A nonlinear model of passive muscle viscosity

Multiscale analysis of Klf10's impact on the passive mechanical properties of murine skeletal muscle

Skeletal muscle is a hierarchical structure composed of multiple organizational scales. A major challenge in the biomechanical evaluation of muscle relates to the difficulty in evaluating the experimental mechanical properties at the different organizational levels of the same tissue. Indeed, the ability to integrate mechanical properties evaluated at various levels will allow for improved assessment of the entire tissue, leading to a better understanding of how changes at each level evolve over time and/or impact tissue function, especially in the case of muscle diseases. Therefore, the purpose of this study was to analyze a genetically engineered mouse model (Klf10 KO: Krüppel-Like Factor 10 knockout) with known skeletal muscle defects to compare the mechanical properties with wild-type (WT) controls at the three main muscle scales: the macroscopic (whole muscle), microscopic (fiber) and submicron (myofibril) levels. Passive mechanical tests (ramp, relaxation) were performed on two types of skeletal muscle (soleus and extensor digitorum longus (EDL)). Results of the present study revealed muscle-type specific behaviors in both genotypes only at the microscopic scale. Interestingly, loss of Klf10 expression resulted in increased passive properties in the soleus but decreased passive properties in the EDL compared to WT controls. At the submicron scale, no changes were observed between WT and Klf10 KO myofibrils for either muscle; these results demonstrate that the passive property differences observed at the microscopic scale (fiber) are not caused by sarcomere intrinsic alterations but instead must originate outside the sarcomeres, likely in the collagen-based extracellular matrix. The macroscopic scale revealed similar passive mechanical properties between WT and Klf10 KO hindlimb muscles. The present study has allowed for a better understanding of the role of Klf10 on the passive mechanical properties of skeletal muscle and has provided reference data to the literature which could be used by the community for muscle multiscale modeling.

Structure-Function relationships in the skeletal muscle extracellular matrix

The vast majority of skeletal muscle biomechanical studies have rightly focused on its active contractile properties. However, skeletal muscle passive biomechanical properties have significant clinical impact in aging and disease and are yet incompletely understood. This review focuses on the passive biomechanical properties of the skeletal muscle extracellular matrix (ECM) and suggests aspects of its structural basis. Structural features of the muscle ECM such as perimysial cables, collagen cross-links and endomysial structures have been described, but the way in which these structures combine to create passive biomechanical properties is not completely known. We highlight the presence and organization of perimysial cables. We also demonstrate that the analytical approaches that define passive biomechanical properties are not necessarily straight forward. For example, multiple equations, such as linear, exponential, and polynomial are commonly used to fit raw stress-strain data. Similarly, multiple definitions of zero strain exist that affect muscle biomechanical property calculations. Finally, the appropriate length range over which to measure the mechanical properties is not clear. Overall, this review summarizes our current state of knowledge in these areas and suggests experimental approaches to measuring the structural and functional properties of skeletal muscle.

Mechanism of elastic energy storage of honey bee abdominal muscles under stress relaxation

Energy storage of passive muscles plays an important part in frequent activities of honey bee abdomens due to the muscle distribution and open circulatory system. However, the elastic energy and mechanical properties of structure in passive muscles remain unclear. In this article, stress relaxation tests on passive muscles from the terga of the honey bee abdomens were performed under different concentrations of blebbistatin and motion parameters. In stress relaxation, the load drop with the rapid and slow stages depending on stretching velocity and stretching length reflects the features of myosin-titin series structure and cross-bridge-actin cyclic connections in muscles. Then a model with 2 parallel modules based on the 2 feature structures in muscles was thus developed. The model described the stress relaxation and stretching of passive muscles from honey bee abdomen well for a good fitting in stress relaxation and verification in loading process. In addition, the stiffness change of cross-bridge under different concentrations of blebbistatin is obtained from the model. We derived the elastic deformation of cross-bridge and the partial derivatives of energy expressions on motion parameters from this model, which accorded the experimental results. This model reveals the mechanism of passive muscles from honey bee abdomens suggesting that the temporary energy storage of cross-bridge in terga muscles under abdomen bending provides potential energy for springback during the periodic abdomen bending of honey bee or other arthropod insects. The finding also provides an experimental and theoretical basis for the novel microstructure and material design of bionic muscle.

Multimodal assessment of spasticity using a point-of-care instrumented glove to separate neural and biomechanical contributions

Accurate assessment of spasticity is crucial for physicians to select the most suitable treatment for patients. However, the current clinical practice standard is limited by imprecise assessment scales relying on perception. Here, we equipped the clinician with a portable, multimodal sensor glove to shift bedside evaluations from subjective perception to objective measurements. The measurements were correlated with biomechanical properties of muscles and revealed dynamic characteristics of spasticity, including catch symptoms and velocity-dependent resistance. Using the biomechanical data, a radar metric was developed for ranking severity in spastic knees and elbows. The continuous monitoring results during anesthesia induction enable the separation of neural and structural contributions to spasticity in 21 patients. This work delineated effects of reflex excitations from structural abnormalities, to classify underlying causes of spasticity that will inform treatment decisions for evidence-based patient care.

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Tool to shift from subjective scales to objective metrics in spasticity evaluation

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Develop a multifaceted metric to rank severity based on biomechanical properties

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Delineate effects of hyper-reflexes and structural abnormalities in spastic muscles

Active muscle stiffness is reduced during rapid unloading in muscles from TtnD112-158 mice with a large deletion to PEVK titin

Evidence suggests that the giant muscle protein, titin functions as a tunable spring in active muscle. However, the mechanisms for increasing titin stiffness with activation are not well understood. Previous studies have suggested that during muscle activation, titin binds to actin which engages the PEVK region of titin thereby increasing titin stiffness. In this study, we investigated the role of PEVK titin in active muscle stiffness during rapid unloading. We measured elastic recoil of active and passive soleus muscles from TtnD112-158 mice characterized by a 75% deletion of PEVK titin and increased passive stiffness. We hypothesized that activated TtnD112-158 muscles are more stiff than wild type muscles due to the increased stiffness of PEVK titin. Using a servomotor force lever, we compared the stress–strain relationships of elastic elements in active and passive muscles during rapid unloading and quantified the change in stiffness upon activation. Results show that the elastic modulus of TtnD112-158 muscles increased with activation. However, elastic elements developed force at 7% longer lengths and exhibited 50% lower active stiffness in TtnD112-158 soleus muscles than wild type muscles. Thus, despite having a shorter, stiffer PEVK segment, during rapid unloading, TtnD112-158 soleus muscles exhibited reduced active stiffness compared to wild type soleus muscles. These results are consistent with the idea that PEVK titin contributes to active muscle stiffness, however, the reduction in active stiffness of TtnD112-158 muscles suggests that other mechanisms compensate for the increased PEVK stiffness.

ANALYSIS OF INDUCED ISOMETRIC FATIGUING CONTRACTIONS IN BICEPS BRACHII MUSCLES USING MYOTONOMETRY AND SURFACE ELECTROMYOGRAPHIC MEASUREMENTS

Viscoelastic properties of skeletal muscle tissue are known to be impacted by fatiguing contractions. In this study, an attempt has been made to utilize myotonometry for analyzing the relationship between muscle viscoelasticity and contractile behaviors in a fatiguing task. For this purpose, thirteen young healthy volunteers are recruited to perform the fatiguing isometric task and the time to task failure (TTF) is recorded. Myotonometric parameters and simultaneous surface electromyographic (sEMG) signals are recorded from the Biceps Brachii muscle of the flexed arm. The correlation between myotonometric parameters and TTF is further analyzed. Cross-validation with sEMG features is also performed. Stiffness of muscle has a positive correlation with TTF in the left hand ([Formula: see text]). Damping property of the nonfatigued muscle is positively associated with the fatigue-induced changes in amplitude features of sEMG signal in the right hand ([Formula: see text]). The normalized rate of change of mean frequency of sEMG signal has a positive correlation with stiffness values in both of the hands ([Formula: see text]). Muscle viscoelasticity is demonstrated to influence the progression of fatigue, although the difference in motor control due to handedness is also found to be an important factor. The results are promising to improve the understanding of the effect of muscle mechanics in fatigue-induced task failure.

