Contribution of mono- and biarticular muscles to extending knee joint moments in runners and cyclists.

Motor actions are governed by coordinated activation of mono- and biarticular muscles. This study considered differences in mono- and biarticular knee extensors between runners and cyclists in the context of adaptations to task-specific movement requirements. Two hypotheses were tested: 1) the length-at-use hypothesis, which is that muscle adapts to have it operate around optimal length; and 2) the contraction-mode hypothesis, which is that eccentrically active muscles prefer to operate on the ascending limb of the length-force curve. Ten runners and ten cyclists performed maximal, isometric knee extensions on a dynamometer at five knee and four hip joint angles. This approach allowed the separation of the contribution of mono- and biarticular extensors. Three major differences occurred: 1) compared with runners, monoarticular extensors of cyclists reach optimal length at larger muscle length; 2) in runners, optimal length of the biarticular extensor is shifted to larger lengths; and 3) the moment generated by monoarticular extensor was larger in cyclists. Mono- and biarticular extensors respond to different adaptation triggers in runners and cyclists. Monoarticular muscles seem to adapt to the length-at-use, whereas biarticular muscles were found to be sensitive to the contraction-mode hypothesis.     

Prediction of Individual Muscle Forces Using Lagrange Multipliers Method — A Model of the Upper Human Limb in the Sagittal Plane: II. Numerical Experiments and Sensitivity Analysis

Abstract

Using the method of Lagrange multipliers an analytical solution of the optimization problem formulated for a two-dimensional, 3DOF model of the human upper limb has been described in Part I of this investigation. The objective criterion used is the following: Σ c_iF_i ², where F_i-s are the muscle forces modelled and c_i-s are unknown weight factors. This study is devoted to the numerical experiments performed in order to investigate which sets of the weight factors may predict physiologically reasonable muscle forces and joint reactions. A sensitivity analysis is also presented. The influence of: the gravity forces, different external loads applied to the hand, changes of the weight factors and of joint angle on the optimal solution is studied. A general conclusion may be drawn: using the above mentioned objective criterion, practically all motor tasks performed by the human upper limb may be described if the c_i-s are properly chosen. These weight factors generally depend on the joint moments and must be different (their magnitudes as well as their signs) for agonistic muscles and for their antagonists.     

Activity of mono- and biarticular leg muscles during sprint running

A cinematographic recording of the movements of the lower limbs together with simultaneous emg tracings from nine lower limb muscles were obtained from two male track sprinters during three phases of a 100 m sprint run. The extensor muscles of the hip joint were found to be the primary movers by acceleration of the body's center of gravity (C.G.) during the ground phase of the running cycle. The extensors of the knee joint were also important in this, but to a minor extent, while the plantar flexors of the ankle joint showed the least contribution. The biarticular muscles functioned in a way different from the monoarticular muscles in the sense that they perform eccentric work during the flight and recovery phases and concentric work during the whole ground phase (support), whereas the monoarticular muscles are restricted first to eccentric work and then to concentric work during the ground phase. Furthermore, the biarticular muscles show variation (and rate of variation) in muscle length to a larger extent than the monoarticular muscles. Paradoxical muscle actions appear to take place around the knee joint, where the hamstring muscles, m. gastrocnemius, m. vastus laterialis and m. vastus medialis act as synergists by extending the knee joint during the last part of the ground phase.     

The Roles of Monoarticular and Biarticular Muscles of the Lower Limbs in Terrestrial Locomotion

Specific features of the functioning of mono- and biarticular muscles were studied using a multijoint movement (a high jump) as an example. The powers of the knee and ankle joint extensors are insufficient for a strong and quick movement such as a high jump. Biarticular muscles (m. rectus femoris) transfer forces/powers from one joint to another, thereby compensating for the physiological shortcoming of monoarticular muscles, that is, a decrease in the tractive force with increasing contraction rate. In a high jump, a power of 300 W may be transferred from the hip to the knee joint via the m. rectus femoris; 230 W, from the knee to the hip joint via the hamstring muscle; 210 W, from the knee joint to the ankle via the m. gastrocnemius; and 15 W, from the metatarsophalangeal joint to the ankle via the mm. flexors.     

