ABSTRACT

Control of wing shape is believed to be a key feature that allows most birds to produce aerodynamically efficient flight behaviors and high maneuverability. Anatomical organization of intrinsic wing muscles suggests specific roles for the different motor elements in wing shape modulation, but testing these hypothesized functions requires challenging measurements of muscle activation and strain patterns, and force dynamics. The wing muscles that have been best characterized during flight are the elbow muscles of the pigeon (Columba livia). In vivo studies during different flight modes revealed variation in strain profile, activation timing and duration, and contractile cycle frequency of the humerotriceps, suggesting that this muscle may alter wing shape in diverse ways. To examine the multifunction potential of the humerotriceps, we developed an in situ work loop approach to measure how activation duration and contractile cycle frequency affected muscle work and power across the full range of activation onset times. The humerotriceps produced predominantly net negative power, likely due to relatively long stimulus durations, indicating that it absorbs work, but the work loop shapes also suggest varying degrees of elastic energy storage and release. The humerotriceps consistently exhibited positive and negative instantaneous power within a single contractile cycle, across all treatments. When combined with previous in vivo studies, our results indicate that both within and across contractile cycles, the humerotriceps can dynamically shift among roles of actuator, brake, and stiff or compliant spring, based on activation properties that vary with flight mode.

INTRODUCTION

The avian wing undergoes substantial shape change during both flapping and gliding (Altshuler et al., 2015; Lentink et al., 2007; Pennycuick, 1968, 2015). The ability to alter wing shape allows birds to control their aerodynamic efficiency (Lentink et al., 2007), and is also hypothesized to contribute to their maneuverability in flight (Altshuler et al., 2015). Some of the change in wing shape is caused by passive tension in soft tissue and inertial forces during flapping, but some shape change is expected to be under active control of the muscles intrinsic to the wing (Chin et al., 2017; Dial, 1992a; Vazquez, 1994). However, most research of avian flight muscles has focused on the two large, bilateral muscles in the pectoral region, which only have their insertions in the wing.

The pectoral muscles, the pectoralis major and the supracoracoideus, power the down- and up-strokes, respectively and have been characterized through in vivo measurements of activation, strain and force. These measurements have demonstrated their primary roles as actuators (Biewener et al., 1998a; Dial, 1992a,b; Ellerby and Askew, 2007a; Robertson and Biewener, 2012; Tobalske, 2007) with contributions to braking and elastic storage during wing turnaround (Biewener et al., 1998a; Dial, 1992b). The specific roles of the muscles intrinsic to the wing are largely unknown. Although anatomical measurements provide general hypotheses for wing muscle functions (Chin et al., 2017; Dial, 1992b; Robertson and Biewener, 2012), measurements of length and force dynamics are required to determine their contributions to wing morphing.

It is challenging to record activation and strain from intrinsic muscles, due to smaller size, increased distance from the body, and, in the case of flapping, high wingbeat frequency. The most extensive muscle activation measurements were performed by Dial and colleagues (Dial et al., 1991). Electromyogram recordings (EMGs) from 11 muscles in the European starling (Sturnus vulgaris), including 9 intrinsic wing muscles, were made during forward flight in a wind tunnel (Dial et al., 1991). EMGs from 17 muscles in the pigeon (Columba livia), including 15 intrinsic to the wing, were made during takeoff, ascending, forward flight, descending and landing (Dial, 1992b). These studies revealed that all of the wing muscles were active during flapping flight, but with considerable variation within and among muscles.

Only one study has included measurements of fascicle strain from intrinsic wing muscles: Robertson and Biewener (2012) obtained EMG recordings and sonomicrometry fascicle strain measurements from pigeons, in the pectoralis major and in the antagonist muscles that span the avian elbow. From this effort, activation and fascicle strain data are available from the humerotriceps, scapulotriceps and biceps brachii, as the birds went through a sequence of takeoff, forward flight and landing. These in vivo measurements are consistent with the hypothesis that the muscles control flexion, extension and stabilization of the avian elbow (Dial, 1992b; Robertson and Biewener, 2012). Control of the elbow joint angle should be important for adjusting wing shape during gliding, stabilizing the wing during the downstroke, and folding the wing during the upstroke to minimize counter-productive forces. However, demonstration of this hypothesis requires measurements of muscle force, work and power (e.g. Ellerby and Askew, 2007a; Roberts and Azizi, 2010).

Here, we build upon the in vivo measurements of muscle activation and fascicle strain obtained by Robertson and Biewener (2012) to measure muscle force in the pigeon humerotriceps. We focused on the humerotriceps because its anatomy and accessibility make it well suited for the work loop procedure. The humerotriceps is a bipennate muscle that originates on the head of the humerus, and in the pneumatic fossa that is located on the ventral side of the head of the humerus, and inserts onto the olecranon process at the proximal end of the ulna on the dorsal side (Chatterjee, 2015; Robertson and Biewener, 2012). Short tendons should produce very little stretch independently of the muscle itself, thereby causing a negligible delay between force production and motion (Konow et al., 2015; Sawicki et al., 2015). At the insertion, the humerotriceps has a short length of tendon (∼0.5 mm) that extends beyond muscle fibre attachment. We therefore assumed that this portion of tendon that extends beyond muscle fibre attachment was too short and stiff to contribute a substantial amount of stretch. However, we appreciate that this may not necessarily be true for this particular muscle–tendon unit. We took advantage of these anatomical features to modify an in situ work loop approach (Nelson et al., 2004; Roberts and Azizi, 2010) because it is not currently feasible to develop an in vivo force measurement technique specific to any of the elbow muscles for which activation and strain data are available.

In situ work loop experiments allow for measurement of muscle performance space, both within and beyond the range of observed parameters from in vivo studies (Josephson, 1985). However, it is not feasible to explore every aspect of potential variation because of degradation in muscle force following multiple trials. We focused on two manipulations that were tested across the full range of activation phases because the functions of cyclic muscles are highly dependent on onset of motor activation relative to the length-change cycle (Ahn and Full, 2002; Dickinson et al., 2000; Josephson, 1985; Roberts et al., 1997; Sawicki et al., 2015). The two focal manipulations were chosen based on the potential shift in muscle role over the range of observations from in vivo studies: (1) we tested two stimulus durations that were representative of the 52–74% of the wingbeat cycle range of activation periods that was observed during previous electromyogram recordings from the pigeon humerotriceps (Dial, 1992b; Robertson and Biewener, 2012); (2) we tested three cycle frequencies that were representative of the 5–10 s−1 range that was observed during previous measurements of wingbeat kinematics (Berg and Biewener, 2008, 2010; Dial, 1992b; Robertson and Biewener, 2012; Usherwood et al., 2011) (Table 1). These results were compared with the in vivo range of values to gain insight into what possible functions the pigeon humerotriceps can perform during different modes of flapping flight.

Table 1.

Flight and muscle variables

Flight and muscle variables
Flight and muscle variables

Duration of humerotriceps muscle activation is an important aspect to probe because it has been shown to occupy over half of its contractile cycle, making it likely that this muscle produces force during both lengthening and shortening. Therefore, each cycle could conceivably contain elements of both positive and negative work. However, it is uncertain how this might affect the in vivo function of this muscle. The wingbeat cycle frequency is also an important aspect to probe because it effectively dictates the contractile cycle frequency of all of the wing muscles, including the humerotriceps (Robertson and Biewener, 2012). A muscle's contractile cycle frequency determines its lengthening and shortening velocities, which would affect the muscle's ability to produce work and power, depending on its inherent properties such as its force–velocity relationship.

