The utility of an empirically derived co-activation ratio for muscle force prediction through optimization

Biomechanical optimization models that apply efficiency-based objective functions often underestimate or negate antagonist co-activation. Co-activation assists movement control, joint stabilization and limb stiffness and should be carefully incorporated into models. The purposes of this study were to mathematically describe co-activation relationships between elbow flexors and extensors during isometric exertions at varying intensity levels and postures, and secondly, to apply these co-activation relationships as constraints in an optimization muscle force prediction model of the elbow and assess changes in predictions made while including these constraints. Sixteen individuals performed 72 isometric exertions while holding a load in their right hand. Surface EMG was recorded from elbow flexors and extensors. A co-activation index provided a relative measure of flexor contribution to total activation about the elbow. Parsimonious models of co-activation during flexion and extension exertions were developed and added as constraints to a muscle force prediction model to enforce co-activation. Three different PCSA data sets were used. Elbow co-activation was sensitive to changes in posture and load. During flexion exertions the elbow flexors were activated about 75% MVC (this amount varied according to elbow angle, shoulder flexion and abduction angles, and load). During extension exertions the elbow flexors were activated about 11% MVC (this amount varied according to elbow angle, shoulder flexion angle and load). The larger PCSA values appeared to be more representative of the subject pool. Inclusion of these co-activation constraints improved the model predictions, bringing them closer to the empirically measured activation levels.     

膝骨性关节炎患者登梯时下肢肌肉活动和膝关节负荷的分析

目的:分析膝骨性关节炎患者(KOA)登梯时下肢肌群肌电活动与关节角冲量与正常人的差异,为康复方案设计提供生物力学参考。方法:采用Qualisys三维运动分析系统以及Delsys无线表面肌电系统对招募10名符合纳排标准的膝骨性关节炎患者和10名正常人进行登梯活动的步态检测,采用下肢肌群均方根值、股内外侧肌协同收缩比值、股二头肌和股外侧肌共同活动比值和髋、膝关节在冠状面和矢状面上角冲量对比分析与两组登梯时下肢肌群收缩模式对关节负荷的影响。结果:与正常对照相比,上梯时膝骨性关节炎患者股直肌均方根值RMS(Root Mean Square)增大(P0.05),膝骨性关节炎患者股内外侧肌收缩均方根值比值(RMS(Vastus Medialis)VM/(Vastus Lateralis)VL)减小(P0.05),膝骨性关节炎患者腘绳肌与股外侧肌收缩比值(RMS(Biceps Femoris)BF/VL增大(P0.05)。下梯时,膝骨性关节炎患者股直肌均方根值(RMS)增大(P0.05),臀大肌均方根值(RMS)减小(P0.05),股内外侧肌收缩均方根比值(RMS VM/VL)减小(P0.05)。上梯时,膝骨性关节炎患者髋、膝关节冠状面上的关节角冲量大于正常人(P0.05),膝关节在矢状面上关节角冲量大于正常组(P0.05),下梯髋、膝关节冠状面、矢状面上的角冲量无统计学差异(P0.05)。KOA组VM/VL、BF/VL与膝关节在冠状面和矢状面上的角冲量的改变没有直接的相关性(P0.05)。结论:膝骨性关节炎患者在登梯活动时股直肌的收缩活动增加,股内外侧肌的协同收缩下降,主动肌与拮抗肌的共同收缩增加,膝骨性关节炎患者在面对登梯活动时下肢肌群选择性激活和高激活状态协调一致,促进关节稳定。虽然下肢神经肌肉的收缩模式和膝关节负荷之间没有直接的相关性,可能是对膝关节负荷产生影响的生物力学因素较多,神经肌肉的收缩模式只是部分影响因素,后续将增加其他生物力学因素进一步研究。     

Optimal compliant-surface jumping: a multi-segment model of springboard standing jumps

