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.     

Modelling motor units in 3D: influence on muscle contraction and joint force via a proof of concept simulation

Functional heterogeneity is a skeletal muscle’s ability to generate diverse force vectors through localised motor unit (MU) recruitment. Existing 3D macroscopic continuum-mechanical finite element (FE) muscle models neglect MU anatomy and recruit muscle volume simultaneously, making them unsuitable for studying functional heterogeneity. Here, we develop a method to incorporate MU anatomy and information in 3D models. Virtual fibres in the muscle are grouped into MUs via a novel “virtual innervation” technique, which can control the units’ size, shape, position, and overlap. The discrete MU anatomy is then mapped to the FE mesh via statistical averaging, resulting in a volumetric MU distribution. Mesh dependency is investigated using a 2D idealised model and revealed that the amount of MU overlap is inversely proportional to mesh dependency. Simultaneous recruitment of a MU’s volume implies that action potentials (AP) propagate instantaneously. A 3D idealised model is used to verify this assumption, revealing that neglecting AP propagation results in a slightly less-steady force, advanced in time by approximately 20 ms, at the tendons. Lastly, the method is applied to a 3D, anatomically realistic model of the masticatory system to demonstrate the functional heterogeneity of masseter muscles in producing bite force. We found that the MU anatomy significantly affected bite force direction compared to bite force magnitude. MU position was much more efficacious in bringing about bite force changes than MU overlap. These results highlight the relevance of MU anatomy to muscle function and joint force, particularly for muscles with complex neuromuscular architecture.

     

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.     

Residual force enhancement and force depression in human single muscle fibres

Residual force depression (rFD) and residual force enhancement (rFE) are intrinsic contractile properties of muscle. rFD is characterized as a decrease in steady-state isometric force following active shortening compared with a purely isometric contraction at the same muscle length and level of activation. By contrast, isometric force is increased following active lengthening compared to a reference isometric contraction at the same muscle length and level of activation; this is termed rFE. To date, there have been no investigations of rFD and rFE in human muscle fibres, therefore the purpose of this study was to determine whether rFD and rFE occur at the single muscle fibre level in humans. rFD and rFE were investigated in maximally activated single muscle fibres biopsied from the vastus lateralis of healthy adults. To induce rFD, fibres were activated and shortened from an average sarcomere length (SL) of 3.2–2.6 μm. Reference isometric contractions were performed at an average SL of 2.6 μm. To induce rFE, fibres were actively lengthened from an average SL of 2.6–3.2 μm and a reference isometric contraction was performed at an average SL of 3.2 μm. Isometric steady-state force was lower following active shortening (p < 0.05), and higher following active lengthening (p < 0.05), as compared to the reference isometric contractions. We demonstrated rFD and rFE in human single fibres which is consistent with previous animal models. The non-responder phenomenon often reported in rFE studies involving voluntary contractions at the whole human level was not observed at the single fibre level.     

Spatial distribution of active muscle fibre characteristics in the upper trapezius muscle and its dependency on contraction level and duration

The aim of this study was to provide direct in vivo information of the physiological and structural characteristics of active muscle fibres from a large part of the upper trapezius muscle. Two-dimensional (2-D) multi-channel surface electromyography recordings were used, with 13 × 10 electrodes covering 6 × 4.5 cm of the skin’s surface. A previously developed method was applied to detect individual propagating motor unit action potentials and to estimate their corresponding muscle fibre conduction velocity (MFCV) and muscle fibre orientation (MFO). Using these estimates, spatial distributions of MFCV and MFO were examined for five male subjects performing isometric shoulder elevation at different force levels. The main results were: (1) the general relationship between MFCV and force generation was non-systematic, with a positive relationship at the inferior part of the muscle, (2) the spatial distribution of MFCV at different force levels and fatigue was inhomogeneous and (3) the MFO was slightly different (6°) of the muscle fibres with origin superior compared to inferior to the C7 vertebra. These findings provide new information of the MFO of contracting muscle fibres and knowledge of the physiological characteristics of a large part of the upper trapezius muscle that previously was based on observations from human cadavers only.     