MATERIALS AND METHODS

Animals

Work loop experiments were performed with four female and five male pigeons [Columba livia (Gmelin 1789)] acquired from a local breeder (Aldergrove, BC). Body mass was 329.5±6.0 g (mean±s.e.m.) for females, and 318±25.7 g for males. Birds were housed at the University of British Columbia in wire cages with a 12 h light:12 h dark cycle and ad libitum access to premium pigeon seed mix, water, mineral and iodine grit, and calcium-enriched grit. All birds that served as experimental subjects for this study were euthanized at the end of the procedure. All procedures were approved by the University of British Columbia Animal Care Committee.

Surgical procedure

We developed an in situ work loop technique to study whole muscle performance in the pigeon wing while maintaining normal body temperature and the flow of nutrients and oxygen through an intact blood supply (Nelson et al., 2004). Anesthesia was induced by 4% isoflurane administered via a gas vaporizing system with a 50:50 mix of pure oxygen and nitrogen delivered at a combined flow rate of 1 l min−1. Maintenance anesthesia level was held with 0.6–1.7% isoflurane throughout the procedure, which lasted up to 6–10 h for useful data collection. An analgesic, 10% (v/v) butorphanol (1 µl g−1 of body mass), was administered intramuscularly via the pectoralis within an hour of induced anesthesia. A half-dose of the analgesic was given 4–5 h after the initial dose. Additionally, 3 ml of 0.9% (w/v) unbuffered saline was administered subcutaneously near the nape of the neck every 2–3 h during surgery and just prior to the start of data collection. Any exposed tissue was covered with 0.9% (w/v) saline-soaked cotton and irrigated regularly throughout the procedure with warm saline.

To prevent interference from contractions of other wing muscles, we isolated most of the humerotriceps muscle in the right wing from surrounding muscles without causing damage to the blood vessels and nerves that supply it. The origin of the humerotriceps, located on (and in) the head of the humerus, and the insertion of its short tendon on the proximal end of the ulna were left intact. Two 1.8 mm holes were drilled in the humerus, one at the distal end and one 1.5 cm proximally, and zero gauge bolts were passed through these holes and screwed into pre-tapped holes in a 6.4 mm (1/4 inch) thick aluminum block mounted on acrylic (Fig. 1A). The entire setup was then fastened to a breadboard with a 2.5 cm (1 inch) hole pattern. We used this method to immobilize the humerus and consequently the origin of the humerotriceps because we had determined that it was sufficient for eliminating undesired movement of these elements during the initial stages of experimental development. A short section of the ulna that contained the tendon insertion of the humerotriceps was isolated and tied to a non-compliant, 0.20 mm, thermally bonded thread (Wildfire 162U-008, Beadalon, Valley Twp, PA). The other end of the thread was tied through a hole on a lever arm connected to a dual-mode lever system arm (Fig. 1A). Both knots were sealed with cyanoacrylate to prevent slippage. The muscle temperature was maintained at 36–41°C throughout the experiments with an external heat source. After the end of each experiment, the humerotriceps muscle was extracted to measure its length and mass.

Fig. 1.

In situ work loop preparation for testing the contractile properties of pigeon humerotriceps muscles. (A) The humerotriceps muscle originates on the head of the humerus and, during the in situ work loop experiments, the insertion is attached to the servo motor arm. Circles indicate where screws were drilled into the humerus to immobilize it. The dorsal branch of the brachial nerve was draped over two hooked electrodes and received an electrical impulse to stimulate the humerotriceps. (B) A sample 8.6 s−1 length-change cycle trace plotted over time, with gray dashed lines indicating where stimulus onset began for −50, −25, 0 (peak muscle length) and 50% phase. (C) Length-change trace with each of the three different frequency treatments denoted using the time scale bars in the top left: 6.1 s−1 (top, green); 8.6 s−1 (middle, black) and 10.1 s−1 (bottom, blue). The stimulus duty cycles are indicated by bars below the trace. Two different experiments were performed: (1) Contractile frequency was tested with 50% stimulus duty cycle (red stimulus bar). (2) Stimulus duty cycle [50% (red) versus 69% (purple)] was tested at a cycle frequency of 8.6 s−1.

Fig. 1.

In situ work loop preparation for testing the contractile properties of pigeon humerotriceps muscles. (A) The humerotriceps muscle originates on the head of the humerus and, during the in situ work loop experiments, the insertion is attached to the servo motor arm. Circles indicate where screws were drilled into the humerus to immobilize it. The dorsal branch of the brachial nerve was draped over two hooked electrodes and received an electrical impulse to stimulate the humerotriceps. (B) A sample 8.6 s−1 length-change cycle trace plotted over time, with gray dashed lines indicating where stimulus onset began for −50, −25, 0 (peak muscle length) and 50% phase. (C) Length-change trace with each of the three different frequency treatments denoted using the time scale bars in the top left: 6.1 s−1 (top, green); 8.6 s−1 (middle, black) and 10.1 s−1 (bottom, blue). The stimulus duty cycles are indicated by bars below the trace. Two different experiments were performed: (1) Contractile frequency was tested with 50% stimulus duty cycle (red stimulus bar). (2) Stimulus duty cycle [50% (red) versus 69% (purple)] was tested at a cycle frequency of 8.6 s−1.

The muscle was activated by stimulating the dorsal branch of the brachial nerve supplying the humerotriceps (King and McLelland, 1984). The nerve was exposed and isolated by incising and reflecting the right pectoralis major, tied with 6-0 silk suture, and severed just distal to the point of emergence from the thoracic cavity (Nelson et al., 2004). The nerve was then draped over a bi-polar nerve hook, made from two insulated (HML) silver wires (California Fine Wires, Grover Beach, CA) with 1 cm exposed tips that were curved (Fig. 1A). The two wires were housed in a small syringe with the exposed tips protruding from the tapered end. The nerve was coated in mineral oil to prevent desiccation without generating a salt bridge between the two electrodes.

We monitored the activation and condition of the humerotriceps muscle using electromyography (EMG) to record the induced muscle potentials throughout the experiments (Fig. S1). We made bipolar EMG electrodes from 3 μm diameter HML-insulated silver bifilar wire (California Fine Wires) with 1 mm tip exposure and 0.5 mm intertip distance (Dial, 1992b). These were inserted directly into the humerotriceps. A ground electrode was made from 4 μm diameter insulated silver BI wire (California Fine Wires) with 1 mm tip exposure, and inserted into the skin, between the left leg and the body.

In situ muscle data collection setup

To record force production and length changes in the humerotriceps muscle we used a Dual-Mode Lever System (Model 305C-LR, Aurora Scientific Inc., Aurora Ontario). This functions as both a force transducer and servo motor; in addition to recording force and position, it receives programmed input to impose the muscle length changes. The nerve-stimulating electrodes were connected to a High-Power Bi-Phase Current Stimulator (Model 701B, Aurora Scientific Inc., Aurora Ontario). The stimulus pattern was added to the experimental protocols written in Dynamic Muscle Control software (ASI 610A v5.415, Aurora Scientific Inc., Aurora Ontario). We programmed, ran and monitored all our work loop and parameter optimizing protocols, and treatment sequences using Dynamic Muscle Control. Data acquisition was done through an A/D signal interface (Model 604A, Aurora Scientific Inc., Aurora Ontario).