A multi-segment model is used to investigate optimal compliant-surface jumping strategies and is applied to springboard standing jumps. The human model has four segments representing the feet, shanks, thighs, and trunk-head-arms. A rigid bar with a rotational spring on one end and a point mass on the other end (the tip) models the springboard. Board tip mass, length, and stiffness are functions of the fulcrum setting. Body segments and board tip are connected by frictionless hinge joints and are driven by joint torque actuators at the ankle, knee, and hip. One constant (maximum isometric torque) and three variable functions (of instantaneous joint angle, angular velocity, and activation level) determine each joint torque. Movement from a nearly straight motionless initial posture to jump takeoff is simulated. The objective is to find joint torque activation patterns during board contact so that jump height can be maximized. Minimum and maximum joint angles, rates of change of normalized activation levels, and contact duration are constrained. Optimal springboard jumping simulations can reasonably predict jumper vertical velocity and jump height. Qualitatively similar joint torque activation patterns are found over different fulcrum settings. Different from rigid-surface jumping where maximal activation is maintained until takeoff, joint activation decreases near takeoff in compliant-surface jumping. The fulcrum-height relations in experimental data were predicted by the models. However, lack of practice at non-preferred fulcrum settings might have caused less jump height than the models' prediction. Larger fulcrum numbers are beneficial for taller/heavier jumpers because they need more time to extend joints.     

Comparison of humeral rotation co-activation of breast cancer population and healthy shoulders

Upper limb morbidities are common amongst the breast cancer population (BCP) and have a direct impact on independence. Comparing muscle co-activation strategies between BCP and healthy populations may assist in identifying muscle dysfunction and promote clinical interpretation of dysfunction, which could direct preventative and therapeutic interventions. The purposes of this study were to define humeral rotation muscle co-activation of a BCP and to compare it with a previously defined co-activation relationship of a healthy population. Fifty BCP survivors performed 18 isometric internal and external rotation exertions at various postures and intensities. Surface and intramuscular electrodes recorded shoulder muscle activity. BCP co-activation was predicted at r² = 0.77 during both exertion types. Humeral abduction angle and task intensity were important factors in the prediction of co-activation in both populations. Comparisons made between populations identified differing muscle strategies used by BCP to maintain postural control. Compared to healthy co-activation, the BCP demonstrated greater activation of internal (IR) and external rotator (ER) type muscles during their respective rotation type. The BCP demonstrated increased (⩾8.7%) activation of pectoralis major. This study has provided insight into how BCP muscles compensate during dysfunction. Continued advancement of this knowledge can provide more understanding of dysfunction, promote generation of evidence-based therapies, and can be useful in biomechanical modeling.     

Are hamstrings activated to counteract shear forces during isometric knee extension efforts in healthy subjects?

The hamstring muscles have the potential to counteract anterior shear forces at the knee joint by co-contracting during knee extension efforts. Such a muscle recruitment pattern might protect the anterior cruciate ligament (ACL) by reducing its strain. In this study we investigated to what extent co-activation of the knee flexors during extension efforts is compatible with the hypothesis that this co-activation serves to counteract anterior tibial shear forces during isometric knee extension efforts in healthy subjects. To this aim, it is investigated whether co-activation varies with the required knee extension moment, with the knee joint angle, and with the position of the external flexing force relative to the knee joint. With unaltered moment and muscle activation, distal positioning of the flexing force on the tibia causes higher resultant (muscular plus external) forward shear forces at the knee as compared to proximal positioning. In ten subjects, knee flexor and extensor EMG was measured during a quasi-isometric positioning task for a range (5-50 degrees) of knee flexion angles. It was found that the co-activation of the knee flexors increased with the extension moment, but this increase was less than proportional (p<0.001). The extension moment increased 2.7 to 3.4 times, whereas the activation of Biceps Femoris and Semitendinosus increased only a factor 1.3 to 2.0 (joint angle dependent). Furthermore, a strong increase in co-activation was seen near full extension of the knee joint. The position of the external extension load on the tibia did not affect the level of co-contraction. It is argued that these results do not suggest a recruitment pattern that is directed at reduction of anterior shear forces in the knee joint during sub-maximal isometric knee extension efforts in healthy subjects.     

Short range stiffness elastic limit depends on joint velocity

Muscles behave as elastic springs during the initial strain phase, indicated as short range stiffness (SRS). Beyond a certain amount of strain the muscle demonstrates a more viscous behavior. The strain at which the muscle transits from elastic- to viscous-like behavior is called the elastic limit and is believed to be the result of breakage of cross-bridges between the contractile filaments. The aim of this study was to test whether the elastic limit, measured in vivo at the wrist joint, depended on the speed of lengthening. Brief extension rotations were imposed to the wrist joint (n=8) at four different speeds and at three different levels of voluntary torque using a servo controlled electrical motor. Using a recently published identification scheme, we quantified the elastic limit from measured joint angle and torque. The results showed that the elastic limit significantly increased with speed in a linear way, indicating to a constant time of approximately 30 ms before cross-bridges break. The implications for movement control of the joint are discussed.     

