirements of the SUPRA during upstroke, we also obtained 3-D kinematic data from unimplanted level and ascending flights in three birds affiliated with Soman et al.(Soman et al., 2005). Mathematical modeling was accomplished using Igor Pro version 4.0.6(Wavemetrics, Inc., Beaverton, OR, USA) and Matlab version 6.5 (The MathWorks Inc., Natick, MA, USA).

During implanted flights, we used a Redlake PCI-500 (San Diego, CA, USA) to obtain a lateral-view video (250 Hz, shutter speed 0.5 ms, stored using PCI-R version 2.18 software) with a pixel:metric scale corrected for parallax using a synchronized Panasonic AG-450 S-VHS camera (60 Hz, shutter speed 1000 Hz)that offered cranio-caudal views of the flight path. We adapted the methods of Hedrick et al. (Hedrick et al.,2003) and Tobalske et al.(Tobalske et al., 2003b) in which 3-D kinematic data were applied to the aerodynamic models of Rayner(Rayner, 1979a; Rayner, 1979b), Pennycuick(Pennycuick, 1975) and Wakeling and Ellington (Wakeling and Ellington, 1997). In the 3-D analysis, fully described in equations 2–7 in Hedrick et al.(Hedrick et al., 2003),separate estimates of induced, profile, parasite and climb power were summed for each video frame, and the sums were then integrated over an entire wingbeat cycle. Lacking the resolution of 3-D data, we instead calculated the component aerodynamic powers for each half of the wingbeat cycle and then integrated over the full cycle (P_aero).

From earlier work (Tobalske and Dial,1996; Tobalske et al.,2003a), we assumed that the wings were fully extended throughout downstroke and that wing span at mid-downstroke was always the same as the morphological wing span of a given bird(Table 1). We then scaled mid-upstroke wing span according to the upstroke:downstroke span ratio within a given wingbeat. Finally, we assumed that wing length did not change throughout upstroke.

Our results were sensitive to our assumptions of wing length, particularly for downstroke. For example, during level flight a 10% decrease in wing length at mid-downstroke increased our estimate of P_aero by 13%(18% increase for induced power, 17% decrease for profile power), and a 10%increase in wing length decreased P_aero by 11% (15%decrease for induced power and 20% increase for profile power). In comparison,10% changes in wing length during upstroke caused the estimated profile power and P_aero to vary by <1%.

We later obtained additional high-speed video cameras, which permitted us to measure 3-D kinematics and, thereby, estimate P_inerduring upstroke (Hedrick et al.,2004). All video recording, camera calibration, data filtering and measurements of mass distribution were accomplished as in Hedrick et al.(Hedrick et al., 2004). We calculated P_iner required for upstroke as the change in kinetic energy of the wing from the start of the upstroke to its maximum divided by wingbeat duration.

Following training, we surgically implanted EMG electrodes and sonomicrometry (SONO) transducers into the SUPRA and PECT muscles by adapting standard methods used for the PECT(Biewener et al., 1998; Tobalske et al., 2005). We also attached two strain gauges (FLE-1, Tokyo Sokki Kenkyujo, Ltd, Tokyo,Japan) to the dorsal surface of the deltopectoral crest adjacent to, and parallel with, the insertion of each muscle(Biewener et al., 1998; Soman et al., 2005)(Fig. 1). One pair of 2.0 mm SONO crystals (Sonometrics, Inc., London, ON, Canada) and a fine-wire bipolar EMG electrode (0.5 mm bared tips with 2 mm spacing; California Fine Wire,Inc., Grover Beach, CA, USA) were implanted parallel to the fascicle axis of the mid-anterior region of the sternobrachial portion of the PECT(Fig. 1A). Another pair of SONO crystals and an EMG electrode were implanted through the PECT and into the mid-anterior SUPRA.

The SONO crystals were implanted at a depth of about 4 mm beneath the superficial fascia of the muscle and at a distance of 8–12 mm apart. For implantation into the SUPRA, two other openings were made through the PECT using fine-tip scissors and watchmaker's forceps. The crystals in the SUPRA were directed through the openings using Silastic tubing, which we subsequently removed. Once each SONO crystal had been inserted and aligned to ensure a maximum signal quality, all openings were sutured with 4–0 silk. A 4–0 silk suture was used to tie down all electrodes a few millimeters away from the exit point on the superficial fascia of the PECT to eliminate movement artifacts. As all tie-down sutures were superficial to the PECT, there was a relatively greater risk that slippage may have occurred in the crystals implanted in the SUPRA. Crystal spacing was approximately 10 mm,so our measurements of muscle length would change by ∼0.1% for 1%slippage.

