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.     

Three-dimensional surface geometries of the rabbit soleus muscle during contraction: input for biomechanical modelling and its validation

There exists several numerical approaches to describe the active contractile behaviour of skeletal muscles. These models range from simple one-dimensional to more advanced three-dimensional ones; especially, three-dimensional models take up the cause of describing complex contraction modes in a realistic way. However, the validation of such concepts is challenging, as the combination of geometry, material and force characteristics is so far not available from the same muscle. To this end, we present in this study a comprehensive data set of the rabbit soleus muscle consisting of the muscles’ characteristic force responses (active and passive), its three-dimensional shape during isometric, isotonic and isokinetic contraction experiments including the spatial arrangement of muscle tissue and aponeurosis–tendon complex, and the fascicle orientation throughout the whole muscle at its optimal length. In this way, an extensive data set is available giving insight into the three-dimensional geometry of the rabbit soleus muscle and, further, allowing to validate three-dimensional numerical models.     

Comparison between the effectiveness of expiration and abdominal bracing maneuvers in maintaining spinal stability following sudden trunk loading

The purpose of this study was to clarify the effectiveness of expiration and abdominal bracing maneuvers in response to sudden trunk loading in healthy subjects. Fifteen healthy male subjects were anteriorly loaded under different experimental conditions. Tests were conducted at rest and while performing each of the stabilization maneuvers (expiration and abdominal bracing) at 15% of the maximal voluntary isometric contraction of the internal oblique muscle. Subjects had no knowledge of the perturbation timing. An electromyographic biofeedback system was used to control the intensity of internal oblique muscle activation. Muscular pre-activation of three trunk muscles (internal oblique, external oblique, and L3 erector spinae muscles) and lumbar acceleration in response to loading were measured. The expiration and abdominal bracing maneuvers promoted torso co-contraction, reduced the magnitude of lumbar acceleration, and increased spinal stability compared to the resting condition. There were no differences between the expiration and abdominal bracing maneuvers in the pre-activation of the three trunk muscles or in lumbar acceleration in response to loading. It appears that both expiration and abdominal bracing maneuvers are effective in increasing spinal stability in response to sudden anterior loading.     

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 Musculoskeletal Model of the Human Knee Joint. Part 1: Theoretical Construction

A three-dimensional model of the knee is developed to study the interactions between the muscles, ligaments, and bones during activity. The geometry of the distal femur, proximal tibia, and patella is based on cadaver data reported for an average-size knee. The shapes of the femoral condyles are represented by high-order polynomials: the tibial plateaux and patellar facets are approximated as flat surfaces. The contacting surfaces of the femur and tibia are modeled as deformable, while those of the femur and patella are assumed to be rigid. Interpenetration of the femur and tibia is taken into account by modeling cartilage as a thin, linear, elastic layer, mounted on rigid bone. Twelve elastic elements describe the geometry and mechanical properties of the cruciate ligaments, the collateral ligaments, and the posterior capsule. The model is actuated by thirteen musculotendinous units, each unit modeled as a three-element muscle in series with tendon. The path of each muscle is approximated as a straight line, except where it contacts and wraps around bone and other muscles; changes in muscle paths are taken into account using data obtained from MRI. In the first part of this paper, the model is used to simulate passive knee flexion. Quantitative comparisons of the model results with experimental data reported in the literature indicate that the relative movements of the bones and the geometry of the ligaments and muscles in the model are similar to those evident in the real knee. In Part II, the model is used to describe knee-ligament function during anterior-posterior draw, axial rotation, and isometric knee-extension and knee-flexion exercises.     

