Needle-induced cavitation: A method to probe the local mechanics of brain tissue

Traditional mechanical characterization of extremely soft tissues is challenging given difficulty extracting tissue, satisfying geometric requirements, keeping tissues hydrated, and securing the tissue in an apparatus without slippage. The heterogeneous nature and structural complexity of brain tissues on small length scales makes it especially difficult to characterize. Needle-induced cavitation (NIC) is a technique that overcomes these issues and can mechanically characterize brain tissues at precise, micrometer-scale locations. This small-scale capability is crucial in order to spatially characterize diseased tissue states like fibrosis or cancer. NIC consists of inserting a needle into a tissue and pressurizing a fluid until a deformation occurs at the tip of the needle at a critical pressure. NIC is a convenient, affordable technique to measure mechanical properties, such as modulus and fracture energy, and to assess the performance of soft materials. Experimental parameters such as needle size and fluid flowrate are tunable, so that the end-user can control the length and time scales, making it uniquely capable of measuring local mechanical properties across a wide range of strain rates. The portable nature of NIC and capability to conduct in vivo experiments makes it a particularly appealing characterization technique compared to traditional methods. Despite significant developments in the technique over the last decade, wide implementation in the biological field is still limited. Here, we address the limitations of the NIC technique specifically when working with soft tissues and provide readers with expected results for brain tissue. Our goal is to assist others in conducting reliable and reproducible mechanical characterization of soft biomaterials and tissues.

Low-velocity nail penetration response of muscle tissue and gelatin

Quantitative estimation of soft tissue injuries due to penetration of sharp objects is a challenging task for forensic pathologists. The severity of injury depends on the force required to penetrate the tissue. This study focuses on investigating the amount of force required to penetrate porcine muscle tissue and gelatin simulants (10 % wt) to mimic human muscle tissue when subjected to sharp objects like nail at velocities below 5 m/s. A custom-made experimental setup was used to examine the influence of penetration velocity and nail diameter on penetration forces. Images captured by a high-speed camera were used to track the position and velocity of the nail. A finite element (FE) model was established to simulate the penetration behavior of the tissue and gelatin. The FE simulations of the nail penetration were validated through direct comparison with the experimental results. In tissues as well as in the simulant, penetration forces were seen to increase with increasing nail diameter and velocity. Porcine muscle tissue showed 23.9-46.5 % higher penetration forces than gelatin simulants (10 % wt) depending on nail diameter and velocity; the difference being higher for higher nail diameter and velocity. The ranges of maximum penetration forces measured were 8.6-59.1 N for porcine muscle tissue and 6.8-34.9 N for gelatin simulant. This study helps to quantify injuries caused by sharp nails at low velocities and offers insights with potential applications in injury management strategies and forensic studies.

Linking myosin heavy chain isoform shift to mechanical properties and fracture modes in skeletal muscle tissue

Muscle fibers play a crucial role in the mechanical action of skeletal muscle tissue. However, it is unclear how the histological variations affect the mechanical properties of tissues. In this study, the shift of myosin heavy chain (MHC) isoforms is used for the first time to establish a linkage between tissue histological variation and passive mechanical properties. The shift of MHC isoform is found not only to induce significant differences in skeletal muscle passive mechanical properties, but also to lead to differences in strain rate responses. Non-negligible rate dependence is observed even in the conventionally defined quasi-static regime. Fidelity in the estimated constitutive parameters, which can be impacted due to variation in MHC isoforms and hence in rate sensitivity, is enhanced using a Bayesian inference framework. Subsequently, scanning electron microscopy and fluorescence microscopy are used to characterize the fracture morphology of muscle tissues and fibers. The fracture mode of both MHC I and II muscle fibers exhibited shearing of endomysium. Results show that the increase in strain rate only leads to stronger rebounding of the muscle fibers during tissue rupture without changing fracture modes.

On a three-dimensional model for the description of the passive characteristics of skeletal muscle tissue

In this work, a three-dimensional model was developed to describe the passive mechanical behaviour of anisotropic skeletal muscle tissue. To validate the model, orientation-dependent axial ([Formula: see text], [Formula: see text], [Formula: see text]) and semi-confined compression experiments (mode I, II, III) were performed on soleus muscle tissue from rabbits. In the latter experiments, specimen deformation is prescribed in the loading direction and prevented in an additional spatial direction, fibre compression at [Formula: see text] (mode I), fibre elongation at [Formula: see text] (mode II) and a neutral state of the fibres at [Formula: see text] where their length is kept constant (mode III). Overall, the model can adequately describe the mechanical behaviour with a relatively small number of model parameters. The stiffest tissue response during orientation-dependent axial compression ([Formula: see text] kPa) occurs when the fibres are oriented perpendicular to the loading direction ([Formula: see text]) and are thus stretched during loading. Semi-confined compression experiments yielded the stiffest tissue ([Formula: see text] kPa) in mode II when the muscle fibres are stretched. The extensive data set collected in this study allows to study the different error measures depending on the deformation state or the combination of deformation states.

