TY - JOUR
AU - Azizi,, Emanuel
AB - Abstract Arboreal frogs navigate complex environments and face diverse mechanical properties within their physical environment. Such frogs may encounter substrates that are damped and absorb energy or are elastic and can store and release energy as the animal pushes off during take-off. When dealing with a compliant substrate, a well-coordinated jump would allow for the recovery of elastic energy stored in the substrate to amplify mechanical power, effectively adding an in-series spring to the hindlimbs. We tested the hypothesis that effective use of compliant substrates requires active changes to muscle activation and limb kinematics to recover energy from the substrate. We designed an actuated force platform, modulated with a real-time feedback controller to vary the stiffness of the substrate. We quantified the kinetics and kinematics of Cuban tree frogs (Osteopilus septentrionalis) jumping off platforms at four different stiffness conditions. In addition, we used electromyography to examine the relationship between muscle activation patterns and substrate compliance during take-off in a knee extensor (m. cruralis) and an ankle extensor (m. plantaris). We find O. septentrionalis do not modulate motor patterns in response to substrate compliance. Although not actively modulated, changes in the rate of limb extension suggest a trade-off between power amplification and energy recovery from the substrate. Our results suggest that compliant substrates disrupt the inertial catch mechanism that allows tree frogs to store elastic energy in the tendon, thereby slowing the rate of limb extension and increasing the duration of take-off. However, the slower rate of limb extension does provide additional time to recover more energy from the substrate. This work serves to broaden our understanding of how the intrinsic mechanical properties of a system may broaden an organism’s capacity to maintain performance when facing environmental perturbations. Introduction In habitats where there is large variation in the environment, whether navigating dense foliage or other physical obstacles, it can be challenging for an organism to preserve locomotor performance. Many organisms maintain performance by using stabilizing mechanisms to help adjust limb stiffness, posture, and muscle force in response to various perturbations to the center of mass (COM) or terrain (Daley and Biewener 2006, 2011; Daley et al. 2007; Biewener and Daley 2007; Gordon et al. 2015). Although many responses to perturbations rely on sensory feedback mechanisms, the intrinsic properties of the musculoskeletal system can also provide rapid, robust, and stable responses to mechanical perturbations (Jindrich and Full 2002; Daley and Biewener 2006). In some cases, the presence of elastic structures can provide intrinsic stability and allow for effective mechanisms to safely dissipate energy (Wilson et al. 2001; Wakeling et al. 2002; Daley et al. 2007; Roberts and Azizi 2011). During cyclical locomotor behaviors, an effective response to a perturbation can allow for recycling of kinetic energy from one hop or stride cycle to the next (McMahon 1985; Biewener and Gillis 1999; Schnyer et al. 2014). Studies on human movements on compliant surfaces have shown active modulation within the first step or hop on a dynamic surface through increased leg stiffness, changes in joint angle and metabolic rates for greater locomotor efficiency (McMahon and Greene 1979; Ferris and Farley 1997; Farley et al. 1998; Ferris et al. 1998, 1999; Kerdok et al. 2002). However, in ballistic systems where a mass rapidly accelerates instead of oscillates, the ability to respond to perturbations may be limited (Kagaya and Patek 2016; Longo, S.J. et al. , manuscript under review). In these systems, actuation is largely powered by elastic elements with little ability to control or modulate the output of the system once recoil is initiated. In some cases, the duration of the behavior is so short that reflexes or feedback control are simply too slow to respond to any potential perturbation in the environment. It is important to note however, that in many vertebrate systems even the fastest behaviors are not solely actuated by a spring, but rather operate with continuous input from skeletal muscles (Astley and Roberts 2012, 2014). The degree to which systems using a combination of both elastic and muscle powered mechanisms to respond to perturbations in the environment remains poorly understood. The ability to recover energy from a compliant substrate has been studied in several vertebrate systems. Previous work in several leaping primates shows use of pumping or oscillations of a substrate results in increased locomotor efficiency (Demes et al. 1995; Thorpe et al. 2007). Whereas, Cuban tree frogs can recover some energy from compliant substrates during a static jump alone (Astley et al. 2015). Conversely, other primates (vertical clingers and leapers) and anole lizards take-off prior to elastic recoil of the substrate, and therefore lose energy imparted to and stored in a deforming substrate (Demes et al. 1995; Channon et al. 2011; Gilman et al. 2012; Gilman and Irschick 2013). Given this disparity in performance, what mechanisms are responsible for allowing an organism to recover energy from a compliant substrate? Substrates of varying mechanical properties from woody branch structures to sand can be modeled as in-series mass, spring, dampers, which have substantial effects on substrate interactions at the whole organism level (James et al. 2006; Aguilar and Goldman 2016). The energy imparted on these substrates can either be stored or dissipated. On elastic substrates, an organism applies a force several times its body weight (BW) to deform the substrate thereby storing