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Contributions of Limb Joints to Energy Absorption during Landing in Cats

Contributions of Limb Joints to Energy Absorption during Landing in Cats Hindawi Applied Bionics and Biomechanics Volume 2019, Article ID 3815612, 13 pages https://doi.org/10.1155/2019/3815612 Research Article Contributions of Limb Joints to Energy Absorption during Landing in Cats 1,2 1,2 3 1,2 1,2 1,2 Xueqing Wu, Baoqing Pei , Yuyang Pei, Nan Wu, Kaiyuan Zhou, Yan Hao, 1,2 and Wei Wang School of Biological Science and Medical Engineering, Beihang University, Beijing 100083, China Beijing Advanced Innovation Centre for Biomedical Engineering, Beihang University, Beijing 100083, China School of Public Health, Nanjing Medical University, Nanjing 211166, China Correspondence should be addressed to Baoqing Pei; pbq@buaa.edu.cn Received 29 November 2018; Revised 31 January 2019; Accepted 20 February 2019; Published 18 August 2019 Academic Editor: Simo Saarakkala Copyright © 2019 Xueqing Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. There is a high risk of serious injury to the lower limbs in a human drop landing. However, cats are able to jump from the same heights without any sign of injury, which is attributed to the excellent performance of their limbs in attenuating the impact forces. The bionic study of the falling cat landing may therefore contribute to improve the landing-shock absorbing ability of lower limbs in humans. However, the contributions of cat limb joints to energy absorption remain unknown. Accordingly, a motion capture system and plantar pressure measurement platform were used to measure the joint angles and vertical ground reaction forces of jumping cats, respectively. Based on the inverse dynamics, the joint angular velocities, moments, powers, and work from different landing heights were calculated to expound the synergistic mechanism and the dominant muscle groups of cat limb joints. The results show that the buffering durations of the forelimbs exhibit no significant difference with increasing height while the hindlimbs play a greater role than the forelimbs in absorbing energy when jumping from a higher platform. Furthermore, the joint angles and angular velocities exhibit similar variations, indicating that a generalized motor program can be adopted to activate limb joints for different landing heights. Additionally, the elbow and hip are recognized as major contributors to energy absorption during landing. This experimental study can accordingly provide biological inspiration for new approaches to prevent human lower limb injuries. 1. Introduction From a biomechanical point of view, external and inter- nal forces can be mediated by manipulating the limb joint kinematics and limb muscle groups that contribute to the Cats are generally acknowledged to have excellent landing reduction and transfer of mechanical energy. By using strain buffering capacities, achieved through natural selection, and gauge-based force transducers, it has been shown that the have accordingly received significant scientific attention. A number of cases have been studied, finding that the death rate force and activity patterns of the gastrocnemius (GA), soleus (SO), and plantaris (PL) muscles are beneficial for transfer- of cats is less than 10% after falling from a high rise [1]. As the ring mechanical energy between adjacent joints during loco- saying goes: cats have nine lives, emphasizing the fact that cats motion [5–7]. Additionally, the activation of cat hindlimb indeed have an extraordinary ability to survive falls. In terms muscles is directed opposite to the endpoint reaction forces of this phenomenon, a number of researchers have studied the body posture of cats as they fall, using high-speed cameras, of these muscles [8]. Similarly, some studies have suggested that the activity of limb muscles is critical in the cat landing and the results show that falling cats make gyroscopic turns process and that this activity is determined by the jumping such that their forelimbs and hindlimbs land successively, condition. For example, to avoid injury, limb muscles become regardless of the cat’s orientation at the start of the fall [2–4]. tensed before touching the ground, and the magnitude and Therefore, it has been suggested that cat limbs play a signif- icant role in dissipating the impact forces during landing. timing of prelanding limb muscle activity are adjusted to be 2 Applied Bionics and Biomechanics appropriate for the jump height [9]. Meanwhile, the responses 3y of the elbow extensors to ground reaction forces (GRFs) have 3x been studied, showing that, for a given cat, both the vertical I 3 Segment 3 and horizontal GRFs increase with jump height while torque values at the elbow joint do not change significantly [10]. Fur- F 휃4 2y 2x thermore, a study on reflexes in cat ankle muscles indicates F 2x 2y that large and rapid reflexes indeed occur during landing 휃3 and the lengths of the ankle extensors begin to increase only I m Segment 2 2 2 after the toes have developed significant dorsal flexion [11]. Additionally, the manner of distribution of impact forces 휃2 between the forelimbs and hindlimbs of cats has been found F 1y 1x to be related to the jump height, and the hindlimbs have been 1x 1y found to play an increasing role in the absorption of energy 휃1 m Segment 1 with increasing jump height [12]. F y1 As stated above, there is currently sufficient evidences to elucidate the role of cat limbs in energy absorption based on (a) limb kinematics, kinetics, and EMG responses of muscles. 7y However, the contributions of various limb joint muscle M 7x groups to the total energy absorption during landing remain 휃8 unknown. It is known that falling from different heights I m 7 7 Segment 3 results in the adoption of different cat limb control strategies 6x in order to effectively attenuate the impact forces. Studies of 휃7 M 6 F 6y 6y joint energy absorption strategies under different jump 6x heights can thus provide comprehensive insight into the inter- nal buffering mechanism of cats during landing. In the previ- 6 Segment 2 ous studies, the GRFs were measured using one or two AMTI 5x force plates, but this method could not be used to differentiate 휃6 M 5y between the GRFs of the forelimbs and hindlimbs of the cats. F 5y 5x As a result, it is not well established that this information is sufficient to provide representative calculations of the 5 휃5 Segment 1 y2 mechanical energy absorbed by the joint muscles of cat limbs. (b) The objective of this paper is therefore to study the con- tributions of different limb joints to energy absorption and Figure 1: The left side shows the angles of the forelimb (a) and to further understand the energy dissipation strategies of hindlimb (b) used in the equations, and the right side shows free- joint muscles during landing in cats. In this study, we con- body diagrams of the same limbs, in which the reaction forces and ducted experiments in which domestic cats self-initiated moments acting on each joint are indicated. jumps from different heights and the vertical ground reaction forces (VGRFs) as well as the kinematic (joint angles and conducted. After each successful training experiment, the angular velocities), kinetic (joint moments and joint powers), cat was given food as a reward. During the six experimental and energetic (joint work) data were analyzed based on the sessions, at least five jumps per height were recorded in ran- planar dynamics and inverse dynamics. Additionally, the dom increments of 0.2 m between 1 m and 2 m, and the cat synergistic mechanism of cat joints was described, making was given enough rest after each jump to ensure that the it possible to visualize the events that occur during the cat results were not affected by physical condition, adaptability, landing process. The results of this study will help to inter- etc. All experimental procedures were approved by the pret and understand the role of dominant joints in energy Science and Ethics Committee of Beihang University. absorption. They will also promote the understanding of the internal buffering mechanisms of cat limbs during land- 2.2. Data Measurement and Analysis. In this study, we inves- ing. A more practical motivation for this study is to provide tigated only the distribution of the vertical ground reaction useful information for the future development of high- forces (VGRFs) between the limb joints, as the forces in the efficiency buffering and energy absorption equipment. mediolateral and fore-aft directions are small enough to be ignored [12]. In order to accurately compare the energy absorption of the forelimbs and hindlimbs, a single MatScan 2. Materials and Methods (150 Hz; Texscan Inc., South Boston, MA, USA) was used to 2.1. Animal Training and Experimental Protocol. Five healthy select and measure only the VGRFs of the right fore (RF) and adult domestic cats (2 45 ± 0 29 years of age, 3 6±0 35 kg) right hind (RH) limbs from the impact on the mat. All raw VGRF data for an individual were scaled to multiples of body were trained to jump down onto a MatScan (Texscan Inc.) from an adjustable platform of height between 1 m and 2 m. weight (BW) for each cat. In particular, the VGRFs of the RF Training was conducted for about half an hour, five times a limbs, displayed as two-dimensional images, were used to week over three weeks before the landing experiments were determine the buffering durations of the forelimbs, defined Applied Bionics and Biomechanics 3 R Joint muscle power was defined as the product of the internal yp joint moment and joint angular velocity, calculated as the rate xp of change of angular displacement. The displacement and angular velocity data were smoothed using a five-piece mov- ing arc to further reduce measurement artifacts [10]. The inte- gral of joint muscle power over the buffering time determined the joint work used to represent the energy absorbed by a given joint. All joint moments, muscle powers, and work were expressed in units of Nm/Kg, W/Kg, and J/Kg, respectively. mg 2.3. Inverse Dynamics Analysis. Each limb segment was assumed to act independently under a combination of joint xd M reaction forces, joint muscle moments, and gravity, as illus- yd trated in Figure 2. Based on Figure 2 [14], the following equations can be Figure 2: Complete free-body diagram of a single limb segment, obtained: showing the reaction and gravitational forces, net moments of force, and all linear and angular accelerations. 