After the experiments, the pigeons were killed using an intravenous overdose of sodium pentabarbitol (100 mg kg^–1) for verification of electrode placement, calibration of strain gauges and measurement of morphology (Table 1).

Recordings were made by connecting the bird to a 12 m shielded cable, which the animal dragged as it flew (the suspended portion of cable weighed ∼80 g). Qualitatively, there was no apparent effect of these elements upon flight kinematics in the pigeons, but we did not obtain a sufficient sample of non-implanted flights to use for a statistical test of this hypothesis. The cable was connected to strain gauge bridge amplifiers (Vishay 2120,Micromeasurements, Inc., Raleigh, NC, USA), a sonomicrometry amplifier (Triton 120.2, Triton Technology, Inc., San Diego, CA, USA) and EMG amplifiers (Grass P5-11, Grass Telefactor, West Warwick, RI, USA). All signals were recorded at 5 kHz onto a Pentium II computer running Windows NT (Microsoft, Inc., Redmond,WA, USA) using a Digidata 1200 A/D converter (Axon Instruments, Union City,CA, USA) at 5 kHz. For analysis of SONO and EMG signals, we used the methods of Hedrick et al. (Hedrick et al.,2002) and Tobalske et al.(Tobalske et al., 2005).

Sonomicrometry signals were corrected to represent the instantaneous average L of the muscle in which the crystals were implanted(Fig. 1A, Table 1). To treat analysis for the PECT and SUPRA equally, we assumed ΔL was uniform throughout the fascicle and throughout the muscle. This assumption merits caution as evidence from a different vertebrate indicates that heterogeneity of strain is apparent even within single fascicles(Ahn et al., 2003). Other studies in pigeons suggest our method may have caused a slight overestimate of muscle strain (ϵ) for the PECT as a whole because the region we implanted includes fibers that exhibit the greatest ΔL within the muscle(Biewener et al., 1998; Soman et al., 2005). No information is available for regional heterogeneity of contractile behavior in the SUPRA. The measured distance between the sonomicrometry crystals was increased by 2.7% to account for the velocity of sound in muscle (1540 m s^–1) (Goldman and Heuter,1956) relative to the value of 1500 m s^–1 assumed by the Triton 120.2 amplifier. This value was then increased by 0.74 mm to account for the higher velocity of sound through the epoxy lens of the 2 mm electrodes relative to muscle tissue(Biewener et al., 1998). We also corrected for a 5 ms phase delay and a frequency-dependent attenuation in the amplitude of the sonomicrometry signals, both of which were due to the 100 Hz linear phase filter inherent to the Triton 120.2 amplifiers(Tobalske and Dial, 2000). Resting length (L_rest) was measured during perching, with the wings folded and the PECT inactive, and ϵ=ΔL L_rest^–1.

To calibrate strain in the bone of the humerus into units of muscle force,we performed pull calibrations (Dial and Biewener, 1993; Biewener et al., 1998; Soman et al.,2005). Silk suture (OO) was secured around the anterior portion of the PECT 2 cm from the insertion on the deltopectoral crest (DPC) or the emergent tendon of the SUPRA immediately adjacent to the belly of the muscle. The other end of the suture was attached to a calibrated force transducer(Kistler 9203, Amherst, NY, USA). The anatomy of the DPC(Fig. 1B) resulted in cross-talk between strain-gauge channels arising from principal strains transmitted when forces were exerted by either muscle on the DPC. Tension produced by either muscle resulted in a compressive principal strain acting perpendicular to the tensile strain and, thus, generally in line with the other muscle's tendon of attachment. In other words, tension in one muscle artificially inflated tension measured for the other muscle. This cross-talk was approximately 50% from the PECT channel to the SUPRA channel and 5% from the SUPRA channel to the PECT channel.

We corrected for cross-talk from the PECT to the SUPRA channel and chose to ignore cross-talk in the opposite direction because of circularity in the underlying argument. Corrections were applied to the SUPRA channel at the stage of raw voltages. Using data obtained during PECT pull calibrations, we regressed SUPRA force upon PECT force. For in vivo data from a given bird, the scaling factor from this regression was multiplied by observed PECT force and added to the uncorrected SUPRA force to provide a corrected SUPRA force. The correction factor affected measurements throughout the wingbeat cycle because residual tension was always present in the PECT during flight. We calculated muscle stress (σ_m, in kPa) as force (N) divided by Acosα (Alexander,1983) (Table 1).

