3D finite element models of shoulder muscles for computing lines of actions and moment arms

Accurate representation of musculoskeletal geometry is needed to characterise the function of shoulder muscles. Previous models of shoulder muscles have represented muscle geometry as a collection of line segments, making it difficult to account for the large attachment areas, muscle–muscle interactions and complex muscle fibre trajectories typical of shoulder muscles. To better represent shoulder muscle geometry, we developed 3D finite element models of the deltoid and rotator cuff muscles and used the models to examine muscle function. Muscle fibre paths within the muscles were approximated, and moment arms were calculated for two motions: thoracohumeral abduction and internal/external rotation. We found that muscle fibre moment arms varied substantially across each muscle. For example, supraspinatus is considered a weak external rotator, but the 3D model of supraspinatus showed that the anterior fibres provide substantial internal rotation while the posterior fibres act as external rotators. Including the effects of large attachment regions and 3D mechanical interactions of muscle fibres constrains muscle motion, generates more realistic muscle paths and allows deeper analysis of shoulder muscle function.     

Static optimization underestimates antagonist muscle activity at the glenohumeral joint: A musculoskeletal modeling study

Static optimization is commonly employed in musculoskeletal modeling to estimate muscle and joint loading; however, the ability of this approach to predict antagonist muscle activity at the shoulder is poorly understood. Antagonist muscles, which contribute negatively to a net joint moment, are known to be important for maintaining glenohumeral joint stability. This study aimed to compare muscle and joint force predictions from a subject-specific neuromusculoskeletal model of the shoulder driven entirely by measured muscle electromyography (EMG) data with those from a musculoskeletal model employing static optimization. Four healthy adults performed six sub-maximal upper-limb contractions including shoulder abduction, adduction, flexion, extension, internal rotation and external rotation. EMG data were simultaneously measured from 16 shoulder muscles using surface and intramuscular electrodes, and joint motion evaluated using video motion analysis. Muscle and joint forces were calculated using both a calibrated EMG-driven neuromusculoskeletal modeling framework, and musculoskeletal model simulations that employed static optimization. The EMG-driven model predicted antagonistic muscle function for pectoralis major, latissimus dorsi and teres major during abduction and flexion; supraspinatus during adduction; middle deltoid during extension; and subscapularis, pectoralis major and latissimus dorsi during external rotation. In contrast, static optimization neural solutions showed little or no recruitment of these muscles, and preferentially activated agonistic prime movers with large moment arms. As a consequence, glenohumeral joint force calculations varied substantially between models. The findings suggest that static optimization may under-estimate the activity of muscle antagonists, and therefore, their contribution to glenohumeral joint stability.     

Comparison between line and surface mesh models to represent the rotator cuff muscle geometry in musculoskeletal models

Accurate muscle geometry (muscle length and moment arm) is required to estimate muscle function when using musculoskeletal modelling. In shoulder, muscles are often modelled as a collection of independent line segments, leading to non-physiological muscles trajectory, especially for the rotator cuff muscles. To prevent this, a surface mesh model was developed and validated against 7 MRI positions in one participant. Mean moment arm errors was 11.4% for the line vs. 8.8% for the mesh model. While the model with independent lines led to some non-physiological trajectories, the mesh model gave lower misestimations of muscle lengths and moment arms.     

Finite element simulation of the behavior of the periodontal ligament: A validated nonlinear contact model

Due to its significance in tooth movement, the stress/deformation field of periodontium and the alveolar bone remodeling process, periodontal ligament (PDL) cannot be excluded from the studies investigating dental biomechanics regarding its excessive deformability. Therefore, many analytical and numerical researches are carried out to simulate its response and to create a constitutive model via experiments intending to discover the material properties of PDL. The aim of this study is to formulate a user specified contact model that can be used in conjunction with finite element (FE) software and reflects PDL’s influence on neighboring structures based on the currently available information, without requiring an actual volumetric finite element mesh of ligament. The results show good agreement with available experimental tooth mobility data. Smooth stress fields are obtained on the tooth root and alveolar bone, which is a significant aspect in bone-remodeling studies. The advantage of simulating PDL as a contact model at the interface of tooth root and the alveolar process instead of a solid-meshed FE model with poor geometric morphology and/or very dense mesh is expected to save pre/post-processing workforce, to increase the accuracy and to contribute to the smoothness of interface stress distributions.     