elastic energy in the substrate (Demes et al. 1995; Astley et al. 2015). If the substrate were to behave as a massless Hookean spring, all of the energy stored in the substrate would be released as the force applied by the organism decreases until take-off. However, in the real world, the substrate has mass and inertia which will delay the recoil of the substrate. Therefore, in order for an organism to recover the stored energy within a compliant substrate this requires some modulation of the timing of take-off. Otherwise, the organism loses a portion or all of the energy stored in the substrate, thus decreasing jump power. Studying the mechanical interactions between the spring-like properties within the substrate and the spring-like properties within the whole organism at the scale of the muscle-tendon provides insight into understanding the mechanics of two interacting in-series spring-mass systems. Cuban tree frogs provide an excellent model to investigate dual mass-spring dynamics given previous studies that show this species uses tendon elastic energy to power jumps (Roberts et al. 2011) and is also capable of recovering a portion of the energy stored in compliant substrates (Astley et al. 2015). We investigate mechanisms that may allow for substrate energy recovery from compliant substrates. We hypothesize frogs may actively modulate their performance by reducing rates of limb extension to delay the timing of take-off. A slower limb extension enables more time for the substrate to accelerate its mass and recoil to accelerate the frog. This may be achieved via changes to motor pattern by differentially recruiting muscles based upon changes in substrate compliance. Alternatively, without active modulation, muscles may be recruited similarly regardless of compliance and thereby the mechanical properties of the environment reduce jump performance. We measured substrate and jump kinetics, as well as limb kinematics during jumps off a dynamic, compliant substrate with varying substrate spring constant, k. In addition, we used in vivo measurements of electromyography (EMG) activity in the two joint extensor muscles, m. plantaris (ankle) and m. cruralis (knee), to understand muscle recruitment patterns in response to compliant substrates. We use these data to examine how organisms navigate the potential trade-offs between the use of elastic mechanisms to increase jump power and the ability to recover energy from a compliant substrate. Material and methods Reactive motor set-up To investigate jump performance and motor response of Cuban tree frogs on compliant substrates, we designed a dynamic, compliant substrate. The spring-like behavior of the servomotor was controlled by a BeagleBone Black single board computer (running Debian Linux on an AM335× 1 GHz ARM Cortex-A8 processor), used to simulate a linear spring. We used a feedback control system, programed based upon a linear spring equation, FVGRF=− kxsub, (1) where FVGRF is the vertical ground reaction force of the frog, k is the spring constant, and xsub is the displacement of the platform. As a result, this reactive substrate is directly tuned to the behavior of the animal during jump take-off. The reactive substrate consisted of a jumping platform, made of acrylic (6.0 cm × 0.3 cm × 5.0 cm; mass = 10.0 g), attached to the lever arm (mass = 25.3 g) of a 50 N dual-mode servomotor (Aurora Scientific Inc., Ontario, CA, USA; 305-C-LR; Fig. 1A). Servomotor force and length voltage outputs were calibrated relative to the center of the acrylic platform. Fig. 1 Open in new tabDownload slide Experimental set-up with a dynamically compliant substrate. (A) The reactive motor set-up built from a 50 N Aurora servomotor and BeagleBone Black computer. The motor was programmed to function as a linear spring based upon a predetermined spring constant, k, relative to BW. Vertical ground reaction force (FVGRF) voltage inputs were sent from the servomotor to the BeagleBone. In response, the BeagleBone voltage outputs were sent to the servomotor with a calculated length change relative to the programmed linear spring equation. Lateral and dorsal views of jumps were filmed using two high-speed video cameras, recording at 1000 frames s−1 to measure rate of limb extension (Vlimb), changes in ankle angle (θA), and timing of the jump. EMG electrodes were surgically implanted to record muscle activity patterns in an ankle extensor, m. cruralis (EMGCR) and a knee extensor, m. plantaris (EMGPL). Sample lateral view high-speed video frames of a Cuban tree frog from (B) the most compliant condition (0.9 mm BW−1). Fig. 1 Open in new tabDownload slide Experimental set-up with a dynamically compliant substrate. (A) The reactive motor set-up built from a 50 N Aurora servomotor and BeagleBone Black computer. The motor was programmed to function as a linear spring based upon a predetermined spring constant, k, relative to BW. Vertical ground reaction force (FVGRF) voltage inputs were sent from the servomotor to the BeagleBone. In response, the BeagleBone voltage outputs were sent to the servomotor with a calculated length change relative to the programmed linear spring equation. Lateral and dorsal views of jumps were filmed using two high-speed video cameras, recording at 1000 frames s−1 to measure rate of limb extension (Vlimb), changes in ankle angle (θA), and timing of the jump. EMG electrodes were surgically implanted to record muscle activity patterns in an ankle extensor, m. cruralis (EMGCR) and a knee extensor, m. plantaris (EMGPL). Sample lateral view high-speed video frames of a Cuban tree frog from (B) the most compliant condition (0.9 mm BW−1). The spring behavior of the reactive motor is governed by an open feedback control loop implemented in C++ running on the BeagleBone. FVGRF