Muscle Fiber Direction Research Articles

The principle, present and prospect of IMCL measurement based on<sup>1</sup>H MRSI technology

It has been found that, as a main mechanism for diabetes, insulin resistance may have appeared more than a decade before the onset of diabetes. Therefore, early detection of insulin resistance has vital significance for the early prevention, diagnosis, and treatment of diabetes. The content of intramyocellular lipid (IMCL) in human calf muscle has close and complex relationship with insulin resistance and metabolic disorders and, therefore, is associated with type 2 diabetes mellitus and even a variety of mental diseases. However, the current “gold standard” for IMCL measurement is the invasive biopsy technology, which is not suitable for large-scale basic research and long-term clinical applications. IMCL measurement technology based on proton magnetic resonance spectroscopy and spectroscopic imaging (1H MRSI) provides a radiation-free, non-invasive, and high-precision detection method. More than this, 1H MRSI has been expected to clarify the relationship between IMCL content and insulin resistance, as well as the relationship between insulin resistance and type 2 diabetes mellitus, and has the potential to be applied in clinical practice. This paper describes and summarizes the technical development of 1H MRSI-based IMCL content measurement. It also points out the challenges and the latest solutions of this technique from the aspects of physiological and structural characteristics of calves, muscle fiber direction, the bulk fat distribution, and the demand for precise quantification of IMCL content. In addition to reviewing the latest technical solutions to these problems, we particularly discuss the combination of 1H MRSI with some new technologies such as multi-mode magnetic resonance imaging (MRI) and magnetic resonance fingerprinting spectroscopy (MRFS), which will synergically provide more diversified, multi-dimensional and multi-scale measurement method for high-precision measurement of IMCL.

Effect of the direction of m. psoas major fibres on the results of tensile test - can we model meat as a material?

The aim of this study was to examine the possibility of tensile-test application at three strain rates (0.01/s and 0.001/s and 0.001/s) on suitable samples of grilled pork meat (musculus psoas major). Differences in the stress-strain curves were observed between the two directions of the muscle fibres (i.e. strain parallel to and transverse to the fibres). However, the strain rate of 0.001/s resulted in the most linear stress-strain curves for strain in both muscle fibre directions. Also, results confirmed that specimens tested transversally to the muscle fibre direction required less stress to fracture. We also concluded that specimens stretch more in the direction transverse to the muscle fibre direction for strain rates of 0.01/s and 0.001/s. Gaining knowledge from different methods of empirical mechanical testing of meat should enhance the possibility of forming material constitutive laws to be used as input to finite element simulations of industrial processes of meat such as cutting or of human oral processing.

Anatomically accurate model of EMG during index finger flexion and abduction derived from diffusion tensor imaging.

This study presents a modelling framework in which information on muscle fiber direction and orientation during contraction is derived from diffusion tensor imaging (DTI) and incorporated in a computational model of the surface electromyographic (EMG) signal. The proposed model makes use of the principle of reciprocity to simultaneously calculate the electric potentials produced at the recording electrode by charges distributed along an arbitrary number of muscle fibers within the muscle, allowing for a computationally efficient evaluation of extracellular motor unit action potentials. The approach is applied to the complex architecture of the first dorsal interosseous (FDI) muscle of the hand to simulate EMG during index finger flexion and abduction. Using diffusion tensor imaging methods, the results show how muscle fiber orientation and curvature in this intrinsic hand muscle change during flexion and abduction. Incorporation of anatomically accurate muscle architecture and other hand tissue morphologies enables the model to capture variations in extracellular action potential waveform shape across the motor unit population and to predict experimentally observed differences in EMG signal features when switching from index finger abduction to flexion. The simulation results illustrate how structural and electrical properties of the tissues comprising the volume conductor, in combination with fiber direction and curvature, shape the detected action potentials. Using the model, the relative contribution of motor units of different sizes located throughout the muscle under both conditions is examined, yielding a prediction of the detection profile of the surface EMG electrode array over the muscle cross-section.

