Jumping mechanics of desert kangaroo rats

Bipedal hopping is a highly specialized mode of terrestrial locomotion that has arisen independently in six lineages of mammals (McGowan and Collins, 2018). It has been hypothesized that bipedal hopping evolved as an adaptation for erratic behavior (e.g. Moore and Biewener, 2015) and extreme jump performance to evade predators (Bartholomew and Caswell, 1951; Webster and Webster, 1980). For example, small hopping species, such as kangaroo rats and jerboas are capable of jumping over 10-times their standing hip height (Biewener and Blickhan, 1988; Moore et al., 2017). Kangaroo rats are also capable of very rapid jump take-off times in response to snake strikes (Freymiller et al., 2017). Alternatively, larger bipedal hopping species (>3 kg) benefit from a decoupling of metabolic cost from steady-speed hopping enabling remarkably efficient locomotion (Dawson and Taylor, 1973; Biewener and Baudinette, 1995).

The morphological specializations associated with bipedal hopping include greatly elongated hind limbs in which the muscle mass is concentrated proximally. These proximal muscles tend to have relatively long fibers and large cross-sectional areas that are well suited for generating muscle power, whereas distal muscles tend to have short, pennate fibers with long tendons that are better suited for developing high force (Biewener and Roberts, 2000). Within larger bipedal hoppers, these long distal tendons are relatively thin, enabling the elastic energy storage and return that contributes to locomotor efficiency in these animals (Biewener et al., 1998), but may also limit acceleration capacity during rapid movements due to low tendon safety factors (Biewener and Bertram, 1991). Studies of tammar wallabies hopping on level and inclined surfaces have shown that a division of labor exists between proximal and distal muscle groups, with proximal muscles providing the work to raise the animals’ center of mass and specialized distal muscle–tendon groups retaining spring-like function (Biewener, 2004; McGowan et al., 2007). While relatively long, the distal tendons of small bipedal hoppers tend to be comparatively thick and probably do not store and return significant elastic energy during hopping (Biewener et al., 1981, 1988; Moore et al., 2017). Rather, these muscle–tendon units (MTUs) are better suited for direct transmission of mechanical work by the muscle to the environment. Therefore, it is not clear if a division of labor exists between proximal and distal muscles in these smaller hopping species when doing work against the environment.

Small bipedal hoppers rely on their ability to jump in order to escape predation, yet relatively little is known about the mechanics of how they achieve these high-power maneuvers. Previous studies of in vivo muscle performance by kangaroo rats (Dipodomys spectabilis) suggest that the ankle plantarflexor MTUs generate extremely high forces (up to 175% of the maximal isometric force) during their highest jumps (Biewener et al., 1988). And an analysis of jumping by jerboas (Jaculus jaculus) indicates that the ankle delivers the majority of the mechanical work done at the joint level (Moore et al., 2017); however, this study did not examine how the distribution of work changed across jump heights. Despite proximal muscles being morphologically better suited for developing power, most jumping animals deliver the highest power outputs at the distal joints (Van Soest et al., 1985; Aerts, 1998; Moore et al., 2017). This distal delivery of power can be facilitated by the return of energy from elastic elements and/or energy transfer from proximal to distal joints, often through biarticular muscles (Gregoire et al., 1984; Bobbert et al., 1986), although power can also be transferred between leg segments through inertial coupling (Zajac et al., 2002). The previous studies of jumping by kangaroo rats and jerboas both concluded that elastic energy storage did not contribute significantly to the power required to achieve the measured jump heights, but neither considered the role of energy transfer.

The aim of this study was to determine how desert kangaroo rats (Dipodomys deserti Stephens 1887) modulate the mechanical output at each joint to power jumps over a range of heights. To achieve our aim, we used an inverse dynamics approach to investigate the hind limb net joint power and work by examining which joints increased power output in response to increasing jump heights. Furthermore, we used a geometric model based on the animals' anatomy to estimate energy transfer from proximal to distal joints. Because these animals lack the distal MTU specialization for elastic energy storage, we hypothesized that increases in net work would be equally divided across leg joints with increases in jump height.

Eight adult, wild-caught desert kangaroo rats were used for this study (body mass of 72–120 g). Animals were caught in the Mojave Desert in southeast Nevada under permits issued by the Nevada Department of Wildlife and the Bureau of Land Management. At least 24 h prior to experiments, the animals were trained to familiarize them with the experimental environment and task. During training sessions, the animals were exposed to jumping obstacles of different heights and they were motivated to jump by hand movements close to the animal. All experimental procedures and the husbandry of the animals were approved by the University of Idaho Institutional Animal Care and Use Committee (IACUC).