On multiscale tension-compression asymmetry in skeletal muscle

Skeletal muscle tissue shows a clear asymmetry with regard to the passive stresses under tensile and compressive deformation, referred to as tension-compression asymmetry (TCA). The present study is the first one reporting on TCA at different length scales, associated with muscle tissue and muscle fibres, respectively. This allows for the first time the comparison of TCA between the tissue and one of its individual components, and thus to identify the length scale at which this phenomenon originates. Not only the passive stress-stretch characteristics were recorded, but also the volume changes during the axial tension and compression experiments. The study reveals clear differences in the characteristics of TCA between fibres and tissue. At tissue level TCA increases non-linearly with increasing deformation and the ratio of tensile to compressive stresses at the same magnitude of strain reaches a value of approximately 130 at 13.5% deformation. At fibre level instead it initially drops to a value of 6 and then rises again to a TCA of 14. At a deformation of 13.5%, the tensile stress is about 6 times higher. Thus, TCA is about 22 times more expressed at tissue than fibre scale. Moreover, the analysis of volume changes revealed little compressibility at tissue scale whereas at fibre level, especially under compressive stress, the volume decreases significantly. The data collected in this study suggests that the extracellular matrix has a distinct role in amplifying the TCA, and leads to more incompressible tissue behaviour. STATEMENT OF SIGNIFICANCE: This article analyses and compares for the first time the tension-compression asymmetry (TCA) displayed by skeletal muscle at tissue and fibre scale. In addition, the volume changes of tissue and fibre specimens with application of passive tensile and compressive loads are studied. The study identifies a key role of the extracellular matrix in establishing the mechanical response of skeletal muscle tissue: It contributes significantly to the passive stress, it is responsible for the major part of tissue-scale TCA and, most probably, prevents/balances the volume changes of muscle fibres during deformation. These new results thus shed light on the origin of TCA and provide new information to be used in microstructure-based approaches to model and simulate skeletal muscle tissue.

Micro-biopsies: a less invasive technique for investigating human muscle fiber mechanics

The purpose of this investigation was to demonstrate that muscle fiber mechanics can be assessed on micro-biopsies obtained from human medial gastrocnemii. Three micro-biopsy samples were collected from female dancers (n=15). Single fibers and fiber bundles were isolated and passively stretched from 2.4 µm to 3.0 µm at 0.015 µm•s−1 and 0.04 µm•s−1 (n=50 fibers total) and in five increments at 0.12 µm•s−1 (n=42 fibers total). Muscle fibers were then activated isometrically at 2.4 µm (n=4 fibers total) and 3.0 µm (n=3 fibers total). Peak stress and steady state stress were significantly greater (p<0.0001) after stretching at 0.04 µm•s−1 than 0.015 µm•s−1. Furthermore, peak stresses and steady state stresses increased non-linearly with fiber length (p<0.0001). We conclude that active and passive muscle fiber mechanics can be investigated using tissue from micro-biopsies.

Systematic review of skeletal muscle passive mechanics experimental methodology

Understanding passive skeletal muscle mechanics is critical in defining structure-function relationships in skeletal muscle and ultimately understanding pathologically impaired muscle. In this systematic review, we performed an exhaustive literature search using PRISMA guidelines to quantify passive muscle mechanical properties, summarized the methods used to create these data, and make recommendations to standardize future studies. We screened over 7500 papers and found 80 papers that met the inclusion criteria. These papers reported passive muscle mechanics from single muscle fiber to whole muscle across 16 species and 54 distinct muscles. We found a wide range of methodological differences in sample selection, preparation, testing, and analysis. The systematic review revealed that passive muscle mechanics is species and scale dependent-specifically within mammals, the passive mechanics increases non-linearly with scale. However, a detailed understanding of passive mechanics is still unclear because the varied methodologies impede comparisons across studies, scales, species, and muscles. Therefore, we recommend the following: smaller scales may be maintained within storage solution prior to testing, when samples are tested statically use 2-3 min of relaxation time, stress normalization at the whole muscle level be to physiologic cross-sectional area, strain normalization be to sarcomere length when possible, and an exponential equation be used to fit the data. Additional studies using these recommendations will allow exploration of the multiscale relationship of passive force within and across species to provide the fundamental knowledge needed to improve our understanding of passive muscle mechanics.

Passive Properties of the Wrist and Fingers Following Chronic Hemiparetic Stroke: Interlimb Comparisons in Persons With and Without a Clinical Treatment History That Includes Botulinum Neurotoxin

Background: Neural impairments that follow hemiparetic stroke may negatively affect passive muscle properties, further limiting recovery. However, factors such as hypertonia, spasticity, and botulinum neurotoxin (BoNT), a common clinical intervention, confound our understanding of muscle properties in chronic stroke. Objective: To determine if muscle passive biomechanical properties are different following prolonged, stroke-induced, altered muscle activation and disuse. Methods: Torques about the metacarpophalangeal and wrist joints were measured in different joint postures in both limbs of participants with hemiparetic stroke. First, we evaluated 27 participants with no history of BoNT; hand impairments ranged from mild to severe. Subsequently, seven participants with a history of BoNT injections were evaluated. To mitigate muscle hypertonia, torques were quantified after an extensive stretching protocol and under conditions that encouraged participants to sleep. EMGs were monitored throughout data collection. Results: Among participants who never received BoNT, no significant differences in passive torques between limbs were observed. Among participants who previously received BoNT injections, passive flexion torques about their paretic wrist and finger joints were larger than their non-paretic limb (average interlimb differences = +42.0 ± 7.6SEM Ncm, +26.9 ± 3.9SEM Ncm, respectively), and the range of motion for passive finger extension was significantly smaller (average interlimb difference = -36.3° ± 4.5°SEM; degrees). Conclusion: Our results suggest that neural impairments that follow chronic, hemiparetic stroke do not lead to passive mechanical changes within the wrist and finger muscles. Rather, consistent with animal studies, the data points to potential adverse effects of BoNT on passive muscle properties post-stroke, which warrant further consideration.

Biochemical and structural basis of the passive mechanical properties of whole skeletal muscle

Passive mechanical properties of whole skeletal muscle are not as well understood as active mechanical properties. Both the structural basis for passive mechanical properties and the properties themselves are challenging to determine because it is not clear which structures within skeletal muscle actually bear passive loads and there are not established standards by which to make mechanical measurements. Evidence suggests that titin bears the majority of the passive load within the single muscle cell. However, at larger scales, such as fascicles and muscles, there is emerging evidence that the extracellular matrix bears the major part of the load. Complicating the ability to quantify and compare across size scales, muscles and species, definitions of muscle passive properties such as stress, strain, modulus and stiffness can be made relative to many reference parameters. These uncertainties make a full understanding of whole muscle passive mechanical properties and modelling these properties very difficult. Future studies defining the specific load bearing structures and their composition and organization are required to fully understand passive mechanics of the whole muscle and develop therapies to treat disorders in which passive muscle properties are altered such as muscular dystrophy, traumatic laceration, and contracture due to upper motor neuron lesion as seen in spinal cord injury, stroke and cerebral palsy.