A microstructurally-based, multi-scale, continuum-mechanical model for the passive behaviour of skeletal muscle tissue

This work presents a novel microstructurally-based, multi-scale model describing the passive behaviour of skeletal muscle tissue. The model is based on the detailed description of the mechanically relevant parts of the microstructure. The effective constitutive material response is obtained by a homogenisation of mechanical energies and stresses from the micro- to the macroscale. The key feature of the new model is that it does not require any constitutive assumptions or calibration on the macroscale. The effective mechanical response is a pure consequence of the stiffness and structural arrangement of microscopic components. In this sense, the model inherits its direction-dependent properties directly from the microstructure. This is achieved by employing a Voigt-type homogenisation and by utilising for the complex collageneous network of the extracellular matrix an angular integration method. For physiologically realistic microscopic model parameters, this model reveals that muscle tissue exhibits a tensile stiffness that is larger transverse to the muscle fibre than in muscle fibre direction. This highlights that muscle tissue in general does not obey a classical fibre-reinforcement solely for tensile stretches of the muscle fibres but rather a general transversely isotropic behaviour. Moreover, the formulation of the effective macroscopic energy is provided in terms of well-known macroscopic strain invariants, which allows for an easy application of the model in standard numerical settings.

Microstructure-based finite element model of left ventricle passive inflation

Isolating the role(s) of microstructural pathological features in affecting diastolic filling is important in developing targeted treatments for heart diseases. We developed a microstructure-based constitutive model of the myocardium and implemented it in an efficient open-source finite element modeling framework to simulate passive inflation of the left ventricle (LV) in a representative 3D geometry based on experimentally measured muscle fiber architecture. The constitutive model was calibrated using previous tissue-level biaxial mechanical test data derived from the canine heart and validated with independent sets of measurements made at both the isolated constituent and organ level. Using the validated model, we investigated the load taken up by each tissue constituent and their effects on LV passive inflation. The model predicts that the LV compliance is sensitive to the collagen ultrastructure, specifically, the collagen fiber azimuthal angle with respect to the local muscle fiber direction and its waviness. The model also predicts that most of the load in the sub-epicardial and sub-endocardial regions is taken up, respectively, by the muscle fibers and collagen fiber network. This result suggests that normalizing LV passive stiffness by altering the collagen fiber network and myocyte stiffness is most effective when applied to the sub-endocardial and sub-epicardial regions, respectively. This finding may have implication for the development of new pharmaceutical treatments targeting individual cardiac tissue constituents to normalize LV filling function in heart diseases. Statement of SignificanceCurrent constitutive models describing the tissue mechanical behavior of the myocardium are largely phenomenological. While able to represent the bulk tissue mechanical behavior, these models cannot distinguish the contribution of the tissue constituents and their ultrastructure to heart function. Although microstructure-based constitutive models can be used to isolate the role of tissue ultrastructure, they have not been implemented in a computational framework that can accommodate realistic 3D organ geometry. The present study addresses these issues by developing and validating a microstructure-based computational modeling framework, which is used to investigate the role of tissue constituents and their ultrastructure in affecting heart function.

Soleus muscle weakness in cerebral palsy: Muscle architecture revealed with Diffusion Tensor Imaging.

Cerebral palsy (CP) is associated with movement disorders and reduced muscle size. This latter phenomenon has been observed by computing muscle volumes from conventional MRI, with most studies reporting significantly reduced volumes in leg muscles. This indicates impaired muscle growth, but without knowing muscle fiber orientation, it is not clear whether muscle growth in CP is impaired in the along-fiber direction (indicating shortened muscles and limited range of motion) or the cross-fiber direction (indicating weak muscles and impaired strength). Using Diffusion Tensor Imaging (DTI) we can determine muscle fiber orientation and construct 3D muscle architectures which can be used to examine both along-fiber length and cross-sectional area. Such an approach has not been undertaken in CP. Here, we use advanced DTI sequences with fast imaging times to capture fiber orientations in the soleus muscle of children with CP and age-matched, able-bodied controls. Cross sectional areas perpendicular to the muscle fiber direction were reduced (37 ± 11%) in children with CP compared to controls, indicating impaired muscle strength. Along-fiber muscle lengths were not different between groups. This study is the first to demonstrate along-fiber and cross-fiber muscle architecture in CP using DTI and implicates impaired cross-sectional muscle growth in children with cerebral palsy.