In vivoestimation of anisotropic mechanical properties of the gastrocnemius during functional loading with MR elastography

Objective.In vivoimaging assessments of skeletal muscle structure and function allow for longitudinal quantification of tissue health. Magnetic resonance elastography (MRE) non-invasively quantifies tissue mechanical properties, allowing for evaluation of skeletal muscle biomechanics in response to loading, creating a better understanding of muscle functional health.Approach. In this study, we analyze the anisotropic mechanical response of calf muscles using MRE with a transversely isotropic, nonlinear inversion algorithm (TI-NLI) to investigate the role of muscle fiber stiffening under load. We estimate anisotropic material parameters including fiber shear stiffness (μ1), substrate shear stiffness (μ2), shear anisotropy (ϕ), and tensile anisotropy (ζ) of the gastrocnemius muscle in response to both passive and active tension.Main results. In passive tension, we found a significant increase inμ1,ϕ,andζwith increasing muscle length. While in active tension, we observed increasingμ2and decreasingϕandζduring active dorsiflexion and plantarflexion-indicating less anisotropy-with greater effects when the muscles act as agonist.Significance. The study demonstrates the ability of this anisotropic MRE method to capture the multifaceted mechanical response of skeletal muscle to tissue loading from muscle lengthening and contraction.

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.

Skeletal muscle surrogates for the acquisition of muscle repair skills in upper limb surgery

INTRODUCTION

The required fidelity of synthetic materials in surgical simulators to teach tissue handling and repair requirements should be as accurate as possible. There is a poor understanding of the relationship between choice of muscle surrogates and training outcome for trainee surgeons. To address this, the mechanical characteristics of several candidate synthetic muscle surrogates were measured, and their subjective biofidelity was qualitatively assessed by surgeons.

METHODS

Silicone was selected after assessing several material options and 16 silicone-based surrogates were evaluated. Three of the closest samples to muscle (Samples 1.1, 1.2, 1.3) and one with inserted longitudinal fibres (1.2F) were mechanically tested in the following: compression and tension, needle puncture force and suture pull-out in comparison with real muscle. The four samples were evaluated by 17 Plastic and Orthopaedic surgeons to determine their views of the fidelity with regard to the handling properties, needle insertion and ease of suture pull-out.

RESULTS

The mechanical testing showed the surrogates exhibited varying characteristics that matched some of the properties of muscle, though none recreated all the mechanical characteristics of native muscle. Good biofidelity was generally achieved for compression stiffness and needle puncture force, but it was evident that tensile stiff was too low for all samples. The pull-out forces were variable and too low, except for the sample with longitudinal fibres. In the qualitative assessment, the overall median scores for the four surrogate samples were all between 30 and 32 (possible range 9-45), indicating limited differentiation of the samples tested by the surgeons.

CONCLUSIONS

The surrogate materials showed a range of mechanical properties bracketing those of real muscle, thus presenting a suitable combination of candidates for use in simulators to attain the requirements as set out in the learning outcomes of muscle repair. However, despite significant mechanical differences between the samples, all surgeons found the samples to be similar to each other.

Age-dependent mechanical and microstructural properties of the rabbit soleus muscle