A micromechanical model of skeletal muscle to explore the effects of fiber and fascicle geometry

Computational models of muscle generally lump the material properties of connective tissue, muscle fibers, and muscle fascicles together into one constitutive relationship that assumes a transversely isotropic microstructure. These models do not take into account how variations in the microstructure of muscle affect its macroscopic material properties. The goal of this work was to develop micromechanical models of muscle to determine the effects of variations in muscle microstructure on the macroscopic constitutive behavior. We created micromechanical models at the fiber and fascicle levels based on histological cross-sections of two rabbit muscles, the rectus femoris (RF) and the soleus, to determine the effects of microstructure geometry (fiber and fascicle shapes) on the along-fiber shear modulus of muscle. The two fiber-level models predicted similar macroscopic shear moduli (within 13.5% difference); however, the two fascicle-level models predicted very different macroscopic shear moduli (up to 161% difference). We also used the micromechanical models to test the assumption that the macroscopic properties of muscle are transversely isotropic about the fiber (or fascicle) direction. The fiber-level models exhibited behavior consistent with the transverse isotropy assumption; however, the fascicle-level models exhibited transversely anisotropic behavior. Micromechanical models, combined with fiber and fiber bundle mechanical experiments, are needed to understand how normal or pathological variations in microstructure give rise to the observed macroscopic behavior of muscle.     

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.     

A Three-Dimensional Musculoskeletal Model of the Human Knee Joint. Part 1: Theoretical Construct

A three-dimensional model of the knee is developed to study the interactions between the muscles, ligaments, and bones during activity. The geometry of the distal femur, proximal tibia, and patella is based on cadaver data reported for an average-size knee. The shapes of the femoral condyles are represented by high-order polynomials; the tibial plateaux and patellar facets are approximated as flat surfaces. The contacting surfaces of the femur and tibia are modeled as deformable, while those of the femur and patella are assumed to be rigid. Interpenetration of the femur and tibia is taken into account by modeling cartilage as a thin, linear, elastic layer, mounted on rigid bone. Twelve elastic elements describe the geometry and mechanical properties of the cruciate ligaments, the collateral ligaments, and the posterior capsule. The model is actuated by thirteen musculotendinous units, each unit modeled as a three-element muscle in series with tendon. The path of each muscle is approximated as a straight line, except where it contacts and wraps around bone and other muscles; changes in muscle paths are taken into account using data obtained from MRI. In the first part of this paper, the model is used to simulate passive knee flexion. Quantitative comparisons of the model results with experimental data reported in the literature indicate that the relative movements of the bones and the geometry of the ligaments and muscles in the model are similar to those evident in the real knee. In Part II, the model is used to describe knee-ligament function during anterior-posterior draw, axial rotation, and isometric knee-extension and knee-flexion exercises.     

Model-based inverse estimation for active contraction stresses of tongue muscles using 3D surface shape in speech production

This paper presents a novel inverse estimation approach for the active contraction stresses of tongue muscles during speech. The proposed method is based on variational data assimilation using a mechanical tongue model and 3D tongue surface shapes for speech production. The mechanical tongue model considers nonlinear hyperelasticity, finite deformation, actual geometry from computed tomography (CT) images, and anisotropic active contraction by muscle fibers, the orientations of which are ideally determined using anatomical drawings. The tongue deformation is obtained by solving a stationary force-equilibrium equation using a finite element method. An inverse problem is established to find the combination of muscle contraction stresses that minimizes the Euclidean distance of the tongue surfaces between the mechanical analysis and CT results of speech production, where a signed-distance function represents the tongue surface. Our approach is validated through an ideal numerical example and extended to the real-world case of two Japanese vowels, /ʉ/ and /ɯ/. The results capture the target shape completely and provide an excellent estimation of the active contraction stresses in the ideal case, and exhibit similar tendencies as in previous observations and simulations for the actual vowel cases. The present approach can reveal the relative relationship among the muscle contraction stresses in similar utterances with different tongue shapes, and enables the investigation of the coordination of tongue muscles during speech using only the deformed tongue shape obtained from medical images. This will enhance our understanding of speech motor control.     