Comparison of global and joint-to-joint methods for estimating the hip joint load and the muscle forces during walking

A three-dimensional musculoskeletal model of the lower limb was developed to study the influence of biarticular muscles on the muscle force distribution and joint loads during walking. A complete walking cycle was recorded for 9 healthy subjects using the standard optoelectronic motion tracking system. Ground contact forces were also measured using a 6-axes force plate. Inverse dynamics was used to compute net joint reactions (forces and torques) in the lower limb. A static optimization method was then used to estimate muscle forces. Two different approaches were used: in the first one named global method, the biarticular muscles exerted a torque on the two joints they spanned at the same time, and in the second one called joint-by-joint method, these biarticular muscles were divided into two mono-articular muscles with geometrical (insertion, origin, via points) and physiological properties remained unchanged. The hip joint load during the gait cycle was then calculated taking into account the effect of muscle contractions. The two approaches resulted in different muscle force repartition: the biarticular muscles were favoured over any set of single-joint muscles with the same physiological function when using the global method. While the two approaches yielded only little difference in the resultant hip load, the examination of muscle power showed that biarticular muscles could produce positive work at one joint and negative work at the other, transferring energy between body segments and thus decreasing the metabolic cost of movement.     

Functional muscle synergies to support the knee against moment specific loads while weight bearing

ObjectiveExternally applied abduction and rotational loads are major contributors to the knee joint injury mechanism; yet, how muscles work together to stabilize the knee against these loads remains unclear. Our study sought to evaluate lower limb functional muscle synergies in healthy young adults such that muscle activation can be directly related to internal knee joint moments.MethodsConcatenated non-negative matrix factorization extracted muscle and moment synergies of 22 participants from electromyographic signals and joint moments elicited during a weight-bearing force matching protocol.ResultsTwo synergy sets were extracted: Set 1 included four synergies, each corresponding to a general anterior, posterior, medial, or lateral force direction. Frontal and transverse moments were coupled during medial and lateral force directions. Set 2 included six synergies, each corresponding to a moment type (extension/flexion, ab/adduction, internal/external rotation). Hamstrings and quadriceps dominated synergies associated with respective flexion and extension moments while quadriceps-hamstring co-activation was associated with knee abduction. Rotation moments were associated with notable contributions from hamstrings, quadriceps, gastrocnemius, and hip ab/adductors, corresponding to a general co-activation muscle synergy.ConclusionOur results highlight the importance of muscular co-activation of all muscles crossing the knee to support it during injury-inducing loading conditions such as externally applied knee abduction and rotation. Functional muscle synergies can provide new insight into the relationship between neuromuscular control and knee joint stability by directly associating biomechanical variables to muscle activation.     

Force, work and power output of lower limb muscles during human maximal-effort countermovement jumping.

The purpose of this study was to simulate human maximal-effort countermovement jumping with a three-dimensional neuromusculoskeletal model. The specific aim was to investigate muscle force, work and power output of major lower limb muscles during the motion. A neuromusculoskeletal model that has nine rigid body segments, 20 degrees of freedom, 32 Hill-type lower limb muscles was developed. The neural activation input signal was represented by a series of step functions with step duration of 0.05 s. The excitation-contraction dynamics of the contractile element, the tissues around the joints to limit the joint range of motion, as well as the foot-ground interaction were implemented. A simulation was started from a standing posture. Optimal pattern of the activation input signal was searched through numerical optimization with a goal of maximizing the height reached by the mass center of body after jumping up. As a result, feasible kinematics, ground reaction force profile and muscle excitation profile were generated. It was found that monoarticular muscles had major contributions of mechanical work and power output, whereas biarticular muscles had minor contributions. Hip adductors, abductors and external rotator muscles were vigorously activated, although their mechanical work and power output was minor because of their limited length change during the motion. Joint flexor muscles such as m. iliopsoas, m. biceps femoris short head and m. tibialis anterior were activated in the beginning of the motion with an effect of facilitating the generation of a countermovement.     

