The relation between the resultant moments at a joint and the moments measured by an isokinetic dynamometer

Isokinetic dynamometers have frequently been used to determine in vivo properties of human skeletal muscles. In these investigations the moments recorded by the dynamometer were often (implicitly) assumed to be the same as the joint moments produced by muscles. This assumption may have contributed to the conflicting results about in vivo muscle properties of human skeletal muscles that are reported in the literature. The purpose of this paper is to present a method for calculating the resultant joint moments from the moments recorded using a Cybex II dynamometer and to determine the differences between these two moments for some typical exercise conditions. The differences between these these moments are shown to be due to (a) gravitational effects, (b) inertial effects, and (c) non-rigidity of the Cybex arm/shank-foot system. The results obtained suggest that the moments recorded using the dynamometer should not be used to derive muscle properties without taking into account the relationship between the resultant joint moments and the moments measured using an isokinetic dynamometer.     

Prestress revealed by passive co-tension at the ankle joint

This study was designed to test the assumption that elastic tissues of the ankle are prestressed, by investigating the presence of simultaneous opposite passive elastic moments and thus, passive co-tension, at the ankle joint. A prestressed two-spring model used to generate qualitative predictions of the effects of stretching the posterior elastic structures of the ankle on the net passive moment of this joint was used. Twenty-seven healthy individuals were subjected to passive evaluation of the net elastic moment of the ankle in the sagittal plane, with the knee positioned at 90°, 60°, 30° and 0° of flexion, in order to change the length of the posterior biarticular elastic structures. The placement of the knee in the more extended positions caused changes in the net passive moment as predicted by the prestressed model. The ankle position in which the net passive moment was equal to zero was shifted to more plantar flexed positions (p<0.001) and there was a global increase in ankle stiffness since both passive dorsiflexion stiffness (p≤0.037) and passive plantar flexion stiffness (p≤0.029) increased. The normalized terminal plantar flexion stiffness also increased (p≤0.047), suggesting that biarticular posterior elastic structures are pre-strained and still under tension when the ankle is maximally plantar flexed and the knee is positioned at 60° of flexion. Resting positions were indicative of equilibrium between opposite passive elastic moments. The results revealed that there is passive co-tension at the ankle, demonstrating the existence of prestress in elastic structures of this joint.     

The effect of isokinetic dynamometer deceleration phase on maximum ankle joint range of motion and plantar flexor mechanical properties tested at different angular velocities

During range of motion (max-ROM) tests performed on an isokinetic dynamometer, the mechanical delay between the button press (by the participant to signal their max-ROM) and the stopping of joint rotation resulting from system inertia induces errors in both max-ROM and maximum passive joint moment. The present study aimed to quantify these errors by comparing data when max-ROM was obtained from the joint position data, as usual (max-ROM_POS), to data where max-ROM was defined as the first point of dynamometer arm deceleration (max-ROM_ACC). Fifteen participants performed isokinetic ankle joint max-ROM tests at 5, 30 and 60° s⁻¹. Max-ROM, peak passive joint moment, end-range musculo-articular (MAC) stiffness and area under the joint moment-position curve were calculated. Greater max-ROM was observed in max-ROM_POS than max-ROM_ACC (P < 0.01) at 5 (0.2 ± 0.15%), 30 (1.8 ± 1.0%) and 60° s⁻¹ (5.9 ± 2.3%), with the greatest error at the fastest velocity. Peak passive moment was greater and end-range MAC stiffness lower in max-ROM_POS than in max-ROM_ACC only at 60° s⁻¹ (P < 0.01), whilst greater elastic energy storage was found at all velocities. Max-ROM and peak passive moment are affected by the delay between button press and eventual stopping of joint rotation in an angular velocity-dependent manner. This affects other variables calculated from the data. When high data accuracy is required, especially at fast joint rotation velocities (≥30° s⁻¹), max-ROM (and associated measures calculated from joint moment data) should be taken at the point of first change in acceleration rather than at the dynamometer’s ultimate joint position.     

