A comparison and update of direct kinematic-kinetic models of leg stiffness in human running

The effects of plyometric jump training on lower-limb stiffness in healthy individuals: A meta-analytical comparison

PURPOSE

This study aimed to examine the effects of plyometric jump training (PJT) on lower-limb stiffness.

METHODS

Systematic searches were conducted in PubMed, Web of Science, and Scopus. Study participants included healthy males and females who undertook a PJT programme isolated from any other training type.

RESULTS

There was a small effect size (ES) of PJT on lower-limb stiffness (ES = 0.33, 95% confidence interval (95%CI): 0.07-0.60, z = 2.47, p = 0.01). Untrained individuals exhibited a larger ES (ES = 0.46, 95%CI: 0.08-0.84, p = 0.02) than trained individuals (ES = 0.15, 95%CI: ‒0.23 to 0.53, p = 0.45). Interventions lasting a greater number of weeks (>7 weeks) had a larger ES (ES = 0.47, 95%CI: 0.06-0.88, p = 0.03) than those lasting fewer weeks (ES = 0.22, 95%CI: ‒0.12 to 0.55, p = 0.20). Programmes with ≤2 sessions per week exhibited a larger ES (ES = 0.39, 95%CI: 0.01-0.77, p = 0.04) than programmes that incorporated >2 sessions per week (ES = 0.20, 95%CI: -0.10 to 0.50, p = 0.18). Programmes with <250 jumps per week (ES = 0.50, 95%CI: 0.02-0.97, p = 0.04) showed a larger effect than programmes with 250-500 jumps per week (ES = 0.36, 95%CI: 0.00-0.72, p = 0.05). Programmes with >500 jumps per week had negative effects (ES = -0.22, 95%CI: -1.10 to 0.67, p = 0.63). Programmes with >7.5 jumps per set showed larger effect sizes (ES = 0.55, 95%CI: 0.02-1.08, p = 0.04) than those with <7.5 jumps per set (ES = 0.32, 95%CI: 0.01-0.62, p = 0.04).

CONCLUSION

PJT enhances lower-body stiffness, which can be optimised with lower volumes (<250 jumps per week) over a relatively long period of time (>7 weeks).

Spring-mass behavioural adaptations to acute changes in prosthetic blade stiffness during submaximal running in unilateral transtibial prosthesis users

BACKGROUND

Individuals with lower-limb amputation can use running specific prostheses (RSP) that store and then return elastic energy during stance. However, it is unclear whether varying the stiffness category of the same RSP affects spring-mass behaviour during self-selected, submaximal speed running in individuals with unilateral transtibial amputation.

RESEARCH QUESTION

The current study investigates how varying RSP stiffness affects limb stiffness, running performance, and associated joint kinetics in individuals with a unilateral transtibial amputation.

METHODS

Kinematic and ground reaction force data were collected from eight males with unilateral transtibial amputation who ran at self-selected submaximal speeds along a 15 m runway in three RSP stiffness conditions; recommended habitual stiffness (HAB) and, following 10-minutes of familiarisation, stiffness categories above (+1) and below (-1) the HAB. Stance-phase centre of mass velocity, contact time, limb stiffness' and joint/RSP work were computed for each limb across RSP stiffness conditions.

RESULTS

With increased RSP stiffness, prosthetic limb stiffness increased, whilst intact limb stiffness decreased slightly (p<0.03). Centre of mass forward velocity during stance-phase (p<0.02) and contact time (p<0.04) were higher in the intact limb and lower in the prosthetic limb but were unaffected by RSP stiffness. Intact limb hip joint positive work increased for both the +1 and -1 conditions but remained unchanged across conditions in the prosthetic limb (p<0.02).

SIGNIFICANCE

In response to changes in RSP stiffness, there were acute increased mechanical demands on the intact limb, reflecting a reliance on the intact limb during running. However, overall running speed was unaffected, suggesting participants acutely adapted to an RSP of a non-prescribed stiffness.

Technological and Energetic Aspects of Multi-Component Co-Digestion of the Beverage Industry Wastes and Municipal Sewage Sludge

In the present study, the co-digestion effectiveness of the selected beverage wastes and municipal sewage sludge in two- and three-component mixtures was evaluated. Orange peels and orange pulp, as well as brewery spent grain were applied as co-substrates to sewage sludge at the following doses: 1.5 and 3.0 g of orange peels, 2.5 and 5 g of orange pulp, and 1.5 g brewery spent grain. Mono-digestion of sewage sludge was used as a control. The experiments were performed under mesophilic conditions in batch reactors. As compared to the control, only in the presence of the highest dose of pulp, brewery spent grain and sewage sludge was the increased methane production of 395 mL CH4 g−1 VS accompanying an additional energy profit of 82% observed. Moreover, in this case, the enhanced volatile solids removal and lower accumulation of p-cymene were found. These results were despite the increased limonene and phenol content in the feedstock, confirming a synergistic effect at the highest dose of pulp, brewery spent grain and sewage sludge.