Passive bipedal walking with phasic muscle contraction

The existence of self-organizing walking patterns is often considered the result of a mechanical system interacting with the environment and a (neural) oscillating unit. The pattern generators might be thought of as an indispensable component for the existence of limit cycle behavior. This paper shows that this is not a necessity for the existence of a self-organizing bipedal walking pattern. Stable walking cycles emerge from a simple passive bipedal structure, with an energy source inevitably present to sustain the oscillation. In this work the energy source is chosen to be phasic muscle contraction. A two-dimensional model is composed of two legs and a hip mass, symbolizing the trunk. The stance leg stiffness is generated by two muscles. The hip stiffness is generated by four muscles. Muscle activation is caused by two reflex-like trigger signals, without feedback control. Human equivalent model parameters such as geometry and mass distribution were assumed. With return map analysis, the model is analyzed on periodic behavior. Stable walking cycles were found and could be manipulated during walking by varying the muscle or reflex parameters, forcing the oscillation to converge to a new attractor. Received: 5 November 1998 / Accepted in revised form: 26 March 1999     

Modelling the mechanical effect of muscles with large attachment sites: Application to the shoulder mechanism

A general theory is described for deriving the mechanical effect of muscles with large attachment sites. In a cadaver experiment the complete attachment sites and bundle distribution of 16 muscles of the shoulder mechanism were recorded. These data were used to calculate the mechanical effect, i.e. the resulting force and moment vector, for a large number (200) and a reduced number (maximal 6) of muscle lines of action. The resulting error between both representations is small. The number of muscle lines of action in the reduced representation depends on the shape of the attachment site and muscle architecture. An important feature of this method is that the necessary number of muscle lines of action is determined afterwards. In the often used centroid line approach the number of muscle lines of action and partitioning of muscles is determined before recording the geometry, leading to unverifiable results.     

Towards mechanical characterization of intact endarterectomy samples of carotid arteries during inflation using Echo-CT

In this study, an experimental framework is described that allows pressurization of intact, human atherosclerotic carotid samples (inflation testing), in combination with ultrasound imaging. Eight fresh human carotid endarterectomy samples were successfully pressurized and tested. About 36 2-D (+t) ultrasound datasets were acquired by rotating the vessel in 10° steps (Echo-CT), from which both 3-D geometry and 3-D strain data were obtained. Both geometry and morphology were assessed with micro-CT imaging, identifying calcified and lipid rich regions. US-based and CT-based geometries were matched for comparison and were found to show good agreement, with an average similarity index of 0.71. Realistic pressure–volume relations were found for 6 out of 9 samples. 3-D strain datasets were reconstructed, revealing realistic strain patterns and magnitudes, although the data did suffer from a relatively high variability. The percentage of fat and calcifications (micro-CT) were compared with the median, 75th and 99th percentile strain values (Echo-CT). A moderate trend was observed for 75th and 99th percentile strains, higher strains were found for more lipid rich plaques, where lower strains were found for highly calcified plaques. However, an inverse numerical modeling technique is necessary for proper mechanical characterization the of plaque components, using the geometry, morphology and wall deformation as input.     

An entropy-assisted musculoskeletal shoulder model

Optimization combined with a musculoskeletal shoulder model has been used to estimate mechanical loading of musculoskeletal elements around the shoulder. Traditionally, the objective function is to minimize the summation of the total activities of the muscles with forces, moments, and stability constraints. Such an objective function, however, tends to neglect the antagonist muscle co-contraction. In this study, an objective function including an entropy term is proposed to address muscle co-contractions. A musculoskeletal shoulder model is developed to apply the proposed objective function. To find the optimal weight for the entropy term, an experiment was conducted. In the experiment, participants generated various 3-D shoulder moments in six shoulder postures. The surface EMG of 8 shoulder muscles was measured and compared with the predicted muscle activities based on the proposed objective function using Bhattacharyya distance and concordance ratio under different weight of the entropy term. The results show that a small weight of the entropy term can improve the predictability of the model in terms of muscle activities. Such a result suggests that the concept of entropy could be helpful for further understanding the mechanism of muscle co-contractions as well as developing a shoulder biomechanical model with greater validity.     

