Modeling the effects of musculoskeletal geometry on scapulohumeral muscle moment arms and lines of action

Abstract

Biomechanical investigations examining shoulder function commonly observe a high degree of inter-individual variability in muscle activity and kinematic patterns during static and dynamic upper extremity exertions. Substantial differences in musculoskeletal geometry between individuals can alter muscle moment arms and lines of action that, theoretically, alter muscle activity and shoulder kinematics. The purposes of this research were to: (i) quantify model-predicted functional roles (moment arms, lines of action) of the scapulohumeral muscles, (ii) compare model predictions to experimental data in the literature, and (iii) evaluate sensitivity of muscle functional roles due to changes in muscle attachment locations using probabilistic modeling. Monte Carlo simulations were performed to iteratively adjust muscle attachment locations at the clavicle, scapula, and humerus of the Delft Shoulder and Elbow Model in OpenSim. Muscle moment arms and lines of action were quantified throughout arm elevation in the scapular plane. In general, model-predicted moment arms agreed well with the reviewed literature; however, notable inconsistencies were observed when comparing lines of action. Variability in moment arms and lines of action were muscle-specific, with 2 standard deviations in moment arm and line of actions as high as 25.8?mm and 18.8° for some muscles, respectively. Moment arms were particularly sensitive to changes in attachment site closest to the joint centre. Variations in muscle functional roles due to differences in musculoskeletal geometry are expected to require different muscle activity and movement patterns for upper extremity exertions.     

Accuracy of generic musculoskeletal models in predicting the functional roles of muscles in human gait

Biomechanical assessments of muscle function are often performed using a generic musculoskeletal model created from anatomical measurements obtained from cadavers. Understanding the validity of using generic models to study movement biomechanics is critical, especially when such models are applied to analyze the walking patterns of persons with impaired mobility. The aim of this study was to evaluate the accuracy of scaled-generic models in determining the moment arms and functional roles of the lower-limb muscles during gait. The functional role of a muscle was described by its potential to contribute to the acceleration of a joint or the acceleration of the whole-body center of mass. A muscle's potential acceleration was defined as the acceleration induced by a unit of muscle force. Dynamic simulations of walking were generated for four children with cerebral palsy and five age-matched controls. Each subject was represented by a scaled-generic model and a model developed from magnetic resonance (MR) imaging. Calculations obtained from the scaled-generic model of each subject were evaluated against those derived from the corresponding MR-based model. Substantial differences were found in the muscle moment arms computed using the two models. These differences propagated to calculations of muscle potential accelerations, but predictions of muscle function (i.e., the direction in which a muscle accelerated a joint or the center of mass and the magnitude of the muscle's potential acceleration relative to that of other muscles) were consistent between the two modeling techniques. Our findings suggest that scaled-generic models and image-based models yield similar assessments of muscle function in both normal and pathological gait.     

Moment arms of the human neck muscles in flexion, bending and rotation

There is a paucity of data available for the moment arms of the muscles of the human neck. The objective of the present study was to measure the moment arms of the major cervical spine muscles in vitro. Experiments were performed on five fresh-frozen human head-neck specimens using a custom-designed robotic spine testing apparatus. The testing apparatus replicated flexion-extension, lateral bending and axial rotation of each individual intervertebral joint in the cervical spine while all other joints were kept immobile. The tendon excursion method was used to measure the moment arms of 30 muscle sub-regions involving 13 major muscles of the neck about all three axes of rotation of each joint for the neutral position of the cervical spine. Significant differences in the moment arm were observed across sub-regions of individual muscles and across the intervertebral joints spanned by each muscle (p<0.05). Overall, muscle moment arms were larger in flexion-extension and lateral bending than in axial rotation, and most muscles had prominent moment arms in at least 2 out of the 3 joint motions investigated. This study emphasizes the importance of detailed representation of a muscle's architecture in prediction of its torque capacity about the individual joints of the cervical spine. The dataset produced may be useful in developing and validating computational models of the human neck.     

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.     

