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.     

A new method for gravity correction of dynamometer data and determining passive elastic moments at the joint

Moments measured by a dynamometer in biomechanics testing often include the gravitational moment and the passive elastic moment in addition to the moment caused by muscle contraction. Gravitational moments result from the weight of body segments and dynamometer attachment, whereas passive elastic moments are caused by the passive elastic deformation of tissues crossing the joint being assessed. Gravitational moments are a major potential source of error in dynamometer measurements and must be corrected for, a procedure often called gravity correction. While several approaches to gravity correction have been presented in the literature, they generally assume that the gravitational moment can be adequately modeled as a simple sine or cosine function. With this approach, a single passive data point may be used to specify the model, assuming that passive elastic moments are negligible at that point. A new method is presented here for the gravity correction of dynamometer data. Gravitational moment is represented using a generalized sinusoid, which is fit to passive data obtained over the entire joint range of motion. The model also explicitly accounts for the presence of passive elastic moments. The model was tested for cases of hip flexion-extension, knee flexion-extension, and ankle plantar flexion-dorsiflexion, and provided good fits in all cases.     

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.     

Three-dimensional dynamical capabilities of the human masticatory muscles

Many habitual human jaw movements are non-symmetrical. Generally, it is observed that when the lower incisors move to one side the contralateral condyle moves forwards onto the articular eminence, whereas the ipsilateral condyle stays in the mandibular fossa, moving slightly to the ipsilateral side. These jaw movements are the result of contractions of active masticatory muscles and guided by the temporomandibular joints, their ligaments and passive elastic properties of the muscles. It is not known whether the movements are primarily dependent on passive guidance, active muscle control or both. Therefore, the objective of this study was to analyse the interplay between these factors during non-symmetrical jaw movements. A six-degrees-of-freedom dynamical biomechanical model of the human masticatory system was used. The movements were not restricted to a priori defined joint axes. Jaw movement simulations were performed by unilateral activity of the muscles. The ligaments or the passive elastic properties of the muscles could be removed during these simulations. Laterodeviations conform to naturally observed ones could be generated by unilateral muscle contractions. The movement of the lower incisors was hardly affected by the absence of passive elastic muscle properties or temporomandibular ligaments. The latter, however, influenced the movement of the condyles. The movements could be understood by analysing the combination of forces and torques with respect to the centre of gravity of the lower jaw. In addition, the loading of the condyles appeared to be an important determinant for the movement. This analysis emphasizes that the movements of the jaw are primarily dependent on the orientation of the contributing muscles with respect to this centre of gravity and not on the temporomandibular ligaments or passive elastic muscle properties.     

The effects of sloped surfaces on locomotion: backward walking as a perturbation

The purpose of this study was to examine lower extremity kinetics and muscle activity during backward slope walking to clarify the relationship between joint moments and powers and muscle activity patterns observed in forward slope walking. Nine healthy volunteers walked backward on an instrumented ramp at three grades (-39% (-21 degrees ), 0% (level), +39% (+21 degrees )). EMG activity was recorded from major lower extremity muscles. Joint kinetics were obtained from kinematic and force platform data. The knee joint moment and power generation increased significantly during upslope walking; hip joint moment and power absorption increased significantly during downslope walking. When compared to data from forward slope walking, these backward walking data suggest that power requirements of a task dictate the muscle activity pattern needed to accomplish that movement. During downslope walking tasks, power absorption increased and changes in muscle activity patterns were directly related to the changes in the joint moment patterns. In contrast, during upslope walking tasks, power generation increased and changes in the muscle activity were related to the changes in the joint moments only at the 'primary' joint; at adjacent joints the changes in muscle activity were unrelated to the joint moment pattern. The 'paradoxical' changes in the muscle activity at the adjacent joints are possibly related to the activation of biarticular muscles required by the increased power generation at the primary joint. In total, these data suggest that changing power requirements at a joint impact the control of muscle activity at that and adjacent joints.     

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.     

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.     

