How cockatiels (Nymphicus hollandicus) modulate pectoralis power output across flight speeds
1 Concord Field Station, Museum of Comparative Zoology, Harvard University,
Old Causeway Road, Bedford, MA 01730, USA
2 Department of Biology, University of Portland, 5000 N. Willamette
Boulevard, Portland, OR 97203, USA
* Author for correspondence (e-mail: thedrick{at}oeb.harvard.edu)
Accepted 29 January 2003
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Summary |
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Key words: cockatiel, Nymphicus hollandicus, flight, muscle, power
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Introduction |
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Two broad strategies can be used to modulate muscle power output in
cyclical locomotor modes such as avian flight. Muscle power output could be
modulated by changes in wingbeat and muscle contraction frequency (strategy 1)
or changes in the amount of work performed per cycle (strategy 2). Pectoralis
work per cycle can, in turn, be modulated by changes in the strain amplitude
experienced by the muscle (strategy 2A), changes in the amount of force
produced by the muscle (strategy 2B) or other details of the contraction cycle
that influence the forcestrain trajectory such as the percentage of the
cycle spent shortening, the timing of force production relative to strain or
the specific strain trajectory (strategy 2C;
Askew and Marsh, 2001). A
previous study of pigeons (Columba livia) found that, over a broad
range of flight performance ranging from descending and level flight to
take-off and vertical climbing flight, pectoralis force only varied by about
40%, much less than the >2-fold overall variation in power output
(Dial and Biewener, 1993
). The
muscle's forcestrain trajectory was also found to vary little over the
range of flight conditions studied. Consequently, we hypothesized that
modulation of muscle strain (strategy 2A) would be the primary source of
variation in power output, with secondary contributions from modulation of
muscle force (strategy 2B) and wingbeat frequency (strategy 1).
In support of strategy 2A, Williamson et al.
(2001) found that differences
in pectoralis power output during take-off versus slow level flight
in mallard ducks (Anas platyrhynchos) were modulated mainly by means
of variation in muscle strain. Warrick et al.
(2001
) also observed
significant variation in muscle strain (1.3-fold) in the pectoralis of magpies
(Pica hudsonia) associated with the modulation of power output across
flight speeds. In their study of pectoralis power output across different
flight modes and during load carrying in pigeons. Dial and Biewener
(1993
) found that muscle force
varied 1.4-fold whereas muscle strain was estimated from kinematics to vary
1.3-fold. Hence, both factors contributed similarly to the 2.3-fold variation
in power output, suggesting that birds may employ a combination of strategies
2A and 2B (strain and force) to modulate work and power output as a function
of flight speed. Shifts in the timing of muscle force production with respect
to muscle strain, included here as strategy 2C, were found to mediate the
shift from minimal muscle power production in level running in turkeys
(Meleagris gallopavo) to positive power production in uphill running
(Roberts et al., 1997
).
However, flying birds must always produce positive power and may optimize the
timing of muscle force versus muscle strain for power production at
all speeds. Finally, although the vortex theory of avian flight (Rayner,
1979a
,b
)
assumes that wingbeat frequency is fixed for a given species, it necessarily
suggests that a change in frequency would have a strong influence on
aerodynamic power output. As certain bird species are known to vary wingbeat
frequency moderately with speed (1.2-fold;
Tobalske, 1995
), it is likely
that some combination of the strategies described above is used to modulate
power output during flight.
In this study, we measured in vivo pectoralis power output in cockatiels flying across a wide range of speeds in a wind tunnel and examined the variation in power due to the four different strategies described above. We also combined our muscle power analysis in vivo with a high-speed, three-dimensional (3-D) kinematic analysis to investigate how the observed changes in muscle power were applied to the environment via the wings.
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Materials and methods |
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Animals and flight training
Five cockatiels (Nymphicus hollandicus Kerr; 78.5±5.0 g,
mean body mass ± S.D.) were purchased from a local licensed animal
vendor and housed in a 1.7 mx2.7 mx3.3 m indoor aviary at the
Concord Field Station animal care facility (Bedford, MA, USA), where they were
provided with food and water ad libitum. The birds were trained to
fly over a range of speeds from 1 m s-1 to 15 m s-1 in
the Concord Field Station wind tunnel
(Hedrick et al., 2002).
Training lasted one month, comprising a minimum of five 30-min bouts of flight
training per week. All individuals tended to fly in the upper forward quadrant
of the working section of the wind tunnel. Cockatiels learned to fly at a
steady speed in the wind tunnel in 2-4 days and were then exercised for at
least three additional weeks to expand the speed range over which they would
fly steadily prior to data recording. The trained cockatiels were willing to
fly for at least 10 min without rest at 9 m s-1. At very fast
(>13 m s-1) and slow (<3 m s-1) speeds, the
duration of flights that the birds were willing to sustain was typically
1
min. The maximum speed of each bird was defined as the highest speed at which
it would voluntarily maintain its position in the wind tunnel for 30 s. All
training and experimental procedures were approved by the Harvard University
Institutional Animal Care and Use Committee.
Surgical procedures
Following training, the birds were anesthetized using isoflurane
administered via a mask in order to implant sterilized sonomicrometry
muscle length transducers, electromyography (EMG) electrodes and a
deltopectoral crest (DPC) bone strain gauge. Once an appropriate plane of
anesthesia was achieved, the feathers over the left shoulder, upper back and
left mid-anterior region of the pectoralis were removed and the skin surfaces
disinfected with betadine solution. A 2-cm incision was made over the ventral
surface of the pectoralis and a 1-cm opening was made in the skin over the
animal's back. These allowed the EMG and sonomicrometry crystal electrodes to
be passed subcutaneously through the axilla and beneath the wing to the
opening over the pectoralis. One pair of 1-mm sonomicrometry crystals
(Sonometrics, Inc., London, Ontario, Canada) and a bipolar EMG electrode were
then implanted parallel to the fascicle axis of the mid-anterior region of the
sternobrachial (SB) portion of the pectoralis
(Fig. 1A). In this region, the
fascicles originate from the keel of the sternum and pass directly to the
muscle's insertion on the ventral surface of the DPC of the humerus.