Muscle‐induced loading as an important source of variation in craniofacial skeletal shape

The shape of the craniofacial skeleton is constantly changing through ontogeny and reflects a balance between developmental patterning and mechanical‐load‐induced remodeling. Muscles are a major contributor to producing the mechanical environment that is crucial for “normal” skull development. Here, we use an F₅ hybrid population of Lake Malawi cichlids to characterize the strength and types of associations between craniofacial bones and muscles. We focus on four bones/bone complexes, with different developmental origins, alongside four muscles with distinct functions. We used micro‐computed tomography to extract 3D information on bones and muscles. 3D geometric morphometrics and volumetric measurements were used to characterize bone and muscle shape, respectively. Linear regressions were performed to test for associations between bone shape and muscle volume. We identified three types of associations between muscles and bones: weak, strong direct (i.e., muscles insert directly onto bone), and strong indirect (i.e., bone is influenced by muscles without a direct connection). In addition, we show that although the shape of some bones is relatively robust to muscle‐induced mechanical stimulus, others appear to be highly sensitive to muscular input. Our results imply that the roles for muscular input on skeletal shape extend beyond specific points of origin or insertion and hold significant potential to influence broader patterns of craniofacial geometry. Thus, changes in the loading environment, either as a normal course of ontogeny or if an organism is exposed to a novel environment, may have pronounced effects on skeletal shape via near and far‐ranging effects of muscular loading.     

Measuring morphological parameters of the pelvic floor for finite element modelling purposes

The goal of this study was to obtain a complete data set needed for studying the complex biomechanical behaviour of the pelvic floor muscles using a computer model based on the finite element (FE) theory. The model should be able to predict the effect of surgical interventions and give insight into the function of pelvic floor muscles. Because there was a lack of any information concerning morphological parameters of the pelvic floor muscle structures, we performed an experimental measurement to uncover those morphological parameters. Geometric parameters as well as muscle parameters of the pelvic floor muscles were measured on an embalmed female cadaver. A three-dimensional (3D) geometric data set of the pelvic floor including muscle fibre directions was obtained using a palpator device. A 3D surface model based on the experimental data, needed for mathematical modelling of the pelvic floor, was created. For all parts of the diaphragma pelvis, the optimal muscle fibre length was determined by laser diffraction measurements of the sarcomere length. In addition, other muscle parameters such as physiological cross-sectional area and total muscle fibre length were determined. Apart from these measurements we obtained a data set of the pelvic floor structures based on nuclear magnetic resonance imaging (MRI) on the same cadaver specimen. The purpose of this experiment was to discover the relationship between the MRI morphology and geometrical parameters obtained from the previous measurements. The produced data set is not only important for biomechanical modelling of the pelvic floor muscles, but it also describes the geometry of muscle fibres and is useful for functional analysis of the pelvic floor in general. By the use of many reference landmarks all these morphologic data concerning fibre directions and optimal fibre length can be morphed to the geometrical data based on segmentation from MRI scans.These data can be directly used as an input for building a mathematical model based on FE theory.     

Volumic patient-specific reconstruction of muscular system based on a reduced dataset of medical images

Three-dimensional mechanical modelling of muscles is essential for various biomechanical applications and clinical evaluation, but it requires a tedious manual processing of numerous images. A muscle reconstruction method is presented based on a reduced set of images to generate an approximate parametric object from basic dimensions of muscle contours. A regular volumic mesh is constructed based on this parametric object. The approximate object and the corresponding mesh are deformed to fit the exact muscles contours yielding patient-specific geometry. Evaluation was performed by comparison of geometry to that obtained by contouring all computed tomography (CT) slices, and by quantification of the mesh quality criteria. Muscle fatty infiltration was estimated using a threshold between fat and muscle. Volumic fat index (VFI) of a muscle was computed using first all the complete CT scan slices containing the muscle (VFI(ref)) and a second time only the slices used for reconstruction (VFI(recons)). Mean volume error estimation was 2.6% and hexahedron meshes fulfilled quality criteria. VFI(recons) respect the individual variation of fat content.     

