Identification of passive elastic joint moment-angle relationships in the lower extremity

Observer-Based Human Knee Stiffness Estimation

OBJECTIVE

We consider the problem of stiffness estimation for the human knee joint during motion in the sagittal plane.

METHODS

The new stiffness estimator uses a nonlinear reduced-order biomechanical model and a body sensor network (BSN). The developed model is based on a two-dimensional knee kinematics approach to calculate the angle-dependent lever arms and the torques of the muscle-tendon-complex. To minimize errors in the knee stiffness estimation procedure that result from model uncertainties, a nonlinear observer is developed. The observer uses the electromyogram (EMG) of involved muscles as input signals and the segmental orientation as the output signal to correct the observer-internal states. Because of dominating model nonlinearities and nonsmoothness of the corresponding nonlinear functions, an unscented Kalman filter is designed to compute and update the observer feedback (Kalman) gain matrix.

RESULTS

The observer-based stiffness estimation algorithm is subsequently evaluated in simulations and in a test bench, specifically designed to provide robotic movement support for the human knee joint.

CONCLUSION

In silico and experimental validation underline the good performance of the knee stiffness estimation even in the cases of a knee stiffening due to antagonistic coactivation.

SIGNIFICANCE

We have shown the principle function of an observer-based approach to knee stiffness estimation that employs EMG signals and segmental orientation provided by our own IPANEMA BSN. The presented approach makes realtime, model-based estimation of knee stiffness with minimal instrumentation possible.

Assessment of net knee moment-angle characteristics by instrumented hand-held dynamometry in children with spastic cerebral palsy and typically developing children

Background

The limited range of motion during walking in children with spastic cerebral palsy (SCP) may be the result of altered mechanical characteristics of muscles and connective tissues around the knee joint. Measurement of static net knee moment-angle relation will provide insights into these alterations, for which instrumented hand-held dynamometry may be applied.

The aims of this study were: (1) to test the measurement error of the estimated net knee moment-angle characteristics, (2) to determine the correlation between knee extension angle measurement at a standardized knee moment and popliteal angle from common physical examination and (3) to compare net knee moment–angle characteristics in SCP versus typically developing children.

Methods

With the child lying in sideward position, the knee was extended by moving the lower leg by a hand-held force transducer on a low friction cart. Force data were collected for a range of knee angles. Data were excluded when activity (EMG) levels of knee extensor and flexor muscles exceeded the EMG level during rest by more than two standard deviations. The net knee flexion moments were calculated from recorded force data and measured moment arm. Reliability for knee angles corresponding with 0.5, 1, 2, 3, and 4 Nm knee net flexion moments was assessed by standard error of measurements (SEM) and smallest detectable difference (SDD).

Results

For between day comparison, SEMs were about 5° and SDDs were below 14° for knee angles at 1-4 Nm net knee flexion moments. In SCP children, the knee angle measured at 4 Nm knee flexion moment was not related to the popliteal angle (r = 0.52). The slope at 4 Nm of the knee moment-angle curve in SCP children was significantly higher than that in typically developing children.

Conclusions

The presented knee hand-held dynamometry allows assessment of net knee flexion moment-knee angle characteristics in typically developing and SCP children and can be used to identify clinically relevant changes as a result of treatment. Overall stiffness of structures that contribute to the net knee flexion moment at the knee (i.e. muscles, tendons, ligaments) is elevated in SCP children.

Electronic supplementary material

The online version of this article (doi:10.1186/s12984-015-0056-y) contains supplementary material, which is available to authorized users.

Medial gastrocnemius muscle growth during adolescence is mediated by increased fascicle diameter rather than by longitudinal fascicle growth

Using a cross-sectional design, the purpose of this study was to determine how pennate gastrocnemius medialis (GM) muscle geometry changes as a function of adolescent age. Sixteen healthy adolescent males (aged 10-19 years) participated in this study. GM muscle geometry was measured within the mid-longitudinal plane obtained from a 3D voxel-array composed of transverse ultrasound images. Images were taken at footplate angles corresponding to standardised externally applied footplate moments (between 4 Nm plantar flexion and 6 Nm dorsal flexion). Muscle activity was recorded using surface electromyography (EMG), expressed as a percentage of maximal voluntary contraction (%MVC). To minimise the effects of muscle excitation, EMG inclusion criteria were set at <10% of MVC. In practice, however, normalised EMG levels were much lower. For adolescent subjects with increasing ages, GM muscle (belly) length increased due to an increase in the length component of the physiological cross-sectional area measured within the mid-longitudinal plane. No difference was found between fascicles at different ages, but the aponeurosis length and pennation angle increased by 0.5 cm year(-1) and 0.5° per year, respectively. Footplate angles corresponding to externally applied 0 and 4 Nm plantarflexion moments were not associated with different adolescent ages. In contrast, footplate angles corresponding to externally applied 4 and 6 Nm dorsal flexion moments decreased by 10° between 10 and 19 years. In conclusion, we found that in adolescents' pennate GM muscles, longitudinal muscle growth is mediated predominantly by increased muscle fascicle diameter.

