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.     

Effect of hip flexibility on optimal stalder performances on high bar

In the optimisation of sports movements using computer simulation models, the joint actuators must be constrained in order to obtain realistic results. In models of a gymnast, the main constraint used in previous studies was maximum voluntary active joint torque. In the stalder, gymnasts reach their maximal hip flexion under the bar. The purpose of this study was to introduce a model of passive torque to assess the effect of the gymnast's flexibility on the technique of the straddled stalder. A three-dimensional kinematics driven simulation model was developed. The kinematics of the shoulder flexion, hip flexion and hip abduction were optimised to minimise torques for four hip flexion flexibilities: 100°, 110°, 120° and 130°. With decreased flexibility, the piked posture period is shorter and occurs later. Moreover the peaks of shoulder and hip torques increase. Gymnasts with low hip flexibility need to be stronger to achieve a stalder; hip flexibility should be considered by coaches before teaching this skill.     

Surface EMG force modeling with joint angle based calibration

In this paper, a calibration method to compensate for changes in SEMG amplitude with joint angle is introduced. Calibration factors were derived from constant amplitude surface electromyogram (SEMG) recordings from the biceps brachii (during elbow flexion) and the triceps brachii (during elbow extension) across seven elbow joint angles. SEMG data were then recorded from the elbow flexors (biceps brachii and brachioradialis) and extensors (triceps brachii) during isometric, constant force flexion and extension contractions at the same joint angles. The resulting force at the wrist was measured. The fast orthogonal search method was used to find a mapping between the system inputs – estimated SEMG amplitudes and joint angle – and the system output – measured force, for both calibrated and non-calibrated SEMG data. Models developed with calibrated data yielded a statistically significant improvement in force estimation compared to models developed with non-calibrated data, suggesting that the calibration method can compensate for changes in the SEMG–force relationship with changing joint angle. It was also found that the number of non-linear, joint angle-dependent terms used in the SEMG–force model was reduced with calibration. Additionally, initial inter-session analysis performed for four subjects suggests that calibration values can be used for subsequent recording sessions, and different output force levels.     

The relationship between strength,power and ballistic performance

The purpose of this investigation was to answer the question, “Does Stronger Mean Faster?”. After a screening for elbow strength and speed, four groups of 8 subjects were selected for further investigation that fell into the extreme quartiles of the strength and speed continuums. The main investigation employed an apparatus that could freely rotate in the sagittal plane. Three isometric trials were performed at 60°, 90° and 120° of elbow extension. Dynamic trials were performed with relative resistances (0, 20, 40, 60 and 80%), determined from the lowest maximum isometric torque produced from the three joint angles mentioned above, and absolute resistances of 1.1 kg and 2.2 kg. A 1:1 relationship between strength and speed was not established (r = 0.498). Normalized peak power proved to be the best kinetic variable for predicting peak velocity (r ranging between 0.793 and 0.918). Individuals with similar peak torques were compared and the patterns of torque development, whether torques peaked early or late during the movement, physiologically agreed with known theoretically established mechanical responses. Similar velocities were also achieved with different peak torques demonstrating a timing issue. Estimated fibre-typing could not account for the performance differences.     

A stochastic model of elbow flexion strength for subjects with and without long head biceps tear

The classical approach of musculoskeletal modeling is to predict muscle forces and joint torques with a deterministic model constructed from parameters of an average subject. However, this type of model does not perform well for outliers, and does not model the effects of parameter variability. In this study, a Monte-Carlo model was used to stochastically simulate the effects of variability in musculoskeletal parameters on elbow flexion strength in healthy normals, and in subjects with long head biceps (LHB) rupture. The goal was to determine if variability in elbow flexion strength could be quantifiably explained with variability in musculoskeletal parameters. Parameter distributions were constructed from data in the literature. Parameters were sampled from these distributions and used to predict muscle forces and joint torques. The median and distribution of measured joint torque was predicted with small errors ( < 5%). Muscle forces for both cases were predicted and compared. In order to predict measured torques for the case of LHB rupture, the median force and mean cross-sectional area in the remaining elbow flexor muscles is greater than in healthy normals. The probabilities that muscle forces for the Tear case exceed median muscle forces for the No-Tear case are 0.98, 0.99 and 0.79 for SH Biceps, brachialis and brachioradialis, respectively. Differences in variability of measured torques for the two cases are explained by differences in parameter variability.     