Predicting muscle tissue response from calibrated component models and histology-based finite element models

Skeletal muscle is an anisotropic soft biological tissue composed of muscle fibres embedded in a structurally complex, hierarchically organised extracellular matrix. In a recent work (Kuravi et al., 2021) we have developed 3D finite element models from series of histological sections. Moreover, based on decellularisation of fresh tissue samples, a novel set of experimental data on the direction dependent mechanical properties of collagenous ECM was established (Kohn et al., 2021). Together with existing information on the material properties of single muscle fibres, the combination of these techniques allows computing predictions of the composite tissue response. To this end, an inverse finite element procedure is proposed in the present work to calibrate a constitutive model of the extracellular matrix, and supplementary biaxial tensile tests on fresh and decellularised tissues are performed for model validation. The results of this rigorously predictive and thus unforgiving strategy suggest that the prediction of the tissue response from the individual characteristics of muscle cells and decellularised tissue is only possible within clear limits. While orders of magnitude are well matched, and the qualitative behaviour in a wide range of load cases is largely captured, the existing deviations point at potentially missing components of the model and highlight the incomplete experimental information in bottom-up multiscale approaches to model skeletal muscle tissue.

Passive stiffness of fibrotic skeletal muscle in mdx mice relates to collagen architecture

KEY POINTS

The amount of fibrotic material in dystrophic mouse muscles relates to contractile function, but not passive function. Collagen fibres in skeletal muscle are associated with increased passive muscle stiffness in fibrotic muscles. The alignment of collagen is independently associated with passive stiffness in dystrophic skeletal muscles. These outcomes demonstrate that collagen architecture rather than collagen content should be a target of anti-fibrotic therapies to treat muscle stiffness.

ABSTRACT

Fibrosis is prominent in many skeletal muscle pathologies including dystrophies, neurological disorders, cachexia, chronic kidney disease, sarcopenia and metabolic disorders. Fibrosis in muscle is associated with decreased contractile forces and increased passive stiffness that limits joint mobility leading to contractures. However, the assumption that more fibrotic material is directly related to decreased function has not held true. Here we utilize novel measurement of extracellular matrix (ECM) and collagen architecture to relate ECM form to muscle function. We used mdx mice, a model for Duchenne muscular dystrophy that becomes fibrotic, and wildtype mice. In this model, extensor digitorum longus (EDL) muscle was significantly stiffer, but with similar total collagen, while the soleus muscle did not change stiffness, but increased collagen. The stiffness of the EDL was associated with increased collagen crosslinking as determined by collagen solubility. Measurement of ECM alignment using polarized light microscopy showed a robust relationship between stiffness and alignment for wildtype muscle that broke down in mdx muscles. Direct visualization of large collagen fibres with second harmonic generation imaging revealed their relative abundance in stiff muscles. Collagen fibre alignment was linked to stiffness across all muscles investigated and the most significant factor in a multiple linear regression-based model of muscle stiffness from ECM parameters. This work establishes novel characteristics of skeletal muscle ECM architecture and provides evidence for a mechanical function of collagen fibres in muscle. This finding suggests that anti-fibrotic strategies to enhance muscle function and excessive stiffness should target large collagen fibres and their alignment rather than total collagen.

Magnetic resonance imaging for the assessment of pathological hepatic findings in nonalcoholic fatty liver disease

The prevalence of nonalcoholic fatty liver disease (NAFLD) is expected to increase because of the current epidemics of obesity and diabetes, and NAFLD has become a major cause of chronic liver disease worldwide. Liver fibrosis is associated with poor long-term outcomes in patients with NAFLD. Additionally, increased mortality and liver-related complications are primarily seen in patients with nonalcoholic steatohepatitis (NASH); however, nonalcoholic fatty liver (NAFL) is believed to be benign and non-progressive. Therefore, distinguishing between NASH and NAFL is clinically important. Liver biopsy is the gold standard method for the staging of liver fibrosis and distinguishing between NASH and NAFL. Unfortunately, liver biopsy is an invasive and expensive procedure. Therefore, noninvasive methods, to replace biopsy, are urgently needed for the staging of liver fibrosis and diagnosing NASH. In this review, we discuss the recent studies on magnetic resonance imaging (MRI), including magnetic resonance elastography, proton density fat fraction measurement, and multiparametric MRI (mpMRI) that can be used in the assessment of NASH components such as liver fibrosis, steatosis, and liver injury including inflammation and ballooning.

Effect of viscoelastic properties on passive torque variations at different velocities of the knee joint extension and flexion movements

This study aimed to investigate the rate of passive torque variations of human knee joint in the different velocities of knee flexion and extension movements. Ten healthy men were invited to participate in the tests. All passive torque tests were performed for the knee joint extension and flexion on the sagittal plane in three different angular velocities of 15, 45, and 120°/s; in 5 consecutive cycles; and within 0° to 100° range of motion. The electrical activity of knee joint extensor and flexor muscles was recorded until there was no muscle activity signal. A Three-element Solid Model (SLS) was used to obtain the viscose and elastic coefficients. As the velocity increases, the stretch rate in velocity-independent tissues increases, and the stretch rate in velocity-dependent tissues decreases. By increasing the velocity, the resistance of velocity-dependent parts increases, and the velocity-independent parts are not affected by velocity. Since the first torque that resists the joint movement is passive torque, the elastic and viscous torques should be simultaneously used. It is better to perform the movement at a low velocity so that less energy is lost. The viscoelastic resistance of tissues diminishes. Graphical abstract.

Mechano-geometrical skeletal muscle fibre characterisation under cyclic and relaxation loading

In the present work, mechano-geometrical characterisations of skeletal muscle fibres in two different deformation states, namely, axial tension and axial compression, were realised. In both cases, cyclic and relaxation tests were performed. Additionally, the changes in the volume of the fibres during deformation were recorded to obtain more detailed information about the muscle fibre load transfer mechanisms. To the best of the authors' knowledge, the present experimental investigation of the mechanical and geometrical characteristics of muscle fibres provides a novel comprehensive data set that can be used to obtain a better understanding of muscle fibre load transfer mechanisms and to construct meaningful models. In the present study, it is shown that muscle fibres exhibit incompressibility (5% volume decrease at maximum deformation) under tension and that this feature is more pronounced under compression loading (37% volume decrease at maximum deformation). These findings are particularly interesting and lead to a further understanding of load transfer mechanisms and to the development of new modelling strategies.

Investigating Passive Muscle Mechanics With Biaxial Stretch

Introduction

The passive stiffness of skeletal muscle can drastically affect muscle function in vivo, such as the case for fibrotic tissue or patients with cerebral palsy. The two constituents of skeletal muscle that dominate passive stiffness are the intracellular protein titin and the collagenous extracellular matrix (ECM). However, efforts to correlate stiffness and measurements of specific muscle constituents have been mixed, and thus the complete mechanisms for changes to muscle stiffness remain unknown. We hypothesize that biaxial stretch can provide an improved approach to evaluating passive muscle stiffness.

Methods

We performed planar biaxial materials testing of passively stretched skeletal muscle and identified three previously published datasets of uniaxial materials testing. We developed and employed a constitutive model of passive skeletal muscle that includes aligned muscle fibers and dispersed ECM collagen fibers with a bimodal von Mises distribution. Parametric modeling studies and fits to experimental data (both biaxial and previously published) were completed.

