On the derivation of a tensor to calculate six degree-of-freedom,musculotendon joint stiffness: Implications for stability and impedance analyses

Major joints, such as the knee, shoulder, and spine, can buckle along the translational degrees-of-freedom (DoF), causing injury to ligaments and other passive tissues. Despite this, stability and impedance analyses have focused primarily on the rotational DoF. As such, mathematical models quantifying musculotendon translational stiffnesses remain limited and, to our knowledge, there are no published works that explicitly describes the interactions between DoF. Using an energy approach, we derived a six DoF stiffness tensor and provided the necessary equations needed to quantify the musculotendon stiffness of any joint. Using a knee model, we then compared the derived stiffness tensor against two commonly used measures: one that excludes translational DoF and another that excludes interactions between DoF. We found that both of these measures had large over-estimations of stiffness, particularly for the rotational DoF, compared to our derived tensor. These findings indicate that previous analyses may have found rotational DoF to be stable when they were unstable.     

Proximal versus distal control of two-joint planar reaching movements in the presence of neuromuscular noise

Determining how the human nervous system contends with neuro-motor noise is vital to understanding how humans achieve accurate goal-directed movements. Experimentally, people learning skilled tasks tend to reduce variability in distal joint movements more than in proximal joint movements. This suggests that they might be imposing greater control over distal joints than proximal joints. However, the reasons for this remain unclear, largely because it is not experimentally possible to directly manipulate either the noise or the control at each joint independently. Therefore, this study used a 2 degree-of-freedom torque driven arm model to determine how different combinations of noise and/or control independently applied at each joint affected the reaching accuracy and the total work required to make the movement. Signal-dependent noise was simultaneously and independently added to the shoulder and elbow torques to induce endpoint errors during planar reaching. Feedback control was then applied, independently and jointly, at each joint to reduce endpoint error due to the added neuromuscular noise. Movement direction and the inertia distribution along the arm were varied to quantify how these biomechanical variations affected the system performance. Endpoint error and total net work were computed as dependent measures. When each joint was independently subjected to noise in the absence of control, endpoint errors were more sensitive to distal (elbow) noise than to proximal (shoulder) noise for nearly all combinations of reaching direction and inertia ratio. The effects of distal noise on endpoint errors were more pronounced when inertia was distributed more toward the forearm. In contrast, the total net work decreased as mass was shifted to the upper arm for reaching movements in all directions. When noise was present at both joints and joint control was implemented, controlling the distal joint alone reduced endpoint errors more than controlling the proximal joint alone for nearly all combinations of reaching direction and inertia ratio. Applying control only at the distal joint was more effective at reducing endpoint errors when more of the mass was more proximally distributed. Likewise, controlling the distal joint alone required less total net work than controlling the proximal joint alone for nearly all combinations of reaching distance and inertia ratio. It is more efficient to reduce endpoint error and energetic cost by selectively applying control to reduce variability in the distal joint than the proximal joint. The reasons for this arise from the biomechanical configuration of the arm itself.     

Activation of the Shoulder Belt and Shoulder Muscles of Humans Related to Different Rates of Generation of Two-Joint Efforts by the Forearm

We studied coordination of central motor commands (CMCs) coming to the muscles that flex and extend the shoulder and elbow joints in the course of generation of voluntary isometric efforts of different directions by the forearm. Dependences of the characteristics of these commands on the direction of the effort and rate of its generation were analyzed. Amplitudes of rectified and averaged EMGs recorded from a number of shoulder belt and shoulder muscles were considered correlates of the CMC intensity. The development of the effort of a given direction and rate of rise was realized in the horizontal-plane operational space; the arm position corresponded to the 30 deg angle in the shoulder joint (external angle with respect to the frontal plane) and 90 deg angle in the elbow joint. We plotted sector diagrams of the relative changes in the level of dynamic and stationary phases of EMG activity of the studied muscles for the entire set of directions of the efforts generated with different rates of rise. In the course of formation of rapid two-joint isometric efforts, realization of nonsynergic motor tasks (extension of one joint and flexion of another one, and vice versa) required significant activation of muscles of different functional directions for both joints. Time organization of EMG activity of extensors and flexors of the shoulder and elbow joints related to the maximum and relatively rapid generation of the effort (rise time 0.12 to 0.13 and 0.25 sec, respectively) was rather complex and included dynamic and stationary phases. With these time parameters of generation of the efforts (both flexion and extension), the appearance at the stationary effort of 40 N was controlled based on coordinated interaction of dynamic phases of the activation of agonistic and antagonistic muscles. It is concluded that CMCs coming to extensors and flexors of both joints upon generation of rapid isometric efforts are rather similar in their parameters to those under conditions of realization of the forearm movements in the space in an isotonic mode.     