Development of a finite element musculoskeletal model with the ability to predict contractions of three-dimensional muscles

Representation of realistic muscle geometries is needed for systematic biomechanical simulation of musculoskeletal systems. Most of the previous musculoskeletal models are based on multibody dynamics simulation with muscles simplified as one-dimensional (1D) line-segments without accounting for the large muscle attachment areas, spatial fibre alignment within muscles and contact and wrapping between muscles and surrounding tissues. In previous musculoskeletal models with three-dimensional (3D) muscles, contractions of muscles were among the inputs rather than calculated, which hampers the predictive capability of these models. To address these issues, a finite element musculoskeletal model with the ability to predict contractions of 3D muscles was developed. Muscles with realistic 3D geometry, spatial muscle fibre alignment and muscle-muscle and muscle-bone interactions were accounted for. Active contractile stresses of the 3D muscles were determined through an efficient optimization approach based on the measured kinematics of the lower extremity and ground force during gait. This model also provided stresses and strains of muscles and contact mechanics of the muscle-muscle and muscle-bone interactions. The total contact force of the knee predicted by the model corresponded well to the in vivo measurement. Contact and wrapping between muscles and surrounding tissues were evident, demonstrating the need to consider 3D contact models of muscles. This modelling framework serves as the methodological basis for developing musculoskeletal modelling systems in finite element method incorporating 3D deformable contact models of muscles, joints, ligaments and bones.     

Validation of a voxel-based FE method for prediction of the uniaxial apparent modulus of human trabecular bone using macroscopic mechanical tests and nanoindentation

Assessment of the mechanical properties of trabecular bone is of major biological and clinical importance for the investigation of bone diseases, fractures and their treatments. Finite element (FE) methods are getting increasingly popular for quantifying the elastic and failure properties of trabecular bone. In particular, voxel-based FE methods have been previously used to calculate the effective elastic properties of trabecular microstructures. However, in most studies, bone tissue moduli were assumed or back-calculated to match the apparent elastic moduli from experiments, which often lead to surprisingly low values when compared to nanoindentation results. In this study, voxel-based FE analysis of trabecular bone is combined with physical measures of volume fraction, micro-CT (microCT) reconstructions, uniaxial mechanical tests and specimen-specific nanoindentation tests for proper validation of the method. Cylindrical specimens of cancellous bone were extracted from human femurs and their volume fraction determined with Archimede's method. Uniaxial apparent modulus of the specimens was measured with an improved tension-compression testing protocol that minimizes boundary artefacts. Their microCT reconstructions were segmented to match the measured bone volume fraction and used to create full-size voxel models with 30-45 microm element size. For each specimen, linear isotropic elastic material properties were defined based on specific nanoindentation measurements of its embedded bone tissue. Linear FE analyses were finally performed to simulate the uniaxial mechanical tests. Additional parametric analyses were performed to evaluate the potential errors on the predicted apparent modulus arising from variations in segmentation threshold, tissue modulus, and the use of 125-mm(3) cubic sub-regions. The results demonstrate an excellent correspondence between experimental measures and FE predictions of uniaxial apparent modulus. In conclusion, the adopted voxel-based FE approach is found to be a robust method to predict the linear elastic properties of human cancellous bone, provided segmentation of the microCT reconstructions is carefully calibrated, tissue modulus is known a priori and the entire region of interest is included in the analysis.     

Model sensitivity and use of the comparative finite element method in mammalian jaw mechanics: mandible performance in the gray wolf

Finite Element Analysis (FEA) is a powerful tool gaining use in studies of biological form and function. This method is particularly conducive to studies of extinct and fossilized organisms, as models can be assigned properties that approximate living tissues. In disciplines where model validation is difficult or impossible, the choice of model parameters and their effects on the results become increasingly important, especially in comparing outputs to infer function. To evaluate the extent to which performance measures are affected by initial model input, we tested the sensitivity of bite force, strain energy, and stress to changes in seven parameters that are required in testing craniodental function with FEA. Simulations were performed on FE models of a Gray Wolf (Canis lupus) mandible. Results showed that unilateral bite force outputs are least affected by the relative ratios of the balancing and working muscles, but only ratios above 0.5 provided balancing-working side joint reaction force relationships that are consistent with experimental data. The constraints modeled at the bite point had the greatest effect on bite force output, but the most appropriate constraint may depend on the study question. Strain energy is least affected by variation in bite point constraint, but larger variations in strain energy values are observed in models with different number of tetrahedral elements, masticatory muscle ratios and muscle subgroups present, and number of material properties. These findings indicate that performance measures are differentially affected by variation in initial model parameters. In the absence of validated input values, FE models can nevertheless provide robust comparisons if these parameters are standardized within a given study to minimize variation that arise during the model-building process. Sensitivity tests incorporated into the study design not only aid in the interpretation of simulation results, but can also provide additional insights on form and function.     