〠F = ma = R − R , x x xp xd as beginning with the touchdown of the RF paws and ending 〠F = ma = R − R − mg, 1 y y yp yd at the time at which the RF wrists began to leave the MatScan. Before the experiment, the areas of interest on the RF and 〠M = I α, RH limbs were shaved. Reflective markers with a diameter of 9 mm were then placed over the shoulder blade, shoulder, where F and F are the forces in the X and Y directions, x y elbow, wrist joint, and fingertip of the RF limb and the pelvis, respectively; m is the segment mass; a and a are the X x y hip, knee, ankle joint, and toe of the RH limb to obtain the and Y components of acceleration of the segment center of eight angles shown in Figure 1. A motion capture system mass (COM), respectively; M is the moment about the seg- (100 Hz; Vicon Inc., Denver, CO, USA), synchronized to ment; and l and α are the moment of inertia and angular the MatScan, was used to collect the positions of these acceleration of the segment in the plane of movement, markers. The buffering durations of the hindlimbs were respectively. defined as beginning with the touchdown of the hind paws The RF and RH limbs of the subject cats were analyzed by and ending with peak knee flexion. During the experiment, splitting each into three rigid links. At the same time, the it was found that the slippage of markers on the elbow and COM was assumed to be at the midpoint of a segment. knee joints was quite serious. In order to diminish measure- Therefore, based on equation (1), the joint moments in the ment artifacts caused by this slippage, an optimization proce- three segments of the RF and RH limbs for each cat in this dure written in MATLAB was used to calculate the positions paper can be calculated as follows. of the elbow and knee joints, which were then optimized For the RF limb using constraints to be closest to the collected positions of Segment 1 elbow and knee joint markers. The constraint placed on the elbow joint in the optimization procedure, for example, was L 2 L 1 1 F = m − θ cos θ − θ sin θ , 1x 1 1 1 1 1 that the distance from the calculated elbow joint to the col- 2 2 lected shoulder and wrist joint be the same as the premea- L 2 L 1 1 sured arm and forearm length, respectively. F + F − m g = m − θ sin θ + θ cos θ , y1 1y 1 1 1 1 1 1 2 2 The limb of each cat was assumed to be a planar link- segment rigid body model. Segment parameters, including L L L 1 1 1 M + F sin θ + F cos θ − F cos θ = −I θ 1 1x 1 y 1 1y 1 1 1 segment mass and moment of inertia, obtained from a previ- 2 2 2 ous study [13] and combined with the kinematic data and VGRFs, were imported into MATLAB to calculate the inter- nal joint moment for each joint based on the inverse solution. Segment 2 2 L 2 F − F = m −L θ cos θ + θ sin θ − θ cos θ + θ sin θ , 2x 1x 2 1 1 1 1 1 2 2 2 2 2 L 2 F − F − m g = m L −θ sin θ + θ cos θ + −θ sin θ + θ cos θ , 2y 1y 2 2 1 1 1 1 1 2 2 2 2 L L L L 2 2 2 2 M − M + F sin θ − F cos θ + F sin θ − F cos θ = −I θ 2 1 2x 2 2y 2 1x 2 1y 2 2 2 2 2 2 2 1 4 Applied Bionics and Biomechanics Segment 3 2 2 L 2 F − F = m −L θ cos θ + θ sin θ − L θ cos θ + θ sin θ + θ cos θ + θ sin θ , 3x 2x 3 1 1 1 1 1 2 2 2 2 2 3 3 3 3 2 2 L 2 F − F − m g = m L −θ sin θ + θ cos θ + L −θ sin θ + θ cos θ + −θ sin θ + θ cos θ , 3y 2y 3 3 1 1 1 1 1 2 2 2 2 2 3 3 3 3 L L L L 3 3 3 3 M − M + F sin θ + F cos θ + F sin θ + F cos θ = I θ 3 2 3x 3 3y 3 2x 3 2y 3 3 3 2 2 2 2 For the RH limb Segment 1 L 2 L 5 5 F = m − θ cos θ − θ sin θ , 5x 5 5 5 5 5 2 2 L 2 L 5 5 F + F − m g = m − θ sin θ + θ cos θ , y2 5y 5 5 5 5 5 5 2 2 L L L 5 5 5 M + F sin θ + F cos θ − F cos θ = −I θ 5 5x 5 y 5 5y 5 5 5 2 2 2 Segment 2 2 L 2 F − F = m −L θ cos θ + θ sin θ + θ cos θ + θ sin θ , 6x 5x 6 5 5 5 5 5 6 6 6 6 2 L 2 F − F − m g = m L −θ sin θ + θ cos θ + −θ sin θ + θ cos θ , 6y 5y 6 6 5 5 5 5 5 6 6 6 6 L L L L 6 6 6 6 M − M + F sin θ + F cos θ + F sin θ + F cos θ = I θ 6 5 6x 6 6y 6 5x 6 5y 6 6 6 2 2 2 2 Segment 3 2 2 L 2 F − F = m −L θ cos θ + θ sin θ + L θ cos θ + θ sin θ − θ cos θ + θ sin θ , 7x 6x 7 5 5 5 5 5 6 6 6 6 6 7 7 7 7 2 2 L 2 F − F − m g = m L −θ sin θ + θ cos θ + L −θ sin θ + θ cos θ + −θ sin θ + θ cos θ , 7y 6y 7 7 5 5 5 5 5 6 6 6 6 6 7 7 7 7 L L L L 7 7 7 7 M − M + F sin θ − F cos θ + F sin θ − F cos θ = I θ 7 6 7x 7 7y 7 6x 7 6y 7 7 7 2 2 2 2 in which all the variables are as defined in Figure 1. durations (t and t ), joint moments (M and M ), joint 1 2 1–3 5–7 reaction forces (F and F ), and joint work, as defined 1–3 5–7 2.4. Statistical Analysis. For all cats at each jump height, the in Figure 1, were analyzed using an analysis of variance magnitudes of the peak vertical ground reaction forces (F (ANOVA). An F-test was performed to determine the statis- y1 tical significance of the test data at p of 0.05. and F ), joint ranges of motion (ROM ), buffering y2 1–6 Applied Bionics and Biomechanics 5 Table 1: Mean and SD of peak VGRFs and ratio of F to total force (F and F ) for each jump height . y2 y1 y2 ∗ ∗ Jump height (m) F (N/kg) F (N/kg) Ratio (%) y1 y2 1.0 29.44 (8.39) 4.27 (1.64) 12.67 1.2 30.13 (9.17) 7.77 (2.16) 20.49 1.4 32.53 (9.36) 8.72 (2.58) 21.14 1.6 36.05 (10.21) 13.04 (4.12) 26.57 1.8 39.58 (11.05) 20.43 (5.22) 34.04 2.0 45.94 (11.34) 26.64 (7.41) 36.70 a b Values in the parentheses are the standard deviations (SD). Significantly different from F at the same height. Parameter shows statistically significant y2 difference between jump heights. 3. Results heights. During the landing phase, the elbow, ankle, and knee joints underwent continuous flexion while the wrist joints 3.1. Vertical Ground Reaction Forces. A summary of the experienced flexion, extension, and then flexion again. VGRFs of the RF and RH limbs is provided in Table 1 and The maximum angular velocity of the wrist joint was graphically presented in Figure 3. Obviously, the peak reached at the beginning of the landing, as was also VGRFs (F and F ) increased significantly (p <0 05) with y1 y2 observed in the angular velocity curve of the ankle joint. increasing jumping height. Double-peak patterns were also As shown in Figure 4, the flexion velocity of the elbow found at all jump heights, which was consistent with the find- joint manifested as a singular upward slope to its peak, ings of a previous study [15]. In a departure, however, the while the angular velocity curve of the knee joint exhibited peak VGRFs of the RF limbs (F ) were always significantly a generally downward opening with a peak in the middle y1 (p <0 05) greater than those of the RH limbs (F ) when of the buffering duration. y2 the jump height was less than 2 m. However, the ratio of 3.3. Kinetics. The peak joint reaction forces, calculated as the the peak VGRF of the RH limb to the total force increased resultant forces in the X and Y directions, and the joint with the increase in jump height, indicating that the hin- moments are presented in Figures 5 and 6, respectively, in dlimbs experience a greater peak VGRF than the forelimbs which it can be seen that the overall trend of the peak joint when the cat jumps from a higher height. moment and the reaction force acting at each joint increases 3.2. Kinematics. The buffering durations of the RF and RH with increasing jump height. In the forelimbs, the peak elbow limbs and the time interval between the touchdown of the moment was significantly greater (p <0 05) than that of the fore paws and that of the hind paws for different jump other two joints; however, there were no differences heights are shown in Table 2, while associated joint ROMs (p >0 05) in the peak joint reaction forces at any of the three are shown in Table 3. In Table 3, ROM indicate the ranges joints. Characteristically, although there were differences in 1–6 of motion of the angle between the fore paw and the ground, the value and direction of the elbow and shoulder moments, wrist joint, and elbow joint and the angle between the hind