Neck muscle paths and moment arms are significantly affected by wrapping surface parameters

In this paper, we studied the effects of wrapping surfaces on muscle paths and moment arms of the neck muscle, semispinalis capitis. Sensitivities to wrapping surface size and the kinematic linkage to vertebral segments were evaluated. Kinematic linkage, but not radius, significantly affected the accuracy of model muscle paths compared to centroid paths from images. Both radius and linkage affected the moment arm significantly. Wrapping surfaces that provided the best match to centroid paths over a range of postures had consistent moment arms. For some wrapping surfaces with poor matches to the centroid path, a kinematic method (tendon excursion) predicted flexion moment arms in certain postures, whereas geometric method (distance to instant centre) predicted extension. This occurred because the muscle lengthened as it wrapped around the surface. This study highlights the sensitivity of moment arms to wrapping surface parameters and the importance of including multiple postures when evaluating muscle paths and moment arm.     

Defining and evaluating wrapping surfaces for MRI-derived spinal muscle paths

Muscle paths can be approximated in biomechanical models by wrapping the path around geometric objects; however, the process for selecting and evaluating wrapping surface parameters is not well defined, especially for spinal muscles. In this study, we defined objective methods to select the shape, orientation, size and location of wrapping surfaces and evaluated the wrapping surfaces using an error metric based on the distance between the modeled muscle path and the centroid path from magnetic resonance imaging (MRI). We applied these methods and the error metric to a model of the neck musculature, where our specific goals were (1) to optimize the vertebral level at which to place a single wrapping surface per muscle; and (2) to define wrapping surface parameters in the neutral posture and evaluate them in other postures. Detailed results are provided for the sternocleidomastoid and the semispinalis capitis muscles. For the sternocleidomastoid, the level where the wrapping surface was placed did not significantly affect the error between the modeled path and the centroid path; use of wrapping surfaces defined from the neutral posture improved the representation of the muscle path compared to a straight line in all postures except contralateral rotation. For the semispinalis capitis, wrapping surfaces placed at C3 or C4 resulted in lower error compared to other levels; and the use of wrapping surfaces significantly improved the muscle path representation in all postures. These methods will be used to improve the estimates of muscle length, moment arm and moment-generating capacity in biomechanical models.     

The convex wrapping algorithm: A method for identifying muscle paths using the underlying bone mesh

Associating musculoskeletal models to motion analysis data enables the determination of the muscular lengths, lengthening rates and moment arms of the muscles during the studied movement. Therefore, those models must be anatomically personalized and able to identify realistic muscular paths. Different kinds of algorithms exist to achieve this last issue, such as the wired models and the finite elements ones. After having studied the advantages and drawbacks of each one, we present the convex wrapping algorithm. Its purpose is to identify the shortest path from the origin to the insertion of a muscle wrapping over the underlying skeleton mesh while respecting possible non-sliding constraints. After the presentation of the algorithm, the results obtained are compared to a classically used wrapping surface algorithm (obstacle set method) by measuring the length and moment arm of the semitendinosus muscle during an asymptomatic gait. The convex wrapping algorithm gives an efficient and realistic way of identifying the muscular paths with respect to the underlying bones mesh without the need to define simplified geometric forms. It also enables the identification of the centroid path of the muscles if their thickness evolution function is known. All this presents a particular interest when studying populations presenting noticeable bone deformations, such as those observed in cerebral palsy or rheumatic pathologies.     

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.     

Automated muscle wrapping using finite element contact detection

Realistic muscle path representation is essential to musculoskeletal modeling of joint function. Algorithms predicting these muscle paths typically rely on a labor intensive predefinition of via points or underlying geometries to guide wrapping for given joint positions. While muscle wrapping using anatomically precise three-dimensional (3D) finite element (FE) models of bone and muscle has been achieved, computational expense and pre-processing associated with this approach exclude its use in applications such as subject-specific modeling. With the intention of combining advantageous features of both approaches, an intermediate technique relying on contact detection capabilities of commercial FE packages is presented. We applied the approach to the glenohumeral joint, and validated the method by comparison against existing experimental data. Individual muscles were modeled as a straight series of deformable beam elements and bones as anatomically precise 3D rigid bodies. Only the attachment locations and a default orientation of the undeformed muscle segment were pre-defined. The joint was then oriented in a static position of interest. The muscle segment free end was then moved along the shortest Euclidean path to its origin on the scapula, wrapping the muscle along bone surfaces by relying on software contact detection. After wrapping for a given position, the resulting moment arm was computed as the perpendicular distance from the line of action vector to the humeral head center of rotation.This approach reasonably predicted muscle length and moment arm for 27 muscle segments when compared to experimental measurements over a wide range of shoulder motion. Artificial via points or underlying contact geometries were avoided, contact detection and multiobject wrapping on the bone surfaces were automatic, and low computational cost permitted wrapping of individual muscles within seconds on a standard desktop PC. These advantages may be valuable for both general and subject-specific musculoskeletal modeling.     