We recorded EMG output using a differential AC amplifier (Model 1700, A-M Systems, Sequim, WA). Live EMG data monitoring was performed during trials using AxoScope (v10.5, Molecular Devices, Inc., Sunnyvale, CA) and a low-noise data acquisition system (Axon Instruments Digidata 1440A, Molecular Devices, Inc., Sunnyvale, CA). The EMG signals were also recorded by the same system that was used to acquire position and force (Aurora Scientific), allowing us to link the muscle activation pattern to the corresponding events in the position and force output traces.

Work loop parameters

We performed a set of parametric tests to optimize the performance of the humerotriceps muscle prior to work loop tests. We determined the stimulus intensity that generated maximum force through a series of two-pulse isometric contractions. Voltage was held at 60 V while current was increased (Lacourpaille et al., 2013) by increments of 1 mA until maximal force was achieved. We then increased the current by another 50%, and used this intensity for the remainder of the experiment (Josephson, 1997). This procedure should ensure full motor unit recruitment, while maintaining longevity of the muscle and nerve. We ran two tetanic contractions and one to two work loops to get an estimate of the maximum force production of the muscle, and to check that the muscle, the knot, the humerus were all secure and properly immobilized before starting the next phase of measurements to evaluate the force-length relationship of the muscle.

We evaluated the force–length relationship of the humerotriceps muscle to determine resting muscle length (L0), using a series of two-pulse isometric contractions. We used doublet stimulation because each pulse within the doublet had a 0.2 ms duration and a frequency of 300 s−1. Given that a stimulus train of 18 pulses did not produce tetany and that a stimulus train of 24 pulses was just enough to produce tetany, it seemed likely that a two-pulse stimulus for isometric contractions would produce negligible differences in force relative to a single pulse stimulus. Between measurements, we increased muscle length by 0.5–1 mm steps. We calculated the difference between the passive tension (baseline) and peak force (Josephson, 1997); this is also known as the developed force. The motor arm position and muscle resting length were then chosen based on a balance between maximized force production and low passive tension. This balance was determined when the developed force no longer exhibited an increase with increasing length. If there was no apparent developed force plateau, the muscle was lengthened until the increase in developed force was negligible relative to the previous length (i.e.: ∼50 mN) due to a near parallel rise in passive tension. In these cases, the shorter of the two muscle lengths exhibiting similar developed forces was chosen as L0. We also used the two-pulse isometric contractions to evaluate the twitch kinetics of the humerotriceps. We measured the time for force to rise from 10% to 90% of its peak value and, subsequently, the time for force to relax from 90% to 10% of peak.

We used one standardized work loop protocol as the control to monitor the condition of the muscle and repeated this control work loop following each treatment. The settings for the control work loop protocol were 8.6 s−1 cycle frequency, stimulus duty cycle of 69% of the cycle, 8.7% strain amplitude and stimulus onset at −30% phase. The control work loop settings were chosen based on in vivo wingbeat frequency, stimulus duty cycle and fascicle strain amplitude (Robertson and Biewener, 2012). We chose the stimulus onset phase based on preliminary data that showed net positive work and power output consistently reached the highest values at −30% phase. Strain amplitude is the total percentage muscle length change relative to L0 (Robertson and Biewener, 2012). We define stimulus onset relative to the length-change cycle, with 0% representing peak muscle length, and 50%/−50% representing minimum muscle length (Fig. 1B).

We chose to examine two work loop parameters in the humerotriceps that exhibited variation during in vivo recordings of pigeon flight (Dial, 1992b; Robertson and Biewener, 2012). These included stimulus duty cycle and wingbeat frequency (equivalent to the wing muscle length-change cycle frequencies). We chose our work loop treatment parameters using ranges that would reflect these observed variations, leading to four different treatments (Table S1).

We examined the effects of stimulus duration and wingbeat frequency by testing across the full range of stimulus phases, where stimulus timing was varied from −50 to 50% of the muscle length-change cycle at 5% intervals, for a total of 20 different stimulus onset phases. −50 and 50% are effectively the same stimulus onset but differ with respect to the number of proceeding cycles within a trial (Table S1). One adjustment was that 10% phase was replaced by 9% to represent the average in vivo activation onset reported by Robertson and Biewener (2012). All experiments presented in this study included measurements at each of the 20 different stimulus phases. Within each set of measurements, stimulus onset phases were tested in randomized order, and the same random order was held constant for each experimental treatment. Every experimental treatment started and ended with one cycle at −30% phase as an additional check for force degradation, for a total of 22 work loop trials per individual, per treatment.

We examined how stimulus duty cycle affected muscle performance by using two durations, 50% and 69% (Table S1). A 50% duty cycle represented in vivo EMG results from Dial (1992b), whereas 69% represented in vivo results from Robertson and Biewener (2012).

We next examined work loop cycle frequency while holding stimulus duty cycle constant at 50% (Table S1). Our standard length-change cycle frequency was based on the average frequency (8.6 s−1) reported by Robertson and Biewener (2012). We examined two other frequencies, 6.1 and 10.1 s−1, which represent the minimum and maximum wingbeat frequencies recorded from multiple flight modes in pigeons, across several studies.

Strain amplitude, nerve stimulus pulse duration, pulse frequency and the number of strain cycles per trial were held constant across all treatments. Strain amplitude was approximated because muscle L0 could not be accurately measured until after the experiments were completed, due to the portion of the humerotriceps' origin that is located inside the head of the humerus, which made full excision necessary for determining muscle length. Therefore, we determined the strain amplitude to be used for all work loops by calculating 8.7% of the average resting length of the humerotriceps muscles based on preliminary experimental data. We used a set stimulus pulse duration of 0.2 ms and pulse frequency of 300 s−1. The number of stimulus pulses per train varied depending on the stimulus duty cycle duration (% cycle) and on the length-change cycle frequency. Every work loop trial, including the control, contained six cycles per trial, regardless of the treatment.

Inspection of the raw sonomicrometry data that were graciously provided by the authors of a previous study, where they measured in vivo fascicle strains from the pigeon humerotriceps (Robertson and Biewener, 2012), revealed that there exists some level of individual variation with respect to the shape of this muscle's strain profile. Matching the in vivo fascicle strain profile of the pigeon humerotriceps would be desirable, but our work loop control software did not have this ability. Although the trajectory of the in vivo fascicle strain profiles differed, they still retained a near-sinusoidal shape. Therefore, during our work loop experiments the strain profile was approximated by a sine wave.

Prior to analysis, we performed several validity checks of the humerotriceps work loop data using custom scripts written in MATLAB (R2016b, MathWorks Inc., Natick, MA, USA). First, we visually examined the EMG, length and force traces of each individual work loop trial to check for anomalies that could result from knot slippage, muscle tearing, servomotor malfunction, or loss of action potential propagation in the muscle. These anomalies would manifest as deviations from a sine wave for the length trace, unexplained changes in force or a substantial decrease in EMG signal amplitude, for example. We next visually inspected the third to fifth work loops in each trial to ensure that none of the work loops from an individual, for a given phase treatment, differed substantially from one another.