Active functional stiffness of the knee joint during activities of daily living: a parameter for improved design of prosthetic limbs

BACKGROUND

Exploring knee joint physiological functional stiffness is crucial for improving the design of prosthetic legs that aim to mimic normal gait. This study hypothesizes that knee joint stiffness varies among different activities of daily living, additionally while the knee performs natural movements; the magnitude of the stiffness indicates the degree of energy storage element sufficiency in terms of harvesting/returning energy.

METHODS

This study examined sagittal plane knee moment vs. knee flexion angle curves from 12 able-bodied subjects during activities of daily living. Slopes of these curves were assessed to find the calculated stiffness during the peak energy return and harvest phases so that the activities, which can be performed when the prosthetic knee is supplemented by a spring, were identified.

FINDINGS

For the energy return and harvest phases, the stiffness varied between 0.006 and 0.046 Nm/kg deg. and 0 and 0.052 Nm/kg deg. respectively. The optimum energy return phase stiffness was 0.024 (SD 0.013) Nm/kg deg. and energy harvest phase stiffness was 0.011 (SD 0.018) Nm/kg deg.

INTERPRETATION

Knee joint stiffness varied significantly during activities of daily living, which indicated that a storage unit with a constant stiffness would not be sufficient in providing energy regenerative gait during all activities. However, by controlling the amount and timing of spring compression and release, an energy-regenerative prosthetic knee device could be developed during most of the activities. This study was directed to the development of a complete data set, which determined the torque-angle properties of the healthy knee joint.

Knee joint passive stiffness and moment in sagittal and frontal planes markedly increase with compression

Knee joints are subject to large compression forces in daily activities. Due to artefact moments and instability under large compression loads, biomechanical studies impose additional constraints to circumvent the compression position-dependency in response. To quantify the effect of compression on passive knee moment resistance and stiffness, two validated finite element models of the tibiofemoral (TF) joint, one refined with depth-dependent fibril-reinforced cartilage and the other less refined with homogeneous isotropic cartilage, are used. The unconstrained TF joint response in sagittal and frontal planes is investigated at different flexion angles (0°, 15°, 30° and 45°) up to 1800 N compression preloads. The compression is applied at a novel joint mechanical balance point (MBP) identified as a point at which the compression does not cause any coupled rotations in sagittal and frontal planes. The MBP of the unconstrained joint is located at the lateral plateau in small compressions and shifts medially towards the inter-compartmental area at larger compression forces. The compression force substantially increases the joint moment-bearing capacities and instantaneous angular rigidities in both frontal and sagittal planes. The varus-valgus laxities diminish with compression preloads despite concomitant substantial reductions in collateral ligament forces. While the angular rigidity would enhance the joint stability, the augmented passive moment resistance under compression preloads plays a role in supporting external moments and should as such be considered in the knee joint musculoskeletal models.

Muscle-tendon units provide limited contributions to the passive stiffness of the index finger metacarpophalangeal joint

The passive stiffness at the MCP joint is a result of the elasticity of muscle-tendon units (MTUs) and capsule ligament complex (CLC), however, the relative contributions of these two components are unknown. We hypothesize that the MTUs provide the majority of the contributions to the joint stiffness by generating resistive forces when the MCP joint is flexed or extended. We used the work done by passive moments as a measure for the determination of the contributions to the joint stiffness. We conducted experiments with ten human subjects and collected joint angle and finger tip force data. The total passive moment and joint angle data were fitted with a double exponential model, and the passive moments due to the MTUs were determined by developing subject-specific models of the passive force-length change relationships. Our results show that for all the subjects, the work done by the passive moments from the MTUs is less than 50% of the total work done, and the CLC provides dominant contributions to the joint stiffness throughout the flexion-extension range of the joint angle. Therefore, the hypothesis that the MTUs provide the majority of the contributions to the MCP joint stiffness is not supported. We also determined that the majority of the MTUs passive moment was generated by the extrinsic MTUs and the contributions of the intrinsic MTUs was negligible.