A volumetric model for growth of arterial walls with arbitrary geometry and loads

Stress and deformation in arterial wall tissue are factors which may influence significantly its response and evolution. In this work we develop models based on nonlinear elasticity and finite element numerical solutions for the mechanical behaviour and the remodelling of the soft tissue of arteries, including anisotropy induced by the presence of collagen fibres. Remodelling and growth in particular constitute important features in order to interpret stenosis and atherosclerosis. The main object of this work is to model accurately volumetric growth, induced by fluid shear stress in the intima and local wall stress in arteries with patient-specific geometry and loads. The model is implemented in a nonlinear finite element setting which may be applied to realistic 3D geometries obtained from in vivo measurements. The capabilities of this method are demonstrated in several examples. Firstly a stenotic process on an idealised geometry induced by a non-uniform shear stress distribution is considered. Following the growth of a right coronary artery from an in vivo reconstructed geometry is presented. Finally, experimental measurements for growth under hypertension for rat carotid arteries are modelled.     

Development of a finite element musculoskeletal model with the ability to predict contractions of three-dimensional muscles

Representation of realistic muscle geometries is needed for systematic biomechanical simulation of musculoskeletal systems. Most of the previous musculoskeletal models are based on multibody dynamics simulation with muscles simplified as one-dimensional (1D) line-segments without accounting for the large muscle attachment areas, spatial fibre alignment within muscles and contact and wrapping between muscles and surrounding tissues. In previous musculoskeletal models with three-dimensional (3D) muscles, contractions of muscles were among the inputs rather than calculated, which hampers the predictive capability of these models. To address these issues, a finite element musculoskeletal model with the ability to predict contractions of 3D muscles was developed. Muscles with realistic 3D geometry, spatial muscle fibre alignment and muscle-muscle and muscle-bone interactions were accounted for. Active contractile stresses of the 3D muscles were determined through an efficient optimization approach based on the measured kinematics of the lower extremity and ground force during gait. This model also provided stresses and strains of muscles and contact mechanics of the muscle-muscle and muscle-bone interactions. The total contact force of the knee predicted by the model corresponded well to the in vivo measurement. Contact and wrapping between muscles and surrounding tissues were evident, demonstrating the need to consider 3D contact models of muscles. This modelling framework serves as the methodological basis for developing musculoskeletal modelling systems in finite element method incorporating 3D deformable contact models of muscles, joints, ligaments and bones.     

Effects of rotator cuff tears on muscle moment arms: a computational study

Rotator cuff tears cause morphologic changes to cuff tendons and muscles, which can alter muscle architecture and moment arm. The effects of these alterations on shoulder mechanical performance in terms of muscle force and joint strength are not well understood. The purpose of this study was to develop a three-dimensional explicit finite element model for investigating morphological changes to rotator cuff tendons following cuff tear. The subsequent objectives were to validate the model by comparing model-predicted moment arms to empirical data, and to use the model to investigate the hypothesis that rotator cuff muscle moment arms are reduced when tendons are divided along the force-bearing direction of the tendon. The model was constructed by extracting tendon, cartilage, and bone geometry from the male Visible Human data set. Infraspinatus and teres minor muscle and tendon paths were identified relative to the humerus and scapula. Kinetic and kinematic boundary conditions in the model replicated experimental protocols, which rotated the humerus from 45 degrees internal to 45 degrees external rotation with constant loads on the tendons. External rotation moment arms were calculated for two conditions of the cuff tendons: intact normal and divided tendon. Predicted moment arms were within the 1-99% confidence intervals of experimental data for nearly all joint angles and tendon sub-regions. In agreement with the experimental findings, when compared to the intact condition, predicted moment arms were reduced for the divided tendon condition. The results of this study provide evidence that one potential mechanism for the reduction in strength observed with cuff tear is reduction of muscle moment arms. The model provides a platform for future studies addressing mechanisms responsible for reduced muscle force and joint strength including changes to muscle length-tension operating range due to altered muscle and tendon excursions, and the effects of cuff tear size and location on moment arms and muscle forces.     

Consideration of multiple load cases is critical in modelling orthotropic bone adaptation in the femur

Functional adaptation of the femur has been investigated in several studies by embedding bone remodelling algorithms in finite element (FE) models, with simplifications often made to the representation of bone’s material symmetry and mechanical environment. An orthotropic strain-driven adaptation algorithm is proposed in order to predict the femur’s volumetric material property distribution and directionality of its internal structures within a continuum. The algorithm was applied to a FE model of the femur, with muscles, ligaments and joints included explicitly. Multiple load cases representing distinct frames of two activities of daily living (walking and stair climbing) were considered. It is hypothesised that low shear moduli occur in areas of bone that are simply loaded and high shear moduli in areas subjected to complex loading conditions. In addition, it is investigated whether material properties of different femoral regions are stimulated by different activities. The loading and boundary conditions were considered to provide a physiological mechanical environment. The resulting volumetric material property distribution and directionalities agreed with ex vivo imaging data for the whole femur. Regions where non-orthogonal trabecular crossing has been documented coincided with higher values of predicted shear moduli. The topological influence of the different activities modelled was analysed. The influence of stair climbing on the properties of the femoral neck region is highlighted. It is recommended that multiple load cases should be considered when modelling bone adaptation. The orthotropic model of the complete femur is released with this study.     

