Biomechanical characteristics of human ankle-joint muscles

Four degree-of-freedom lumped parameter model of the foot-ankle system exposed to vertical vibration from 10 to 60 Hz with varying centre of pressure conditions

Modelling the foot-ankle system (FAS) while exposed to foot-transmitted vibration (FTV) is essential for designing inhibition methods to prevent the effects of vibration-induced white-foot. K-means analysis was conducted on a data set containing vibration transmissibility from the floor to 24 anatomical locations on the right foot of 21 participants. The K-means analysis found three locations to be sufficient for summarising the FTV response. A three segment, four degrees-of-freedom lumped parameter model of the FAS was designed to model the transmissibility response at three locations when exposed to vertical vibration from 10 to 60 Hz. Reasonable results were found at the ankle, midfoot, and toes in the natural standing position (mean-squared error (ε) = 0.471, 0.089, 0.047) and forward centre of pressure (COP) (ε = 0.539, 0.058, 0.057). However, when the COP is backward, the model does not sufficiently capture the transmissibility response at the ankle (ε = 1.09, 0.219, 0.039). Practitioner summary The vibration transmissibility response of the foot-ankle system (FAS) was modelled with varying centre of pressure (COP) locations. Modelling the FAS using three transmissibility locations and two foot segments (rearfoot and forefoot) demonstrated reasonable results in a natural standing and forward COP position to test future intervention strategies. Abbreviations: COP: centre of pressure; DOF: degrees-of-freedom; FAS: foot-ankle system; FTV: foot-transmitted vibration; HAVS: hand-arm vibration syndrome; LDV: laser Doppler vibrometer; LP: lumped-parameter; VWT: vibration-induced white-toes; WBV: whole-body vibration.

Ankle Mechanical Impedance During Waling in Chronic Stroke: Preliminary Results

Dynamic joint mechanics, collectively known as mechanical impedance, are often altered following upper motoneuron disease, which can hinder mobility for these individuals. Typically, assessments of altered limb mechanics are obtained while the patient is at rest, which differs from the dynamic conditions of mobility. The purpose of this study was to quantify ankle impedance during walking in individuals post-stroke, determine differences from the healthy population, and assess the relationship between impedance impairment and clinical outcome measures. Preliminary data were collected in four individuals post-stroke. Displacement perturbations were applied to the ankle during stance phase, and least-squares system identification was performed to estimate ankle impedance. In comparison to the healthy population, the paretic ankle showed reduced variation of stiffness during mid-stance of walking, and damping estimates during early and mid-stance were increased. Clinical measures obtained during dynamic tasks showed strong correlation with changes to the stiffness component of impedance, while clinical measures obtained passively were not correlated to stiffness. Impairment in ankle damping was not correlated with any of the measures tested. This work provides novel, preliminary insight into paretic ankle impedance during walking, differences from healthy data, and elucidates how current clinical metrics correspond to the true values of ankle stiffness and damping during gait.

Mechanical Impedance and Its Relations to Motor Control, Limb Dynamics, and Motion Biomechanics

The concept of mechanical impedance represents the interactive relationship between deformation kinematics and the resulting dynamics in human joints or limbs. A major component of impedance, stiffness, is defined as the ratio between the force change to the displacement change and is strongly related to muscle activation. The set of impedance components, including effective mass, inertia, damping, and stiffness, is important in determining the performance of the many tasks assigned to the limbs and in counteracting undesired effects of applied loads and disturbances. Specifically for the upper limb, impedance enables controlling manual tasks and reaching motions. In the lower limb, impedance is responsible for the transmission and attenuation of impact forces in tasks of repulsive loadings. This review presents an updated account of the works on mechanical impedance and its relations with motor control, limb dynamics, and motion biomechanics. Basic questions related to the linearity and nonlinearity of impedance and to the factors that affect mechanical impedance are treated with relevance to upper and lower limb functions, joint performance, trunk stability, and seating under dynamic conditions. Methods for the derivation of mechanical impedance, both those for within the system and material-structural approaches, are reviewed. For system approaches, special attention is given to methods aimed at revealing the correct and sufficient degree of nonlinearity of impedance. This is particularly relevant in the design of spring-based artificial legs and robotic arms. Finally, due to the intricate relation between impedance and muscle activity, methods for the explicit expression of impedance of contractile tissue are reviewed.