measurements are broadcast by the Aurora Scientific mechanical servomotor as analog signals in the ±10 V range. A peripheral 16-bit sampling analog-to-digital (A/D) unit (Texas Instruments ADS7813, Dallas, TX, USA) on a custom printed circuit board converted this signal to a digital force measurement, which is then passed via the serial peripheral interface bus to the BeagleBone, where it is smoothed with a software-implemented low-pass filter. The smoothed force estimate and a predetermined k are used to calculate the displacement of a linear spring (platform) with the given k in the presence of the measured FVGRF. The digital displacement value is then passed from the BeagleBone to a peripheral 16-bit multiplying digital-to-analog converter chip (Analog Devices AD7849, Norwood, MA, USA), where it is converted to an analog control signal. The analog position signal is sent to the Aurora Scientific mechanical servomotor, which in turn controls the position of the platform. This control loop executes at ∼1.4 kHz. However, the motor’s on-board memory updates at 250 Hz, and filtering the force signal introduces an additional delay. As a result, the platform responds to external forces in a linear spring fashion with programmable stiffness (Fig. 2A, B) with an approximate delay of 0.026 ± 0.021 s (mean ± standard deviation [SD]). The inertial mass of the compliant substrate was ∼0.075 kg. Considering this delay, the dynamic substrate acts more similarly to a damped spring-mass. However, the material properties of tree trunks and subsequent branches naturally act as in-series spring-mass-dampers (James 2003; James et al. 2006). Therefore, these frogs are less likely to experience a perfect spring-mass system, but rather a damped spring-mass. Fig. 2 Open in new tabDownload slide In vivo representative traces of recorded (A) vertical ground reaction forces and (B) dynamic substrate length change in response to the feedback controller at four different compliances: 0.0, 0.3, 0.6, and 0.9 mm BW−1. (C, D) Relative EMG activity patterns during the four compliant conditions for the m. cruralis (EMGCR) and m. plantaris (EMGPL) muscles. Fig. 2 Open in new tabDownload slide In vivo representative traces of recorded (A) vertical ground reaction forces and (B) dynamic substrate length change in response to the feedback controller at four different compliances: 0.0, 0.3, 0.6, and 0.9 mm BW−1. (C, D) Relative EMG activity patterns during the four compliant conditions for the m. cruralis (EMGCR) and m. plantaris (EMGPL) muscles. Prior to entering the spring behavior control loop, the BeagleBone samples and averages 1000 force measurements. This average was used as a passive force estimate and subtracted from forces measured within the control loop. Therefore, the displacement of the platform is a function of active force in excess of the passive ground reaction force exerted on the platform by the animal’s BW prior to a jump. All force and length data were collected at 1000 Hz using a 16-bit A/D converter (National Instruments, Austin, TX, USA) and Igor Pro Software (Wavemetrics Corp., Lake Oswego, OR, USA) for data acquisition. Jump trials This study used wild-caught, female Cuban tree frogs (Osteopilus septentrionalis), purchased from a herpetological vendor (mean ± standard error of the mean [SEM]; snout–vent length = 79.26 ± 2.27 mm, mass = 31.71 ± 3.07 g). Animals were housed and handled in accordance with the US Public Health Service Policy for the humane care and use of laboratory animals and all protocols were approved by the UC Irvine Institutional Animal and Care Use Committee. Five individuals were used for kinetic and kinematic jump trials and six individuals were used for EMG jump trials. Due to size constraints in performing surgery on the largest individuals, only three individuals were used across both kinematic and EMG trials. Across frogs and each compliant condition, a predetermined k was calculated relative to BW for each frog based on four desired displacement conditions of 0.0, 0.3, 0.6, and 0.9 mm BW−1. Tested k values ranged from 237 to 1217 N m−1. The range of k values were constrained by the response time of the servomotor; k values smaller than 100 N m−1 required too rapid of a timestep for the servomotor to function as programmed by the BeagleBone. Despite these constraints, the tested range of k values are representative of biologically relevant ranges tested in various tree stems and branches, up to 20 mm thick (van Gelder et al. 2006) and can span even greater stiffness (Kerzenmacher and Gardiner 1998; James 2003). However, leaf compliances are far more compliant than our tested conditions (Niinemets and Fleck 2002). Frogs were placed on the platform and allowed to jump the distance of the arena (61.0 cm × 29.0 cm × 60.5 cm), which included places for refuge to incentivize jumping. The frogs were encouraged to jump with a gentle tap on the sacrum with a cotton swab, however many frogs jumped off the substrate voluntarily without probing. Experiments were performed in temperatures 23.9°C ± 0.81°C (mean ± SD) and percent humidity ranged between 31% and 47%. We filmed jumping events using three-dimensional (3D) high-speed videography, with two video cameras (Phantom M120 Cameras, Vision Research Inc., Wayne, NJ, USA) positioned posteriorly and laterally to the individual and the compliant surface (Fig. 1B). Cameras recorded at 1000 frames s−1. All servomotor force–length data were synchronized to high-speed video data using an external trigger. Each individual performed at least five jumps at each compliance (0.0, 0.3, 0.6, and 0.9 mm BW−1). Jump trials from a given compliance were selected at random, however each frog jumped off a single compliance during a jump session to detect any learning or increase in performance