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The avian pectoralis is well suited for making in vivo measurements of fascicle length change by means of sonomicrometry because of the parallel organization of the muscle's fibers at its superficial surface. In all birds, the sonomicrometry crystals were implanted at a depth of appoximately 4 mm beneath the superficial fascia of the muscle and at a distance of 8-12 mm apart. Small openings parallel to the fascicles were made by puncturing the surface of the muscle and spreading with small, pointed scissors. After inserting each sonomicrometry crystal and aligning them to ensure a maximum signal quality, these openings were sutured closed with 6-0 silk. A 4-0 silk suture was used to tie down the sonomicrometry lead wires a few millimetres away from the implantation site for strain relief and to eliminate movement artefact in the recorded signals. A fine-wire bipolar silver hook EMG electrode (0.5-mm bared tips with 2-mm spacing; California Fine Wire, Inc., Grover Beach, CA, USA) was implanted immediately adjacent to the sonomicrometry crystals to confirm that length change recordings represented activated muscle fibers. The EMG electrode was inserted at a shallow angle parallel to the fascicle axis using a 23-gauge hypodermic needle and anchored by a 6-0 silk suture at the exit point from the muscle's surface. A second tie was also made further back, close to the keel of the sternum, with a small loop of wire between the two ties that served as strain relief and helped to reduce movement artefact in the EMG signal.
Sonomicrometry
Sonomicrometry provides a direct measurement of muscle fascicle length
change by recording the transit time of a series of ultrasonic sound pulses
that are emitted by one crystal and received by the other of a pair. Use of
the Triton 120.2 sonomicrometry system (Triton Technology Inc., San Diego,
USA) requires a positive 2.7% correction to account for faster speed of sound
transmission in skeletal muscle (1540 m s-1; Goldman and Hueter,
1956) and an offset adjustment of +0.16 mm for the faster sound movement
through the epoxy lens of the 1.0 mm crystals, as well as a 5 ms correction
for the phase delay introduced by the amplifier's filter. We verified the 5 ms
phase delay using a signal generator and oscilloscope. Measurements of length
change (l) are made between the two crystals; the resting
length of the muscle fascicles (Lrest) was defined as the
length that was recorded at the end of the flight sequence, after the bird had
landed on the perch and remained at rest with its wings held at its sides.
This was also verified by obtaining post-mortem length recordings. Fractional
length change, or fascicle strain (
), was determined as
=
l/Lrest. To calculate muscle work
and muscle power, total fascicle length change (
L) was
calculated as
L=
L0 (where
L0 is the resting length of the entire fascicle along
which the crystals were implanted). Measurements of
L
therefore assume uniform length change along the entire length of the
fascicle. Following the completion of the experimental recordings, we
performed a post-mortem dissection to verify the alignment of the
sonomicrometry crystal implants with respect to the fascicle axis using a
protractor. In all cases, the crystals were found to be well-aligned
(±2° with the muscle fascicle axis, rendering alignment errors of
muscle length change insignificant).
DPC strain recordings of muscle force
In addition to implanting sonomicrometry and EMG electrodes within the
pectoralis, we also attached a single element metal-foil strain gauge (FLE-1,
Tokyo Sokki Kenkyujo, Ltd, Tokyo, Japan) to the dorsal surface of the
deltopectoral crest (DPC) of the cockatiel humerus
(Fig. 1A). This was done by
making a small (10 mm) incision over the left shoulder and reflecting the
overlying deltoid muscle to expose the bony surface of the DPC. The strain
gauge and its lead wires were passed subcutaneously and deep to the deltoid
muscle to the DPC installation site. After lightly scraping the overlying
periosteum with a scalpel and drying the bone surface with a cotton applicator
dipped in methyl-ethyl-ketone, the strain gauge was bonded to the dorsal
surface of the DPC, perpendicular to the humeral shaft, using a
self-catalyzing cyanoacrylate adhesive. Strain recordings obtained from the
DPC were used to quantify pectoralis force generation under in vivo
flight conditions (see below). During the downstroke, the DPC is pulled
ventrally by the contracting pectoralis, so that the dorsal surface develops a
principal axis of tensile strain that is nearly perpendicular to the long axis
of the humerus (Dial and Biewener,
1993). This makes the strain gauge sensitive to forces produced by
the pectoralis but not to other muscle or aerodynamic forces transmitted by
the bone between the elbow and the shoulder.
Following implantation of the DPC strain gauge and the muscle electrodes, all of the wounds were sutured closed. A customized miniature back plug, previously soldered to the transducers' lead wires and insulated prior to surgery, was anchored to the skin and vertebral ligaments using 3-0 silk. The animals were then allowed to recover for 24 h prior to making experimental recordings in the wind tunnel.
Flight recordings
Experimental recordings of pectoralis EMG, fascicle length change and DPC
strain were made during the following day. These recordings were made by
connecting the animal to a lightweight multi-lead cable that ran a distance of
1 m from the back connector on the animal to a small (0.75 cm diameter)
opening at the top of the wind tunnel's working section. The combined mass of
the data cable section within the wind tunnel and the back plug was 12.8 g, or
15% of the animal's body mass. This lightweight cable connected to a heavier,
shielded cable that ran to the recording amplifiers (Micromeasurements Vishay
2120 strain gauge bridge amplifier; Grass P-511 EMG amplifier; and Triton
120.2 sonomicrometry amplifier). The outputs of each of these amplifiers were
sampled by an A/D converter (Axoscope Digidata 1200) at 5 kHz and stored on a
computer for subsequent analysis. Muscle strain and force recordings were
subsequently filtered with a 50 Hz digital Butterworth low-pass filter to
remove high-frequency noise; EMG recordings were filtered with a 250 Hz
digital Butterworth high-pass filter to remove low-frequency artefacts.