We measured work (mJ) and power (W) for each muscle using the work loop technique (Josephson, 1985; Biewener et al., 1998). A work loop `shape factor' (Hedrick et al.,2003) was calculated as the observed area of a work loop relative to the area of a rectangle with the same range of stress and strain. Net work per wingbeat duration yielded muscle power (P_mus), and mass-specific power (W kg^–1) was calculated as P_mus divided by M(Table 1).

We analyzed contractile properties and timing for 242 wingbeats using the onset of PECT shortening to identify the start of individual wingbeats and the onset of PECT lengthening to identify the start of upstroke.

For each variable, we computed the mean value within each bird for each flight mode. We then tested for a significant effect of mode upon each variable using a univariate repeated-measures analysis of variance (StatView version 5.0.1, SAS Institute, Inc., Cary, NC, USA). Values are presented as means ± s.d.

During flight, the SUPRA and PECT muscles exhibited contraction cycles that alternated with each other and were relatively uniform during most of the flight sequence (Fig. 2). The first one or two wingbeats during take-off and last several wingbeats prior to landing featured lower amplitude muscle strain, stress and EMG voltage. Wingbeat frequency averaged 8.6±0.2 Hz (wingbeat duration=116 ms) and did not vary significantly (P=0.0926) among flight modes. Likewise,flight mode did not have a significant effect upon the relative timing of most of the contractile events in the wingbeat cycle(Fig. 3). There were two exceptions. First, the SUPRA started shortening earlier during ascending flight (48±8%) relative to level (49±7%) and descending(50±8%) flight (P=0.0313). Second, the relative offset of SUPRA EMG activity occurred later during ascending (77±5%) compared with level (70±7%) and descending (71±11%) flight(P=0.0172).

Peak stress (σ_m) in the SUPRA occurred at 65±8% of the wingbeat cycle, immediately after the transition between downstroke and upstroke (lag time averaged 4% of the wingbeat cycle). Peakσ _m in the PECT occurred during the middle of downstroke. For either muscle, a peak σ_m occurred as the muscle was shortening. Shortening in the SUPRA lasted 54±7% of the wingbeat cycle and shortening in the PECT lasted 62±4%. Neuromuscular activation preceded the onset of shortening in both muscles with a relative lead time of 10±7% in the SUPRA and 12±4% in the PECT. The duration of EMG activity in the SUPRA was shorter than in the pectoralis, at 33±3% and 58±5%, respectively, relative to cycle duration. Consequently, a considerable fraction of force development by both muscles lasted beyond EMG offset (SUPRA, 29±9%; PECT, 39±7%). The pigeons consistently exhibited overlap in force production by the SUPRA and PECT muscles (Figs 2, 3, 4). An interval of simultaneous, antagonistic force took place during late downstroke, as force was declining in the PECT, and another occurred during late upstroke, as force was declining in the SUPRA. When positive σ_m was present in its antagonist muscle, negative work absorbed by the SUPRA was–16±16 mJ and by the PECT was –48±7 mJ. These values were 9% of the net work performed by either muscle(Table 2). The magnitude of overlap in antagonistic force was increased by our method of correction of cross-talk from the PECT for ϵ measured by the SUPRA strain gauge;nevertheless, overlap remained apparent even when uncorrected (raw) signals from the SUPRA strain gauge were evaluated relative to the strain-gauge signal from the PECT (Fig. 4).

Many of the contractile properties that we measured varied significantly according to flight mode (Table 2). Overall, ϵ, σ_m, work and power reached maximum values during ascending flight, were least during descending flight,and were intermediate during level flight. The only exception to this pattern was fractional lengthening in the PECT, which remained nearly the same(P=0.3016) during ascent (28±7%) and level flight(28±7%).

Stress (σ_m) was greater in the SUPRA than in the PECT(Fig. 5A), and there was a significant effect of flight mode upon the peak σ_m exhibited by the SUPRA (P=0.0463) and PECT (P=0.0017; Table 2). In the SUPRA, peakσ _m varied from 85±30 kPa during descent to 125±65 kPa during ascent. Peak σ_m during descent in the PECT was 50±12 kPa and it was 58±15 kPa during ascending flight.