their variation patterns were remarkably similar, showing paw and the ground, ankle joint, and knee joint, respectively. multiple distinctive peaks. Only one peak was found in the Because the angle between the fore paw and the ground even- wrist moments, where the variation was relatively small. In tually becomes zero during the landing process, ROM equals the hindlimbs, the peak moment of the hip joint was signifi- the initial angle at which the fore paw lands. Thus, as the cantly greater (p <0 05) than that of the ankle and knee jump height increases, the decreasing value of ROM indi- joints, and the same was true for the joint reaction force. cates that before a cat jumps, it makes a subjective judgment The joint moments of the ankle and knee increased but in to adjust the initial angle of its fore paw landing according to opposite directions. A single significant peak and valley was the jump height. Although no significant differences observed in the hip joint moment curve during the impact (p >0 05) were found in ROM for any jump heights, other phase of landing. Additionally, it can be observed that the ROM values decreased significantly (p <0 05) as the jump joint moments and reaction forces acting on the joints of cats height increased. are of the same order of magnitude as that of humans, We also analyzed the buffering durations, finding that which is extremely large relative to the body size of cats, there were no differences (p >0 05)in t for all jump heights indicating that the synergistic mechanism employed by cat joints can indeed help to dissipate relatively tremen- but that t increased significantly (p <0 05) with increasing height. Additionally, the time interval between the touch- dous impact forces. down of the fore paws and that of the hind paws also Joint power and work represent the maximum effort decreased with jump height. exerted by certain muscle groups during energy absorption. In order to investigate the synergistic mechanism of cat Similar variation patterns, showing multiple distinctive peaks, were present in both the elbow and shoulder joint joints, the values of angular velocity (deg/s) and angle (deg) for the wrist, elbow, ankle, and knee joints during a 1.4 m power curves. A single peak was observed in the wrist power jump down were plotted as shown in Figure 4. Similar pat- curve similar to the wrist moment curve. The values of hip terns of change were found across all cats for all jump power varied more than those of the knee joint and ankle 6 Applied Bionics and Biomechanics 0.00 0.01 0.02 0.03 0.04 0.05 Time (s) 1 m 1.6 m 1.2 m 1.8 m 1.4 m 2 m (a) 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.00 0.01 0.02 0.03 0.04 0.05 0.06 Time (s) 1 m 1.6 m 1.2 m 1.8 m 1.4 m 2 m (b) Figure 3: Representative average VGRF curves of the (a) RF and (b) RH limbs during the landing period from all jump heights. joint (Figure 7). The means and standard deviations of 4. Discussion joint work are provided in Table 4 and graphically repre- sented in Figure 8. Although the forelimb was found to 4.1. Synergistic Mechanism of Cat Limb Joints. There have absorb more energy when the jumping height was less been several studies describing the body posture and muscle than 2 m, the ratio of energy absorbed by the hindlimb activity of cats in the take-off phase of a typical jump down. to the total energy increased with the increase in landing However, the synergistic mechanism of cat limb joints in height. Therefore, it can be speculated that the hindlimb the landing phase was still unclear. The results of this study plays a greater role in the dissipation of energy as the jump suggest that there are general increases in the peak VGRF height increases. Meanwhile, all cats utilized the elbow as and the ratio of the peak VGRF in the RH limb to the total the primary joint absorbing energy during the buffering force with increasing jumping height. Although the VGRF durations of the forelimbs, and the hip joints in the hin- in the RF limb was greater when the cats jumped from a dlimbs provided greater relative contributions to overall height less than 2 m, it is logical to argue that the hindlimb energy absorption. will be utilized as the dominant limb to attenuate landing Vertical ground reaction force (BW) Vertical ground reaction force (BW) Applied Bionics and Biomechanics 7 Table 2: Means and SD of the buffering durations of the RF (t ) and RH (t ) limbs, in a time interval (Δt) between the touchdown of the fore 1 2 paws and the hind paws, for different jump heights . Jump height (m) t (ms) t (ms) Δt (ms) 1 2 1.0 47.29 (1.56) 33.67 (4.27) 60.00 (8.22) 1.2 46.18 (2.28) 40.33 (3.62) 30.26 (6.31) 1.4 48.67 (1.09) 42.28 (1.91) 27.57 (5.24) 1.6 47.33 (3.62) 53.67 (2.13) 23.33 (7.10) 1.8 46.96 (1.33) 57.00 (5.84) 17.42 (8.99) 2.0 48.21 (2.77) 59.19 (4.38) −10.00 (10.57) a ∗ Values in the parentheses are the standard deviations (SD). Parameter shows statistically significant difference between jump heights. Table 3: Mean and SD of the selected ROMs across jump heights . ∗ ∗ ∗ ∗ ∗ Height (m) ROM (deg) ROM (deg) ROM (deg) ROM (deg) ROM (deg) ROM (deg) 1 2 3 4 5 6 1.0 52.03 (7.28) 49.86 (8.96) 68.25 (11.93) 15.84 (3.91) 30.64 (10.36) 37.13 (8.09) 1.2 47.83 (8.35) 34.16 (6.31) 78.49 (12.54) 20.51 (5.15) 41.22 (8.69) 56.75 (12.67) 1.4 45.82 (6.27) 31.35 (6.53) 80.93 (13.10) 26.51 (6.44) 42.52 (9.42) 61.70 (14.95) 1.6 39.99 (7.99) 30.41 (5.08) 88.90 (14.97) 32.61 (5.98) 43.40 (11.67) 73.90 (15.38) 1.8 37.18 (5.84) 32.97 (9.76) 90.12 (15.75) 34.29 (8.16) 43.62 (10.20) 74.07 (19.17) 2.0 36.08 (4.18) 46.08 (6.30) 97.76 (15.35) 46.70 (9.76) 70.89 (17.09) 120.26 (23.63) Values in the parentheses are the standard deviation (SD). ROM are the ranges of motion of the angle between the fore paw and the ground, wrist joint, 1–6 and elbow joint and the angle between the hind paw and the ground, ankle joint, and knee joint. Parameter shows statistically significant difference between jump heights. impulses from a jump of greater height, explaining the of the leg that lands first after the flight phase. Notably, in observed phenomenon that fractures in the hindlimb human skipping gaits, the knee and ankle joint angles at the (61.5%) are more likely to occur than those in the forelimb touchdown of the leading leg were not found to change (38.5%) in falling cats [1]. Moreover, double-peak patterns between even and uneven conditions. However, in our were manifested in the VGRFs of both the forelimb and hin- results, the hindlimbs of cats were found to dissipate the dlimb. Obviously, the first peak is due to the transmission of greater impact force mainly through a larger joint ROM the accumulated downward momentum of the cat’s mass (attributable to increased buffering durations and joint after its paw touches the MatScan. We suspect that the sec- ROMs with higher jumping height). It is logical to argue that ond peak in the VGRFs of the forelimb is due to the rotation adjustments of the trailing leg (forelimb) and coupled control of the spine, suggesting that the forelimb actively shares the with the leading leg (hindlimb) enhance stability and robust- force in the hindlimb. We also infer that the second peak in ness, which may be the reason why these gaits are used in the VGRFs of the hindlimb is due to the general forward experimental situations by both humans and cats. movement after a cat has finished cushioning its landing. We also analyzed the angles and angular velocities of the In general, landing conditions are the best predictors of wrist, elbow, ankle, and knee joints, finding that the angles of body dynamics throughout locomotion [16]. Accordingly, all joints except the wrist gradually decreased with increasing time after contact. As can be seen from the change in the we further investigated the ROMs, buffering durations, and time intervals between the touchdown of the fore paws and wrist angle, the wrist joint serves more of a support and rota- that of the hind paws. Based on these results, we found that tion function in the process of forelimb cushioning, spinal when jumping from different heights, a cat will make subjec- rotation, hindlimb cushioning, and forward movement, tive judgments to adjust the speed of spinal rotation and the rather serving to absorb energy. The angular velocities of the joints were large at the initial stage of contact and then initial angle between the fore paw and the ground to ensure no significant difference in the buffering durations of the tended to decrease. Additionally, the angular velocity varia- forelimbs. The way cats land (forelimbs land before hin- tions of different joints were not completely the same, but dlimbs) seems to be comparable to skipping gaits. In a recent the same joint did show similar changes under different land- study [17] on human skipping on uneven ground, the ing heights. These results suggest that a generalized motor program can be adopted to activate limb joints for different authors found that the trailing leg touched the ground with a flatter leg angle for a lowered touchdown surface, suggest- landing heights. In the future development of related exoskel- ing that the subjects were aware of the perturbation and low- etal