Recordings were obtained over a range of speeds for each animal (1 m
s-1, 3 m s-1, 5 m s-1, 7 m s-1, 9
m s-1, 11 m s-1 and 13 m s-1). Although the
cockatiels were trained to fly at speeds of up to 15 m s-1 in the
wind tunnel, none of the individuals were able to attain this speed following
surgery and with the additional drag of the data cable and plug.
Wind tunnel
The Concord Field Station wind tunnel is an open-circuit tunnel with a
closed flight chamber (Hedrick et al.,
2002). Briefly, it has a working section 1.2 mx1.2 m in
cross-section and 1.4 m in length and can operate at wind speeds from 0 m
s-1 to 28.5 m s-1. Average variation in mean flow
velocity within the working section is 1.03%, and average turbulence is 1.10%.
In order to make our measurements, obtained under the atmospheric conditions
of the tunnel's location in Bedford, MA, USA (58 m above sea level; mean air
temperature during data collection was 26.1°C, and air pressure was 100.6
kPa), comparable with measurements obtained from studies involving wind
tunnels at other locations, we followed Pennycuick et al.
(1997
) in reporting equivalent
wind speed (Ve) rather than true wind speed:
![]() | (1) |
Video recording and 3-D coordinate reconstruction
Flight trials were recorded using two synchronized, highspeed digital video
cameras (Redlake PCI 500) operating at 250 frames s-1 or 125 frames
s-1 with a shutter speed of 1/1250th of a second. The lower
recording frequency was used for later trials in order to double the recording
duration to facilitate analysis of a greater number of wing beats, as it was
not found to have a significant effect on our kinematic analyses (see below).
One camera was placed lateral to the flight chamber and the other above and
behind it. The camera data were synchronized with the sonomicrometry, strain
gauge and EMG data by recording the camera's digital trigger together with the
muscle signals via the A/D converter. The cameras were calibrated
using the modified direct linear transformation (DLT) technique with a
54-point calibration frame (measuring 0.624 mx0.900 mx0.700 m in
xyz coordinate space) that was recorded at the end of each set of
trials (Hatze, 1988). Trials
were recorded at flight speeds of 1-13 m s-1 in 2 m s-1
intervals. Flight speed sequence was not restricted to a particular order and
the birds were allowed to rest between trials as necessary to maintain
satisfactory performance (typically 2-5 min of steady flight).
Three points (dorsal and ventral surfaces of the shoulder, wrist and tip of the ninth primary) were identified on the right wing of each bird using 5-mm-diameter circles of white tape marked with a black center dot. In addition, markers were placed on the back plug where it attached to the dorsal midline between the wings and at the base of the tail. Flight sequences consisting of a minimum of three successive wingbeats with minimal lateral and vertical movement within the flight chamber (within-chamber speed <0.3 m s-1) were selected from the video data and digitized using custom software written in Matlab v.5.3 (The MathWorks, Natick, MA, USA). In the few cases where sequential wingbeats with minimal change in wind tunnel position were not available, we selected additional wingbeats from the recorded flight sequence, digitizing at least three wingbeats for each individual at each speed. In trials that were recorded at 250 Hz, we digitized every other frame, resulting in an effective video recording frequency of 125 Hz for all trials.
The raw coordinate data obtained from the digitized trials were resolved
into a single 3-D space using the DLT coefficients derived from the
calibration frame (Hatze,
1988). In addition to resolving the dorsal and lateral 2-D camera
views into a single 3-D space, the DLT method also corrects for parallax and
other lens distortions. Individual points having a DLT root mean square error
(rms error) two standard deviations greater than the median rms error for that
point (approximately 4% of the points) were removed prior to analysis. Median
rms error ranged from 1.84 mm for the shoulder marker to 6.62 mm for the ninth
primary tip. Occasionally, a point was not in the view of both cameras,
resulting in a gap in the reconstructed point sequence; this occurred in
approximately 5% of the points digitized. All points were filtered, and
missing or dropped points were interpolated with a quintic spline fit to known
rms using the Generalized Cross Validatory/Spline (GCVSPL) program
(Woltring, 1986
). This method
uses the rms from the DLT reconstruction to filter the positional data and
then fills any gaps with a quintic spline interpolation. The results from this
technique were similar to those obtained by smoothing the positional data
using a 37 Hz digital Butterworth low-pass filter. However, the quintic spline
method also allows direct calculation of velocity and acceleration derivatives
from the spline curves, providing the most accurate method for obtaining
higher order derivatives from positional data
(Walker, 1998
).
Morphological measurements
After experimental recordings were completed, the animals were euthanized
by an overdose of sodium pentobarbitol (100 mg kg-1, i.v.) in order
to obtain morphometric measurements. These included pectoralis mass, fascicle
length and pinnation angle, wingspan and mean wing chord
(Table 1).
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Aerodynamic power analysis and muscle power calibration
Aerodynamic power (Paero) produced by the pectoralis
muscle was estimated on a per-wingbeat basis from the 3-D kinematic
reconstruction by summing separate estimates of induced
(Pind), profile (Ppro), parasite
(Ppar) and climb power (dEp/dt, where
Ep is potential energy and t is time) for each
video frame then integrating over a complete wingbeat cycle (typically 13-18
frames):
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Parasite power was estimated by:
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We estimated induced power as:
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![]() | (5) |
![]() | (6) |
Profile power was estimated by:
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After estimating the aerodynamic power requirement for a given wingbeat, we compared this value to the uncalibrated muscle power for that wingbeat and calculated the correction factor, F, necessary to make uncalibrated muscle power equal to aerodynamic power. Because the only unknown in the conversion from uncalibrated to calibrated muscle power is a constant term converting strain gauge voltage to newtons, F is the strain gauge calibration constant. For each bird, we calculated a mean F from at least five wingbeats at flight speeds of 7 m s-1 and 9 m s-1 and used this mean F to calibrate muscle power for all wingbeats at all speeds for that individual. We used these speeds to calculate F because the assumptions employed in the aerodynamic power calculation are most reasonable at intermediate flight speeds. The mean coefficient of variation (CV) of F was 12.5±5.0% within individuals. All calculations were performed in Matlab v.5.3.
