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.     

Single syllable tongue motion analysis using tagged cine MRI

The complicated muscle activity of the human tongue and the resultant surface shapes can give us important clues about speech motor control and pathological tongue motion. This study uses tagged magnetic resonance imaging to provide a 2D surface deformation analysis of the tongue, as well as a 4D compression–expansion analysis, during utterances of four different syllables (/ba/, /ta/, /sha/ and /ga/). All speech tasks were performed several times to confirm the repeatability of the motion analysis. The results showed that the tongue has unique motion patterns for utterances of different syllables, and these differences, which may not be observed by a simple surface analysis, can be examined thoroughly by a 4D motion model-based analysis of the tongue muscles.     

A biomechanical model of sagittal tongue bending

The human tongue is a structurally complex and extremely flexible organ. In order to better understand the mechanical basis for lingual deformations, we modeled a primitive movement of the tongue, sagittal tongue bending. We hypothesized that sagittal bending is a synergistic deformation derived from co-contraction of the longitudinalis and transversus muscles. Our model of tongue bending was based on classical bimetal strip theory, in which curvature is produced when one muscle layer contracts more so than another. Contraction was modulated via mismatched thermal expansion coefficients and temperature change (to simulate muscular contraction). Our results demonstrated that synergistic contraction produced curvature and strain results which were in better correspondence to empirical results derived from tagging MRI than were the results of contraction of the longitudinalis muscle alone. This fundamental reliance of tongue bending on the synergistic contraction of its intrinsic fibers supports the muscular hydrostat theory of tongue function.     

A 3D skeletal muscle model coupled with active contraction of muscle fibres and hyperelastic behaviour

This paper presents a three-dimensional finite element model of skeletal muscle which was developed to simulate active and passive non-linear mechanical behaviours of the muscle during lengthening or shortening under either quasi-static or dynamic condition. Constitutive relation of the muscle was determined by using a strain energy approach, while active contraction behaviour of the muscle fibre was simulated by establishing a numerical algorithm based on the concept of the Hill's three-element muscle model. The proposed numerical algorithm could be used to predict concentric, eccentric, isometric and isotonic contraction behaviours of the muscle. The proposed numerical algorithm and constitutive model for the muscle were derived and implemented into a non-linear large deformation finite element programme ABAQUS by using user-defined material subroutines. A number of scenarios have been used to demonstrate capability of the model for simulating both quasi-static and dynamic response of the muscle. Validation of the proposed model has been performed by comparing the simulated results with the experimental ones of frog gastrocenemius muscle deformation. The effects of the fusiform muscle geometry and fibre orientation on the stress and fibre stretch distributions of frog muscle during isotonic contraction have also been investigated by using the proposed model. The predictability of the present model for dynamic response of the muscle has been demonstrated by simulating the extension of a squid tentacle during a strike to catch prey.     

A control model of human tongue movements in speech

Tongue movements during speech production have been investigated by means of a simple yet realistic biomechanical model, based on a finite elements modeling of soft tissues, in the framework of the equilibrium point hypothesis (-model) of motor control. In particular, the model has been applied to the estimation of the “central” control commands issued to the muscles, for a data set of mid-sagittal digitized tracings of vocal tract shape, r ecorded by means of low-intensity X-ray cineradiographies during speech. In spite of the highly non-linear mapping between the shape of the oral cavity and its acoustic consequences, the organization of control commands preserves the peculiar spatial organization of vowel phonemes in acoustic space. A factor analysis of control commands, which have been decomposed into independent or “orthogonal” muscle groups, has shown that, in spite of the great mobility of the tongue and the highly complex arrangement of tongue muscles, its movements can be explained in terms of the activation of a small number of independent muscle groups, each corresponding to an elementary or “primitive” movement. These results are consistent with the hypothesis that the tongue is controlled by a small number of independent “articulators”, for which a precise biomechanical substrate is provided. The influence of the effect of jaw and hyoid movements on tongue equilibrium has also bee n evaluated, suggesting that the bony structures cannot be considered as a moving frame of reference, but, indeed, there may be a substantial interaction between them and the tongue, that may only be accounted for by a “global” model. The reported results also define a simple control model for the tongue and, in analogy with similar modelling studies, they suggest that, because of the peculiar geometrical arrangement of tongue muscles, the central nervous system (CNS) may not need a de tailed representation of tongue mechanics but rather may make use of a relatively small number of muscle synergies, that are invariant over the whole space of tongue configurations. Received: 27 August 1996 / Accepted in revised form: 25 February 1997     