An EMG-driven musculoskeletal model to estimate muscle forces and knee joint moments in vivo

This paper examined if an electromyography (EMG) driven musculoskeletal model of the human knee could be used to predict knee moments, calculated using inverse dynamics, across a varied range of dynamic contractile conditions. Muscle-tendon lengths and moment arms of 13 muscles crossing the knee joint were determined from joint kinematics using a three-dimensional anatomical model of the lower limb. Muscle activation was determined using a second-order discrete non-linear model using rectified and low-pass filtered EMG as input. A modified Hill-type muscle model was used to calculate individual muscle forces using activation and muscle tendon lengths as inputs. The model was calibrated to six individuals by altering a set of physiologically based parameters using mathematical optimisation to match the net flexion/extension (FE) muscle moment with those measured by inverse dynamics. The model was calibrated for each subject using 5 different tasks, including passive and active FE in an isokinetic dynamometer, running, and cutting manoeuvres recorded using three-dimensional motion analysis. Once calibrated, the model was used to predict the FE moments, estimated via inverse dynamics, from over 200 isokinetic dynamometer, running and sidestepping tasks. The inverse dynamics joint moments were predicted with an average R(2) of 0.91 and mean residual error of approximately 12 Nm. A re-calibration of only the EMG-to-activation parameters revealed FE moments prediction across weeks of similar accuracy. Changing the muscle model to one that is more physiologically correct produced better predictions. The modelling method presented represents a good way to estimate in vivo muscle forces during movement tasks.     

The role of intersegmental dynamics during rapid limb oscillations

The interactive dynamic effects of muscular, inertial and gravitational moments on rapid, multi-segmented limb oscillations were studied. Using three-segment, rigid-body equations of motion, hip, knee and ankle intersegmental dynamics were calculated for the steady-state cycles of the paw-shake response in adult spinal cats. Hindlimb trajectories were filmed to obtain segmental kinematics, and myopotentials of flexors and extensors at each of the three joints were recorded synchronously with the ciné film. The segmental oscillations that emerged during the paw-shake response were a consequence of an interplay between active and passive musculotendinous forces, inertial forces, and gravity. During steady-state oscillations, the amplitudes of joint excursions, peak angular velocities, and peak angular accelerations increased monotonically and significantly in magnitude from the proximal joint (hip) to the most distal joint (ankle). In contrast to these kinematic relationships, the maximal values of net moments at the hip and knee were equal in magnitude, but of significantly lower magnitude than the large net moment at the ankle joint. At both the ankle and the knee, the flexor and extensor muscle moments were equal, but at the hip the magnitude of the peak flexor muscle moment was significantly greater than the extensor muscle moment. Muscle moments at the hip not only acted to counterbalance accelerations of the more distal segments, but also acted to maintain the postural orientation of the hindlimb. Large muscle moments at the knee functioned to counterbalance the large inertial moments generated by the large angular accelerations of the paw. At the ankle, the muscle moments dominated the generation of the paw accelerations. At the ankle and the knee, muscle moments controlled limb dynamics by slowing and reversing joint motions, and the active muscle forces contributing to ankle and knee moments were derived from lengthening of active musculotendinous units. In contrast to the more distal joints, the active muscles crossing the hip predominantly shortened as a result of the interplay among inertial forces and gravitational moments. The muscle function and kinetic data explain key features of the complex interactions that occur between central control mechanisms and multi-segmented, oscillating limb segments during the paw-shake response.     

The passive elastic moment at the hip

The passive elastic moment at the hip was measured in normal male subjects in situ. The influence of two joint muscles crossing the hip was evaluated by performing hip moment measurements over a continuous range of hip angles and at prescribed knee angles. The experimentally acquired data was fitted by exponential functions which separately modeled the moment contribution of tissues deformed by hip flexion and extension. The results of the investigation are discussed with regard to the possible role of the passive joint moments as an energy storage and release mechanism during human walking.     

Identification of passive elastic joint moments in the lower extremities.