Insight into the hierarchical control governing leg stiffness during the stance phase of running

Leg stiffness plays a key role in the storage and release of elastic energy during stance. However, the extent to which a runner is able to reuse stored energy remains a limiting factor in determining their running effectiveness. In this study, ten habitual rearfoot strikers and ten habitual forefoot strikers were asked to run on a treadmill in three footwear conditions: traditional, neutral, and minimal running shoes. We examined the effect of habitual foot strike pattern and footwear on leg stiffness control within three task-relevant phases of stance (i.e. touch-down, loading, unloading). Control was quantified using stride-to-stride leg stiffness time-series and the coefficient of variability and detrended fluctuation analysis (DFA). The results are interpreted within a theoretical framework that blends dynamic systems theory and optimal feedback control. Results indicate that leg stiffness control is tightly regulated by an active control process during the loading period of stance. In contrast, the touch-down and unloading phases are driven mostly by passive allometric control mechanisms. The effect of footwear on leg stiffness control was inconclusive due to inconsistent trends across three shoe types. However, stiffness control was affected by landing technique. Habitual rearfoot strike runners have reduced DFA values during the touch-down and unloading phases. These sub-phases are associated with an allometric control process and suggests that rearfoot strike runners express a reduction in system complexity for leg stiffness control and hence, a less adaptable system.

Using statistical parametric mapping to assess the association of duty factor and step frequency on running kinetic

Duty factor (DF) and step frequency (SF) were previously defined as the key running pattern determinants. Hence, this study aimed to investigate the association of DF and SF on 1) the vertical and fore-aft ground reaction force signals using statistical parametric mapping; 2) the force related variables (peaks, loading rates, impulses); and 3) the spring-mass characteristics of the lower limb, assessed by computing the force-length relationship and leg stiffness, for treadmill runs at several endurance running speeds. One hundred and fifteen runners ran at 9, 11, and 13 km/h. Force data (1000 Hz) and whole-body three-dimensional kinematics (200 Hz) were acquired by an instrumented treadmill and optoelectronic system, respectively. Both lower DF and SF led to larger vertical and fore-aft ground reaction force fluctuations, but to a lower extent for SF than for DF. Besides, the linearity of the force-length relationship during the leg compression decreased with increasing DF or with decreasing SF but did not change during the leg decompression. These findings showed that the lower the DF and the higher the SF, the more the runner relies on the optimization of the spring-mass model, whereas the higher the DF and the lower the SF, the more the runner promotes forward propulsion.

Effects of footwear cushioning on leg and longitudinal arch stiffness during running

During running, humans increase leg stiffness on more compliant surfaces through an in-series spring relationship to maintain constant support mechanics. Following this notion, the compliant midsole material of standard footwear may cause individuals to increase leg stiffness while running, especially in footwear with very thick midsoles. Recently, researchers have also proposed that footwear stiffness can affect the stiffness of the foot's longitudinal arch (LA) via a similar mechanism. To test these ideas, we used 3D motion capture to record 20 participants running on a forceplate-instrumented treadmill while barefoot, and while wearing three types of sandals composed of materials ranging an order of magnitude in Young's modulus: ethylene vinyl acetate (EVA), and two varieties of polyurethane rubber (R30 and R60). We calculated leg stiffness using standard methods, and measured LA stiffness based on medial midfoot kinematics. While there was an overall significant effect of footwear on leg stiffness (P = 0.047), post-hoc tests revealed no significant differences among individual pairs of conditions, and there was no effect of footwear on LA stiffness. However, participants exhibited significantly greater LA compression when barefoot than when running in EVA (P = 0.004) or R30 (P = 0.036) sandals. These results indicate that standard footwear midsole materials are too stiff to appreciably affect leg stiffness during running, meaning that increasing midsole thickness is unlikely to cause individuals to alter their leg stiffness. However, use of footwear does cause individuals to restrict LA compression when compared to running barefoot, and further research is needed to understand why.