During growth there are serious changes in the skeletal muscles to compensate for the changed requirements in terms of body weight and size. In this study, the age-dependent (between 21 and 100 days) mechanical and microstructural properties of rabbit soleus muscle tissue were investigated. For this purpose, morphological properties (animal mass, soleus muscle mass, tibial length) were measured at 5 different times during aging. On the other hand, fibre orientation-dependent axial and semi-confined compression experiments were realised. In addition, the essential components (muscle fibres, extracellular matrix, remaining components), dominating the microstructure of muscle tissue, were analysed. While the mechanical results show hardly any age-dependent differences, the morphological and microstructural results show clear age-dependent differences. All morphological parameters increase significantly (animal mass by 839.2%, muscle mass 1050.6%, tibial length 233.6%). In contrast, microstructural parameters change differently. The percentage of fibres (divided into slow-twitch (ST) and fast-twitch (FT) fibres) increases significantly (137.6%), while the proportions of the extracellular matrix and the remaining components (48.2% and 46.1%) decrease. At the same time, the cross-sectional area of the fibres increases significantly (697.9%). The totality of this age-dependent information provides a deeper understanding of age-related changes in muscle structure and function and may contribute to successful development and validation of growth models in the future. STATEMENT OF SIGNIFICANCE: This article reports the first comprehensive data set on age-dependent morphological (animal mass, soleus muscle mass, tibial length), mechanical (axial and semi-confined compression), and microstructural (muscle fibres, extracellular matrix, remaining components) properties of the rabbit soleus muscle. On the one hand, the results of this study contribute to the understanding of muscle mechanics and thus to understanding of load transfer mechanisms inside the muscle tissue during growth. On the other hand, these results are relevant to the fields of constitutive formulation of age-dependent muscle tissue.

Influence of nonlinear soft tissue modeling on the external and internal forces during lateral hip impacts

Soft tissues in the hip region, which are typically considered the natural shock-absorbers during falls, attenuate the applied forces to the underlying hard tissue. The soft tissue thickness is, therefore, a significant parameter in the force attenuation. Another factor that could affect the assessment of the force attenuation in numerical simulations is the choice of constitutive model and material parameters for the soft tissue. Several constitutive models and parameters for muscle and adipose tissue were suggested in the published literature; however, the biofidelity of the proposed models for the lateral impacts has not been assessed yet. To achieve this purpose, we used a previously developed human body model named THUMS v4.02 and modified the mechanical properties and geometry of the soft tissues in the hip region. The simulations consisted of regional hip models and whole-body models. The biofidelity of the constitutive models of muscle and adipose tissue was determined objectively using the CORrelation and Analysis (CORA) rating. Moreover, the potential force attenuating effect of the adipose tissue thickness was investigated in the regional models. We collected and fitted several available nonlinear material models for muscle and adipose tissue and implemented them. The CORA ratings for several constitutive models for adipose tissue in the regional model were above 0.8. Among the muscle constitutive models, three Ogden models consistently rated above 0.58 for the whole-body model. Moreover, the impact forces in the selected adipose tissue model attenuated 47 N for every 1 mm increase in thickness. Overall, the choice of the nonlinear material model for the adipose and muscle tissue influences the external and internal force, and the difference between the material models is more pronounced when the thickness of the soft tissue increases.

Direct measurement of the direction-dependent mechanical behaviour of skeletal muscle extracellular matrix

This paper reports the first comprehensive data set on the anisotropic mechanical properties of isolated endo- and perimysial extracellular matrix of skeletal muscle, and presents the corresponding protocols for preparing and testing the samples. In particular, decellularisation of porcine skeletal muscle is achieved with caustic soda solution, and mechanical parameters are defined based on compressive and tensile testing in order to identify the optimal treatment time such that muscle fibres are dissolved whereas the extracellular matrix remains largely intact and mechanically functional. At around 18 h, a time window was found and confirmed by histology, in which axial tensile experiments were performed to characterise the direction-dependent mechanical response of the extracellular matrix samples, and the effect of lateral pre-compression was studied. The typical, large variability in the experimental stress response could be largely reduced by varying a single scalar factor, which was attributed to the variation of the fraction of extracellular matrix within the tissue. While experimental results on the mechanical properties of intact muscle tissue and single muscle fibres are increasingly available in literature, there is a lack of information on the properties of the collagenous components of skeletal muscle. The present work aims at closing this gap and thus contributes to an improved understanding of the mechanics of skeletal muscle tissue and provides a missing piece of information for the development of corresponding constitutive and computational models.

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.

Mechanics of human vocal folds layers during finite strains in tension, compression and shear

During phonation, human vocal fold tissues are subjected to combined tension, compression and shear loading modes from small to large finite strains. Their mechanical behaviour is however still not well understood. Herein, we complete the existing mechanical database of these soft tissues, by characterising, for the first time, the cyclic and finite strains behaviour of the lamina propria and vocalis layers under these loading modes. To minimise the inter or intra-individual variability, particular attention was paid to subject each tissue sample successively to the three loadings. A non-linear mechanical behaviour is observed for all loading modes: a J-shape strain stiffening in longitudinal tension and transverse compression, albeit far less pronounced in shear, stress accommodation and stress hysteresis whatever the loading mode. In addition, recorded stress levels during longitudinal tension are much higher for the lamina propria than for the vocalis. Conversely, the responses of the lamina propria and the vocalis in transverse compression as well as transverse and longitudinal shears are of the same orders of magnitude. We also highlight the strain rate sensitivity of the tissues, as well as their anisotropic properties.