Finally, we examined the peak forces produced during the control work loops, which were run before and after each treatment. Since the net work and power output of the control work loops were not always positive, we chose to compare the means of peak forces of each control work loop to determine whether a given treatment should be included in the final dataset. We set a limit for force degradation based on the control work loop. Treatments were included if the control work loop that was tested just following a treatment had ≥59% of the peak force of the initial control work loop. We did not apply a correction to muscle force data based on degradation, but instead included degradation value in the statistical analysis.

We used 59% peak force as the cut-off because nearly all treatment sequences below this value exhibited one or both of the following problems: (1) notable departure of work loop shape from those typically observed for a given treatment, commonly through horizontal flattening of the loops or through marked decrease in area within each loop; (2) a substantial decrease (by close to half) in absolute power output at several, if not all of the phases. Two treatment sequences that were well below the 59% cut-off did not exhibit either problem but were excluded for consistency.

To further justify our decision to set the force degradation cut-off at ≥59%, we performed two sensitivity analyses on the work loop data, which demonstrated that the conclusions of the study were unaffected by this force degradation cut-off. We first reanalyzed our data using a more restrictive (higher) force degradation cut-off of ≥70%, relative to the control work loop (see Ellerby and Askew, 2007a). The 8.6 s−1 and 69% stimulus duty cycle treatment had four trials above the more restrictive cut-off, whereas the 8.6 s−1 and 50% stimulus duty cycle treatment had one trial above the cut-off. The power output curves and the summary statistics of these trials are plotted in Fig. S2. Comparison with similar plots for the larger data set indicated that the same conclusions are reached for comparable treatments.

We next performed an analysis of work loop data with varying force degradation cut-offs for the same treatments, including lower values. For the 8.6 s−1 and 50% stimulus duty cycle treatment, we compared two trials, one with a force cut-off of 71% and the other with a force cut-off of 60% (Fig. S3A). For the 10.1 s−1 50% stimulus duty cycle treatment, we compared three trials, with cut-offs of 64%, 60% and 59% (Fig. S3B). Visual inspection of the GAM fits of the data reveal that the magnitudes and locations of net power values (with respect to stimulus onset) are not influenced by the force degradation cut-off.

Net work was calculated from the force and length data and was multiplied by frequency to obtain net power output using custom MATLAB scripts, and mass specific values were determined in R (v3.3.2, R Development Core Team, 2016). We averaged power output across the third through fifth work loops within each trial for a given stimulus onset phase for consistency and because not all trials contained six complete work loop cycles. These three values were also consistent and included the maximum values within each of the first set of four complete work loop cycles.

Statistical analysis

Twitch kinetics data for developed force and relaxation durations were compared using a paired sample t-test to test for significance. Our measures of developed force and relaxation durations were from 10 to 90% of peak force, thus constituting 80% of the full durations. We approximated the full developed force and relaxation durations by linearly extrapolating their respective time intervals from 80 to 100%. This information was then used to predict the maximum contractile cycle frequency of the muscle and provide additional description of basic properties of the pigeon humerotriceps. However, it should be noted that this prediction will likely differ from the maximum contractile cycle frequency in a shortening cycle, because force can be enhanced by stretch (Askew and Marsh, 1998). Specifically, relaxation is more rapid when the muscle is allowed to shorten (Askew and Marsh, 1998).

To evaluate the sinusoidal quality and frequency of the in vivo fascicle strain profiles of the pigeon humerotriceps we used a fast Fourier transform (FFT) to determine the main component frequencies, and their respective power spectral density (PSD) for strain profiles from five birds. This evaluation was also performed on the in situ strain profiles that we used during our work loop experiments. For the in vivo fascicle strains, we determined PSD of the main component frequencies from the FFT amplitudes averaged across five trials for each bird. A given frequency was considered to contribute to the shape of the waveform if that frequency's PSD was greater than an arbitrarily selected threshold of 1.42×10−9 mm2 s. If deemed to be a contributing frequency, then the PSD of all of that frequency's harmonics were included in the total harmonic PSD that we used to determine the percentage that each fundamental frequency contributes to overall waveform shape. We determined what percentage of each of component frequency contributed to shaping the strain profiles of each bird by using the ratio of the PSD of each component frequency to the total harmonic PSD. We then determined the weighted mean fundamental frequency from the component frequencies of the strain profiles from each bird. We used these fundamental frequencies to qualitatively assess the similarity of the in vivo strain profiles from each bird, to those of the mechanically generated strain profiles that were used during our in situ work loop experiments.

To examine the contributions of stimulus phase to changes in power output and consequently the potential in vivo function of the pigeon humerotriceps within a given stimulus duration or cycle frequency treatment, we analyzed the power output of the humerotriceps across the full range of stimulus phases by fitting these data with a linear mixed-effects model. We then used a likelihood ratio test to compare this model to a null model that excluded phase as an explanatory variable. This method allowed us to compare power output among the different stimulus phases within each treatment (Table S1), while taking into account that there were repeated measures and autocorrelation over the duration of an experiment.

We addressed our first and second questions of how stimulus duty cycle and of how cycle frequency affects the muscle power output and thus its potential role in vivo by fitting the data from each treatment within these two comparison groups with a generalized additive model (GAM). The GAMs were fit for the power output across the full range of stimulus phases and included a cyclic component to account for the inclusion of both −50 and 50% phase, which are effectively the same. These models provided visual and quantitative characterization of the changes in power output that occur across the different treatment groups. We used the individual fits of each model to derive four summary statistics that quantify changes in shape of the power output curve: (1) mean power over the full range of phases, (2) maximum and (3) minimum power output, and (4) the percentage of the full stimulus phase cycle over which positive power is produced, hereafter referred to as actuation percentage. It is important to note that the mean power output at −30% phase was determined from both the first and the last trials within a treatment because this stimulus phase protocol was used to check for degradation every work loop treatment. We used an analysis of variance (ANOVA) to compare each of the four summary statistics of a given treatment to those of all other treatments within each of the two comparison groups. All statistical analyses were performed using R (v3.3.2, R Development Core Team, 2016).

RESULTS

Muscle twitch kinetics

Isometric contractions provided measures of the twitch kinetics of the pigeon humerotriceps muscle (Fig. 2A). As is typical for skeletal muscle, the humerotriceps muscle takes significantly longer to relax than to develop force (P≤0.0001; Fig. 2B; Table 2).

Fig. 2.

Twitch kinetics of the pigeon humerotriceps muscle. (A) Sample two-pulse isometric contraction, with developed force (from 10 to 90% of peak force) shown on the ascending arm of the force trace and relaxation (from 90 to 10% of peak force) shown on the descending arm. (B) Developed force duration, from 10 to 90% peak force (dark gray), and relaxation duration, from 90 to 10% peak force (light gray). Each symbol represents a different individual subject (n=9). The mean developed force and relaxation durations differed significantly (P<0.0001).

Fig. 2.

Twitch kinetics of the pigeon humerotriceps muscle. (A) Sample two-pulse isometric contraction, with developed force (from 10 to 90% of peak force) shown on the ascending arm of the force trace and relaxation (from 90 to 10% of peak force) shown on the descending arm. (B) Developed force duration, from 10 to 90% peak force (dark gray), and relaxation duration, from 90 to 10% peak force (light gray). Each symbol represents a different individual subject (n=9). The mean developed force and relaxation durations differed significantly (P<0.0001).

Table 2.