Compressive Mechanical Response of Porcine Muscle at Intermediate (100/s-102/s) Strain Rates

Compressive stress-strain response of porcine muscle was experimentally determined at intermediate strain rates (100/s-102/s) in this study. A hydraulically driven materials testing system with a dynamic testing mode was used to perform the compressive experiments on porcine muscle tissue with loading directions parallel and perpendicular to muscle fiber direction. Experiments at quasi-static strain rates were also conducted to investigate the strain-rate effects over a wider range. The experimental results show that, at intermediate strain rates, the porcine muscle’s compressive stress-strain responses are non-linear and strain-rate sensitive. The porcine muscle’s compressive mechanical response exhibits no significant difference between the two fiber orientation cases at quasi-static and intermediate strain rates. An Ogden model with two material constants was adopted to describe the rate-dependent compressive behavior of the porcine muscle.

Ventricular Myocardial Sheet

Background: Despite the fact that the exact architecture and orientation of ventricular myocardium are critical to cardiac functions either in health or disease, it is still debated.
 Objectives: Anatomical demonstration of the ventricle myocardium (VM)as a single, long and continuous muscular sheet and this muscular sheet can be dived into 3-segments. As a new anatomical concept the left ventricle is a triple layers wall; whether the right ventricle is a single layer wall.Histological demonstration of different directions of muscle-fibers at each layer of ventricular myocardium.
 Type of the study: Cross- sectional study.
 Methods: In this study 100-heart (fish, chicken, goat, sheep and cow) were dissected and analyzed. Dental lacrona and wax knife used majorly in the dissection, boiling of the hearts with distilled water and finally opening them by the “opening-technique”.
 Results: Ventricular myocardium is a single, long and continuous muscular sheet in 100-samples of different species which had been included in the study (passing from the fish toward the cow). VMS can be divided into 3-segments in (100% of cow, 95% of goat and 85% of sheep). The left ventricle is a triple layers wall; whether the right ventricle is single layer wall, this result observed in (100% of cow, 95% of goat and 85% of sheep).Finally different directions of muscle fibers observed at each layer of ventricular myocardium where the subendocardial layer shows transverse running pattern of muscle fibers, mesocardial layer shows longitudinal running pattern of muscle fibers and subepicardial layer shows mixed running patterns of muscle fibers.
 Conclusion: Ventricular myocardium is single, long and continuous muscular sheet. This sheet consists of 3-segments. These segments coils in spiral track and form the triple layers left ventricular wall and the single layer right ventricular wall. By histological examination of ventricular myocardial layers different directions of muscle fibers observed at each layer.

Surgical reinforcement alters collagen alignment and turnover in healing myocardial infarcts.

Previous studies have suggested that the composition and global mechanical properties of the scar tissue that forms after a myocardial infarction (MI) are key determinants of long-term survival, and emerging therapies such as biomaterial injection are designed in part to alter those mechanical properties. However, recent evidence suggests that local mechanics regulate scar formation post-MI, so that perturbing infarct mechanics could have unexpected consequences. We therefore tested the effect of changes in local mechanical environment on scar collagen turnover, accumulation, and alignment in 77 Sprague-Dawley rats at 1, 2, 3 and 6 wk post-MI by sewing a Dacron patch to the epicardium to eliminate circumferential strain while permitting continued longitudinal stretching with each heart beat. We found that collagen in healing infarcts aligned parallel to regional strain and perpendicular to the preinfarction muscle and collagen fiber direction, strongly supporting our hypothesis that mechanical environment is the primary determinant of scar collagen alignment. Mechanical reinforcement reduced levels of carboxy-terminal propeptide of type I procollagen (PICP; a biomarker for collagen synthesis) in samples collected by microdialysis significantly, particularly in the first 2 wk. Reinforcement also reduced carboxy-terminal telopeptide of type I collagen (ICTP; a biomarker for collagen degradation), particularly at later time points. These alterations in collagen turnover produced no change in collagen area fraction as measured by histology but significantly reduced wall thickness in the reinforced scars compared with untreated controls. Our findings confirm the importance of regional mechanics in regulating scar formation after infarction and highlight the potential for therapies that reduce stretch to also reduce wall thickness in healing infarcts. NEW & NOTEWORTHY This study shows that therapies such as surgical reinforcement, which reduce stretch in healing infarcts, can also reduce collagen synthesis and wall thickness and modify collagen alignment in postinfarction scars.