An experimental and computational investigation of the effects of volumetric boundary conditions on the compressive mechanics of passive skeletal muscle

Computational modeling, such as finite element analysis, is employed in a range of biomechanics specialties, including impact biomechanics and surgical planning. These models rely on accurate material properties for skeletal muscle, which comprises roughly 40% of the human body. Due to surrounding tissues, compressed skeletal muscle in vivo likely experiences a semi-confined state. Nearly all previous studies investigating passively compressed muscle at the tissue level have focused on muscle in unconfined compression. The goals of this study were to (1) examine the stiffness and time-dependent material properties of skeletal muscle subjected to both confined and unconfined compression (2) develop a model that captures passive muscle mechanics under both conditions and (3) determine the extent to which different assumptions of volumetric behavior affect model results. Muscle in confined compression exhibited stiffer behavior, agreeing with previous assumptions of near-incompressibility. Stress relaxation was found to be faster under unconfined compression, suggesting there may be different mechanisms that support load these two conditions. Finite element calibration was achieved through nonlinear optimization (normalized root mean square error <6%) and model validation was strong (normalized root mean square error <17%). Comparisons to commonly employed assumptions of bulk behavior showed that a simple one parameter approach does not accurately simulate confined compression. We thus recommend the use of a properly calibrated, nonlinear bulk constitutive model for modeling of skeletal muscle in vivo. Future work to determine mechanisms of passive muscle stiffness would enhance the efforts presented here.

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.

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.

Influence of experimental conditions on visco-hyperelastic properties of skeletal muscle tissue using a Box-Behnken design

The Mechanical characterization of skeletal muscles is strongly dependent on numerous experimental design factors. Nevertheless, significant knowledge gaps remain on the characterization of muscle mechanics and a large number of experiments should be implemented to test the influence of a large number of factors. In this study, we propose a design of experiment method (DOE) to study the parameter sensitivity while minimizing the number of tests. A Box-Behnken design was then implemented to study the influence of strain rate, preconditioning and preloading conditions on visco-hyperelastic mechanical parameters of two rat forearm muscles. The results show that the strain rate affects the visco-hyperelastic parameters for both muscles. These results are consistent with previous work demonstrating that stiffness and viscoelastic contributions increase with strain rate. Thus, DOE has been shown to be a valid method to determine the effect of the experimental conditions on the mechanical behaviour of biological tissues such as skeletal muscle. This method considerably reduces the number of experiments. Indeed, the presented study using 3 parameters at 3 levels would have required at least 54 tests per muscle against 14 for the proposed DOE method.

MODELING AND SIMULATION OF SKELETAL MUSCLE BASED ON COMBINED EXPONENTIAL AND POLYNOMIAL MODEL

With the aim to build an accurate skeletal muscle simulation model, the biomechanical modeling and solution method of skeletal muscle were developed. First, the Mooney–Rivlin model, polynomial model, exponential model, logarithmic model, combined exponential and polynomial model were compared. The biomechanical model of skeletal muscle was built by combining the exponential and polynomial models. Second, the geometric non-linearity problem and material non-linearity problem of the biomechanical model were solved by using the finite element method. The program for this solution was implemented using Visual Studio 2012. Finally, the simulation results were compared to the experimental results. The maximum error between the simulation curve and the experiment stress–strain curve was 0.00149[Formula: see text]MPa. Finite element simulation for the lateral femoral muscle was conducted using the program developed in this study.

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.

A case for poroelasticity in skeletal muscle finite element analysis: experiment and modeling

Finite element models of skeletal muscle typically ignore the biphasic nature of the tissue, associating any time dependence with a viscoelastic formulation. In this study, direct experimental measurement of permeability was conducted as a function of specimen orientation and strain. A finite element model was developed to identify how various permeability formulations affect compressive response of the tissue. Experimental and modeling results suggest the assumption of a constant, isotropic permeability is appropriate. A viscoelastic only model differed considerably from a visco-poroelastic model, suggesting the latter is more appropriate for compressive studies.