A Neuro-Mechanical Model of a Single Leg Joint Highlighting the Basic Physiological Role of Fast and Slow Muscle Fibres of an Insect Muscle System

In legged animals, the muscle system has a dual function: to produce forces and torques necessary to move the limbs in a systematic way, and to maintain the body in a static position. These two functions are performed by the contribution of specialized motor units, i.e. motoneurons driving sets of specialized muscle fibres. With reference to their overall contraction and metabolic properties they are called fast and slow muscle fibres and can be found ubiquitously in skeletal muscles. Both fibre types are active during stepping, but only the slow ones maintain the posture of the body. From these findings, the general hypothesis on a functional segregation between both fibre types and their neuronal control has arisen. Earlier muscle models did not fully take this aspect into account. They either focused on certain aspects of muscular function or were developed to describe specific behaviours only. By contrast, our neuro-mechanical model is more general as it allows functionally to differentiate between static and dynamic aspects of movement control. It does so by including both muscle fibre types and separate motoneuron drives. Our model helps to gain a deeper insight into how the nervous system might combine neuronal control of locomotion and posture. It predicts that (1) positioning the leg at a specific retraction angle in steady state is most likely due to the extent of recruitment of slow muscle fibres and not to the force developed in the individual fibres of the antagonistic muscles; (2) the fast muscle fibres of antagonistic muscles contract alternately during stepping, while co-contraction of the slow muscle fibres takes place during steady state; (3) there are several possible ways of transition between movement and steady state of the leg achieved by varying the time course of recruitment of the fibres in the participating muscles.     

Influence of cartilage cap modelling on FEM simulation of femoral head stress]

The present study reports on the finite element analysis (FEA) of the femoral head in a process of preparation for a program for the realistic simulation of correctional osteotomies of the proximal femur. While the material properties have been studied extensively, only few publications consider the influence of the cartilage layer geometry on FE stimulation of the hip joint. Various models of the femoral head with and without the cartilage layer are generated and analysed. On looking at the maximum surface stresses, we found a strong influence of the cartilage layer and the subchondral osseous layer on the magnitude of the von Mises equivalent stress. The model with an anatomically realistic cartilage layer and compact bone shows stresses of between 4 and 5.5 MPa, depending on the position of the joint, while the model with a concentric cartilage layer has a maximum von Mises stress of 0.8 MPa. Only on simulation of a "realistic" cartilage layer, with a maximum thickness at the "pole" and minimum thickness at the "equator" do the changes in stress distribution--determined by changes in the position of the femoral head--become visible. Owing to major artefacts and the inability to create a realistic cartilage layer, voxel-based models of the femur are not suitable for the simulation of the femoral head surface.     

Surface electromyography and peak torque of repetitive maximum isokinetic plantar flexions in relation to aspects of muscle morphology.

This study investigates the relationships between surface electromyography (EMG [Mean frequency of the power spectrum (MNF)]) and peak torque variables obtained during 100 maximum concentric plantar flexions with the right limb at 60 degrees s(-1) and different muscle morphological variables. Surface EMG was recorded from the right gastrocnemius lateralis and muscle biopsies were taken from the same site as the EMG electrodes were positioned. Muscle fibre area and fibre type composition were determined on serial muscle cross sections using both histochemistry (myofibrillar adenosine triphosphatase) and immunohistochemistry (monoclonal antibodies against specific myosin heavy chain isoforms). Forty-three female and nine male students participated in the study. Gastrocnemius lateralis contained predominantly type I fibres (50%) and type IIA fibres (40%) in both sexes and large individual differences were found. Principal component analysis (PCA) was used for the intercorrelation analyses, and projection to latent structures (PLS) was used for the multivariate regression analysis. MNF correlated positively with different fibre areas and with the proportion of type I fibres. Fibre areas and sex were the most important factors in the regression of maximum peak torque. High proportion of type I fibres and sex were the most important regressors of peak torque endurance normalised for lean body mass. More studies are needed to understand the complex interrelationships between intrinsic muscle properties and the frequency content of the surface EMG before theoretical models can be formulated that incorporate both fibre areas and fibre type proportions.     