Between 10 and 20 jumping trials with different obstacle heights were performed by each animal. High-speed video data were recorded at 200 frames s⁻¹ using a camera (Xcitex, Woburn, MA, USA), which was positioned with a sagittal view of the animal. The jump arena had plexi-glass walls and included a built-in force plate (AMTI HE6x6, Watertown, MA, USA). Animals were encouraged to jump over an obstacle of a given height (ranging from 0.12 to 0.45 m) after taking off from a force plate that was sampled at 600 Hz. Animals landed on a foam pad on the opposite side of the barrier.

Trials were selected for analysis based on completeness (complete set of video and force plate data) and on jump performance (total n=62; 4–15 trials per animal). Jump performance requirements were that the animal was oriented sagittal to the camera and took off from both legs simultaneously. Trial length was determined based on the GRF pattern. Start time of the trial was designated as the time at which the force exceeded body weight (BW). Countermovements, visible in the force trace as a drop below BW, occurred in a few trials, but the amount of change in force in these trials was minimal (<6.5% BW). If countermovements occurred, then the starting point of the trial was defined as prior to the countermovement when the force trace was still equal to BW. The end of the jump was defined as the first point in time at which the vertical GRF was zero.

Prior to the experiment, markers were placed on the animals' hind leg joint centers of rotation [toe, metatarsophalangeal (MTP), ankle, knee, hip]. An additional marker was placed on the ischium. Following the experiment, these markers and the position of the eye were digitized using ProAnalyst software (Xcitex) and a low-pass fourth-order Butterworth filter was applied with a cut-off frequency of 30 Hz. The coordinate data were used to calculate joint angles and joint angular velocities. GRFs were filtered with a low-pass second-order Butterworth filter with a cut-off frequency of 55 Hz. Owing to skin movement, the knee joint position was calculated based on the position of ankle and hip joint and segment lengths of the tibia and femur (McGowan et al., 2005a). Net joint moments about the MTP, ankle, knee and hip were obtained from the kinematic and force plate data with custom inverse dynamics analysis software (McGowan et al., 2005a) written in MATLAB 2015a. Joint power was calculated by multiplying joint moment by joint angular velocity. Net joint work was calculated by integrating joint power with respect to time.

In some trials, the feet were not aligned with respect to the sagittal plane. In these cases, the center of pressure (COP) from the force plate was not in the appropriate horizontal location for the leg of interest and we therefore corrected the COP for the difference in x coordinates between the left and right longest toes. We checked the new position of the COP by plotting the GRF vector relative to left hind leg joint positions and examined the behavior of the COP during the jumping trial. Since the position of the COP changed during the trials, only trials where the COP stayed between the MTP joint and the tip of the toes were used for further analysis.

To examine how mechanical variables changed with jump height, we performed linear regression analysis on joint excursions, peak extensor moments, joint power and joint work using R version 3.1.1 (2008, R Core Team, Vienna, Austria). We considered linear correlation statistically significant where P<0.05. In cases of P<0.05, values of R², and F_1,59 statistics are provided. In addition, we used a general linear model (GLM) in JMP 14.0.1 (2018, SAS Institute) to test for any individual effects, which were not found.

The jumps recorded ranged from 0.08 to 0.40 m. The highest jump was equal to 8.8-times standing hip height (average hip height at the start of the jumping motion was 45.7 mm). The total power required to produce these jumps ranged from 10.2 to 43.2 W kg⁻¹ BM, which corresponds to an estimated 365.44 W kg⁻¹ muscle in the highest jump. The average peak GRF for one leg was 3.48 BW, with a minimum of 2.03 BW and a maximum of 4.68 BW for the highest jump recorded (Fig. 1). There is a positive association between jump height and peak vertical GRF (P<0.001, R²=0.48, F=58.39). MTP and ankle joints flexed before they extended but the ankle flexion was minimal. The MTP joint flexed gradually followed by a relatively rapid extension of similar magnitude; the hip and knee joints only extended in all trials. MTP and ankle joint moments were predominately positive for all trials, whereas there was more variation in the knee and hip joint moments (Fig. 2).