Results

Biaxial data exhibited differences in time dependent behavior based on orientation (p < 0.0001), suggesting different mechanisms supporting load in the direction of muscle fibers (longitudinal) and in the perpendicular (transverse) directions. Model parametric studies and fits to experimental data exhibited the robustness of the model (<20% error) and how differences in tissue stiffness may not be observed in uniaxial longitudinal stretch, but are apparent in biaxial stretch.

Conclusion

This work presents novel materials testing data of passively stretched skeletal muscle and use of constitutive modeling and finite element analysis to explore the interaction between stiffness, constituent variability, and applied deformation in passive skeletal muscle. The results highlight the importance of biaxial stretch in evaluating muscle stiffness and in further considering the role of ECM collagen in modulating passive muscle stiffness.

Changes in the Viscoelastic Properties of the Vastus Lateralis Muscle With Fatigue

We investigated the in vivo effects of voluntary fatiguing isometric contractions of the knee extensor muscles on the viscoelastic properties of the vastus lateralis (VL). Twelve young males (29.0 ± 4.5 years) performed an intermittent voluntary fatigue protocol consisting of 6 sets × 10 repetitions of 5-s voluntary maximal isometric contractions with 5-s passive recovery periods between repetitions. Voluntary and evoked torque were assessed before, immediately after, and 20 min after exercise. The shear modulus (μ) of the VL muscle was estimated at rest and during a ramped isometric contraction using a conventional elastography technique. An index of active muscle stiffness was then calculated (slope from the relationship between shear modulus and absolute torque). Resting muscle viscosity (η) was quantified using a shear-wave spectroscopy sequence to measure the shear-wave dispersion. Voluntary and evoked torque decreased by ∼37% (P < 0.01) immediately after exercise. The resting VL μ was lower at the end of the fatigue protocol (-57.9 ± 5.4%, P < 0.001), whereas the resting VL η increased (179.0 ± 123%, P < 0.01). The active muscle stiffness index also decreased with fatigue (P < 0.05). By 20 min post-fatigue, there were no significant differences from the pre-exercise values for VL η and the active muscle stiffness index, contrary to the resting VL μ. We show that the VL μ is greatly reduced and η greatly enhanced by fatigue, reflecting a more compliant and viscous muscle. The quantification of both shear μ and η moduli in vivo may contribute to a better understanding of the mechanical behavior of muscles during fatigue in sports medicine, as well as in clinical situations.

The Effect of Freezing Time on Muscle Fiber Mechanical Properties

The purpose of this study was to investigate the effect of freezing time on the functional behavior of mouse muscle fibers. Passive mechanical tests were performed on single soleus muscle fibers from fresh (0 month) and preserved (stored at -20°C for 3, 6, 9 and 12 months) 3 month old mice. The Young's modulus and the dynamic and the static stresses were measured. A viscoelastic Hill model of 3rd order was used to fit the experimental relaxation test data. The statistical analysis corresponding to the elastic modulus of single muscle fibers did not differ when comparing fresh and stored samples for 3 and 6 months at -20 °C. From 9 months, fibers were less resistant and the mechanical properties were damaged. The primary goal of this study was to complete the gold standard process of muscle fiber preservation for subsequent mechanical property studies. We have demonstrated that muscle fibers can be stored at -20°C for up to 6 months without altering their mechanical properties.

Indirect actuation reduces flight power requirements in Manduca sexta via elastic energy exchange

In many insects, wing movements are generated indirectly via exoskeletal deformations. Measurements of inertial and aerodynamic power suggest that elastic recovery of energy between wingstrokes might reduce power requirements of flight. We tested three questions. (1) Can the thorax itself provide significant energy return? (2) Does a simple damped elastic model describe the bulk mechanical behaviour? (3) Are different regions of the thorax specialized for elastic energy exchange? We measured deformation mechanics of the hawkmoth Manduca sexta thorax by recording the force required to sinusoidally deform the thorax over a wide frequency range. Elastic energy storage in the thorax is sufficient to minimize power requirements. However, we find that a structural (frequency-independent) damping model, not a viscoelastic model, best describes the thorax's mechanical properties. We next performed complementary experiments on a structurally damped homogeneous hemisphere. In contrast to the hemispherical shell, we find that mechanical coupling between different regions of the thorax improves energy exchange performance and that local mechanical properties depend on global strain patterns. Specifically, the scutum region provides energy recovery with low dissipation, while the majority of energy loss occurred in the wing hinge region, highlighting the specificity of thorax regions for flight energetics.

Modeling Skeletal Muscle Stress and Intramuscular Pressure: A Whole Muscle Active-Passive Approach

Clinical treatments of skeletal muscle weakness are hindered by a lack of an approach to evaluate individual muscle force. Intramuscular pressure (IMP) has shown a correlation to muscle force in vivo, but patient to patient and muscle to muscle variability results in difficulty of utilizing IMP to estimate muscle force. The goal of this work was to develop a finite element model of whole skeletal muscle that can predict IMP under passive and active conditions to further investigate the mechanisms of IMP variability. A previously validated hypervisco-poroelastic constitutive approach was modified to incorporate muscle activation through an inhomogeneous geometry. Model parameters were optimized to fit model stress to experimental data, and the resulting model fluid pressurization data were utilized for validation. Model fitting was excellent (root-mean-square error or RMSE <1.5 kPa for passive and active conditions), and IMP predictive capability was strong for both passive (RMSE 3.5 mmHg) and active (RMSE 10 mmHg at in vivo lengths) conditions. Additionally, model fluid pressure was affected by length under isometric conditions, as increases in stretch yielded decreases in fluid pressurization following a contraction, resulting from counteracting Poisson effects. Model pressure also varied spatially, with the highest gradients located near aponeuroses. These findings may explain variability of in vivo IMP measurements in the clinic, and thus help reduce this variability in future studies. Further development of this model to include isotonic contractions and muscle weakness would greatly benefit this work.

Theoretical elastic tensile behavior of muscle fiber bundles in traumatic loading events

BACKGROUND

The mechanical characterization of skeletal muscle under high-rate loading regimes is important for predicting traumatic injuries due to traffic accidents and contact sports. However, it is difficult to perform dynamic mechanical tests at rates relevant to such rapid loading events.

METHODS

In the present study, a series of stress relaxation tests were conducted on rabbit hind-limb muscle fiber bundles using a custom tensile tester. Using relatively moderate loading conditions compared to those typically associated with traumatic injuries, the passive stress-decaying mechanical properties of muscle fiber bundles were characterized. In addition, stress relaxation responses to various ramp-hold stretches were theoretically predicted by a custom-built code.

FINDINGS

The results showed that the muscle fiber bundles exhibit greater stress relaxation at higher loading rates and greater stretch magnitudes. Based on these results, the data points representing the "elastic" stress-strain tensile behavior typical of traumatic injury were extrapolated using curve fitting. The theoretical model revealed rate-dependent characteristics of the muscle fiber bundles under traumatic loading conditions, which would result in tensile strengths of 300-500 kPa at the maximum engineering strain of 54%. This strength is on the order of magnitude as the maximum isometric stress of an active muscle contraction.

INTERPRETATION

The proposed numerical model is expected to serve as a powerful research tool to investigate injury mechanisms of the skeletal muscle. Moreover, the elastic response that was theoretically predicted here will be useful in the development of effective countermeasures to prevent traumatic injuries due to rapid loading events.