Fibre conduction velocity and fibre composition in human vastus lateralis

The relationship between muscle fibre composition and fibre conduction velocity was investigated in 19 male track athletes, 12 sprinters and 7 distance runners, aged 20-24 years, using needle biopsy samples from vastus lateralis. Cross sectional areas of the fast twitch (FT) and slow twitch (ST) fibres were determined by histochemical analysis. The percentage of FT fibre areas ranged from 22.6 to 93.6%. Sprinters had a higher percentage of FT fibres than distance runners. Muscle fibre conduction velocity was measured with a surface electrode array placed along the muscle fibres, and calculated from the time delay between 2 myoelectric signals recorded during a maximal voluntary contraction. The conduction velocity ranged from 4.13 to 5.20 m.s-1. A linear correlation between conduction velocity and the relative area of FT fibres was statistically significant (r = 0.84, p less than 0.01). This correlation indicates that muscle fibre composition can be estimated from muscle fibre conduction velocity measured noninvasively with surface electrodes.     

The relationship of voluntary running to fibre type composition, fibre area and capillary supply in rat soleus and plantaris muscles

Twenty 4-week-old Wistar rats exercised voluntarily in running wheels each day for 45 days. Fibre type composition, fibre cross-sectional area and the number of capillaries around a fibre of the slow-twitch soleus and fast-twitch plantaris muscles were examined and compared with animals which had no access to running wheels. The exercise group had a higher percentage of fast-twitch oxidative glycolytic (FOG) fibres and a lower percentage of fast-twitch glycolytic (FG) fibres in the deep portion of the plantaris muscle. The area of FOG fibres in the surface portion of the plantaris muscle was also greater in the exercise group. In the exercised animals, there was a positive relationship between the running distance and the area of FOG fibres in both the deep and surface portions of the plantaris muscle. In addition, the running distance correlated positively with the percentage of FOG fibres and negatively with that of FG fibres in the deep portion of the plantaris muscle. There were no relationships between the running distance and fibre type composition, or fibre area and capillary supply in the soleus muscle. These results suggested that the increase in the percentage and area of FOG fibres in the fast-twitch muscle was closely related to voluntary running.     

Localization of hyaluronan in various muscular tissues

Summary The histochemical distribution of hyaluronan (hyaluronic acid, HYA) was analysed in various types of muscles in the rat by use of a hyaluronan-binding protein (HABP) and the avidin-biotin/peroxidase complex staining procedure. Microwave-aided fixation was used to retain the extracellular location of the glycosaminoglycan. In skeletal muscles, HYA was detected in the connective tissue sheath surrounding the muscles (epimysium), in the septa subdividing the muscle fibre bundles (perimysium) and in the connective tissue surrounding each muscle fibre (endomysium). HYA was heterogeneously distributed in all striated muscles. In skeletal muscles with small fibre dimensions (e.g., the lateral rectus muscle of the eye and the middle ear muscles), HYA was predominantly accumulated around the individual muscle fibres. Perivascular and perineural connective tissue formations were distinctly HYA-positive. In cardiac muscles, HYA was randomly distributed around the branching and interconnecting muscle fibres. In comparison, smooth muscle tissue was devoid of HYA.     

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.     

