Force measurements during running on different instrumented treadmills

One method to determine the forces produced during running is to conduct extensive kinematic and kinetic analysis. These analyses can be performed by having an individual perform repeated over-ground running trials or simply run continuously on an instrumented treadmill. The forces produced during over-ground running may not be the same as the forces during treadmill running and these differences could be attributed to a number of factors, including the design of the instrumented treadmill. The purpose of this paper was to determine whether there are differences in force measurements on different instrumented treadmill setups in comparison to over-ground running and to correct for any of these differences using a theoretical model. 11 participants ran on three different treadmills and performed over-ground running at 2.7, 3.6, and 4.5 m/s. Ground reaction forces were measured via force plates and an instrumented pressure insole. We found that the magnitude of the vertical ground reaction force differed between the three treadmills and over-ground running. The difference in ground reaction forces estimated by the pressure insole and the treadmill-force-plate system or instrumented treadmill can be explained by a three degree of freedom mechanical model of a person running on a treadmill and this model could potentially be used to correct for errors in force measurement from instrumented treadmills. The model included a force plate, a treadmill, and a wobbling mass with varying natural frequencies and damping characteristics, and constant masses. These findings provide researchers a method to correct forces from an instrumented treadmill set-up to determine a close approximation of the actual forces experienced by a participant during treadmill running.     

Modification of soft tissue vibrations in the leg by muscular activity.

Vibration characteristics were recorded for the soft tissues of the triceps surae, tibialis anterior, and quadriceps muscles. The frequency and damping of free vibrations in these tissues were measured while isometric and isotonic contractions of the leg were performed. Soft tissue vibration frequency and damping increased with both the force produced by and the shortening velocity of the underlying muscle. Both frequency and damping were greater in a direction normal to the skin surface than in a direction parallel to the major axis of each leg segment. Vibration characteristics further changed with the muscle length and between the individuals tested. The range of the measured vibration frequencies coincided with typical frequencies of impact forces during running. However, observations suggest that soft tissue vibrations are minimal during running. These results support the strategy that increases in muscular activity may be used by some individuals to move the frequency and damping characteristics of the soft tissues away from those of the impact force and thus minimize vibrations during walking and running.     

An algorithmic approach to constructing the on-line estimation system for the specific growth rate

The objective of this article is to propose an algorithm for the on-line estimation of the specific growth rate in a batch or a fed-batch fermentation process. The algorithm shows the practical procedure for the estimation method utilizing the macroscopic balance and the extended Kalman filter. A number of studies of the on line estimation have been presented. However, there are few studies discussing about the selection of the observed variables and for the tuning of some parameters of the extended Kalman filter, such as covariance matrix and initial values of the state.The beginning of this article is devoted to explain the selection of the observed variable. This information is very important in terms of the practical know-how for using technique. It is discovered that the condition number is a practically useful and valid criterion for number is a practically useful and valid criterion for choosing the variable to be observed.Next, when the extended Kalman filter in applied to the online estimation of the specific growth rate, which is directly unmeasurable, criteria for judging the validity of the estimated value from the observed data are proposed. Based on the proposed criterial, the system equation of the specific growth rate is selected and initial value of the state variable and covariance matrix of the system noises are adjusted. From many experiments, it is certified that the specific growth rate in the batch or fed -batch fermentation can be estimated accurately by means of the algorithm proposed here. In these experiments, that is, when the cell concentration is measured directly, the extended Kalman filter using the convariance matrix with a constant element can estimate more accurately values of the specific growth rate than the adaptive extended Kalman filter does.     

Muscle activity damps the soft tissue resonance that occurs in response to pulsed and continuous vibrations.

This study tested the hypotheses that when the excitation frequency of mechanical stimuli to the foot was close to the natural frequency of the soft tissues of the lower extremity, the muscle activity increases 1) the natural frequency and 2) the damping to minimize resonance. Soft tissue vibrations were measured with triaxial accelerometers, and muscle activity was measured by using surface electromyography from the quadriceps, hamstrings, tibialis anterior, and triceps surae groups from 20 subjects. Subjects were presented vibrations while standing on a vibrating platform. Both continuous vibrations and pulsed bursts of vibrations were presented, across the frequency range of 10-65 Hz. Elevated muscle activity and increased damping of vibration power occurred when the frequency of the input was close to the natural frequency of each soft tissue. However, the natural frequency of the soft tissues did not change in a manner that correlated with the frequency of the input. It is suggested that soft tissue damping may be the mechanism by which resonance is minimized at heel strike during running.     