Effect of manual compressive therapy on latent myofascial trigger point pressure pain thresholds

OBJECTIVE

This study compared the effects of 90 s of manual compressive therapy (MCT) on latent myofascial trigger points (LTPs) for 3 sessions per week for 4 weeks to determine changes in individual pressure pain threshold (PPT). A total of 30 (15 males, 15 females; age = 22 ± 4 y/o, height = 175 ± 18 cm, weight = 162.5 ± 57.5 kg) symptomatic subjects with LTPs volunteered for the study.

METHODS

PPT was measured at baseline and pre- and post-treatment for all 12 sessions with a pressure algometer across the 4-week treatment time frame. The MCT was applied to the control group on their LTP at pressure intended to provide a sham condition (1/10 on verbalized analog scale (VAS)). Two experimental groups had MCT applied either directly on the LTP (d-TP) or in close-proximity to their LTP (cp-TP) at moderate pressure (7/10 on VAS).

RESULTS

There was a significant increase in PPT from the first through twelfth treatment sessions (p < 0.001, partial η² = 0.914). A significant increase in PPTs between treatment groups was acutely observed from pre- to post-therapy tests (p = 0.001, partial η² = 0.146). The differences between pre- versus post-treatment PPT measures indicated significant differences (d-TP vs. control, p < 0.001; cp-TP vs. control, p = 0.007). No differences were observed between experimental groups (p = 0.215).

CONCLUSIONS

PPT continued to increase after several weeks of MCT when applied directly on or within 2.5 cm of an identified LTP compared to control.

Which Confounders Have the Largest Impact in Shear Wave Elastography of Muscle and How Can They be Minimized? An Elasticity Phantom, Ex Vivo Porcine Muscle and Volunteer Study Using a Commercially Available System

The goal of the study was to investigate the quantitative impact of region of interest (ROI), software choice, muscle fiber orientation and preload tension on shear wave velocity (SWV). First, SWV was assessed in an isotropic elasticity phantom and ex vivo porcine muscle using a commercially available clinical ultrasound system. Secondly, SWV was acquired in relaxed and stretched calf muscles of healthy volunteers (dorsal extension of the talocrural joint), for both parallel and transverse probe direction to the fibers, as well as for different ROIs and software versions. The effect of intermediate probe-fiber alignments was also analyzed. Finally, the impact of confounding factors on SWV reproducibility was minimized with a second force-controlled volunteer study, in which the calf was isometrically loaded, and fiber orientation and ROI were well-defined. 2046 in vivoSWE images were acquired to analyze SWV reproducibility with different confounder settings. In healthy volunteers, the main variance-contributing factors were in order of importance muscle tension, fiber orientation, horizontal ROI size and insertion depth. Regression analysis showed significantly reduced SWV with increasing insertion depth for each study material. Parallel probe-fiber orientation, muscle stretch and increasing horizontal ROI size led to significantly higher SWV. Based on the results of the study, we provide recommendations to minimize the impact of confounders in musculoskeletal elastography and discuss the main confounding mechanisms and trade-offs between confounding variables. Coefficients of variation can be significantly reduced with a controlled protocol, if the confounders are clinically taken into account.

Changes in shear wave propagation within skeletal muscle during active and passive force generation

Muscle force can be generated actively through changes in neural excitation, and passively through externally imposed changes in muscle length. Disease and injury can disrupt force generation, but it can be challenging to separate passive from active contributions to these changes. Ultrasound elastography is a promising tool for characterizing the mechanical properties of muscles and the forces that they generate. Most prior work using ultrasound elastography in muscle has focused on the group velocity of shear waves, which increases with increasing muscle force. Few studies have quantified the phase velocity, which depends on the viscoelastic properties of muscle. Since passive and active forces within muscle involve different structures for force transmission, we hypothesized that measures of phase velocity could detect changes in shear wave propagation during active and passive conditions that cannot be detected when considering only group velocity. We measured phase and group velocity in the human biceps brachii during active and passive force generation and quantified the differences in estimates of shear elasticity obtained from each of these measurements. We found that measures of group velocity consistently overestimate the shear elasticity of muscle. We used a Voigt model to characterize the phase velocity and found that the estimated time constant for the Voigt model provided a way to distinguish between passive and active force generation. Our results demonstrate that shear wave elastography can be used to distinguish between passive and active force generation when it is used to characterize the phase velocity of shear waves propagating in muscle.

Investigating the passive mechanical behaviour of skeletal muscle fibres: Micromechanical experiments and Bayesian hierarchical modelling

Characterisation of the skeletal muscle's passive properties is a challenging task since its structure is dominated by a highly complex and hierarchical arrangement of fibrous components at different scales. The present work focuses on the micromechanical characterisation of skeletal muscle fibres, which consist of myofibrils, by realising three different deformation states, namely, axial tension, axial compression, and transversal compression. To the best of the authors' knowledge, the present study provides a novel comprehensive data set representing of different deformation states. These data allow for a better understanding of muscle fibre load transfer mechanisms and can be used for meaningful modelling approaches. As the present study shows, axial tension and compression experiments reveal a strong tension-compression asymmetry at fibre level. In comparison to the tissue level, this asymmetric behaviour is more pronounced at the fibre scale, elucidating the load transfer mechanism in muscle tissue and aiding in the development of future modelling strategies. Further, a Bayesian hierarchical modelling approach was used to consider the experimental fluctuations in a parameter identification scheme, leading to more comprehensive parameter distributions that reflect the entire observed experimental uncertainty. STATEMENT OF SIGNIFICANCE: This article examines for the first time the mechanical properties of skeletal muscle fibres under axial tension, axial compression, and transversal compression, leading to a highly comprehensive data set. Moreover, a Bayesian hierarchical modelling concept is presented to identify model parameters in a broad way. The results of the deformation states allow a new and comprehensive understanding of muscle fibres' load transfer mechanisms; one example is the effect of tension-compression asymmetry. On the one hand, the results of this study contribute to the understanding of muscle mechanics and thus to the muscle's functional understanding during daily activity. On the other hand, they are relevant in the fields of skeletal muscle multiscale, constitutive modelling.

Muscle thixotropy-where are we now?

Relaxed skeletal muscle has an inbuilt resistance to movement. In particular, the resistance manifests itself as a substantial stiffness for small movements. The stiffness is impermanent, because it forms only when the muscle is stationary for some time and is reduced upon active or passive movement. Because the resistance to movement increases with time at rest and is reduced by movement, this behavior has become known as muscle thixotropy. In this short review, we describe the phenomenon of thixotropy and illustrate its significance in postural control with particular emphasis on human standing. We show how thixotropy came to be unambiguously associated with muscle mechanics and we review present knowledge of the molecular basis of thixotropic behavior. Specifically, we examine how recent knowledge about titin, and about the control of cross-bridge cycling, has impacted on the role of non-cross-bridge mechanisms and cross-bridge mechanisms in explaining thixotropy. We describe how thixotropic changes in muscle stiffness that occur during transitions from posture to movement can be tracked by analyzing physiological tremor. Finally, because skeletal muscle contains sensory receptors, and because some of these receptors are themselves thixotropic, we outline some of the consequences of muscle thixotropy for proprioception.

