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.     

A muscle-path-plane method for representing muscle contraction during joint movement

Traditional muscle paths (the straight-line model and the viapoint-line model) emphasise either the mechanical properties that arouse joint movement or the morphological characteristics of the muscles. To consider both the factors, a muscle-path-plane (MPP) method is introduced to model the paths of muscles during joint movement. This method is based on the premise that there is a MPP, constructed by origin, insertion and MPP control point, which represents the major direction of the muscle contraction for an arbitrary joint configuration at any time. Then, we can calculate the functions and the lengths of the muscle paths during instantaneous joint movement in MPP by mathematical approaches. Taking the triceps brachii as an example, the lengths of its paths during elbow flexion are calculated and compared with the relative studies reported in the literature. It is concluded that this method can provide an insight into the simulation of the muscle contraction.     

Application of spherical and cylindrical wrapping algorithms in a musculoskeletal model of the upper limb

In the modelling of the upper limb, many muscles cannot be represented as a straight line from origin to insertion due to the complex morphology causing them to wrap around passive structures. The majority of bony contours that form these obstructions can be described adequately as simple geometric shapes such as spheres and cylinders.A novel technique for the parameterisation of muscle paths as they wrap around such shapes has been developed for use in an upper limb model. The new method involves the definition of moving co-ordinate systems in which the path of a wrapped muscle does not move, allowing simplified specification. In addition, an analytical calculation of the wrapping path around a cylinder is presented over previous approximate methods.Muscle moment arms were pre-calculated from vector considerations and within SIMM by tendon excursion. Close agreement between the two suggests that the proposed implementations accurately follow the theoretical relationship and can be used with confidence in musculoskeletal models.     

Dynamic coordinate data for describing muscle-tendon paths: a mathematical approach

When modelling the musculoskeletal system over a range of joint angles the use of fixed points to describe muscle-tendon paths has inherent limitations. These result in fewer deflection points and the use of effective insertions to accommodate both relative marker movement and avoid muscle paths contacting bony structures. Model performance is dependent on the joint angle relative to the anatomical position where the muscle-tendon paths were defined. The present study proposes a scheme for the implementation of dynamic coordinates for describing muscle-tendon paths. For each muscle-tendon element a plane is defined in which the muscle-tendon complex acts when crossing a given joint. The muscle-tendon plane is dependent on 3D segment orientations and describes one degree of freedom, while the remaining two degrees of freedom are described by polar coordinates and locate the dynamic point in the muscle-tendon plane. The dynamic approach is implemented on four muscles of the lower limb in modelled and simulated joint movements and offers a significant improvement on previous approaches based on fixed deflection points. The scheme accommodates compound 3D rotations about joint axes, is not computationally difficult or require large data sets, and does not impose limitations on the number of points that may be defined along a muscle-tendon path.     

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.     

A noninvasive technique for in vivo measurement of joint torques of biarticular muscles.

The objective of this work was to develop a noninvasive method to measure the joint torques produced by biarticular muscles at two joints simultaneously. During intramuscular stimulation of the cat medial gastrocnemius (MG) muscle, torques at the ankle and knee joints were calculated from forces measured in two dimensions at the end point of the cat paw under isometric conditions. The method was verified by the known anatomical properties of cat MG muscle and the tibialis anterior (TA) muscle. The MG muscle was shown to produce a significant flexion torque at the knee, besides an extension torque at the ankle. This was in agreement with its anatomical arrangement. The TA muscle produced primarily an ankle flexion torque. The small knee torque, due to measurement errors, yielded an estimate of measurement accuracy of 3.0 +/- 2.1% (n = 52). The coupling ratio of the MG muscle, defined as T(ankle)/T(knee), varied significantly with both knee and ankle angles. The profile of MG mechanical coupling agreed qualitatively with changes in limb configuration. The method can be used to measure recruitment properties of electrically stimulated biarticular muscles, and may potentially be used to study the biomechanics of biarticular coupling.     

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.     

Intermuscular coordination in a sprint push-off.