We adjusted the strain gauge calibration constant using the aerodynamic
power method as described above rather than using the direct `pull'
calibration method we have used in the past (Biewener et al.,
1992,
1998
;
Dial and Biewener, 1993
). We
adopted this approach because we found our previous method to be unreliable
owing to the difficulty of accurately representing the in vivo
transmission of tensile force by the pectoralis to the base of the DPC in this
and another (ringed turtle-dove, Streptopelia risoria) species.
Repeated pull calibrations performed on the cockatiels had a mean CV of
24.5±11.0% among individuals. By directly pulling along the superficial
surface of the muscle beneath its insertion site, force transmission is likely
biased to the more distal region of the DPC. To the extent that this occurs,
this will increase the bending moment applied to the DPC and result in an
underestimate of strain-calibrated force. In addition, this calibration method
can give varying forcestrain slopes for differing cranio-caudal
orientations of pull, which may also be problematic given the varying
orientation with which the pectoralis can pull on the DPC due to its own fiber
architecture and the changing elevation and depression of the humerus during
the wingbeat cycle.
We evaluated the accuracy of the aerodynamic power calculated from 250 Hz versus 125 Hz video data by digitizing results at several speeds at 250 Hz, calculating the aerodynamic power, then reducing the data to 125 Hz by selecting every other point and re-calculating the aerodynamic power. In each case, the aerodynamic power estimates for the two different recording frequencies were within 5% of one another and not significantly different [analysis of variance (ANOVA), d.f.=13, P=0.72]. Consequently, we concluded that a 125 Hz video acquisition frequency was sufficient for this study. We also examined the influence of our aerodynamic assumptions on F by recalculating the aerodynamic power results using alternative `low-power' and `high-power' values of kind, CD,pro and CD,par. In the low-power case, kind was decreased from 1.2 to 1.0, and CD,par and CD,pro were decreased by 50% to 0.065 and 0.01, respectively; for the high-power case, kind was increased to 1.4, and CD,par and CD,pro were increased by 50% to 0.195 and 0.03, respectively. This allowed us to bracket the likely range of pectoralis power that might be observed at any particular flight speed. Had we used the `pull' calibration technique in this study, the power output results would have been similar in magnitude to the low-power aerodynamic calibration but would have exhibited greater inter-individual variation. Finally, although the calibration factor F is necessary for calculating the magnitude of muscle power output, it does not affect the percentage variation in power across speeds with respect to the mean power. This makes our analysis of the factors contributing to variation in power output insensitive to differences in the value of F.
Potential effects of wind tunnels on bird flight performance
Conditions within a wind tunnel undoubtedly affect bird flight performance
(Rayner, 1994). The unusual
surroundings, noise and lights have unknown effects upon performance, and we
tried to minimize these effects with adequate acclimation and training of the
birds. Additionally, the wake of the bird may circulate within the flight
chamber, reflect off the walls of the closed-section flight chamber and
interact with the bound circulation on the wings. Due to this phenomenon,
flight speeds and mechanical power requirements are expected to be less in a
closed flight chamber compared with free flight without ground effect
(Rayner, 1994
). The effects of
wake reflection are expected to decrease with increasing flight speed.
Windtunnel effects are well documented for fixed-wing models
(Barlow et al., 1999
) but not
for birds engaged in flapping flight. One study that compares wind tunnel and
free flight performance in a bird suggests that mean wingbeat frequency is
lower in the field, and other wing kinematics exhibit slight differences
between tunnel and free flight (Tobalske
et al., 1997
).
Aerodynamic corrections for bird flight in a closed-section wind tunnel
take into account the ratio of the diameter of the flight chamber to the
wingspan and also the position of the bird inside the chamber. The chamber
diameter:wing-span ratio was 2.48 for the cockatiels, and they generally flew
near the horizontal mid-plane or slightly above. This position equates to
h/H values that ranged from 0 to 0.25, where h is altitude
of the body above the midline of the flight chamber, and H is
vertical height of the flight chamber
(Rayner, 1994). Using Rayner's
(1994
) model, for these animal
dimensions and positions, minimum power and maximum range speeds may have been
reduced by 3%, and mechanical power at these speeds may have been reduced by
up to 10% relative to the same speeds in free flight. Given the uncertain
nature of these adjustments, we do not make any corrections for wind tunnel
effects in the results we report.
Statistical analysis
Comparisons across individuals and speed were performed using
repeated-measures ANOVA. Least squares and multiple regression statistics were
used to examine the effect and importance of different factors both within and
among individuals and speeds. In cases where we examined a series of
sequential wingbeats, we tested for serial autocorrelation using Durbin's
h test (Durbin,
1970). When autocorrelation was detected (P
0.05), we
removed it by sampling every other wingbeat from the original data set, which
reduced h to acceptable levels in each case. We also employed
Fisher's protected least-significant difference (PLSD) in certain pairwise
comparisons and used a path analysis to place the multiple regression results
in the context of a general model for muscle power output
(Sokal and Rohlf, 1995
).
Statistical analysis was performed using Stata 6.0 (Stata Corporation, College
Station, TX, USA); P values of
0.05 were used to denote
significance. We report means ± S.D. among individuals, which were
obtained from a minimum of 17 and a mean of 46 wingbeats per individual per
flight speed.
