A review of models of vertical,leg, and knee stiffness in adults for running,jumping or hopping tasks

Abstract

The ‘stiffness’ concept originates from Hooke's law which states that the force required to deform an object is related to a spring constant and the distance that object is deformed. Research into stiffness in the human body is undergoing unprecedented popularity; possibly because stiffness has been associated with sporting performance and some lower limb injuries. However, some inconsistencies surrounding stiffness measurement exists bringing into question the integrity of some research related to stiffness. The aim of this study was to review literature which describes how vertical, leg and knee stiffness has been measured in adult populations while running, jumping or hopping. A search of the entire MEDLINE, PubMed and SPORTDiscus databases and an iterative reference check was performed. Sixty-seven articles were retrieved; 21 measured vertical stiffness, 51 measured leg stiffness, and 22 measured knee stiffness. Thus, some studies measured several ‘types’ of stiffness. Vertical stiffness was typically the quotient of ground reaction force and centre of mass displacement. For leg stiffness it was and change in leg length, and for the knee it was the quotient of knee joint moments and change in joint angle. Sample size issues and measurement techniques were identified as limitations to current research.     

Stiffness,intralimb coordination,and joint modulation during a continuous vertical jump test

This study analysed the modulation of jump performance, vertical stiffness as well as joint and intralimb coordination throughout a 30-s vertical jump test. Twenty male athletes performed the test on a force plate while undergoing kinematic analysis. Jump height, power output, ground contact time, vertical stiffness, maximum knee and hip flexion angles, and coordination by continuous relative phase (CRP) were analysed. Analysis of variance was used to compare variables within deciles, and t-tests were used to compare CRP data between the initial and final jumps. Results showed reduction in jump height, power output, and vertical stiffness, with an increase in contact time found during the test. Maximum knee and hip flexion angles declined, but hip angle decreased earlier (10–20% of the test) than knee angle (90–100%). No changes were observed in CRP for thigh–leg coupling when comparing initial and final jumps, but the trunk–thigh coupling was more in-phase near the end of the test. We conclude that fatigue causes reduction in jump performance, as well as changes in stiffness and joint angles. Furthermore, changes in intralimb coordination appear at the last 10% of the test, suggesting a neuromotor mechanism to counterbalance the loss of muscle strength.     

Sex differences in lower extremity stiffness and kinematics alterations during double-legged drop landings with changes in drop height

The aim of this study was to determine whether sex differences and effect of drop heights exist in stiffness alteration of the lower extremity during a landing task with a drop height increment. Twelve male participants and twelve female participants performed drop landings at two drop heights (DL40 and DL60; in cm). The leg and joint stiffnesses were calculated using a spring–mass model, and the joint angular kinematics were calculated using motion capture. Ground reaction forces (GRFs) were recorded using a force plate. The peak vertical GRF of the females was significantly increased when the drop height was raised from 40 to 60 cm. Significantly less leg and knee stiffness was observed for DL60 in females. The ankle, knee, and hip angular displacement during landing were significantly increased with drop height increment in both sexes. The knee and hip flexion angular velocities at contact were significantly greater for the 60 cm drop height relative to the 40 cm drop height in males. These sex disparities regarding the lower extremity stiffness and kinematics alterations during drop landing with a drop height increment would predispose females to lower extremity injury.     

Ground reaction forces and knee mechanics in the weight acceptance phase of a dance leap take-off and landing

Aesthetic constraints allow dancers fewer technique modifications than other athletes to negotiate the demands of leaping. We examined vertical ground reaction force and knee mechanics during a saut de chat performed by healthy dancers. It was hypothesized that vertical ground reaction force during landing would exceed that of take-off, resulting in greater knee extensor moments and greater knee angular stiffness. Twelve dancers (six males, six females; age 18.9 ± 1.2 years, mass 59.2 ± 9.5 kg, height 1.68 ± 0.08 m, dance training 8.9 ± 5.1 years) with no history of low back pain or lower extremity pathology participated in the study. Saut de chat data were captured using an eight-camera Vicon system and AMTI force platforms. Peak ground reaction force was 26% greater during the landing phase, but did not result in increased peak knee extensor moments. Taking into account the 67% greater knee angular displacement during landing, this resulted in less knee angular stiffness during landing. In conclusion, landing was accomplished with less knee angular stiffness despite the greater peak ground reaction force. A link between decreased joint angular stiffness and increased soft tissue injury risk has been proposed elsewhere; therefore, landing from a saut de chat may be more injurious to the knee soft tissue than take-off.     

