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.     

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.     

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.     

Tonic finite element model of the lower limb

It is widely admitted that muscle bracing influences the result of an impact, facilitating fractures by enhancing load transmission and reducing energy dissipation. However, human numerical models used to identify injury mechanisms involved in car crashes hardly take into account this particular mechanical behavior of muscles. In this context, in this work we aim to develop a numerical model, including muscle architecture and bracing capability, focusing on lower limbs. The three-dimensional (3-D) geometry of the musculoskeletal system was extracted from MRI images, where muscular heads were separated into individual entities. Muscle mechanical behavior is based on a phenomenological approach, and depends on a reduced number of input parameters, i.e., the muscle optimal length and its corresponding maximal force. In terms of geometry, muscles are modeled with 3-D viscoelastic solids, guided in the direction of fibers with a set of contractile springs. Validation was first achieved on an isolated bundle and then by comparing emergency braking forces resulting from both numerical simulations and experimental tests on volunteers. Frontal impact simulation showed that the inclusion of muscle bracing in modeling dynamic impact situations can alter bone stresses to potentially injury-inducing levels.     

The muscle line of action in current models of the human cervical spine: a comparison with in vivo MRI data

Cervical muscles are commonly represented by line-of-action models. This investigation evaluates the performance of three types of model implementations, based on their ability to mimic geometric in-vivo aspects of muscles. Five prominent pairs of neck muscles were reconstructed in three head positions using magnetic resonance imaging. Based on the reconstructions, muscle approximations were created that represent the muscles with piecewise straight lines. Measured and modelled muscle approximations were compared with respect to their pulling directions at the attachment sites and the overall distance between the muscle paths. Muscle lengths were evaluated in two ways. First, length discrepancies were determined between measured and modelled muscles depending on the head position. Second, the difference of muscle lengths in neutral and deflected head positions for measurement and models were calculated. The results indicate considerable differences between models and measurements. Pulling directions, for instance, differed by up to 40°, depending on the chosen muscle and the type of muscle implementation.     

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.     

Morphometry, ultrastructure, myosin isoforms, and metabolic capacities of the "mini muscles" favoured by selection for high activity in house mice

Prolonged selective breeding of mice (Mus musculus) for high levels of voluntary wheel running has favoured an unusual phenotype ("mini muscles"), apparently caused by a single Mendelian recessive allele, in which most hind-limb muscles are markedly reduced in mass, but have increased mass-specific activities of mitochondrial enzymes. We examined whether these changes reflect changes in fibre size, number or ultrastructure in normal and "mini-muscle" mice within the two (of four) selectively bred lines (lab designations L3 and L6) that exhibit the phenotype at generations 26 and 27. In both lines, the gastrocnemius and plantaris muscles are smaller in mass (by >50% and 20%, respectively) in affected individuals. The mass-specific activities of mitochondrial enzymes in the gastrocnemius and plantaris muscles were increased in the mini phenotype in both lines, with stronger effects in the gastrocnemius muscle. In the gastrocnemius, the % myosin heavy chain (MHC) IIb was reduced by 50% in L3 and by 30% in L6, whereas the % MHC IIa and I were higher, particularly in L3. Fibre number in the plantaris muscle did not significantly differ between mini and normal muscles, although muscle mass was a significant positive correlate of fibre number. Small fibres were more abundant in mini than normal muscles in L3. Mitochondrial volume density was significantly higher in mini than normal muscle fibres in L3, but not in L6. Microscopy revealed a surprising attribute of the mini muscles: an abundance of small, minimally differentiated, myofibril-containing cells positioned in a disorderly fashion, particularly in the surface layer. We hypothesise that these unusual cells may be satellite cells or type IIb fibres that did not complete their differentiation. Together, these observations suggest that mice with the mini phenotype have reduced numbers of type IIb fibres in many of their hind-limb muscles, leading to a decrease in mass and an increase in mass-specific aerobic capacity in muscles that typically have a high proportion of type IIb fibres. Moreover, the several statistically significant interactions between muscle phenotype and line indicate that the effect of the underlying allele is altered by genetic background.     

