Modelling, simulation and optimisation of a human vertical jump.

This paper describes an efficient biomechanical model of the human lower limb with the aim of simulating a real human jump movement consisting of an upword propulsion, a flying and a landing phase. A multiphase optimal control technique is used to solve the muscle force sharing problem. To understand how intermuscular control coordinates limb muscle excitations, the human body is reduced to a single lower limb consisting of three rigid bodies. The biomechanical system is activated by nine muscle-tendon actuators representing the basic properties of muscles during force generation. For the calculation of the minimal muscle excitations of the jump movement, the trajectory of the hip joint is given as a rheonomic constraint and the contact forces (ground reaction forces) are determined by force plates. Based on the designed musculoskeletal model and on the differential equations of the multibody system, muscle excitations and muscle forces necessary for a vertical jump movement are calculated. The validity of the system is assessed comparing the calculated muscle excitations with the registered surface electromyogramm (EMG) of the muscles. The achieved results indicate a close relationship between the predicted and the measured parameters.     

Modulation of shoulder muscle and joint function using a powered upper-limb exoskeleton

Robotic-assistive exoskeletons can enable frequent repetitive movements without the presence of a full-time therapist; however, human-machine interaction and the capacity of powered exoskeletons to attenuate shoulder muscle and joint loading is poorly understood. This study aimed to quantify shoulder muscle and joint force during assisted activities of daily living using a powered robotic upper limb exoskeleton (ArmeoPower, Hocoma). Six healthy male subjects performed abduction, flexion, horizontal flexion, reaching and nose touching activities. These tasks were repeated under two conditions: (i) the exoskeleton compensating only for its own weight, and (ii) the exoskeleton providing full upper limb gravity compensation (i.e., weightlessness). Muscle EMG, joint kinematics and joint torques were simultaneously recorded, and shoulder muscle and joint forces calculated using personalized musculoskeletal models of each subject’s upper limb. The exoskeleton reduced peak joint torques, muscle forces and joint loading by up to 74.8% (0.113 Nm/kg), 88.8% (5.8%BW) and 68.4% (75.6%BW), respectively, with the degree of load attenuation strongly task dependent. The peak compressive, anterior and superior glenohumeral joint force during assisted nose touching was 36.4% (24.6%BW), 72.4% (13.1%BW) and 85.0% (17.2%BW) lower than that during unassisted nose touching, respectively. The present study showed that upper limb weight compensation using an assistive exoskeleton may increase glenohumeral joint stability, since deltoid muscle force, which is the primary contributor to superior glenohumeral joint shear, is attenuated; however, prominent exoskeleton interaction moments are required to position and control the upper limb in space, even under full gravity compensation conditions. The modeling framework and results may be useful in planning targeted upper limb robotic rehabilitation tasks.     

Anterior hip joint force increases with hip extension, decreased gluteal force, or decreased iliopsoas force

Abnormal or excessive force on the anterior hip joint may cause anterior hip pain, subtle hip instability and a tear of the acetabular labrum. We propose that both the pattern of muscle force and hip joint position can affect the magnitude of anterior joint force and thus possibly lead to excessive force and injury. The purpose of this study was to determine the effect of hip joint position and of weakness of the gluteal and iliopsoas muscles on anterior hip joint force. We used a musculoskeletal model to estimate hip joint forces during simulated prone hip extension and supine hip flexion under four different muscle force conditions and across a range of hip extension and flexion positions. Weakness of specified muscles was simulated by decreasing the modeled maximum force value for the gluteal muscles during hip extension and the iliopsoas muscle during hip flexion. We found that decreased force contribution from the gluteal muscles during hip extension and the iliopsoas muscle during hip flexion resulted in an increase in the anterior hip joint force. The anterior hip joint force was greater when the hip was in extension than when the hip was in flexion. Further studies are warranted to determine if increased utilization of the gluteal muscles during hip extension and of the iliopsoas muscle during hip flexion, and avoidance of hip extension beyond neutral would be beneficial for people with anterior hip pain, subtle hip instability, or an anterior acetabular labral tear.     