due to experience on a given compliance. Individual and jump sequences were accounted as factors during statistical analyses. In our dynamic substrate system, the position where force is applied along the lever arm can result in a different output force and resulting length change from the dynamic substrate. Therefore, to reduce inaccuracies due to animal placement on the platform, we consistently placed animals on the marked center of the platform where the frog was limited to a small, calibrated area of the motor’s operating length. Jumps were chosen based upon robust performance with no foot or limb slippage from the platform. Analyzed content was chosen based upon the criteria that the body was centered on the platform, with both limbs on the platform, and ended with both hindlimb phalanges on the platform until the instant of toe-off. In addition, we accounted for any slight variation in placement of the frog relative to the calibrated center of the platform by multiplying a force correction factor to FVGRF to more accurately calculate jump power, a force dependent calculation made during post experimental analyses. The force correction factor was characterized as the ratio between the calibrated lever arm length to the center of the platform and the lever arm length to the toe (typically situated directly under the animal’s COM). Despite careful placement of the animal on the platform relative to the calibrated area, under- or overestimation of relative k of the platform was possible however minimal considering variation in the force correction factor was 0.999 ± 0.068 (mean ± SD). Hindlimb kinematics and kinetics For each jump, we used MATLAB to calculate the 3D position of the hindlimb (closest to the lateral view camera) relative to the platform. To calibrate the jumps, we used a custom calibration cube with 48 non-planar points with direct-linear transformation software from Hedrick (2008) in MATLAB (The MathWorks, Natick, MA, USA). Using the direct-linear transformation scripts, we manually tracked the tip of the longest phalange, metatarsal, ankle, knee, and hip on the left leg, the limb closest to the lateral view camera. We digitized the approximate frog COM at the center of the sacrum. In addition, five separate landmarks on the substrate were digitized to characterize the position of the platform relative to the frog limb. Video data were used to determine the rate of limb extension (Vlimb) and onset of ankle joint extension over a jump. Vlimb was characterized as the rate of change in the vector magnitude originating from the hip directed to the tip of the longest phalange. Limb extension traces were interpolated in Igor Pro using a smoothing spline with a factor of 0.005 to minimize any noise due to manual digitization. The 3D coordinates were used to calculate relative ankle joint angles during a jump within the local reference frame. Joint angles were interpolated using a smoothing spline with a factor of 0.01 to reduce any noise, then differentiated with respect to time to calculate joint angular velocities during jumps and determine timing of joint extension onset. Total frog and substrate energies were calculated using both high-speed video footage and force–length servomotor outputs. Servomotor force and length traces were interpolated using Igor Pro to minimize noise with smoothing spline factors of 0.09 and 0.00003, respectively. To characterize energy during the loading and unloading phases of the substrate, jumps were divided into two different phases: (1) the loading phase, defined as the start of the jump until the time of maximum substrate deflection and (2) the unloading phase was characterized as the time after maximum substrate deflection until the instant before the foot was no longer in contact with the substrate (toe-off). Total substrate energy (Esub) was calculated as the sum of the translational energy and the spring potential energy of the platform, Esub=msubΔxsubasub+(12kg(Δxsub)2), (2) where msub is the total mass of the acrylic platform and servomotor lever arm, asub is substrate acceleration, and g is gravitational acceleration. Esub was characterized for the loading and unloading phases of the jump. The proportion of energy recovered from the platform was characterized as efficiency (η); the proportion of energy recovered before toe-off (Erecovered) relative to the total energy loaded into the substrate (Eloaded), at maximum deflection, η =ErecoveredEloaded. (3) Total frog energy (Efrog) was calculated as the sum of the kinetic and potential energy of the COM, Efrog=(12 mfrogVcom2)+(mfrogg Δxcom), (4) where mfrog is the frog mass, the velocity of the frog COM (Vcom) and the displacement of the frog COM (xcom) were calculated from the digitized COM of the frog. Lastly, jump power (Pfrog) was calculated as, Pfrog=Vcom·FVGRFmfrog. (5) Pfrog was normalized to watts per unit muscle mass, estimated as 18% of body mass (Roberts et al. 2011). The relative contribution of substrate energy to jump energy was characterized as the proportion of energy recovered from the platform to the total energy of the frog COM at toe-off. This parameter was calculated to detect any increase in jump performance with increased exposure to a certain compliance. EMG We studied a knee and an ankle extensor, the cruralis and plantaris, respectively. These muscles play an important role during the jump take-off phase. EMG transducers were made with fine-wire bipolar electrodes (Medwire, Corp., Mt. Vernon, NY, USA), by twisting two bipolar wires together with the insulation stripped-off about 1 mm, with an approximate offset of 1 mm. EMG transducers were then surgically implanted in the muscles of interest. Tree frogs were anesthetized with immersion in 2 L of tricaine mesylate solution (MS-222, 2.0 