Application of Leg, Vertical, and Joint Stiffness in Running Performance: A Literature Overview

Stiffness, the resistance to deformation due to force, has been used to model the way in which the lower body responds to landing during cyclic motions such as running and jumping. Vertical, leg, and joint stiffness provide a useful model for investigating the store and release of potential elastic energy via the musculotendinous unit in the stretch-shortening cycle and may provide insight into sport performance. This review is aimed at assessing the effect of vertical, leg, and joint stiffness on running performance as such an investigation may provide greater insight into performance during this common form of locomotion. PubMed and SPORTDiscus databases were searched resulting in 92 publications on vertical, leg, and joint stiffness and running performance. Vertical stiffness increases with running velocity and stride frequency. Higher vertical stiffness differentiated elite runners from lower-performing athletes and was also associated with a lower oxygen cost. In contrast, leg stiffness remains relatively constant with increasing velocity and is not strongly related to the aerobic demand and fatigue. Hip and knee joint stiffness are reported to increase with velocity, and a lower ankle and higher knee joint stiffness are linked to a lower oxygen cost of running; however, no relationship with performance has yet been investigated. Theoretically, there is a desired “leg-spring” stiffness value at which potential elastic energy return is maximised and this is specific to the individual. It appears that higher “leg-spring” stiffness is desirable for running performance; however, more research is needed to investigate the relationship of all three lower limb joint springs as the hip joint is often neglected. There is still no clear answer how training could affect mechanical stiffness during running. Studies including muscle activation and separate analyses of local tissues (tendons) are needed to investigate mechanical stiffness as a global variable associated with sports performance.

The effect of a low-load plyometric running intervention on leg stiffness in youth with cerebral palsy: A randomised controlled trial

AIM

To determine whether a running intervention utilising plyometric activities improved leg stiffness in youth with cerebral palsy (CP), GMFCS levels I and II.

METHOD

This stratified randomised controlled trial examined the lower limb kinetics and kinematics of a sample of youths with CP during sub-maximal hopping and running, prior to and immediately following a 12-week running intervention that incorporated low load plyometric training. Included participants were 13 in the control group (mean age 13 years 2 months [SD 2 years 7 months]; six males; nine GMFCS level I; six unilateral) and 18 in the intervention group (mean age 12 years 9 months [SD 2 years 10 months]; 13 males; 11 GMFCS level I; nine unilateral). Derived variables included three-dimensional leg stiffness as well as resultant ground reaction force and change in leg length. Generalised linear mixed models were developed for statistical analysis.

RESULTS

At follow-up the intervention group had greater leg stiffness than the control group during submaximal hopping (Intervention median = 3278Nm^-1; Control median = 1556Nm^-1; p < 0.01). At follow-up, participants in the intervention group in GMFCS Level I had greater leg stiffness than the control group during jogging (Intervention mean=38.84 (SD=25.55); Control mean=29.38 (SD=11.11); t = 2.61 p = 0.01).

INTERPRETATION

A running training intervention which includes plyometric activities can improve leg stiffness in young people with CP, especially those in GMFCS level I.

Comparing Leg Quasi-Stiffness Methods Across Running Velocities

This study investigated the differences between 5 commonly used methods to calculate leg stiffness over a range of running velocities. Thirteen male, habitually rearfoot, recreational runners ran on a force instrumented treadmill for a 5-minute running session. Each session consisted of 30-second intervals at 6 progressively faster speeds from 2.5 m·s-1 through 5.0 m·s-1 with each interval speed increasing by 0.5 m·s-1. Two-way within-factors repeated-measures analyses of variance were used to evaluate leg stiffness and length. A one-way repeated-measures analysis of variance was used to evaluate the slope of each trend line of each model across speeds. Pearson correlations were used to compare the relationship between the different computational methods. The results indicated that the direct stiffness methods increased with speed whereas the indirect stiffness methods did not. The direct methods were strongly correlated with each other as were the indirect methods. However, there were no strong correlations between the direct and indirect methods. These differences can be mostly attributed to how each individual stiffness method calculated leg length. It is important for researchers to understand these differences when conducting future studies and comparing past studies.