A method for estimating three-dimensional human arm movement with two electromagnetic sensors

Measurement of upper-limb movements is important in various domains. In this article, an upper-limb three-dimensional movement recording technique is proposed based on only two electromagnetic sensors. Two joints are considered with a total of seven degrees of freedom (DoF; three translations and four rotations). The chosen sequence of joint rotations is compliant with ISB recommendations: the shoulder is modelled with a ball and socket joint with three DoF and the elbow with a one DoF revolute joint. This article is focused on the procedure used to calibrate and sense the upper-limb movements from the raw data coming from the flock of birds sensors. The principle of the method is to define the centre of the wrist, elbow and shoulder joints in the frame of the adequate sensor. This operation is done by performing calibration gestures. Results are proposed and commented.     

A method for estimating three-dimensional human arm movement with two electromagnetic sensors

Measurement of upper-limb movements is important in various domains. In this article, an upper-limb three-dimensional movement recording technique is proposed based on only two electromagnetic sensors. Two joints are considered with a total of seven degrees of freedom (DoF; three translations and four rotations). The chosen sequence of joint rotations is compliant with ISB recommendations: the shoulder is modelled with a ball and socket joint with three DoF and the elbow with a one DoF revolute joint. This article is focused on the procedure used to calibrate and sense the upper-limb movements from the raw data coming from the flock of birds sensors. The principle of the method is to define the centre of the wrist, elbow and shoulder joints in the frame of the adequate sensor. This operation is done by performing calibration gestures. Results are proposed and commented.     

An experimental and analytic study of the dynamic properties of the human leg

Certain problems in the dynamics of the human body are characterized by large displacements of the parts of the body compared to the deformations of the tissues themselves. In such problems, it is convenient to think of the human body as a chain of rigid links, representing the anatomical segments, with joints between the rigid links representing the articulations of the human body.

Skeletal muscles are capable of creating torques at the joints of the body. The joint torques of the rigid link model should portray the static strength of skeletal muscle, the degradation of muscle strength with rate of shortening, the feedback control of the stretch reflex, and the viscoelastic properties of the muscles, tendons, and joint capsules.

In this study a sinusoidal test is performed upon the knee joints of nine subjects. The increment of knee moment required to flex and extend the knee slightly for various conditions of knee angle, knee angular velocity, and steady knee moment is measured. The hip angle is maintained constant. After the effects of leg inertia are removed, the resulting data are shown to obey a Maxwell fluid model in which the model coefficients depend upon the absolute value of the knee moment.     

Some principles of ligament function, with examples from the tarsal joints of the sheep (Ovis aries)

The effects of ligaments, in limiting or controlling movement, depend on the positions of their attachments relative to the axes of joints. Such effects are explored in a theoretical section, which considers ligaments that cross a single, congruent hinge joint; ligaments that cross two congruent hinge joints; and non-congruent hinge joints controlled by crossed ligaments. The principles derived in the theoretical section are used to explain the complex mechanism of the sheep tarsal joints.     

Trunk muscle activation and associated lumbar spine joint shear forces under different levels of external forward force applied to the trunk.

High anterior intervertebral shear loads could cause low back injuries and therefore the neuromuscular system may actively counteract these forces. This study investigated whether, under constant moment loading relative to L3L4, an increased externally applied forward force on the trunk results in a shift in muscle activation towards the use of muscles with more backward directed lines of action, thereby reducing the increase in total joint shear force. Twelve participants isometrically resisted forward forces, applied at several locations on the trunk, while moments were held constant relative to L3L4. Surface EMG and lumbar curvature were measured, and an EMG-driven muscle model was used to calculate compression and shear forces at all lumbar intervertebral joints. Larger externally applied forward forces resulted in a flattening of the lumbar lordosis and a slightly more backward directed muscle force. Furthermore, the overall muscle activation increased. At the T12L1 to L3L4 joint, resulting joint shear forces remained small (less than 200N) because the average muscle force pulled backward relative to those joints. However, at the L5S1 joint the average muscle force pulled the trunk forward so that the increase in muscle force with increasing externally applied forward force caused a further rise in shear force (by 102.1N, SD=104.0N), resulting in a joint shear force of 1080.1N (SD=150.4N) at 50Nm moment loading. It is concluded that the response of the neuromuscular system to shear force challenges tends to increase rather than reduce the shear loading at the lumbar joint that is subjected to the highest shear forces.     