Biarticular hip extensor and knee flexor muscle moment arms of the feline hindlimb

Moment arms are important for understanding muscular behavior and for calculating internal muscle forces in musculoskeletal simulations. Biarticular muscles cross two joints and have moment arms that depend on the angle of both joints the muscles cross. The tendon excursion method was used to measure the joint angle-dependence of hamstring (biceps femoris, semimembranosus and semitendinosus) moment arm magnitudes of the feline hindlimb at the knee and hip joints. Knee angle influenced hamstring moment arm magnitudes at the hip joint; compared to a flexed knee joint, the moment arm for semimembranosus posterior at the hip was at most 7.4 mm (25%) larger when the knee was extended. On average, hamstring moment arms at the hip increased by 4.9 mm when the knee was more extended. In contrast, moment arm magnitudes at the knee varied by less than 2.8 mm (mean=1.6 mm) for all hamstring muscles at the two hip joint angles tested. Thus, hamstring moment arms at the hip were dependent on knee position, while hamstring moment arms at the knee were not as strongly associated with relative hip position. Additionally, the feline hamstring muscle group had a larger mechanical advantage at the hip than at the knee joint.     

Finger Muscle Attachments for an OpenSim Upper-Extremity Model

We determined muscle attachment points for the index, middle, ring and little fingers in an OpenSim upper-extremity model. Attachment points were selected to match both experimentally measured locations and mechanical function (moment arms). Although experimental measurements of finger muscle attachments have been made, models differ from specimens in many respects such as bone segment ratio, joint kinematics and coordinate system. Likewise, moment arms are not available for all intrinsic finger muscles. Therefore, it was necessary to scale and translate muscle attachments from one experimental or model environment to another while preserving mechanical function. We used a two-step process. First, we estimated muscle function by calculating moment arms for all intrinsic and extrinsic muscles using the partial velocity method. Second, optimization using Simulated Annealing and Hooke-Jeeves algorithms found muscle-tendon paths that minimized root mean square (RMS) differences between experimental and modeled moment arms. The partial velocity method resulted in variance accounted for (VAF) between measured and calculated moment arms of 75.5% on average (range from 48.5% to 99.5%) for intrinsic and extrinsic index finger muscles where measured data were available. RMS error between experimental and optimized values was within one standard deviation (S.D) of measured moment arm (mean RMS error = 1.5 mm < measured S.D = 2.5 mm). Validation of both steps of the technique allowed for estimation of muscle attachment points for muscles whose moment arms have not been measured. Differences between modeled and experimentally measured muscle attachments, averaged over all finger joints, were less than 4.9 mm (within 7.1% of the average length of the muscle-tendon paths). The resulting non-proprietary musculoskeletal model of the human fingers could be useful for many applications, including better understanding of complex multi-touch and gestural movements.     

Scaling of peak moment arms of elbow muscles with upper extremity bone dimensions.

It is often assumed that moment arms scale with size and can be normalized by body segment lengths or limb circumferences. However, quantitative scaling relationships between moment arms and anthropometric dimensions are generally not available. We hypothesized that peak moment arms of the elbow flexor and extensor muscles scale with the shorter distance (D(s)) between the elbow flexion axis and a muscle's origin and insertion. To test this hypothesis, we estimated moment arms of six muscles that cross the elbow, digitized muscle attachment sites and bone surface geometry, and estimated the location of the elbow flexion axis in 10 upper extremity cadaveric specimens which ranged in size from a 5'0" female to a 6'4" male. D(s) accurately reflected the differences in peak moment arms across different muscles, explaining 93-99% of the variation in peaks between muscles in the same specimen. D(s) also explained between 55% and 88% of the interspecimen variation in peak moment arms for brachioradialis, biceps, and ECRL. Triceps peak moment arm was significantly correlated to the anterior-posterior dimension of the ulna measured at the olecranon (r(2)=0.61, p=0.008). Radius length provides a good measure of the interspecimen variation in peaks for brachioradialis, biceps, and ECRL. However, bone lengths were not significantly correlated to triceps moment arm or anterior-posterior bone dimensions. This work advances our understanding of the variability and scaling dimensions for elbow muscle moment arms across subjects of different sizes.     