Conformity of modified O-ring test and maximal pinch strength for cross tape application direction.

Background:Although cross tape has recently been used by clinicians for various musculoskeletal conditions, scientific studies on the direction of cross tape application are lacking.Methods:The present study aimed to investigate whether the direction of cross tape application affected the outcomes of the modified O-ring test and maximal pinch strength using a pinch gauge and the conformity between these 2 tests when cross tape was applied to the forearm muscles of individuals with no upper extremity pain and no restriction of joint range of motion.This study used a single-blinding crossover design. The subjects comprised 39 adults (16 men and 23 women). Cross tape was applied to the dominant hand so that the 4 rows were at an angle of 45° to the right or left of the direction of the flexor digitorum superficialis muscle fibers, and then the subjects underwent a modified O-ring test and a test of maximal pinch strength using a pinch gauge. Both tests were performed in both directions, and the order of the directions and tests was randomized. SPSS 18.0 was used for statistical analysis. Cohen's kappa coefficient was used to analyze the conformity of the results from the 2 tests. The statistical significance level was P < .05.Results:A positive response in the modified O-ring test and maximal pinch strength were both affected by cross tape direction. The modified O-ring test and maximal pinch strength using pinch gauge results were in agreement (P < .00), and the kappa coefficient was significant at 1.00.Conclusion:The direction of cross tape application that produced a positive response in the modified O-ring test also produced greater maximal pinch strength. Thus, we propose that when applying cross tape to muscles, the direction of the 4 lines of the cross tape should be 45° relative to the direction of the muscle fibers, toward the side that produces a positive response in the modified O-ring test or produces the greatest maximal pinch strength using a pinch gauge.

Intermuscular Coherence Between Surface EMG Signals Is Higher for Monopolar Compared to Bipolar Electrode Configurations.

Introduction: The vasti muscles have to work in concert to control knee joint motion during movements like walking, running, or squatting. Coherence analysis between surface electromyography (EMG) signals is a common technique to study muscle synchronization during such movements and gain insight into strategies of the central nervous system to optimize neuromuscular performance. However, different assessment methods related to EMG data acquisition, e.g., different electrode configurations or amplifier technologies, have produced inconsistent observations. Therefore, the aim of this study was to elucidate the effect of different EMG acquisition techniques (monopolar vs. bipolar electrode configuration, potential vs. current amplifier) on the magnitude, reliability, and sensitivity of intermuscular coherence between two vasti muscles during stable and unstable squatting exercises.Methods: Surface EMG signals from vastus lateralis (VL) and medialis (VM) were obtained from eighteen adults while performing series of stable und unstable bipedal squats. The EMG signals were acquired using three different recording techniques: (1) Bipolar with a potential amplifier, (2) monopolar with a potential amplifier, and (3) monopolar electrodes with a current amplifier. VL-VM coherence between the respective raw EMG signals was determined during two trials of stable squatting and one trial of unstable squatting to compare the coherence magnitude, reliability, and sensitivity between EMG recording techniques.Results: VL-VM coherence was about twice as high for monopolar recordings compared to bipolar recordings for all squatting exercises while coherence was similar between monopolar potential and current recordings. Reliability measures were comparable between recording systems while the sensitivity to an increase in intermuscular coherence during unstable vs. stable squatting was lowest for the monopolar potential system.Discussion and Conclusion: The choice of electrode configuration can have a significant effect on the magnitude of EMG-EMG coherence, which may explain previous inconsistencies in the literature. A simple simulation of cross-talk could not explain the large differences in intermuscular coherence. It is speculated that inevitable errors in the alignment of the bipolar electrodes with the muscle fiber direction leads to a reduction of information content in the differential EMG signals and subsequently to a lower resolution for the detection of intermuscular coherence.