Inferior olive mirrors joint dynamics to implement an inverse controller

To produce smooth and coordinated motion, our nervous systems need to generate precisely timed muscle activation patterns that, due to axonal conduction delay, must be generated in a predictive and feedforward manner. Kawato proposed that the cerebellum accomplishes this by acting as an inverse controller that modulates descending motor commands to predictively drive the spinal cord such that the musculoskeletal dynamics are canceled out. This and other cerebellar theories do not, however, account for the rich biophysical properties expressed by the olivocerebellar complex's various cell types, making these theories difficult to verify experimentally. Here we propose that a multizonal microcomplex's (MZMC) inferior olivary neurons use their subthreshold oscillations to mirror a musculoskeletal joint's underdamped dynamics, thereby achieving inverse control. We used control theory to map a joint's inverse model onto an MZMC's biophysics, and we used biophysical modeling to confirm that inferior olivary neurons can express the dynamics required to mirror biomechanical joints. We then combined both techniques to predict how experimentally injecting current into the inferior olive would affect overall motor output performance. We found that this experimental manipulation unmasked a joint's natural dynamics, as observed by motor output ringing at the joint's natural frequency, with amplitude proportional to the amount of current. These results support the proposal that the cerebellum-in particular an MZMC-is an inverse controller; the results also provide a biophysical implementation for this controller and allow one to make an experimentally testable prediction.

Assessing musculo-articular stiffness using free oscillations: theory, measurement and analysis

Stiffness, the relationship between applied load and elastic deformation, is an important neuromechanical component related to muscular performance and injury risk. The free-oscillation technique is a popular method for stiffness assessment. There has been wide application of this technique assessing a variety of musculature, including the triceps surae, knee flexors, knee extensors and pectorals. The methodology involves the modelling of the system as a linear damped mass-spring system. The use of such a model has certain advantages and limitations that will be discussed within this review. Perhaps the major advantage of such a model is the specificity of the measure, whereby it is possible for the assessment conditions to simulate the type of loading witnessed during functional tasks and sporting situations. High levels of reliability and construct validity have typically been reported using such procedures. Despite these assurances of accuracy, a number of issues have also been identified. The literature reveals some concerns surrounding the use of a linear model for stiffness assessment. Further, procedural issues surrounding the administration of the perturbation, attention focus of the participant during the perturbation, signal collection, data processing and analysis, presentation of stiffness as a linear or torsional value, assessment load (single vs multiple vs maximal) and the stiffness-load relationship have been identified, and are all fundamentally related to the quality of the calculated output data. Finally, several important considerations for practitioners have been recommended to ensure the quality and consistency of stiffness data collection, processing and interpretation.

Biomechanical behavior of muscle-tendon complex during dynamic human movements

This paper reviews the research findings regarding the force and length changes of the muscle-tendon complex during dynamic human movements, especially those using ultrasonography and computer simulation. The use of ultrasonography demonstrated that the tendinous structures of the muscle-tendon complex are compliant enough to influence the biomechanical behavior (length change, shortening velocity, and so on) of fascicles substantially. It was discussed that the fascicles are a force generator rather than a work generator; the tendinous structures function not only as an energy re-distributor but also as a power amplifier, and the interaction between fascicles and tendinous structures is essential for generating higher joint power outputs during the late pushoff phase in human vertical jumping. This phenomenon could be explained based on the force-length/velocity relationships of each element (contractile and series elastic elements) in the muscle-tendon complex during movements. Through computer simulation using a Hill-type muscle-tendon complex model, the benefit of making a countermovement was examined in relation to the compliance of the muscle-tendon complex and the length ratio between the contractile and series elastic elements. Also, the integral roles of the series elastic element were simulated in a cyclic human heel-raise exercise. It was suggested that the storage and reutilization of elastic energy by the tendinous structures play an important role in enhancing work output and movement efficiency in many sorts of human movements.

In vivo determination of triceps surae muscle-tendon complex viscoelastic properties

Viscoelastic properties of muscles and tendons have an important influence on human motion performance. Proper determination of these properties is essential in the analysis and modelling of human motion dynamics. The purpose of our study was to develop a method for in vivo determination of the viscoelastic properties of the entire triceps surae muscle-tendon complex (MTC) including the gastrocnemius. Ten trained male subjects participated in this study. The measurement procedure consisted of two parts: soleus and Achilles tendon stiffness and viscosity were determined in the first part while the gastrocnemius stiffness and viscosity were determined in the second part. The measurement device and the procedure have been designed in such a manner that as few human body segments move as possible during the measurement. Thus, the measurement uncertainty due to the approximation of the properties of the human body segments was minimized. Triceps surae MTC viscoelastic properties of both legs were measured for each subject. There were no significant differences in viscoelastic coefficients for left and right lower extremities; however, there were noticeable differences between subjects. The soleus stiffness coefficient was greater than the gastrocnemius stiffness coefficient by 87.6 m(-1) in average. For all subjects, soleus viscosity was equal or greater than gastrocnemius viscosity. Values of viscoelastic parameters obtained by our method can be used in the analysis and modelling of human movement in situations where the knee joint is not necessarily flexed and there is coactivation of the soleus and the gastrocnemius.

