The effect of speed on leg stiffness and joint kinetics in human running

The goals of this study were to examine the following hypotheses: (a) there is a difference between the theoretically calculated (McMahon and Cheng, 1990. Journal of Biomechanics 23, 65-78) and the kinematically measured length changes of the spring-mass model and (b) the leg spring stiffness, the ankle spring stiffness and the knee spring stiffness are influenced by running speed. Thirteen athletes took part in this study. Force was measured using a "Kistler" force plate (1000 Hz). Kinematic data were recorded using two high-speed (120 Hz) video cameras. Each athlete completed trials running at five different velocities (approx. 2.5, 3.5, 4.5, 5.5 and 6.5 m/s). Running velocity influences the leg spring stiffness, the effective vertical spring stiffness and the spring stiffness at the knee joint. The spring stiffness at the ankle joint showed no statistical difference (p < 0.05) for the five velocities. The theoretically calculated length change of the spring-mass model significantly (p < 0.05) overestimated the actual length change. For running velocities up to 6.5 m/s the leg spring stiffness is influenced mostly by changes in stiffness at the knee joint.     

Mechanical model for theoretical determination of maximum running speed in mammals

A mechanical model for the determination of maximum speed in terrestrial tetrapods, designed for application to extinct species, is proposed. Only external bone measures and average body mass estimations are used as input data, and the hypothesis is made that leg bones are strong enough to endure the stress of running at maximum speed at a certain universal safety factor. The model is applied to a broad sample of living mammalian species to test its predictive power, and it is found to provide very good estimates of maximum running speed.     

Consequences of forward translation of the point of force application for the mechanics of running

In running humans, the point of force application between the foot and the ground moves forwards during the stance phase. Our aim was to determine the mechanical consequences of this 'point of force translation' (POFT). We modified the planar spring-mass model of locomotion to incorporate POFT, and then compared spring-mass simulations with and without POFT. We found that, if leg stiffness is adjusted appropriately, it is possible to maintain very similar values of peak vertical ground reaction force (GRF), stance time, contact length and vertical centre of mass displacement, whether or not POFT occurs. The leg stiffness required to achieve this increased as the distance of POFT increased. Peak horizontal GRF and mechanical work per step were lower when POFT occurred. The results indicate that the lack of POFT in the traditional spring-mass model should not prevent it from providing good predictions of peak vertical GRF, stance time, contact length and vertical centre of mass displacement in running humans, if an appropriate spring stiffness is used. However, the model can be expected to overestimate peak horizontal GRF and mechanical work per step. When POFT occurs, the spring stiffness in the traditional spring-mass model is not equivalent to leg stiffness. Therefore, caution should be exercised when using spring stiffness to understand how the musculoskeletal system adapts to different running conditions. This can explain the contradictory results in the literature regarding the effect of running speed on leg stiffness.     

How well can spring-mass-like telescoping leg models fit multi-pedal sagittal-plane locomotion data?

Idealized mathematical models of animals, with point-mass bodies and spring-like legs, have been used by researchers to study various aspects of terrestrial legged locomotion. Here, we fit a bipedal spring-mass model to the ground reaction forces of human running, a horse trotting, and a cockroach running. We find that, in all three cases, while the model captures center-of-mass motions and vertical force variations well, horizontal forces are less well reproduced, primarily due to variations in net force vector directions that the model cannot accommodate. The fits result in different apparent leg stiffnesses in the three animals. Assuming a simple fixed leg-angle touch-down strategy, we find that the gaits of these models are stable in different speed-step length regimes that overlap with those used by humans and horses, but not with that used by cockroaches.     