The effect of knee angle on the external validity of isometric measures of lower body neuromuscular function

The aim of this study was to evaluate the effect of varying knee angle (120 degrees and 90 degrees) on the external validity of an isometric leg press test with reference to vertical jump performance. Isometric peak force (PF120 and PF90), rate of force development (RFD120 and RFD90), and maximum height reached with a squat jump and counter-movement jump were measured in 14 males. Although RFD120 was significantly correlated with squat jump and counter-movement jump performance (r = 0.71 and 0.69), and the correlations with PF120 approached statistical significance (r = 0.53 and 0.50), neither PF90 nor RFD90 was significantly related to vertical jump performance. Furthermore, although both RFD120 and PF120 were significantly different between the best five and the worst five jumpers, RFD90 and PF90 did not differentiate between individuals' vertical jump performance. We conclude that the choice of joint angle affects the external validity of isometric strength testing. Based on our results, we recommend accurate control of biomechanical specificity and assessment at different angles to find the position at which isometric strength testing is most comfortable.     

Joint torque and mechanical energy flow in the support legs of skilled race walkers

This study analyzed the joint torque and the mechanical energy flow in the support legs of skilled male race walkers. Twelve race walkers were videotaped using a high-speed camera at a frame rate of 250 Hz set perpendicular to the sagittal plane of motion; their ground reaction forces were measured with two force platforms. A two-dimensional, 14-segment, linked model was used to calculate the kinetics of the support leg joints. In the initial part of the support phase, the mechanical energy flowed into the thigh and shank by the torque of the large hip extensors and knee flexors. In the middle part, the mechanical energy generated by the torque of the large plantar flexors flowed to the foot and from the foot to the shank by the ankle joint force. The mechanical energy flow by the forward joint force of the support hip was significantly related to the walking speed in the final part of the support phase. Our findings suggest that race walkers in the final part of the support phase should exert the torque of the knee extensors and hip flexors to transfer the mechanical energy more effectively to the support thigh and shank.     

The effect of knee angle on the external validity of isometric measures of lower body neuromuscular function

The aim of this study was to evaluate the effect of varying knee angle (120° and 90°) on the external validity of an isometric leg press test with reference to vertical jump performance. Isometric peak force (PF 120 and PF 90 ), rate of force development (RFD 120 and RFD 90 ), and maximum height reached with a squat jump and counter-movement jump were measured in 14 males. Although RFD 120 was significantly correlated with squat jump and counter-movement jump performance ( r = 0.71 and 0.69), and the correlations with PF 120 approached statistical significance ( r = 0.53 and 0.50), neither PF 90 nor RFD 90 was significantly related to vertical jump performance. Furthermore, although both RFD 120 and PF 120 were significantly different between the best five and the worst five jumpers, RFD 90 and PF 90 did not differentiate between individuals' vertical jump performance. We conclude that the choice of joint angle affects the external validity of isometric strength testing. Based on our results, we recommend accurate control of biomechanical specificity and assessment at different angles to find the position at which isometric strength testing is most comfortable.     

我国优秀男子跳高运动员起跳阶段摆动腿技术的运动学研究

背越式跳高起跳技术主要由起跳腿的蹬伸技术与摆动腿的摆动技术所组成。目前,大多数人们集中于跳高起跳的"蹬伸"技术研究,对起跳阶段的"摆动"技术研究相对较少。文章运用现场技术录像和运动图像解析的方法,对我国优秀男子跳高运动员在起跳阶段摆动技术进行解析研究,结果表明:我国优秀男子跳高运动员起跳前摆动腿最大缓冲幅度比较大;在起跳阶段摆动腿蹬离瞬间,摆动腿膝关节角度变化较小。背越式跳高起跳过程中的摆动腿缓冲阶段,身体重心的高度、摆动腿膝角的变化情况与助跑水平速度的损失有显著性相关。助跑最后一步摆动腿的伸膝角度、伸膝速度与起跳腿着地时摆动腿的摆动速度、摆动腿离地后的最大摆动速度都有高度的相关性。     