Muscle activity reduces soft-tissue resonance at heel-strike during walking

Muscle activity has previously been suggested to minimize soft-tissue resonance which occurs at heel-strike during walking and running. If this concept were true then the greatest vibration damping would occur when the input force was closest to the resonant frequency of the soft-tissues at heel-strike. However, this idea has not been tested. The purpose of this study was to test whether muscle activity in the lower extremity is used to damp soft-tissue resonance which occurs at heel-strike during walking. Hard and soft shoe conditions were tested in a randomized block design. Ground reaction forces, soft-tissue accelerations and myoelectric activity were measured during walking for 40 subjects. Soft-tissue mass was estimated from anthropologic measurements, allowing inertial forces in the soft-tissues to be calculated. The force transfer from the ground to the tissues was compared with changes in the muscle activity. The soft condition resulted in relative frequencies (input/tissue) to be closer to resonance for the main soft-tissue groups. However, no increase in force transmission was observed. Therefore, the vibration damping in the tissues must have increased. This increase concurred with increases in the muscle activity for the biceps femoris and lateral gastrocnemius. The evidence supports the proposal that muscle activity damps soft-tissue resonance at heel-strike. Muscles generate forces which act across the joints and, therefore, shoe design may be used to modify muscle activity and thus joint loading during walking and running.     

The dynamics of quadrupedal locomotion

This paper presents a dynamical analysis of quadrupedal locomotion, with specific reference to an adult Nubian goat. Measurements of ground reaction forces and limb motion are used to assess variations in intersegmental forces, joint moments, and instantaneous power for three discernible gaits: walking, running, and jumping. In each case, inertial effects of the torso are shown to dominate to the extent that lower-extremity contributions may be considered negligible. Footforces generated by the forelimbs exceed those exerted by the hindlimbs; and, in general, ground reactions increase with speed. The shoulder and hip dominate mechanical energy production during walking, while the knee plays a more significant role in running. In both cases, however, the elbow absorbs energy, and by so doing functions primarily as a damping (control) element. As opposed to either walking or running, jumping requires total horizontal retardation of the body's center of mass. In this instance, generating the necessary vertical thrust amounts to energy absorption at all joints of the lower extremities.     

Analysis and implementation of a neural extended Kalman filter for target tracking

Having a better motion model in the state estimator is one way to improve target tracking performance. Since the motion model of the target is not known a priori, either robust modeling techniques or adaptive modeling techniques are required. The neural extended Kalman filter is a technique that learns unmodeled dynamics while performing state estimation in the feedback loop of a control system. This coupled system performs the standard estimation of the states of the plant while estimating a function to approximate the difference between the given state-coupling function model and the behavior of the true plant dynamics. At each sample step, this new model is added to the existing model to improve the state estimate. The neural extended Kalman filter has also been investigated as a target tracking estimation routine. Implementation issues for this adaptive modeling technique, including neural network training parameters, were investigated and an analysis was made of the quality of performance that the technique can have for tracking maneuvering targets.     

Estimation of running frequency spectra using a Kalman filter algorithm

A method is suggested for the computation of running frequency spectra from non-stationary oscillations in a long time series. The method is based on an autoregressive model where the coefficients are assumed to vary slowly. The coefficients are updated using the Kalman filter technique. The method is shown to be superior to ordinary autoregressive spectral estimation based on stationary theory in recognizing rapid changes in the frequencies of oscillations.     

Effect of Footwear Modifications on Oscillations at the Achilles Tendon during Running on a Treadmill and Over Ground: A Cross-Sectional Study

Background

Achilles tendon injuries are known to commonly occur in runners. During running repeated impacts are transferred in axial direction along the lower leg, therefore possibly affecting the oscillation behavior of the Achilles tendon. The purpose of the present study was to explore the effects of different footwear modifications and different ground conditions (over ground versus treadmill) on oscillations at the Achilles tendon.

Methods

Oscillations were measured in 20 male runners using two tri-axial accelerometers. Participants ran in three different shoe types on a treadmill and over ground. Data analysis was limited to stance phase and performed in time and frequency space. Statistical comparison was conducted between oscillations in vertical and horizontal direction, between running shoes and between ground conditions (treadmill versus over ground running).

Results

Differences in the oscillation behavior could be detected between measurement directions with peak accelerations in the vertical being lower than those in the horizontal direction, p < 0.01. Peak accelerations occurred earlier at the distal accelerometer than at the proximal one, p < 0.01. Average normalized power differed between running shoes (p < 0.01) with harder damping material resulting in higher power values. Little to no power attenuation was found between the two accelerometers. Oscillation behavior of the Achilles tendon is not influenced by ground condition.