equipment, these kinematic data can be combined to ered their center of mass in preparation for the drop. The drive the equipment and achieve a cat-like buffering mecha- comparison of results indicates that both cats and humans nism that allows limb joints to reduce mechanical energy and improve energy absorption efficiency. at least somewhat actively control and adapt the parameters 8 Applied Bionics and Biomechanics 0.00 0.01 0.02 0.03 0.04 0.05 Time (s) Elbow Ankle Wrist Knee (a) −1000 −2000 −3000 −4000 −5000 0.00 0.01 0.02 0.03 0.04 0.05 Time (s) Elbow Ankle Wrist Knee (b) Figure 4: (a) Angles and (b) angular velocities of the wrist, elbow, ankle, and knee joints during landing from a 1.4 m jump. 4.2. Dominant Limb Joint Muscle Groups in Energy limb joints to energy absorption when landing from different Absorption. Energy flows give rise to a variety of forms of jump heights. As can be seen from the joint moment and joint power movement that would not have taken place without them. The only source of energy generation and the major site of curves of Figures 6 and 7, in the early phase of forelimb land- energy absorption in all living things are the muscles, as only ing, there is a process of energy transfer from the wrist to the a small portion of energy is dissipated by joint friction and elbow and shoulder. However, in Figure 7, it can be seen that connective tissue adhesion. Therefore, it can be considered the power curve of the shoulder fluctuates up and down that energy continuously flows into and out of the limb mus- around a joint power value of 0, indicating that most of the cles between each limb segment. Here, using inverse dynam- energy is absorbed by the elbow. We believe that the shoulder ics, we calculated the joint moments, joint reaction forces, serves more of a weight-bearing and rotation function during and joint powers, then quantified the contributions of the landing similar to that of the wrist. Differently, the hip Angle (°) Angular velocity (°/s) Applied Bionics and Biomechanics 9 −1 1.0 1.2 1.4 1.6 1.8 2.0 Height (m) Wrist Ankle Elbow Knee Shoulder Hip (a) 1.0 1.2 1.4 1.6 1.8 2.0 Height (m) Wrist Ankle Elbow Knee Shoulder Hip (b) Figure 5: Mean and SD of the peak (a) joint moment and (b) joint reaction force versus jumping height for each joint during landing. absorbs more energy in the early phase of hindlimb landing are relatively large. One reason cats do not experience injury because some of the energy is transferred to the hip by the as readily is that cats can control joint motion and attenuate the impact force experienced during landing in accordance rotation of the spine. In the late phase of hindlimb landing, the ankle starts to produce some energy, which we theorize with the synergistic mechanism described in the previous because the cat is beginning to get up and move forward. section. Another reason we suspect for this resistance to The magnitudes of the peak joint moment and peak joint injury is that the microstructures of cat bones, especially their reaction force experienced by each cat in response to increas- claws, are beneficial for avoiding impact injuries. However, further studies on cat anatomy and micro-CT scanning are ing jump height indicate that cats tend to distribute the greater demands from higher jump heights to the elbow still required. It is worth noting that because we simplified and hip. Compared to the maximum joint moments in a the jump down of each cat as a two-dimensional motion in study of human landing [18], the moments in the cats’ joints the sagittal plane, the forces in the mediolateral direction Peak joint reaction force (N/Kg) Peak joint moment (Nm/Kg) 10 Applied Bionics and Biomechanics 2.5 2.0 1.5 1.0 0.5 0.0 −0.5 −1.0 0.00 0.01 0.02 0.03 0.04 0.05 Time (s) Wrist Elbow Shoulder (a) 2.0 1.5 1.0 0.5 0.0 −0.5 0.00 0.01 0.02 0.03 0.04 Time (s) Ankle Knee Hip (b) Figure 6: Joint moment in (a) the RF wrist, elbow, and shoulder joints and (b) the RH ankle, knee, and hip joints during landing from a 1.2 m jump. were neglected. Additionally, the peak forces in the fore-aft . However, the exact effects of this assumption on other direction were only 2–4% of the peak VGRFs (from unpub- joints cannot be determined because the signs of the joint lished data of this study) and their directions should be reaction forces and joint moments are not constant. backward to steady the paws as they strike the ground. Based Biarticular muscles generate moments at both joints the on equations (2)–(7), this assumption leads directly to an muscles cross and are used to transport mechanical energy increase in F and F , which will always be negative, during locomotion [19–21]. A number of studies have been 1x 2x resulting in a decrease in the negative values of M and M conducted on the muscle activities in the elbows of cats 1 2 Joint moment (Nm/Kg) Joint moment (Nm/Kg) Applied Bionics and Biomechanics 11 −20 −40 −60 −80 −100 −120 0.00 0.01 0.01 0.01 0.01 0.01 Time (s) Wrist Elbow Shoulder (a) −5 −10 −15 −20 0.00 0.01 0.02 0.03 0.04 Time (s) Ankle Knee Hip (b) Figure 7: Joint power of (a) the RF wrist, elbow, and shoulder joints and (b) the RH ankle, knee, and hip joints during landing from a 1.2 m jump. during various forms of locomotion [10, 22, 23], and it has penniform shape, which is well suited for the dissipation been suggested that the long head of the triceps and biceps, of energy [24, 25]. In the hindlimbs, the feline hamstring both biarticular muscles, play a major role during landing. muscle group (biceps femoris, semitendinosus, and semi- The biceps is a fusiform muscle in the front of the humerus membranosus) has a larger mechanical advantage at the and the long head of the triceps, triangular in shape, connects hip [20]. The biceps femoris is a large flat muscle that the scapula to the olecranon. Importantly, both have long covers two-thirds of the lateral side of the femur, the tendons and the muscle fascicules are arranged in a semitendinosus is a slender muscle with thin and firm Joint power (W/Kg) Joint power (W/Kg) 12 Applied Bionics and Biomechanics Table 4: Mean and SD of energy absorbed by the RF and RH limb joints across all jump heights . b c Height (m) Wrist (J/kg) Elbow (J/kg) Shoulder (J/kg) Ankle (J/kg) Knee (J/kg) Hip (J/kg) 1.0 2.1696 (0.65) 7.7547 (1.19) 1.3223 (0.34) 0.2714 (0.04) 0.1552 (0.02) 0.61 (0.06) 1.2 2.6243 (0.78) 9.661 (2.01) 1.0907 (0.28) 0.6408 (0.09) 0.1184 (0.01) 1.0944 (0.30) 1.4 1.7404 (0.49) 9.4252 (1.89) 0.7686 (0.16) 1.0496 (0.22) 0.2508 (0.04) 1.9049 (0.61) 1.6 2.1053 (0.51) 9.6083 (2.34) 1.2798 (0.33) 1.9996 (0.56) 1.9437 (0.40) 4.6483 (0.90) 1.8 1.8471 (0.37) 8.7272 (1.88) 1.8247 (0.42) 3.3068 (0.90) 0.5844 (0.07) 5.7561 (1.08) 2.0 2.524 (0.44) 11.352 (2.70) 1.2378 (0.35) 4.7424 (1.11) 1.4591 (0.41) 6.9656 (1.23) a b Values in the parentheses are the standard deviation (SD). Parameter shows a statistically significant difference from the wrist and shoulder at each height. Parameter shows a statistically significant difference from the ankle and hip at each height. 1.0 1.2 1.4 1.6 1.8 2.0 Height (m) Knee Wrist Shoulder Ankle Elbow Hip Figure 8: Mean joint work values for the wrist, elbow, shoulder, ankle, knee, and hip. tendons, and the semimembranosus has the same shape as a motion in a two-dimensional plane, as in previous studies, the long head of the triceps, with firm and flat tendons. This while in fact, during the jump, the movement planes should arrangement allows energy to be transported from segment be divided into the sagittal, coronal, and transverse planes, to segment and then be absorbed by the hip extensors. so further study is warranted to capture the effects of move- ments in these directions. 5. Conclusions Data Availability Using the principle of inverse dynamics and summarizing the results of cat landing experiments, we are able to explain All data included in this study are available upon request by how cats control joint motion to dissipate impact force and to contact with the corresponding author. analyze the joint energy absorption strategies employed during landing, gaining insight into the internal buffering Conflicts of Interest mechanism. Our results show that cats can adopt a general mechanism of limb movement that is quite beneficial in The authors declare that there is no conflict of interest attenuating impact force. Notably, the elbow and hip muscle regarding the publication of this paper. groups were found to be dominant in energy absorption. The results of this study can provide biological inspiration for Acknowledgments high-efficiency buffering and energy-absorption equipment to reduce landing fall injuries in humans. It should be noted We are indebted to Jie Yao and Xiaoyu Liu for providing the that, in this study, we simplified the jump down of each cat as experimental apparatus and the members of the lab for their Energy (J/kg) Applied Bionics and Biomechanics 13 [17] R. Müller and E. Andrada, “Skipping on uneven ground: trail- assistance with animal care. We would also like to thank ing leg adjustments simplify control and enhance robustness,” Zhiqiang Zhang for his help and advice. Finally, we would Royal Society Open Science, vol. 5, no. 1, article 172114, 2018. like to thank Editage (https://www.editage.com) for English [18] S. N. Zhang, B. T. Bates, and J. S. Dufek, “Contributions of language editing. This project was funded by the Defense lower extremity joints to energy dissipation during landings,” Industrial Technology Development Program under the Medicine & Science in Sports & Exercise, vol. 32, no. 4, Grant JCKY2018601B106 and JCKY2017205B032. pp. 812–819, 2000. [19] M. F. 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Contributions of Limb Joints to Energy Absorption during Landing in Cats