Strain Map of the Tongue in Normal and ALS Speech Patterns from Tagged and Diffusion MRI.

Amyotrophic Lateral Sclerosis (ALS) is a neurological disease that causes death of neurons controlling muscle movements. Loss of speech and swallowing functions is a major impact due to degeneration of the tongue muscles. In speech studies using magnetic resonance (MR) techniques, diffusion tensor imaging (DTI) is used to capture internal tongue muscle fiber structures in three-dimensions (3D) in a non-invasive manner. Tagged magnetic resonance images (tMRI) are used to record tongue motion during speech. In this work, we aim to combine information obtained with both MR imaging techniques to compare the functionality characteristics of the tongue between normal and ALS subjects. We first extracted 3D motion of the tongue using tMRI from fourteen normal subjects in speech. The estimated motion sequences were then warped using diffeomorphic registration into the b0 spaces of the DTI data of two normal subjects and an ALS patient. We then constructed motion atlases by averaging all warped motion fields in each b0 space, and computed strain in the line of action along the muscle fiber directions provided by tractography. Strain in line with the fiber directions provides a quantitative map of the potential active region of the tongue during speech. Comparison between normal and ALS subjects explores the changing volume of compressing tongue tissues in speech facing the situation of muscle degradation. The proposed framework provides for the first time a dynamic map of contracting fibers in ALS speech patterns, and has the potential to provide more insight into the detrimental effects of ALS on speech.

Effect of cryopreservation at -80°C on visco-hyperelastic properties of skeletal muscle tissue.

This paper investigated the effect of cryopreservation at -80°C on mechanical visco-hyperelastic properties of skeletal muscle. For that, both tensile and compression relaxation tests were performed on porcine tissues samples in fibre and cross-fibre directions. Material parameters were identified by using first order Ogden's strain energy function coupled with second order Maxwell's model. The results revealed that the cryopreservation conditions at -80°C with conservative and cryoprotectant solution significantly affected the mechanical properties of the skeletal muscle. Thus, cryopreserved tissue showed a higher instantaneous initial Young's modulus than for the fresh tissue in both tensile and compression deformations, and in the two muscular fibre directions. Furthermore, in compression tests, cryopreserved tissue exhibited a smaller non-linearity and a higher total relaxation ratio in both muscle fibre directions than for the fresh tissue.

Collagen fibril organization in chicken and porcine skeletal muscle perimysium under applied tension and compression

The tension/compression asymmetry observed in the stress-stretch response of skeletal muscle is not well understood. The collagen network in the extracellular matrix (ECM) almost certainly plays a major role, but the details are unknown. This paper reports qualitatively and quantitatively on skeletal muscle ECM reorganization during applied deformation using confocal imaging of collagen through use of a fluorescently-tagged specific collagen binding protein (CNA35-EGFP) of porcine and chicken muscle samples under tensile and compressive deformation in both the fibre and cross-fibre directions. This reveals the overall three-dimensional structure of collagen in perimysium in planes perpendicular and parallel to the muscle fibres in both species. Furthermore, there is clear evidence of the reorganization of these structures under compression and tension applied in both the muscle fibre and cross-fibre directions. These observations improve our understanding of perimysium structure and response to three-dimensional deformations and are an important basis for constitutive models of passive skeletal muscle. Although overall behaviour was similar, some differences in perimysium structure were observed between chicken and porcine muscle tissue. Further work is required to better understand which structures are responsible for the tension and compression stress-strain asymmetry previously observed in the mechanical response of passive skeletal muscle.