跑步疲劳进程中下肢生物力学模式的非线性变化研究

目的:确定跑步疲劳进程中下肢生物力学模式的变化,包括垂直和前后地面反作用力(ground reaction force,GRF)、垂直地面反作用力(vertical ground reaction force,vGRF)负载率、关节力学和刚度。方法:14名男性受试,采用Vicon红外摄像头和Bertec三维测力跑台,每隔2 min采集受试疲劳干预中的15 s GRF数据以及标记点轨迹。受试需穿着统一的跑鞋在测力跑台以恒速3.33 m/s跑至疲劳。满足以下标准时,干预结束:1)最大心率大于当下年龄的90%;2)受试不能继续跑步。对比受试跑至疲劳进程中4个时刻(疲劳前、33%、67%和100%)的着地冲击和下肢三关节触地角度、最大角度、关节活动度、角度变化量、关节蹬伸力矩和刚度等特征,采集并分析受试安静状态、疲劳后即刻、疲劳后4 min、疲劳后9 min的血乳酸浓度。结果:与疲劳前相比,1)血乳酸浓度在疲劳后即刻、疲劳后4 min和疲劳后9 min均显著增加;2)垂直/前后矢状轴GRF和vGRF负载率等参数在疲劳干预过程中均未观察到显著性变化;3)髋关节活动度在疲劳过程的33%、67%和100%时刻显著增加,膝关节活动度在67%时刻显著增加;4)踝关节运动学及踝、膝和髋关节的蹬伸力矩峰值均无变化;5)垂直刚度在67%和100%时刻显著降低。结论:疲劳干预过程中,GRF特征参数均没有明显变化,但是观察到下肢运动学和动力学模式的非线性改变。特别是从疲劳干预中期开始,人体下肢通过增加髋、膝关节活动度并减小垂直刚度实现“软着陆”策略,维持相似的冲击力特征,以减小长时间跑步可能带来损伤的风险。     

青年女性着高跟鞋平地行走时步态的生物力学研究

通过SIMI-MOTION录像解析系统和F-scan足底压力分布解析系统对青年女性穿高跟鞋行走时的步态进行运动学和动力学测量和分析。结果表明:青少年女性穿高跟鞋行走时的步态特征表现为:步长短,步速慢,步态周期长,重心起伏幅度大,单支撑时相占支撑时相比例低,说明青少年女性穿高跟鞋行走时下肢肌肉机能减弱;青少年女性穿跟高6.5cm以上的高跟鞋行走时,足底第一跖趾关节最大受力值是青少年女性穿球鞋行走时该点最大受力值的4倍,是青少年女性穿中跟鞋和松糕鞋行走时该点最大受力值的2倍。     

Isokinetic knee extension and vertical jumping: are they related?

The aim of this study was to examine joint power generation during a concentric knee extension isokinetic test and a squat vertical jump. The isokinetic test joint power was calculated using four different methods. Five participants performed concentric knee extensions at 0.52, 1.57, 3.14 and 5.23 rad x s(-1) on a Lido isokinetic dynamometer. The squat vertical jump was performed on a Kistler force plate. Kinematic data from both tests were collected and analysed using an ELITE optoelectronic system. An inverse dynamics model was applied to measure knee joint moment in the vertical jump. Knee angular position data from the kinematic analysis in the isokinetic test were used to derive the actual knee angular velocity and acceleration, which, in turn, was used to correct the dynamometer moment for inertial effects. Power was measured as the product of angular velocity and moment at the knee joint in both tests. Significant differences (P < 0.05) were found between mean (+/- s) peak knee joint power in the two tests (squat vertical jump: 2255 +/- 434 W; isokinetic knee extension: 771 +/- 81 W). Correlation analysis revealed that there is no relationship between the peak knee joint power during the vertical jump and the slow velocity isokinetic tests. Higher isokinetic velocity tests show better relationships with the vertical jump but only if the correct method for joint power calculation is used in the isokinetic test. These findings suggest that there are important differences in muscle activation and knee joint power development that must be taken into consideration when isokinetic tests are used to predict jumping performance.     

散打鞭腿动作技术的二环节链模型的运动学分析

鞭腿动作是散打腿法技术的核心,将散打鞭腿动作简化为一个二环节运动链模型,对散打鞭腿动作的髋、膝关节和大腿、小腿环节在三维平面内进行位置矢量的确定,以此确定在鞭腿动作中,各关节和环节的运动学参数,然后确定目标函数(末端速度V),建立了人体鞭腿动作的三维运动学方程,将鞭腿动作各环节要领数学化描述,结论认为:(1)鞭腿动作中大腿的角速度由腰部角速度和髋关节角速度决定,小腿的角速度由大腿和膝关节的角速度决定,三者密切配合共同决定着鞭腿末端的速度;(2)在T1阶,大小腿下潜完曲度不易超过450,在进攻腿离地瞬间,小腿环节的角速度大于大腿环节的角速度时最有利于膝关节速度的增加,进攻退离地时膝关节的角速度主要由小腿蹬地时的地面反作用力决定;(3)在T2阶段,大小腿充分折叠有利于膝关节角速度的加大;(4)人体的鞭腿环节链模型中,鞭打原理遵从动量由近端环节向远端环节传递的原理,通过髋关节及时有效的制动可使膝关节动量增加,通过膝关节的制动可使动量传递到末端,引起末端加速。(5)在散打鞭腿环节链模型中只有多环节和关节依次协调配合才能使末端发挥最佳击打效果。     