The activity pattern of shoulder muscles in subjects with and without subacromial impingement

Altered shoulder muscle activity is frequently believed to be a pathogenetic factor of subacromial impingement (SI) and therapeutic interventions have been directed towards restoring normal motor patterns. Still, there is a lack of scientific evidence regarding the changes in muscle activity in patients with SI. The aim of the study was to determine and compare the activity pattern of the shoulder muscles in subjects with and without SI. Twenty-one subjects with SI and 20 healthy controls were included. Electromyography (EMG) was assessed from eight shoulder muscles from both shoulders during motion. In the symptomatic shoulder, there was a significantly greater EMG activity during abduction in the supraspinatus and latissimus muscles and less activity in serratus anterior compared to the healthy subjects. During external rotation, there was significantly less activity of the infraspinatus and serratus anterior muscles on the symptomatic side compared to the healthy subjects. On the asymptomatic side, the groups showed different muscle activity during external rotation. Our findings of an altered shoulder muscle activity pattern on both the symptomatic and asymptomatic side in patients indicate that the different motor patterns might be a pathogenetic factor of SI, perhaps due to inappropriate neuromuscular strategies affecting both shoulders.     

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 effect of fatigued internal rotator and external rotator muscles of the shoulder on the shoulder position sense

The purpose of this study was to investigate which muscle group, the agonist or antagonist, contributes most to the shoulder position sense (SPS). The SPS was tested under 2 conditions: fatigued shoulder internal rotator (IR) muscles (pectoralis major and latissimus dorsi) and fatigued external rotator (ER) muscles (infraspinatus). In each condition, the SPS was measured before and after a fatiguing task involving the IR or ER muscles by repeating shoulder joint rotation. SPS was measured using a method in which subjects reproduced a memorized shoulder joint rotation angle. The position error values in all conditions (fatigued IR and ER muscles) and measurement periods (before- and after-fatigue task) were compared using 2-way analysis of variance with repeated measures (IR/ER × before/after). Position error increased significantly after both fatigue tasks (before- vs. after-fatigue: IR muscle, 2.68° vs. 4.19°; ER muscle, 2.32° vs. 4.05°). In other words, SPS accuracy decreased when either the agonist or antagonist muscle was fatigued. This finding indicated that SPS may be affected by an integrated information of the afferent signals in the agonist and antagonist muscles.     

Virtual musculo-skeletal model for the biomechanical analysis of the upper limb

In this paper, a musculo-skeletal model of the upper limb is presented. The limb is modelled as a three-dimensional 7 degrees-of-freedom system, linked to the shoulder, which has been considered as frame. The upper limb model is made up of four links corresponding to the most important body segments: the humerus, the ulna, the radius and the hand, considered as a single rigid body. Particular attention has been paid to the modelling of joints in order to mimic all the possible arm and forearm movements (including prono-supination). The model also includes 24 muscles. The mathematical model used to describe the muscles is that proposed by Zajac in 1989, modified by the authors. The kinematic analysis has been performed including an ergonomics index to take into account the posture and joint physical limits. Moreover an optimization criterion based on minimum activation pattern has been included in order to find muscular activation coefficients. The results of the proposed methodology concerning muscular activations have been compared to those coming from processed EMG signals, which have been acquired during experimental tests.     

The effect of handedness on electromyographic activity of human shoulder muscles during movement.

The aim of the study was to investigate whether there was a difference in the electromyographic (EMG) activity of human shoulder muscles between the dominant and nondominant side during movement and to explore whether a possible side-difference depends on the specific task. We compared the EMG activity with surface and intramuscular electrodes in eight muscles of both shoulders in 20 healthy subjects whose hand preference was evaluated using a standard questionnaire. EMG signals were recorded during abduction and external rotation. During abduction, the normalized EMG activity was significantly smaller on the dominant side compared to the nondominant side for all the muscles except for infraspinatus and lower trapezius (P 相似文献   

Development and validation of a subject-specific finite element model of a human clavicle