In Situ Polyphosphate Nanoparticle Formation in Hybrid Poly(vinyl alcohol)/Karaya Gum Hydrogels: A Porous Scaffold Inducing Infiltration of Mesenchymal Stem Cells

The preparation and characterization of a porous hybrid cryogel based on the two organic polymers, poly(vinyl alcohol) (PVA) and karaya gum (KG), into which polyphosphate (polyP) nanoparticles have been incorporated, are described. The PVA/KG cryogel is prepared by intermolecular cross-linking of PVA via freeze-thawing and Ca2+-mediated ionic gelation of KG to form stable salt bridges. The incorporation of polyP as amorphous nanoparticles with Ca2+ ions (Ca-polyP-NP) is achieved using an in situ approach. The polyP constituent does not significantly affect the viscoelastic properties of the PVA/KG cryogel that are comparable to natural soft tissue. The exposure of the Ca-polyP-NP within the cryogel to medium/serum allows the formation of a biologically active polyP coacervate/protein matrix that stimulates the growth of human mesenchymal stem cells in vitro and provides the cells a suitable matrix for infiltration superior to the polyP-free cryogel. In vivo biocompatibility studies in rats reveal that already two to four weeks after implantation into muscle, the implant regions containing the polyP-KG/PVA material become replaced by initial granulation tissue, whereas the controls are free of any cells. It is proposed that the polyP-KG/PVA cryogel has the potential to become a promising implant material for soft tissue engineering/repair.

Swing Velocity Profiles of Small Limbs Can Arise from Transient Passive Torques of the Antagonist Muscle Alone

In large limbs, changing motor neuron activity typically controls within-movement velocity. For example, sequential agonist-antagonist-agonist motor neuron firing typically underlies the slowing often present at the end of human reaches. In physiological movements of large limbs, antagonistic muscle passive torque is generally negligible. In small limbs, alternatively, passive torques can determine limb rest position, generate restoring movements to it, and decrease agonist-generated movement amplitude and velocity maxima. These observations suggest that, in small limbs, passive forces might also control velocity changes within movements. We investigated this issue in stick insect middle leg femur-tibia (FT) joint. During swing, the FT joint extensor muscle actively shortens and the flexor muscle passively lengthens. As in human reaching, after its initial acceleration, FT joint velocity continuously decreases. We measured flexor passive forces during imposed stretches spanning the ranges of FT joint angles, angular velocities, and movement amplitudes present in leg swings. The viscoelastic "transient" passive force that occurs during and soon after stretch depended on all three variables and could be tens of times larger than the "steady-state" passive force commonly measured long after stretch end. We combined these data, the flexor and extensor moment arms, and an existing extensor model to simulate FT joint swing. To measure only passive (flexor) muscle-dependent effects, we used constant extensor activations in these simulations. In simulations using data from ten flexor muscles, flexor passive torque could always produce swings with, after swing initiation, continuously decreasing velocities. Antagonist muscle passive torques alone can thus control within-movement velocity.

Relationship between extensibility and collagen expression in immobilized rat skeletal muscle

INTRODUCTION

This study investigated longitudinal changes in muscle extension and collagen expression in an immobilized rat soleus muscle, and assessed the relationship between both elements.

METHODS

Soleus muscles of the control and immobilization groups (1, 2, 4, 8, and 12 weeks) were used for analysis of muscle extensibility and collagen expression.

RESULTS

The slope value/physiological cross-sectional area (PCSA; a parameter for muscle extensibility) and hydroxyproline (a parameter for collagen expression) were significantly higher in the immobilization group than in the control group for all experimental time points. In the immobilization group, both factors were significantly higher at 4, 8, and 12 weeks than at 1 and 2 weeks after immobilization. A significant positive correlation was observed between the slope value/PCSA and hydroxyproline expression.

DISCUSSION

The present study indicated that a decrease in muscle extensibility depended on collagen overexpression in immobilized rat soleus muscles. Muscle Nerve 57: 672-678, 2018.

The effects of 4 weeks stretching training to the point of pain on flexibility and muscle tendon unit properties

PURPOSE

The purpose of this study was to compare the benefits and possible problems of 4 weeks stretching when taken to the point of pain (POP) and to the point of discomfort (POD).

METHODS

Twenty-six physically active women (20 ± 1.1 years) took part in group-based stretching classes of the hamstring muscles, 4 times per week for 4 weeks, one group one stretching to POD, the other to POP. Passive stiffness, joint range of motion (ROM), maximal isometric torque and concentric knee flexion torque, were measured before training and 2 days after the last training session.

RESULTS

Hip flexion ROM increased by 14.1° (10.1°-18.1°) and 19.8° (15.1°-24.5°) and sit-and-reach by 7.6 (5.2-10.0) cm and 7.5 (5.0-10.0) cm for POD and POP, respectively (Mean and 95% CI; p < 0.001 within group; NS between groups), with no evidence of damage in either group. Despite the large increases in flexibility there were no changes in either compliance or viscoelastic properties of the muscle tendon unit (MTU).

CONCLUSION

Hamstrings stretching to POP increased flexibility and had no detrimental effects on muscle function but the benefits were no better than when stretching to POD so there is no justification for recommending painful stretching. The improvements in flexibility over 4 weeks of stretching training appear to be largely due to changes in the perception of pain rather than physical properties of the MTU although less flexible individuals benefited more from the training and increased hamstring muscle length.

A validated model of passive skeletal muscle to predict force and intramuscular pressure

The passive properties of skeletal muscle are often overlooked in muscle studies, yet they play a key role in tissue function in vivo. Studies analyzing and modeling muscle passive properties, while not uncommon, have never investigated the role of fluid content within the tissue. Additionally, intramuscular pressure (IMP) has been shown to correlate with muscle force in vivo and could be used to predict muscle force in the clinic. In this study, a novel model of skeletal muscle was developed and validated to predict both muscle stress and IMP under passive conditions for the New Zealand White Rabbit tibialis anterior. This model is the first to include fluid content within the tissue and uses whole muscle geometry. A nonlinear optimization scheme was highly effective at fitting model stress output to experimental stress data (normalized mean square error or NMSE fit value of 0.993) and validation showed very good agreement to experimental data (NMSE fit values of 0.955 and 0.860 for IMP and stress, respectively). While future work to include muscle activation would broaden the physiological application of this model, the passive implementation could be used to guide surgeries where passive muscle is stretched.

Impact of TIEG1 Deletion on the Passive Mechanical Properties of Fast and Slow Twitch Skeletal Muscles in Female Mice

As transforming growth factor (TGF)-β inducible early gene-1 is highly expressed in skeletal muscle, the effect of TIEG1 gene deletion on the passive mechanical properties of slow and fast twitch muscle fibers was analyzed. Twenty five muscle fibers were harvested from soleus (Sol) and extensor digitorum longus (EDL) muscles from TIEG1^-/^- (N = 5) and control (N = 5) mice. Mechanical tests were performed on fibers and the dynamic and static stresses were measured. A viscoelastic Hill model of 3rd order was used to fit the experimental relaxation test data. In parallel, immunohistochemical analyses were performed on three serial transverse sections to detect the myosin isoforms within the slow and fast muscles. The percentage and the mean cross sectional area of each fiber type were calculated. These tests revealed a significant increase in the mechanical stress properties for the TIEG1^-/^- Sol fibers while a significant decrease appeared for the TIEG1^-/^- EDL fibers. Hill model tracked the shape of the experimental relaxation curve for both genotypes and both fiber types. Immunohistochemical results showed hypertrophy of all fiber types for TIEG1^-/^- muscles with an increase in the percentage of glycolytic fibers (IIX, and IIB) and a decrease of oxidative fibers (I, and IIA). This study has provided new insights into the role of TIEG1, known as KLF10, in the functional (Sol_typeI: more resistant, EDL_typeIIB: less resistant) and morphological (glycolytic hypertrophy) properties of fast and slow twitch skeletal muscles. Further investigation at the cellular level will better reveal the role of the TIEG1 gene in skeletal muscle tissue.