Magnitude of forward trunk flexion influences upper limb muscular efforts and dynamic postural stability requirements during sitting pivot transfers in individuals with spinal cord injury

The purpose of this study was to investigate the effects of imposing different degrees of forward trunk flexion during sitting pivot transfers on electromyographic activity at the leading and trailing upper limb muscles and on dynamic stability requirements. Thirty-two individuals with a spinal cord injury performed three types of sitting pivot transfers: natural technique, exaggerated forward trunk flexion and upright trunk position. Ground reaction forces, trunk kinematics, and bilateral electromyographic activity of eight upper limb muscles were recorded. Electromyographic data were analyzed using the area under the curve of the muscular utilization ratio. Dynamic stability requirements of sitting pivot transfers were assess using a dynamic equilibrium model. Compared to the natural strategy, significantly greater muscle activities were found for the forward trunk flexion condition at the anterior deltoid and both heads of the pectorialis major, whereas the upright trunk strategy yielded greater muscle activity at the latissimus dorsii and the triceps. The forward flexed condition was found to be more dynamically stable, with a lower stabilizing force, increased area of base of support and greater distance traveled. Thus, transferring with a more forward trunk inclination, even though it increases work of few muscles, may be a beneficial trade-off because increased dynamic stability of this technique and versatility in terms of potential distance of the transfer.     

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.     

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.     

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.     

Shoulder muscle function depends on elbow joint position: an illustration of dynamic coupling in the upper limb

Shoulder muscle function has been documented based on muscle moment arms, lines of action and muscle contributions to contact force at the glenohumeral joint. At present, however, the contributions of individual muscles to shoulder joint motion have not been investigated, and the effects of shoulder and elbow joint position on shoulder muscle function are not well understood. The aims of this study were to compute the contributions of individual muscles to motion of the glenohumeral joint during abduction, and to examine the effect of elbow flexion on shoulder muscle function. A three-dimensional musculoskeletal model of the upper limb was used to determine the contributions of 18 major muscles and muscle sub-regions of the shoulder to glenohumeral joint motion during abduction. Muscle function was found to depend strongly on both shoulder and elbow joint positions. When the elbow was extended, the middle and anterior deltoid and supraspinatus were the greatest contributors to angular acceleration of the shoulder in abduction. In contrast, when the elbow was flexed at 90°, the anterior deltoid and subscapularis were the greatest contributors to joint angular acceleration in abduction. This dependence of shoulder muscle function on elbow joint position is explained by the existence of dynamic coupling in multi-joint musculoskeletal systems. The extent to which dynamic coupling affects shoulder muscle function, and therefore movement control, is determined by the structure of the inverse mass matrix, which depends on the configuration of the joints. The data provided may assist in the diagnosis of abnormal shoulder function, for example, due to muscle paralysis or in the case of full-thickness rotator cuff tears.     

Modeling the biomechanics of swine mastication – An inverse dynamics approach

A novel reconstructive alternative for patients with severe facial structural deformity is Le Fort-based, face-jaw-teeth transplantation (FJTT). To date, however, only ten surgeries have included underlying skeletal and jaw-teeth components, all yielding sub-optimal results and a need for a subsequent revision surgery, due to size mismatch and lack of precise planning. Numerous studies have proven swine to be appropriate candidates for translational studies including pre-operative planning of transplantation. An important aspect of planning FJTT is determining the optimal muscle attachment sites on the recipient?s jaw, which requires a clear understanding of mastication and bite mechanics in relation to the new donated upper and/or lower jaw. A segmented CT scan coupled with data taken from literature defined a biomechanical model of mandible and jaw muscles of a swine. The model was driven using tracked motion and external force data of one cycle of chewing published earlier, and predicted the muscle activation patterns as well as temporomandibular joint (TMJ) reaction forces and condylar motions. Two methods, polynomial and min/max optimization, were used for solving the muscle recruitment problem. Similar performances were observed between the two methods. On average, there was a mean absolute error (MAE) of <0.08 between the predicted and measured activation levels of all muscles, and an MAE of <7 N for TMJ reaction forces. Simulated activations qualitatively followed the same patterns as the reference data and there was very good agreement for simulated TMJ forces. The polynomial optimization produced a smoother output, suggesting that it is more suitable for studying such motions. Average MAE for condylar motion was 1.2 mm, which reduced to 0.37 mm when the input incisor motion was scaled to reflect the possible size mismatch between the current and original swine models. Results support the hypothesis that the model can be used for planning of facial transplantation.     