Mechanical energy expenditure on human movement and the anthropomorphic mechanism]

Mechanical energy expenditures of the man and anthropomorphic locomotion machine during movement are compared theoretically. Sources of the mechanical energy affecting movement of human's lower extremity are modelled by 8 muscles, 3 of which are the two-joint muscles. The model of the lower extremity of anthropomorphic locomotion machine is moved by joint moments. It was shown that in the same movement the model of the human lower extremity can spend less mechanical energy than that of the model of the anthropomorphic locomotion machine. It is caused by the presence of two-joint muscles in the first model. Such an economy of mechanical energy expenditures realized by the two-joint muscle is possible at simultaneous execution of three conditions: 1) signs of the muscle powers, which are produced by that muscle at both joints, are opposite; 2) moments produced by that muscle at each of both joints have the same direction with the joint moments at these joints; 3) one-joint antagonistic muscles are not active. An expression which makes it possible to estimate the mechanical energy savings by the two-joint muscles during humans' movement was developed.     

A three-dimensional kinematic and dynamic model of the lower limb

A model describing the kinematics and dynamics of the lower limb is presented. The lower limb is modeled as a sequence of four rigid links connected by three universal rotary joints representing the hip, knee and ankle joints. Each joint is modeled as a sequence of three single axis rotational joints thus ascribing to the lower limb a total of 12 degrees of freedom. A method is described to measure the gait variables so that all nine angles can be computed based on the positions of nine markers placed on the subject during a gait study. The gait variables are then used in an iterative Newton-Euler formulation to compute the moments exerted about the axes of each joint during gait.     

Modeling the stance leg in two-dimensional analyses of sprinting: inclusion of the MTP joint affects joint kinetics

Two-dimensional analyses of sprint kinetics are commonly undertaken but often ignore the metatarsalphalangeal (MTP) joint and model the foot as a single segment. Due to the linked-segment nature of inverse dynamics analyses, the aim of this study was to investigate the effect of ignoring the MTP joint on the calculated joint kinetics at the other stance leg joints during sprinting. High-speed video and force platform data were collected from four to five trials for each of three international athletes. Resultant joint moments, powers, and net work at the stance leg joints during the first stance phase after block clearance were calculated using three different foot models. By ignoring the MTP joint, peak extensor moments at the ankle, knee, and hip were on average 35% higher (p < .05 for each athlete), 40% lower (p < .05), and 9% higher (p > .05), respectively, than those calculated with the MTP joint included. Peak ankle and knee joint powers and net work at all joints were also significantly (p < .05) different. By ignoring a genuine MTP joint plantar flexor moment, artificially high peak ankle joint moments are calculated, and these also affect the calculated joint kinetics at the knee.     

An induced acceleration index for examining joint couplings

A muscle produces moments at the joints it crosses, but these moments can also cause accelerations at joints not crossed by the muscle. This phenomenon, the acceleration of a joint caused by a muscle not crossing the joint, is referred to as induced acceleration. For a system of rigid bodies this study examines how system configuration, and segmental inertial properties dictate the potential of one joint to cause the acceleration of other joints in the system. From the equations of motion for a series of rigid bodies, an induced acceleration index (IAI) was developed. The IAI permits quantification of the relative potential of moments produced at joints in the kinematic chain to accelerate other joints in the kinematic chain. The IAI is a function of system orientation, segment lengths, and inertial properties. The IAI was used to examine the roles of the ankle and hip joints in quiet standing. The ankle joint had over 12 times the ability to accelerate the hip joint, than the hip had to accelerate the ankle joint. These results in part explain the relative merits of the two strategies predominantly used to maintain upright stance: the ankle and hip strategies. This index permits an understanding of how the induced accelerations are dependent on system configuration and inertial properties. The IAI is also useful in situations where the inertial properties of the system under investigation changes, for example due to the fitting of a new prostheses to a trans-tibial amputee.     