Muscle coordination in cycling: effect of surface incline and posture

The purpose of the present study was to examine theneuromuscular modifications of cyclists to changes in grade andposture. Eight subjects were tested on a computerized ergometer underthree conditions with the same work rate (250 W): pedaling on the level while seated, 8% uphill while seated, and 8% uphill while standing (ST). High-speed video was taken in conjunction with surfaceelectromyography (EMG) of six lower extremity muscles. Results showedthat rectus femoris, gluteus maximus (GM), and tibialis anterior hadgreater EMG magnitude in the ST condition. GM, rectus femoris, and the vastus lateralis demonstrated activity over a greater portion of thecrank cycle in the ST condition. The muscle activities of gastrocnemiusand biceps femoris did not exhibit profound differences amongconditions. Overall, the change of cycling grade alone from 0 to 8%did not induce a significant change in neuromuscular coordination. However, the postural change from seated to ST pedaling at 8% uphillgrade was accompanied by increased and/or prolonged muscle activity of hip and knee extensors. The observed EMG activity patternswere discussed with respect to lower extremity joint moments.Monoarticular extensor muscles (GM, vastus lateralis) demonstratedgreater modifications in activity patterns with the change in posturecompared with their biarticular counterparts. Furthermore, musclecoordination among antagonist pairs of mono- and biarticular muscleswas altered in the ST condition; this finding provides support for thenotion that muscles within these antagonist pairs have differentfunctions.

     

Intermuscular coordination in a sprint push-off.

This study was designed to investigate the patterns of intermuscular coordination during a sprinting event. In previous research it was found that despite the indeterminacy problem of movement control, movements like vertical jumping, speed skating and cycling are performed in a stereotyped manner. It was hypothesized that this might be due to constraints associated with the transformation of joint rotations into the desired translation. The objective of the present study was to determine the extent to which the intermuscular coordination patterns during other movements also are performed in a stereotyped manner and, if that is true, whether this can be understood on the basis of such constraints. Seven elite sprint runners were instructed to execute an explosive sprinting dash. Ground reaction forces and cinematographic data were recorded for the second stance phase of the sprint. Simultaneously, electromyographic activity of nine leg muscles was recorded telemetrically. Linked-segment modeling was used to obtain net joint moments and net joint powers. Different athletes appeared to perform the sprint in a stereotyped manner. The muscle coordination pattern is characterized by a proximo to distal sequence in timing of the monoarticular muscles. When compared to the sequential pattern found in jumping, the biarticular hamstrings and rectus femoris muscles behave differently; in the sprint a more pronounced reciprocal activity between these muscles exists. The resulting movement pattern is characterized by a sequence of upper leg extension and plantar flexion. The observed sequence in timing of muscle activation patterns is aimed at solving the problems associated with the earlier identified geometrical and anatomical constraint. However, the coordination pattern cannot be fully understood on the basis of these constraints. A specific constraint is identified with respect to the direction of the ground reaction force, which explains the pronounced reciprocal activity of the biarticular hamstring and rectus femoris muscles. The intermuscular coordination pattern in the sprint can be seen as a compromise between the specific requirement of the sprint and the advantageous effect of a proximo to distal sequence as found previously for jumping.     

The force resulting from the action of mono- and biarticular muscles in a limb.

Human and animal limbs can be modelled as a chain of segments connected at joints. For a static limb, the force exerted at the endpoint due to the force of a single muscle has been calculated. It turns out that there are marked differences in the action of mono- vs. biarticular muscles. Monoarticular muscles produce an endpoint force that is directed in the lengthwise direction of the limb, i.e. in the direction of one of the segments. The force from biarticular muscles can have a marked transverse component. The 'principal direction' of this endpoint force is also the movement direction of the endpoint which is the most favourable for the muscle to do work. The reasoning presented can explain e.g. the differences in the activity of mono- and biarticular muscles in cycling.     

Muscle mass in musculoskeletal models

Most current models of musculoskeletal dynamics lump a muscle's mass with its body segment, and then simulate the dynamics of these body segments connected by joints. As shown here, this popular approach leads to errors in the system's inertia matrix and hence in all aspects of the dynamics. Two simplified mathematical models were created to capture the relevant features of monoarticular and biarticular muscles, and the errors were analyzed. The models were also applied to two physiological examples: the triceps surae muscles that plantar flex the human ankle and the biceps femoris posterior muscle of the rat hind limb. The analysis of errors due to lumping showed that these errors can be large. Although the errors can be reduced in some postures, they cannot be easily eliminated in models that use segment lumping. Some options for addressing these errors are discussed.     

Uncertainty of knee joint muscle activity during knee joint torque exertion: the significance of controlling adjacent joint torque.