Twitch kinetic data and estimates from two pulse isometric contractions in the pigeon humerotriceps

Twitch kinetic data and estimates from two pulse isometric contractions in the pigeon humerotriceps
Twitch kinetic data and estimates from two pulse isometric contractions in the pigeon humerotriceps

Strain profile

We compared the in vivo and in situ strain profiles using an FFT analysis and the resultant weighted means of each strain profile's component frequencies (Fig. 3; see Table S2 for details). The comparison revealed a weighted mean fundamental frequency of 7.71 s−1 for the in vivo strain profiles from bird 1, 7.92 s−1 for bird 2, 7.57 s−1 for bird 3, 8.01 s−1 for bird 4 and 8.29 s−1 for bird 5 (Fig. 3B). These were close to the weighted mean fundamental frequency of 8.54 s−1 for the 8.6 s−1in situ strain profile (Fig. 3B,C). The two extreme frequencies that we used had fundamental frequencies of 6.07 s−1, and 10.1 s−1 for the 6.1 s−1 and 10.1 s−1in situ strain profiles, respectively (Fig. 3C).

Fig. 3.

Comparison of in vivo and in situ strain profiles for the pigeon humerotriceps. (A) Time course of fascicle strain measurements for two in vivo recordings (top two traces; refer to key in B) and representative in situ recordings (bottom three traces; see key in C) at the three cycle frequencies tested in this study. In vivo data are from sonomicrometry measurements in Robertson and Biewener (2012). In situ data were measured directly from the motor arm during work loop experiments. (B) Power spectral density (PSD; mm2 s) from the fast Fourier transform (FFT) amplitudes averaged across five flights per bird for in vivo recordings from five birds [1: 7.7 s−1 (light blue); 2: 7.9 s−1 (orange); 3: 7.6 s−1 (brown); 4: 8.0 s−1 (pink); 5: 8.3 s−1 (violet)] are plotted with the PSD from the FFT of the in situ strains from the 8.6 s−1 cycle frequency treatments (black). (C) PSD from the FFT of the in situ strains from all three of the contractile cycle frequencies tested (6.1 s−1, green; 8.6 s−1, black; 10.1 s−1, blue).

Fig. 3.

Comparison of in vivo and in situ strain profiles for the pigeon humerotriceps. (A) Time course of fascicle strain measurements for two in vivo recordings (top two traces; refer to key in B) and representative in situ recordings (bottom three traces; see key in C) at the three cycle frequencies tested in this study. In vivo data are from sonomicrometry measurements in Robertson and Biewener (2012). In situ data were measured directly from the motor arm during work loop experiments. (B) Power spectral density (PSD; mm2 s) from the fast Fourier transform (FFT) amplitudes averaged across five flights per bird for in vivo recordings from five birds [1: 7.7 s−1 (light blue); 2: 7.9 s−1 (orange); 3: 7.6 s−1 (brown); 4: 8.0 s−1 (pink); 5: 8.3 s−1 (violet)] are plotted with the PSD from the FFT of the in situ strains from the 8.6 s−1 cycle frequency treatments (black). (C) PSD from the FFT of the in situ strains from all three of the contractile cycle frequencies tested (6.1 s−1, green; 8.6 s−1, black; 10.1 s−1, blue).

Work loop dynamics

The work loop technique provides measurements of how muscle force changes during the shortening–lengthening cycle, and further allows for other muscle performance measurements across the full cycle including maximum and minimum force, work, and power output. Representative results obtained through the in situ work loop technique are provided in Fig. 4. The time-dependent changes in stress (kPa), force (N) and muscle length (mm) are given for six consecutive length-change cycles of a single trial (Fig. 4A). In our experiments we covered the full suite of stimulus onset phases from −50 to 50% and because the sequence of length-change cycles always began and ended at −25%, trials where stimulus phases were earlier than this received incomplete stimulation in their first cycle. Conversely, trials where stimulus onset phase was 25% or later (depending on stimulus duration) received incomplete stimulation in the last cycle in a sequence. We therefore used six consecutive cycles because that accounted for changes in stimulus onset to ensure that at least four complete cycles were available for analysis. Plotting this data sequence as force and stress versus length for the four consistently complete cycles produces work loops (Fig. 4B). The area within each work loop is integrated to determine the net work output of each muscle contraction cycle (Fig. 4C). Absolute net work increases with cycle number but leveled off for the last three consistently complete work loops within a trial (Fig. 4C). The mean of these three cycles was therefore multiplied by frequency to determine the net power output of the humerotriceps muscle during each trial. Net power output values were then normalized using muscle mass.

Fig. 4.

Muscle force and length change from a work loop recording of the pigeon humerotriceps muscle. (A) The force (gray) and length (purple) are plotted as a function of time, with the scale for stress also provided for reference. Thick bands on the length trace indicate the period of applied stimulus to the nerve. (B) The resultant work loop traces are plotted as force versus length change, with the stress scale provided for reference. Arrows depict the direction of the loops, and counter-clockwise loop directionality indicates that the net work is positive. Work loops 2 through 5 are shown because varying stimulus onset phase caused either the first or the last of the six work loop cycles to receive incomplete muscle stimulation, and these four cycles were consistently complete. The start and end of the stimulus period are indicated by ‘on’ and ‘off’ marks, respectively. (C) The net work output from work loop cycles 2 to 5 within a trial is determined from the integrated area within each loop. The net work from the first and last loops is not shown. The box indicates the three work loops within a trial whose mean net work was used to calculate net power for the trial. The specific strain and stimulus parameters used in this recording were used for all control work loop trials. All control work loops were run at a cycle frequency of 8.6 s−1, a stimulus onset phase of −30% cycle, and a stimulus duty cycle of 69%. The control work loop trials were run in between experimental treatment sequences to check the force degradation.

Fig. 4.

Muscle force and length change from a work loop recording of the pigeon humerotriceps muscle. (A) The force (gray) and length (purple) are plotted as a function of time, with the scale for stress also provided for reference. Thick bands on the length trace indicate the period of applied stimulus to the nerve. (B) The resultant work loop traces are plotted as force versus length change, with the stress scale provided for reference. Arrows depict the direction of the loops, and counter-clockwise loop directionality indicates that the net work is positive. Work loops 2 through 5 are shown because varying stimulus onset phase caused either the first or the last of the six work loop cycles to receive incomplete muscle stimulation, and these four cycles were consistently complete. The start and end of the stimulus period are indicated by ‘on’ and ‘off’ marks, respectively. (C) The net work output from work loop cycles 2 to 5 within a trial is determined from the integrated area within each loop. The net work from the first and last loops is not shown. The box indicates the three work loops within a trial whose mean net work was used to calculate net power for the trial. The specific strain and stimulus parameters used in this recording were used for all control work loop trials. All control work loops were run at a cycle frequency of 8.6 s−1, a stimulus onset phase of −30% cycle, and a stimulus duty cycle of 69%. The control work loop trials were run in between experimental treatment sequences to check the force degradation.

The experiments were designed to examine the role of stimulus duty cycle and cycle frequency across the full range of stimulus onset phases. These work loop experiments quantified the changes in muscle work and power output with shifts in muscle activation timing at different activation durations, and contractile cycle frequencies (Figs 5 and 6). Across all of the treatments, work loops were primarily clockwise at nearly all of the stimulus onset phases, indicating work absorption and brake-like function (Fig. 5 and Fig. S4). However, as stimulus onset phase shifted from between −35 and −30% phase toward peak length (0% phase), work loops transitioned to counter-clockwise, indicating work production and actuator-like function (Fig. 5 and Fig. S2). Once stimulus phase surpassed peak length direction reversal was punctuated by work loops looping back on themselves such that they both produced and absorbed work and resembled a figure eight (Fig. 5). These figure eight-shaped loops had reduced force amplitude, indicating little to no net work or power output (Figs 5 and 6, respectively). Several of these stimulus phases yielded relatively steep work loops with reduced hysteresis, which were most prominent at the highest frequency, and provide evidence for high energy return that is characteristic of a spring (Fig. 5 and Fig. S2).