Musculotendon actuators produce active and passive moments at the joints they span. Due to the existence of bi-articular muscles, the passive elastic joint moments are influenced by the angular positions of adjacent joints. To obtain quantitative information about this passive elastic coupling between lower limb joints, we examined the passive elastic joint properties of the hip, knee, and ankle joint of ten healthy subjects. Passive elastic joint moments were found to considerably depend on the adjacent joint angles. We present a simple mathematical model that describes these properties on the basis of a double-exponential expression. The model can be implemented in biomechanical models of the lower extremities, which are generally used for the simulation of multi-joint movements such as standing-up, walking, running, or jumping.     

Joint moments and contact forces in the foot during walking

The net force and moment of a joint have been widely used to understand joint disease in the foot. Meanwhile, it does not reflect the physiological forces on muscles and contact surfaces. The objective of the study is to estimate active moments by muscles, passive moments by connective tissues and joint contact forces in the foot joints during walking. Joint kinematics and external forces of ten healthy subjects (all males, 24.7 ± 1.2 years) were acquired during walking. The data were entered into the five-segment musculoskeletal foot model to calculate muscle forces and joint contact forces of the foot joints using an inverse dynamics-based optimization. Joint reaction forces and active, passive and net moments of each joint were calculated from muscle and ligament forces. The maximum joint reaction forces were 8.72, 4.31, 2.65, and 3.41 body weight (BW) for the ankle, Chopart’s, Lisfranc and metatarsophalangeal joints, respectively. Active and passive moments along with net moments were also obtained. The maximum net moments were 8.6, 8.4, 5.4 and 0.8%BW∙HT, respectively. While the trend of net moment was very similar between the four joints, the magnitudes and directions of the active and passive moments varied between joints. The active and passive moments during walking could reveal the roles of muscles and ligaments in each of the foot joints, which was not obvious in the net moment. This method may help narrow down the source of joint problems if applied to clinical studies.     

Elastic properties of an intact and ACL-ruptured knee joint: measurement, mathematical modelling, and haptic rendering

An analytical, dynamic model of the human knee joint has been developed to simulate the unloaded knee joint behaviour in 6 degrees of freedom. It is based on extensive robot-based measurements of the elastic properties of a human cadaver knee joint. The measured data are compared with data from the literature to ensure that a proper database for modelling is used. The analytical modelling of the passive elastic joint properties is done with Local Linear Model Trees. The deduced knee joint model incorporates passive elastic properties of the internal knee joint structures, passive elastic muscle forces, damping forces, gravitational forces, and external forces. There are two sets of parameters, one simulating the movement of the intact knee joint, and a second simulating the knee joint with ruptured anterior cruciate ligament. The dynamic model can be easily processed in real-time. It is implemented in the haptic display of the Munich Knee Joint Simulator (MKS), which enables a person to move a plastic leg driven by a robot manipulator and feel the simulated knee joint force. Orthopaedic physicians judged the performance of the dynamic knee joint model by executing physical knee joint tests at the MKS.     

Muscle forces predicted using optimization methods are coordinate system dependent

Optimization methods are widely used to predict in vivo muscle forces in musculoskeletal joints. Moment equilibrium at the joint center (usually chosen as the origin of the joint coordinate system) has been used as a constraint condition for optimization procedures and the joint reaction moments were assumed zero. This study, through the use of a three-dimensional elbow model, investigated the effect of coordinate system origin (joint center) location on muscle forces predicted using a nonlinear static optimization method. The results demonstrated that moving the origin of the coordinate system medially and laterally along the flexion-extension axis caused dramatic variations in the predicted muscle forces. For example, moving the origin of the coordinate system from a position 5mm medial to 5mm lateral of the geometric elbow center caused the predicted biceps force to vary from 12% to 46% and the brachialis force to vary from 80% to 34% of the total muscle loading. The joint reaction force reduced by 24% with this medial to lateral variation of the coordinate system origin location. This data revealed that the muscle forces predicted using the optimization method are sensitive to the coordinate system origin location due to the zero joint reaction moment assumption in the moment constraint condition. For accurate prediction of muscle load distributions using optimization methods, it is necessary to determine the accurate coordinate system origin location where the condition of a zero joint reaction moment is satisfied.     