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.     

Residual force enhancement contributes to increased performance during stretch-shortening cycles of human plantar flexor muscles in vivo

It is well known that muscular force production is history-dependent, which results in enhanced (RFE) and depressed (RFD) steady-state forces after stretching and shortening, respectively. However, it remains unclear if force-enhancing mechanisms can contribute to increased performance during in vivo stretch-shortening cycles (SSCs) of human locomotor muscles. The purpose of this study was to investigate whether RFE-related mechanisms contribute to enhanced force and power output during SSCs of the human plantar flexor muscles. Net ankle torques of fourteen participants were measured during and after pure isometric, pure stretch, pure shortening, and SSC contractions when the triceps surae muscles were electrically stimulated at a submaximal level that resulted in 30% of their maximum isometric torque. Dynamic contractions were performed over an amplitude of 15°, from 5° plantar flexion to 10° dorsiflexion, at a speed of 120° s⁻¹. External ankle work during shortening was 11.6% greater during SSCs compared to pure shortening contractions (p = .003). Additionally, RFD after SSCs (8.6%) was reduced compared to RFD after pure shortening contractions (12.0%; p < .05). It is therefore concluded that RFE-related mechanisms contribute to increased performance following SSCs of human locomotor muscles. Since RFD after SSCs decreased although work during shortening was increased, we speculate that the relevant mechanism lies outside actin-myosin interaction. Finally, our data suggests that RFE might be relevant and beneficial for human locomotion whenever a muscle is stretched, but this needs to be confirmed.     

Comparison of fascicle behaviors between superficial and deeper muscles of triceps brachii during isometric contractions

PurposeWe assessed fascicle behaviors of the upper extremities during isometric contractions at different joint angles in this study.MethodsThirteen healthy men and women performed isometric elbow extension tasks at 50% and 75% of maximal voluntary contraction (MVC) at 60°, 90°, and 120° of elbow extension (full extension = 180°). Extended field-of-view B-mode ultrasonography was used to obtain sagittal plane panoramic images of the long head (TB-Long) and medial head (TB-Med) of the triceps brachii at rest and during contraction; fascicle length and pennation angle were measured.ResultsIn the TB-Long, significant fascicle shortening from rest was found during 50% and 75%MVC at 60° and during 75%MVC at 90° of extension. There was no significant fascicle shortening in the TB-Med muscle under any conditions. There was no significant pennation angle change from rest in either muscle. The pennation angle of the TB-Long was significantly greater than that of the TB-Med under all conditions.ConclusionsThese results suggest that fascicle shortening in the TB-Long muscle occurs in flexion; however, no change was found in the TB-Med. In the upper extremity muscle–tendon complex, the superficial and deeper muscles may have different force-transmission efficiency at flexed joint angles.     

Effect of elbow joint angle on force–EMG relationships in human elbow flexor and extensor muscles

The purpose of this study was to examine the effect of joint angle on the relationship between force and electromyogram (EMG) amplitude and median frequency, in the biceps, brachioradialis and triceps muscles. Surface EMG were measured at eight elbow angles, during isometric flexion and extension at force levels from 10% to 100% of maximum voluntary contraction (MVC). Joint angle had a significant effect on MVC force, but not on MVC EMG amplitude in all of the muscles examined. The median frequency of the biceps and triceps EMG decreased with increasing muscle length, possibly due to relative changes in electrode position or a decrease in muscle fibre diameter. The relationship between EMG amplitude and force, normalised with respect to its maximum force at each angle, did not vary with joint angle in the biceps or brachioradialis muscles over all angles, or in the triceps between 45° and 120° of flexion. These results suggest that the neural excitation level to each muscle is determined by the required percentage of available force rather than the absolute force required. It is, therefore, recommended that when using surface EMG to estimate muscle excitation, force should be normalised with respect to its maximum value at each angle.     