Leg and Joint Stiffness Adaptations to Minimalist and Maximalist Running Shoes

The running footwear literature reports a conceptual disconnect between shoe cushioning and external impact loading: footwear or surfaces with greater cushioning tend to result in greater impact force characteristics during running. Increased impact loading with maximalist footwear may reflect an altered lower-extremity gait strategy to adjust for running in compliant footwear. The authors hypothesized that ankle and knee joint stiffness would change to maintain the effective vertical stiffness, as cushioning changed with minimalist, traditional, and maximalist footwear. Eleven participants ran on an instrumental treadmill (3.5 m·s-1) for a 5-minute familiarization in each footwear, plus an additional 110 seconds before data collection. Vertical, leg, ankle, and knee joint stiffness and vertical impact force characteristics were calculated. Mixed model with repeated measures tested differences between footwear conditions. Compared with traditional and maximalist, the minimalist shoes were associated with greater average instantaneous and average vertical loading rates (P < .050), greater vertical stiffness (P ≤ .010), and less change in leg length between initial contact and peak resultant ground reaction force (P < .050). No other differences in stiffness or impact variables were observed. The shoe cushioning paradox did not hold in this study due to a similar musculoskeletal strategy for running in traditional and maximalist footwear and running with a more rigid limb in minimalist footwear.

A comparison of leg stiffness in running between typically developing children and children with cerebral palsy

BACKGROUND

Leg stiffness is important during running to increase velocity and maximise efficiency by facilitating use of the stretch-shortening cycle. Children with cerebral palsy who have neuromuscular impairments may have altered leg stiffness. The aim of this study was to describe leg stiffness during running in typically developing children and those with cerebral palsy in Gross Motor Function Classification Scale levels I and II at a range of speeds.

METHODS

This cross-sectional study examined kinematic data collected from typically developing children (n = 21) and children with cerebral palsy (Gross Motor Function Classification Scale level I n = 25, Gross Motor Function Classification Scale level II n = 13) during jogging, running and sprinting. Derived variables were resultant ground reaction force, change in leg length and three-dimensional leg stiffness. Linear mixed models were developed for statistical analysis.

FINDINGS

Children with cerebral palsy had reduced stiffness when jogging (Gross Motor Function Classification Scale level I affected t = 3.81 p < 0.01; non-affected t = 2.19 p = 0.03; Gross Motor Function Classification Scale level II affected t = 2.04 p = 0.04) and running (Gross Motor Function Classification Scale level I affected t = 3.23 p < 0.01) compared to typically developing children. Affected legs were less stiff than non-affected legs only in Gross Motor Function Classification Scale level I during running (t = 2.26 p = 0.03) and sprinting (t = 2.95 p < 0.01).

INTERPRETATION

Children with cerebral palsy have atypical leg stiffness profiles which differ according to functional classification.

The human foot functions like a spring of adjustable stiffness during running

Like other animals, humans use their legs like springs to save energy during running. One potential contributor to leg stiffness in humans is the longitudinal arch (LA) of the foot. Studies of cadaveric feet have demonstrated that the LA can function like a spring, but it is unknown whether humans can adjust LA stiffness in coordination with more proximal joints to help control leg stiffness during running. Here, we used 3D motion capture to record 27 adult participants running on a forceplate-instrumented treadmill, and calculated LA stiffness using beam bending and midfoot kinematics models of the foot. Because changing stride frequency causes humans to adjust overall leg stiffness, we had participants run at their preferred frequency and frequencies 35% above and 20% below preferred frequency to test for similar adjustments in the LA. Regardless of which foot model we used, we found that participants increased LA quasi-stiffness significantly between low and high frequency runs, mirroring changes at the ankle, knee and leg overall. However, among foot models, we found that the model incorporating triceps surae force into bending force on the foot produced unrealistically high LA work estimates, leading us to discourage this modeling approach. Additionally, we found that there was not a consistent correlation between LA height and quasi-stiffness values among the participants, indicating that static LA height measurements are not good predictors of dynamic function. Overall, our findings support the hypothesis that humans dynamically adjust LA stiffness during running in concert with other structures of the leg.

Lower-limb stiffness mediates speed but not turning angle during unplanned side-step cutting

An inability to pre-plan a side-step cutting maneuver results in a greater reduction in speed and shallower cut angle. Although leg stiffness has not been directly quantified in cutting, indirect evidence suggest that greater stiffness may benefit cutting speed, but lower stiffness may benefit cut angle. No studies have investigated if stiffness causally mediates the relationship between anticipation, cutting speed and angle. The aims of the present study were to determine the influence of anticipatory cues on leg stiffness, and quantify the mediation effects of stiffness on cutting speed and angle. Seventeen healthy participants performed a 45° cut at an approach speed of 4 m/s. Leg stiffness (% bodyweight/leg length [BW/LL]), cutting angle and change in running speed between initial contact and toe-off of the cut were calculated. Causal mediation analysis was performed with anticipatory cues as the independent variable, cutting speed and angle as the dependent variables, and stiffness as the mediator. Unanticipated cutting significantly increased leg stiffness (β=3.82%BW/LL,P=0.005) compared to anticipated cutting. The average causal mediation effect of stiffness on cutting angle was not significant (P = 0.68). The average causal mediation effect of stiffness on cutting speed was significant (-0.02 m/s [95%CI -0.04 to 0.00 m/s, P = 0.016). Reduced preplanning time in cutting increased leg stiffness. Alterations in leg stiffness only explained the change in speed, and not angle, associated with cutting under different anticipatory cues. Loss of speed when cutting is unplanned may be mitigated by improving leg stiffness.