Fig. 5.

Work loop shape changes substantially with stimulus onset phase, and modestly with changes in cycle frequency and stimulus duty cycle. (A) 6.1 s−1 and 50% stimulus duty cycle from bird 1 (green; n=2). (B) 8.6 s−1 and 69% stimulus duty cycle from bird 1 (purple; n=4 for all phases except −45, 0, 15 and 40%; n=3). (C) 8.6 s−1 and 50% stimulus duty cycle from bird 6 (red; n=2). (D) 10.1 s−1 and 50% stimulus duty cycle from bird 8 (blue; n=3). Representative work loops from the suite of stimulus onset phases are shown for all four treatments and are as follows: −50, −40, −30, −20, −10, 0, 9, 20, 25, 30, 35 and 45% phase. All work loops are the fourth loop from each trial and are plotted on the same scale: absolute length change and force are shown at −20% stimulus phase (A; horizontal and vertical bars, respectively). The in vivo ranges of phases recorded by Dial (1992b), and Robertson and Biewener (2012) are highlighted (A; horizontal yellow and gray bars, respectively).

Fig. 5.

Work loop shape changes substantially with stimulus onset phase, and modestly with changes in cycle frequency and stimulus duty cycle. (A) 6.1 s−1 and 50% stimulus duty cycle from bird 1 (green; n=2). (B) 8.6 s−1 and 69% stimulus duty cycle from bird 1 (purple; n=4 for all phases except −45, 0, 15 and 40%; n=3). (C) 8.6 s−1 and 50% stimulus duty cycle from bird 6 (red; n=2). (D) 10.1 s−1 and 50% stimulus duty cycle from bird 8 (blue; n=3). Representative work loops from the suite of stimulus onset phases are shown for all four treatments and are as follows: −50, −40, −30, −20, −10, 0, 9, 20, 25, 30, 35 and 45% phase. All work loops are the fourth loop from each trial and are plotted on the same scale: absolute length change and force are shown at −20% stimulus phase (A; horizontal and vertical bars, respectively). The in vivo ranges of phases recorded by Dial (1992b), and Robertson and Biewener (2012) are highlighted (A; horizontal yellow and gray bars, respectively).

Variation in stimulus duty cycle, and in contractile cycle frequency both had modest effects on work loop shape. Increasing stimulus duration primarily caused a greater range of phases to exhibit spring-like function (Fig. 5B,C). Increasing frequency primarily caused a shift from low to higher stiffness, as indicated by the increase in work loop steepness (Fig. 5A,C,D).

Representative examples of work loops that indicate brake-like function (clockwise loops) occurred at 20% phase for all three frequencies, at 50% stimulus duty cycle (Fig. 5A,C,D). The best evidence for actuation occurred in work loops that were produced between −20% and 0% phase for 6.1 s−1, and between −20% and −10% phase for 8.6 s−1, both at 50% stimulus duty cycle (Fig. 5A,C). Work loops that exemplified relatively compliant spring-like function (loops with lower steepness reduced and hysteresis) occurred between 30 and 45% phase at 8.6 s−1 and 69% stimulus duty cycle (Fig. 5B), whereas work loops produced at these phases but at 10.1 s−1 and 50% stimulus duty cycle were steeper, providing evidence for stiffer spring-like function (Fig. 5D).

Effects of stimulus duty cycle on net muscle power output

We used the work loop technique to examine two different values for stimulus duty cycle (50% and 69% cycle) and tested each across the full range of stimulus phases to cover the high level of variability in the in vivo measurements of activation onset timing in flying pigeons. Stimulus onset phase had a significant effect on the net power output of the humerotriceps muscle, regardless of stimulus duty cycle (P<0.0001 for both stimulus duty cycles). Net muscle power output was also affected by stimulus duty cycle but both net power output curves retained similar shapes across the full range of stimulus onset phases. Moreover, the peak, trough and crossover regions of the net power output curves were similar.

The primary effect of reducing stimulus duty cycle from 69% to 50% was to increase the range of the humerotriceps net power output curve (Fig. 6B,C,E–G). The maximum net positive power output represents the most positive contractile work, whereas maximum net negative power output represents the most negative contractile work, and the lower stimulus duty cycle had the higher extrema (Fig. 6F). Although there was an increase in maximum net positive power as stimulus duration was decreased from 69% to 50% duty cycle (Fig. 6D), the difference between the two maxima was marginally insignificant (P=0.076). The maximum net negative power output did, however, show a significant increase when stimulus duty cycle was shifted from 69% to 50% (P=0.0034; Fig. 6F).

Fig. 6.

Net power output from the pigeon humerotriceps shifts as a result of changes in stimulus onset phase, stimulus duty cycle and cycle frequency. (A–D) Net power output of the humerotriceps muscle across the full stimulus phase cycle (−50 to 50%) was tested at two stimulus duty cycles for 8.6 s−1 and three cycle frequencies, for a total of four treatments (experimental parameters, sample sizes, colors and the in vivo ranges of phases as in Fig. 5). Symbols for individual birds as in Fig. 2. (E–G) Summary statistics determined from the individual fits of the generalized additive model. (E) The mean net power output across the full range of phases (−50 to 50%) within a treatment sequence. (F) The range of net power denoted using the maximum net positive and maximum net negative power produced by the humerotriceps. (G) The percentage of stimulus onset phases over which the net power output is positive. Net power output by stimulus phase response curves of all treatments had a slope that differed significantly from zero (P<0.05). Letters indicate significant differences (P<0.05) among frequency treatments. Numbers indicate significant differences (P<0.05) between the two stimulus duty cycle treatments, both tested at 8.6 s−1. Horizontal yellow and gray bars as described in Fig. 5.

Fig. 6.

Net power output from the pigeon humerotriceps shifts as a result of changes in stimulus onset phase, stimulus duty cycle and cycle frequency. (A–D) Net power output of the humerotriceps muscle across the full stimulus phase cycle (−50 to 50%) was tested at two stimulus duty cycles for 8.6 s−1 and three cycle frequencies, for a total of four treatments (experimental parameters, sample sizes, colors and the in vivo ranges of phases as in Fig. 5). Symbols for individual birds as in Fig. 2. (E–G) Summary statistics determined from the individual fits of the generalized additive model. (E) The mean net power output across the full range of phases (−50 to 50%) within a treatment sequence. (F) The range of net power denoted using the maximum net positive and maximum net negative power produced by the humerotriceps. (G) The percentage of stimulus onset phases over which the net power output is positive. Net power output by stimulus phase response curves of all treatments had a slope that differed significantly from zero (P<0.05). Letters indicate significant differences (P<0.05) among frequency treatments. Numbers indicate significant differences (P<0.05) between the two stimulus duty cycle treatments, both tested at 8.6 s−1. Horizontal yellow and gray bars as described in Fig. 5.