Chimpanzee thumb muscle cross sections, moment arms and potential torques, and comparisons with humans.

This study investigates the morphological basis of differences between humans and chimpanzees in the kinematical and dynamical parameters of the musculature of the thumb. It is partly intended to test an hypothesis that human thumb muscles can exert significantly greater torques, due to larger muscle cross-sectional areas or to longer tendon moment arms or to both. We focus on the estimation of the potentials of thumb muscles to exert torques about joint axes in a sample of eight chimpanzee cadaver hands. The potential torque of a muscle is estimated by taking the product of a muscle's physiological cross-sectional area (an estimator of force) with its dynamical moment arm (derived from the slope of tendon excursion versus joint angular displacement, obtained during passive movements of cadaver thumb joints). Comparison of our results with similar data obtained for humans at the same Mayo Clinic laboratory shows significant differences between humans and chimpanzees in potential torque of most thumb muscles, those of humans generally exhibiting larger values. The primary reason for the larger torques in humans is that their average moment arms are significantly longer, permitting greater torque for a given muscle size. An additional finding is that chimpanzees and humans differ in the direction of secondary thumb metacarpal movements elicited by contraction of some muscles, as shown by differences in moment arm signs for a given movement in the same muscle. The differences appear to be related to differences in the musculo-skeletal structures of the trapeziometacarpal joint.     

Muscle moment arm and normalized moment contributions as reference data for musculoskeletal elbow and wrist joint models

A geometric musculoskeletal model of the elbow and wrist joints was developed to calculate muscle moment arms throughout elbow flexion/extension, forearm pronation/supination, wrist flexion/extension and radial/ulnar deviation. Model moment arms were verified with data from cadaver specimen studies and geometric models available in the literature. Coefficients of polynomial equations were calculated for all moment arms as functions of joint angle, with special consideration to coupled muscles as a function of two joint angles. Additionally, a “normalized potential moment (NPM)” contribution index for each muscle across the elbow and wrist joints in four degrees-of-freedom was determined using each muscle's normalized physiological cross-sectional area (PCSA) and peak moment arm (MA). We hypothesize that (a) a geometric model of the elbow and wrist joints can represent the major attributes of MA versus joint angle from many literature sources of cadaver and model data and (b) an index can represent each muscle's normalized moment contribution to each degree-of-freedom at the elbow and wrist. We believe these data serve as a simple, yet comprehensive, reference for how the primary 16 muscles across the elbow and wrist contribute to joint moment and overall joint performance.     

Level of subject-specific detail in musculoskeletal models affects hip moment arm length calculation during gait in pediatric subjects with increased femoral anteversion

Biomechanical parameters of gait such as muscle's moment arm length (MAL) and muscle-tendon length are known to be sensitive to anatomical variability. Nevertheless, most studies rely on rescaled generic models (RGMo) constructed from averaged data of cadaveric measurements in a healthy adult population. As an alternative, deformable generic models (DGMo) have been proposed. These models integrate a higher level of subject-specific detail by applying characteristic deformations to the musculoskeletal geometry. In contrast, musculoskeletal models based on magnetic resonance (MR) images (MRMo) reflect the involved subject's characteristics in every level of the model. This study investigated the effect of the varying levels of subject-specific detail in these three model types on the calculated hip MAL during gait in a pediatric population of seven cerebral palsy subjects presenting aberrant femoral geometry. Our results show large percentage differences in calculated MAL between RGMo and MRMo. Furthermore, the use of DGMo did not uniformly reduce inter-model differences in calculated MAL. The magnitude of these percentage differences stresses the need to take these effects into account when selecting the level of subject-specific detail one wants to integrate in musculoskeletal. Furthermore, the variability of these differences between subjects and between muscles makes it very difficult to a priori estimate their importance for a biomechanical analysis of a certain muscle in a given subject.     