Muscle synergy in isometric flexion of the elbow]

A technique was developed for calculating the torque generated by two individual muscles (biceps brachii and brachioradialis) that contribute to the isometric flexion of the elbow. The external torque is the sum of individual torques which are unknown. Each individual torque (CB or CBR) can be related to the corresponding integrated surface EMG (QB or QBR) by means of coefficients (pB or PBR). A block of several equations C = pB QB + pBR QBR is obtained by exploring several experimental conditions. In these conditions, isometric flexion efforts of the elbow were associated to isometric efforts of supination or pronation so as to vary integrated EMG by reciprocal inhibition. By means of a least square method it was possible to know the coefficients PB and PBR. With these coefficients, it was possible to calculate the individual torques generated by the biceps brachii and brachioradialis muscles in each experimental condition.     

A geometric approach to study the contact mechanisms in the patellofemoral joint of normal versus patellofemoral pain syndrome subjects

The biomechanics of the patellofemoral (PF) joint is complex in nature, and the aetiology of such manifestations of PF instability as patellofemoral pain syndrome (PFPS) is still unclear. At this point, the particular factors affecting PFPS have not yet been determined. This study has two objectives: (1) The first is to develop an alternative geometric method using a three-dimensional (3D) registration technique and linear mapping to investigate the PF joint contact stress using an indirect measure: the depth of virtual penetration (PD) of the patellar cartilage surface into the femoral cartilage surface. (2) The second is to develop 3D PF joint models using the finite element analysis (FEA) to quantify in vivo cartilage contact stress and to compare the peak contact stress location obtained from the FE models with the location of the maximum PD. Magnetic resonance images of healthy and PFPS subjects at knee flexion angles of 15°, 30° and 45° during isometric loading have been used to develop the geometric models. The results obtained from both approaches demonstrated that the subjects with PFPS show higher PD and contact stresses than the normal subjects. Maximum stress and PD increase with flexion angle, and occur on the lateral side in healthy and on the medial side in PFPS subjects. It has been concluded that the alternative geometric method is reliable in addition to being computationally efficient compared with FEA, and has the potential to assess the mechanics of PFPS with an accuracy similar to the FEA.     

Relationships between individual isometric muscle forces, EMG activity and joint torque in monkeys

The aim of the present work was to determine the EMG activity and the moment of force developed by the main elbow flexor muscles, and to establish on this basis the degree of their participation in isometric contractions performed at various positions of the elbow. This was achieved by recording the following biomechanical parameters: EMG and tensile stress (or force) from biceps brachii (BB) and brachioradialis (BR); EMG from brachialis; external resultant force (FE). There was: a linear or quadratic relationship between the integrated EMG from each muscle and FE; a linear relationship between the force produced by BB or BR and FE. The slope of these relationships depended on the elbow angle, except for that between BB force and FE. It is proposed that iEMG changes compensate for those of the force lever arm. It has been calculated that the contribution of BR to external torque decreased from the extension to flexion while that of BB increased from 70 degrees to 90 degrees and then decreased. How far these data can be extrapolated to man is a matter of discussion based on iEMG and anthropometrical data.     

The Sense of Effort and two Models of Single-Joint Motor Control

Two sets of experiments were carried out. In the first set, human subjects were asked to make the same effort with the elbow flexors at different joint angles under isometric conditions. In some experiments, the subjects were standing with the arm in a vertical (parasagittal) plane; in others, they were seated with the arm in a horizontal (transverse) plane. When muscular torque at a given effort level (ordinate) was plotted as a function of elbow joint angle (abscissa), the resulting isoeffort torque-angle profiles tended to be flat or negatively sloping over a range from 45° to 135°, and they were often nonmonotonic. Increases in effort up to near-maximal levels caused the isoeffort torque-angle profiles to shift upward with little alteration in shape. In the second set of experiments, seated subjects with the arm horizontal resisted baseline torques produced by a motor that acted to extend the elbow joint. Unexpected increases and decreases in torque were superimposed on the baseline torque. The subjects either were instructed to intervene and return the elbow to the initial (90°) position, or were told, “Do not intervene voluntarily; let the motor move your arm.” Effort was reported both under baseline conditions and after the changes in torque. It was found that changes in effort were a function of the changes in torque opposed by the elbow flexors, and were similar whether the subject had repositioned the arm or allowed it to be moved by the motor. In the latter case, the arm came to rest after displacements that were a function of the size and direction of the torque change. For individual subjects, the largest angular displacements ranged from ° 10° to °20° for changes in torque of ° 10 N.m. There was no evidence for any angular dependence of the effort judgments at a given torque over this angular range. Depending on whether effort is primarily an efferent perception proportional to voluntary motor activity or also has a significant afferent (involuntary) component, different models of motor control are supported by these data.     