Co-activation of upper limb muscles during reaching in post-stroke subjects: An analysis of the contralesional and ipsilesional limbs

The purpose of this study was to analyze the change in antagonist co-activation ratio of upper-limb muscle pairs, during the reaching movement, of both ipsilesional and contralesional limbs of post-stroke subjects. Nine healthy and nine post-stroke subjects were instructed to reach and grasp a target, placed in the sagittal and scapular planes of movement. Surface EMG was recorded from postural control and movement related muscles. Reaching movement was divided in two sub-phases, according to proximal postural control versus movement control demands, during which antagonist co-activation ratios were calculated for the muscle pairs LD/PM, PD/AD, TRIlat/BB and TRIlat/BR. Post-stroke’s ipsilesional limb presented lower co-activation in muscles with an important role in postural control (LD/PM), comparing to the healthy subjects during the first sub-phase, when the movement was performed in the sagittal plane (p < 0.05). Conversely, the post-stroke’s contralesional limb showed in general an increased co-activation ratio in muscles related to movement control, comparing to the healthy subjects. Our findings demonstrate that, in post-stroke subjects, the reaching movement performed with the ipsilesional upper limb seems to show co-activation impairments in muscle pairs associated to postural control, whereas the contralesional upper limb seems to have signs of impairment of muscle pairs related to movement.     

Maximum voluntary joint torque as a function of joint angle and angular velocity: model development and application to the lower limb

Measurements of human strength can be important during analyses of physical activities. Such measurements have often taken the form of the maximum voluntary torque at a single joint angle and angular velocity. However, the available strength varies substantially with joint position and velocity. When examining dynamic activities, strength measurements should account for these variations. A model is presented of maximum voluntary joint torque as a function of joint angle and angular velocity. The model is based on well-known physiological relationships between muscle force and length and between muscle force and velocity and was tested by fitting it to maximum voluntary joint torque data from six different exertions in the lower limb. Isometric, concentric and eccentric maximum voluntary contractions were collected during hip extension, hip flexion, knee extension, knee flexion, ankle plantar flexion and dorsiflexion. Model parameters are reported for each of these exertion directions by gender and age group. This model provides an efficient method by which strength variations with joint angle and angular velocity may be incorporated into comparisons between joint torques calculated by inverse dynamics and the maximum available joint torques.     

Active trunk stiffness increases with co-contraction.

Trunk dynamics, including stiffness, mass and damping were quantified during trunk extension exertions with and without voluntary recruitment of antagonistic co-contraction. The objective of this study was to empirically evaluate the influence of co-activation on trunk stiffness. Muscle activity associated with voluntary co-contraction has been shown to increase joint stiffness in the ankle and elbow. Although biomechanical models assume co-active recruitment causes increase trunk stiffness it has never been empirically demonstrated. Small trunk displacements invoked by pseudorandom force disturbances during trunk extension exertions were recorded from 17 subjects at two co-contraction conditions (minimal and maximal voluntary co-contraction recruitment). EMG data were recorded from eight trunk muscles as a baseline measure of co-activation. Increased EMG activity confirms that muscle recruitment patterns were different between the two co-contraction conditions. Trunk stiffness was determined from analyses of impulse response functions (IRFs) of trunk dynamics wherein the kinematics were represented as a second-order behavior. Trunk stiffness increased 37.8% (p < 0.004) from minimal to maximal co-activation. Results support the assumption used in published models of spine biomechanics that recruitment of trunk muscle co-contraction increases trunk stiffness thereby supporting conclusions from those models that co-contraction may contribute to spinal stability.     