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Results |
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Wing kinematics versus in vivo pectoralis length
change
We found that kinematic measurements of downstroke initiation and duration
differed from those obtained via sonomicrometry
(Fig. 2). Both the wrist and
wing-tip motion in the vertical axis lagged muscle shortening, with a greater
lag at the end of the downstroke than at the start. The wing-tip had a
noticeably greater lag (12.5±3.1 ms), possibly due to bending of the
feathers at the beginning and end of the downstroke
(Fig. 2). However, wrist motion
also lagged muscle contraction by a small margin (3.9±3.2 ms). This lag
is probably due to (1) long-axis rotation of the wing causing vertical
movement of the wrist, (2) movement at the elbow joint and (3) the difficulty
of precisely tracking the relatively small amplitude motions of the wrist.
Although the difference between the sonomicrometer and video sampling
frequencies (5000 Hz versus 125 Hz) could contribute to the observed
lag between muscle shortening and kinematics, we found that video trials
digitized at 250 Hz compared with 125 Hz had no observable effect on the lag
between these variables. Use of wrist kinematics, rather than direct
recordings of pectoralis shortening, therefore, results in a shorter estimate
of downstroke duration (mean reduction for all flight speeds: 19%) and
corresponding longer estimate of upstroke duration.
Pectoralis power output
We measured the pectoralis power output by dividing the muscle work
performed in a wingbeat cycle by the cycle duration; in vivo
mechanical work performed by the pectoralis during a wingbeat was quantified
using the `work loop' technique
(Josephson, 1985). In most
wingbeats, the work loops were wholly positive
(Fig. 3). On occasion, a very
small (<1.5% of the total area) negative work region of the loop occurred
at the start of muscle shortening. However, only positive work contributes to
aerodynamic power (Askew et al.,
2001
) and we based all further analyses of work on the positive
component only. As previously reported
(Tobalske et al., 2003
),
pectoralis power output varied 2.1-fold (P<0.0001) over the range
of flight speeds examined in this study
(Fig. 4A; Table 2) and was greatest at
the slowest and fastest speeds tested (1 m s-1 and 13 m
s-1). The cockatiels' minimum power speed flying in the wind tunnel
was 5 m s-1, and their maximum range speed or minimum cost of
transport occurred at 9 m s-1. The overall relationship between
muscle mechanical power output and speed was generally U-shaped, similar to
that predicted by aerodynamic theory. The relationship of power
versus speed was similar for the individual birds studied
(Fig. 4B). Variation in power
output among sequential wingbeats within a bird at a given speed was generally
large (mean CV=0.19) and was minimized at the intermediate speed of 5 m
s-1 (mean CV=0.13). We report power output as the mean of
measurements obtained for
17 individual wingbeats of each bird flying at a
given speed (Table 2).
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Wingbeat frequency and pectoralis duty factor
Wingbeat duration varied significantly by a factor of 1.2 across the range
of speeds studied (Fig. 5;
Table 2). Maximum wingbeat
duration occurred at a flight speed of 11 m s-1, only slightly
slower than the maximum speed the birds sustained in this study (13 m
s-1). Partitioning total wingbeat duration into muscle lengthening
(upstroke) and muscle shortening (downstroke) phases
(Fig. 6A) showed that
shortening duration did not vary significantly across flight speeds. Thus, all
variation in wingbeat duration was due to changes in muscle lengthening
duration (Table 2). Lengthening
duration was less than shortening duration at slow flight speeds (1-5 m
s-1) and at the fastest speed (13 m s-1), whereas the
duration of the two phases was approximately equal at intermediate speeds
(7-11 m s-1). We found similar overall patterns when we measured
upstroke and downstroke via the vertical motion of the wrist in the
3-D kinematic reconstruction rather than muscle length change, but the
relative durations of the phases differed between the two methods
(Fig. 6). Downstroke duration
measured kinematically was also constant across speeds but was shorter by an
average of 12.9±3.1 m s-1 (13% of the wingbeat cycle) and
upstroke was correspondingly longer. This shift was sufficient to make
kinematic upstroke equal in duration to downstroke at slow speeds and fast
speeds and much greater at intermediate speeds
(Fig. 6B).
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Although wingbeat frequency varied with flight speed, downstroke duration did not. Therefore, the duty cycle of the pectoralis, the percentage of the wingbeat cycle spent shortening, was not independent of wingbeat frequency. Pectoralis duty cycle varied from 61.5±3.2% of the cycle at 1 m s-1 to 49.6±2.9% at 11 m s-1, following the same pattern of variation as wingbeat frequency (Fig. 6A). Because duty cycle was not independent of wingbeat frequency, we were unable to incorporate duty cycle into our component model of power output (see below). As a result, any effects due to the variation in duty cycle were included in the effect of wingbeat frequency, which accounted for only 10% of the variation in power output among speeds.
Pectoralis work
In addition to calculating the work loop areas, we quantified work loop
shape by dividing the area within the loop by the theoretical maximum
(rectangular) area defined by the observed force and strain. This work loop
`shape factor' averaged 0.54±0.01 (i.e. 54±1% of the theoretical
work space was achieved by the muscle's contraction). Interestingly, this did
not vary significantly across speeds (Table
2). Pectoralis work per wingbeat varied significantly across the
range of speeds by a factor of 2.3 (Fig.
5; Table 2).
Pectoralis work reached a minimum at 5 m s-1; the same speed at
which power was minimized.
Modulation of pectoralis force and length change as a function of
speed
Whereas muscle power output is determined by muscle work in relation to
wingbeat frequency, muscle work is determined by the particular pattern of
force in relation to length change that a muscle develops. Although the
particular work loop shape of a muscle cannot be explicitly defined in simple
mathematical terms, patterns of peak muscle force and total muscle length
change should be good predictors of the work performed by a muscle over a
contractile cycle. Pectoralis force, length change and strain rate all varied
significantly with speed, exhibiting minima and maxima at the same speeds as
pectoralis power output (Fig.