对我国男子优秀跳高运动员起跳技术的三维运动学分析

采用两台SONY高速摄像机对我国部分男子优秀背越式跳高运动员进行赛场同步拍摄,运用爱捷运动录像反馈系统进行解析.结果表明:在起跳开始瞬间,身体重心的垂直速度较低;起跳腿的髋、膝、踝3关节蹬伸不充分,摆动腿的摆动速度和高度较低,助跑水平速度未能合理地转化为起跳的垂直速度.起跳的垂直速度是影响我国男子跳高运动员成绩的主要因素.     

Isokinetic knee extension and vertical jumping: Are they related?

The aim of this study was to examine joint power generation during a concentric knee extension isokinetic test and a squat vertical jump. The isokinetic test joint power was calculated using four different methods. Five participants performed concentric knee extensions at 0.52, 1.57, 3.14 and 5.23 rad?·?s^?1 on a Lido isokinetic dynamometer. The squat vertical jump was performed on a Kistler force plate. Kinematic data from both tests were collected and analysed using an ELITE optoelectronic system. An inverse dynamics model was applied to measure knee joint moment in the vertical jump. Knee angular position data from the kinematic analysis in the isokinetic test were used to derive the actual knee angular velocity and acceleration, which, in turn, was used to correct the dynamometer moment for inertial effects. Power was measured as the product of angular velocity and moment at the knee joint in both tests. Significant differences (P <?0.05) were found between mean (?± s) peak knee joint power in the two tests (squat vertical jump: 2255?±?434W; isokinetic knee extension: 771?±?81W). Correlation analysis revealed that there is no relationship between the peak knee joint power during the vertical jump and the slow velocity isokinetic tests. Higher isokinetic velocity tests show better relationships with the vertical jump but only if the correct method for joint power calculation is used in the isokinetic test. These findings suggest that there are important differences in muscle activation and knee joint power development that must be taken into consideration when isokinetic tests are used to predict jumping performance.     

Reactive and eccentric strength contribute to stiffness regulation during maximum velocity sprinting in team sport athletes and highly trained sprinters

ABSTRACT

This study investigated the role of reactive and eccentric strength in stiffness regulation during maximum velocity sprinting (Vmax) in team sport athletes compared with highly trained sprinters. Thirteen team sport athletes and eleven highly trained sprinters were recruited. Vmax was measured using radar, and stiffness regulation was inferred from modelled vertical and leg spring stiffness. Reactive strength (RSI) was determined from a 0.50 m drop jump, and an eccentric back squat was used to assess maximum isoinertial eccentric force. Trained sprinters attained a higher Vmax than team sport athletes, partly due to a briefer contact time and higher vertical stiffness. Trained sprinters exhibited a moderately higher RSI via the attainment of a briefer and more forceful ground contact phase, while RSI also demonstrated large to very large associations with vertical stiffness and Vmax, respectively. Isoinertial eccentric force was largely correlated with Vmax, but only moderately correlated with vertical stiffness. Reactive and eccentric strength contribute to the ability to regulate leg spring stiffness at Vmax, and subsequently, the attainment of faster sprinting speeds in highly trained sprinters versus team sport athletes. However, stiffness regulation appears to be a task-specific neuromuscular skill, reinforcing the importance of specificity in the development of sprint performance.     

Dynamics of the support leg in soccer instep kicking

Abstract

We aimed to illustrate support leg dynamics during instep kicking to evaluate the role of the support leg action in performance. Twelve male soccer players performed maximal instep kicks. Their motions and ground reaction forces were recorded by a motion capture system and a force platform. Moments and angular velocities of the support leg and pelvis were computed using inverse dynamics. In most joints of the support leg, the moments were not associated with or counteracting the joint motions except for the knee joint. It can be interpreted that the initial knee flexion motion counteracting the extension joint moment has a role to attenuate the shock of landing and the following knee extension motion associated with the extension joint moment indirectly contributes to accelerate the swing of kicking leg. Also, appreciable horizontal rotation of the pelvis coincided with increase of the interaction moment due to the hip joint reaction force on the support leg side. It can be assumed that the interaction moment was the main factor causing the pelvis counter-clockwise rotation within the horizontal plane from the overhead view that precedes a proximal-to-distal sequence of segmental action of the swing leg.     