Crouched postures reduce the capacity of muscles to extend the hip and knee during the single-limb stance phase of gait

Many children with cerebral palsy walk in a crouch gait that progressively worsens over time, decreasing walking efficiency and leading to joint degeneration. This study examined the effect of crouched postures on the capacity of muscles to extend the hip and knee joints and the joint flexions induced by gravity during the single-limb stance phase of gait. We first characterized representative mild, moderate, and severe crouch gait kinematics based on a large group of subjects with cerebral palsy (N=316). We then used a three-dimensional model of the musculoskeletal system and its associated equations of motion to determine the effect of these crouched gait postures on (1) the capacity of individual muscles to extend the hip and knee joints, which we defined as the angular accelerations of the joints, towards extension, that resulted from applying a 1N muscle force to the model, and (2) the angular acceleration of the joints induced by gravity. Our analysis showed that the capacities of almost all the major hip and knee extensors were markedly reduced in a crouched gait posture, with the exception of the hamstrings muscle group, whose extension capacity was maintained in a crouched posture. Crouch gait also increased the flexion accelerations induced by gravity at the hip and knee throughout single-limb stance. These findings help explain the increased energy requirements and progressive nature of crouch gait in patients with cerebral palsy.     

Extrinsic flexor muscles generate concurrent flexion of all three finger joints

The role of the forearm (extrinsic) finger flexor muscles in initiating rotation of the metacarpophalangeal (MCP) joint and in coordinating flexion at the MCP, the proximal interphalangeal (PIP), and distal interphalangeal (DIP) joints remains a matter of some debate. To address the biomechanical feasibility of the extrinsic flexors performing these actions, a computer simulation of the index finger was created. The model consisted of a planar open-link chain comprised of three revolute joints and four links, driven by the change in length of the flexor muscles. Passive joint characteristics, included in the model, were obtained from system identification experiments involving the application of angular perturbations to the joint of interest. Simulation results reveal that in the absence of passive joint torque, shortening of the extrinsic flexors results in PIP flexion (80°), but DIP (8°) and MCP (7°) joint extension. The inclusion of normal physiological levels of passive joint torque, however, results in simultaneous flexion of all three joints (63° for DIP, 75° for PIP, and 43° for MCP). Applicability of the simulation results was confirmed by recording finger motion produced by electrical stimulation of the extrinsic flexor muscles for the index finger. These findings support the view that the extrinsic flexor muscles can initiate MCP flexion, and produce simultaneous motion at the MCP, PIP, and DIP joints.     

Individual muscle contributions to the axial knee joint contact force during normal walking

Muscles are significant contributors to the high joint forces developed in the knee during human walking. Not only do muscles contribute to the knee joint forces by acting to compress the joint, but they also develop joint forces indirectly through their contributions to the ground reaction forces via dynamic coupling. Thus, muscles can have significant contributions to forces at joints they do not span. However, few studies have investigated how the major lower-limb muscles contribute to the knee joint contact forces during walking. The goal of this study was to use a muscle-actuated forward dynamics simulation of walking to identify how individual muscles contribute to the axial tibio-femoral joint force. The simulation results showed that the vastii muscles are the primary contributors to the axial joint force in early stance while the gastrocnemius is the primary contributor in late stance. The tibio-femoral joint force generated by these muscles was at times greater than the muscle forces themselves. Muscles that do not cross the knee joint (e.g., the gluteus maximus and soleus) also have significant contributions to the tibio-femoral joint force through their contributions to the ground reaction forces. Further, small changes in walking kinematics (e.g., knee flexion angle) can have a significant effect on the magnitude of the knee joint forces. Thus, altering walking mechanics and muscle coordination patterns to utilize muscle groups that perform the same biomechanical function, yet contribute less to the knee joint forces may be an effective way to reduce knee joint loading during walking.     