This study was designed to investigate the patterns of intermuscular coordination during a sprinting event. In previous research it was found that despite the indeterminacy problem of movement control, movements like vertical jumping, speed skating and cycling are performed in a stereotyped manner. It was hypothesized that this might be due to constraints associated with the transformation of joint rotations into the desired translation. The objective of the present study was to determine the extent to which the intermuscular coordination patterns during other movements also are performed in a stereotyped manner and, if that is true, whether this can be understood on the basis of such constraints. Seven elite sprint runners were instructed to execute an explosive sprinting dash. Ground reaction forces and cinematographic data were recorded for the second stance phase of the sprint. Simultaneously, electromyographic activity of nine leg muscles was recorded telemetrically. Linked-segment modeling was used to obtain net joint moments and net joint powers. Different athletes appeared to perform the sprint in a stereotyped manner. The muscle coordination pattern is characterized by a proximo to distal sequence in timing of the monoarticular muscles. When compared to the sequential pattern found in jumping, the biarticular hamstrings and rectus femoris muscles behave differently; in the sprint a more pronounced reciprocal activity between these muscles exists. The resulting movement pattern is characterized by a sequence of upper leg extension and plantar flexion. The observed sequence in timing of muscle activation patterns is aimed at solving the problems associated with the earlier identified geometrical and anatomical constraint. However, the coordination pattern cannot be fully understood on the basis of these constraints. A specific constraint is identified with respect to the direction of the ground reaction force, which explains the pronounced reciprocal activity of the biarticular hamstring and rectus femoris muscles. The intermuscular coordination pattern in the sprint can be seen as a compromise between the specific requirement of the sprint and the advantageous effect of a proximo to distal sequence as found previously for jumping.     

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.     

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.     

An iterative procedure to estimate muscle lines of action in vivo

A method is described to estimate the line of action of muscles in the three-dimensional space from serial images of parallel muscle sections obtained in vivo by means of CT or MRI scanning. The external shape of a muscle, reconstructed from the series of parallel sections, is mathematically divided into a series of imaginary slices directed arbitrarily in the three-dimensional space. The line of action is estimated initially as a regression line through the centroids of these mathematical slices. A new series of mathematical slices is constructed perpendicular to the regression line and a new estimate of the line of action is obtained from their centroids. This procedure is repeated until the estimated line of action is perpendicular to the mathematical slices; it can then be considered as a reliable estimate of the line of action. The accuracy of the method has been tested for various reconstruction parameters and muscle shapes. The results of these tests show that the accuracy is relatively independent of the direction in which the sectional images have been made and that, except for relatively short and thick muscles, the estimated lines of action deviated less than about 2 degrees from the theoretical one. The presented method is a relatively simple mathematical technique which can be used easily for muscles reconstructed in vivo from routinely obtained sectional MRI or CT images.     

Three-dimensional model of the feline hindlimb

This article describes a three-dimensional musculoskeletal model of the feline hindlimb based on digitized musculoskeletal anatomy. The model consists of seven degrees of freedom: three at the hip and two each at the knee and ankle. Lines of action and via points for 32 major muscles of the limb are described. Interspecimen variability of muscle paths was surprisingly low; most via points displayed a scatter of only a few millimeters. Joint axes identified by mechanical techniques as noncoincident and nonorthogonal were further honed to yield moment arms consistent with previous reports. Interspecimen variability in joint axes was greater than that of muscle paths and highlights the importance of joint axes in kinematic models. The contribution of specific muscles to the direction of endpoint force generation is discussed.     

Analysis of human mandibular mechanics based on screw theory and in vivo data

In this paper the mechanics of human mandibular function is described in terms of the associated screws. The two distinct, yet related features of jaw mechanics, involving the motion itself as well as the forces, are both functions of the anatomical constraints, namely the contact areas that exist within the temporomandibular joint, and the forces of the muscles and tendons that allow motion to occur. The relationships that exist between these two aspects of jaw-motion are identified in this paper showing that muscle forces can be uniquely represented in terms of the action screw. This new approach to analyzing the mechanics of jaw-motion also incorporates the previously studied motion screw or helical axis. A consistent dynamic model is formulated where the action screw is used to represent the action of the closing muscle forces while the moment arms of the muscle forces are determined about the motion screw representing mandibular kinematics. The action screw formulation is verified using in vivo motion data and MR image information for a single asymptomatic subject. The results confirm the feasibility of the method and its application in dental research. A general increase in the mechanical advantage of most muscles, in the distance between action and motion screws as well as in the expended energy towards the end of the jaw-closing phase was observed. Asymmetries in the distribution of muscle force magnitudes appeared to influence the resultant force and moment of the action screw but had little effect on its spatial location. The method presented is intended to facilitate understanding of mandibular function and dysfunction.     