Visualisation of Collagen in fixed skeletal muscle tissue using fluorescently tagged Collagen binding protein CNA35

Detection and visualisation of Collagen structure are important to understand the relationship between mechanical behaviour and microstructure in skeletal muscle since Collagen is the main structural protein in animal connective tissues, and is primarily responsible for their passive load-bearing properties. In the current study, the direct detection and visualization of Collagen using fluorescently tagged CNA35 binding protein (fused to EGFP or tdTomato) is reported for the first time on fixed skeletal muscle tissue. This Technical Note also establishes a working protocol by examining tissue preparation, dilution factor, exposure time etc. for sensitivity and specificity. Penetration of the binding protein into intact mature skeletal muscle was found to be very limited, but detection works well on tissue sections with higher sensitivity on wax embedded sections compared to frozen sections. CNA35 fused to tdTomato has a higher sensitivity than CNA35 fused to EGFP but both show specific detection. Best results were obtained with 15μm wax embedded sections, with blocking of non-specific binding in 1% BSA and antigen retrieval in Sodium Citrate. There was a play-off between dilution of the binding protein and time of incubation but both CNA35-tdTomato and CNA35-EGFP worked well with approximately 100μg/ml of purified protein with overnight incubation, while CNA35-tdTomato could be utilized at 5 fold less concentration. This approach can be applied to study the relationship between skeletal muscle micro-structure and to observe mechanical response to applied deformation. It can be used more broadly to detect Collagen in a variety of fixed tissues, useful for structure-functions studies, constitutive modelling, tissue engineering and assessment of muscle tissue pathologies.

How does tissue preparation affect skeletal muscle transverse isotropy?

The passive tensile properties of skeletal muscle play a key role in its physiological function. Previous research has identified conflicting reports of muscle transverse isotropy, with some data suggesting the longitudinal direction is stiffest, while others show the transverse direction is stiffest. Accurate constitutive models of skeletal muscle must be employed to provide correct recommendations for and observations of clinical methods. The goal of this work was to identify transversely isotropic tensile muscle properties as a function of post mortem handling. Six pairs of tibialis anterior muscles were harvested from Giant Flemish rabbits and split into two groups: fresh testing (within four hours post mortem), and non-fresh testing (subject to delayed testing and a freeze/thaw cycle). Longitudinal and transverse samples were removed from each muscle and tested to identify tensile modulus and relaxation behavior. Longitudinal non-fresh samples exhibited a higher initial modulus value and faster relaxation than longitudinal fresh, transverse fresh, and transverse rigor samples (p<0.05), while longitudinal fresh samples were less stiff at lower strain levels than longitudinal non-fresh, transverse fresh, and transverse non-fresh samples (p<0.05), but exhibited more nonlinear behavior. While fresh skeletal muscle exhibits a higher transverse modulus than longitudinal modulus, discrepancies in previously published data may be the result of a number of differences in experimental protocol. Constitutive modeling of fresh muscle should reflect these data by identifying the material as truly transversely isotropic and not as an isotropic matrix reinforced with fibers.

Fully non-linear hyper-viscoelastic modeling of skeletal muscle in compression

Understanding the behavior of skeletal muscle is critical to implementing computational methods to study how the body responds to compressive loading. This work presents a novel approach to studying the fully nonlinear response of skeletal muscle in compression. Porcine muscle was compressed in both the longitudinal and transverse directions under five stress relaxation steps. Each step consisted of 5% engineering strain over 1 s followed by a relaxation period until equilibrium was reached at an observed change of 1 g/min. The resulting data were analyzed to identify the peak and equilibrium stresses as well as relaxation time for all samples. Additionally, a fully nonlinear strain energy density-based Prony series constitutive model was implemented and validated with independent constant rate compressive data. A nonlinear least squares optimization approach utilizing the Levenberg-Marquardt algorithm was implemented to fit model behavior to experimental data. The results suggested the time-dependent material response plays a key role in the anisotropy of skeletal muscle as increasing strain showed differences in peak stress and relaxation time (p < 0.05), but changes in equilibrium stress disappeared (p > 0.05). The optimizing procedure produced a single set of hyper-viscoelastic parameters which characterized compressive muscle behavior under stress relaxation conditions. The utilized constitutive model was the first orthotropic, fully nonlinear hyper-viscoelastic model of skeletal muscle in compression while maintaining agreement with constitutive physical boundaries. The model provided an excellent fit to experimental data and agreed well with the independent validation in the transverse direction.

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.