Tetrodotoxin blocks mechanical response in mammalian muscle in the presence of tetrodotoxin-resistant action potentials

The effect of tetrodotoxin (TTX) (10(-5)-10(-6)M) on the mechanical activity and on the action potential of innervated and denervated muscle of the rat was studied. The twitch tension was reduced to 10 % of the control values within 20 min of TTX 10(-6) introduction. This effect was reversible. The mean twitch tension in the presence of 10(-6)M TTX expressed as a percentage of control was 9.3 +/- 2.4 (SEM) for innervated muscle and 10.9 +/- 2.5 for denervated muscle. The dose-effect twitch relation for denervated muscles was not significantly different from that observed in control innervated muscles in the 10(-3)-10(-6) TTX range. Action potentials of innervated muscles could not be elicited in 10(-6)M TTX. In the presence of this (TTX) fibers of chronically denervated muscles consistently responded to stimulation with action potentials which were slower and smaller but still with overshoot, contrasting with fibrillation potentials that had been described to be blocked by TTX.     

Transformation methods for estimation of subject-specific scapular muscle attachment sites

The parameters that describe the soft tissue structures are among the most important anatomical parameters for subject-specific biomechanical modelling. In this paper, we study one of the soft tissue parameters, namely muscle attachment sites. Two new methods are proposed for transformation of the muscle attachment sites of any reference scapula to any destination scapula based on four palpable bony landmarks. The proposed methods as well as one previously proposed method have been applied for transformation of muscle attachment sites of one reference scapula to seven other scapulae. The transformation errors are compared among the three methods. Both proposed methods yield significantly less (p < 0.05) prediction error as compared to the currently available method. Furthermore, we investigate whether there exists a reference scapula that performs significantly better than other scapulae when used for transformation of muscle attachment sites. Seven different scapulae were used as reference scapula and their resulting transformation errors were compared with each other. In the considered statistical population, no such a thing as an ideal scapula was found. There was, however, one outlier scapula that performed significantly worse than the other scapulae when used as a reference. The effect of perturbations in both muscle attachment sites and other muscle properties is studied by comparing muscle force predictions of a musculoskeletal model between perturbed and non-perturbed versions of the model. It is found that 10 mm variations in muscle attachments have more significant effect on muscle force predictions than 10% variations in any of the other four analysed muscle properties.     

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.     

Volar/dorsal compressive mechanical behavior of the transverse carpal ligament

Mechanical insult to the median nerve caused by contact with the digital flexor tendons and/or carpal tunnel boundaries may contribute to the development of carpal tunnel syndrome. Since the transverse carpal ligament (TCL) comprises the volar boundary of the carpal tunnel, its mechanics in part govern the potential insult to the median nerve. Using unconfined compression testing in combination with a finite element-based optimization process, nominal stiffness measurements and first-order Ogden hyperelastic material coefficients (μ and α ) were determined to describe the volar/dorsal compressive behavior of the TCL. Five different locations on the TCL were tested, three of which were deep to the origins of the thenar and hypothenar muscles. The average (± standard deviation) low-strain and high-strain TCL stiffness values in compression sites outside the muscle attachment region were 3.6 N/mm (±2.7) and 28.0 N/mm (±20.2), respectively. The average stiffness values at compression sites with muscle attachments were notably lower, with low-strain and high-strain stiffness values of 1.2 N/mm (±0.5) and 9.7 N/mm (±4.8), respectively. The average Ogden coefficients for the muscle attachment region were 51.6 kPa (±16.5) for μ and 16.5 (±2.0) for α, while coefficients for the non-muscle attachment region were 117.8 kPa (±86.8) for μ and 17.2 (±1.6) for α. These TCL compressive mechanical properties can help inprove computational models, which can be used to provide insight into the mechanisms of median nerve injury leading to the onset of carpal tunnel syndrome symptoms.     