A new method for measuring passive length-tension properties of human gastrocnemius muscle in vivo

The study of muscle growth and muscle length adaptations requires measurement of passive length-tension properties of individual muscles, but until now such measurements have only been made in animal muscles. We describe a new method for measuring passive length-tension properties of human gastrocnemius muscles in vivo. Passive ankle torque and ankle angle data were obtained as the ankle was rotated through its full range with the knee in a range of positions. To extract gastrocnemius passive length-tension curves from passive torque-angle data it was assumed that passive ankle torque was the sum of torque due to structures which crossed only the ankle joint (this torque was a 6-parameter function of ankle joint angle) and a torque due to the gastrocnemius muscle (a 3-parameter function of knee and ankle angle). Parameter values were estimated with non-linear regression and used to reconstruct passive length-tension curves of the gastrocnemius. The reliability of the method was examined in 11 subjects by comparing three sets of measurements: two on the same day and the other at least a week later. Length-tension curves were reproducible: the average root mean square error was 5.1+/-1.1 N for pairs of measurements taken within a day and 7.3+/-1.2 N for pairs of measurements taken at least a week apart (about 3% and 6% of maximal passive tension, respectively). Length-tension curves were sensitive to mis-specification of moment arms, but changes in length-tension curves were not. The new method enables reliable measurement of passive length-tension properties of human gastrocnemius in vivo, and is likely to be useful for investigation of changes in length-tension curves over time.     

Muscle-damaging exercise affects isokinetic torque more at short muscle length

The aim of this study was to investigate the differences in the length-dependent changes in quadriceps muscle torque during voluntary isometric and isokinetic contractions performed after severe muscle-damaging exercise. Thirteen physically active men (age = 23.8 ± 3.2 years, body weight = 77.2 ± 4.5 kg) performed stretch-shortening cycle (SSC) exercise comprising 100 drop jumps with 30-second intervals between each jump. Changes in the voluntary and electrically evoked torque in concentric and isometric conditions at different muscle lengths, muscle soreness, and plasma creatine kinase (CK) activity were assessed within 72 hours after SSC exercise. Isokinetic knee extension torque decreased significantly (p < 0.05) at all joint angles after SSC exercise. At 2 minutes and at 72 hours after SSC exercise, the changes in knee torque were significantly smaller at 80° (where 180° = full knee extension) than at 110-130°. At 2 minutes after SSC exercise, the optimal angle for isokinetic knee extension torque shifted by 9.5 ± 8.9° to a longer muscle length (p < 0.05). Electrically induced torque at low-frequency (20-Hz) stimulation decreased significantly more at a knee joint angle of 130° than at 90°. The subjects felt acute muscle pain and CK activity in the blood increased to 1,593.9 ± 536.2 IU·L?1 within 72 hours after SSC exercise (p < 0.05). This study demonstrates that the effect of muscle-damaging exercise on isokinetic torque is greatest for contractions at short muscle lengths. These findings have practical importance because the movements in most physical activities are dynamic in nature, and the decrease in torque at various points in the range of motion during exercise might affect overall performance.     

Afferent and efferent components of joint position sense; interpretation of kinaesthetic illusion

The present model of joint angle perception is based on the following hypotheses: the perception and control of joint angle are closely interrelated processes; central motor commands are adequately expressed by shifts of an equilibrium point resulting from the interaction of antagonistic muscles and a load; two fundamental commands-reciprocal (r) and coactivative (c) provide for changes in activity of the antagonistic muscle pair. The dependence of joint angle on static muscle torque and r and c commands is derived (Eq. 5). The following principles of joint position sense are formulated: 1) the r component of the efferent copy plays the role of a reference point which shifts during voluntary regulation of muscle state, but remains unchanged during any passive alterations of joint position; 2) muscle afferent signals deliver not absolute but relative information (i.e. measured relatively to the central reference point). These signals turn out to be related to active muscle torque; 3) the nervous system evaluates muscle afferent signals on the basis of a scale determined by the level of coactivation of the antagonistic muscles. Kinaesthetic illusions appear to be due to disruptions in perception of afferent and/or efferent components of position sense. The present model is consistent with all the variety of kinaesthetic illusions observed experimentally. A qualitative neurophysiological schema for joint angle perception is proposed involving efferent copy and information concerning muscle torque delivered by the tendon organ, muscle spindle, and perhaps, articular receptors. It is known that the cerebellum incorporates both afferent and efferent information concerning movement. One may presume that it plays an essential role in position sense.     