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Copyright © 2019 Xueqing Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Hindawi Applied Bionics and Biomechanics Volume 2019, Article ID 3815612, 13 pages https://doi.org/10.1155/2019/3815612 Research Article Contributions of Limb Joints to Energy Absorption during Landing in Cats 1,2 1,2 3 1,2 1,2 1,2 Xueqing Wu, Baoqing Pei , Yuyang Pei, Nan Wu, Kaiyuan Zhou, Yan Hao, 1,2 and Wei Wang School of Biological Science and Medical Engineering, Beihang University, Beijing 100083, China Beijing Advanced Innovation Centre for Biomedical Engineering, Beihang University, Beijing 100083, China School of Public Health, Nanjing Medical University, Nanjing 211166, China Correspondence should be addressed to Baoqing Pei; pbq@buaa.edu.cn Received 29 November 2018; Revised 31 January 2019; Accepted 20 February 2019; Published 18 August 2019 Academic Editor: Simo Saarakkala Copyright © 2019 Xueqing Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. There is a high risk of serious injury to the lower limbs in a human drop landing. However, cats are able to jump from the same heights without any sign of injury, which is attributed to the excellent performance of their limbs in attenuating the impact forces. The bionic study of the falling cat landing may therefore contribute to improve the landing-shock absorbing ability of lower limbs in humans. However, the contributions of cat limb joints to energy absorption remain unknown. Accordingly, a motion capture system and plantar pressure measurement platform were used to measure the joint angles and vertical ground reaction forces of jumping cats, respectively. Based on the inverse dynamics, the joint angular velocities, moments, powers, and work from different landing heights were calculated to expound the synergistic mechanism and the dominant muscle groups of cat limb joints. The results show that the buffering durations of the forelimbs exhibit no significant difference with increasing height while the hindlimbs play a greater role than the forelimbs in absorbing energy when jumping from a higher platform. Furthermore, the joint angles and angular velocities exhibit similar variations, indicating that a generalized motor program can be adopted to activate limb joints for different landing heights. Additionally, the elbow and hip are recognized as major contributors to energy absorption during landing. This experimental study can accordingly provide biological inspiration for new approaches to prevent human lower limb injuries. 1. Introduction From a biomechanical point of view, external and inter- nal forces can be mediated by manipulating the limb joint kinematics and limb muscle groups that contribute to the Cats are generally acknowledged to have excellent landing reduction and transfer of mechanical energy. By using strain buffering capacities, achieved through natural selection, and gauge-based force transducers, it has been shown that the have accordingly received significant scientific attention. A number of cases have been studied, finding that the death rate force and activity patterns of the gastrocnemius (GA), soleus (SO), and plantaris (PL) muscles are beneficial for transfer- of cats is less than 10% after falling from a high rise [1]. As the ring mechanical energy between adjacent joints during loco- saying goes: cats have nine lives, emphasizing the fact that cats motion [5–7]. Additionally, the activation of cat hindlimb indeed have an extraordinary ability to survive falls. In terms muscles is directed opposite to the endpoint reaction forces of this phenomenon, a number of researchers have studied the body posture of cats as they fall, using high-speed cameras, of these muscles [8]. Similarly, some studies have suggested that the activity of limb muscles is critical in the cat landing and the results show that falling cats make gyroscopic turns process and that this activity is determined by the jumping such that their forelimbs and hindlimbs land successively, condition. For example, to avoid injury, limb muscles become regardless of the cat’s orientation at the start of the fall [2–4]. tensed before touching the ground, and the magnitude and Therefore, it has been suggested that cat limbs play a signif- icant role in dissipating the impact forces during landing. timing of prelanding limb muscle activity are adjusted to be 2 Applied Bionics and Biomechanics appropriate for the jump height [9]. Meanwhile, the responses 3y of the elbow extensors to ground reaction forces (GRFs) have 3x been studied, showing that, for a given cat, both the vertical I 3 Segment 3 and horizontal GRFs increase with jump height while torque values at the elbow joint do not change significantly [10]. Fur- F 휃4 2y 2x thermore, a study on reflexes in cat ankle muscles indicates F 2x 2y that large and rapid reflexes indeed occur during landing 휃3 and the lengths of the ankle extensors begin to increase only I m Segment 2 2 2 after the toes have developed significant dorsal flexion [11]. Additionally, the manner of distribution of impact forces 휃2 between the forelimbs and hindlimbs of cats has been found F 1y 1x to be related to the jump height, and the hindlimbs have been 1x 1y found to play an increasing role in the absorption of energy 휃1 m Segment 1 with increasing jump height [12]. F y1 As stated above, there is currently sufficient evidences to elucidate the role of cat limbs in energy absorption based on (a) limb kinematics, kinetics, and EMG responses of muscles. 7y However, the contributions of various limb joint muscle M 7x groups to the total energy absorption during landing remain 휃8 unknown. It is known that falling from different heights I m 7 7 Segment 3 results in the adoption of different cat limb control strategies 6x in order to effectively attenuate the impact forces. Studies of 휃7 M 6 F 6y 6y joint energy absorption strategies under different jump 6x heights can thus provide comprehensive insight into the inter- nal buffering mechanism of cats during landing. In the previ- 6 Segment 2 ous studies, the GRFs were measured using one or two AMTI 5x force plates, but this method could not be used to differentiate 휃6 M 5y between the GRFs of the forelimbs and hindlimbs of the cats. F 5y 5x As a result, it is not well established that this information is sufficient to provide representative calculations of the 5 휃5 Segment 1 y2 mechanical energy absorbed by the joint muscles of cat limbs. (b) The objective of this paper is therefore to study the con- tributions of different limb joints to energy absorption and Figure 1: The left side shows the angles of the forelimb (a) and to further understand the energy dissipation strategies of hindlimb (b) used in the equations, and the right side shows free- joint muscles during landing in cats. In this study, we con- body diagrams of the same limbs, in which the reaction forces and ducted experiments in which domestic cats self-initiated moments acting on each joint are indicated. jumps from different heights and the vertical ground reaction forces (VGRFs) as well as the kinematic (joint angles and conducted. After each successful training experiment, the angular velocities), kinetic (joint moments and joint powers), cat was given food as a reward. During the six experimental and energetic (joint work) data were analyzed based on the sessions, at least five jumps per height were recorded in ran- planar dynamics and inverse dynamics. Additionally, the dom increments of 0.2 m between 1 m and 2 m, and the cat synergistic mechanism of cat joints was described, making was given enough rest after each jump to ensure that the it possible to visualize the events that occur during the cat results were not affected by physical condition, adaptability, landing process. The results of this study will help to inter- etc. All experimental procedures were approved by the pret and understand the role of dominant joints in energy Science and Ethics Committee of Beihang University. absorption. They will also promote the understanding of the internal buffering mechanisms of cat limbs during land- 2.2. Data Measurement and Analysis. In this study, we inves- ing. A more practical motivation for this study is to provide tigated only the distribution of the vertical ground reaction useful information for the future development of high- forces (VGRFs) between the limb joints, as the forces in the efficiency buffering and energy absorption equipment. mediolateral and fore-aft directions are small enough to be ignored [12]. In order to accurately compare the energy absorption of the forelimbs and hindlimbs, a single