Direct and indirect effects of joint torque inputs during an induced speed analysis of a swinging motion

This study proposed a method to quantify direct and indirect effects of the joint torque inputs in the speed-generating mechanism of a swinging motion. Linear and angular accelerations of all segments within a multi-linked system can be expressed as the sum of contributions from a joint torque term, gravitational force term and motion-dependent term (MDT), where the MDT is a nonlinear term consisting of centrifugal force, Coriolis force and gyroscopic effect moment components. Direct effects result from angular accelerations induced by a joint torque at a given instant, whereas indirect effects arise through the MDT induced by joint torques exerted in the past. These two effects were quantified for the kicking-side leg during a rugby place kick. The MDT was the largest contributor to the foot centre of gravity (CG)’s speed at ball contact. Of the factors responsible for generating the MDT, the direct and indirect effects of the hip flexion-extension torque during both the flight phase (from the final kicking foot take-off to support foot contact) and the subsequent support phase (from support foot contact to ball contact) were important contributors to the foot CG’s speed at ball contact. The indirect effect of the ankle plantar-dorsal flexion torque and the direct effect of the knee flexion-extension torque during the support phase showed the largest positive and negative contributions to the foot CG’s speed at ball contact, respectively. The proposed method allows the identification of which individual joint torque axes are crucial and the timings of joint torque exertion that are used to generate a high speed of the distal point of a multi-linked system.     

Three-dimensional knee joint loading during seated cycling.

The hypothesis which motivated the work reported in this article was that neglecting pure moments developed between the foot and pedal during cycling leads to a substantial error in computing axial and varus/valgus moments at the knee. To test this hypothesis, a mathematical procedure was developed for computing the three-dimensional knee loads using three-dimensional pedal forces and moments. In addition to data from a six-load-component pedal dynamometer, the model used pedal position and orientation and knee position in the frontal plane to determine the knee joint loads. Experimental data were collected from the right leg of 11 male subjects during steady-state cycling at 90 rpm and 225 W. The mean peak varus knee moment calculated was 15.3 N m and the mean peak valgus knee moment was 11.2 N m. Neglecting the pedal moment about the anterior/posterior axis resulted in an average absolute error of 2.6 N m and a maximum absolute error of 4.0 N m in the varus/valgus knee moment. The mean peak internal and external axial knee moments were 2.8 N m and 2.3 N m, respectively. The average and maximum absolute errors in the axial knee moment for not including the moment about an axis normal to the pedal were found to be 2.6 N m and 5.0 N m, respectively. The results strongly support the use of three-dimensional pedal loads in the computation of knee joint moments out of the sagittal plane.     

Identification of knee joint models for varus-valgus and internal-external rotations: snow skiing experiments

Sprains at the knee are the most frequent of the severe injuries occurring during alpine snow skiing. This paper discusses the development of analytical models describing rotations across the knee joint caused by varus-valgus and internal-external moments applied at the foot during skiing. Identification of an ARMAX model requires simultaneous measurements of the rotations across the knee and the moments at the foot during skiing. As the models only relate the measured input (moment) and output (rotation) data, they also identify components of apparent rotation resulting from imperfect fixation of the rotation measuring instrument on the test subject and resulting from other inputs. The models identified for all subjects are of order four or five for both varus-valgus and internal-external rotation, and they describe modes with oscillatory and exponentially decaying components. Application of the models to prediction of rotation across the knee from the measured moment at the foot is illustrated by example. A new, and virtually mechanically uncoupled, six degrees-of-freedom, strain gauge dynamometer is developed to record the moments at the foot during skiing. The concept of the dynamometer design has general application.     