Predicting the influence of hip and lumbar flexibility on lifting motions using optimal control

Computational models of the human body coupled with optimization can be used to predict the influence of variables that cannot be experimentally manipulated. Here, we present a study that predicts the motion of the human body while lifting a box, as a function of flexibility of the hip and lumbar joints in the sagittal plane. We modeled the human body in the sagittal plane with joints actuated by pairs of agonist-antagonist muscle torque generators, and a passive hamstring muscle. The characteristics of a stiff, average and flexible person were represented by co-varying the lumbar range-of-motion, lumbar passive extensor-torque and the hamstring passive muscle-force. We used optimal control to solve for motions that simulated lifting a 10 kg box from a 0.3 m height. The solution minimized the total sum of the normalized squared active and passive muscle torques and the normalized passive hamstring muscle forces, over the duration of the motion. The predicted motion of the average lifter agreed well with experimental data in the literature. The change in model flexibility affected the predicted joint angles, with the stiffer models flexing more at the hip and knee, and less at the lumbar joint, to complete the lift. Stiffer models produced similar passive lumbar torque and higher hamstring muscle force components than the more flexible models. The variation between the motion characteristics of the models suggest that flexibility may play an important role in determining lifting technique.     

Postural differences in shoulder dynamics during pushing and pulling

Assessments of shoulder dynamics (e.g. the inertial, viscous, and stiffness properties of the joint) can provide important insights into the stability of the joint at rest and during volitional contraction. The purpose of this study was to investigate how arm posture influences shoulder dynamics while generating pushing or pulling torques in the horizontal plane. Sixteen healthy participants were examined in seven postures encompassing a large workspace of the shoulder. At each posture, the participant’s shoulder was rapidly perturbed while measuring the resultant change in shoulder torque about the glenohumeral axis. Participants were examined both at rest and while producing horizontal flexion and extension torques scaled to 15% of a maximum voluntary contraction. Shoulder stiffness, viscosity, and damping ratio were estimated using impedance-based matching, and changes in these outcome measures with torque level, elevation angle, and plane of elevation angle were explored with a linear mixed effects model. Shoulder stiffness was found to decrease with increasing elevation angles (p < 0.001) without subsequent changes in viscosity, leading to a greater damping ratios at higher elevation angles (p < 0.001). Shoulder stiffness, viscosity, and damping ratio (all p < 0.05) were all found to significantly increase as the plane of elevation of the arm was increased. The relationship between the viscosity, stiffness and the damping ratio of the shoulder is one that the central nervous system must regulate in order to maintain stability, protect against injury, and control the shoulder joint as the inertial and muscle contributions change across different arm postures.     

Neuromechanical control of the forearm muscles during gripping with sudden flexion and extension wrist perturbations

The purpose of this study was to investigate how gripping modulates forearm muscle co-contraction prior to and during sudden wrist perturbations. Ten males performed a sub-maximal gripping task (no grip, 5% and 10% of maximum) while a perturbation forced wrist flexion or extension. Wrist joint angles and activity from 11 muscles were used to determine forearm co-contraction and muscle contributions to wrist joint stiffness. Co-contraction increased in all pairs as grip force increased (from no grip to 10% grip), corresponding to a 36% increase in overall wrist joint stiffness. Inclusion of individual muscle contributions to wrist joint stiffness enhanced the understanding of forearm co-contraction. The extensor carpi radialis longus (ECRL) and brevis had the largest stiffness contributions (34.5 ± 1.3% and 20.5 ± 2.3%, respectively), yet muscle pairs including ECRL produced the lowest co-contraction. The muscles contributing most to wrist stiffness were consistent across conditions (ECRL for extensors; Flexor Digitorum Superficialis for flexors), suggesting enhanced contributions rather than muscular redistribution. This work provides investigation of the neuromuscular response to wrist perturbations and gripping demands by considering both co-contraction and muscle contributions to joint stiffness. Individual muscle stiffness contributions can be used to enhance the understanding of forearm muscle control during complex tasks.     