Finger joint force minimization in pianists using optimization techniques

A numerical optimization procedure was used to determine finger positions that minimize and maximize finger tendon and joint force objective functions during piano play. A biomechanical finger model for sagittal plane motion, based on finger anatomy, was used to investigate finger tendon tensions and joint reaction forces for finger positions used in playing the piano. For commonly used piano key strike positions, flexor and intrinsic muscle tendon tensions ranged from 0.7 to 3.2 times the fingertip key strike force, while resultant inter-joint compressive forces ranged from 2 to 7 times the magnitude of the fingertip force. In general, use of a curved finger position, with a large metacarpophalangeal joint flexion angle and a small proximal interphalangeal joint flexion angle, reduces flexor tendon tension and resultant finger joint force.     

A dynamic model of the forearm including fatigue

A biomechanical model of the forearm, consisting of 61 muscle-tendon systems or tendons and 8 sections, is presented. The model can be used to calculate the muscle forces when resultant of the external forces and the motion is known. Calculations are based on constraints of muscle forces, joint forces, contact forces, and tendon junctions, and a load sharing principle telling which of the feasible solutions are likely and which are not. Fatigue is accounted for by updating the upper limits of the muscle forces according to the loading history. As an example, the model is used to predict the load sharing between the fingers when they are pressed against a table with a given total force.     

The effect of finger extensor mechanism on the flexor force during isometric tasks.

The role of the intrinsic finger flexor muscles was investigated during finger flexion tasks. A suspension system was used to measure isometric finger forces when the point of force application varied along fingers in a distal-proximal direction. Two biomechanical models, with consideration of extensor mechanism Extensor Mechanism Model (EMM) and without consideration of extensor mechanism Flexor Model (FM), were used to calculate forces of extrinsic and intrinsic finger flexors. When the point of force application was at the distal phalanx, the extrinsic flexor muscles flexor digitorum profundus, FDP, and flexor digitorum superficialis, FDS, accounted for over 80% of the summed force of all flexors, and therefore were the major contributors to the joint flexion at the distal interphalangeal (DIP), proximal interphalangeal (PIP), and metacarpophalangeal (MCP) joints. When the point of force application was at the DIP joint, the FDS accounted for more than 70% of the total force of all flexors, and was the major contributor to the PIP and MCP joint flexion. When the force of application was at the PIP joint, the intrinsic muscle group was the major contributor for MCP flexion, accounting for more than 70% of the combined force of all flexors. The results suggest that the effects of the extensor mechanism on the flexors are relatively small when the location of force application is distal to the PIP joint. When the external force is applied proximally to the PIP joint, the extensor mechanism has large influence on force production of all flexors. The current study provides an experimental protocol and biomechanical models that allow estimation of the effects of extensor mechanism on both the extrinsic and intrinsic flexors in various loading conditions, as well as differentiating the contribution of the intrinsic and extrinsic finger flexors during isometric flexion.     

Sensitivity of intervertebral joint forces to center of rotation location and trends along its migration path

Translational vertebral motion during functional tasks manifests itself in dynamic loci for center of rotation (COR). A shift of COR affects moment arms of muscles and ligaments; consequently, muscle and joint forces are altered. Based on posture- and level-specific trends of COR migration revealed by in vivo dynamic radiography during functional activities, it was postulated that the instantaneous COR location for a particular joint is optimized in order to minimize the joint reaction forces. A musculoskeletal multi-body model was employed to investigate the hypotheses that (1) a posterior COR in upright standing and (2) an anterior COR in forward flexed posture leads to optimized lumbar joint loads. Moreover, it was hypothesized that (3) lower lumbar levels benefit from a more superiorly located COR.The COR in the model was varied from its initial position in posterior-anterior and inferior-superior direction up to ±6 mm in steps of 2 mm. Movement from upright standing to 45° forward bending and backwards was simulated for all configurations. Joint reaction forces were computed at levels L2L3 to L5S1. Results clearly confirmed hypotheses (1) and (2) and provided evidence for the validity of hypothesis (3), hence offering a biomechanical rationale behind the migration paths of CORs observed during functional flexion/extension movement. Average sensitivity of joint force magnitudes to an anterior shift of COR was +6 N/mm in upright and −21 N/mm in 30° forward flexed posture, while sensitivity to a superior shift in upright standing was +7 N/mm and −8 N/mm in 30° flexion. The relation between COR loci and joint loading in upright and flexed postures could be mainly attributed to altered muscle moment arms and consequences on muscle exertion. These findings are considered relevant for the interpretation of COR migration data, the development of numerical models, and could have an implication on clinical diagnosis and treatment or the development of spinal implants.     