In addition to comparing the extrema of the net power output curves, comparison of the mean net power across all stimulus phases, and of the actuation percentages allowed us to further quantify any overall shifts in both the locality and the range of the net power output by phase curves between the two treatments (Fig. 6E and G, respectively). The mean net power output of the two treatments did not differ significantly across the full range of stimulus onset phases (P=0.559; Fig. 6E). The actuation percentage also did not differ among the two treatments (P=0.178; Fig. 6G).

Effects of contractile cycle frequency on net muscle power output

We tested three values of cycle frequency that represent the minimum, mean and maximum values determined from in vivo measurements of flying pigeons. As with the stimulus duty cycle treatments, each frequency was tested across the full range of stimulus phases. Cycle frequency affected humerotriceps net power production by increasing the overall range of the net power output curve with increasing frequency (Fig. 6A,C–G). Despite this increased range, net power produced by the humerotriceps was still increasingly negative as frequency increased (Fig. 6A,C–G).

The net power output by phase curves retained overall similarities in their shape, despite changes to the cycle frequency. This included the retention in location of the peak, trough and crossover regions. Varying stimulus onset phase had a significant effect on the net power output of the humerotriceps within each frequency treatment (P<0.0001 for all three frequencies).

Changes in the overall range of the power output curve among the three frequency treatments were again quantified through comparisons of extrema. As cycle frequency increased from 6.1 s−1 to 10.1 s−1, there was a significant increase in the maximum net positive power output (P=0.0094; Fig. 6F). Increasing cycle frequency also caused a significant increase in maximum net negative power output (P<0.0001; Fig. 6F).

Shifts in location and range of the net power output curves across the three frequency treatments were again, further quantified by comparing the mean net power across the full suite of stimulus onset phases and the actuation percentages. Across the three frequency treatments, the mean net power output exhibited significant changes among the three frequencies (P<0.0001); mean net power output was lowest at 6.1 s−1, and highest at 10.1 s−1 (Fig. 6E). The actuation percentages showed a significant decrease with increasing frequency (P=0.0068; Fig. 6G).

DISCUSSION

The muscles intrinsic to the avian wing are hypothesized to control wing morphing, but the specific functions of these muscles are uncertain because there have been no previous measurements of force dynamics. Wingbeat frequency, and in vivo activation and fascicle strain measurements are available for the humerotriceps muscle of pigeons (Dial, 1992b; Robertson and Biewener, 2012). Here, we adapted the in situ work loop technique (Nelson et al., 2004; Roberts and Azizi, 2010) to explore how natural variation in cycle frequency and muscle activation features affected its potential roles (Fig. 1). The in situ work loops varied in shape and direction, and across the in vivo ranges of stimulus phases, the humerotriceps muscle transitioned in the degree to which it functioned as an actuator, brake and spring (Fig. 5, Fig. S4). Variation in cycle frequency and stimulus duration had modest effects on the magnitude of muscle function, which was reflected through gradual changes in power output (Fig. 6). The overall high level of functional variation was observed within the ranges of in vivo parameters, which suggest that across even a small number of distinct flight modes, pigeons can radically alter the role of the humerotriceps.

In addition to the in vivo fascicle strain profile from the pigeon humerotriceps displayed in Robertson and Biewener (2012), the authors generously shared additional strain profiles from the same study. This included 25 fascicle strain profiles, five from each of five birds. The shortening-to-lengthening ratio was highly variable among these in vivo measures, with the shortening phase occupying as much as 61% or as little as 41% of the contractile cycle. Our experimental setup allowed for 50:50 shortening-to-lengthening phase ratio in a pure sine wave for the strain of the complete muscle-tendon unit. Comparison of the fast Fourier transforms of the in vivo fascicle strains and the in situ muscle-tendon sine wave strain at 8.6 s−1 indicates that almost all variation in the temporal domain is accounted for by the primary oscillation frequency (Fig. 3). Differences in the shortening-to-lengthening ratio may have had a more substantial effect on our interpretation of the muscle's potential functions. The twitch kinetics that we measured from the pigeon humerotriceps demonstrate that force development duration was less than half that of its relaxation duration (Fig. 2). When this kinetic result is coupled with the highly variable in vivo shortening-to-lengthening ratio, it becomes evident that at key activation phases, the in vivo strain profile could generate substantially different contractile forces than for equivalent in situ measurements. For example, strain profiles with longer shortening periods would have increased net work and power output (Askew and Marsh, 1997; Ellerby and Askew, 2007a,b; Josephson, 1993; Sawicki et al., 2015). These strain profiles would likely result in more phases that exhibit the capacity for actuation. By contrast, strain profiles with longer lengthening periods would have decreased net work and power output (Askew and Marsh, 1997; Ellerby and Askew, 2007a,b; Josephson, 1993; Sawicki et al., 2015). These strain profiles would likely result in more phases exhibiting spring- or brake-like functions. Thus, the in situ setup may have limited the humerotriceps muscle's net work and power output by restricting its shortening-to-lengthening phase ratio (Askew and Marsh, 1997; Ellerby and Askew, 2007a,b; Josephson, 1993; Sawicki et al., 2015).

During flapping flight, it has previously been hypothesized that birds use their humerotriceps muscles to fill two roles: (1) to actuate elbow extension and wing expansion; (2) to stabilize the elbow joint angle, smoothing the transition from the upstroke to the downstroke (Dial, 1992b; Robertson and Biewener, 2012). It is possible to evaluate if these roles are fulfilled by plotting the instantaneous power through the stroke cycle, for key activation phases within the in vivo ranges. Overall, the instantaneous power that is produced by the pigeon humerotriceps through the stroke cycle provides support for both of these hypotheses for the role of this muscle (Fig. 7).

Fig. 7.

Instantaneous power from the pigeon humerotriceps. (A–D) Instantaneous power output from representative individuals for each of the four different treatments used for this study plotted over time for six out of the 22 stimulus onset phases, which highlight key phases within the in vivo ranges of activation onsets. Individuals used for plotting, experimental parameters, sample sizes, and colors as in Fig. 5. All instantaneous power plots are from the fourth loop from each trial and are plotted on the same scale: instantaneous power and time are shown at −5% stimulus phase (A; vertical and horizontal bars, respectively). US and DS (A) denote the up- and down-stroke (white and gray bars, respectively), with wingbeat cycle percentages and ratios taken as the grand means that were measured by Robertson and Biewener (2012).

Fig. 7.

Instantaneous power from the pigeon humerotriceps. (A–D) Instantaneous power output from representative individuals for each of the four different treatments used for this study plotted over time for six out of the 22 stimulus onset phases, which highlight key phases within the in vivo ranges of activation onsets. Individuals used for plotting, experimental parameters, sample sizes, and colors as in Fig. 5. All instantaneous power plots are from the fourth loop from each trial and are plotted on the same scale: instantaneous power and time are shown at −5% stimulus phase (A; vertical and horizontal bars, respectively). US and DS (A) denote the up- and down-stroke (white and gray bars, respectively), with wingbeat cycle percentages and ratios taken as the grand means that were measured by Robertson and Biewener (2012).