Limb dynamics in agility jumps of beginner and advanced dogs

A considerable body of work has examined the dynamics of different dog gaits, but there are no studies that have focused on limb dynamics in jumping. Jumping is an essential part of dog agility, a dog sport in which handlers direct their dogs through an obstacle course in a limited time. We hypothesized that limb parameters like limb length and stiffness indicate the skill level of dogs. We analyzed global limb parameters in jumping for 10 advanced and 10 beginner dogs. In experiments, we collected 3D kinematics and ground reaction forces during dog jumping at high forward speeds. Our results revealed general strategies of limb control in jumping and highlighted differences between advanced and beginner dogs. In take-off, the spatially leading forelimb was 75% (P<0.001) stiffer than the trailing forelimb. In landing, the trailing forelimb was 14% stiffer (P<0.001) than the leading forelimb. This indicates a strut-like action of the forelimbs to achieve jumping height in take-off and to transfer vertical velocity into horizontal velocity in landing (with switching roles of the forelimbs). During landing, the more (24%) compliant forelimbs of beginner dogs (P=0.005) resulted in 17% (P=0.017) higher limb compression during the stance phase. This was associated with a larger amount of eccentric muscle contraction, which might in turn explain the soft tissue injuries that frequently occur in the shoulder region of beginner dogs. For all limbs, limb length at toe-off was greater for advanced dogs. Hence, limb length and stiffness might be used as objective measures of skill.

Running in highly cushioned shoes increases leg stiffness and amplifies impact loading

Running shoe cushioning has become a standard method for managing impact loading and consequent injuries due to running. However, despite decades of shoe technology developments and the fact that shoes have become increasingly cushioned, aimed to ease the impact on runners' legs, running injuries have not decreased. To better understand the shoe cushioning paradox, we examined impact loading and the spring-like mechanics of running in a conventional control running shoe and a highly cushioned maximalist shoe at two training speeds, 10 and 14.5 km/h. We found that highly cushioned maximalist shoes alter spring-like running mechanics and amplify rather than attenuate impact loading. This surprising outcome was more pronounced at fast running speed (14.5 km/h), where ground reaction force impact peak and loading rate were 10.7% and 12.3% greater, respectively, in the maximalist shoe compared to the conventional shoe, whereas only a slightly higher impact peak (6.4%) was found at the 10 km/h speed with the maximalist shoe. We attribute the greater impact loading with the maximalist shoes to stiffer leg during landing compared to that of running with the conventional shoes. These discoveries may explain why shoes with more cushioning do not protect against impact-related running injuries.

Lower limb stiffness testing in athletic performance: a critical review

Stiffness describes the resistance of a body to deformation. In regard to athletic performance, a stiffer leg-spring would be expected to augment performance by increasing utilisation of elastic energy. Two-dimensional spring-mass and torsional spring models can be applied to model whole-body (vertical and/or leg stiffness) and joint stiffness. Various tasks have been used to characterise stiffness, including hopping, gait, jumping, sledge ergometry and change of direction tasks. Appropriate levels of reliability have been reported in most tasks, although they vary between investigations. Vertical stiffness has demonstrated the strongest reliability across tasks and may be more sensitive to changes in high-velocity running performance than leg stiffness. Joint stiffness demonstrates the weakest reliability, with ankle stiffness more reliable than knee stiffness. Determination of stiffness has typically necessitated force plate analyses; however, validated field-based equations permit determination of whole-body stiffness without force plates. Vertical, leg and joint stiffness measures have all demonstrated relationships with performance measures. Greater stiffness is typically demonstrated with increasing intensity (i.e., running velocity or hopping frequency). Greater stiffness is observed in athletes regularly subjecting the limb to high ground reaction forces (i.e., sprinters). Careful consideration should be given to the most appropriate assessment of stiffness on a team/individual basis.