Effects of lumbo-pelvic rhythm on trunk muscle forces and disc loads during forward flexion: A combined musculoskeletal and finite element simulation study

Previous in-vivo studies suggest that the ratio of total lumbar rotation over pelvic rotation (lumbo-pelvic rhythm) during trunk sagittal movement is essential to evaluate spinal loads and discriminate between low back pain and asymptomatic population. Similarly, there is also evidence that the lumbo-pelvic rhythm is key for evaluation of realistic muscle and joint reaction forces and moments predicted by various computational musculoskeletal models. This study investigated the effects of three lumbo-pelvic rhythms defined based on in-vivo measurements on the spinal response during moderate forward flexion (60°) using a combined approach of musculoskeletal modeling of the upper body and finite element model of the lumbosacral spine. The muscle forces and joint loads predicted by the musculoskeletal model, together with the gravitational forces, were applied to the finite element model to compute the disc force and moment, intradiscal pressure, annular fibers strain, and load-sharing. The results revealed that a rhythm with high pelvic rotation and low lumbar flexion involves more global muscles and increases the role of the disc in resisting spinal loads, while its counterpart, with low pelvic rotation, recruits more local muscles and engages the ligaments to lower the disc loads. On the other hand, a normal rhythm that has balanced pelvic and lumbar rotations yields almost equal disc and ligament load-sharing and results in more balanced synergy between global and local muscles. The lumbo-pelvic rhythm has less effect on the intradiscal pressure and annular fibers strain. This work demonstrated that the spinal response during forward flexion is highly dependent on the lumbo-pelvic rhythm. It is therefore, essential to adapt this parameter instead of using the default values in musculoskeletal models for accurate prediction of muscle forces and joint reaction forces and moments. The findings provided by this work are expected to improve knowledge of spinal response during forward flexion, and are clinically relevant towards low back pain treatment and disc injury prevention.     

The interaction of muscle moment arm,knee laxity,and torque in a multi-scale musculoskeletal model of the lower limb

IntroductionMusculoskeletal modeling allows insight into the interaction of muscle force and knee joint kinematics that cannot be measured in the laboratory. However, musculoskeletal models of the lower extremity commonly use simplified representations of the knee that may limit analyses of the interaction between muscle forces and joint kinematics. The goal of this research was to demonstrate how muscle forces alter knee kinematics and consequently muscle moment arms and joint torque in a musculoskeletal model of the lower limb that includes a deformable representation of the knee.MethodsTwo musculoskeletal models of the lower limb including specimen-specific articular geometries and ligament deformability at the knee were built in a finite element framework and calibrated to match mean isometric torque data collected from 12 healthy subjects. Muscle moment arms were compared between simulations of passive knee flexion and maximum isometric knee extension and flexion. In addition, isometric torque results were compared with predictions using simplified knee models in which the deformability of the knee was removed and the kinematics at the joint were prescribed for all degrees of freedom.ResultsPeak isometric torque estimated with a deformable knee representation occurred between 45° and 60° in extension, and 45° in flexion. The maximum isometric flexion torques generated by the models with deformable ligaments were 14.6% and 17.9% larger than those generated by the models with prescribed kinematics; by contrast, the maximum isometric extension torques generated by the models were similar. The change in hamstrings moment arms during isometric flexion was greater than that of the quadriceps during isometric extension (a mean RMS difference of 9.8 mm compared to 2.9 mm, respectively).DiscussionThe large changes in the moment arms of the hamstrings, when activated in a model with deformable ligaments, resulted in changes to flexion torque. When simulating human motion, the inclusion of a deformable joint in a multi-scale musculoskeletal finite element model of the lower limb may preserve the realistic interaction of muscle force with knee kinematics and torque.     