A QUASI-LINEAR VISCOELASTIC MODEL FOR THE PASSIVE PROPERTIES OF THE HUMAN HIP JOINT

Properties of passive elastic structures constituting the human hip joint can be exploited to increase efficiency of human locomotion. As studies estimating the passive contributions to the net joint moment often disregard damping properties of the joint such contributions overestimate the energy gained during leg retraction within swing and stance phase. We built an experimental apparatus to measure moment-angle-relations during motor guided cyclic movements over a wide range of angular velocities and step-like changes in hip angle. On the basis of the experimentally gained data set the objective of this study was to model the elastic as well as the damping characteristics of the joint in the sagittal plane utilizing the Quasi-Linear Viscoelastic theory (QLV). A double exponential function was conveniently employed to describe the elastic response. The dependency of the hip joint stiffness on biarticular muscles was incorporated by repeating the measurement protocol for different knee angles. Due to the fact that the stiffness characteristics of the elastic response were merely shifted over knee angles we introduced an equilibrium angle at the hip joint as exponential function of the knee angle eventually yielding an elastic response as a function of hip and knee angle. In order to cover the damping characteristics the reduced relaxation function comprising a continuous spectrum of relaxation was utilized. We exemplify the applicability of the QLV model on published kinematic data on human walking and estimated that approximately 27% of the energy passively stored at the hip dissipates during the gait cycle.

Hamstring musculotendon dynamics during stance and swing phases of high-speed running

INTRODUCTION

Hamstring strain injuries are common in sports that involve high-speed running. It remains uncertain whether the hamstrings are susceptible to injury during late swing phase, when the hamstrings are active and lengthening, or during stance, when contact loads are present. In this study, we used forward dynamic simulations to compare hamstring musculotendon stretch, loading, and work done during stance and swing phases of high-speed running.

METHODS

Whole-body kinematics, EMG activities, and ground reactions were collected as 12 subjects ran on an instrumented treadmill at speeds ranging from 80% to 100% of maximum (avg max speed = 7.8 m·s(-1)). Subject-specific simulations were then created using a whole-body musculoskeletal model that included 52 Hill-type musculotendon units acting about the hip and the knee. A computed muscle control algorithm was used to determine muscle excitation patterns that drove the limb to track measured hip and knee sagittal plane kinematics, with measured ground reactions applied to the limb.

RESULTS

The hamstrings lengthened under load from 50% to 90% of the gait cycle (swing) and then shortened under load from late swing through stance. Although peak hamstring stretch was invariant with speed, lateral hamstring (biceps femoris) loading increased significantly with speed and was greater during swing than stance at the fastest speed. The biarticular hamstrings performed negative work on the system only during swing phase, with the amount of negative work increased significantly with speed.

CONCLUSION

We concluded that the large inertial loads during high-speed running appear to make the hamstrings most susceptible to injury during swing phase. This information is relevant for scientifically establishing muscle injury prevention and rehabilitation programs.

Influence of stretching and warm-up on Achilles tendon material properties

BACKGROUND

Controversy exists on stretching and warm-up in injury prevention. We hypothesized that warm up has a greater effect on Achilles tendon biomechanics than static stretching. This study investigated static stretching and warm-up on Achilles tendon biomechanics in recreational athletes, in vivo.

MATERIALS AND METHODS

Ten active, healthy subjects, 5 males, 5 females, With a mean age of 22.9 years with no previous Achilles tendon injuries were recruited. Typical stretching and warm-up routines were created. Testing was performed in a randomized cross-over design. A custom-built dynamometer was utilized to perform controlled isometric plantarflexion. A low profile ultrasound probe was utilized to visualize the musculotendinous junction of the medial gastrocnemius. An eight-camera motion capture system was used to capture ankle motion. Custom software calculated Achilles tendon biomechanics.

RESULTS

Achilles tendon force production was consistent. No statistically significant differences were detected in stretch, stiffness, and strain between pre-, post-stretching, and post-warm-up interventions.

CONCLUSION

Stretching or warm-up alone, and combined did not demonstrate statistically significant differences. Stretching and warm-up may have an equivalent effect on Achilles tendon biomechanics. Prolonged and more intense protocols may be required for changes to occur.

CLINICAL RELEVANCE

Stretching and warm-up of the Achilles before exercise are commonly practiced. Investigating the effect of stretching and warm-up may shed light on potential injury prevention.