Changes in joint angles were generally independent of jump height, except for those in the ankle (Fig. 2B and Fig. 3). The MTP joint underwent a flexion (negative values)–extension (positive values) pattern that did not change with jump height (flexion P=0.71, extension P=0.29). In the 33 trials with a countermovement, the ankle underwent an initial flexion, which was inconsistent and independent of jump height. Ankle extension increased significantly with jump height (P<0.001, R²=0.42, F=44.97), ranging from approximately 60 deg at low jumps to 110 deg at the high jumps. Knee and hip excursion did not increase significantly with increasing jump height (P=0.231 and P=0.569, respectively).

Peak joint moments increase significantly with jump height at all joints except the knee (Fig. 4) (MTP, P<0.003, R²=0.12, F=9.66; ankle, P<0.001, R²=0.35, F=33.74; hip, P<0.001, R²=0.23, F=23.2). Peak extensor moments at the knee varied widely and were independent of jump height (P=0.584).

As jump height increased, peak joint power increased at the hip and ankle (Fig. 5). Energy was absorbed, indicated by negative power, at the MTP joint during dorsiflexion because the joint was flexing with an extensor moment. During the fast extension of the MTP joint at the end of the take-off, power output became positive. The ankle produced the highest peak power, which increased significantly with jump height (P<0.001, R²=0.49, F=59.41). Peaks of knee powers arose around the same time as peaks in ankle power occurred but were independent of jump height (P=0.329). Hip power peaked first, before peak power in other joints, and increased significantly with jump height (P<0.001, R²=0.16, F=12.58).

To determine that the work done by the limbs accounted for the majority of the work done on the COM, we plotted work done on the COM against the sum of all work done by the hind limbs (Fig. 6). The slope of the best fit line, solid line, was 0.92. Potential work that was not accounted for in the sum of work done by the hind legs probably originates from the work done by trunk extension.

The mechanical role of individual joints during jumping was examined by calculating net joint work for individual jumps across jump heights (Fig. 7). Net MTP work was near zero (−0.434 to 0.159 J kg⁻¹ BW) and decreased with increasing jump height (P<0.001, R²=0.18, F=14.66). Net joint work by the ankle (P<0.001, R²=0.73, F=165.5), knee (P=0.018, R²=0.08, F=5.97) and hip (P=0.002, R²=0.14, F=10.48) all correlated positively with jump height. The relative contribution to the total positive joint work done by the hind limb was greatest at the ankle and ranged between 56% at low jumps to 70% at high jumps (Fig. 8). The relative contributions to total positive work by the knee and hip both decreased with jump height, from 24% and 20%, respectively, at low jumps to ∼15% for both joints during high jumps.

The net work delivered at the ankle is the sum of the work done by the ankle extensor muscles and the work transferred from proximal muscles via the bi-articular MTU. During jumping, there was an increase with increasing jump height in both the work done by the ankle extensors (P<0.01, R²=0.50, F=61.2) and the work that was transferred (P<0.01, R²=0.43, F=47.02) (Fig. 9). Although there was a high level of variation, on average, the amount of transferred work was 48% and equal over all jump heights (P=0.801) (Fig. 10).

Vertical jumps by the kangaroo rats in this study ranged from 0.08 m to 0.40 m, with the highest jump reaching almost 9-times resting hip height. The average power required for the highest jump was 2.78 W, which is equivalent to 365 W kg⁻¹ of muscle, assuming all leg extensor muscles contribute to the jump. Across the range of jump heights examined in this study, the ankle joint provided the greatest contribution to the power and work of vertical jumping. These results do not support our hypothesis that increases in net joint work would be equally divided across hind leg joints with increasing jump height.

Several species of vertebrates have been shown to produce power outputs during jumping that far exceed the capacity of vertebrate skeletal muscles (reported averages for maximum power range from 250 to 433 W kg⁻¹ muscle: Weis-Fogh and Alexander, 1977; Lutz and Rome, 1994; Marsh and John-Adler, 1994; Askew et al., 2001). For galagos and Cuban tree frogs, peak muscle power values were reported to be 1700 W kg⁻¹ muscle and 1650 W kg⁻¹ muscle, respectively (Aerts, 1998; Peplowski and Marsh, 1997). For wallabies, an average muscle power value of 495 W kg⁻¹ muscle was reported (McGowan et al., 2005b). Animals exceeding maximal power outputs of skeletal muscles must use a mechanism, in the form of a countermovement, elastic energy storage and return, and/or inertial catch mechanism, to enhance their power output. Power values reported here, for jumping kangaroo rats (365 W kg⁻¹ muscle) did not exceed the maximum power capacity of skeletal muscles, suggesting that these animals do not require a power enhancement mechanism to produce these jumps.