The contribution of the wrist, elbow and shoulder joints to single-finger tapping

We aimed to determine the role of the wrist, elbow and shoulder joints to single-finger tapping. Six human subjects tapped with their index finger at a rate of 3 taps/s on a keyswitch across five conditions, one freestyle (FS) and four instructed tapping strategies. The four instructed conditions were to tap on a keyswitch using the finger joint only (FO), the wrist joint only (WO), the elbow joint only (EO), and the shoulder joint only (SO). A single-axis force plate measured the fingertip force. An infra-red active-marker three-dimensional motion analysis system measured the movement of the fingertip, hand, forearm, upper arm and trunk. Inverse dynamics estimated joint torques for the metacarpal-phalangeal (MCP), wrist, elbow, and shoulder joints. For FS tapping 27%, 56%, and 18% of the vertical fingertip movement were a result of flexion of the MCP joint and wrist joint and extension of the elbow joint, respectively. During the FS movements the net joint powers between the MCP, wrist and elbow were positively correlated (correlation coefficients between 0.46 and 0.76) suggesting synergistic efforts. For the instructed tapping strategies (FO, WO, EO, and SO), correlations decreased to values below 0.35 suggesting relatively independent control of the different joints. For FS tapping, the kinematic and kinetic data indicate that the wrist and elbow contribute significantly, working in synergy with the finger joints to create the fingertip tapping task.     

Evidence of changes in load sharing during isometric elbow flexion with ramped torque

This study aimed to: (1) test the repeatability of Supersonic Shear Imaging measures of muscle shear elastic modulus of four elbow flexor muscles during isometric elbow flexion with ramped torque; (2) determine the relationship between muscle shear elastic modulus and elbow torque for the four elbow flexor muscles, and (3) investigate changes in load sharing between synergist elbow flexor muscles with increases in elbow flexor torque. Ten subjects performed ten isometric elbow flexions consisting of linear torque ramps of 30-s from 0 to 40% of maximal voluntary contraction. The shear elastic modulus of each elbow flexor muscle (biceps brachii long head [BB(LH)], biceps brachii short head [BB(SH)], brachialis [BA], and brachoradialis [BR]) and of triceps brachii long head [TB] was measured twice with individual muscles recorded in separate trials in random order. A good repeatability of the shape of the changes in shear elastic modulus as a function of torque was found for each elbow flexor muscle (r-values: 0.85 to 0.94). Relationships between the shear elastic modulus and torque were best explained by a second order polynomial, except BA where a higher polynomial was required. Statistical analysis showed that BB(SH) and BB(LH) had an initial slow change at low torques followed by an increasing rate of increase in modulus with higher torques. In contrast, the BA shear elastic modulus increased rapidly at low forces, but plateaued at higher forces. These results suggest that changes in load sharing between synergist elbow flexors could partly explain the non-linear EMG-torque relationship classically reported for BB during isometric efforts.     

Do relevant shear forces appear in isokinetic shoulder testing to be implemented in biomechanical models?

Isokinetic dynamometers measure joint torques about a single fixed rotational axis. Previous studies yet suggested that muscles produce both tangential and radial forces during a movement, so that the contact forces exerted to perform this movement are multidirectional. Then, isokinetic dynamometers might neglect the torque components about the two other Euclidean space axes. Our objective was to experimentally quantify the shear forces impact on the overall shoulder torque, by comparing the dynamometer torque to the torque computed from the contact forces at the hand and elbow. Ten healthy women performed isokinetic maximal internal/external concentric/eccentric shoulder rotation movements. The hand and elbow contact forces were measured using two six-axis force sensors. The main finding is that the contact forces at the hand were not purely tangential to the direction of the movement (effectiveness indexes from 0.26 ± 0.25 to 0.54 ± 0.20), such that the resulting shoulder torque computed from the two force sensors was three-dimensional. Therefore, the flexion and abduction components of the shoulder torque measured by the isokinetic dynamometer were significantly underestimated (up to 94.9%). These findings suggest that musculoskeletal models parameters should not be estimated without accounting for the torques about the three space axes.     