Conclusion

Differences in shoe configurations may lead to variations in running technique and impact forces and therefore result in alterations of the vibration behavior at the Achilles tendon. The absence of power attenuation may have been caused by either a short distance between the two accelerometers or high stiffness of the tendon. High stiffness of the tendon will lead to complete transmission of the signal along the Achilles tendon and therefore no attenuation occurs.     

Towards a footwear design tool: Influence of shoe midsole properties and ground stiffness on the impact force during running

Several spring–damper–mass models of the human body have been developed in order to reproduce the measured ground vertical reaction forces during human running (McMahon and Cheng, 1990; Ferris et al., 1999; Liu and Nigg, 2000). In particular, Liu and Nigg introduced at the lower level of their model, i.e. at the interface between the human body and the ground, a nonlinear element representing simultaneously the shoe midsoles and the ground flexibility. The ground reaction force is modelled as the force supported by this nonlinear element, whose parameters are identified from several sets of experimental data. This approach proved to be robust and quite accurate. However, it does not explicitly take into account the shoe and the ground properties. It turns out to be impossible to study the influence of shoe materials on the impact force, for instance for footwear design purposes. In this paper, a modification of the Liu and Nigg's model is suggested, where the original nonlinear element is replaced with a bi-layered spring–damper–mass model: the first layer represents the shoe midsole and the second layer is associated with the ground.Ground is modelled as an infinite elastic half-space. We have assumed a viscoelastic behaviour of the shoe material, so the damping of shoe material is taken into account. A methodology for the shoe-soles characterization is proposed and used together with the proposed model. A parametric study is then conducted and the influence of the shoe properties on the impact force is quantified. Moreover, it is shown that impact forces are strongly affected by the ground stiffness, which should therefore be considered as an essential parameter in the footwear design.     

Differences in muscle activity between natural forefoot and rearfoot strikers during running

Running research has focused on reducing injuries by changing running technique. One proposed method is to change from rearfoot striking (RFS) to forefoot striking (FFS) because FFS is thought to be a more natural running pattern that may reduce loading and injury risk. Muscle activity affects loading and influences running patterns; however, the differences in muscle activity between natural FFS runners and natural RFS runners are unknown. The purpose of this study was to measure muscle activity in natural FFS runners and natural RFS runners. We tested the hypotheses that tibialis anterior activity would be significantly lower while activity of the plantarflexors would be significantly greater in FFS runners, compared to RFS runners, during late swing phase and early stance phase. Gait kinematics, ground reaction forces and electromyographic patterns of ten muscles were collected from twelve natural RFS runners and ten natural FFS runners. The root mean square (RMS) of each muscle?s activity was calculated during terminal swing phase and early stance phase. We found significantly lower RMS activity in the tibialis anterior in FFS runners during terminal swing phase, compared to RFS runners. In contrast, the medial and lateral gastrocnemius showed significantly greater RMS activity in terminal swing phase in FFS runners. No significant differences were found during early stance phase for the tibialis anterior or the plantarflexors. Recognizing the differences in muscle activity between FFS and RFS runners is an important step toward understanding how foot strike patterns may contribute to different types of injury.     

Vibration settling time of the gastrocnemius remains constant during an exhaustive run in rear foot strike runners

In this study, vibrations of human gastrocnemius during an exhaustive run protocol are considered for analysis. Previous studies have shown increased vibration intensity and damping coefficient within the soft tissue with fatigue. The question of this study was to investigate if the vibration settling time remains constant during a prolonged running. Eleven semi-professional middle/long distance runners ran to exhaustion on a treadmill with their preferred constant speed (4.29 ± 0.33 m/s) for 3873 ± 1147 m. Vibration of the gastrocnemius lateralis, electrical activity of the tibialis anterior and the gastrocnemius medialis along with ground reaction force (GRF) were recorded. The results demonstrated significant increase in impact peak and loading rate, and the frequency content of the impact, with no significant change in active peak of the vertical GRF. Fatigue resulted in increased vibration intensity, damping coefficient, and energy dissipation of vibration with no change in vibration settling time. Furthermore, peak acceleration significantly linearly (R = 0.59) increased as a function of running time. The mean frequency of muscle activity of the gastrocnemius medialis and the intensity of muscle activity in TA significantly decreased. The results suggest that constant vibration settling time might either be an objective for muscle tuning which is more pronounced in fatigued state or a passive by-product of muscle function in running. Further studies are needed to address this point.     