Our measurements of peak σ_t in the tendon of the SUPRA averaged 24±14 MPa, which provided an estimate of recovered energy of 58±27 mJ among flight modes. This represented 33±5% of the net work performed by the SUPRA and 8±2.2% of the net work performed in sum by the PECT and SUPRA. Although U_rec in the SUPRA tendon during ascending flight was over twice the amount estimated for descending flight (88±85% versus 36±29%, Table 2), substantial variance among birds resulted in a marginally non-significant effect of flight mode upon U_rec (P=0.0548).

Muscle strain (ϵ) during wingbeats was generally similar in the two muscles (SUPRA: 36±3%; PECT: 38±4%). During flight, the SUPRA tended to operate over a range of L that was less than L_rest, whereas the PECT operated over lengths greater than L_rest (Fig. 1 and Fig. 5A). Flight mode did not have a significant effect upon fractional shortening in the SUPRA (P=0.0762) or fractional lengthening in the PECT(P=0.3015). In contrast, the observed variation associated with flight mode was significant for ϵ in the SUPRA (P=0.0039),fractional lengthening in the SUPRA (P=0.0105), ϵ in the PECT(P=0.008) and fractional shortening in the PECT(P=0.0452).

The comparatively brief duration of SUPRA shortening(Fig. 3) resulted in the SUPRA having higher average strain rates compared with the PECT(Table 2). Strain rate in the SUPRA varied between 5±2 and 7±2 Ls^–1, and from 5±1 to 6±1 Ls^–1 in the PECT. Strain rate also varied significantly among flight modes for both muscles (SUPRA, P=0.0042; PECT, P=0.0023).

Work loops differed in shape factor between the two muscles and among modes of flight (Fig. 6). For example, in Fig. 6, the shape factors of the work loops in the PECT were 18±4% greater than the shape factors for work loops in the SUPRA. This difference in shape factor is consistent with the comparatively steeper shoulders of the SUPRA work loops on either side of peak σ_m.

Among flight modes, net work of the PECT was 3.2±0.5 times greater than that of the SUPRA (mean 535±77 versus 172±54 mJ). Although flight mode had a significant effect upon positive and net work in the SUPRA and the PECT (all P<0.03), negative work, or absorption of external energy by the muscles, did not vary significantly with mode(P=0.3381, SUPRA; P=0.2297, PECT; Table 2). The amount of negative work relative to positive work was similar in the two muscles,representing 16±3% in the SUPRA and 19±2% in the PECT.

SUPRA mass-specific power varied from 106±50 W kg^–1during descent to 194±98 W kg^–1 during ascent(P=0.0178; Table 2). Expressed as P_mus and doubled to represent the output from both muscles, the mean among flight modes was 3±1 W(Fig. 7). These measurements of P_mus were 2.5 and 2.3 times greater than our estimates of P_iner required from the SUPRA muscles for upstroke during level and ascending flight, respectively. However, the estimated P_iner required from the muscles was within 1 s.d. of 2P_mus (Fig. 7).

In contrast, the P_mus in the PECT, doubled to represent both muscles, was much less (44±3%) than our estimates of P_aero (Fig. 7). PECT mass-specific power was also 36±9% less than mass-specific power in the SUPRA (Table 2). Mass-specific power in the PECT varied among flight modes(P=0.0124) and was maximal during ascent at 105±14 W kg^–1.

Most aspects of our four hypotheses pertaining to the comparative function of the SUPRA and PECT were supported by our results: (1) Peakσ _m in the SUPRA occurred at the transition between downstroke and upstroke (Figs 2, 3, 4); (2) the SUPRA stored substantial elastic energy, ranging from 36 to 88 mJ(Table 2, Fig. 5A); (3) there was overlap of antagonistic force at the end of each half stroke (Figs 2, 3, 4); and (4) P_mus in the SUPRA was close to the estimated P_iner for upstroke(Fig. 7). However, two inconsistencies with our predictions were apparent. Contrary to hypothesis(2), ϵ in the SUPRA was over 30% and only slightly less than in the PECT. Also, contrary to (4), power output in the PECT was less than half of the estimated P_aero.

These discrepancies with our predictions emphasize the role of proximal muscles as producers of work and indicate that independent methods are needed to further explore P_mus for the pectoralis and P_aero in bird flight.