g L−1) for 20 min. Following anesthesia, EMG transducers were surgically implanted into muscles of interest. Incisions were made by scalpel over the dorsal midline and along the skin covering each muscle. EMG transducers were slid under the skin and along the left leg to each muscle. One electrode was implanted per muscle using a 22-gauge hypodermic needle. Electrodes were sutured in place at the surface of each muscle using 6.0 suture silk. The ground wire was implanted subdermal along the dorsal side of the frog. All three skin incisions were sutured closed with 4.0 suture silk, with the transducer sutured in place on the animals’ back. Frogs were allowed to recover for 24 h before jump trials were performed. Muscle activities were recorded during compliant jump trials at all four compliant conditions. While instrumented, frogs were recorded using the previously explained experimental set-up with high-speed video and force actuated platform. Five jumps per compliance were analyzed for each of the six individuals. After EMG jump trials tree frogs were euthanized by MS-222 submersion followed by a double pithing protocol. EMG signals were amplified 1000× using a differential amplifier (A-M systems, Sequim, WA, USA) and recorded at 1000 Hz using Igor Pro software. Data were filtered with a finite impulse response filter (Fig. 2C, D) and rectified using Igor Pro. EMG signals were normalized to the maximum intensity of the rectified signal off a rigid substrate relative to each muscle (electrode). The onset and offset of muscle activity were identified and evaluated with respect to take-off timing. Then, rectified and normalized EMG signals were integrated between onset and offset of muscle activity to calculate muscle activation intensity during a jump. Statistical analysis All subsequent statistical analyses were performed using RStudio (v. 1.0.136, Boston, MA, USA). For each variable, mean values per individual were calculated and used for mean and standard error calculations across the different compliant substrates. To examine the effect of substrate compliance on energy recovery, Vlimb, max jump power, and joint extension onset, we used a mixed-model analysis of variance (ANOVA) to compare performance across compliance, accounting for variance within individuals and jump sequence. Post-hoc comparisons were made with false discovery rate tests to examine the effect between various compliant substrates. To detect whether there was learning or increased performance with exposure to a particular compliance we performed linear regressions for each compliance. We used repeated measures ANOVA to compare muscle recruitment intensities across compliance relative to each muscle. In addition, we performed repeated measures two-way ANOVAs on muscle activation onset and offset accounting for variance within individuals. To account for multiple statistical tests, Holm–Bonferroni step-wise method was used to test our hypotheses with an alpha level of 0.05 (Supplementary Table S1). Ethics Animal husbandry and experimental procedures were approved by the University of California, Irvine Institutional Animal Care and Use Committee (Protocol AUP-17-170). Results A total of 220 jumps were analyzed between six animals, with a total of 120 jumps collected for EMG analysis. Frogs generally loaded about 3–4 times their BW (Fig. 2A), with a 40% decrease in vertical ground reaction force with increased compliance (P = 0.001). For compliant conditions, platform deflections ranged from 0.5 to 2.5 mm. Across all compliances, only 50% of the original energy stored into the substrate was recovered before toe-off (Fig. 3A). There was no relationship between previous experience with a certain compliance and the contribution of substrate energy to the mechanical energy of the frog at take-off (Supplementary Fig. S1). Frogs did not improve their performance with increased experience or repetitions on a particular compliance. Fig. 3 Open in new tabDownload slide Osteopilus septentrionalis kinetics and limb kinematics across variable compliances. Means ± SEM shown for five individuals. Means were calculated using individual means from five jumps at each compliance. (A) Energy recovery efficiency across variable compliant substrates. Across all compliances O. septentrionalis recovered about 50% of the energy stored in the substrate before jump take-off. (B) Limb extension velocity (Vlimb), calculated at the instant of maximum ground reaction force across jump trials. Rate of limb extension decreases with increasing compliance (P = 0.008). Significant differences across compliance are denoted with letters a, ab, b, etc., compliances not sharing the same letters are significantly different (P < 0.05). Fig. 3 Open in new tabDownload slide Osteopilus septentrionalis kinetics and limb kinematics across variable compliances. Means ± SEM shown for five individuals. Means were calculated using individual means from five jumps at each compliance. (A) Energy recovery efficiency across variable compliant substrates. Across all compliances O. septentrionalis recovered about 50% of the energy stored in the substrate before jump take-off. (B) Limb extension velocity (Vlimb), calculated at the instant of maximum ground reaction force across jump trials. Rate of limb extension decreases with increasing compliance (P = 0.008). Significant differences across compliance are denoted with letters a, ab, b, etc., compliances not sharing the same letters are significantly different (P < 0.05). We examined limb kinematics and jump performance to determine whether there were any changes in performance across these compliant substrates. We found a 20% decrease in limb extension velocity with compliance (P = 0.008; Fig. 3B). Vlimb tended to decrease significantly for all substrate