Loss of electrical anisotropy is an unrecognized feature of dystrophic muscle that may serve as a convenient index of disease status.

We sought to understand the alteration in the anisotropic, or direction dependent, character of muscle as measured by electrical impedance myography (EIM) in subjects with Duchenne muscular dystrophy (DMD) and its potential to serve as a biomarker of disease status. Thirty-six boys with DMD and 27 healthy controls were measured with EIM, with electrical current applied both parallel and perpendicular to the major muscle fiber direction. In addition, muscle extracted from 10 mdx and 10 wild-type mice were measured analogously. Normalized reactance anisotropy, a direction-dependent measure of membrane charge storage capability, was significantly lower in the four muscles of DMD subjects as compared to controls (p<0.01). Normalized reactance anisotropy also decreased with increasing age in DMD subjects (r=-0.36, p=0.031), but not in healthy boys. Analogous changes were observed in mdx mouse gastrocnemius as compared to wild type (p=0.019). These results support that loss of electrical anisotropy is a previously unrecognized feature of dystrophic muscle. Anisotropic alterations may offer novel indices to assist in neuromuscular disease diagnosis and to serve as easy-to-obtain biomarkers in clinical therapeutic trials.

Combined magnetic resonance and diffusion tensor imaging analyses provide a powerful tool for in vivo assessment of deformation along human muscle fibers

Muscle fiber direction strain provides invaluable information for characterizing muscle function. However, methods to study this for human muscles in vivo are lacking. Using magnetic resonance (MR) imaging based deformation analyses and diffusion tensor (DT) imaging based tractography combined, we aimed to assess muscle fiber direction local tissue deformations within the human medial gastrocnemius (GM) muscle. Healthy female subjects (n=5, age=27±1 years) were positioned prone within the MR scanner in a relaxed state with the ankle angle fixed at 90°. The knee was brought to flexion (140.8±3.0°) (undeformed state). Sets of 3D high resolution MR, and DT images were acquired. This protocol was repeated at extended knee joint position (177.0±1.0°) (deformed state). Tractography and Demons nonrigid registration algorithm was utilized to calculate local deformations along muscle fascicles. Undeformed state images were also transformed by a synthetic rigid body motion to calculate strain errors. Mean strain errors were significantly smaller then mean fiber direction strains (lengthening: 0.2±0.1% vs. 8.7±8.5%; shortening: 3.3±0.9% vs. 7.5±4.6%). Shortening and lengthening (up to 23.3% and 116.7%, respectively) occurs simultaneously along individual fascicles despite imposed GM lengthening. Along-fiber shear strains confirm the presence of much shearing between fascicles. Mean fiber direction strains of different tracts also show non-uniform distribution. Inhomogeneity of fiber strain indicates epimuscular myofascial force transmission. We conclude that MR and DT imaging analyses combined provide a powerful tool for quantifying deformation along human muscle fibers in vivo. This can help substantially achieving a better understanding of normal and pathological muscle function and mechanisms of treatment techniques.

Shear wave elastography using ultrasound: effects of anisotropy and stretch stress on a tissue phantom and in vivo reactive lymph nodes in the neck

PurposeThe purpose of this study was to evaluate how the anisotropy and the static stretch stress of the cervical musculature influence the measured shear modulus in a tissue-mimicking phantom and in cervical lymph nodes in vivo by using shear wave elastography (SWE).MethodsSWE was performed on a phantom using a pig muscle and on the middle jugular cervical lymph nodes in six volunteers. Tissue elasticity was quantified using the shear modulus and a supersonic shear wave imaging technique. For the phantom study, first, the optimal depth for measurement was determined, and then, SWE was performed in parallel and perpendicular to the muscle fiber orientation with and without strain stress. For the in vivo study, SWE was performed on the cervical lymph nodes in parallel and perpendicular to the sternocleidomastoid muscle fiber direction with and without neck stretching. The mean values of the shear modulus (meanSM) were then analyzed.ResultsIn the phantom study, the measured depth significantly influenced the meanSM with a sharp decrease at the depth of 1.5 cm (P<0.001). Strain stress increased the meanSM, irrespective of the muscle fiber orientation (P<0.001). In the in vivo study, the meanSM values obtained in parallel to the muscle fiber orientation were greater than those obtained perpendicular to the fiber orientation, irrespective of the stretch stress (P<0.001). However, meanSM was affected significantly by the stretch stress parallel to the muscle fiber orientation (P<0.001).ConclusionThe anisotropic nature of the cervical musculature and the applied stretch stress explain the variability of the SWE measurements and should be identified before applying SWE for the interpretation of the measured shear modulus values.