Mechanical correction of dynamometer moment for the effects of segment motion during isometric knee-extension tests

The purpose of this study was to determine the effect of dynamometer and joint axis misalignment on measured isometric knee-extension moments using inverse dynamics based on the actual joint kinematic information derived from the real-time X-ray video and to compare the errors when the moments were calculated using measurements from external anatomical surface markers or obtained from the isokinetic dynamometer. Six healthy males participated in this study. They performed isometric contractions at 90° and 20° of knee flexion, gradually increasing to maximum effort. For the calculation of the actual knee-joint moment and the joint moment relative to the knee-joint center, determined using the external marker, two free body diagrams were used of the Cybex arm and the lower leg segment system. In the first free body diagram, the mean center of the circular profiles of the femoral epicondyles was used as the knee-joint center, whereas in the second diagram, the joint center was assumed to coincide with the external marker. Then, the calculated knee-joint moments were compared with those measured by the dynamometer. The results indicate that 1) the actual knee-joint moment was different from the dynamometer recorded moment (difference ranged between 1.9% and 4.3%) and the moment calculated using the skin marker (difference ranged between 2.5% and 3%), and 2) during isometric knee extension, the internal knee angle changed significantly from rest to the maximum contraction state by about 19°. Therefore, these differences cannot be neglected if the moment-knee-joint angle relationship or the muscle mechanical properties, such as length-tension relationship, need to be determined.     

Effect of contraction form and contraction velocity on the differences between resultant and measured ankle joint moments

During a maximal isometric plantar flexion effort the moment measured at the dynamometer differs from the resultant ankle joint moment. The present study investigated the effects of contraction form and contraction velocity during isokinetic plantar/dorsal flexion efforts on the differences between resultant and measured moments due to the misalignment between ankle and dynamometer axes. Eleven male subjects (age: 31+/-6 years, mass: 80.6+/-9.6 kg, height: 178.4+/-7.4 cm) participated in this study. All subjects performed isometric-shortening-stretch-isometric contractions induced by electrical stimulation at three different angular velocities (25 degrees /s, 50 degrees /s and 100 degrees /s) on a customised dynamometer. The kinematics of the leg were recorded using the vicon 624 system with eight cameras operating at 250 Hz. The resultant moments at the ankle joint were calculated through inverse dynamics. The relative differences between resultant and measured ankle joint moments due to axis misalignment were fairly similar in all phases of the isometric-shortening-stretch-isometric contraction (in average 5-9% of the measured moment). Furthermore these findings were independent of the contraction velocity. During dynamic plantar/dorsal flexion contractions the differences between measured and resultant joint moment are high enough to influence conclusions regarding the mechanical response of ankle extensor muscles. However the relative differences were not increased during dynamic contractions as compared to isometric contractions.     

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

The purpose of this study was to develop a method for identifying subject-specific passive elastic joint moment-angle relationships in the lower extremity, which could subsequently be used to estimate passive contributions to joint kinetics during gait. Twenty healthy young adults participated in the study. Subjects were positioned side-lying with their dominant limb supported on a table via low-friction carts. A physical therapist slowly manipulated the limb through full sagittal hip, knee, and ankle ranges of motion using two hand-held 3D load cells. Lower extremity kinematics, measured with a passive marker motion capture system, and load cell readings were used to compute joint angles and associated passive joint moments. We formulated a passive joint moment-angle model that included eight exponential functions to account for forces generated via the passive stretch of uni-articular structures and bi-articular muscles. Model parameters were estimated for individual subjects by minimizing the sum of squared errors between model predicted and experimentally measured moments. The model predictions closely replicated measured joint moments with average root-mean-squared errors of 2.5, 1.4, and 0.7 Nm about the hip, knee, and ankle respectively. We show that the models can be coupled with gait kinematics to estimate passive joint moments during walking. Passive hip moments were substantial from terminal stance through initial swing, with energy being stored as the hip extended and subsequently returned during pre- and initial swing. We conclude that the proposed methodology could provide quantitative insights into the potentially important role that passive mechanisms play in both normal and abnormal gait.     

On the relation between joint moments and pedalling rates at constant power in bicycling

Joint moments are of interest because they bear some relation to muscular effort and hence rider performance. The general objective of this study is to explore the relation between joint moments and pedalling rate (i.e. cadence). Joint moments are computed by modelling the leg-bicycle system as a five-bar linkage constrained to plane motion. Using dynamometer pedal force data and potentiometer crank and pedal position data, system equations are solved on a computer to produce moments at the ankle, knee and hip joints. Cadence and pedal forces are varied inversely to maintain constant power. Results indicate that average joint moments vary considerably with changes in cadence. Both hip and knee joints show an average moment which is minimum near 105 rotations min-1 for cruising cycling. It appears that an optimum rotations min-1 can be determined from a mechanical approach for any given power level and bicycle-rider geometry.     