7; Table 2).
However, their respective ranges of variation were less than that of
pectoralis work and power. Length change and peak force varied 1.4-fold and
1.7-fold, respectively, compared with a 2.3-fold variation in pectoralis work.
Because downstroke duration did not vary with speed whereas muscle length
change (strain) varied by a factor of 1.3, the rate of muscle shortening also
varied 1.3-fold (Table 2).
|
A component model of pectoralis power output
We used a component model to quantify the variation in power output across
flight speeds due to changes in wingbeat frequency, muscle length change, peak
muscle force and work loop shape (Fig.
8). This path analysis indicates the strength of the relationship
between components by showing the partial regression coefficients along the
relationship lines. We found that approximately 90% of the variation in power
output was attributable to variation in the work performed per wingbeat; the
remaining portion was attributable to changes in wingbeat frequency. Work per
wingbeat itself was most influenced by the peak force developed during
contraction, which accounted for approximately 70% of the variation in work
and therefore 65% of the variation in power. Muscle length change accounted
for approximately 20% of the variation in work. Changes in work loop shape
accounted for the balance but were inversely related to muscle length change.
The overall effect of increasing shape factor (increasing the realized
fraction of ideal muscle work space), therefore, was to reduce the
work performed per wingbeat. A multiple regression analysis of power output
using the three most basic factors wingbeat frequency, peak muscle
force and muscle length change was highly significant and had an
r2 of 0.82 (Fig.
8). In summary, peak muscle force was the best predictor of muscle
work per wingbeat, which was the best predictor of power output. The
relationship of these factors to the modulation of power output over
successive wingbeats within any particular flight speed was more complex, with
significant correlations observed between various performance components of
the model (Table 3).
Nevertheless, peak muscle force remained the dominant factor.
|
|
Muscle recruitment in relation to force and shortening velocity
For the two cockatiels in which high-quality EMG signals were recorded, we
found that pectoralis EMG mean spike amplitude (measured as rectified area
divided by duration) was a good predictor of muscle force, and therefore of
pectoralis power output, across a range of flight speeds
(Fig. 9A;
Table 3). Pectoralis EMG
amplitude was also a good predictor of muscle shortening velocity
(Fig. 9B), leading to a strong
positive correlation between muscle force and muscle shortening velocity
(r2=0.92). Because of differences in electrode geometry
and recording site among individual animals, EMG amplitude only performed well
when compared as a predictor of muscle force or shortening velocity within an
individual over a range of motor performance
(Table 4; see
Loeb and Gans, 1986). However,
despite these difficulties in comparing among individuals, the analyses were
still significant. Normalizing both EMG amplitude and muscle force prior to
performing the regression tests compensated for some of the differences among
individuals, improving the fit of the data
(Table 4). Among wingbeats
within a given speed, the variation in peak muscle force exceeds that of EMG
amplitude, resulting in a weaker relationship between amplitude and force when
considering results from a single flight speed
(Table 4). This difference in
the magnitude of variation between EMG amplitude and force within a speed
probably reflects how changes in wing position and the aerodynamic resistance
to wing motion affect the peak force developed by the cockatiel pectoralis on
a wingbeat-by-wingbeat basis. Finally, we found that the relationship between
EMG amplitude and both force and mean shortening velocity during downstroke
was not significant among wingbeats at speeds of 11 m s-1 and 13 m
s-1 (Fig. 9).
|
|
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Discussion |
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Despite many differences in the requirements for flight versus
terrestrial locomotion, our results indicate that flying birds and running
animals both modulate muscle force production in relation to changes in speed.
In flapping flight, muscle force modulates muscle power output, and therefore
speed, and is presumably linked to changes in the metabolic cost of flight
with speed. Similarly, in terrestrial animals, muscle force production is an
important determinant of the metabolic cost of locomotion and maximum speed
(Kram and Taylor, 1990;
Taylor, 1985
;
Weyand et al., 2000
). Thus, as
an underlying component of muscle work and power, force production plays a
central role in determining performance in flight, just as it does in
terrestrial locomotion.
Modulation of muscle power via work, force and
strain
The cockatiels in this study modulated pectoralis power output primarily by
altering the amount of mechanical work performed during each wingbeat cycle.
Muscle work was, in turn, modulated primarily by the amount of force developed
by the pectoralis and secondarily by the magnitude of muscle shortening and
changes in work loop shape. Peak muscle force and muscle strain both exhibited
minima and maxima at the same speeds as overall muscle power output and also
varied over a fairly wide range: 1.7-fold and 1.4-fold, respectively. Whereas
the range of variation in muscle strain was similar to that found in a
previous study of magpies (1.3-fold;
Warrick et al., 2001), the
variation in force was much greater than that reported previously across
flight modes in pigeons (1.4-fold; Dial and
Biewener, 1993
) and mallard ducks (1.05-fold;
Williamson et al., 2001
).
Because peak muscle force varied more than muscle strain, it represented the main influence on muscle work and power output. The observed change in muscle force could have been due to the recruitment of additional muscle fibers and/or a shift in the muscle's forcevelocity curve towards a slower strain rate and greater force. However, we found that mean strain rate during shortening increased in a manner similar to peak muscle force (Table 2), suggesting that the higher forces were due to greater motor recruitment. This was supported by the strong correlation of EMG amplitude with peak muscle force (Fig. 9A).