Comparison of an EMG-based and a stress-based method to predict shoulder muscle forces

The estimation of muscle forces in musculoskeletal shoulder models is still controversial. Two different methods are widely used to solve the indeterminacy of the system: electromyography (EMG)-based methods and stress-based methods. The goal of this work was to evaluate the influence of these two methods on the prediction of muscle forces, glenohumeral load and joint stability after total shoulder arthroplasty. An EMG-based and a stress-based method were implemented into the same musculoskeletal shoulder model. The model replicated the glenohumeral joint after total shoulder arthroplasty. It contained the scapula, the humerus, the joint prosthesis, the rotator cuff muscles supraspinatus, subscapularis and infraspinatus and the middle, anterior and posterior deltoid muscles. A movement of abduction was simulated in the plane of the scapula. The EMG-based method replicated muscular activity of experimentally measured EMG. The stress-based method minimised a cost function based on muscle stresses. We compared muscle forces, joint reaction force, articular contact pressure and translation of the humeral head. The stress-based method predicted a lower force of the rotator cuff muscles. This was partly counter-balanced by a higher force of the middle part of the deltoid muscle. As a consequence, the stress-based method predicted a lower joint load (16% reduced) and a higher superior–inferior translation of the humeral head (increased by 1.2 mm). The EMG-based method has the advantage of replicating the observed cocontraction of stabilising muscles of the rotator cuff. This method is, however, limited to available EMG measurements. The stress-based method has thus an advantage of flexibility, but may overestimate glenohumeral subluxation.     

Residual force enhancement during voluntary contractions of knee extensors and flexors at short and long muscle lengths

Residual force enhancement (RFE) is a term describing the observation that muscle tension during a contraction that includes a stretch and hold remains above that during an isometric contraction at the hold length. RFE has been observed during in vitro and in vivo experiments, but results involving voluntary contractions are mixed, particularly with respect to large muscles. The purpose of this study was to determine if RFE can be observed in large muscles such as knee extensors and flexors at joint configurations corresponding to the ascending and descending limbs of the muscle force-length curve. Two groups of twenty participants (ten males and ten females per group) performed maximum voluntary contractions on a Biodex machine in purely isometric conditions and in isometric conditions immediately following eccentric stretch. Knee extension trials were performed at 40° (short muscles) and 100° (long muscles) flexion from full extension (0°), and knee flexion trials were performed at 70° (short muscles) and 10° (long muscles) flexion. Stretch-isometric trials terminated at these angles following 30° of eccentric motion at 30°/s. Statistically-significant RFE was observed for both tasks at long-muscle joint configurations, but was not observed for either task at short-muscle joint configurations. Passive torque enhancement was also observed following muscle relaxation at long-muscle joint configurations for both tasks, but for only knee flexion at short-muscle joint configurations. These results reinforce for voluntary contractions of large muscles the RFE behavior observed in smaller muscles, and provide further evidence that RFE occurs primarily on the descending limb of the muscle force-length curve.     

A biomechanical model for the analysis of the cervical spine in static postures.

To gain a better understanding of the forces working on the cervical spine, a spatial biomechanical computer model was developed. The first part of our research was concerned with the development of a kinematic model to establish the axes of rotation and the mutual position of the head and vertebrae with regard to flexion, extension, lateroflexion and torsion. The next step was the introduction of lines of action of muscle forces and an external load, created by gravity and accelerations in different directions, working on the centre of gravity of the head and possibly a helmet. Although the results of our calculations should be interpreted cautiously in the present stage of our research, some conclusions can be drawn with respect to different head positions. During flexion muscle forces and joint reaction forces increase, except the force between the odontoid and the ligamentum transversum atlantis. This force shows a minimum during moderate flexion. The joint reaction forces on the levels C0-C1, C1-C2, and C7-T1 reach minimum values during extension, each in different stages of extension. Axial rotation less than 35 degrees does not need great muscle forces, axial rotation further than 35 degrees causes muscle forces and joint reaction forces to increase fast. While performing, lateral flexion muscle forces and joint reaction forces must increase rapidly to balance the head. We obtained some indications that the order of magnitude of the calculated forces is correct.