A diffusion-weighted imaging informed continuum model of the rabbit triceps surae complex

The NZ white rabbit is the animal of choice for much experimental work due to its muscular frame and similar response to human diseases, and is one of the few mammals that have had their genome sequenced. However, continuum-level computational models of rabbit muscle detailing fibre architecture are limited in the literature, especially the triceps surae complex (gastrocnemius, plantaris and soleus), which has similar biomechanics and translatable findings to the human. This study presents a geometrical model of the rabbit triceps surae informed with diffusion-weighted imaging (DWI)-based fibres. Passive rabbit-specific material properties are estimated using known muscle deformation inferred from magnetic resonance imaging data and dorsiflexion force measured with a custom-built rabbit rig and transducer. Muscle shape prediction is evaluated against a second rabbit. This study revealed that the triceps surae steady-state force post-rigor is close to post-mortem for small deformations but increases by a fixed ratio as the deformation increases and can be used to evaluate the passive behaviour of muscle. DWI fibre orientation significantly influences shape and mechanics during simulated computational muscle contraction. The presented triceps surae force and material properties may be used to inform the constitutive behaviour of continuum rabbit muscle models used to investigate pathology and musculotendon treatments that may be translated to the human condition.     

The force-length relationship of a muscle-tendon complex: experimental results and model calculations

Models are useful when studying how architectural and physiological properties of muscle-tendon complexes are related to function, because they allow for the simulation of the behaviour of such complexes during natural movements. In the construction of these models, evaluation of their accuracy is an important step. In the present study, a model was constructed to calculate the isometric force-length relationship of the rat extensor digitorum longus muscle-tendon complex. The model is based on the assumption that a muscle-tendon complex is a collection of independent units, each consisting of a muscle fibre in series with a tendon fibre. By intention, values for model parameters were derived indirectly, using only the measured maximal isometric tetanic force, the distance between origin and insertion at which it occurred (optimum lOI) and an estimate of muscle fibre optimal length. The accuracy of the calculated force-length relationship was subsequently evaluated by comparing it to the relationship measured in isometric tetanic contractions of a real complex in the rat. When the length of distal muscle fibres, measured during isometric contraction at optimal lOI of the whole complex, was used as an estimate for muscle fibre optimal length of all muscle fibre-tendon fibre units in the model, the calculated relationship was too narrow. That is, both on the ascending limb and on the descending limb the calculated tetanic force was lower than the measured tetanic force.(ABSTRACT TRUNCATED AT 250 WORDS)     

Characterization of the capillary network in skeletal muscles from 3D data

In this review we present immunohistochemical methods for visualization of capillaries and muscle fibres in thick muscle sections. Special attention is paid to the procedures that preserve good morphology. Applying confocal microscopy and virtual 3D stereological grids, or tracing of capillaries in virtual reality, length of capillaries within a muscle volume or length of capillaries adjacent to a muscle fibre per fibre length, fibre surface area or fibre volume can be evaluated by an unbiased approach. Moreover, 3D models of capillaries and muscle fibres can be produced. Comparison of the developed methods with counting capillary profiles from 2D sections is discussed and the reader is warned that counting capillary profiles from 2D sections can underestimate the capillary length by as much as 75 percent. Application of the described 3D methodology is illustrated by the anatomical remodelling of capillarity during acute denervation and early reinnervation in the rat soleus and extensor digitorum longus muscles.     

Application of skinned single muscle fibres to determine myofilament function in ageing and disease

The chemically skinned fibre is a suitable preparation to determine whether alterations in myofilament function contribute to muscle dysfunction during ageing and disorders such as chronic obstructive pulmonary disease (COPD). In this preparation the sarcolemma is chemically permeabilized and the myofilament lattice kept intact, functioning under controlled near-physiological conditions. As force generating capacity is an important determinant of muscle function and is related to fibre crosssectional area (FCSA), we compared several methods employed by researchers to determine FCSA. Specific tension, force divided by FCSA, has a co-efficient of variation of 27%, 37%, or 30% when the FCSA was measured from the width and depth assuming an elliptical circumference, the width assuming a circular circumference, and the width while the fibre was suspended in the air, respectively. The last method showed the closest relation with the FCSA in histological sections. The velocity of maximal unloaded shortening (V(0)) varied with fibre type, with fibres expressing the Beta/slow (type I) myosin heavy chain (MyHC) isoform being the slowest and fibres expressing the IIb MyHC isoform the fastest. While muscle weakness experienced after surgery could not be explained by changes in specific tension or FCSA of individual fibres, the preparation revealed significant changes in myofilament function during ageing and COPD.