An optimized transversely isotropic, hyper-poro-viscoelastic finite element model of the meniscus to evaluate mechanical degradation following traumatic loading

Hyperelastic meniscal material characterization via inverse parameter identification for knee arthroscopic simulations

Understanding the complex behavior of menisci is of growing interest in many fields including sports medicine, surgical simulation, and implant design. The selection of an appropriate material model and accurate model parameters contribute to identifying the degree of degeneration of the meniscus. Incorporating patient-specific material parameters could further improve the safe handling of tissue during probing in knee arthroscopy simulations, supporting more informed intraoperative decision-making. The objective of this study is to identify hyperelastic material parameters of individual human menisci based on an inverse parameter identification approach using optimization and demonstrate a real-time interactive surgical simulation using identified parameters. Mechanical tests were conducted in indentation of the anterior, mid-body, and posterior regions of five lateral and medial menisci to obtain experimental force-displacement data. An inverse parameter identification based on these tests and finite element (FE) models was employed to minimize the differences between the experimental and simulated force. The region-specific FE models considered the predominant collagen fiber orientation of the meniscus. Anisotropic hyperelastic material parameters were optimized using a particle swarm optimization algorithm. Finally, the optimized parameters were used in simulation open framework architecture (SOFA) and demonstrated a real-time probe-meniscus interaction during the arthroscopic meniscus examination. The optimized values revealed subject-specific characteristics, along with anatomical and regional variations, with high shear modulus observed in the anterior region of the medial meniscus (0.76 ± 0.28 MPa for 1 mm indentation). Additionally, an increase in shear modulus was observed with increased indentation depth (p<0.05 except for the mid-body of the medial meniscus).

Non-invasive regional parameter identification of degenerated human meniscus

Accurate identification of local changes in the biomechanical properties of the normal and degenerative meniscus is critical to better understand knee joint osteoarthritis onset and progression. Ex-vivo material characterization is typically performed on specimens obtained from different locations, compromising the tissue's structural integrity and thus altering its mechanical behavior. Therefore, the aim of this in-silico study was to establish a non-invasive method to determine the region-specific material properties of the degenerated human meniscus. In a previous experimental magnetic resonance imaging (MRI) study, the spatial displacement of the meniscus and its root attachments in mildly degenerated (n = 12) and severely degenerated (n = 12) cadaveric knee joints was determined under controlled subject-specific axial joint loading. To simulate the experimental response of the lateral and medial menisci, individual finite element models were created utilizing a transverse isotropic hyper-poroelastic constitutive material formulation. The superficial displacements were applied to the individual models to calculate the femoral reaction force in an inverse finite element analysis. During particle swarm optimization, the four most sensitive material parameters were varied to minimize the error between the femoral reaction force and the force applied in the MRI loading experiment. Individual global and regional parameter sets were identified. In addition to in-depth model verification, prediction errors were determined to quantify the reliability of the identified parameter sets. Both compressibility of the solid meniscus matrix (+141 %, p ≤ 0.04) and hydraulic permeability (+53 %, p ≤ 0.04) were significantly increased in the menisci of severely degenerated knees compared to mildly degenerated knees, irrespective of the meniscus region. By contrast, tensile and shear properties were unaffected by progressive knee joint degeneration. Overall, the optimization procedure resulted in reliable and robust parameter sets, as evidenced by mean prediction errors of <1 %. In conclusion, the proposed approach demonstrated high potential for application in clinical practice, where it might provide a non-invasive diagnostic tool for the early detection of osteoarthritic changes within the knee joint.

Finite element analysis of meniscus contact mechanical behavior based on kinematic simulation of abnormal gait

The meniscus plays a crucial role in the proper functioning of the knee joint, and when it becomes damaged, partial removal or replacement is necessary to restore proper function. Understanding the stress and deformation of the meniscus during various movements is essential for developing effective materials for meniscus repair. However, accurately estimating the contact mechanics of the knee joint can be challenging due to its complex shape and the dynamic changes it undergoes during movement. To address this issue, the open-source software SCONE can be used to establish a kinematics model that monitors the different states of the knee joint during human motion and obtains relevant gait kinematics data. To evaluate the stress and deformation of the meniscus during normal human movement, values of different states in the movement gait can be selected for finite element analysis (FEA) of the knee joint. This analysis enables researchers to assess changes in the meniscus. To evaluate meniscus damage, it is necessary to obtain changes in its mechanical behavior during abnormal movements. This information can serve as a reference for designing and optimizing the mechanical performance of materials used in meniscus repair and replacement.