Determination of passive moment-angle relationships at the trapeziometacarpal joint

While modeling the trapeziometacarpal (TMC) joint for determination of tendon forces, the TMC has been considered frictionless and passive moments created by soft tissues neglected. This, however, becomes inaccurate when reaching the joint end range of motion and considering that the TMC is entirely crossed by a complex network of skin, ligaments, soft tissues, and tendons. The objective of this study was to evaluate the passive moments with respect to joint posture in order to further include this relationship in biomechanical modeling. An experimental method was proposed to estimate in vivo a global passive moment including the sum of the actions of each passive anatomical structure. An external force was applied at the level of the metacarpophalangeal joint in various directions ranging from neutral position to full extension and full adduction to full abduction. The passive moment was computed and expressed as a function of the adopted joint angles. An exponential regression was then developed to fit the experimental data and to propose a generic passive moment model. Results showed a good agreement between the proposed exponential regression model and the experimental measures. Moreover, it was shown that joint stiffness could represent more than 60% of the net joint moment during a typical pulp grip task. These results showed the necessity to include the data in biomechanical modeling. The results may help predict more realistic tendons force especially in abduction/adduction muscles.

Hamstring strain injuries: recommendations for diagnosis, rehabilitation, and injury prevention

Hamstring strain injuries remain a challenge for both athletes and clinicians, given their high incidence rate, slow healing, and persistent symptoms. Moreover, nearly one third of these injuries recur within the first year following a return to sport, with subsequent injuries often being more severe than the original. This high reinjury rate suggests that commonly utilized rehabilitation programs may be inadequate at resolving possible muscular weakness, reduced tissue extensibility, and/or altered movement patterns associated with the injury. Further, the traditional criteria used to determine the readiness of the athlete to return to sport may be insensitive to these persistent deficits, resulting in a premature return. There is mounting evidence that the risk of reinjury can be minimized by utilizing rehabilitation strategies that incorporate neuromuscular control exercises and eccentric strength training, combined with objective measures to assess musculotendon recovery and readiness to return to sport. In this paper, we first describe the diagnostic examination of an acute hamstring strain injury, including discussion of the value of determining injury location in estimating the duration of the convalescent period. Based on the current available evidence, we then propose a clinical guide for the rehabilitation of acute hamstring injuries, including specific criteria for treatment progression and return to sport. Finally, we describe directions for future research, including injury-specific rehabilitation programs, objective measures to assess reinjury risk, and strategies to prevent injury occurrence.

LEVEL OF EVIDENCE

Diagnosis/therapy/prevention, level 5.

The relationships between muscle, external, internal and joint mechanical work during normal walking

Muscle mechanical work is an important biomechanical quantity in human movement analyses and has been estimated using different quantities including external, internal and joint work. The goal of this study was to investigate the relationships between these traditionally used estimates of mechanical work in human walking and to assess whether they can be used as accurate estimates of musculotendon and/or muscle fiber work. A muscle-actuated forward dynamics walking simulation was generated to quantify each of the mechanical work measures. Total joint work (i.e. the time integral of absolute joint power over a full gait cycle) was found to underestimate total musculotendon work due to agonist-antagonist co-contractions, despite the effect of biarticular muscle work and passive joint work, which acted to decrease the underestimation. We did find that when the net passive joint work over the gait cycle is negligible, net joint work (i.e. the time integral of net joint power) was comparable to the net musculotendon work (and net muscle fiber work because net tendon work is zero over a complete gait cycle). Thus, during walking conditions when passive joint work is negligible, net joint work may be used as an estimate of net muscle work. Neither total external nor total internal work (nor their sum) provided a reasonable estimate of total musculotendon work. We conclude that joint work is limited in its ability to estimate musculotendon work, and that external and internal work should not be used as an estimation of musculotendon work.

Effect of hip flexibility on optimal stalder performances on high bar

In the optimisation of sports movements using computer simulation models, the joint actuators must be constrained in order to obtain realistic results. In models of a gymnast, the main constraint used in previous studies was maximum voluntary active joint torque. In the stalder, gymnasts reach their maximal hip flexion under the bar. The purpose of this study was to introduce a model of passive torque to assess the effect of the gymnast's flexibility on the technique of the straddled stalder. A three-dimensional kinematics driven simulation model was developed. The kinematics of the shoulder flexion, hip flexion and hip abduction were optimised to minimise torques for four hip flexion flexibilities: 100 degrees, 110 degrees, 120 degrees and 130 degrees. With decreased flexibility, the piked posture period is shorter and occurs later. Moreover the peaks of shoulder and hip torques increase. Gymnasts with low hip flexibility need to be stronger to achieve a stalder; hip flexibility should be considered by coaches before teaching this skill.