Dynamics of cross-bridge cycling, ATP hydrolysis, force generation, and deformation in cardiac muscle

Despite extensive study over the past six decades the coupling of chemical reaction and mechanical processes in muscle dynamics is not well understood. We lack a theoretical description of how chemical processes (metabolite binding, ATP hydrolysis) influence and are influenced by mechanical processes (deformation and force generation). To address this need, a mathematical model of the muscle cross-bridge (XB) cycle based on Huxley's sliding filament theory is developed that explicitly accounts for the chemical transformation events and the influence of strain on state transitions. The model is identified based on elastic and viscous moduli data from mouse and rat myocardial strips over a range of perturbation frequencies, and MgATP and inorganic phosphate (Pi) concentrations. Simulations of the identified model reproduce the observed effects of MgATP and MgADP on the rate of force development. Furthermore, simulations reveal that the rate of force re-development measured in slack-restretch experiments is not directly proportional to the rate of XB cycling. For these experiments, the model predicts that the observed increase in the rate of force generation with increased Pi concentration is due to inhibition of cycle turnover by Pi. Finally, the model captures the observed phenomena of force yielding suggesting that it is a result of rapid detachment of stretched attached myosin heads.

Cross-Sectional Nakagami Images in Passive Stretches Reveal Damage of Injured Muscles

Muscle strain is still awanting a noninvasive quantitatively diagnosis tool. High frequency ultrasound (HFU) improves image resolution for monitoring changes of tissue structures, but the biomechanical factors may influence ultrasonography during injury detection. We aim to illustrate the ultrasonic parameters to present the histological damage of overstretched muscle with the consideration of biomechanical factors. Gastrocnemius muscles from mice were assembled and ex vivo passive stretching was performed before or after injury. After injury, the muscle significantly decreased mechanical strength. Ultrasonic images were obtained by HFU at different deformations to scan in cross and longitudinal orientations of muscle. The ultrasonography was quantified by echogenicity and Nakagami parameters (NP) for structural evaluation and correlated with histological results. The injured muscle at its original length exhibited decreased echogenicity and NP from HFU images. Cross-sectional ultrasonography revealed a loss of correlation between NP and passive muscle stretching that suggested a special scatterer pattern in the cross section of injured muscle. The independence of NP during passive stretching of injured muscle was confirmed by histological findings in ruptured collagen fibers, decreased muscle density, and increased intermuscular fiber space. Thus, HFU analysis of NP in cross section represents muscle injury that may benefit the clinical diagnosis.

Skeletal muscle tensile strain dependence: Hyperviscoelastic nonlinearity

INTRODUCTION

Computational modeling of skeletal muscle requires characterization at the tissue level. While most skeletal muscle studies focus on hyperelasticity, the goal of this study was to examine and model the nonlinear behavior of both time-independent and time-dependent properties of skeletal muscle as a function of strain.

MATERIALS AND METHODS

Nine tibialis anterior muscles from New Zealand White rabbits were subject to five consecutive stress relaxation cycles of roughly 3% strain. Individual relaxation steps were fit with a three-term linear Prony series. Prony series coefficients and relaxation ratio were assessed for strain dependence using a general linear statistical model. A fully nonlinear constitutive model was employed to capture the strain dependence of both the viscoelastic and instantaneous components.

RESULTS

Instantaneous modulus (p<0.0005) and mid-range relaxation (p<0.0005) increased significantly with strain level, while relaxation at longer time periods decreased with strain (p<0.0005). Time constants and overall relaxation ratio did not change with strain level (p>0.1). Additionally, the fully nonlinear hyperviscoelastic constitutive model provided an excellent fit to experimental data, while other models which included linear components failed to capture muscle function as accurately.

CONCLUSIONS

Material properties of skeletal muscle are strain-dependent at the tissue level. This strain dependence can be included in computational models of skeletal muscle performance with a fully nonlinear hyperviscoelastic model.

Spasticity and its contribution to hypertonia in cerebral palsy

Spasticity is considered an important neural contributor to muscle hypertonia in children with cerebral palsy (CP). It is most often treated with antispasticity medication, such as Botulinum Toxin-A. However, treatment response is highly variable. Part of this variability may be due to the inability of clinical tests to differentiate between the neural (e.g., spasticity) and nonneural (e.g., soft tissue properties) contributions to hypertonia, leading to the terms “spasticity” and “hypertonia” often being used interchangeably. Recent advancements in instrumented spasticity assessments offer objective measurement methods for distinction and quantification of hypertonia components. These methods can be applied in clinical settings and their results used to fine-tune and improve treatment. We reviewed current advancements and new insights with respect to quantifying spasticity and its contribution to muscle hypertonia in children with CP. First, we revisit what is known about spasticity in children with CP, including the various definitions and its pathophysiology. Second, we summarize the state of the art on instrumented spasticity assessment in CP and review the parameters developed to quantify the neural and nonneural components of hypertonia. Lastly, the impact these quantitative parameters have on clinical decision-making is considered and recommendations for future clinical and research investigations are discussed.

Collagen crosslinking does not dictate stiffness in a transgenic mouse model of skeletal muscle fibrosis

Skeletal muscle fibrosis is characterized by increases in tissue stiffness and collagen content. However, a very weak correlation exists between collagen content and stiffness in skeletal muscle. Recently, it has been hypothesized that collagen crosslinking explains tissue stiffness in fibrotic skeletal muscle. Therefore, we addressed this hypothesis by correlating tissue stiffness with lysyl-pyridinoline, hydroxylysyl-pyridinoline, and pentosidine collagen crosslinks. Stepwise regression revealed that, separate or together, collagen crosslinks did not correlate with tissue stiffness. Our result demonstrates that increased tissue stiffness in skeletal muscle fibrosis is not simply explained by increased collagen crosslinks and/or collagen crosslink density. We suggest that collagen organization may affect tissue stiffness.

A highly efficient semiphenomenological model of a half-sarcomere for real-time prediction of mechanical behavior

With existent biomechanical models of skeletal muscle, challenges still exist in implementing real-time predictions for contraction statuses that are particularly significant to biomechanical and biomedical engineering. Because of this difficulty, this paper proposed a decoupled scheme of the links involved in the working process of a sarcomere and established a semiphenomenological model integrating both linear and nonlinear frames of no higher than a second-order system. In order to facilitate engineering application and cybernetics, the proposed model contains a reduced number of parameters and no partial differential equation, making it highly concise and computationally efficient. Through the simulations of various contraction modes, including isometric, isotonic, successive stretch and release, and cyclic contractions, the correctness and efficiency of the model, are validated. Although this study targets half-sarcomeres, the proposed model can be easily extended to describe the larger-scale mechanical behavior of a muscle fiber or a whole muscle.

Effects of immediate vs. delayed massage-like loading on skeletal muscle viscoelastic properties following eccentric exercise

BACKGROUND

This study compared immediate versus delayed massage-like compressive loading on skeletal muscle viscoelastic properties following eccentric exercise.

METHODS

Eighteen rabbits were surgically instrumented with peroneal nerve cuffs for stimulation of the tibialis anterior muscle. Rabbits were randomly assigned to a massage loading protocol applied immediately post exercise (n=6), commencing 48h post exercise (n=6), or exercised no-massage control (n=6). Viscoelastic properties were evaluated in vivo by performing a stress-relaxation test pre- and post-exercise and daily pre- and post-massage for four consecutive days of massage loading. A quasi-linear viscoelastic approach modeled the instantaneous elastic response (AG0), fast (g1(p)) and slow (g2(p)) relaxation coefficients, and the corresponding relaxation time constants τ1 and τ2.