The increase in mechanical work required to achieve higher jump heights was produced by increases in positive net work from the hip, knee, and ankle; whereas the MTP tended to absorb more energy as jump height increased (Fig. 7). The increases in positive net work were greatest at the ankle, leading to an increase in the relative contribution of this joint compared with the knee and hip across jump heights. During the highest jumps, the ankle produced over 4-times more work than the knee or hip. This is consistent with previous studies that showed the ankle plays a primary role in powering jumps (e.g. Aerts, 1998). In a recent study of jumping by jerboas, which are hopping bipeds similarly sized to the kangaroo rat, Moore et al. (2017) showed that the ankle also contributes the most net joint work, but its relative contribution to total work was less than that found for kangaroo rats. For example, in a comparable jump of 0.37 m, the ankle joint of kangaroo rats produced a net work of 1.19 J kg⁻¹, while the knees produced 0.29 J kg⁻¹ and the hip 0.29 J kg⁻¹, whereas for jerboas, these values were 0.23 J kg⁻¹, 0.18 J kg⁻¹ and 0.13 J kg⁻¹, respectively (Moore et al., 2017). Although both species produce the most work at the ankle, kangaroo rats produce substantially more work per unit body mass compared with jerboas. Both species have net energy absorption at the MTP joint during jumping; although kangaroo rats have a flexion-extension pattern at the MTP which produces some positive power just before take-off whereas jerboas do not. This difference may be due to the fact that jerboas have relatively short toes compared with kangaroo rats.

While most net mechanical work done during jumping was delivered at the ankle, caution is needed when inferring contributions from individual muscles. Inverse dynamics analyses have limitations and cannot account for the effects of co-contraction, biarticular muscles or elastic energy storage and return. The role of biarticular muscles is particularly important during high acceleration tasks, where energy from proximal muscles is delivered at the ankle via multi-joint muscles (Jacobs et al., 1996; Aerts, 1998; Dutto et al., 2004). This is clearly the case during jumping by desert kangaroo rats as well. In this species, all major ankle extensor muscles (gastrocnemii and plantaris) are biarticular, with origins on the femur and insertions on the calcaneus. The uniarticular ankle extensors are vestigial (e.g. soleus). This anatomical arrangement enables the ankle extensors to act as both a motor, producing mechanical work by shortening, and a strut, transferring energy from proximal muscles. Consistent with the MTU operating like a strut, the ankle and knee joints undergo a coordinated extension pattern (Fig. 2). Based on muscle moment arms and joint angle changes during jumping, we estimated that, on average, 48% of the work done at the ankle is transferred from proximal muscles, with the remaining work being done by the muscle shortening (Figs 8 and 9). This substantial amount of energy transfer is greater than the 25% that had been calculated for human jumping (Gregoire et al., 1984; Bobbert et al., 1986), but less than the 65% estimated for galagos (Aerts, 1998).

The experimental design of this study provides insights into the general mechanics of vertical jumping by desert kangaroo rats; however, it must be noted that these jumps do not represent true escape responses. In contrast to their ballistic escape maneuvers in the wild, the staging gave the animals in our study time to ‘plan’ their jumps, resulting somewhat variable jump strategies. Starting from a range of initial postures, animals in 33 of 62 trials had a small countermovement at the ankle prior to extension for the jump. However, these minimal countermovements were not reflected in the GRF patterns and likely contributed little to the jumping mechanics. During a predator attack in the wild, the time it takes to produce a countermovement could be detrimental to the animals' ability to escape, since a quicker response increases escape success (Freymiller et al., 2017). This may explain why we did not observe substantial countermovements in our study. This is consistent with what has been observed for jerboas under similar experimental conditions (Moore et al., 2017).

Kangaroo rats are capable of extreme jumping behaviors, typically associated with predator avoidance. The highest jumps recorded in this study required average power outputs of over 360 W kg⁻¹ of muscle and did not involve countermovements or other significant elastic energy storage and return. This suggests that kangaroo rats power jumping via high power muscle output, although this remains to be tested directly. The animals in this study increased their jump height by increasing joint power and work across all joints, with the ankle joint contributing the largest percentage. However, a substantial portion of work delivered at the ankle joint (on average 48%) was transferred from proximal muscles via the biarticular ankle extensor MTU. Future studies, using sonomicrometry techniques, could give direct measures of the contributions of the ankle and knee extensors.

The authors acknowledge Dr J. W. Rankin and Dr C. E. Collins for helping with data collection and analysis, and for providing comments on earlier versions of this manuscript.