Moleskin is essential for the formation of the myotendinous junction in Drosophila

It is the precise connectivity between skeletal muscles and their corresponding tendon cells to form a functional myotendinous junction (MTJ) that allows for the force generation required for muscle contraction and organismal movement. The Drosophila MTJ is composed of secreted extracellular matrix (ECM) proteins deposited between integrin-mediated hemi-adherens junctions on the surface of muscle and tendon cells. In this paper, we have identified a novel, cytoplasmic role for the canonical nuclear import protein Moleskin (Msk) in Drosophila embryonic somatic muscle attachment. Msk protein is enriched at muscle attachment sites in late embryogenesis and msk mutant embryos exhibit a failure in muscle–tendon cell attachment. Although the muscle–tendon attachment sites are reduced in size, components of the integrin complexes and ECM proteins are properly localized in msk mutant embryos. However, msk mutants fail to localize phosphorylated focal adhesion kinase (pFAK) to the sites of muscle–tendon cell junctions. In addition, the tendon cell specific proteins Stripe (Sr) and activated mitogen-activated protein kinase (MAPK) are reduced in msk mutant embryos. Our rescue experiments demonstrate that Msk is required in the muscle cell, but not in the tendon cells. Moreover, muscle attachment defects due to loss of Msk are rescued by an activated form of MAPK or the secreted epidermal growth factor receptor (Egfr) ligand Vein. Taken together, these findings provide strong evidence that Msk signals non-autonomously through the Vein-Egfr signaling pathway for late tendon cell late differentiation and/or maintenance.     

Skeletal Muscle Fascicle Arrangements Can Be Reconstructed Using a Laplacian Vector Field Simulation

Skeletal muscles are characterized by a large diversity in anatomical architecture and function. Muscle force and contraction are generated by contractile fiber cells grouped in fascicle bundles, which transmit the mechanical action between origin and insertion attachments of the muscle. Therefore, an adequate representation of fascicle arrangements in computational models of skeletal muscles is important, especially when investigating three-dimensional muscle deformations in finite element models. However, obtaining high resolution in vivo measurements of fascicle arrangements in skeletal muscles is currently still challenging. This motivated the development of methods in previous studies to generate numerical representations of fascicle trajectories using interpolation templates. Here, we present an alternative approach based on the hypothesis of a rotation and divergence free (Laplacian) vector field behavior which reflects observed physical characteristics of fascicle trajectories. To obtain this representation, the Laplace equation was solved in anatomical reconstructions of skeletal muscle shapes based on medical images using a uniform flux boundary condition on the attachment areas. Fascicle tracts were generated through a robust flux based tracing algorithm. The concept of this approach was demonstrated in two-dimensional synthetic examples of typical skeletal muscle architectures. A detailed evaluation was performed in an example of the anatomical human tibialis anterior muscle which showed an overall agreement with measurements from the literature. The utility and capability of the proposed method was further demonstrated in other anatomical examples of human skeletal muscles with a wide range of muscle shapes and attachment morphologies.     

Using EMG data to constrain optimization procedure improves finger tendon tension estimations during static fingertip force production

Determining tendon tensions of the finger muscles is crucial for the understanding and the rehabilitation of hand pathologies. Since no direct measurement is possible for a large number of finger muscle tendons, biomechanical modelling presents an alternative solution to indirectly evaluate these forces. However, the main problem is that the number of muscles spanning a joint exceeds the number of degrees of freedom of the joint resulting in mathematical under-determinate problems. In the current study, a method using both numerical optimization and the intra-muscular electromyography (EMG) data was developed to estimate the middle finger tendon tensions during static fingertip force production. The method used a numerical optimization procedure with the muscle stress squared criterion to determine a solution while the EMG data of three extrinsic hand muscles serve to enforce additional inequality constraints. The results were compared with those obtained with a classical numerical optimization and a method based on EMG only. The proposed method provides satisfactory results since the tendon tension estimations respected the mechanical equilibrium of the musculoskeletal system and were concordant with the EMG distribution pattern of the subjects. These results were not observed neither with the classical numerical optimization nor with the EMG-based method. This study demonstrates that including the EMG data of the three extrinsic muscles of the middle finger as inequality constraints in an optimization process can yield relevant tendon tensions with regard to individual muscle activation patterns, particularly concerning the antagonist muscles.     