FINDINGS

Exercise increased AG0 in all groups (P<0.05). After adjusting for the three multiple comparisons, recovery of AG0 was not significant in the immediate (P=0.021) or delayed (P=0.048) group compared to the control group following four days of massage. However, within-day (pre- to post-massage) analysis revealed a decrease in AG0 in both massage groups. Following exercise, g1(p) increased and g2(p) and τ1 decreased for all groups (P<0.05). Exercise had no effect on τ2 (P>0.05). After four days of massage, there was no significant recovery of the relaxation parameters for either massage loading group compared to the control group.

INTERPRETATION

Our findings suggest that massage loading following eccentric exercise has a greater effect on reducing muscle stiffness, estimated by AG0, within-day rather than affecting recovery over multiple days. Massage loading also has little effect on the relaxation response.

Muscle as a molecular machine for protecting joints and bones by absorbing mechanical impacts

We hypothesize that dissipation of mechanical energy of external impact to absorb mechanical shock is a fundamental function of skeletal muscle in addition to its primary function to convert chemical energy into mechanical energy. In physical systems, the common mechanism for absorbing mechanical shock is achieved with the use of both elastic and viscous elements and we hypothesize that the viscosity of the skeletal muscle is a variable parameter which can be voluntarily controlled by changing the tension of the contracting muscle. We further hypothesize that an ability of muscle to absorb shock has been an important factor in biological evolution, allowing the life to move from the ocean to land, from hydrodynamic to aerodynamic environment with dramatically different loading conditions for musculoskeletal system. The ability of muscle to redistribute the energy of mechanical shock in time and space and unload skeletal joints is of key importance in physical activities. We developed a mathematical model explaining the absorption of mechanical shock energy due to the increased viscosity of contracting skeletal muscles. The developed model, based on the classical theory of sliding filaments, demonstrates that the increased muscle viscosity is a result of the time delay (or phase shift) between the mechanical impact and the attachment/detachment of myosin heads to binding sites on the actin filaments. The increase in the contracted muscle's viscosity is time dependent. Since the forward and backward rate constants for binding the myosin heads to the actin filaments are on the order of 100s(-1), the viscosity of the contracted muscle starts to significantly increase with an impact time greater than 0.01s. The impact time is one of the key parameters in generating destructive stress in the colliding objects. In order to successfully dampen a short high power impact, muscles must first slow it down to engage the molecular mechanism of muscle viscosity. Muscle carries out two functions, acting first as a nonlinear spring to slow down impact and second as a viscous damper to absorb the impact. Exploring the ability of muscle to absorb mechanical shock may shed light to many problems of medical biomechanics and sports medicine. Currently there are no clinical devices for real-time quantitative assessment of viscoelastic properties of contracting muscles in vivo. Such assessment may be important for diagnosis and monitoring of treatment of various muscle disorders such as muscle dystrophy, motor neuron diseases, inflammatory and metabolic myopathies and many more.

The passive properties of muscle fibers are velocity dependent

The passive properties of skeletal muscle play an important role in muscle function. While the passive quasi-static elastic properties of muscle fibers have been well characterized, the dynamic visco-elastic passive behavior of fibers has garnered less attention. In particular, it is unclear how the visco-elastic properties are influenced by lengthening velocity, in particular for the range of physiologically relevant velocities. The goals of this work were to: (i) measure the effects of lengthening velocity on the peak stresses within single muscle fibers to determine how passive behavior changes over a range of physiologically relevant lengthening rates (0.1-10Lo/s), and (ii) develop a mathematical model of fiber viscoelasticity based on these measurements. We found that passive properties depend on strain rate, in particular at the low loading rates (0.1-3Lo/s), and that the measured behavior can be predicted across a range of loading rates and time histories with a quasi-linear viscoelastic model. In the future, these results can be used to determine the impact of viscoelastic behavior on intramuscular stresses and forces during a variety of dynamic movements.

Use of a Poroelastic Model to Predict Intramuscular Pressure

Measurement of individual muscle tension in a clinical setting has yet to be achieved. Previous investigators have suggested that the tension in skeletal muscle, comprised of approximately 70% fluid, could be determined using interstitial muscle fluid pressure (IMP). A computational model is needed to aid in understanding IMP distribution in muscles of varying geometry and contractile states without exhaustive testing. The first aim of this study was to determine a set of transversely isotropic material properties (i.e., permeability, relaxed modulus, and drained Poisson's ratio) for excised skeletal muscle using inverse finite element analysis with a poroelastic constitutive formulation on tension data from either longitudinal or transverse uniaxial load-relaxation tests of skeletal muscle tissue. The second aim was to compare pore pressure estimated from a model to experimental pressure measurements to assess its ability to accurately predict IMP. Results of this study indicated that skeletal muscle was transversely isotropic under load-relaxation as demonstrated by significant differences in the drained Poisson's ratio. It was also noted that the drained Poisson's ratios under both longitudinal and transverse loading were negative in these tests of excised muscle tissue. Pore pressure calculated with this model provided a good prediction of the development of IMP. These results point to the benefit of using a poroelastic model of skeletal muscle to predict IMP.

Cognitive regulation of saccadic velocity by reward prospect

It is known that expectation of reward speeds up saccades. Past studies have also shown the presence of a saccadic velocity bias in the orbit, resulting from a biomechanical regulation over varying eccentricities. Nevertheless, whether and how reward expectation interacts with the biomechanical regulation of saccadic velocities over varying eccentricities remains unknown. We addressed this question by conducting a visually guided double-step saccade task. The role of reward expectation was tested in monkeys performing two consecutive horizontal saccades, one associated with reward prospect and the other not. To adequately assess saccadic velocity and avoid adaptation, we systematically varied initial eye positions, saccadic directions and amplitudes. Our results confirmed the existence of a velocity bias in the orbit, i.e., saccadic peak velocity decreased linearly as the initial eye position deviated in the direction of the saccade. The slope of this bias increased as saccadic amplitudes increased. Nevertheless, reward prospect facilitated velocity to a greater extent for saccades away from than for saccades toward the orbital centre, rendering an overall reduction in the velocity bias. The rate (slope) and magnitude (intercept) of reward modulation over this velocity bias were linearly correlated with amplitudes, similar to the amplitude-modulated velocity bias without reward prospect, which presumably resulted from a biomechanical regulation. Small-amplitude (≤ 5°) saccades received little modulation. These findings together suggest that reward expectation modulated saccadic velocity not as an additive signal but as a facilitating mechanism that interacted with the biomechanical regulation.

Mechanical Response of the Herniated Human Abdomen to the Placement of Different Prostheses

This paper describes a method designed to model the repaired herniated human abdomen just after surgery and examine its static mechanical response to the maximum intra-abdominal pressure provoked by a physiological movement (standing cough). The model is based on the real geometry of the human abdomen bearing a large incisional hernia with several anatomical structures differentiated by MRI. To analyze the outcome of hernia repair, the surgical procedure was simulated by modeling a prosthesis placed over the hernia. Three surgical meshes with different mechanical properties were considered: an isotropic heavy-weight mesh (Surgipro®), a slightly anisotropic light-weight mesh (Optilene®), and a highly anisotropic medium-weight mesh (Infinit®). Our findings confirm that anisotropic implants need to be positioned such that the most compliant axis of the mesh coincides with the craneo-caudal direction of the body.