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.     

Three-dimensional model to predict muscle forces and their relation to motor variances in reaching arm movements

A three-dimensional (3-D) arm movement model is presented to simulate kinematic properties and muscle forces in reaching arm movements. Healthy subjects performed reaching movements repetitively either with or without a load in the hand. Joint coordinates were measured. Muscle moment arms, 3-D angular acceleration, and moment of inertias of arm segments were calculated to determine 3-D joint torques. Variances of hand position, arm configuration, and muscle activities were calculated. Ratios of movement variances observed in the two conditions (load versus without load) showed no differences for hand position and arm configuration variances. Virtual muscle force variances for all muscles except deltoid posterior and EMG variances for four muscles increased significantly by moving with the load. The greatly increased variances in muscle activity did not imply equally high increments in kinematic variances. We conclude that enhanced muscle cooperation through synergies helps to stabilize movement at the kinematic level when a load is added.     

Ankle joint mechanics and foot proportions differ between human sprinters and non-sprinters

Recent studies of sprinters and distance runners have suggested that variations in human foot proportions and plantarflexor muscle moment arm correspond to the level of sprint performance or running economy. Less clear, however, is whether differences in muscle moment arm are mediated by altered tendon paths or by variation in the centre of ankle joint rotation. Previous measurements of these differences have relied upon assumed joint centres and measurements of bone geometry made externally, such that they would be affected by the thickness of the overlying soft tissue. Using magnetic resonance imaging, we found that trained sprinters have shorter plantarflexor moment arms (p = 0.011) and longer forefoot bones (p = 0.019) than non-sprinters. The shorter moment arms of sprinters are attributable to differences in the location of the centre of rotation (p < 0.001) rather than to differences in the path of the Achilles tendon. A simple computer model suggests that increasing the ratio of forefoot to rearfoot length permits more plantarflexor muscle work during plantarflexion that occurs at rates expected during the acceleration phase following the sprint start.     

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.     

Musculoskeletal Model of the Upper Limb Based on the Visible Human Male Dataset

A mathematical model of Ihe human upper limb was developed based on high-resolution medical images of the muscles and bones obtained from the Visible Human Male ( HM) project. Three-dimensional surfaces of the muscles and bones were reconstructed from Computed Tomography (CT) images and Color Cryosection images obtained from the VHM cadaver. Thirteen degrees of freedom were used to describe the orientations of seven bones in the model: clavicle, scapula, humerus, radius, ulna, carpal bones, and hand. All of the major articulations from the shoulder girdle down to the wrist were included in the model. The model was actuated by 42 muscle bundles, which represented the actions of 26 muscle groups in the upper limb. The paths of the muscles were modeled using a new approach called the Obstacle-set Method (33) The calculated paths of the muscles were verified by comparing the muscle moment arms computed in the model with the results of anatomical studies reported in the literature, In-vivo measurements of maximum isometric muscle torques developed at the shoulder, elbow, and wrist were also used to estimate the architectural properties of each musculotendon actuator in the model. The entire musculoskeletal model can be reconstructed using the data given in this paper, along with information presented in a companion paper which defines the kinematic structure of the model (26)     

Influence of muscle anatomical cross-sectional area on the moment arm length of the triceps brachii muscle at the elbow joint

The purpose of this study was to test the hypothesis that the musculotendon moment arm length is affected by the muscle anatomical cross-sectional area. The moment arm length of the triceps brachii (TB) muscle at 30°, 50°, 70°, 90°, 110° elbow flexion positions was measured in sagittal magnetic resonance images (MRI) of 18 subjects as the perpendicular distance between the center of the pulley of the humerus to the line through the center of the TB tendon. The moment arm increased as the elbow flexion angle decreased, from 1.74±0.13 cm at 110° to 2.39±0.14 cm at 30°. The maximal anatomical cross-sectional area of the TB muscle was significantly correlated with the moment arms at all joint positions (r=0.545–0.803, p<0.05). Furthermore, the circumference of the upper arm was also significantly correlated with the moment arms at all joint positions, except for 70° (r=0.504–0.702, p<0.05). These results indicate that the moment arm length of the TB muscle is affected by the muscle anatomical cross-sectional area.     

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.     