Modulation of power via wingbeat frequency
Our hypothesis that muscle power output would be only slightly affected by
changes in wingbeat frequency was supported, as wingbeat frequency had a much
smaller effect on power than muscle force or strain
(Fig. 8). Although wingbeat
frequency and pectoralis power both varied in a curvilinear manner with speed,
their respective minima occur at different speeds (5 m s-1
versus 11 m s-1) and their overall ranges of variation
differ substantially (2.1-fold versus 1.2-fold), resulting in a low,
but significant, correlation between wingbeat frequency and power output. We
also found that minimum muscle power output occurred at a speed less than half
that of minimum wingbeat frequency. Consequently, our results indicate that
minimum wingbeat frequency is not necessarily a good experimental indicator of
minimum power speed in avian species, contrary to the suggestion of Pennycuick
et al. (1996).
Rather than directly reflecting variation in power output, changes in
wingbeat frequency may instead be associated with changes in aerodynamic gait.
Two gaits have been recognized: a vortex-ring gait used at slower speeds and a
continuous vortex gait used at faster speeds
(Rayner, 1993; Spedding,
1986
,
1987
). The distinguishing
feature of the vortex-ring gait is that the upstroke produces no useful
aerodynamic force, whereas the upstroke of the continuous-vortex gait actively
produces lift (Rayner, 1993
).
Because downstroke duration of the cockatiel remained constant, all changes in
wingbeat frequency with speed were due to changes in upstroke duration, which
was significantly greater (lower frequency) at the intermediate flight speeds
of 7-11 m s-1 (Fisher's PLSD; P<0.0001, d.f.=4;
Fig. 5). These speeds
correspond to the range over which cockatiels apparently use a continuous
vortex gait (Hedrick et al.,
2002
). Thus, cockatiels prolong the upstroke phase of the wingbeat
at speeds at which upstroke is thought to produce useful aerodynamic
forces.
Although wingbeat frequency, rather than power output, appears to mediate
gait change in cockatiels, this may not be the case in all species. Some
species, such as the magpie and members of the Phasianidae, do not appear to
change gait with speed (Tobalske,
2000). In these species, wingbeat frequency might share a minimum
with power output, as has been assumed
(Pennycuick et al., 1996
).
Variations in muscle duty factor with speed, gait and power
Previous studies in vitro have found that asymmetric sawtooth
contraction cycles lead to higher work output than do sinusoidal cycles, when
the shortening phase is increased relative to the lengthening phase
(Askew and Marsh, 2001). This
finding is consistent with previous in vivo muscle length change
results obtained for magpies (Warrick et
al., 2001
), mallards
(Williamson et al., 2001
),
pigeons (Biewener et al., 1998
)
and quail (Askew et al., 2001
),
in which pectoralis shortening occupies 62-67% of the wingbeat cycle. We
expected that cockatiels would also use a muscle duty factor greater than 50%
at all flight speeds, especially in very slow and fast flight where power
requirements are greatest. This also suggests the possibility that modulation
of downstroke duration might be a key means for varying muscle work and power
output. However, neither of these expectations was strongly supported. The
cockatiels did employ an asymmetric `sawtooth-like' cycle at all speeds, but
muscle duty factor was relatively low (54%) at the fastest and highest power
speed. Furthermore, downstroke duration did not change significantly with
speed, tightly coupling changes in muscle duty factor to changes in wingbeat
frequency. Although this prevented direct incorporation of muscle duty factor
into our component model of power output, the influence of wingbeat frequency
and, therefore, muscle duty factor on power output was negligible. Changes in
muscle duty factor should most influence muscle force development and length
change, and hence muscle work, rather than muscle power
(Askew and Marsh, 2001
).
However, again we found no significant relationships between wingbeat
frequency and muscle strain, peak force or work (P=0.89, 0.63 and
0.80, respectively). Consequently, cockatiels do not appear to modulate their
pectoralis shortening duty cycle in order to modulate muscle work and power
output as a function of flight speed. Instead, duty cycle appears to be
modulated more by changes in underlying gait kinematics.
Changes in work loop shape across speeds
Due to the differing ranges of variation in muscle strain (1.4-fold) and
peak force (1.7-fold), work loop shape did not remain uniform across flight
speeds. For example, the work loops in Fig.
3B,C appear quite similar, but the loop in
Fig. 3C (13 m s-1)
has a 60% greater force and only a 40% greater strain than the loop in
Fig. 3B (7 m s-1).
However, when work loop shape was quantified as the percentage of the
theoretical maximum area actually occupied by the loop, we found that work
loop shape did not change significantly with speed
(Table 2). We also found that
the work loop `shape factor' had a negative correlation with muscle strain,
indicating that there may well be a trade-off between the muscle's ability to
optimize its realized `work space' (for a given force and strain range) and
maximizing muscle strain and total work per cycle
(Fig. 8). Changes in work loop
shape, however, may be an important modulator of muscle power output in
situations where there is a shift from minimal power production to positive
power, such as when a terrestrial animal shifts from level to uphill running
or accelerates.
Muscle force and aerodynamic coefficients
The peak muscle forces generated by the pectoralis during downstroke should
generally correspond in timing and relative magnitude to the peak aerodynamic
forces experienced by the wings. These aerodynamic forces are proportional to
wing shape and area, but we found that the wing adopts a stereotypic, fully
outstretched wing posture during peak muscle force production at all flight
speeds. Given the invariance in wing shape and assuming that the position of
the center of lift on the wing does not change with flight speed, we are able
to use the variation in peak muscle force to estimate the variation in the
coefficients of lift and drag across a range of flight speeds. In our previous
3-D kinematic analysis (Hedrick et al.,
2002), we found that the mean airflow velocity over the distal
portion of the wing increased steadily from 7 m s-1 to 14 m
s-1 when flight speed increased from 1 m s-1 to 13 m
s-1. Results from the present study show that minimum peak muscle
force occurred at 5 m s-1. At this speed, we previously found a
mean distal wing flow velocity of 8.3 m s-1. With an increase in
flight speed from 5 m s-1 to 13 m s-1, therefore, our
observed 1.7-fold increase in muscle force corresponds to a 1.9-fold increase
in air flow velocity past the wing. Because aerodynamic forces increase with
the square of flow velocity, this suggests a 3.7-fold increase in aerodynamic
force. Thus, in order to maintain an equal relationship between muscle and
aerodynamic forces, the mean coefficients of lift and drag must decrease by
2.2-fold over a speed increase from 5 m s-1 to 13 m s-1.