Interaction against different environmental dynamics during a leg extension task is controlled by temporal rather than amplitude scaling of muscular activity

Force exertion against different mechanical environments can affect motor control strategies in order to account for the altered environmental dynamics and to maintain the ability to produce force. Here, we investigated the change of muscular activity of selected muscles of the lower extremities while the participants interacted with an external mechanical device of variable stability. Twenty-five healthy participants exerted force against the device by performing a unilateral ballistic leg extension task under 1 or 3 degrees of freedom (DoF). Directional force data and electromyographic responses from four leg muscles (TA, VM, GM, PL) were recorded. Muscle responses to the altered experimental conditions were analyzed by calculating time to peak electrical activity (TTP), peak electrical activity (PEA), slope of EMG-signal and muscle activity. It was found that neuromuscular system adjustments to the task are expressed mainly by temporal (TTP) rather than amplitude (PEA) scaling of muscular activity. This change was specific for the investigated muscles. Moreover, a selective increase of muscle activity occurred while increasing external DoF. This scheme was accompanied by a significant reduction of applicable force against the device in the unstable 3 DoF condition. The findings suggest that orchestration of movement control is linked to environmental dynamics also affecting the ability to produce force under dynamic conditions. The adjustments of the neuromuscular system are rather temporal in nature being consistent with the impulse timing hypothesis of motor control.     

Inter-joint coupling effects on muscle contributions to endpoint force and acceleration in a musculoskeletal model of the cat hindlimb

The biomechanical principles underlying the organization of muscle activation patterns during standing balance are poorly understood. The goal of this study was to understand the influence of biomechanical inter-joint coupling on endpoint forces and accelerations induced by the activation of individual muscles during postural tasks. We calculated induced endpoint forces and accelerations of 31 muscles in a 7 degree-of-freedom, three-dimensional model of the cat hindlimb. To test the effects of inter-joint coupling, we systematically immobilized the joints (excluded kinematic degrees of freedom) and evaluated how the endpoint force and acceleration directions changed for each muscle in 7 different conditions. We hypothesized that altered inter-joint coupling due to joint immobilization of remote joints would substantially change the induced directions of endpoint force and acceleration of individual muscles. Our results show that for most muscles crossing the knee or the hip, joint immobilization altered the endpoint force or acceleration direction by more than 90° in the dorsal and sagittal planes. Induced endpoint forces were typically consistent with behaviorally observed forces only when the ankle was immobilized. We then activated a proximal muscle simultaneous with an ankle torque of varying magnitude, which demonstrated that the resulting endpoint force or acceleration direction is modulated by the magnitude of the ankle torque. We argue that this simple manipulation can lend insight into the functional effects of co-activating muscles. We conclude that inter-joint coupling may be an essential biomechanical principle underlying the coordination of proximal and distal muscles to produce functional endpoint actions during motor tasks.     

An equation to calculate individual muscle contributions to joint stability

The purpose of the current paper was to use the energy approach to develop a simplified equation for quantifying individual muscle contributions to mechanical stability about all three axes of a particular joint. Specific examples are provided for muscles acting about the lumbar spine's L4/L5 joint. The stability equation requires input of: (1) origin and insertion coordinates, relative to the joint of interest, (2) muscle force, and (3) muscle stiffness. The muscle force must be derived from a biomechanical analysis that first results in static equilibrium about all axes being studied. The equation can also accommodate muscles with nodes that change the line of action, with respect to a particular joint, as it passes from the origin to insertion. The results from this equation were compared to those from a Moment approach using more than two million simulated muscles with three-dimensional orientations. The differences between approaches were negligible in all cases. The primary advantage of the current method is that it is very easy to implement into any 2D or 3D biomechanical model of any joint, or system of joints. Furthermore, this approach will be useful in dissecting total joint stability into the individual contributions of each muscle for various systems, joints, postures and recruitment patterns.     

Effect of landing height on frontal plane kinematics, kinetics and energy dissipation at lower extremity joints

Lack of the necessary magnitude of energy dissipation by lower extremity joint muscles may be implicated in elevated impact stresses present during landing from greater heights. These increased stresses are experienced by supporting tissues like cartilage, ligaments and bones, thus aggravating injury risk. This study sought to investigate frontal plane kinematics, kinetics and energetics of lower extremity joints during landing from different heights. Eighteen male recreational athletes were instructed to perform drop-landing tasks from 0.3- to 0.6-m heights. Force plates and motion-capture system were used to capture ground reaction force and kinematics data, respectively. Joint moment was calculated using inverse dynamics. Joint power was computed as a product of joint moment and angular velocity. Work was defined as joint power integrated over time. Hip and knee joints delivered significantly greater joint power and eccentric work (p<0.05) than the ankle joint at both landing heights. Substantial increase (p<0.05) in eccentric work was noted at the hip joint in response to increasing landing height. Knee and hip joints acted as key contributors to total energy dissipation in the frontal plane with increase in peak ground reaction force (GRF). The hip joint was the top contributor to energy absorption, which indicated a hip-dominant strategy in the frontal plane in response to peak GRF during landing. Future studies should investigate joint motions that can maximize energy dissipation or reduce the need for energy dissipation in the frontal plane at the various joints, and to evaluate their effects on the attenuation of lower extremity injury risk during landing.     