Musculoskeletal model of the upper limb based on the visible human male dataset

A mathematical model of the human upper limb was developed based on high-resolution medical images of the muscles and bones obtained from the Visible Human Male (VHM) project. Three-dimensional surfaces of the muscles and bones were reconstructed from Computed Tomography (CT) images and Color Cryosection images obtained from the VHM cadaver. Thirteen degrees of freedom were used to describe the orientations of seven bones in the model: clavicle, scapula, humerus, radius, ulna, carpal bones, and hand. All of the major articulations from the shoulder girdle down to the wrist were included in the model. The model was actuated by 42 muscle bundles, which represented the actions of 26 muscle groups in the upper limb. The paths of the muscles were modeled using a new approach called the Obstacle-set Method [33]. The calculated paths of the muscles were verified by comparing the muscle moment arms computed in the model with the results of anatomical studies reported in the literature. In-vivo measurements of maximum isometric muscle torques developed at the shoulder, elbow, and wrist were also used to estimate the architectural properties of each musculotendon actuator in the model. The entire musculoskeletal model can be reconstructed using the data given in this paper, along with information presented in a companion paper which defines the kinematic structure of the model [26].     

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.     

Muscle wrapping on arbitrary meshes with the heat method

Muscle paths play an important role in musculoskeletal simulations by determining a muscle’s length and how its force is distributed to joints. Most previous approaches estimate the way in which muscles ‘wrap’ around bones and other structures with smooth analytical wrapping surfaces. In this paper, we employ Newton’s method with discrete differential geometry to permit muscle wrapping over arbitrary polygonal mesh surfaces that represent underlying bones and structures. Precomputing distance fields allows us to speed up computations for the common situation where many paths cross the same wrapping surfaces. We found positive results for the accuracy, robustness, and efficiency of the method. However the method did not exhibit continuous changes in path length for dynamic simulations. Nonetheless this approach provides a valuable step toward fast muscle wrapping on arbitrary meshes.     

Moving muscle points provide accurate curved muscle paths in a model of the cervical spine

Muscle paths in musculoskeletal models have been modeled using several different methods; however, deformation of soft tissue with changes in posture is rarely accounted for, and often only the neutral posture is used to define a muscle path. The objective of this study was to model curved muscle paths in the cervical spine that take into consideration soft tissue deformation with changes in neck posture. Two subject-specific models were created from magnetic resonance images (MRI) in 5 different sagittal plane neck postures. Curved paths of flexor and extensor muscles were modeled using piecewise linear lines-of-action in two ways; (1) using fixed via points determined from muscle paths in the neutral posture and (2) using moving muscle points that moved relative to the bones determined from muscle paths in all 5 postures. Accuracy of each curved modeled muscle path was evaluated by an error metric, the distance from the anatomic (centroid) muscle path determined from the MRI. Error metric was compared among three modeled muscle path types (straight, fixed via and moving muscle point) using a repeated measures one-way ANOVA (α=0.05). Moving muscle point paths had 21% lower error metric than fixed via point paths over all 15 pairs of neck muscles examined over 5 postures (3.86 mm vs. 4.88 mm). This study highlights the importance of defining muscle paths in multiple postures in order to properly define the changing curvature of a muscle path due to soft tissue deformation with posture.     

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.     

Musculotendon lengths and moment arms for a three-dimensional upper-extremity model

Generating muscle-driven forward dynamics simulations of human movement using detailed musculoskeletal models can be computationally expensive. This is due in part to the time required to calculate musculotendon geometry (e.g., musculotendon lengths and moment arms), which is necessary to determine and apply individual musculotendon forces during the simulation. Modeling upper-extremity musculotendon geometry can be especially challenging due to the large number of multi-articular muscles and complex muscle paths. To accurately represent this geometry, wrapping surface algorithms and/or other computationally expensive techniques (e.g., phantom segments) are used. This paper provides a set of computationally efficient polynomial regression equations that estimate musculotendon length and moment arms for thirty-two (32) upper-extremity musculotendon actuators representing the major muscles crossing the shoulder, elbow and wrist joints. Equations were developed using a least squares fitting technique based on geometry values obtained from a validated public-domain upper-extremity musculoskeletal model that used wrapping surface elements (Holzbaur et al., 2005). In general, the regression equations fit well the original model values, with an average root mean square difference for all musculotendon actuators over the represented joint space of 0.39 mm (1.1% of peak value). In addition, the equations reduced the computational time required to simulate a representative upper-extremity movement (i.e., wheelchair propulsion) by more than two orders of magnitude (315 versus 2.3 s). Thus, these equations can assist in generating computationally efficient forward dynamics simulations of a wide range of upper-extremity movements.     

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.