Leg stiffness increases with speed to modulate gait frequency and propulsion energy

Bipedal walking models with compliant legs have been employed to represent the ground reaction forces (GRFs) observed in human subjects. Quantification of the leg stiffness at varying gait speeds, therefore, would improve our understanding of the contributions of spring-like leg behavior to gait dynamics. In this study, we tuned a model of bipedal walking with damped compliant legs to match human GRFs at different gait speeds. Eight subjects walked at four different gait speeds, ranging from their self-selected speed to their maximum speed, in a random order. To examine the correlation between leg stiffness and the oscillatory behavior of the center of mass (CoM) during the single support phase, the damped natural frequency of the single compliant leg was compared with the duration of the single support phase. We observed that leg stiffness increased with speed and that the damping ratio was low and increased slightly with speed. The duration of the single support phase correlated well with the oscillation period of the damped complaint walking model, suggesting that CoM oscillations during single support may take advantage of resonance characteristics of the spring-like leg. The theoretical leg stiffness that maximizes the elastic energy stored in the compliant leg at the end of the single support phase is approximated by the empirical leg stiffness used to match model GRFs to human GRFs. This result implies that the CoM momentum change during the double support phase requires maximum forward propulsion and that an increase in leg stiffness with speed would beneficially increase the propulsion energy. Our results suggest that humans emulate, and may benefit from, spring-like leg mechanics.     

Muscle mechanical advantage of human walking and running: implications for energy cost.

Muscular forces generated during locomotion depend on an animal's speed, gait, and size and underlie the energy demand to power locomotion. Changes in limb posture affect muscle forces by altering the mechanical advantage of the ground reaction force (R) and therefore the effective mechanical advantage (EMA = r/R, where r is the muscle mechanical advantage) for muscle force production. We used inverse dynamics based on force plate and kinematic recordings of humans as they walked and ran at steady speeds to examine how changes in muscle EMA affect muscle force-generating requirements at these gaits. We found a 68% decrease in knee extensor EMA when humans changed gait from a walk to a run compared with an 18% increase in hip extensor EMA and a 23% increase in ankle extensor EMA. Whereas the knee joint was extended (154-176 degrees) during much of the support phase of walking, its flexed position (134-164 degrees) during running resulted in a 5.2-fold increase in quadriceps impulse (time-integrated force during stance) needed to support body weight on the ground. This increase was associated with a 4.9-fold increase in the ground reaction force moment about the knee. In contrast, extensor impulse decreased 37% (P < 0.05) at the hip and did not change at the ankle when subjects switched from a walk to a run. We conclude that the decrease in limb mechanical advantage (mean limb extensor EMA) and increase in knee extensor impulse during running likely contribute to the higher metabolic cost of transport in running than in walking. The low mechanical advantage in running humans may also explain previous observations of a greater metabolic cost of transport for running humans compared with trotting and galloping quadrupeds of similar size.     

Bone contact forces on the distal tibia during the stance phase of running

Although the tibia is a common site of stress fractures in runners, the loading of the tibia during running is not well understood. An integrated experimental and modeling approach was therefore used to estimate the bone contact forces acting on the distal end of the tibia during the stance phase of running, and the contributions of external and internal sources to these forces. Motion capture and force plate data were recorded for 10 male runners as they ran at 3.5-4 m/s. From these data, the joint reaction force (JRF), muscle forces, and bone contact force on the tibia were computed at the ankle using inverse dynamics and optimization methods. The distal end of the tibia was compressed and sheared posteriorly throughout most of stance, with respective peak forces of 9.00+/-1.13 and 0.57+/-0.18 body weights occurring during mid stance. Internal muscle forces were the primary source of tibial compression, whereas the JRF was the primary source of tibial shear due to the forward inclination of the leg relative to the external ground reaction force. The muscle forces and JRF both acted to compress the tibia, but induced tibial shear forces in opposing directions during stance, magnifying tibial compression and reducing tibial shear. The superposition of the peak compressive and posterior shear forces at mid stance may contribute to stress fractures in the posterior face of the tibia. The implications are that changes in running technique could potentially reduce stress fracture risk.     