An inverse approach for the mechanical characterisation of vascular tissues via a generalised rule of mixtures

Mechanical factors such as stresses and strains play a major role in the growth and remodelling of soft biological tissues. The main constituents of tissue undergo different processes reacting to mechanical stimulus. Thereby, the characterisation of growth and remodelling requires an accurate estimation of the stresses and strains of their main components. Many soft tissues can be considered as composite materials and can be analysed using an appropriate rule of mixtures. Particularly, arterial tissue can be modelled as an isotropic soft matrix reinforced with preferentially oriented collagen fibres. An inverse approach to obtain the mechanical characterisation of each main component is proposed in this work. The procedure is based on a rule of mixtures raised in a finite deformation framework and generalised to include kinematics and compatibility equations for serial–parallel behaviour. This methodology allows obtaining the stress–strain relationship of the components fitting experimental data.     

Laplace-based modeling of fiber orientation in the tongue

Mechanical modeling of tongue deformation plays a significant role in the study of breathing, swallowing, and speech production. In the absence of internal joints, fiber orientations determine the direction of sarcomeric contraction and have great influence over real and simulated tissue motion. However, subject-specific experimental observations of fiber distribution are difficult to obtain; thus, models of fiber distribution are generally used in mechanical simulations. This paper describes modeling of fiber distribution using solutions of Laplace equations and compares the effectiveness of this approach against tractography from diffusion tensor magnetic resonance imaging. The experiments included qualitative comparison of streamlines from the fiber model against experimental tractography, as well as quantitative differences between biomechanical simulations focusing in the region near the genioglossus. The model showed good overall agreement in terms of fiber directionality and muscle positioning when compared to subject-specific imaging results and the literature. The angle between the fiber distribution model against tractography in the genioglossus and geniohyoid muscles averaged \(22^{\circ }\) likely due to experimental noise. However, kinematic responses were similar between simulations with modeled fibers versus experimentally obtained fibers; average discrepancy in surface displacement ranged from 1 to 7 mm, and average strain residual magnitude ranged from \(4\times 10^{-3}\) to 0.2. The results suggest that, for simulation purposes, the modeled fibers can act as a reasonable approximation for the tongue’s fiber distribution. Also, given its agreement with the global tongue anatomy, the approach may be used in model-based reconstruction of displacement tracking and diffusion results.     

Mechanical compression-induced pressure sores in rat hindlimb: muscle stiffness, histology, and computational models.

Pressure sores affecting muscles are severe injuries associated with ischemia, impaired metabolic activity, excessive tissue deformation, and insufficient lymph drainage caused by prolonged and intensive mechanical loads. We hypothesize that mechanical properties of muscle tissue change as a result of exposure to prolonged and intensive loads. Such changes may affect the distribution of stresses in soft tissues under bony prominences and potentially expose additional uninjured regions of muscle tissue to intensified stresses. In this study, we characterized changes in tangent elastic moduli and strain energy densities of rat gracilis muscles exposed to pressure in vivo (11.5, 35, or 70 kPa for 2, 4, or 6 h) and incorporated the abnormal properties that were measured in finite element models of the head, shoulders, pelvis, and heels of a recumbent patient. Using in vitro uniaxial tension testing, we found that tangent elastic moduli of muscles exposed to 35 and 70 kPa were 1.6-fold those of controls (P < 0.05, for strains /=5%). Histological (phosphotungstic acid hematoxylin) evaluation showed that this stiffening accompanied extensive necrotic damage. Incorporating these effects into the finite element models, we were able to show that the increased muscle stiffness in widening regions results in elevated tissue stresses that exacerbate the potential for tissue necrosis. Interfacial pressures could not predict deep muscle (e.g., longissimus or gluteus) stresses and injuring conditions. We conclude that information on internal muscle stresses is required to establish new criteria for pressure sore prevention.     

An anatomically based patient-specific finite element model of patella articulation: towards a diagnostic tool