Estimation of passive ankle joint moment during standing and walking

This study estimated the passive ankle joint moment during standing and walking initiation and its contribution to total ankle joint moment during that time. The decrement of passive joint moment due to muscle fascicle shortening upon contraction was taken into account. Muscle fascicle length in the medial gastrocnemius, which was assumed to represent muscle fascicle length in plantarflexors, was measured using ultrasonography during standing, walking initiation, and cyclical slow passive ankle joint motion. Total ankle joint moment during standing and walking initiation was calculated from ground reaction forces and joint kinematics. Passive ankle joint moment during the cyclical ankle joint motion was measured via a dynamometer. Passive ankle joint moment during standing and at the time (Tp) when the MG muscle-tendon complex length was longest in the stance phase during walking initiation were 2.3 and 5.4 Nm, respectively. The muscle fascicle shortened by 2.9 mm during standing compared with the length at rest, which decreased the contribution of passive joint moment from 19.9% to 17.4%. The muscle fascicle shortened by 4.3 mm at Tp compared with the length at rest, which decreased the contribution of passive joint moment from 8.0% to 5.8%. These findings suggest that (a) passive ankle joint moment plays an important role during standing and walking initiation even in view of the decrement of passive joint moment due to muscle fascicle shortening upon muscle contraction, and (b) muscle fascicle shortening upon muscle contraction must be taken into account when estimating passive joint moment during movements.     

The demands of stair descent relative to maximum capacities in elderly and young adults.

In this study, we aimed to establish the joint moment and joint range of motion requirements of stair descent and the demands relative to maximal capacities in elderly and young adults. Participants descended a custom-built standard dimension four-step staircase, at their self-selected speed in a step-over manner. Kinetic data were acquired from force platforms embedded into each of the steps and into the floor at the base of the stairs. A motion analysis system was used to acquire kinematic data and joint moments were calculated using the kinematic and kinetic data. Maximum capacities (joint moment and joint range of motion) were assessed using a dynamometer. During stair descent the elderly generated lower absolute ankle joint moments than the young, which enabled them to operate at a similar relative proportion of their maximal capacity compared to young adults (75%). The knee joint moments during stair descent were similar between groups, but the elderly operated at a higher proportion of their maximal capacity (elderly: 42%; young: 30%). Ankle plantarflexion-dorsiflexion angle changes were similar between groups, which meant that the elderly operated at a higher proportion of their maximal assisted dorsiflexion angle. These results indicate that the elderly redistribute the joint moments in order to maintain the task demands within 'safe' limits.     

Isokinetic plantar flexion: experimental results and model calculations

In isokinetic experiments on human subjects, conducted to determine moments that can be exerted about a joint at different angular velocities, joint rotation starts as soon as the moment increases above the resting level. This contraction history differs from the one in experiments on isolated muscle, where the force is allowed to increase to an isometric level before shortening is initiated. The purpose of the present study was to determine the influence of contraction history on plantar flexing moments found during maximal voluntary plantar flexion on an isokinetic dynamometer. In ten subjects, plantar flexing moments were measured as a function of ankle angle at different angular velocities. They were also calculated using a model of the muscle-tendon complex of the human triceps surae. The model incorporates elastic tendinous tissue in series with muscle fibers. The input of the model consists of time histories of active state (the force generating capacity of contractile elements) and shortening velocity of the muscle-tendon complex. Different time courses of active state were offered at fixed length of the muscle-tendon complex. The time course yielding a close match between the calculated rise of plantar flexing moment and the rise measured during fixed angle contractions was used to calculate moment-angle curves for isokinetic plantar flexion. The active state value reached when a peak occurred in calculated moment-angle curves was found to be lower if the angular velocity was made higher. Comparing measured and calculated results, it was concluded that moment-angular velocity diagrams determined in studies of isokinetic plantar flexion in human subjects reflect not only the influence of shortening velocity of contractile elements on the force which can be produced by plantar flexors.