Computational simulation of hemodynamic-driven growth and remodeling of embryonic atrioventricular valves

Embryonic heart valves develop under continuous and demanding hemodynamic loading. The particular contributions of fluid pressure and shear tractions in valve morphogenesis are difficult to decouple experimentally. To better understand how fluid loads could direct valve formation, we developed a computational model of avian embryonic atrioventricular (AV) valve (cushion) growth and remodeling using experimentally derived parameters for the blood flow and the cushion stiffness. Through an iterative scheme, we first solved the fluid loads on the axisymmetric AV canal and cushion model geometry. We then applied the fluid loads to the cushion and integrated the evolution equations to determine the growth and remodeling. After a set time of growth, we updated the fluid domain to reflect the change in cushion geometry and resolved for the fluid forces. The rate of growth and remodeling was assumed to be a function of the difference between the current stress and an isotropic homeostatic stress state. The magnitude of the homeostatic stress modulated the rate of volume addition during the evolution. We found that the pressure distribution on the AV cushion was sufficient to generate leaflet-like elongation in the direction of flow, through inducing tissue resorption on the inflow side of cushion and expansion on the outflow side. Conversely, shear tractions minimally altered tissue volume, but regulated the remodeling of tissue near the cushion surface, particular at the leading edge. Significant shear and circumferential residual stresses developed as the cushion evolved. This model offers insight into how natural and perturbed mechanical environments may direct AV valvulogenesis and provides an initial framework on which to incorporate more mechano-biological details.     

Muscle activity in the leg is tuned in response to impact force characteristics

Based on results from quasi-static experiments, it has been suggested that the lower extremity muscle activity is adjusted in reaction to impact forces with the goal of minimizing soft-tissue vibrations. It is not known whether a similar muscle tuning occurs during dynamic activities. Thus, the purpose of this study was to determine the effect of changes in the input signal on (a) vibrations of lower extremity soft-tissue packages and (b) EMG activity of related muscles during heel-toe running. Subjects performed heel-toe running in five different shoe conditions. Ground reaction forces were measured with a KISTLER force platform, soft-tissue vibrations were measured with tri-axial accelerometers and muscle activity was measured using surface EMG from the quadriceps, hamstrings, tibialis anterior and triceps surae groups from 10 subjects. By changing both the speed of running and the shoe midsole material the impact force characteristics were changed. There was no effect of changes in the input signal on the soft-tissue peak acceleration following impact. A significant correlation (R2=0.819) between the EMG pre-activation intensity and the impact loading rate changes was found for the quadriceps. In addition, the input frequency was shown to approach the vibration frequency of the quadriceps. This evidence supports the proposed paradigm that muscle activity is tuned to impact force characteristics to control the soft-tissue vibrations.     

A hybrid asymptotic-Kalman observer for bioprocesses

The exponential observers (extended Kalman or Luenberger observers, high gain observers) allow the use of a tuning parameter for managing the rate of convergence of the state estimate towards the true state. But their results are strongly dependent on the model quality (especially the kinetic model in bioprocesses). On the other hand, asymptotic observers (like the observer of Bastin and Dochain) have a rate of convergence which is a function of the experimental conditions (namely the dilution rate). However, this lack of tuning parameter is compensated by the absence of need for any kinetic model. In this paper, a hybrid technique is proposed which allows to jointly estimate the state and identify on-line the confidence on the kinetic model. The two limit cases (100 and 0 confidence) allow to recover rigorously the extended Kalman filter and the asymptotic observer of Bastin and Dochain. A simulation example (a fed-batch bacterial culture) is proposed and exhibits very satisfactory results.     

A constrained extended Kalman filter for the optimal estimate of kinematics and kinetics of a sagittal symmetric exercise

This paper presents a method for real-time estimation of the kinematics and kinetics of a human body performing a sagittal symmetric motor task, which would minimize the impact of the stereophotogrammetric soft tissue artefacts (STA). The method is based on a bi-dimensional mechanical model of the locomotor apparatus the state variables of which (joint angles, velocities and accelerations, and the segments lengths and inertial parameters) are estimated by a constrained extended Kalman filter (CEKF) that fuses input information made of both stereophotogrammetric and dynamometric measurement data. Filter gains are made to saturate in order to obtain plausible state variables and the measurement covariance matrix of the filter accounts for the expected STA maximal amplitudes. We hypothesised that the ensemble of constraints and input redundant information would allow the method to attenuate the STA propagation to the end results. The method was evaluated in ten human subjects performing a squat exercise. The CEKF estimated and measured skin marker trajectories exhibited a RMS difference lower than 4 mm, thus in the range of STAs. The RMS differences between the measured ground reaction force and moment and those estimated using the proposed method (9 N and 10 N m) were much lower than obtained using a classical inverse dynamics approach (22 N and 30 N m). From the latter results it may be inferred that the presented method allows for a significant improvement of the accuracy with which kinematic variables and relevant time derivatives, model parameters and, therefore, intersegmental moments are estimated.