MatScan 2. Materials and Methods (150 Hz; Texscan Inc., South Boston, MA, USA) was used to 2.1. Animal Training and Experimental Protocol. Five healthy select and measure only the VGRFs of the right fore (RF) and adult domestic cats (2 45 ± 0 29 years of age, 3 6±0 35 kg) right hind (RH) limbs from the impact on the mat. All raw VGRF data for an individual were scaled to multiples of body were trained to jump down onto a MatScan (Texscan Inc.) from an adjustable platform of height between 1 m and 2 m. weight (BW) for each cat. In particular, the VGRFs of the RF Training was conducted for about half an hour, five times a limbs, displayed as two-dimensional images, were used to week over three weeks before the landing experiments were determine the buffering durations of the forelimbs, defined Applied Bionics and Biomechanics 3 R Joint muscle power was defined as the product of the internal yp joint moment and joint angular velocity, calculated as the rate xp of change of angular displacement. The displacement and angular velocity data were smoothed using a five-piece mov- ing arc to further reduce measurement artifacts [10]. The inte- gral of joint muscle power over the buffering time determined the joint work used to represent the energy absorbed by a given joint. All joint moments, muscle powers, and work were expressed in units of Nm/Kg, W/Kg, and J/Kg, respectively. mg 2.3. Inverse Dynamics Analysis. Each limb segment was assumed to act independently under a combination of joint xd M reaction forces, joint muscle moments, and gravity, as illus- yd trated in Figure 2. Based on Figure 2 [14], the following equations can be Figure 2: Complete free-body diagram of a single limb segment, obtained: showing the reaction and gravitational forces, net moments of force, and all linear and angular accelerations. 〠F = ma = R − R , x x xp xd as beginning with the touchdown of the RF paws and ending 〠F = ma = R − R − mg, 1 y y yp yd at the time at which the RF wrists began to leave the MatScan. Before the experiment, the areas of interest on the RF and 〠M = I α, RH limbs were shaved. Reflective markers with a diameter of 9 mm were then placed over the shoulder blade, shoulder, where F and F are the forces in the X and Y directions, x y elbow, wrist joint, and fingertip of the RF limb and the pelvis, respectively; m is the segment mass; a and a are the X x y hip, knee, ankle joint, and toe of the RH limb to obtain the and Y components of acceleration of the segment center of eight angles shown in Figure 1. A motion capture system mass (COM), respectively; M is the moment about the seg- (100 Hz; Vicon Inc., Denver, CO, USA), synchronized to ment; and l and α are the moment of inertia and angular the MatScan, was used to collect the positions of these acceleration of the segment in the plane of movement, markers. The buffering durations of the hindlimbs were respectively. defined as beginning with the touchdown of the hind paws The RF and RH limbs of the subject cats were analyzed by and ending with peak knee flexion. During the experiment, splitting each into three rigid links. At the same time, the it was found that the slippage of markers on the elbow and COM was assumed to be at the midpoint of a segment. knee joints was quite serious. In order to diminish measure- Therefore, based on equation (1), the joint moments in the ment artifacts caused by this slippage, an optimization proce- three segments of the RF and RH limbs for each cat in this dure written in MATLAB was used to calculate the positions paper can be calculated as follows. of the elbow and knee joints, which were then optimized For the RF limb using constraints to be closest to the collected positions of Segment 1 elbow and knee joint markers. The constraint placed on the elbow joint in the optimization procedure, for example, was L 2 L 1 1 F = m − θ cos θ − θ sin θ , 1x 1 1 1 1 1 that the distance from the calculated elbow joint to the col- 2 2 lected shoulder and wrist joint be the same as the premea- L 2 L 1 1 sured arm and forearm length, respectively. F + F − m g = m − θ sin θ + θ cos θ , y1 1y 1 1 1 1 1 1 2 2 The limb of each cat was assumed to be a planar link- segment rigid body model. Segment parameters, including L L L 1 1 1 M + F sin θ + F cos θ − F cos θ = −I θ 1 1x 1 y 1 1y 1 1 1 segment mass and moment of inertia, obtained from a previ- 2 2 2 ous study [13] and combined with the kinematic data and VGRFs, were imported into MATLAB to calculate the inter- nal joint moment for each joint based on the inverse solution. Segment 2 2 L 2 F − F = m −L θ cos θ + θ sin θ − θ cos θ + θ sin θ , 2x 1x 2 1 1 1 1 1 2 2 2 2 2 L 2 F − F − m g = m L −θ sin θ + θ cos θ + −θ sin θ + θ cos θ , 2y 1y 2 2 1 1 1 1 1 2 2 2 2 L L L L 2 2 2 2 M − M + F sin θ − F cos θ + F sin θ − F cos θ = −I θ 2 1 2x 2 2y 2 1x 2 1y 2 2 2 2 2 2 2 1 4 Applied Bionics and Biomechanics Segment 3 2 2 L 2 F − F = m −L θ cos θ + θ sin θ − L θ cos θ + θ sin θ + θ cos θ + θ sin θ , 3x 2x 3 1 1 1 1 1 2 2 2 2 2 3 3 3 3 2 2 L 2 F − F − m g = m L −θ sin θ + θ cos θ + L −θ sin θ + θ cos θ + −θ sin θ + θ cos θ , 3y 2y 3 3 1 1 1 1 1 2 2 2 2 2 3 3 3 3 L L L L 3 3 3 3 M − M + F sin θ + F cos θ + F sin θ + F cos θ = I θ 3 2 3x 3 3y 3 2x 3 2y 3 3 3 2 2 2 2 For the RH limb Segment 1 L 2 L 5 5 F = m − θ cos θ − θ sin θ , 5x 5 5 5 5 5 2 2 L 2 L 5 5 F + F − m g = m − θ sin θ + θ cos θ , y2 5y 5 5 5 5 5 5 2 2 L L L 5 5 5 M + F sin θ + F cos θ − F cos θ = −I θ 5 5x 5 y 5 5y 5 5 5 2 2 2 Segment 2 2 L 2 F − F = m −L θ cos θ + θ sin θ + θ cos θ + θ sin θ , 6x 5x 6 5 5 5 5 5 6 6 6 6 2 L 2 F − F − m g = m L −θ sin θ + θ cos θ + −θ sin θ + θ cos θ , 6y 5y 6 6 5 5 5 5 5 6 6 6 6 L L L L 6 6 6 6 M − M + F sin θ + F cos θ + F sin θ + F cos θ = I θ 6 5 6x 6 6y 6 5x 6 5y 6 6 6 2 2 2 2 Segment 3 2 2 L 2 F − F = m −L θ cos θ + θ sin θ + L θ cos θ + θ sin θ − θ cos θ + θ sin θ , 7x 6x 7 5 5 5 5 5 6 6 6 6 6 7 7 7 7 2 2 L 2 F − F − m g = m L −θ sin θ + θ cos θ + L −θ sin θ + θ cos θ + −θ sin θ + θ cos θ , 7y 6y 7 7 5 5 5 5 5 6 6 6 6 6 7 7 7 7 L L L L 7 7 7 7 M − M + F sin θ − F cos θ + F sin θ − F cos θ = I θ 7 6 7x 7 7y 7 6x 7 6y 7 7 7 2 2 2 2 in which all the variables are as defined in Figure 1. durations (t and t ), joint moments (M and M ), joint 1 2 1–3 5–7 reaction forces (F and F ), and joint work, as defined 1–3 5–7 2.4. Statistical Analysis. For all cats at each jump height, the in Figure 1, were analyzed using an analysis of variance magnitudes of the peak vertical ground reaction forces (F (ANOVA). An F-test was performed to determine the statis- y1 tical significance of the test data at p of 0.05. and F ), joint ranges of motion (ROM ), buffering y2 1–6 Applied Bionics and Biomechanics 5 Table 1: Mean and SD of peak VGRFs and ratio of F to total force (F and F ) for each jump height . y2 y1 y2 ∗ ∗ Jump height (m) F (N/kg) F (N/kg) Ratio (%) y1 y2 1.0 29.44 (8.39) 4.27 (1.64) 12.67 1.2 30.13 (9.17) 7.77 (2.16) 20.49 1.4 32.53 (9.36) 8.72 (2.58) 21.14 1.6 36.05 (10.21) 13.04 (4.12) 26.57 1.8 39.58 (11.05) 20.43 (5.22) 34.04 2.0 45.94 (11.34) 26.64 (7.41) 36.70 a b Values in the parentheses are the standard deviations (SD). Significantly different from F at the same height. Parameter shows statistically significant y2 difference between jump heights. 3. Results heights. During the landing phase, the elbow, ankle, and knee joints underwent continuous flexion while the wrist joints 3.1. Vertical Ground Reaction Forces. A summary of the experienced flexion, extension, and then flexion again. VGRFs of the RF and RH limbs is provided in Table 1 and The maximum angular velocity of the wrist joint was graphically presented in Figure 3. Obviously, the peak reached at the beginning of the landing, as was also VGRFs (F and F ) increased significantly (p <0 05) with y1 y2 observed in the angular velocity curve of the ankle joint. increasing jumping height. Double-peak patterns were also As shown in Figure 4, the flexion velocity of the elbow found at all jump heights, which was consistent with the find- joint manifested as a singular upward slope to its peak, ings of a previous study [15]. In a departure, however, the while the angular velocity curve of the knee joint exhibited peak VGRFs of the RF limbs (F ) were always significantly a generally downward opening with a peak in the middle y1 (p <0 05) greater than those of the RH limbs (F ) when of the buffering duration. y2 the jump height was less than 2 m. However, the ratio of 3.3. Kinetics. The peak joint reaction forces, calculated as the the peak VGRF of the RH limb to the total force increased resultant forces in the X and Y directions, and the joint with the increase in jump height, indicating that the hin- moments are presented in Figures 5 and 6, respectively, in dlimbs experience a greater peak VGRF than the forelimbs which it can be seen that the overall trend of the peak joint when the cat jumps from a higher height. moment and the reaction force acting at each joint increases 3.2. Kinematics. The buffering durations of the RF and RH with increasing jump height. In the forelimbs, the peak elbow limbs and the time interval between the touchdown of the moment was significantly greater (p <0 05) than that of the fore paws and that of the hind paws