What visual information is used for navigation around obstacles in a cluttered environment?

The goal of this study was to determine what visual information is used to navigate around barriers in a cluttered terrain. Twelve traffic pylons were arranged randomly in a 4.55 x 3.15 m travel area: there were 20 different arrangements. For each arrangement, individuals (N = 6) were positioned in 1 of 3 locations on the outside border with their eyes closed: on verbal command they were instructed to open their eyes and quickly go to 1 of 2 specified goals (2 vertical posts defining a door) located on one edge of the travel area. The movement of the body was tracked using the OPTOTRAK system, with the IREDS placed on a collar worn by the subjects. Experimental data of travel path chosen were compared with those predicted by models that incorporated different types of visual information to control path trajectory. The 6 models basically use 2 different strategies for route selection: reactive control based on visual input about the obstacle encountered in the line-of-sight travel path (Model # 1) and path planning based on different visual information (Model # 2, 3, 4, 5, and 6). The models that involve path planning are grouped into 2 categories: models 2, 3, 4, and 5 need detailed geometrical configuration of the obstacles to plan a route while model 6 plans a route based on identifying and avoiding a cluster of obstacles in the travel path. Two measures were used to compare model performance with the actual travel path: the difference in area between predicted and actual travel path and the number of trials that accurately predicted the number of turns during travel. The results suggest that route selection is not based on reactive control, but does involve path planning. The model that best predicts the travel paths taken by the individuals uses visual information about cluster of obstacles and identification of safe corridors to plan a route.     

Mechanical demand and multijoint control during landing depend on orientation of the body segments relative to the reaction force.

The purpose of this study was to determine how diverse momentum conditions and anatomical orientation at contact influences mechanical loading and multijoint control of the reaction force during landings. Male collegiate gymnasts (n=6) performed competition style landings (n=3) of drop jumps, front saltos, and back saltos from a platform (0.72 m) onto landing mats (0.12 m). Kinematics (200 fps), reaction forces (800 Hz) and muscle activation patterns (surface EMG, 1600 Hz) of seven lower extremity muscles were collected simultaneously. Between-task differences in segment orientation relative to the reaction force contributed to significant between-task differences in knee and hip net joint moments (NJM) during the impact phase. During the stabilization phase, ankle, knee, and hip NJMs acted to control joint flexion. Between-task differences in muscle activation patterns indicated that gymnasts scaled biarticular muscle activation to accommodate for between-task differences in NJM after contact. Activation of muscles on both sides of the joint suggests that impedance like control was used to stabilize the joints and satisfy the mechanical demand imposed on the lower extremity. Between-subject differences in the set of muscles used to control total body center of mass (TBCM) trajectory and achieve lower extremity NJMs suggests that control of multijoint movements involving impact needs to incorporate mechanical objectives at both the total body and local level. The functional consequences of such a control structure may prove to be an asset to gymnasts, particularly when required to perform a variety of landing tasks under a variety of environmental constraints.     

A myoelectrically based dynamic three-dimensional model to predict loads on lumbar spine tissues during lateral bending.

This work describes a dynamic model of the low back that incorporates extensive anatomical detail of the musculo-ligamentous-skeletal system to predict the load time histories of individual tissues. The dynamic reaction moment about L4/L5 was determined during lateral bending from a linked-segment model. This reaction moment was partitioned into restorative components provided by the disc, ligament strain, and active-muscle contraction using a second model of the spine that incorporated a detailed representation of the anatomy. Muscle contraction forces were estimated using both information from surface electromyograms, collected from 12 sites, and consideration of the modulating effects of muscle length, cross-sectional area and passive elasticity. This modelling technique is sensitive to the different ways in which individuals recruit their musculature to satisfy moment constraints. Time histories of muscle forces are provided. High muscle loads are consistent with the common clinical observation of muscle strain often produced by load handling. Furthermore, the coactivation measured in muscles on both sides of the trunk suggests that muscles are recruited to satisfy the lateral bending reaction torque in addition to performing other mechanical roles such as spine stabilization. If an estimate of the intervertebral joint compression is desired for assessment of lateral bends in industry, then a single equivalent lateral muscle with a moment arm of approximately 3.0-4.0 cm would conservatively capture the effects of muscle co-contraction quantified in this study.     

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.     

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.     

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.