With a decrease in flight speed from 5 m s-1 to 1 m s-1,
we found in the present study that muscle force increases 1.4-fold, whereas
our earlier results indicate that the square of flow velocity decreases by a
factor of 0.7. This differential indicates that mean lift and drag
coefficients probably increase 2-fold as cockatiels reduce their flight speed
from 5 m s-1 to 1 m s-1. Therefore, our results suggest
that changes in wing orientation result in a 4-fold decrease in the
coefficients of lift and drag as a cockatiel's flight speed increases from 1 m
s-1 to 13 m s-1. This range of variation is compatible
with recent experimental tests of bird wing lift and drag coefficients in
revolution (Usherwood and Ellington,
2002
), given the observed range of variation in estimated angle of
attack with speed for cockatiels flying in our wind tunnel (37° to 6°;
Hedrick et al., 2002
).
The 4-fold range of variation in the coefficients of lift and drag
predicted for cockatiel wings based on our muscle force results may provide an
indirect explanation for why the maximum flight speed of magpies is not
limited by muscle power output (Dial et
al., 1997). An interesting difference between magpies compared
with cockatiels and ringed turtle-doves is that the latter two species
generate their respective maximal muscle power outputs at very fast flight
speeds, whereas magpies fail to achieve the elevated power outputs at high
speeds that they are briefly able to produce when hovering
(Tobalske et al., 2003
).
Consequently, magpies exhibit a rather flat power curve (due to the absence of
a significant rise in power at fast speeds), whereas the power curves of
cockatiels and ringed turtle-doves are both more acutely concave. Although we
have not yet determined coefficients of lift and drag for cockatiel wings,
their apparent angles of attack at high speeds are very low, suggesting
particularly reduced aerodynamic coefficients
(Hedrick et al., 2002
). By
contrast, magpies have relatively large and broad wings (aspect ratio=5),
which may not be capable of being reconfigured to reduce coefficients of drag
and lift sufficiently at high flight speeds to avoid a sharp increase in power
requirements that might otherwise result.
Flight power modulation across species
The mechanisms used to modulate power output may also scale with body mass.
Whereas magpies vary both muscle force and strain similarly to modulate power
output (Dial et al., 1997;
Warrick et al., 2001
), our
findings here for cockatiels and our preliminary analysis of ringed
turtle-doves (Tobalske et al.,
2003
) indicate that changes in muscle force are the main means by
which these two species vary power output in relation to flight speed. The
capacity for enhanced recruitment of muscle force in these smaller species may
reflect their ability to elevate power output in fast flight beyond that
required at very slow speeds. Earlier studies of pigeons and mallard ducks
across a range of flight modes found that pectoralis force also varied only
moderately and was not the dominant factor controlling muscle power output.
Instead, variation in muscle strain accounted for a majority of the change in
power output (Dial and Biewener,
1993
; Williamson et al.,
2001
). Size may be a factor because the two smallest species
(cockatiels, 83 g; turtle-doves, 140 g) show the greatest variation in muscle
force (1.7-fold and 1.9-fold, respectively), whereas the larger species
(pigeons, 649 g; mallards, 995 g) display similar variation in muscle strain
(1.3-fold and 1.2-fold, respectively) and force (1.4-fold and 1.1-fold,
respectively). Because of their size, larger species in general are believed
to have smaller scopes for changing muscle and metabolic power output
(Pennycuick, 1968
;
Ellington, 1991
). This is
borne out by past metabolic and mechanical power studies of pigeons, which
display rather narrow ranges of power output (20-50%;
Rothe et al., 1987
;
Dial and Biewener, 1993
). This
suggests that, for species in which flight power varies only moderately, both
pectoralis force and strain are important to power modulation. In species such
as cockatiels, which display a wide range of power outputs, the relative
importance of variation in muscle force via muscle recruitment may be
increased due to muscle forcelength limitations on the possible range
of variation in muscle strain.
Because of the limited sample of in vivo flight performance data that is currently available, these interpretations about flight performance, and the possible limits to elevating power output usefully at very fast speeds in larger species or ones with broad, low aspect ratio wings, require additional study. Nevertheless, the underlying mechanisms by which pectoralis contractile function is modulated to vary mechanical, and ultimately aerodynamic power output, are clearly an important determinant of a bird's flight performance range.
Summary
We found that pectoralis contractile function in cockatiels is highly
conserved across speed and over a wide range of aerodynamic power
requirements. Power output is primarily modulated by muscle force rather than
by muscle strain or cycle frequency. Strain rate and EMG results suggest that
the additional force is mainly provided via increasing pectoralis
recruitment rather than by changes in the contractile dynamics force
and length relative to activation phase of the muscle. Hence, despite
the 2-fold range of variation in muscle power output, many aspects of muscle
performance vary little. The duration of muscle shortening is invariant, and
overall wingbeat frequency and muscle strain vary to a much lesser degree than
do muscle power or work. Changes in upstroke duration and, hence, wingbeat
frequency may accentuate or facilitate changes in aerodynamic gait: cockatiels
appear to use a slow upstroke (continuous vortex gait) at speeds of 7-11 m
s-1 and a faster upstroke (vortex-ring gait) at other speeds. Due
to their effect on the transfer of muscle work into useful aerodynamic work,
changes in wing position and orientation during the downstroke probably also
affect the magnitude of muscle force developed for a given level of motor
recruitment. Analysis of the variation in muscle force and airflow over the
wing suggests that lift and drag coefficients probably vary by as much as
4-fold over the speed range examined in this study.
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Acknowledgments |
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