Our in vivo experiments show that a major role of the SUPRA is for supination of the humerus at the end of downstroke, entirely consistent with the in situ experiments of Poore et al.(Poore et al., 1997). Peakσ _m occurred at wing turnaround(Fig. 2B, Figs 3 and 4), and the shapes of the work loops generated by the SUPRA (Fig. 6) revealed that stress declined rapidly during mid- and late upstroke when wing elevation was occurring(Tobalske and Dial, 1996; Tobalske, 2000). Poore et al.(Poore et al., 1997) argued that long-axis rotation of the humerus was a critical step during the evolution of flapping flight. Nevertheless, our data show that the SUPRA also elevates the wing, as σ_m>0 Pa throughout the upstroke(Figs 2, 3, 4).

Given the complexity of the musculature of the avian wing(Dial, 1992a; Baumel et al., 1993), it is sobering that our predictions of function from anatomy were only partially correct. This suggests that in vivo studies are required to adequately understand muscle function. It would be more convenient if all muscles could be neatly categorized as either force producers or work producers; however, such a simple dichotomy is often unlikely to be the case. Given the morphology of the SUPRA (Fig. 1A) and patterns exhibited by terrestrial animals with leg muscles featuring long tendons of insertion [e.g. tammar wallabies, Macropus eugenii (Biewener and Baudinette,1995)], we expected low ϵ in the muscle. Our measurements of relatively large ϵ (Table 2, Fig. 5) are consistent with a compromise in muscle design that permits the SUPRA to generate work and power to match P_iner for upstroke(Fig. 7), while at the same time favoring economical force generation(Biewener and Roberts, 2000). As the SUPRA is a proximal muscle, our results are similar to those of experiments in mammalian terrestrial locomotion in which greater ϵ is exhibited by proximal muscles of the limb compared with distal muscles(Gregersen et al., 1998; Gillis and Biewener,2001).

Elastic energy recovered from the SUPRA tendon is a novel result for muscles of the avian wing. Aside from the role of the furcula(Jenkins et al., 1988),elastic energy storage is not presently recognized as a mechanism available to flying birds (Harrison and Roberts,2000). Storage and recovery of energy in tendons saves energy during terrestrial locomotion (Taylor and Heglund, 1982; Alexander,1988; Biewener and Baudinette,1995; Baudinette and Biewener,1998; Biewener and Roberts,2000). Energy recovery (U_rec) of the order of 8% relative to the combined work output of the SUPRA and PECT(Table 2) should be included when estimating the efficiency of bird flight. At 32% of the net work of the SUPRA, U_rec approached the lower end of the range of recovery reported for the extensor tendons in the legs of tammar wallabies(38–52%) (Biewener and Baudinette,1995). The capacity for energy storage merits further study in other muscles of the wing that exhibit long tendons of insertion, including the tensor propatagialis longus and flexors and extensors of the distal wing(Dial, 1992a; Baumel et al., 1993).

It is widely recognized that co-activation of antagonist muscles provides stability about a musculoskeletal joint, such as the knee(Baratta et al., 1988; Kellis, 1998), and improves the accuracy of arm movements (Suzuki et al., 2001; Gribble et al.,2003). However, Poore et al.(Poore et al., 1997) were the first to suggest that antagonistic forces of the SUPRA and PECT might function to improve wing control during the rapid wing oscillations that occur during bird flight. Our results provide the first direct evidence for such a role(Figs 2, 3, 4). Whereas the two muscles are activated simultaneously during gliding flight(Tobalske, 1995; Tobalske, 2000), neuromuscular activation of these muscles does not overlap during flapping flight. Instead,because the decay of force within each muscle substantially lags the offset of EMG activity (Fig. 3), a significant overlap of antagonistic force occurs at wing turnaround.

The SUPRA generated work and power sufficient to meet the inertial requirements of wing upstroke (Fig. 7), which were within 1 s.d. of combined P_mus. Based on kinematic inferences, there has been some debate over the aerodynamic function of upstroke during slow flight in pigeons and other birds with wings of relatively high aspect ratio (Tobalske,2000). Our experiments provide new evidence that the upstroke is largely an aerodynamically inactive recovery; additional evidence includes the wake analysis of Spedding et al. (Spedding et al., 2003) on a thrush nightingale (Luscinia luscinia)and pressure measurements made about the wings of pigeons by Usherwood et al.(Usherwood et al., 2005). The small discrepancy between observed SUPRA P_mus and estimated P_iner (Fig. 7) suggests that any induced or profile power requirements of upstroke are <10% of P_aero for slow flight.