for different jump other two joints; however, there were no differences heights are shown in Table 2, while associated joint ROMs (p >0 05) in the peak joint reaction forces at any of the three are shown in Table 3. In Table 3, ROM indicate the ranges joints. Characteristically, although there were differences in 1–6 of motion of the angle between the fore paw and the ground, the value and direction of the elbow and shoulder moments, wrist joint, and elbow joint and the angle between the hind their variation patterns were remarkably similar, showing paw and the ground, ankle joint, and knee joint, respectively. multiple distinctive peaks. Only one peak was found in the Because the angle between the fore paw and the ground even- wrist moments, where the variation was relatively small. In tually becomes zero during the landing process, ROM equals the hindlimbs, the peak moment of the hip joint was signifi- the initial angle at which the fore paw lands. Thus, as the cantly greater (p <0 05) than that of the ankle and knee jump height increases, the decreasing value of ROM indi- joints, and the same was true for the joint reaction force. cates that before a cat jumps, it makes a subjective judgment The joint moments of the ankle and knee increased but in to adjust the initial angle of its fore paw landing according to opposite directions. A single significant peak and valley was the jump height. Although no significant differences observed in the hip joint moment curve during the impact (p >0 05) were found in ROM for any jump heights, other phase of landing. Additionally, it can be observed that the ROM values decreased significantly (p <0 05) as the jump joint moments and reaction forces acting on the joints of cats height increased. are of the same order of magnitude as that of humans, We also analyzed the buffering durations, finding that which is extremely large relative to the body size of cats, there were no differences (p >0 05)in t for all jump heights indicating that the synergistic mechanism employed by cat joints can indeed help to dissipate relatively tremen- but that t increased significantly (p <0 05) with increasing height. Additionally, the time interval between the touch- dous impact forces. down of the fore paws and that of the hind paws also Joint power and work represent the maximum effort decreased with jump height. exerted by certain muscle groups during energy absorption. In order to investigate the synergistic mechanism of cat Similar variation patterns, showing multiple distinctive peaks, were present in both the elbow and shoulder joint joints, the values of angular velocity (deg/s) and angle (deg) for the wrist, elbow, ankle, and knee joints during a 1.4 m power curves. A single peak was observed in the wrist power jump down were plotted as shown in Figure 4. Similar pat- curve similar to the wrist moment curve. The values of hip terns of change were found across all cats for all jump power varied more than those of the knee joint and ankle 6 Applied Bionics and Biomechanics 0.00 0.01 0.02 0.03 0.04 0.05 Time (s) 1 m 1.6 m 1.2 m 1.8 m 1.4 m 2 m (a) 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.00 0.01 0.02 0.03 0.04 0.05 0.06 Time (s) 1 m 1.6 m 1.2 m 1.8 m 1.4 m 2 m (b) Figure 3: Representative average VGRF curves of the (a) RF and (b) RH limbs during the landing period from all jump heights. joint (Figure 7). The means and standard deviations of 4. Discussion joint work are provided in Table 4 and graphically repre- sented in Figure 8. Although the forelimb was found to 4.1. Synergistic Mechanism of Cat Limb Joints. There have absorb more energy when the jumping height was less been several studies describing the body posture and muscle than 2 m, the ratio of energy absorbed by the hindlimb activity of cats in the take-off phase of a typical jump down. to the total energy increased with the increase in landing However, the synergistic mechanism of cat limb joints in height. Therefore, it can be speculated that the hindlimb the landing phase was still unclear. The results of this study plays a greater role in the dissipation of energy as the jump suggest that there are general increases in the peak VGRF height increases. Meanwhile, all cats utilized the elbow as and the ratio of the peak VGRF in the RH limb to the total the primary joint absorbing energy during the buffering force with increasing jumping height. Although the VGRF durations of the forelimbs, and the hip joints in the hin- in the RF limb was greater when the cats jumped from a dlimbs provided greater relative contributions to overall height less than 2 m, it is logical to argue that the hindlimb energy absorption. will be utilized as the dominant limb to attenuate landing Vertical ground reaction force (BW) Vertical ground reaction force (BW) Applied Bionics and Biomechanics 7 Table 2: Means and SD of the buffering durations of the RF (t ) and RH (t ) limbs, in a time interval (Δt) between the touchdown of the fore 1 2 paws and the hind paws, for different jump heights . Jump height (m) t (ms) t (ms) Δt (ms) 1 2 1.0 47.29 (1.56) 33.67 (4.27) 60.00 (8.22) 1.2 46.18 (2.28) 40.33 (3.62) 30.26 (6.31) 1.4 48.67 (1.09) 42.28 (1.91) 27.57 (5.24) 1.6 47.33 (3.62) 53.67 (2.13) 23.33 (7.10) 1.8 46.96 (1.33) 57.00 (5.84) 17.42 (8.99) 2.0 48.21 (2.77) 59.19 (4.38) −10.00 (10.57) a ∗ Values in the parentheses are the standard deviations (SD). Parameter shows statistically significant difference between jump heights. Table 3: Mean and SD of the selected ROMs across jump heights . ∗ ∗ ∗ ∗ ∗ Height (m) ROM (deg) ROM (deg) ROM (deg) ROM (deg) ROM (deg) ROM (deg) 1 2 3 4 5 6 1.0 52.03 (7.28) 49.86 (8.96) 68.25 (11.93) 15.84 (3.91) 30.64 (10.36) 37.13 (8.09) 1.2 47.83 (8.35) 34.16 (6.31) 78.49 (12.54) 20.51 (5.15) 41.22 (8.69) 56.75 (12.67) 1.4 45.82 (6.27) 31.35 (6.53) 80.93 (13.10) 26.51 (6.44) 42.52 (9.42) 61.70 (14.95) 1.6 39.99 (7.99) 30.41 (5.08) 88.90 (14.97) 32.61 (5.98) 43.40 (11.67) 73.90 (15.38) 1.8 37.18 (5.84) 32.97 (9.76) 90.12 (15.75) 34.29 (8.16) 43.62 (10.20) 74.07 (19.17) 2.0 36.08 (4.18) 46.08 (6.30) 97.76 (15.35) 46.70 (9.76) 70.89 (17.09) 120.26 (23.63) Values in the parentheses are the standard deviation (SD). ROM are the ranges of motion of the angle between the fore paw and the ground, wrist joint, 1–6 and elbow joint and the angle between the hind paw and the ground, ankle joint, and knee joint. Parameter shows statistically significant difference between jump heights. impulses from a jump of greater height, explaining the of the leg that lands first after the flight phase. Notably, in observed phenomenon that fractures in the hindlimb human skipping gaits, the knee and ankle joint angles at the (61.5%) are more likely to occur than those in the forelimb touchdown of the leading leg were not found to change (38.5%) in falling cats [1]. Moreover, double-peak patterns between even and uneven conditions. However, in our were manifested in the VGRFs of both the forelimb and hin- results, the hindlimbs of cats were found to dissipate the dlimb. Obviously, the first peak is due to the transmission of greater impact force mainly through a larger joint ROM the accumulated downward momentum of the cat’s mass (attributable to increased buffering durations and joint after its paw touches the MatScan. We suspect that the sec- ROMs with higher jumping height). It is logical to argue that ond peak in the VGRFs of the forelimb is due to the rotation adjustments of the trailing leg (forelimb) and coupled control of the spine, suggesting that the forelimb actively shares the with the leading leg (hindlimb) enhance stability and robust- force in the hindlimb. We also infer that the second peak in ness, which may be the reason why these gaits are used in the VGRFs of the hindlimb is due to the general forward experimental situations by both humans and cats. movement after a cat has finished cushioning its landing. We also analyzed the angles and angular velocities of the In general, landing conditions are the best predictors of wrist, elbow, ankle, and knee joints, finding that the angles of body dynamics throughout locomotion [16]. Accordingly, all joints except the wrist gradually decreased with increasing time after contact. As can be seen from the change in the we further investigated the ROMs, buffering durations, and time intervals between the touchdown of the fore paws and wrist angle, the wrist joint serves more of a support and rota- that of the hind paws. Based on these results, we found that tion function in the process of forelimb cushioning, spinal when jumping from different heights, a cat will make subjec- rotation, hindlimb cushioning, and forward movement, tive judgments to adjust the speed of spinal rotation and the rather serving to absorb energy. The angular velocities of the joints were large at the initial stage of contact and then initial angle between the fore paw and the ground to ensure no significant difference in the buffering durations of the tended to decrease. Additionally, the angular velocity varia- forelimbs. The way cats land (forelimbs land before hin- tions of different joints were not completely the same, but dlimbs) seems to be comparable to skipping gaits. In a