Modeling of the passive mechanical properties of the musculo-articular complex: acute effects of cyclic and static stretching

The primary aim of this study was to implement a rheological model of the mechanical behavior of the passive musculo-articular complex (MAC). The second objective was to adapt this model to simulate changes in the passive MAC's mechanical properties induced by passive stretching protocols commonly performed in sport and rehabilitation programs. Nine healthy subjects performed passive ankle dorsi-flexion and plantar-flexion cycles at different velocities (from 0.035 to 2.09 rads(-1)) on an isokinetic dynamometer. This procedure enabled the articular angle to be controlled and the passive torque developed by the MAC in resistance to stretch to be measured. Our rheological model, dependent on nine parameters, was composed of two non-linear (exponential) springs for both plantar- and dorsi-flexion, a linear viscoelastic component and a solid friction component. The model was implemented with the Simulink software package, and the nine parameters were identified, for each subject, by minimizing the square-difference between experimental torque-angle relationships and modeled curves. This model is in good agreement with experiment, whatever the considered stretching velocity. Finally, the model was adapted to incorporate static stretching (4x2.5 min) and cyclic stretching (five loading/unloading cycles) protocols. Our results indicate that the model could be used to simulate the effects of stretching protocols by adjusting a single (different) parameter for each protocol.

Mechanical efficiency of limb swing during walking and running in guinea fowl (Numida meleagris)

Understanding the mechanical determinants of the energy cost of limb swing is crucial for refining our models of locomotor energetics, as well as improving treatments for those suffering from impaired limb-swing mechanics. In this study, we use guinea fowl (Numida meleagris) as a model to explore whether mechanical work at the joints explains limb-swing energy use by combining inverse dynamic modeling and muscle-specific energetics from blood flow measurements. We found that the overall efficiencies of the limb swing increased markedly from walking (3%) to fast running (17%) and are well below the usually accepted maximum efficiency of muscle, except at the fastest speeds recorded. The estimated efficiency of a single muscle used during ankle flexion (tibialis cranialis) parallels that of the total limb-swing efficiency (3% walking, 15% fast running). Taken together, these findings do not support the hypothesis that joint work is the major determinant of limb-swing energy use across the animal's speed range and warn against making simple predictions of energy use based on joint mechanical work. To understand limb-swing energy use, mechanical functions other than accelerating the limb segments need to be explored, including isometric force production and muscle work arising from active and passive antagonist muscle forces.

The contribution of passive-elastic mechanisms to lower extremity joint kinetics during human walking

The purpose of this study was to investigate the contribution of passive mechanisms to lower extremity joint kinetics in normal walking at slow, comfortable, and fast speeds. Twenty healthy young adults participated in a passive testing protocol in which the relaxed lower limb was manipulated through full sagittal hip, knee, and ankle ranges of motion while kinematics and applied forces were simultaneously measured. The relationship between passive joint moments and angles was modeled by a set of exponential functions that accounted for the stretch of uniarticular structures and biarticular muscles. Subject specific walking kinematics (80%, 100%, and 120% of preferred speed) were input into the passive models to estimate joint moments, power, and work attributable to passive mechanisms. Passive hip flexion moments were substantial from late stance through early swing, absorbing approximately 40% of the net negative work done during hip extension and producing over half of the net positive work done during the hip flexor power burst (H3). Passive ankle plantarflexor moments were also produced during pre-swing, but generated a smaller percentage ( approximately 10%) of the net ankle plantarflexor power burst (A2). The joint work attributed to passive structures increased significantly (p<0.05) with walking speed. The biarticular rectus femoris and gastrocnemius allowed for net passive energy absorption at the knee and subsequent return at the hip and ankle (p<0.05). Together, these results suggest that passive-elastic mechanisms can contribute substantially to normal human walking and that biarticular muscles play a role in passively transferring energy between joints.

Active and passive contributions to joint kinetics during walking in older adults

The objectives of this study were to characterize the active and passive contributions to joint kinetics during walking in healthy young and older adults, and assess whether isokinetic ankle strength is associated with ankle power output during walking. Twenty healthy young (18-35 years) and 20 healthy older (65-85 years) adults participated in this study. We measured subject-specific passive-elastic joint moment-angle relationships in the lower extremity and tested maximum isokinetic ankle strength at 30 deg/s. Passive moment-angle relationships were used to estimate active and passive joint moment, power, and work quantities during walking at 80%, 100% and 120% of preferred walking speed. There were no significant differences in walking speed, step length, or cadence between the older and young adults. However, the older adults produced significantly more net positive work at the hip but less net positive work at the ankle at all walking speeds. Passive contributions to hip and ankle work did not significantly differ between groups, inferring that the older adults generated the additional hip work actively. Maximum isokinetic ankle strength was significantly less in the older adults, and correlated with peak positive plantar-flexor power at both the preferred and fast walking speeds. The results of this study suggest that age-related shifts in joint kinetics do not arise as a result of increased passive hip joint stiffness, but seem to be reflected in plantar-flexor weakness.