Three-dimensional temporomandibular joint muscle attachment morphometry and its impacts on musculoskeletal modeling

In musculoskeletal models of the human temporomandibular joint (TMJ), muscles are typically represented by force vectors that connect approximate muscle origin and insertion centroids (centroid-to-centroid force vectors). This simplification assumes equivalent moment arms and muscle lengths for all fibers within a muscle even with complex geometry and may result in inaccurate estimations of muscle force and joint loading. The objectives of this study were to quantify the three-dimensional (3D) human TMJ muscle attachment morphometry and examine its impact on TMJ mechanics. 3D muscle attachment surfaces of temporalis, masseter, lateral pterygoid, and medial pterygoid muscles of human cadaveric heads were generated by co-registering measured attachment boundaries with underlying skull models created from cone-beam computerized tomography (CBCT) images. A bounding box technique was used to quantify 3D muscle attachment size, shape, location, and orientation. Musculoskeletal models of the mandible were then developed and validated to assess the impact of 3D muscle attachment morphometry on joint loading during jaw maximal open-close. The 3D morphometry revealed that muscle lengths and moment arms of temporalis and masseter muscles varied substantially among muscle fibers. The values calculated from the centroid-to-centroid model were significantly different from those calculated using the ‘Distributed model’, which considered crucial 3D muscle attachment morphometry. Consequently, joint loading was underestimated by more than 50% in the centroid-to-centroid model. Therefore, it is necessary to consider 3D muscle attachment morphometry, especially for muscles with broad attachments, in TMJ musculoskeletal models to precisely quantify the joint mechanical environment critical for understanding TMJ function and mechanobiology.     

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.     

Approximating complex musculoskeletal biomechanics using multidimensional autogenerating polynomials

Computational models of the musculoskeletal system are scientific tools used to study human movement, quantify the effects of injury and disease, plan surgical interventions, or control realistic high-dimensional articulated prosthetic limbs. If the models are sufficiently accurate, they may embed complex relationships within the sensorimotor system. These potential benefits are limited by the challenge of implementing fast and accurate musculoskeletal computations. A typical hand muscle spans over 3 degrees of freedom (DOF), wrapping over complex geometrical constraints that change its moment arms and lead to complex posture-dependent variation in torque generation. Here, we report a method to accurately and efficiently calculate musculotendon length and moment arms across all physiological postures of the forearm muscles that actuate the hand and wrist. Then, we use this model to test the hypothesis that the functional similarities of muscle actions are embedded in muscle structure. The posture dependent muscle geometry, moment arms and lengths of modeled muscles were captured using autogenerating polynomials that expanded their optimal selection of terms using information measurements. The iterative process approximated 33 musculotendon actuators, each spanning up to 6 DOFs in an 18 DOF model of the human arm and hand, defined over the full physiological range of motion. Using these polynomials, the entire forearm anatomy could be computed in <10 μs, which is far better than what is required for real-time performance, and with low errors in moment arms (below 5%) and lengths (below 0.4%). Moreover, we demonstrate that the number of elements in these autogenerating polynomials does not increase exponentially with increasing muscle complexity; complexity increases linearly instead. Dimensionality reduction using the polynomial terms alone resulted in clusters comprised of muscles with similar functions, indicating the high accuracy of approximating models. We propose that this novel method of describing musculoskeletal biomechanics might further improve the applications of detailed and scalable models to describe human movement.     

Anatomy of raccoon (Procyon lotor) and coati (Nasua narica and N. nasua) forearm and leg muscles: relations between fiber length, moment-arm length, and joint-angle excursion

Muscle architecture, moment arms, and locomotor movements in the distal limb segments of the procyonids Nasua (coati) and Procyon (raccoon) are analyzed with reference to patterns of muscle fiber length. This study addresses the hypothesis that relative fiber lengths among muscles in a muscle group can be predicted on the basis of correlates of muscle tension. The results include the following: consistent patterns of fiber length of muscles in a muscle group exist within and between the two genera. Differences in fiber length between muscles can be accounted for by two principal correlates of muscle excursion--length of a muscle's moment arm about a joint and joint-angle excursion. Muscle fiber pinnation permits increased tendon excursion, but this effect is relatively small in comparison to the effects of moment-arm length and joint-angle excursion. Corollary action between two or more joints (or lack thereof) is an important factor in determination of fiber lengths.     