In vivo determination of muscle viscoelasticity in the human leg

The purpose of this study was to examine the methodological validity of the free vibration technique for determining individual viscoelastic characteristics of the human triceps surae muscle-tendon complex (MTC) in vivo. Six subjects sat with first phalangeal joint of the forefoot on the edge of a force-plate. The special frame on the knee was loaded with weight (0-40 kg) for testing. Oscillations of the triceps surae MTC system were initiated with a hand-held hammer by tapping the weight. In order to keep the same posture, the output of the force plate was displayed on the oscilloscope and subjects were asked to maintain the beam on the oscilloscope at a particular location in relation to a reference line. The damped oscillations in conjunction with the equation of motion of a damped mass-spring model were used to calculate the viscosity of muscle (b) and the elasticity of muscle fibres and tendon (k) in each subject, considering moment arm of the ankle joint. With this arrangement, we have obtained high reproducibility in this method. The coefficient of variations (CVs) of b and k in five trials at each weight were quite small (range: 0.5-18.7% in b and 1.0-15.1% in k). There were no significant differences in viscoelastic coefficients between right and left legs. Therefore, it appears that free vibration technique, used here, is adequate in describing the viscoelastic characteristics of the triceps surae in vivo in humans.

Investigation into the relationship between the passive flexibility and active stiffness of the ankle plantar-flexor muscles

OBJECTIVE

The purpose of the study was to investigate the relationship between measurements of passive flexibility and active stiffness of the ankle plantar-flexor muscles.

DESIGN

The study was a correlation design.

BACKGROUND

Flexibility has passive and active components. Little information is available regarding the relationship of these measurements in terms of the information that they yield on the state of the muscle-tendon unit.

METHODS

Free oscillation data representing active stiffness was obtained using applied masses equivalent to 30%, 60% and 90% of the subject's maximal voluntary contraction. The angle of dorsiflexion, representing passive flexibility, was measured in standing using computer digitisation to obtain the angle.Results. Mean active stiffness values were 14280 N/m (30% maximal voluntary contraction), 22260 N/m (60% maximal voluntary contraction) and 28010 N/m (90% maximal voluntary contraction). Dorsiflexion measurement gave a mean of 34.3 degrees (S.D. 4.8). Correlation's obtained for the association between range of motion and active stiffness were r=0.01 (30% maximal voluntary contraction), r=0.09 (60% maximal voluntary contraction) and r=0.04 (90% maximal voluntary contraction). Moderate reliability coefficients of 0.71 (30% maximal voluntary contraction), 0.78 (60% maximal voluntary contraction) and 0.68 (90% maximal voluntary contraction) were obtained.

CONCLUSIONS

The results imply that measurements of passive flexibility and active stiffness of the lower leg musculature are independent measures of components of muscle-tendon unit flexibility.

RELEVANCE

Flexibility is a construct with different components of measurement. Etiological studies typically relate static flexibility measurements to injury with conflicting outcomes. This study suggests that static and active flexibility measures yield different information about the muscle tendon unit of the ankle plantar flexors, and that researchers should consider this point in the design of etiological studies.

An analysis of the sources of musculoskeletal system impedance

When antagonistic muscles co-contract, the impedance of musculoskeletal systems to applied loads is known to increase. In this paper a physiologically-based, higher-order, nonlinear antagonistic muscle-joint model is utilized to clarify the sources of impedance modulation during a variety of tasks, ranging from resisting transient loads to holding steady loads to making fast movements in unpredictable surroundings. It is shown that impedance modulation occurs automatically as a function of the specific operating ranges utilized during a given task by each of four different muscle-joint mechanical relations. The relative contribution of each relation depends on the type of task, with impedance during quasi-static conditions sensitive to muscle tension-length and sometimes joint parallel elastic properties and during dynamic tasks dominated by the series element and muscle force-velocity properties. Elimination of any of these causes a decrease in built-in biomechanical capabilities. These findings raise questions concerning past theories on stiffness-impedance modulation which appear to underestimate the role of inherent biomechanical properties.

Estimated mechanical properties of synergistic muscles involved in movements of a variety of human joints

One of the most challenging aspects of biomechanical modelling is parameter estimation. Parameter values that define the nonlinear relations within the classic Hill-based muscle model structure have been estimated for a large number of muscles involved in movements of a number of joints. The technique used to estimate these parameters is based on combining information on muscle as a material with geometrical data on muscle-joint anatomy. The resulting relations are compatible with available human experimental data and with past modelling estimates. An estimation of the relative importance of the various synergistic muscle properties during dynamic movement tasks is also provided, aided by examples of muscle load-sharing as a function of optimization criteria including measures of position error, muscle stress and neural effort.