Elbow and wrist joint contact forces during occupational pick and place activities

A three-dimensional, mathematical model of the elbow and wrist joints, including 15 muscle units, 3 ligaments and 4 joint forces, has been developed. A new strain gauge transducer has been developed to measure functional grip forces. The device measures radial forces divided into six components and forces of up to 250N per segment can be measured with an accuracy of +/-1%. Ten normal volunteers were asked to complete four tasks representing occupational activities, during which time their grip force was monitored. Together with kinematic information from the six-camera Vicon data, the moment effect of these loads at the joints was calculated. These external moments are assumed to be balanced by the internal moments, generated by the muscles, passive soft tissue and bone contact. The effectiveness of the body's internal structures in generating joint moments was assessed by studying the geometry of a simplified model of the structures, where information about the lines of action and moment arms of muscles, tendons and ligaments is contained. The assumption of equilibrium between these external and internal joint moments allows formulation of a set of equations from which muscle and joint forces can be calculated. A two stage, linear optimisation routine minimising the overall muscle stress and the sum of the joint forces has been used to overcome the force-sharing problem. Humero-ulnar forces of up to 1600N, humero-radial forces of up to 800N and wrist joint forces of up to 2800N were found for moderate level activity. The model was validated by comparison with other studies.     

Analysis of human abnormal walking using zero moment joint: required compensatory actions

This paper presents a multi-body model which can simulate human normal and abnormal walking. The abnormal walking model has a zero moment joint, abbreviated as ZMJ, representing a diseased joint of one leg. The joint can transmit a force to adjacent connected bodies, but cannot generate a moment about the joint to control motions of the bodies. Thus the ZMJ can be considered an extreme case of the diseased joint. Compensatory actions are required to make up for the lost function at the ZMJ in different patterns of variables, such as moments at sound joints, motions of upper torso, and so on. The characteristics of the abnormal walking having the ZMJ at the hip joint became so pronounced that the model could not walk in a realistic manner, not the case in the ZMJ at the knee.     

Incorporating the length-dependent passive-force generating muscle properties of the extrinsic finger muscles into a wrist and finger biomechanical musculoskeletal model

Dynamic movement trajectories of low mass systems have been shown to be predominantly influenced by passive viscoelastic joint forces and torques compared to momentum and inertia. The hand is comprised of 27 small mass segments. Because of the influence of the extrinsic finger muscles, the passive torques about each finger joint become a complex function dependent on the posture of multiple joints of the distal upper limb. However, biomechanical models implemented for the dynamic simulation of hand movements generally don’t extend proximally to include the wrist and distal upper limb. Thus, they cannot accurately represent these complex passive torques. The purpose of this short communication is to both describe a method to incorporate the length-dependent passive properties of the extrinsic index finger muscles into a biomechanical model of the upper limb and to demonstrate their influence on combined movement of the wrist and fingers. Leveraging a unique set of experimental data, that describes the net passive torque contributed by the extrinsic finger muscles about the metacarpophalangeal joint of the index finger as a function of both metacarpophalangeal and wrist postures, we simulated the length-dependent passive properties of the extrinsic finger muscles. Dynamic forward simulations demonstrate that a model including these properties passively exhibits coordinated movement between the wrist and finger joints, mimicking tenodesis, a behavior that is absent when the length-dependent properties are removed. This work emphasizes the importance of incorporating the length-dependent properties of the extrinsic finger muscles into biomechanical models to study healthy and impaired hand movements.     

Differences in lower limb transverse plane joint moments during gait when expressed in two alternative reference frames