A 3D anatomically based patient-specific finite element (FE) model of patello-femoral (PF) articulation is presented to analyse the main features of patella biomechanics, namely, patella tracking (kinematics), quadriceps extensor forces, surface contact and internal patella stresses. The generic geometries are a subset from the model database of the International Union of Physiological Sciences (IUPS) (http://www.physiome.org.nz) Physiome Project with soft tissue derived from the widely used visible human dataset, and the bones digitised from an anatomically accurate physical model with muscle attachment information. The models are customised to patient magnetic resonance images using a variant of free-form deformation, called 'host-mesh' fitting. The continuum was solved using the governing equation of finite elasticity, with the multibody problem coupled through contact mechanics. Additional constraints such as tissue incompressibility are also imposed. Passive material properties are taken from the literature and implemented for deformable tissue with a non-linear micro-structurally based constitutive law. Bone and cartilage are implemented using a 'St-Venant Kirchoff' model suitable for rigid body rotations. The surface fibre directions have been estimated from anatomy images of cadaver muscle dissections and active muscle contraction was based on a steady-state calcium-tension relation. The 3D continuum model of muscle, tendon and bone is compared with experimental results from the literature, and surgical simulations performed to illustrate its clinical assessment capabilities (a Maquet procedure for reducing patella stresses and a vastus lateralis release for a bipartite patella). Finally, the model limitations, issues and future improvements are discussed.     

Electrohydrodynamic Model of Vesicle Deformation in Alternating Electric Fields

We develop an analytical theory to explain the experimentally observed morphological transitions of quasispherical giant vesicles induced by alternating electric fields. The model treats the inner and suspending media as lossy dielectrics, and the membrane as an impermeable flexible incompressible-fluid sheet. The vesicle shape is obtained by balancing electric, hydrodynamic, bending, and tension stresses exerted on the membrane. Our approach, which is based on force balance, also allows us to describe the time evolution of the vesicle deformation, in contrast to earlier works based on energy minimization, which are able to predict only stationary shapes. Our theoretical predictions for vesicle deformation are consistent with experiment. If the inner fluid is more conducting than the suspending medium, the vesicle always adopts a prolate shape. In the opposite case, the vesicle undergoes a transition from a prolate to oblate ellipsoid at a critical frequency, which the theory identifies with the inverse membrane charging time. At frequencies higher than the inverse Maxwell-Wagner polarization time, the electrohydrodynamic stresses become too small to alter the vesicle's quasispherical rest shape. The model can be used to rationalize the transient and steady deformation of biological cells in electric fields.     

Work behaviors of artificial muscle based on cation driven polypyrrole

A soft actuator mimicking natural muscles (artificial muscle) has been developed using a flexible conducting polymer of polypyrrole films, which were driven by electrical stimulus in a saline solution. The work characteristics were studied under various load stresses and found to behave like natural muscles. The artificial muscles shrunk and stiffened by the positive electrical stimulus by 2-3% at the maximum force of 5 MPa, and relaxed by application of negative voltages. At larger load stresses, the artificial muscle shrunk slowly as natural muscles do. The driving current also lasted longer at larger loads, indicating that the muscle sensed the magnitude of the load stress. During contraction of the muscle, the conversion efficiency from the electrical input and mechanical output energies was estimated to be around 0.06%. The maximum volumetric work was approximately estimated to be 100 kJ m(-3). These figures are unexpectedly small compared with those of natural muscles.     

Influence of tongue muscle contraction and transmural pressure on nasopharyngeal geometry in the rat

The mammalian pharynx is a hollow muscular tube that participates in ingestion and respiration, and its size, shape, and stiffness can be altered by contraction of skeletal muscles that lie inside or outside of its walls. MRI was used to determine the interaction between pharyngeal pressure and selective stimulation of extrinsic tongue muscles on the shape of the rat nasopharynx. Pressure (-9, -6, -3, 3, 6, and 9 cmH?O) was applied randomly to the isolated pharyngeal airway of anesthetized rats that were positioned in a 4.7-T MRI scanner. The anterior-posterior (AP) and lateral diameters of the nasopharynx were measured in eight axial slices at each level of pressure, with and without bilateral hypoglossal nerve stimulation (0.1-ms pulse, 1/3 maximal force, 80 Hz). The rat nasopharynx is nearly circular, and positive pharyngeal pressure caused similar expansion of AP and lateral diameters; as a result, airway shape (ratio of lateral to AP diameter) remained constant. Negative pressure did not change AP or lateral diameter significantly, suggesting that a negative pressure reflex activated the tongue or other pharyngeal muscles. Stimulation of tongue protrudor muscles alone or coactivation of protrudor and retractor muscles caused greater AP than lateral expansion, making the nasopharynx slightly more elliptical, with the long axis in the AP direction. These effects tended to be more pronounced at negative pharyngeal pressures and greater in the caudal than rostral nasopharynx. These data show that stimulation of rodent tongue muscles can adjust pharyngeal shape, extending previous work showing that tongue muscle contraction alters pharyngeal compliance and volume, and provide physiological insight that can be applied to the treatment of obstructive sleep apnea.     

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.     