This study aimed to develop and validate a finite element (FE) model of a human clavicle which can predict the structural response and bone fractures under both axial compression and anterior–posterior three-point bending loads. Quasi-static non-injurious axial compression and three-point bending tests were first conducted on a male clavicle followed by a dynamic three-point bending test to fracture. Then, two types of FE models of the clavicle were developed using bone material properties which were set to vary with the computed tomography image density of the bone. A volumetric solid FE model comprised solely of hexahedral elements was first developed. A solid-shell FE model was then created which modelled the trabecular bone as hexahedral elements and the cortical bone as quadrilateral shell elements. Finally, simulations were carried out using these models to evaluate the influence of variations in cortical thickness, mesh density, bone material properties and modelling approach on the biomechanical responses of the clavicle, compared with experimental data. The FE results indicate that the inclusion of density-based bone material properties can provide a more accurate reproduction of the force–displacement response and bone fracture timing than a model with uniform bone material properties. Inclusion of a variable cortical thickness distribution also slightly improves the ability of the model to predict the experimental response. The methods developed in this study will be useful for creating subject-specific FE models to better understand the biomechanics and injury mechanism of the clavicle.     

Towards a model for force predictions in the human shoulder.

In this paper the concept of a three-dimensional biomechanical model of the human shoulder is introduced. This model is used to analyze static load sharing between the muscles, the bones and the ligaments. The model consists of all shoulder structures, which means that different positions and different load situations may be analyzed using the same model. Solutions can be found for the complete range of shoulder motion. However, this article focuses only on elevation in the scapular plane and on forces in structures attached to the humerus. The intention is to expand the model in future studies to also involve the forces acting on the other shoulder bones: the scapula and the clavicle. The musculoskeletal forces in the shoulder complex are predicted utilizing the optimization technique with the sum of squared muscle stresses as an objective function. Numerical results predict that among the muscles crossing the glenohumeral joint parts of the deltoideus, the infraspinatus, the supraspinatus, the subscapularis, the pectoralis major, the coracobrachialis and the biceps are the muscles most activated during this sort of abduction. Muscle-force levels reached values of 150 N when the hand load was 1 kg. The results from the model seem to be qualitatively accurate, but it is concluded that in the future development of the model the direction of the contact force in the glenohumeral joint must be constrained.     

Geometry parameters for musculoskeletal modelling of the shoulder system.

A dynamical finite-element model of the shoulder mechanism consisting of thorax, clavicula, scapula and humerus is outlined. The parameters needed for the model are obtained in a cadaver experiment consisting of both shoulders of seven cadavers. In this paper, in particular, the derivation of geometry parameters from the measurement data is described. The results for one cadaver are presented as a typical example. Morphological structures are modelled as geometrical forms. Parameters describing this form are estimated from 3-D position coordinates of a large number of datapoints on the morphological structure, using a least-squares criterion. Muscle and ligament attachments are represented as a plane or as a (curved) line. Muscle paths are determined by a geometrical form of the bony contour around which the muscle is wrapped. Muscle architecture is determined by the distribution of muscle bundles over the attachment area, mapping the distribution of the origin to the insertion. Joint rotation centers are derived from articular surfaces. Hence, muscle moment arms can be calculated. The result of this study is a set of parameters for each cadaver, describing very precisely the geometry of the shoulder mechanism. This set allows positioning of muscle force vectors a posteriori, and recalculation of position coordinates and moment arms for any position of the shoulder.     

The shape of the mandible in the domestic sheep: a biomechanical analysis using EMG as an estimator of muscle force

Analysis of the maximal loads to which a skeletal element is subjected in vivo offers attractive possibilities of explaining the shape of the element. The underlying assumption is that the element will be constructed in such a way that deformations (strains) which result from mechanical stress will not exceed certain limits and that stresses will be evenly distributed. The sheep mandible shows a number of characteristic morphological features that invite this kind of explanation. We investigated the patterns of activity of the masticatory musculature by multichannel electromyography, expressing the activity of any particular muscle during a given interval as a percentage of the highest activity recorded for the muscle in question. In combination with data on the physiological cross sections of the muscles, which provide indications of the maximal forces which can be exerted by the muscles, three-dimensional patterns of relative muscular forces acting on the mandible can be constructed for successive stages of a masticatory cycle. No absolute forces can be measured or even estimated by this technique. A two-dimensional finite element model of the mandible was designed, by means of which predictions of stress and strain resulting from the muscular loading can be made. Calculations were based on the highest loads that occurred, during the power stroke of rumination. It is concluded that mechanical loading of the mandible provides a partial explanation of the form, and that a more satisfactory model should include other than purely mechanical influences.