compliance relative to a rigid substrate jump (0.3 mm BW−1, P = 0.01; 0.6 mm BW−1, P = 0.002; 0.9 mm BW−1, P = 0.036). These changes in limb velocity were reflected in jump power. Powers on compliant substrates trended toward the maximum power output of muscle alone, suggesting that the use of elastic energy to increase jump power may be limited (Fig. 4). Maximum power output across a jump tended to decrease with compliance (P = 0.002; Fig. 4B). Jump power on a rigid substrate was greater than on each compliant condition (0.3 mm BW−1, P = 0.038; 0.6 mm BW−1, P = 0.005; 0.9 mm BW−1, P = 0.028; Fig. 4B). Jump power between the three compliance conditions did not differ significantly. This pattern suggests all three compliant conditions may only be marginally different from one another. Given this observed decrease in jump performance, we examined whether this change in performance was actively modulated by muscle activation. Fig. 4 Open in new tabDownload slide Muscle mass-specific jump power on rigid and compliant substrates. Data points and SEM represent means across five individuals. Means were calculated using individual means from five jumps at each compliance. The dashed line designates maximum muscle power output at 300 W kg−1. (A) Average jump power profile during a jump. All averaged data are shown as a bolded line with standard error denoted with like-color shaded regions around the averaged traces. Average power output on compliant substrates range around the maximum power output of the muscle. In comparison, power output on rigid substrates exceeds the power output on compliant substrates by nearly two-fold. (B) Absolute maximum jump power (mean ± SEM) decreases with increasing compliance (P = 0.002). Significant comparisons are indicated with a, b, and ab; means not sharing the same letters are significantly different (P < 0.05). Fig. 4 Open in new tabDownload slide Muscle mass-specific jump power on rigid and compliant substrates. Data points and SEM represent means across five individuals. Means were calculated using individual means from five jumps at each compliance. The dashed line designates maximum muscle power output at 300 W kg−1. (A) Average jump power profile during a jump. All averaged data are shown as a bolded line with standard error denoted with like-color shaded regions around the averaged traces. Average power output on compliant substrates range around the maximum power output of the muscle. In comparison, power output on rigid substrates exceeds the power output on compliant substrates by nearly two-fold. (B) Absolute maximum jump power (mean ± SEM) decreases with increasing compliance (P = 0.002). Significant comparisons are indicated with a, b, and ab; means not sharing the same letters are significantly different (P < 0.05). Both extensor muscles activated at similar times and intensities prior to body or joint movement across each compliance (Figs. 2, 5). Muscle activation intensities did not change across compliance for both plantaris and cruralis muscles (Fig. 5A). Despite nonsignificant relationships, a later onset of muscle activation timing was observed on more compliant substrates, which tended to show a shorter jump duration (Fig. 5B). Muscle activation offset did not differ between muscles within compliance. On 0.3 and 0.9 mm BW−1 substrates, the extensor muscles tended to continue activation until the timing of toe-off. Whereas, on rigid and 0.6 mm BW−1 offset occurred milliseconds prior to toe-off. Despite no clear active modulation in the two joint extensor muscles, we observed a significant decrease in jump power on more compliant substrates. Fig. 5 Open in new tabDownload slide Average muscle activation patterns for m. cruralis and m. plantaris during jumps from various compliant substrates (mean ± SEM). Data points and SEM represent means for six individuals. Means were calculated using individual means from five jumps at each compliance. (A) There was no difference in muscle activation intensity across compliance in both joint extensor muscles. (B) Bar graphs represent EMG extensor muscle onset and offset, with (C) ankle joint extension onset represented as a scatter plot. Muscle activation occurred around similar times across compliance, however offset differed significantly (P = 0.033). Joint angle onset began earlier with increased compliance (P < 0.001). Significant comparisons are indicated with a, b, and ab; means not sharing the same letters are significantly different (P < 0.05). Fig. 5 Open in new tabDownload slide Average muscle activation patterns for m. cruralis and m. plantaris during jumps from various compliant substrates (mean ± SEM). Data points and SEM represent means for six individuals. Means were calculated using individual means from five jumps at each compliance. (A) There was no difference in muscle activation intensity across compliance in both joint extensor muscles. (B) Bar graphs represent EMG extensor muscle onset and offset, with (C) ankle joint extension onset represented as a scatter plot. Muscle activation occurred around similar times across compliance, however offset differed significantly (P = 0.033). Joint angle onset began earlier with increased compliance (P < 0.001). Significant comparisons are indicated with a, b, and ab; means not sharing the same letters are significantly different (P < 0.05). Our results suggest an early onset of limb extension may be due to the displacement of the compliant substrate, which in turn decreases power output by nearly half. The onset of ankle extension tended to occur sooner on compliant substrates (Fig. 5C;P < 0.0001). This was also reflected in ankle joint extension over time and joint angular velocities (Supplementary Fig. S2). The timing between EMG onset and relative joint extension onset (prior to any change in mechanical advantage), corresponds to the timing of elastic energy storage. This suggests frogs may have a longer time to store elastic energy on rigid substrates (Fig. 5C). As a result, with increased energy storage to the system, we observe greater force and power outputs, and thus a faster limb extension. Discussion Cuban tree frogs lose a substantial portion of the elastic energy loaded into the substrate (Fig. 3A) and show little improvement in energy recovery with increased exposure to a particular substrate (Supplementary Fig. S1). Our results support previous research demonstrating the use of elastic recoil energy from a compliant substrate (Astley et al. 2015). Given the limited range of tested compliance, we did not find a clear trade-off in energy recovery, efficiency, or performance for a certain compliance. However, Astley et al. (2015) has shown this trade-off on substrates up to double our experimented compliance. We acknowledge our tested perturbations are relatively small displacements; however, we still find an effect of compliance on performance (Figs. 3B, 4). It is possible we do not find any dose response in Vlimb or efficiency (Fig. 3) with increasing compliance either due to tree frogs not sensing the difference between compliant conditions or the conditions are not distinct enough from one another, effectively making the strategies binary (complaint vs. rigid responses). We suspect that more pronounced perturbations will only enhance the patterns observed in our data. Even this slight perturbation shows the influence compliance and substrate mechanics may have on ballistic systems, where a geometric latching mechanism interacts directly with the substrate. In a system driven by an elastic mechanism, we find evidence that direct mechanical interactions of the limb and substrate may play a greater role in modulating performance than active changes in muscle activity patterns. We initially hypothesized that an organism must slow down the rate of limb extension to await substrate recoil to fully recover energy stored within the substrate. We found rate of limb extension slows down with increased compliance (Fig. 3B). A decrease in rate of limb extension allows these frogs to remain on the platform until the substrate recoils, recovering a portion of the stored energy. Previously, Astley et al. (2015) showed a decreasing trend in take-off velocity of the COM with increased compliance, which is consistent with our results showing a slowing rate of limb extension resulting from a compromised elastic energy storage mechanism. Gibbons and anoles decrease COM velocities on compliant substrates (Channon et al. 2011; Gilman et al. 2012); however, it is difficult to extrapolate to these systems where energy is not recovered from the substrate. Feedforward jump mechanism Across all substrates, we recorded muscle activation patterns to detect any changes in the timing and intensity of recruitment. Given the observed decrease in the rate of limb extension, we expected active modulation to coordinate with these changes. However, we found no significant patterns in activation intensity or onset across both extensor muscles (Fig. 5A, B). These results support the idea that Cuban tree frogs do not actively adjust in response to feedback during jump take-off, but rather may operate with a feedforward control program. At this timescale, jump performance may be too fast for active modulation (Kagaya and Patek 2016). Our results are consistent with this assertion and suggest that visual, vestibular, proprioceptive feedback may not play a direct role in modulating Cuban tree frog jumps. Once a jump is initiated, the frog does little to modify the motor program. Though we would expect the timeframe of the loading phase and substrate deflection to be within the timing of a reflex loop, it is possible that the loading time pushes up against the limits of the motor pattern response. We hypothesize that organisms that use elastic elements to power fast movements potentially give up the ability to actively respond to perturbations. This is highlighted by the lack of adjustments in performance with increased experience on a particular compliant substrate (Supplementary Fig. S1). This hypothesis could be tested in species where jumps are more reliant on direct muscle power rather than the recoil of elastic elements. For example, Cuban tree frogs have been shown to use elastic energy to produce jumps with up to four times the mechanical power output of cane toads (Roberts et al. 2011). In comparison, toads have been shown to accurately predict the jump distance and modulate activation patterns in their forelimbs in anticipation of landing (Gillis et al. 2010; Akella and Gillis 2011; Azizi and Abbott 2013; Cox and Gillis 2016, 2017). We predict that species that rely less on elastic energy storage and have significantly longer take-off durations may have a greater ability to actively modulate jump performance in response to substrate perturbations. In contrast, systems that utilize substrate oscillation for momentum demonstrate active behavioral modulation. Models have shown how humans can coordinate joint extension from a standing jump off a springboard (Cheng and Hubbard 2004, 2005). Channon et al. (2011) showed gibbons actively minimize substrate deflection by modifying behavior in two ways: avoiding a subset of leap types that would otherwise be freely used on rigid substrates and demonstrating a preference for jumping from a particular section of the stiffer substrate. In contrast to tree frogs, jump power in gibbons on compliant substrates was not affected, with no changes to joint extension timing. Gibbons are not constrained to powerful ballistic movements like tree frogs, but rather perform work