Our measurements of PECT P_mus, at 44% of estimated P_aero, are enigmatic. We reported similar results previously (Biewener et al.,1998), wherein mass-specific power from the PECT was 70.2 W kg^–1 in level flight, slightly less than the 87 W kg^–1 we observed here(Table 2). In contrast, Soman et al. (Soman et al., 2005)recently obtained measurements of 207 W kg^–1 for level flight of pigeons under similar conditions. Their analysis used positive work rather than net work to calculate P_mus. Calculated in this way,our measurement of mass-specific power during level flight(Table 2) would be 105 W kg^–1, and 108 W kg^–1 in an earlier study(Biewener et al., 1998). Mean PECT ϵ during level flight is similar among these studies: 36.2% in the present study (Table 2), 32% in Biewener et al. (Biewener et al.,1998) and 31.9% in Soman et al.(Soman et al., 2005). Likewise, morphology, wingbeat frequency and general work loop shapes are similar among the studies. Thus, differences in P_mus are due to calibrations of the strain gauges used to calculate PECT force.

Uncertainties over pull calibrations were previously reported for other experiments (Hedrick et al.,2003; Tobalske et al.,2003b), in which pull calibrations were abandoned and aerodynamic models were instead used to calibrate force. We hypothesize that our measurements of PECT force in pigeons were low because superficial, cranial PECT fibers adjacent to the DPC exerted a disproportionately large bending moment on the crest during our pull calibrations. In contrast, pull calibrations of the SUPRA appeared less sensitive to the location along the tendon at which we pulled. The insertion of the SUPRA is restricted in area,and the tendon passes through a foramen triosseum, which restricts the line of action upon the humerus (Baumel et al.,1993). Nevertheless, the potential inaccuracy of the pull calibrations means that caution is necessary when interpreting our reportedσ _m, work and P_mus for both muscles.

The accuracy of aerodynamic models of slow flapping flight is uncertain because unsteady effects may dominate the local flow field and make quasi-steady models inaccurate (Spedding,1993; Dickson and Dickinson, 2003). Other empirical studies,independent of sonomicrometry and strain gauge technology, also show deficits in power output relative to required power. Early flow measurements identified only 60% of the necessary momentum in the wake to account for weight support in the pigeon (Spedding et al.,1984). Higher resolution of the flow field may eliminate this measurement deficit (Spedding et al.,2003), but attempts have not yet been undertaken using pigeons. Differential pressure transducers on the wings and tails of pigeons yield measurements of power output sufficient to support 82% of body weight, with an estimated mass-specific power of 273 W kg^–1 under similar level, slow flight conditions (Usherwood et al., 2005).

It appears promising that in vitro measurements of P_mus in the PECT of blue-breasted quail (Coturnix chinensis) exceed P_aero predicted using quasi-steady aerodynamic models (Askew and Marsh,2001; Askew et al.,2001). These measurements use an ergometer to measure force in isolated fascicle bundles that are stimulated and strained according to in vivo EMG and sonomicrometry data but, even so, neglect large negative work components measured in situ that are judged to be artifacts of the technique (Askew and Marsh,2001). With integration of in vitro work loop techniques(Askew et al., 2001), higher resolution analysis of wake dynamics(Spedding et al., 2003; Warrick et al., 2005) and novel measurements of local pressure(Usherwood et al., 2005),together with continued development of DPC strain–force recordings, an improved understanding of the aerodynamics of flight in birds should emerge. Nevertheless, our combined force, length change and activation recordings of the PECT and SUPRA reveal novel functions of these two muscles that depend on in vivo observations of muscle function.

List of symbols and abbreviations

 
• α

  fascicle angle

 
• ϵ

  muscle strain

 
• ρ

  muscle density

 
• σt

  tendon stress

 
• σm

  muscle stress

 
• A

  muscle cross-sectional area

 
• E

  elastic modulus

 
• L

  fascicle length

 
• L_rest

  fascicle length at rest

 
• M

  muscle mass

 
• P_aero

  aerodynamic power

 
• P_iner

  inertial power

 
• P_mus

  muscle power

 
• U_rec

  elastic energy recovery

 
• V_t

  tendon volume

We thank M. Williamson, D. Stark, R. Hicks and G. Gillis for assistance during experimentation, D. Sheridan and A. Daus for assistance during modeling of aerodynamic power, T. Hedrick for analysis of 3-D kinematics and inertial power requirements, and P. Ramirez for animal care. We also thank C. Ellington and J. van Leeuwen for inviting us to participate in the World Congress of Biomechanics conference session on Swimming and Flying. Supported by NSF grants IBN-9723699 to A.A.B. and IOB-0615648 to B.W.T.