Age- and gender-related development of stretch shortening cycle during a sub-maximal hopping task

The aim of this study was to analyse the effects of age and gender (and their interaction) on a stretch shortening cycle solicited during a hopping task. For this aim, 147 girls and 148 boys aged 11 to 20 years, who were enrolled in middle school or secondary school with no experience in sport activity, or training less than three times per week, performed 3×5 hops in place. Leg-stiffness, jump-height and reactive-strength indices were assessed using an accelerometer (Myotest). The participants were selected in order to form five age groups: 11 12, 13-14, 15-16, 17-18 and 19-20 years. Regression analysis between force and centre of mass displacement revealed spring-mass behaviour for all groups (r²=.73-.89), meaning that beginning at the age of 11 years, children are able to perform complex inter-muscular coordination of the lower limbs, revealing efficient neural control early in childhood. Leg stiffness increased from 24.7 ± 10.6 kN · m⁻¹ at 11-12 years to 44.1 ± 14 kN · m⁻¹ in boys, with a small increase until 16 years (+17%) and a large increase between 17 and 20 years (+32.7%). In girls, leg stiffness increased from 26.6 ± 9 kN · m⁻¹ at 11-12 years to 39.4 ± 10.9 kN · m⁻¹ at 19-20 years, with a curious decrease in leg stiffness at 17-18 years, probably due to an increase in the percentage of fat at this age (25%). While no gender effect was found, the reactive-strength index revealed that, from 15-16 years onward, boys were better able to produce high levels of force in a shorter time than girls. The age of 15-16 years is a threshold of maturity and gender differentiation, where the boys investigated are more efficient in the stretch shortening cycle.     

CMV与SP双启动子增强外源基因在小鼠骨骼肌中的表达效率

构建分别含有CMV、肌肉特异启动子SP及双启动子CMV-SP的真核报告基因EGFP表达载体（pCMV-EGFP、pSP-EGFP及pCMV-SP-EGFP）和生长激素释放因子（GRF）表达载体（pCMV-GRF、pSP-GRF和pCMV-SP-GRF）.将3种EGFP表达质粒分别注射至小鼠骨骼肌.注射后1周、2周、3周以及4周时,分别提取肌肉组织RNA,应用半定量RT-PCR检测报告基因（EGFP）的表达量,发现pCMV-SP-EGFP组EGFP表达量显著高于pCMV-EGFP组和pSP-EGFP组（P<0.01）;经荧光检测得到了较强的荧光信号.将3种GRF表达质粒分别注射至小鼠骨骼肌,在注射后每10 d记录小鼠累积增重,采血并用RIA法测定血清胰岛素样生长因子Ⅰ（IGF-Ⅰ）浓度,结果pCMVSP-GRF组累积增重、IGF-I浓度分别高于生理盐水组、pCMV-GRF组和pSP-GRF组（P<0.05）.结果表明：CMV与SP两种启动子组合,在小鼠骨骼肌内使外源基因表达效率提高.本研究为提高外源基因在肌肉组织的表达提供了新的途径.     

Pendular activity of human upper limbs during slow and normal walking

When walking at normal and fast speeds, humans swing their upper limbs in alternation, each upper limb swinging in phase with the contralateral lower limb. However, at slow and very slow speeds, the upper limbs swing forward and back in unison, at twice the stride frequency of the lower limbs. The change from “single swinging” (in alternation) to “double swinging” (in unison) occurs consistently at a certain stride frequency for agiven individual, though different individuals may change at different stride frequencies. To explain this change in the way we use our upper limbs and individual variations in the occurrence of the change, the upper limb is modelled as a compound pendulum. Based on the kinematic properties of pendulums, we hypothesize that the stride frequency at which the change from “single swinging” to “double swinging” occurs will be at or slightly below the natural pendular frequency (NPF) of the upper limbs. Twenty-seven subjects were measured and then filmed while walking at various speeds. The mathematically derived NPF of each subject's upper limbs was compared to the stride frequency at which the subject changed from “single swinging” to “double swinging.” The results of the study conform very closely to the hypothesis, even when the NPF is artificially altered by adding weights to the subjects' hands. These results indicate that the pendulum model of the upper limb will be useful in further investigations of the function of the upper limbs in human walking. © 1994 Wiley-Liss, Inc.     