In the single-joint torque exertion task, which has been widely used to control muscle activity, only the relevant joint torque is specified. However, the neglect of the neighboring joint could make the procedure unreliable, considering our previous result that even monoarticular muscle activity level is indefinite without specifying the adjacent joint torque. Here we examined the amount of hip joint torque generated with knee joint torque and its influence on the activity of the knee joint muscles. Twelve healthy subjects were requested to exert various levels of isometric knee joint torque. The knee and hip joint torques were obtained by using a custom-made device. Because no information about hip joint torque was provided to the subjects, the hip joint torque measured here was a secondary one associated with the task. The amount of hip joint torque varied among subjects, indicating that they adopted various strategies to achieve the task. In some subjects, there was a considerable internal variability in the hip joint torque. Such variability was not negligible, because the knee joint muscle activity level with respect to the knee joint torque, as quantified by surface electromyography (EMG), changed significantly when the subjects were requested to change the strategy. This change occurred in a very systematic manner: in the case of the knee extension, as the hip flexion torque was larger, the activity of mono- and biarticular knee extensors decreased and increased, respectively. These results indicate that the conventional single knee joint torque exertion has the drawback that the intersubject and/or intertrial variability is inevitable in the relative contribution among mono- and biarticular muscles because of the uncertainty of the hip joint torque. We discuss that the viewpoint that both joint torques need to be considered will bring insights into various controversial problems such as the shape of the EMG-force relationship, neural factors that help determine the effect of muscle strength training, and so on.     

Reconstruction of the human gastrocnemius force-length curve in vivo: part 1-model-based validation of method

The muscle fiber force-length relationship has been explained in terms of the cross-bridge theory at the sarcomere level. In vivo, for a physiologically realistic range of joint motion, and therefore range of muscle fiber lengths, only part of the force-length curve may be used; that is, the section of the force-length curve expressed can vary. The purpose of this study was to assess the accuracy of a method for determining the expressed section of the force-length curve for biarticular muscles. A muscle model was used to simulate the triceps surae muscle group. Three model formulations were used so that the gastrocnemius operated over different portions of the force-length curve: the ascending limb, the plateau region, and the descending limb. Joint moment data were generated for a range of joint configurations and from this simulated data the region of the force- length relationship that the gastrocnemius muscle operated over was successfully reconstructed using the algorithm of Herzog and ter Keurs (1988a). Further simulations showed that the correct region of the force-length curve was accurately reconstructed even in the presence of random and systematic noise generated to reflect the effects of sampling errors, and incomplete muscle activation.     

Prediction of Individual Muscle Forces Using Lagrange Multipliers Method - A Model of the Upper Human Limb in the Sagittal Plane: II. Numerical Experiments and Sensitivity Analysis

Using the method of Lagrange multipliers an analytical solution of the optimization problem formulated for a two-dimensional, 3DOF model of the human upper limb has been described in Part I of this investigation. The objective criterion used is the following: [formula: see text], where F(i) -s are the muscle forces modelled and c(i) -s are unknown weight factors. This study is devoted to the numerical experiments performed in order to investigate which sets of the weight factors may predict physiologically reasonable muscle forces and joint reactions. A sensitivity analysis is also presented. The influence of: the gravity forces, different external loads applied to the hand, changes of the weight factors and of joint angle on the optimal solution is studied. A general conclusion may be drawn: using the above mentioned objective criterion, practically all motor tasks performed by the human upper limb may be described if the c(i) -s are properly chosen. These weight factors generally depend on the joint moments and must be different (their magnitudes as well as their signs) for agonistic muscles and for their antagonists.     

Are fixed limb inertial models valid for dynamic simulations of human movement?