Elastic Cherenkov effects in transversely isotropic soft materials-II: Ex vivo and in vivo experiments

In part I of this study, we investigated the elastic Cherenkov effect (ECE) in an incompressible transversely isotropic (TI) soft solid using a combined theoretical and computational approach, based on which an inverse method has been proposed to measure both the anisotropic and hyperelastic parameters of TI soft tissues. In this part, experiments were carried out to validate the inverse method and demonstrate its usefulness in practical measurements. We first performed ex vivo experiments on bovine skeletal muscles. Not only the shear moduli along and perpendicular to the direction of muscle fibers but also the elastic modulus EL and hyperelastic parameter c2 were determined. We next carried out tensile tests to determine EL, which was compared with the value obtained using the shear wave elastography method. Furthermore, we conducted in vivo experiments on the biceps brachii and gastrocnemius muscles of ten healthy volunteers. To the best of our knowledge, this study represents the first attempt to determine EL of human muscles using the dynamic elastography method and inverse analysis. The significance of our method and its potential for clinical use are discussed.

Active behavior of abdominal wall muscles: Experimental results and numerical model formulation

In the present study a computational finite element technique is proposed to simulate the mechanical response of muscles in the abdominal wall. This technique considers the active behavior of the tissue taking into account both collagen and muscle fiber directions. In an attempt to obtain the computational response as close as possible to real muscles, the parameters needed to adjust the mathematical formulation were determined from in vitro experimental tests. Experiments were conducted on male New Zealand White rabbits (2047±34g) and the active properties of three different muscles: Rectus Abdominis, External Oblique and multi-layered samples formed by three muscles (External Oblique, Internal Oblique, and Transversus Abdominis) were characterized. The parameters obtained for each muscle were incorporated into a finite strain formulation to simulate active behavior of muscles incorporating the anisotropy of the tissue. The results show the potential of the model to predict the anisotropic behavior of the tissue associated to fibers and how this influences on the strain, stress and generated force during an isometric contraction.

A multi-scale continuum model of skeletal muscle mechanics predicting force enhancement based on actin-titin interaction.

Although recent research emphasises the possible role of titin in skeletal muscle force enhancement, this property is commonly ignored in current computational models. This work presents the first biophysically based continuum-mechanical model of skeletal muscle that considers, in addition to actin-myosin interactions, force enhancement based on actin-titin interactions. During activation, titin attaches to actin filaments, which results in a significant reduction in titin's free molecular spring length and therefore results in increased titin forces during a subsequent stretch. The mechanical behaviour of titin is included on the microscopic half-sarcomere level of a multi-scale chemo-electro-mechanical muscle model, which is based on the classic sliding-filament and cross-bridge theories. In addition to titin stress contributions in the muscle fibre direction, the continuum-mechanical constitutive relation accounts for geometrically motivated, titin-induced stresses acting in the muscle's cross-fibre directions. Representative simulations of active stretches under maximal and submaximal activation levels predict realistic magnitudes of force enhancement in fibre direction. For example, stretching the model by 20% from optimal length increased the isometric force at the target length by about 30%. Predicted titin-induced stresses in the muscle's cross-fibre directions are rather insignificant. Including the presented development in future continuum-mechanical models of muscle function in dynamic situations will lead to more accurate model predictions during and after lengthening contractions.