The activation duration of the pigeon's humerotriceps muscle is relatively long, causing it to have substantial positive and negative work, and positive and negative instantaneous power. Moreover, this attribute occurred consistently across all of the stimulus duration and cycle frequency treatments within the in vivo ranges of activation onset phases (Fig. 7). We observed transitions between positive and negative work (and power) in a single contractile cycle that had steep work loops with reduced hysteresis and low net work. The portion of one wingbeat or contractile cycle over which positive instantaneous power is produced by the humerotriceps muscle suggests that it is serving as an actuator by contributing energy towards elbow extension and wing expansion (Fig. 7). The portion of a contractile cycle over which negative instantaneous power is produced by the humerotriceps muscle suggests that it is serving to stabilize the elbow by resisting wing folding that is caused by aerodynamic forces. It also suggests that the muscle can act as a brake by absorbing energy that is likely contributed by the biceps to fold the wing, effectively slowing wing folding and helping smooth the transition from the upstroke to the downstroke. Negative instantaneous power suggests that the muscle is serving as a brake and resisting elbow flexion during that particular portion of its contractile cycle. In most cases, the muscle primarily produced negative instantaneous power over the course of one cycle (Fig. 7), which implies that stabilization of the elbow joint and resistance to wing folding likely requires more work than does elbow extension and wing expansion. Collectively, these results suggest that the muscle is able to fulfill both actuation and stabilization within a single contractile cycle, by having an extended stimulation duty cycle.

Multifunctional roles within a cycle have previously been demonstrated during terrestrial locomotion including in hopping tammar wallabies (Macropus eugenii) (Biewener et al., 1998b) and running turkeys (Meleagris gallopavo) (Gabaldón et al., 2004). Thus, during hopping, running and now flying, there is evidence for functional shifts over the course of one contractile cycle, where the muscles serve as stabilizers or brakes during one portion and propulsors or actuators during another.

The relative contributions of positive and negative power within a cycle will be determined in part by activation onset phase. Several in vivo studies provide evidence that pigeons shift activation onset phase of the humerotriceps as a function of flight mode (Dial, 1992b; Robertson and Biewener, 2012; see also Table 1). For example, with an early activation onset at the average wingbeat frequency (8.6 s−1) that might be observed during level flight, peak positive power occurs at the transition from the downstroke to the upstroke, suggesting that the humerotriceps is being used to maintain elbow extension through to the end of the downstroke. During the downstroke itself, the muscle produces negative power, suggesting that it is being used to resist elbow flexion and stabilize the joint (see Table 1 and first panels of Fig. 7B,C). In contrast, with a later activation onset, and higher wingbeat frequency (10.1 s−1) that might be observed during takeoff, the positive and negative components of instantaneous power would be shifted. Peak positive power would coincide with the upstroke to downstroke transition, and peak negative power would coincide with the downstroke to upstroke transition (see Table 1 and the three rightmost panels of Fig. 7D). In this case, the former would suggest that the muscle is being used to help initiate elbow extension rather than maintain it, and the latter would again suggest resistance to elbow flexion and contributions to joint stability.

Shifting activation onset phase to generate different muscle functions has previously been demonstrated in terrestrial locomotion. Sawicki and colleagues (2015) found that in the plantaris of bullfrogs (Lithobates catesbeianus), shifting the onset of muscle activation produced a sinusoidal power output by onset phase response curve, indicating that this shift effectively allows the bullfrog's plantaris to transition from actuator to spring to brake. Interestingly, they also noted it was difficult to generate strut-like behavior through changes in activation phase alone, as contractions exhibited both positive and negative work components (Sawicki et al., 2015), much like we observed in our study (Fig. 7). Ahn and Full (2002) noted that in two seemingly redundant leg muscles (177c and 179) of cockroaches (Blaberus discoidalis), activation onset phase contributes to functional differences among these two muscles during running. Under in vivo conditions, muscle 177c is activated slightly later relative to its length-change cycle than muscle 179 such that the former always produces positive power and the latter always produces negative power. This type of functional modulation has also been documented in the peroneus longus muscles of wild turkeys. The timing of peak force can be shifted such that during downhill running, it occurs early in the stance phase allowing this muscle to produce negative work, whereas during uphill running it occurs late in the stance phase to produce positive work (Gabaldón et al., 2004).

Although the results of our study provide clues as to how pigeons use their humerotriceps muscles during certain flight modes, it is worth drawing attention back to the anatomical complexity of the intrinsic wing musculature. There are likely co-contracting synergistic and antagonistic muscles whose contributions need to be taken into account when determining in vivo muscle function. Therefore, we acknowledge that the function of the pigeon humerotriceps may not be as clear cut as what is presented here.

An additional mechanism that has the potential to shift functional roles of a muscle is to vary the shortening-to-lengthening ratio. Highly asymmetrical strains are commonly observed in isolated, ballistic movements such as leaping in anurans (Ahn et al., 2003; Gillis and Biewener, 2000; Olson and Marsh, 1998), vertical jumping in cats (Abraham and Loeb, 1985) and fast starts in fish (Ellerby and Altringham, 2001; Goldbogen et al., 2005; James and Johnston, 1998; Wakeling and Johnston, 1999). Cyclic movements are constrained to have more symmetrical shortening and lengthening (Girgenrath and Marsh, 1997). However, deviations from symmetry have been observed in nearly all previous measurements from level flight (Biewener et al., 1998a; Ellerby and Askew, 2007b; Hedrick et al., 2003; Robertson and Biewener, 2012; Tobalske and Biewener, 2008; Williamson et al., 2001). The shortening phase of the pectoralis major, which powers the downstroke, is typically upwards of 60% during low- or high-speed level flight (Biewener et al., 1998a; Ellerby and Askew, 2007b; Hedrick et al., 2003; Tobalske and Biewener, 2008; Williamson et al., 2001), which has the potential to enhance the positive power (Biewener et al., 1998a; Ellerby and Askew, 2007a,b). The shortening-to-lengthening ratio from the in vivo fascicle strain measurements of the pigeon humerotriceps can vary substantially, ranging from 41:59 to 61:39. It is unknown how these fascicle strain ratios translate to whole muscle–tendon unit shortening-to-lengthening ratios. However, these results are highly suggestive that pigeons may be varying shortening-to-lengthening ratio to further modify muscle function. This hypothesis could be tested using in vivo strain profiles from the muscle–tendon unit in an in situ experiment with the capacity for asymmetrical strain trajectories.

Acknowledgements

We thank L. Kolody and K. Morden for assistance with surgical procedures and experiments. M. S, Armstrong, V. B. Baliga, R. Dakin, A. H. Gaede, C. Harvey, P. G. D. Matthews, W. K. Milsom, D. A. Skandalis, D. Schluter, G. C. Smyth, D. A. Syme and J. Wong provided helpful suggestions and edits.

Footnotes

Author contributions

Conceptualization: J.S.T., J.W.B., R.E.S., D.L.A.; Methodology: J.S.T., J.W.B.; Software: J.S.T., J.W.B.; Investigation: J.S.T.; Data curation: J.S.T.; Writing - original draft: J.S.T., D.L.A.; Writing - review & editing: J.S.T., J.W.B., R.E.S., D.L.A.; Visualization: J.S.T.; Supervision: D.L.A.; Funding acquisition: D.L.A.

Funding

The research was funded by the U.S. Air Force Office of Scientific Research, grant number FA9550-16-1-0182, monitored by Dr B. L. Lee, and by the Natural Sciences and Engineering Research Council of Canada (NSERC, RGPIN-2016-05381). J.S.T. was also supported by an NSERC Canada Graduate Scholarship.

Data availability

All data and scripts are available through Figshare at dx.doi.org/10.6084/m9.figshare.7336085.

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Competing interests

The authors declare no competing or financial interests.

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