During human movement, muscle activation and limb movement result in subtle changes in muscle mass distribution. Muscle mass redistribution can affect limb inertial properties and limb dynamics, but it is not currently known to what extent. The objectives of this study were to investigate: (1) how physiological alterations of muscle and tendon length affect limb inertial characteristics, and (2) how such changes affect dynamic simulations of human movement. To achieve these objectives, a digital model of a human leg, custom software, and Software for interactive musculoskeletal modeling were used to simulate mass redistribution of muscle–tendon structures within a limb segment during muscle activation and joint movement. Thigh and shank center of mass and moments of inertia for different muscle activation and joint configurations were determined and compared. Limb inertial parameters representing relaxed muscles and fully active muscles were input into a simulated straight-leg movement to evaluate the effect inertial parameter variations could have on movement simulation results. Muscle activation and limb movement altered limb segment center of mass and moments of inertia by less than 0.04 cm and 1.2%, respectively. These variations in limb inertial properties resulted in less than 0.01% change in maximum angular velocity for a simulated straight-leg hip flexion task. These data demonstrate that, for the digital human leg model considered, assuming static quantities for segment center of masses and moments of inertia in movement simulations appear reasonable and induce minimal errors in simulated movement dynamics.     

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.     

Control model of human stance using fuzzy logic

 A control model of human stance is proposed based on knowledge from behavioral experiments and physiological systems. The proposed model is based on the control of global variables specific to body orientation and alignment, rather than on the control of the body’s center of mass within the base of support. Furthermore, the proposed control model is not based on purely inverted pendulum body mechanics where only motion at one joint is controlled, as for instance the ankle. In the proposed model, the degrees of freedom are controlled by using reciprocal and synergistic muscle actions at multiple joints. The control model is based on three sets of different global variables which act in parallel: (1) limb length and its derivative, (2) limb orientation and its derivative, and (3) trunk attitude and its derivative. An important feature of the control model is the use of fuzzy logic, which enables us to model experimental findings and physiological knowledge in a meaningful and explicit way using fuzzy if-then rules. In the control model, 36 fuzzy if-then rules are implemented and applied using a four-linked segment model consisting of a trunk, thigh, shank and foot. Uni- and biarticular limb muscles and trunk muscles are represented as torque actuators at each individual joint. In the model, three sets of global variables act in parallel and make corrective and coordinated responses to internal, self-induced perturbations. The data show that the use of global variables and fuzzy logic successfully enables us to model human standing with sway about a point of equilibrium. Small changes in, for example, total body sway are comparable to those seen during natural sway in human stance. The selected controllers—limb length, limb orientation and trunk attitude—seem to be appropriate for human stance control. Received: 30 October 1996/Accepted in revised form: 7 April 1997     

A noninvasive technique for in vivo measurement of joint torques of biarticular muscles.

The objective of this work was to develop a noninvasive method to measure the joint torques produced by biarticular muscles at two joints simultaneously. During intramuscular stimulation of the cat medial gastrocnemius (MG) muscle, torques at the ankle and knee joints were calculated from forces measured in two dimensions at the end point of the cat paw under isometric conditions. The method was verified by the known anatomical properties of cat MG muscle and the tibialis anterior (TA) muscle. The MG muscle was shown to produce a significant flexion torque at the knee, besides an extension torque at the ankle. This was in agreement with its anatomical arrangement. The TA muscle produced primarily an ankle flexion torque. The small knee torque, due to measurement errors, yielded an estimate of measurement accuracy of 3.0 +/- 2.1% (n = 52). The coupling ratio of the MG muscle, defined as T(ankle)/T(knee), varied significantly with both knee and ankle angles. The profile of MG mechanical coupling agreed qualitatively with changes in limb configuration. The method can be used to measure recruitment properties of electrically stimulated biarticular muscles, and may potentially be used to study the biomechanics of biarticular coupling.     

Individual muscle force parameters and fiber operating ranges for elbow flexion-extension and forearm pronation-supination

We have quantified individual muscle force and moment contributions to net joint moments and estimated the operating ranges of the individual muscle fibers over the full range of motion for elbow flexion/extension and forearm pronation/supination. A three dimensional computer graphics model was developed in order to estimate individual muscle contributions in each degree of freedom over the full range of motion generated by 17 muscles crossing the elbow and forearm. Optimal fiber length, tendon slack length, and muscle specific tension values were adjusted within the literature range from cadaver studies such that the net isometric joint moments of the model approximated experimental joint moments within one standard deviation. Analysis of the model revealed that the muscles operate on varying portions of the ascending limb, plateau region, and descending limb of the force-length curve. This model can be used to further understand isometric force and moment contributions of individual muscles to net joint moments of the arm and forearm and can serve as a comprehensive reference for the forces and moments generated by 17 major muscles crossing the elbow and wrist.