recent the same joint did show similar changes under different land- study [17] on human skipping on uneven ground, the ing heights. These results suggest that a generalized motor program can be adopted to activate limb joints for different authors found that the trailing leg touched the ground with a flatter leg angle for a lowered touchdown surface, suggest- landing heights. In the future development of related exoskel- ing that the subjects were aware of the perturbation and low- etal equipment, these kinematic data can be combined to ered their center of mass in preparation for the drop. The drive the equipment and achieve a cat-like buffering mecha- comparison of results indicates that both cats and humans nism that allows limb joints to reduce mechanical energy and improve energy absorption efficiency. at least somewhat actively control and adapt the parameters 8 Applied Bionics and Biomechanics 0.00 0.01 0.02 0.03 0.04 0.05 Time (s) Elbow Ankle Wrist Knee (a) −1000 −2000 −3000 −4000 −5000 0.00 0.01 0.02 0.03 0.04 0.05 Time (s) Elbow Ankle Wrist Knee (b) Figure 4: (a) Angles and (b) angular velocities of the wrist, elbow, ankle, and knee joints during landing from a 1.4 m jump. 4.2. Dominant Limb Joint Muscle Groups in Energy limb joints to energy absorption when landing from different Absorption. Energy flows give rise to a variety of forms of jump heights. As can be seen from the joint moment and joint power movement that would not have taken place without them. The only source of energy generation and the major site of curves of Figures 6 and 7, in the early phase of forelimb land- energy absorption in all living things are the muscles, as only ing, there is a process of energy transfer from the wrist to the a small portion of energy is dissipated by joint friction and elbow and shoulder. However, in Figure 7, it can be seen that connective tissue adhesion. Therefore, it can be considered the power curve of the shoulder fluctuates up and down that energy continuously flows into and out of the limb mus- around a joint power value of 0, indicating that most of the cles between each limb segment. Here, using inverse dynam- energy is absorbed by the elbow. We believe that the shoulder ics, we calculated the joint moments, joint reaction forces, serves more of a weight-bearing and rotation function during and joint powers, then quantified the contributions of the landing similar to that of the wrist. Differently, the hip Angle (°) Angular velocity (°/s) Applied Bionics and Biomechanics 9 −1 1.0 1.2 1.4 1.6 1.8 2.0 Height (m) Wrist Ankle Elbow Knee Shoulder Hip (a) 1.0 1.2 1.4 1.6 1.8 2.0 Height (m) Wrist Ankle Elbow Knee Shoulder Hip (b) Figure 5: Mean and SD of the peak (a) joint moment and (b) joint reaction force versus jumping height for each joint during landing. absorbs more energy in the early phase of hindlimb landing are relatively large. One reason cats do not experience injury because some of the energy is transferred to the hip by the as readily is that cats can control joint motion and attenuate the impact force experienced during landing in accordance rotation of the spine. In the late phase of hindlimb landing, the ankle starts to produce some energy, which we theorize with the synergistic mechanism described in the previous because the cat is beginning to get up and move forward. section. Another reason we suspect for this resistance to The magnitudes of the peak joint moment and peak joint injury is that the microstructures of cat bones, especially their reaction force experienced by each cat in response to increas- claws, are beneficial for avoiding impact injuries. However, further studies on cat anatomy and micro-CT scanning are ing jump height indicate that cats tend to distribute the greater demands from higher jump heights to the elbow still required. It is worth noting that because we simplified and hip. Compared to the maximum joint moments in a the jump down of each cat as a two-dimensional motion in study of human landing [18], the moments in the cats’ joints the sagittal plane, the forces in the mediolateral direction Peak joint reaction force (N/Kg) Peak joint moment (Nm/Kg) 10 Applied Bionics and Biomechanics 2.5 2.0 1.5 1.0 0.5 0.0 −0.5 −1.0 0.00 0.01 0.02 0.03 0.04 0.05 Time (s) Wrist Elbow Shoulder (a) 2.0 1.5 1.0 0.5 0.0 −0.5 0.00 0.01 0.02 0.03 0.04 Time (s) Ankle Knee Hip (b) Figure 6: Joint moment in (a) the RF wrist, elbow, and shoulder joints and (b) the RH ankle, knee, and hip joints during landing from a 1.2 m jump. were neglected. Additionally, the peak forces in the fore-aft . However, the exact effects of this assumption on other direction were only 2–4% of the peak VGRFs (from unpub- joints cannot be determined because the signs of the joint lished data of this study) and their directions should be reaction forces and joint moments are not constant. backward to steady the paws as they strike the ground. Based Biarticular muscles generate moments at both joints the on equations (2)–(7), this assumption leads directly to an muscles cross and are used to transport mechanical energy increase in F and F , which will always be negative, during locomotion [19–21]. A number of studies have been 1x 2x resulting in a decrease in the negative values of M and M conducted on the muscle activities in the elbows of cats 1 2 Joint moment (Nm/Kg) Joint moment (Nm/Kg) Applied Bionics and Biomechanics 11 −20 −40 −60 −80 −100 −120 0.00 0.01 0.01 0.01 0.01 0.01 Time (s) Wrist Elbow Shoulder (a) −5 −10 −15 −20 0.00 0.01 0.02 0.03 0.04 Time (s) Ankle Knee Hip (b) Figure 7: Joint power of (a) the RF wrist, elbow, and shoulder joints and (b) the RH ankle, knee, and hip joints during landing from a 1.2 m jump. during various forms of locomotion [10, 22, 23], and it has penniform shape, which is well suited for the dissipation been suggested that the long head of the triceps and biceps, of energy [24, 25]. In the hindlimbs, the feline hamstring both biarticular muscles, play a major role during landing. muscle group (biceps femoris, semitendinosus, and semi- The biceps is a fusiform muscle in the front of the humerus membranosus) has a larger mechanical advantage at the and the long head of the triceps, triangular in shape, connects hip [20]. The biceps femoris is a large flat muscle that the scapula to the olecranon. Importantly, both have long covers two-thirds of the lateral side of the femur, the tendons and the muscle fascicules are arranged in a semitendinosus is a slender muscle with thin and firm Joint power (W/Kg) Joint power (W/Kg) 12 Applied Bionics and Biomechanics Table 4: Mean and SD of energy absorbed by the RF and RH limb joints across all jump heights . b c Height (m) Wrist (J/kg) Elbow (J/kg) Shoulder (J/kg) Ankle (J/kg) Knee (J/kg) Hip (J/kg) 1.0 2.1696 (0.65) 7.7547 (1.19) 1.3223 (0.34) 0.2714 (0.04) 0.1552 (0.02) 0.61 (0.06) 1.2 2.6243 (0.78) 9.661 (2.01) 1.0907 (0.28) 0.6408 (0.09) 0.1184 (0.01) 1.0944 (0.30) 1.4 1.7404 (0.49) 9.4252 (1.89) 0.7686 (0.16) 1.0496 (0.22) 0.2508 (0.04) 1.9049 (0.61) 1.6 2.1053 (0.51) 9.6083 (2.34) 1.2798 (0.33) 1.9996 (0.56) 1.9437 (0.40) 4.6483 (0.90) 1.8 1.8471 (0.37) 8.7272 (1.88) 1.8247 (0.42) 3.3068 (0.90) 0.5844 (0.07) 5.7561 (1.08) 2.0 2.524 (0.44) 11.352 (2.70) 1.2378 (0.35) 4.7424 (1.11) 1.4591 (0.41) 6.9656 (1.23) a b Values in the parentheses are the standard deviation (SD). Parameter shows a statistically significant difference from the wrist and shoulder at each height. Parameter shows a statistically significant difference from the ankle and hip at each height. 1.0 1.2 1.4 1.6 1.8 2.0 Height (m) Knee Wrist Shoulder Ankle Elbow Hip Figure 8: Mean joint work values for the wrist, elbow, shoulder, ankle, knee, and hip. tendons, and the semimembranosus has the same shape as a motion in a two-dimensional plane, as in previous studies, the long head of the triceps, with firm and flat tendons. This while in fact, during the jump, the movement planes should arrangement allows energy to be transported from segment be divided into the sagittal, coronal, and transverse planes, to segment and then be absorbed by the hip extensors. so further study is warranted to capture the effects of move- ments in these directions. 5. Conclusions Data Availability Using the principle of inverse dynamics and summarizing the results of cat landing experiments, we are able to explain All data included in this study are available upon request by how cats control joint motion to dissipate impact force and to contact with the corresponding author. analyze the joint energy absorption strategies employed during landing, gaining insight into the internal buffering Conflicts of Interest mechanism. Our results show that cats can adopt a general mechanism of limb movement that is quite beneficial in The authors declare that there is no conflict of interest attenuating impact force. Notably, the elbow and hip muscle regarding the publication of this paper. groups were found to be dominant in energy absorption. The results of this study can provide biological inspiration for Acknowledgments high-efficiency buffering and energy-absorption equipment to reduce landing fall injuries in humans. 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