When comparing previous studies that have measured the three-dimensional moments acting about the lower limb joints (either external moments or opposing internal joint moments) during able-bodied adult gait, significant variation is apparent in the profiles of the reported transverse plane moments. This variation cannot be explained on the basis of adopted convention (i.e. external versus internal joint moment) or inherent variability in gait strategies. The aim of the current study was to determine whether in fact the frame in which moments are expressed has a dominant effect upon transverse plane moments and thus provides a valid explanation for the observed inconsistency in the literature. Kinematic and ground reaction force data were acquired from nine able-bodied adult subjects walking at a self-selected speed. Three-dimensional hip, knee and ankle joint moments during gait were calculated using a standard inverse dynamics approach. In addition to calculating internal joint moments, the components of the external moment occurring in the transverse plane at each of the lower limb joints were calculated to determine their independent effects. All moments were expressed in both the laboratory frame (LF) as well as the anatomical frame (AF) of the distal segment. With the exception of the ankle rotation moment in the foot AF, lower limb transverse plane joint moments during gait were found to display characteristic profiles that were consistent across subjects. Furthermore, lower limb transverse plane joint moments during gait differed when expressed in the distal segment AF compared to the LF. At the hip, the two alternative reference frames produced near reciprocal joint moment profiles. The components of the external moment revealed that the external ground reaction force moment was primarily responsible for this result. Lower limb transverse plane joint moments during gait were therefore found to be highly sensitive to a change in reference frame. These findings indicate that the different transverse plane joint moment profiles during able-bodied adult gait reported in the literature are likely to be explained on this basis.     

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.     

Segment interactions within the swing leg during unloaded and loaded running

In this study, designed to determine the effect of lower extremity inertia manipulation on joint kinetics and segment energetics during the swing phase, 15 male distance runners were filmed as they performed treadmill running (3.35 m s-1) under five load conditions: no added load and loads of 0.25 kg and 0.50 kg added to each thigh or each foot. Results of this study demonstrated that the energetics of the lower extremity movements during the swing phase of the running cycle were dominated by mechanical energy transfers between adjacent segments attributed to the joint reaction forces, which acted to redistribute mechanical energy within the system. These contributions were considerably greater than those of the net joint moments, which primarily reflected muscular generation and dissipation of mechanical energy. Lower extremity loading caused little change in the movement pattern of the swing leg. However, increases in the joint reaction forces and net moments and in the amount of work done and the energy transfer attributed to the reaction forces and moments were observed, but were limited to the joints proximal to the location of the added load. These results were consistent with the increased aerobic demand associated with increases in lower extremity inertia that have been reported elsewhere and also have implications for the manner in which the neuromuscular system controls the motion of the legs during running.     

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.     

Fatigue effects on the coordinative pattern during cycling: Kinetics and kinematics evaluation

The aim of the present study was to analyze the net joint moment distribution, joint forces and kinematics during cycling to exhaustion. Right pedal forces and lower limb kinematics of ten cyclists were measured throughout a fatigue cycling test at 100% of PO_MAX. The absolute net joint moments, resultant force and kinematics were calculated for the hip, knee and ankle joint through inverse dynamics. The contribution of each joint to the total net joint moments was computed. Decreased pedaling cadence was observed followed by a decreased ankle moment contribution to the total joint moments in the end of the test. The total absolute joint moment, and the hip and knee moments has also increased with fatigue. Resultant force was increased, while kinematics has changed in the end of the test for hip, knee and ankle joints. Reduced ankle contribution to the total absolute joint moment combined with higher ankle force and changes in kinematics has indicated a different mechanical function for this joint. Kinetics and kinematics changes observed at hip and knee joint was expected due to their function as power sources. Kinematics changes would be explained as an attempt to overcome decreased contractile properties of muscles during fatigue.     

Computer Simulation of Flagellar Movement: I. Demonstration of Stable Bend Propagation and Bend Initiation by the Sliding Filament Model

A program has been developed for digital computer simulation of the movement of a flagellar model consisting of straight segments connected by joints at which bending occurs. The program finds values for the rate of bending at each joint by solving equations which balance active, viscous, and elastic bending moments at each joint. These bending rates are then used to compute the next position of the model. Stable swimming movements, similar to real flagellar movements, can be generated routinely with a 25-segment model using 16 time steps/beat cycle. These results depend on four assumptions about internal flagellar mechanisms: (a) Bending is generated by a sliding filament process. (b) The active process is controlled locally by the curvature of the flagellum. (c) Nonlinear elastic resistances stabilize the amplitude of the movement. (d) Internal viscous resistances stabilize the wavelength of the movement and explain the relatively low sensitivity of flagellar movement to changes in external viscosity.