Musculoskeletal stiffness during hopping and running does not change following downhill backwards walking

Eccentric contractions that provide spring energy can also cause muscle damage. The aim of this study was to explore leg and vertical stiffness following muscle damage induced by an eccentric exercise protocol. Twenty active males completed 60 minutes of backward-walking on a treadmill at 0.67 m/s and a gradient of ? 8.5° to induce muscle damage. Tests were performed immediately before; immediately post; and 24, 48, and 168 hours post eccentric exercise. Tests included running at 3.35 m/s and hopping at 2.2 Hz using single- and double-legged actions. Leg and vertical stiffness were measured from kinetic and kinematic data, and electromyography (EMG) of five muscles of the preferred limb were recorded during hopping. Increases in pain scores (over 37%) occurred post-exercise and 24 and 48 hours later (p < 0.001). A 7% decrease in maximal voluntary contraction occurred immediately post-exercise (p = 0.019). Changes in knee kinematics during single-legged hopping were observed 168 hours post (p < 0.05). No significant changes were observed in EMG, creatine kinase activity, leg, or vertical stiffness. Results indicate that knee mechanics may be altered to maintain consistent levels of leg and vertical stiffness when eccentric exercise-induced muscle damage is present in the lower legs.     

Joint stiffness and running economy during imposed forefoot strike before and after a long run in rearfoot strike runners

Research has focused on the effects of acute strike pattern modifications on lower extremity joint stiffness and running economy (RE). Strike pattern modifications on running biomechanics have mostly been studied while runners complete short running bouts. This study examined the effects of an imposed forefoot strike (FFS) on RE and ankle and knee joint stiffness before and after a long run in habitual rearfoot strike (RFS) runners. Joint kinetics and RE were collected before and after a long run. Sagittal joint kinetics were computed from kinematic and ground reaction force data that were collected during over-ground running trials in 13 male runners. RE was measured during treadmill running. Knee flexion range of motion, knee extensor moment and ankle joint stiffness were lower while plantarflexor moment and knee joint stiffness were greater during imposed FFS compared with RFS. The long run did not influence the difference in ankle and knee joint stiffness between strike patterns. Runners were more economical during RFS than imposed FFS and RE was not influenced by the long run. These findings suggest that using a FFS pattern towards the end of a long run may not be mechanically or metabolically beneficial for well-trained male RFS runners.     

Lower limb joint kinetics and ankle joint stiffness in the sprint start push-off

Sprint push-off technique is fundamental to sprint performance and joint stiffness has been identified as a performance-related variable during dynamic movements. However, joint stiffness for the push-off and its relationship with performance (times and velocities) has not been reported. The aim of this study was to quantify and explain lower limb net joint moments and mechanical powers, and ankle stiffness during the first stance phase of the push-off. One elite sprinter performed 10 maximal sprint starts. An automatic motion analysis system (CODA, 200 Hz) with synchronized force plates (Kistler, 1000 Hz) collected kinematic profiles at the hip, knee, and ankle and ground reaction forces, providing input for inverse dynamics analyses. The lower-limb joints predominately extended and revealed a proximal-to-distal sequential pattern of maximal extensor angular velocity and positive power production. Pearson correlations revealed relationships (P < 0.05) between ankle stiffness (5.93 ± 0.75 N x m x deg(-1)) and selected performance variables. Relationships between negative power phase ankle stiffness and horizontal (r = -0.79) and vertical (r = 0.74) centre of mass velocities were opposite in direction to the positive power phase ankle stiffness (horizontal: r = 0.85; vertical: r = -0.54). Thus ankle stiffness may affect the goals of the sprint push-off in different ways, depending on the phase of stance considered.     

从对蹬冰加速理论的质疑点看克莱普冰刀的设计构想

从对蹬冰加速理论的质疑点角度，探讨了克莱普冰刀的设计构想。结果表明，克莱普冰刀的设计思想不仅仅是延长了蹬冰时间、提高了踩关节的灵活性、加大了蹬冰腿膝关节的伸展范围、保持了城关节的平稳移动，更重要的意义在于揭示重心沿滑行方向上的前移作用。它改变了以往人们对加速理论中，只有在与滑行方向水平面内相垂直的蹬冰力才对加速起贡献作用的传统认识，暗示出在滑行方向上切向和法向速度均对重心的加速起作用的观点。