On simulating sustained isometric muscle fatigue: a phenomenological model considering different fiber metabolisms

The present study shows a new computational FEM technique to simulate the evolution of the mechanical response of 3D muscle models subjected to fatigue. In an attempt to obtain very realistic models, parameters needed to adjust the mathematical formulation were obtained from in vivo experimental tests. The fatigue contractile properties of three different rat muscles (Tibialis Anterior, Extensor Digitorium Longus and Soleus) subjected to sustained maximal isometric contraction were determined. Experiments were conducted on three groups \((n=5)\) of male Wistar rats \((313 \pm 81.14\,\hbox {g})\) using a protocol previously developed by the authors for short tetanic contractions. The muscles were subjected to an electrical stimulus to achieve tetanic contraction during 10 s. The parameters obtained for each muscle were incorporated into a finite strain formulation for simulating active and passive behavior of muscles with different fiber metabolisms. The results show the potential of the model to predict muscle fatigue under high-frequency stimulation and the 3D distribution of mechanical variables such as stresses and strains.     

Structural changes in muscle crossbridges accompanying force generation

We have investigated the structure of the crossbridges in muscles rapidly frozen while relaxed, in rigor, and at various times after activation from rigor by flash photolysis of caged ATP. We used Fourier analysis of images of cross sections to obtain an average view of the muscle structure, and correspondence analysis to extract information about individual crossbridge shapes. The crossbridge structure changes dramatically between relaxed, rigor, and with time after ATP release. In relaxed muscle, most crossbridges are detached. In rigor, all are attached and have a characteristic asymmetric shape that shows strong left-handed curvature when viewed from the M-line towards the Z-line. Immediately after ATP release, before significant force has developed (20 ms) the homogeneous rigor population is replaced by a much more diverse collection of crossbridge shapes. Over the next few hundred milliseconds, the proportion of attached crossbridges changes little, but the distribution of the crossbridges among different structural classes continues to evolve. Some forms of attached crossbridge (presumably weakly attached) increase at early times when tension is low. The proportion of several other attached non-rigor crossbridge shapes increases in parallel with the development of active tension. The results lend strong support to models of muscle contraction that have attributed force generation to structural changes in attached crossbridges.     

Correspondence between laryngeal vocal fold movement and muscle activity during speech and nonspeech gestures.

To better understand the role of each of the laryngeal muscles in producing vocal fold movement, activation of these muscles was correlated with laryngeal movement during different tasks such as sniff, cough or throat clear, and speech syllable production. Four muscles [the posterior cricoarytenoid, lateral cricoarytenoid, cricothyroid (CT), and thyroarytenoid (TA)] were recorded with bipolar hooked wire electrodes placed bilaterally in four normal subjects. A nasoendoscope was used to record vocal fold movement while simultaneously recording muscle activity. Muscle activation level was correlated with ipsilateral vocal fold angle for vocal fold opening and closing. Pearson correlation coefficients and their statistical significance were computed for each trial. Significant effects of muscle (P < or = 0.0005) and task (P = 0.034) were found on the r (transformed to Fisher's Z') values. All of the posterior cricoarytenoid recordings related significantly with vocal opening, whereas CT activity was significantly correlated with opening only during sniff. The TA and lateral cricoarytenoid activities were significantly correlated with vocal fold closing during cough. During speech, the CT and TA activity correlated with both opening and closing. Laryngeal muscle patterning to produce vocal fold movement differed across tasks; reciprocal muscle activity only occurred on cough, whereas speech and sniff often involved simultaneous contraction of muscle antagonists. In conclusion, different combinations of muscle activation are used for biomechanical control of vocal fold opening and closing movements during respiratory, airway protection, and speech tasks.     

Theoretical models in mechanics of the left ventricle

Different rheological concepts and theoretical studies have been recently presented using models of myocardial mechanics. Complex analysis of the mechanical behavior of the left ventricular wall have been developed in order to estimate the local stresses and deformations that occur during the heart cycle as well as the ventricular stroke volume and pressure. Theoretical models have taken into account non-linear and viscoelastic passive properties of the myocardium tissue, when subjected to large deformations, through given strain energy functions or stress-strain relations. Different prolate spheroid geometries have been considered for such thick shell cardiac structure. During the active state of the contraction, the rheological behavior of the fibers has been described using different muscle models and relationships between fiber tension and strain, and activation degree. A forthcoming approach for bridging the gap between the knowledge of the muscle fiber microrheological properties and the study of the mechanical behavior of the entire ventricle, consists in including anisotropic and inhomogeneous effects through fiber direction field.     

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.