A transformation method to estimate muscle attachments based on three bony landmarks

In order to create musculoskeletal models that can be scalable to different subject specificities the calculation of the exact locations of muscle attachment is required. For this purpose, a scaling method is presented that estimates muscle attachment locations in homologous segments using three bony landmarks per segment.A data-set of 17 muscles’ attachment lines from the shoulders of seven cadavers was used to assess the estimation quality of the scaling method. By knowing from the cadaver data the measured location of the muscles’ attachment lines it is possible to assess the quality of the estimated ones. The scaling results showed an overall mean RMSE for the scapula and humerus muscles of 7.6 and 11.1 mm, respectively. These results were then analyzed with an upper extremity model, in order to compute the influence of the RMSE in glenohumeral elevation muscle moment arms in the scapular plane.The results presented were considered to be satisfactory. Among other error contributors, the inter- and intra-subject variability should be further investigated, along with the sensitivity of a biomechanical model to these error variations.     

Musculature,nervous system and glands of metasomal abdominal segments of the male of Nomia melanderi Ckll. (Hymenoptera,Apoidea)

Each muscle of the third metasomal segment of the male of Nomia melanderi Ckll. is described in detail. The points of attachment of each muscle are compared with their homologs in other pregenital segments and with their homologs in the female. The function desgnated for each muscle describes its action alone or in conjunction with other muscle(s). New names are given to genital muscles by referring in the name to their points of attachment. Each intratergal muscle has homologous points of attachment in the pregenital segments of both sexes. The median tergo-dorsoplical muscle of the seventh segment and the oblique tergo-dorsoplical muscle of the eighth segment have changed their points of attachment. The intrasternal muscles are modified to suit the needs of courtship and mating, thus they are different from their homologs in the female. The spiracular muscles are well developed in all segments except the eighth, where the sterno-spiracular muscle is absent. The extrinsic genital muscles are derived from the intrasternal muscles of the eighth and ninth segments. The parameral and volsellar muscles are reduced in number. The aedeagal muscles, except the aedeago-phallic, have retained similar points of attachment to those found in primitive Hymenoptera. The topography of the metasomal nervous system is reported in detail by following each nerve and nervule to its termination. The study shows that (at least in Nomia) the criterion of nerve-concentration should not be used alone to indicate evolutionary levels. To accommodate the morphological changes in the terminal segments the Anterior and Posterior Lateral Nerves have migrated to new locations. The pattern of nerve topography (even at the nervule level) is homologous both in the different pregenital segments and between the sexes. The fact that homology does not exist between the external genitalia of the male and the modified ovipositor of the female supports the thesis that the male genital capsule is of phallic rather than prephallic origin. A pair of intersegmental membrane glands located between the seventh and eighth sterna is described. These glands may be the source of a pheromon responsible for gregariousness among “sleeping” males.     

Effect of lung volume on the respiratory action of the canine pectoral muscles.

Lung volume influences the mechanical action of the primary inspiratory and expiratory muscles by affecting their precontraction length, alignment with the rib cage, and mechanical coupling to agonistic and antagonistic muscles. We have previously shown that the canine pectoral muscles exert an expiratory action on the rib cage when the forelimbs are at the torso's side and an inspiratory action when the forelimbs are held elevated. To determine the effect of lung volume on intrathoracic pressure changes produced by the canine pectoral muscles, we performed isolated bilateral supramaximal electrical stimulation of the deep pectoral and superficial pectoralis (descending and transverse heads) muscles in 15 adult supine anesthetized dogs during hyperventilation-induced apnea. Lung volume was altered by application of a negative or positive pressure (+/- 30 cmH2O) to the airway. In all animals, selective electrical stimulation of the descending, transverse, and deep pectoral muscles with the forelimbs held elevated produced negative intrathoracic pressure changes (i.e., an inspiratory action). Moreover, with the forelimbs elevated, increasing lung volume decreased both pectoral muscle fiber precontraction length and the negative intrathoracic pressure changes generated by contraction of each of these muscles. Conversely, with the forelimbs along the torso, increasing lung volume lengthened pectoral muscle precontraction length and augmented the positive intrathoracic pressure changes produced by muscle contraction (i.e., an expiratory action). These results indicate that lung volume significantly affects the length of the canine pectoral muscles and their mechanical actions on the rib cage.