Simulating the GRF of Humanoid Robot Vertical Jumping Using a Simplified Model with a Foot Structure for Foot Design

There are many theories and tools for human or robot motion simulation,but most of them require complex calculations.The LNZN model(a simplified model named by the proposers)simplifies the human model and facilitates simulation of the Ground Reaction Force(GRF)of body landing by spring damping model and ignoring joint rotation movements,which can reduce the amount of computation obviously.In this paper,the LNZN model of human running is selected as the basis and is modified to obtain the LNZN model of a robot,which expands the application of the LNZN model.According to the structure of the human foot,a foot structure is then added to the simplified model to reduce the GRF.We also applied driving forces to the new model to simulate the whole high jump motion of the robot to expand the functions of the LNZN model.The obtained GRF data were anastomotic to the actual experimental results.In addition,the effects of variables,such as the mass,hardness,and damping,of the foot on the GRF at the moment of landing were also explored.Finally,based on the guidelines obtained for the design of the robot's foot structure,we fabricated new robot's feet and installed them on the actual robot and achieved a better cushioning effect than the original foot in experiments.     

The spring-mass model and the energy cost of treadmill running

During running, the behaviour of the support leg was studied by modelling the runner using an oscillating system composed of a spring (the leg) and of a mass (the body mass). This model was applied to eight middle-distance runners running on a level treadmill at a velocity corresponding to 90% of their maximal aerobic velocity [mean 5.10 (SD 0.33) m · s⁻¹]. Their energy cost of running (C _r ), was determined from the measurement of O₂ consumption. The work, the stiffness and the resonant frequency of both legs were computed from measurements performed with a kinematic arm. The C _r was significantly related to the stiffness (P < 0.05, r = −0.80) and the absolute difference between the resonant frequency and the step frequency (P < 0.05, r = 0.79) computed for the leg producing the highest positive work. Neither of these significant relationships were obtained when analysing data from the other leg probably because of the work asymmetry observed between legs. It was concluded that the spring-mass model is a good approach further to understand mechanisms underlying the interindividual differences in C _r . Accepted: 18 August 1997     

Somatostatin inhibits growth hormone-releasing factor-stimulated adenylate cyclase activity in GH, cells

GH3 cells were used to study the effect of rat growth hormone-releasing factor on adenylate cyclase activity and its interaction with somatostatin. Rat GRF stimulates adenylate cyclase activity (ED5 0 = 6 X 10(-8) M) and somatostatin-14 inhibits this GRF-stimulated activity in a non-competitive manner without affecting the basal enzyme levels. Inhibition by somatostatin-14 is observed at concentrations as low as 10(-11) M and the half-maximal effect is obtained with 10(-8) M. Somatostatin-28 is more potent than SS-14 and has an ED5 0 of 3 X 10(-11) M. VIP is more active than rat GRF in stimulating adenylate cyclase activation. We conclude that in GH3 cells rat GRF behaves as a partial VIP agonist by interacting with VIP-preferring receptors and its effects are inhibited by somatostatin.     

Costs versus benefits: best possible and best practical treatment regimens for HIV

Current HIV therapy, although highly effective, may cause very serious side effects, making adherence to the prescribed regimen difficult. Mathematical modeling may be used to evaluate alternative treatment regimens by weighing the positive results of treatment, such as higher levels of helper T cells, against the negative consequences, such as side effects and the possibility of resistance mutations. Although estimating the weights assigned to these factors is difficult, current clinical practice offers insight by defining situations in which therapy is considered “worthwhile”. We therefore use clinical practice, along with the probability that a drug-resistant mutation is present at the start of therapy, to suggest methods of rationally estimating these weights. In our underlying model, we use ordinary differential equations to describe the time course of in-host HIV infection, and include populations of both activated CD4⁺ T cells and CD8⁺ T cells. We then determine the best possible treatment regimen, assuming that the effectiveness of the drug can be continually adjusted, and the best practical treatment regimen, evaluating all patterns of a block of days “on” therapy followed by a block of days “off” therapy. We find that when the tolerance for drug-resistant mutations is low, high drug concentrations which maintain low infected cell populations are optimal. In contrast, if the tolerance for drug-resistant mutations is fairly high, the optimal treatment involves periods of reduced drug exposure which consequently boost the immune response through increased antigen exposure. We elucidate the dependence of the optimal treatment regimen on the pharmacokinetic parameters of specific antiviral agents.