Normal force distribution and posture of a hand pressing on a flat surface

Hand strength data are needed to understand and predict hand postures and finger loads while placing the hand on an object or surface. This study aims to analyze the effect of hand posture and surface orientation on hand force while pressing a flat surface. Twelve participants, 6 females and 6 males ages 19–25, performed three exertions (100%, 30% and 10% MVC- Maximum Voluntary Contraction) perpendicular to a plate in 4 angles (−45°, 0°, 45° and 90° with respect to the horizontal plane) at elbow height. Exertions involved pushing in two postures: (1) whole hand and (2) constrained to only using the fingertips. Inter-digit joint angles were recorded to map hand and finger motions and estimate joint moments for each condition. Participants exerted twice the force when pushing with whole hand vs. fingertips. 72–75% of the total force was exerted over the base of the palm, while only 11–13% with the thumb for exertions at 90°, 45° or 0° plate angles. Males maximum force for pushing at 0°, 45° and 90° plates averaged 49% higher than females for the whole hand and 62% for the fingertips (p < 0.01). There was no significant sex difference (p > 0.05) for the −45° plate. Thumb joint loads were generally higher than the other individual fingers (p < 0.05) in all % MVC and accounted for 12% of total force during whole hand exertions. On average, joint moments were 30% higher during fingertip conditions vs. whole hand. Thumb and finger joint moment magnitudes when pushing the plate at 100% MVC indicated that Metacarpophalangeal (MCP) joint moments were higher (p < 0.05) than Distal Interphalangeal joints (DIP) and Proximal Interphalangeal joints (PIP) under whole hand and fingertips conditions.     

Maximum isometric arm forces in the horizontal plane

In this paper, we measured the maximum isometric force at the hand in eight directions in the horizontal plane and at five positions in the workplace. These endpoint forces were the result of shoulder horizontal adduction/abduction and elbow flexion/extension torques. We found that the normalized maximum forces of all the six subjects deviated less than 15%, despite intra-subject differences in muscle strength of more than a factor of two. The maximum forces were found to systematically depend on the force direction and on the hand position in the workspace. The largest forces were found in a direction approximately along the line connecting shoulder joint and hand, and the smallest forces perpendicular to that line, thereby forming an elliptically shaped pattern. The elongation of the pattern was the largest for those hand positions having the more extended elbow joint. By using a lumped six-muscle model, with two mono-articular muscle pairs and one bi-articular pair, we were able to predict the observed force patterns. Here, we assumed that one of the muscles generates its maximum force and the others adjust their output to point the endpoint force in the required direction. We used a principal component analysis of the surface EMGs of simultaneously measured representatives of four of the six muscles. With the same model, we were then able to determine the principal directions of all the six muscle groups.     

A stochastic model of elbow flexion strength for subjects with and without long head biceps tear

The classical approach of musculoskeletal modeling is to predict muscle forces and joint torques with a deterministic model constructed from parameters of an average subject. However, this type of model does not perform well for outliers, and does not model the effects of parameter variability. In this study, a Monte-Carlo model was used to stochastically simulate the effects of variability in musculoskeletal parameters on elbow flexion strength in healthy normals, and in subjects with long head biceps (LHB) rupture. The goal was to determine if variability in elbow flexion strength could be quantifiably explained with variability in musculoskeletal parameters. Parameter distributions were constructed from data in the literature. Parameters were sampled from these distributions and used to predict muscle forces and joint torques. The median and distribution of measured joint torque was predicted with small errors (< 5%). Muscle forces for both cases were predicted and compared. In order to predict measured torques for the case of LHB rupture, the median force and mean cross-sectional area in the remaining elbow flexor muscles is greater than in healthy normals. The probabilities that muscle forces for the Tear case exceed median muscle forces for the No-Tear case are 0.98, 0.99 and 0.79 for SH Biceps, brachialis and brachioradialis, respectively. Differences in variability of measured torques for the two cases are explained by differences in parameter variability.