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.     

A technical method using musculoskeletal model to analyse dynamic properties of muscles during human movement

An effective way to avoid invading or injuring the subjects is to use the musculoskeletal model when studying the dynamic properties of muscles in vivo. So, we put forward a joint coordinate system-based method, which mainly focuses on the coordinate's transformation of corresponding muscle attachment points, respectively, in the model and the subject in order to reproduce the movement of the subject on the model. As muscle moment arm is usually used to evaluate the dynamic properties of muscles, the moment arms in elbow flexion for each of the major muscles crossing the elbow in 50 healthy subjects (25 males and 25 females), ranging in height from 1.50 to 1.80 m (mean 1.6542 m) are calculated and compared with the measured data obtained from anatomical studies reported in the literature. The trends of the value basically coincide with each other. So, this novel method can be valid.     

Effect of muscle wrapping on model estimates of neck muscle strength

Of the computational models of the cervical spine reported in the literature, not one takes into account the changes in muscle paths due to the underlying vertebrae. Instead, all model the individual muscle paths as straight-line segments. The major aim of this study was to quantify the changes in muscle moment arm, muscle force and joint moment due to muscle wrapping in the cervical spine. Five muscles in a straight-line model of the cervical spine were wrapped around underlying vertebrae, and the results obtained from this model were compared against the original. The two models were then validated against experimental and computational data. Results show that muscle wrapping has a significant effect on muscle moment arms and therefore joint moments and should not be neglected.     

Effect of muscle wrapping on model estimates of neck muscle strength

Of the computational models of the cervical spine reported in the literature, not one takes into account the changes in muscle paths due to the underlying vertebrae. Instead, all model the individual muscle paths as straight-line segments. The major aim of this study was to quantify the changes in muscle moment arm, muscle force and joint moment due to muscle wrapping in the cervical spine. Five muscles in a straight-line model of the cervical spine were wrapped around underlying vertebrae, and the results obtained from this model were compared against the original. The two models were then validated against experimental and computational data. Results show that muscle wrapping has a significant effect on muscle moment arms and therefore joint moments and should not be neglected.     

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.     

Wrist tendon moment arms: Quantification by imaging and experimental techniques

Subject-specific musculoskeletal models require accurate values of muscle moment arms. The aim of this study was to compare moment arms of wrist tendons obtained from non-invasive magnetic resonance imaging (MRI) to those obtained from an in vitro experimental approach. MRI was performed on ten upper limb cadaveric specimens to obtain the centrelines for the flexor carpi radialis (FCR), flexor carpi ulnaris (FCU), extensor carpi radialis longus (ECRL), extensor carpi radialis brevis (ECRB), extensor carpi ulnaris (ECU), and abductor pollicis longus (APL) tendons. From these, the anatomical moment arms about each of the flexion-extension (FE) and radioulnar deviation (RUD) axes of the wrist were calculated. Specimens were mounted on a physiologic wrist simulator to obtain functional measurements of the moment arms using the tendon excursion method. No differences were observed between anatomical and functional values of the FE and RUD moment arms of FCR, ECRL and ECRB, and the RUD moment arm of ECU (p > .075). Scaling the anatomical moment arms relative to ECRB in FE and ECU in RUD reduced differences in the FE moment arm of FCU and the RUD moment arm of APL to less than 15% (p > .139). However, differences persisted in moment arms of FCU in RUD, and ECU and APL in FE (p < .008). This study shows that while measurements of moment arms of wrist tendons using imaging do not always conform to values obtained using in vitro experimental approaches, a stricter protocol could result in the acquisition of subject-specific moment arms to personalise musculoskeletal models.