and minimize power requirements during jumps (Channon et al. 2010, 2012). We suspect use of elastic energy storage in this system is less likely given their ability to learn and actively modulate behavior. Trade-off in elastic energy storage We found substrate compliance negatively impacted jump power (Fig. 4). These frogs are using the same jump motor patterns throughout all compliances, however do not amplify power as effectively on compliant substrates. This pattern was also observed in Astley et al. (2015) that shows decreased power with increased compliance. Cuban tree frogs are known for their high-powered jumps and are thought to utilize elastic energy storage to achieve high performance (Marsh and John-Alder 1994; Peplowski and Marsh 1997). The inertial catch mechanism acts as a latch to allow elastic energy storage in tendons early in the take-off phase. This mechanism relies on the inertia of the body as well as a dynamically changing mechanical advantage to resist the forces produced by muscles early in the jump. A clear signature of this mechanism is the activation of muscles preceding the actuation of the joint allowing energy to be transferred from muscle to tendon. We suspect that the deformation of the compliant substrate causes premature extension of the ankle and increases mechanical advantage thereby releasing (or unlatching) the latch earlier in the push-off phase (Fig. 6). Consistent with this interpretation, we observed an earlier onset of ankle extension with increased compliance (Fig. 5C). This early extension of the joint moves the joint’s center of rotation closer to the ground reaction force vector which increases mechanical advantage and limits the time available for elastic energy storage. In addition to the hypothesized changes to the effectiveness of the latching mechanism in this system, jump performance may also be affected by the intrinsic muscle properties (Daley and Biewener 2006) as the early initiation of shortening on compliant substrates likely disrupts the development of force (due to force–velocity effects) resulting in lower ground reaction forces, less energy stored in the tendon, and lower jump powers. We provide the first evidence of how an organism’s environment or substrate may interfere with the latching mechanisms, thus disrupting a necessary component of a system reliant on the storage and release of elastic energy. Fig. 6 Open in new tabDownload slide Schematic showing the disruption of the inertial catch mechanism at two distinct time points during a jump on a compliant and rigid substrate: (A) t1, during loading at the start of a jump, (B) t2, on a compliant substrate versus (C) t2, on a rigid substrate. Jumps on a compliant substrate begin ankle joint extension sooner than jumps off a rigid substrate. A rigid substrate likely allows for more time to load energy into elastic structures before the joints begin to extend. Fig. 6 Open in new tabDownload slide Schematic showing the disruption of the inertial catch mechanism at two distinct time points during a jump on a compliant and rigid substrate: (A) t1, during loading at the start of a jump, (B) t2, on a compliant substrate versus (C) t2, on a rigid substrate. Jumps on a compliant substrate begin ankle joint extension sooner than jumps off a rigid substrate. A rigid substrate likely allows for more time to load energy into elastic structures before the joints begin to extend. Conclusions The potential reduction in both elastic energy storage and release results in lower power output and slower rate of limb extension, allowing the frog to remain on the substrate until partial recoil. A reduced rate of limb extension provides the frog more time for energy recovery from a compliant substrate. With the timing of elastic energy storage disrupted, power output decreases, and slows down the rate of limb extension enough to keep the frog on the substrate in order to recover energy from the substrate. Therefore, we conclude that systems that rely on changes in mechanical advantage as an integral part of a latch mechanism may be robust to variation in the environment as the disruption of the latch provides some benefit in the organism’s ability to recover energy from a compliant substrate. Authors’ contributions C.M.R., C.E.E., and E.A. conceived the study; C.E.E. constructed and developed the force actuated BeagleBone controller set-up; C.M.R., G.A.S., and E.A. carried out experiments; C.M.R. and G.A.S. analyzed the data; C.M.R., C.E.E., G.A.S., and E.A. drafted and edited the manuscript. From the symposium “Playing with Power: Mechanisms of Energy Flow in Organismal Movement” presented at the annual meeting of the Society for Integrative and Comparative Biology, January 3–7, 2019 at Tampa, Florida. Acknowledgments The authors would specifically like to thank the following MURI team members, collaborators, and their labs: Sheila Patek, Sarah Bergbreiter, Alfred Crosby, Robert Wood, and Gregory Sutton. They also thank doctoral committee members for C.M.R. (Matt McHenry and Donovan German). They are thankful to Ben Perlman for help with data collection and animal husbandry. In addition, we thank Jordan Balaban, Elizabeth Mendoza, Matthew Mickle, Chloe Nouzille, Pouyan Pouresfandiari, and Nuria Varela for help with animal husbandry. Thank you to Playing with Power symposium organizers: Jeffery Olberding, Michael Rosario, and Stephen Deban. 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TI - Compliant Substrates Disrupt Elastic Energy Storage in Jumping Tree Frogs
JF - Integrative and Comparative Biology
DO - 10.1093/icb/icz069
DA - 2019-12-01
UR - https://www.deepdyve.com/lp/oxford-university-press/compliant-substrates-disrupt-elastic-energy-storage-in-jumping-tree-xORoitS0FU
SP - 1535
VL - 59
IS - 6
DP - DeepDyve
ER -