Position dependence of ankle joint dynamics--I. Passive mechanics

System identification techniques were used to examine the position dependence of passive ankle joint mechanics. The relaxed ankle was stochastically perturbed about different angles in the range of motion (ROM). The linear dynamic relation between ankle position and torque was identified and modelled as a second-order underdamped system, having inertial (I), viscous (B) and elastic (K) parameters. Mean joint torque changed as the ankle was rotated through the ROM; it was small at mid-range and became much larger toward either extreme. While I remained constant both B and K changed as a function of ankle angle. At the extremes of the ROM, K was much larger than previously assumed and the relation between stiffness and the passive torque generated when the ankle was placed at different mean positions was linear. These results show that large variations in joint mechanics are possible even in the absence of voluntary muscle contraction. Moreover, these changes appear to be related to the torque generated when passive joint structures are stretched.     

The effect of leg flexion angle on the mechanomyographic responses to isometric muscle actions

The purpose of this investigation was to examine the effect of leg flexion angle on the relationship between mechanomyographic (MMG) amplitude and isometric torque production. Adult males (n = 9) performed isometric muscle actions of the leg extensors at 25, 50, 75, and 100 percent maximal voluntary contraction (%MVC) on a calibrated CYBEX 6000 dynamometer at 25, 50, and 75° below full extension. A piezoelectric MMG recording device was placed over the mid-portion of the rectus femoris. At 25° of leg flexion, the MMG amplitude increased to 100%MVC. At 50 and 75° of leg flexion, however, MMG amplitude increased to 75%MVC, and then did not change significantly (P > 0.05) between 75 and 100%MVC. These findings indicate that the MMG amplitude-isometric torque relationship is joint angle specific and may be the result of leg flexion angle differences in: (1) muscle stiffness, or (2) motor unit activation strategies. Accepted: 2 March 1998     

A three-dimensional model of the rat hindlimb: musculoskeletal geometry and muscle moment arms

As a first step towards developing a dynamic model of the rat hindlimb, we measured muscle attachment and joint center coordinates relative to bony landmarks using stereophotogrammetry. Using these measurements, we analyzed muscle moment arms as functions of joint angle for most hindlimb muscles, and tested the hypothesis that postural change alone is sufficient to alter the function of selected muscles of the leg. We described muscle attachment sites as second-order curves. The length of the fit parabola and residual errors in the orthogonal directions give an estimate of muscle attachment sizes, which are consistent with observations made during dissection. We modeled each joint as a moving point dependent on joint angle; relative endpoint errors less than 7% indicate this method as accurate. Most muscles have moment arms with a large range across the physiological domain of joint angles, but their moment arms peak and vary little within the locomotion domain. The small variation in moment arms during locomotion potentially simplifies the neural control requirements during this phase. The moment arms of a number of muscles cross zero as angle varies within the quadrupedal locomotion domain, indicating they are intrinsically stabilizing. However, in the bipedal locomotion domain, the moment arms of these muscles do not cross zero and thus are no longer intrinsically stabilizing. We found that muscle function is largely determined by the change in moment arm with joint angle, particularly the transition from quadrupedal to bipedal posture, which may alter an intrinsically stabilizing arrangement or change the control burden.     

Reduction of neuromuscular redundancy for postural force generation using an intrinsic stability criterion

Postural control requires the coordination of multiple muscles to achieve both endpoint force production and postural stability. Multiple muscle activation patterns can produce the required force for standing, but the mechanical stability associated with any given pattern may vary, and has implications for the degree of delayed neural feedback necessary for postural stability. We hypothesized that muscular redundancy is reduced when muscle activation patterns are chosen with respect to intrinsic musculoskeletal stability as well as endpoint force production. We used a three-dimensional musculoskeletal model of the cat hindlimb with 31 muscles to determine the possible contributions of intrinsic muscle properties to limb stability during isometric force generation. Using dynamic stability analysis we demonstrate that within the large set of activation patterns that satisfy the force requirement for posture, only a reduced subset produce a mechanically stable limb configuration. Greater stability in the frontal-plane suggests that neural control mechanisms are more highly active for sagittal-plane and for ankle joint control. Even when the limb was unstable, the time-constants of instability were sufficiently great to allow long-latency neural feedback mechanisms to intervene, which may be preferential for movements requiring maneuverability versus stability. Local joint stiffness of muscles was determined by the stabilizing or destabilizing effects of moment-arm versus joint angle relationships. By preferentially activating muscles with high local stiffness, muscle activation patterns with feedforward stabilizing properties could be selected. Such a strategy may increase intrinsic postural stability without co-contraction, and may be useful criteria in the force-sharing problem.