Mechanical demand and multijoint control during landing depend on orientation of the body segments relative to the reaction force.

The purpose of this study was to determine how diverse momentum conditions and anatomical orientation at contact influences mechanical loading and multijoint control of the reaction force during landings. Male collegiate gymnasts (n=6) performed competition style landings (n=3) of drop jumps, front saltos, and back saltos from a platform (0.72 m) onto landing mats (0.12 m). Kinematics (200 fps), reaction forces (800 Hz) and muscle activation patterns (surface EMG, 1600 Hz) of seven lower extremity muscles were collected simultaneously. Between-task differences in segment orientation relative to the reaction force contributed to significant between-task differences in knee and hip net joint moments (NJM) during the impact phase. During the stabilization phase, ankle, knee, and hip NJMs acted to control joint flexion. Between-task differences in muscle activation patterns indicated that gymnasts scaled biarticular muscle activation to accommodate for between-task differences in NJM after contact. Activation of muscles on both sides of the joint suggests that impedance like control was used to stabilize the joints and satisfy the mechanical demand imposed on the lower extremity. Between-subject differences in the set of muscles used to control total body center of mass (TBCM) trajectory and achieve lower extremity NJMs suggests that control of multijoint movements involving impact needs to incorporate mechanical objectives at both the total body and local level. The functional consequences of such a control structure may prove to be an asset to gymnasts, particularly when required to perform a variety of landing tasks under a variety of environmental constraints.     

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.     

Osteoarthritis of the First Carpometacarpal Joint

The first carpometacarpal (trapeziometacarpal) joints are a frequent site of osteoarthritis in postmenopausal women. This osteoarthritis, which is typically bilateral both clinically and roentgenographically, may be mistaken for tenosynovitis unless its characteristic features are recognized. These features include tenderness, stiffness, crepitus, swelling, and pain on wringing movements or other motions that cause abduction of the thumb. The swelling, radial subluxation of the metacarpal and atrophy of the thenar muscles give the hand a squared appearance.In severe cases, conservative medical therapy is generally unsatisfactory. Intra-articular corticosteroids and local anesthetic give only transient relief. Results of surgical therapy, including excision of the trapezium or arthrodesis of the trapeziometacarpal joint, were in general good. Distinct indications exist for each type of operation.     

Muscle moment arm and normalized moment contributions as reference data for musculoskeletal elbow and wrist joint models

A geometric musculoskeletal model of the elbow and wrist joints was developed to calculate muscle moment arms throughout elbow flexion/extension, forearm pronation/supination, wrist flexion/extension and radial/ulnar deviation. Model moment arms were verified with data from cadaver specimen studies and geometric models available in the literature. Coefficients of polynomial equations were calculated for all moment arms as functions of joint angle, with special consideration to coupled muscles as a function of two joint angles. Additionally, a “normalized potential moment (NPM)” contribution index for each muscle across the elbow and wrist joints in four degrees-of-freedom was determined using each muscle's normalized physiological cross-sectional area (PCSA) and peak moment arm (MA). We hypothesize that (a) a geometric model of the elbow and wrist joints can represent the major attributes of MA versus joint angle from many literature sources of cadaver and model data and (b) an index can represent each muscle's normalized moment contribution to each degree-of-freedom at the elbow and wrist. We believe these data serve as a simple, yet comprehensive, reference for how the primary 16 muscles across the elbow and wrist contribute to joint moment and overall joint performance.     

Computational biomechanics of knee joint in open kinetic chain extension exercises

Open kinetic chain (OKC) extension exercises are commonly performed to strengthen quadriceps muscles and restore joint function in performance enhancement programs, in exercise therapies and following joint reconstruction. Using a validated 3D nonlinear finite element model, the detailed biomechanics of the entire joint in OKC extension exercises are investigated at 0, 30, 60 and 90 degrees joint angles. Two loading cases are simulated; one with only the weight of the leg and the foot while the second considers also a moderate resistant force of 30 N acting at the ankle perpendicular to the tibia. The presence of the 30 N markedly influences the results both in terms of the magnitude and the trend. The resistant load substantially increases the required quadriceps, patellar tendon, cruciate ligaments and joint contact forces, especially at near 90 degrees angles with the exception of ACL force that is increased at 0 degrees angle. At post-ACL reconstruction period or in the joint with ACL injury, the exercise should preferably be avoided at near full extension positions under large resistant forces.