Determining skeletal muscle architecture with Laplacian simulations: a comparison with diffusion tensor imaging

Determination of skeletal muscle architecture is important for accurately modeling muscle behavior. Current methods for 3D muscle architecture determination can be costly and time-consuming, making them prohibitive for clinical or modeling applications. Computational approaches such as Laplacian flow simulations can estimate muscle fascicle orientation based on muscle shape and aponeurosis location. The accuracy of this approach is unknown, however, since it has not been validated against other standards for muscle architecture determination. In this study, muscle architectures from the Laplacian approach were compared to those determined from diffusion tensor imaging in eight adult medial gastrocnemius muscles. The datasets were subdivided into training and validation sets, and computational fluid dynamics software was used to conduct Laplacian simulations. In training sets, inputs of muscle geometry, aponeurosis location, and geometric flow guides resulted in good agreement between methods. Application of the method to validation sets showed no significant differences in pennation angle (mean difference \(0.5{^{\circ }})\) or fascicle length (mean difference 0.9 mm). Laplacian simulation was thus effective at predicting gastrocnemius muscle architectures in healthy volunteers using imaging-derived muscle shape and aponeurosis locations. This method may serve as a tool for determining muscle architecture in silico and as a complement to other approaches.     

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.     

Brace yourself: How abdominal bracing affects intersegmental lumbar spine kinematics in response to sudden loading

Abdominal bracing is a voluntary method of increasing spine stiffness to restrict spine displacement. Previous investigations of abdominal bracing have measured effects on whole lumbar motion; however, how this effect is distributed across the lumbar spine is unknown. Therefore, this study was designed to test the influence of abdominal bracing on spine intersegmental (T9/T10 to L5/S1) flexion, measured via skin surface markers, in response to sudden loading perturbations applied through the hands in 16 young healthy participants. Abdominal and back muscle activation responses were also measured. The results demonstrated that abdominal bracing significantly reduced sagittal plane motion at intersegmental levels T12/L1 to L4/L5, by 45% (0.74 degrees) at L4/L5 to 94% (0.71 degrees) at L1/L2 compared to control. L5/S1 experienced a 50% (0.36 degrees) reduction, but this was not statistically significant. Additionally, abdominal bracing resulted in greater baseline activation of all abdominal and back muscles, but did not affect onset times or response magnitudes of any of the back muscles acting counter to the perturbation. Therefore, the elevated baseline activation of trunk musculature during an abdominal brace serves to restrict flexion motion at the majority of the intersegmental lumbar spine (T12/L1 to L4/5) in response to sudden trunk flexion perturbations.     

A shell finite element model of the pelvic floor muscles

The pelvic floor gives support to the organs in the abdominal cavity. Using the dataset made public in (Janda et al. J. Biomech. (2003) 36(6), pp. 749-757), we have reconstructed the geometry of one of the most important parts of the pelvic floor, the levator ani, using NURB surfaces. Once the surface is triangulated, the corresponding mesh is used in a finite element analysis with shell elements.Based on the 3D behavior of the muscle we have constructed a shell that takes into account the direction of the muscle fibers and the incompressibility of the tissue. The constitutive model for the isotropic strain energy and the passive strain energy stored in the fibers is adapted from Humphrey's model for cardiac muscles. To this the active behavior of the skeletal muscle is added.We present preliminary results of a simulation of the levator ani muscle under pressure and with active contraction. This research aims at helping simulate the damages to the pelvic floor that can occur after childbirth.