Aponeurosis structure-function properties: Evidence of heterogeneity and implications for muscle function

Aponeurosis is a sheath-like connective tissue that aids in force transmission from muscle to tendon and can be found throughout the musculoskeletal system. The key role of aponeurosis in muscle-tendon unit mechanics is clouded by a lack of understanding of aponeurosis structure-function properties. This work aimed to determine the heterogeneous material properties of porcine triceps brachii aponeurosis tissue with materials testing and evaluate heterogeneous aponeurosis microstructure with scanning electron microscopy. We found that aponeurosis may exhibit more microstructural collagen waviness in the insertion region (near the tendon) compared to the transition region (near the muscle midbelly) (1.20 versus 1.12, p = 0.055), which and a less stiff stress-strain response in the insertion versus transition regions (p < 0.05). We also showed that different assumptions of aponeurosis heterogeneity, specifically variations in elastic modulus with location can alter the stiffness (by more than 10x) and strain (by approximately 10% muscle fiber strain) of a finite element model of muscle and aponeurosis. Collectively, these results suggest that aponeurosis heterogeneity could be due to variations in tissue microstructure and that different approaches to modeling tissue heterogeneity alters the behavior of computational models of muscle-tendon units. STATEMENT OF SIGNIFICANCE: Aponeurosis is a connective tissue found in many muscle tendon units that aids in force transmission, yet little is known about the specific material properties of aponeurosis. This work aimed to determine how the properties of aponeurosis tissue varied with location. We found that aponeurosis exhibits more microstructural waviness near the tendon compared to near the muscle midbelly, which was associated with differences in tissue stiffness. We also showed that different variations in aponeurosis modulus (stiffness) can alter the stiffness and stretch of a computer model of muscle tissue. These results show that assuming uniform aponeurosis structure and modulus, which is common, may lead to inaccurate models of the musculoskeletal system.

Volume Loss and Recovery in Bovine Knee Meniscus Loaded in Circumferential Tension

Load-induced volume change is an important aspect of knee meniscus function because volume loss creates fluid pressure, which minimizes friction and helps support compressive loads. The knee meniscus is unusual amongst cartilaginous tissues in that it is loaded not only in axial compression, but also in circumferential tension between its tibial attachments. Despite the physiologic importance of the knee meniscus' tensile properties, its volumetric strain in tension has never been directly measured, and predictions of volume strain in the scientific literature are inconsistent. In this study, we apply uniaxial tension to bovine knee meniscus and use biplanar imaging to directly observe the resulting three-dimensional volume change and unloaded recovery, revealing that tension causes volumetric contraction. Compression is already known to also cause contraction; therefore, all major physiologic loads compress and pressurize the meniscus, inducing fluid outflow. Although passive unloaded recovery is often described as slow relative to loaded loss, here we show that at physiologic strains the volume recovery rate in the meniscus upon unloading is faster than the rate of volume loss. These measurements of volumetric strain are an important step toward a complete theory of knee meniscus fluid flow and load support.

Region- and layer-specific investigations of the human menisci using SHG imaging and biaxial testing

In this paper, we examine the region- and layer-specific collagen fiber morphology via second harmonic generation (SHG) in combination with planar biaxial tension testing to suggest a structure-based constitutive model for the human meniscal tissue. Five lateral and four medial menisci were utilized, with samples excised across the thickness from the anterior, mid-body, and posterior regions of each meniscus. An optical clearing protocol enhanced the scan depth. SHG imaging revealed that the top samples consisted of randomly oriented fibers with a mean fiber orientation of 43.3 ^o . The bottom samples were dominated by circumferentially organized fibers, with a mean orientation of 9.5 ^o . Biaxial testing revealed a clear anisotropic response, with the circumferential direction being stiffer than the radial direction. The bottom samples from the anterior region of the medial menisci exhibited higher circumferential elastic modulus with a mean value of 21 MPa. The data from the two testing protocols were combined to characterize the tissue with an anisotropic hyperelastic material model based on the generalized structure tensor approach. The model showed good agreement in representing the material anisotropy with a mean r ² = 0.92.

Experiments and hyperelastic modeling of porcine meniscus show heterogeneity at high strains

Constitutive modeling of the meniscus is critical in areas like knee surgery and tissue engineering. At low strain rates, the meniscus can be described using a hyperelastic model. Calibration of hyperelastic material models of the meniscus is challenging on many fronts due to material variability and friction. In this study, we present a framework to determine the hyperelastic material parameters of porcine meniscus (and similar soft tissues) using no-slip uniaxial compression experiments. Because of the nonhomogeneous deformation in the specimens, a finite element solution is required at each step of the iterative calibration process. We employ a Bayesian calibration approach to account for the inherent material variability and a Bayesian optimization approach to minimize the resulting cost function in the material parameter space. Cylindrical specimens of porcine meniscus from the anterior, middle and posterior regions are tested up to 30% compressive strain and the Yeoh form of hyperelastic strain energy density function is used to describe the material response. The results show that the Yeoh form is able to accurately describe the compressive response of porcine meniscus and that the Bayesian calibration and optimization approaches are able to calibrate the model in a computationally efficient manner while taking into account the inherent material variability. The results also show that the shear modulus or the initial stiffness is roughly uniform across the different areas of the meniscus, but there is significant spatial heterogeneity in the response at high strains. In particular, the middle region is considerably stiffer at high strains. This heterogeneity is important to consider in modeling the response of the meniscus for clinical applications.

Bioinspired material architectures from bighorn sheep horncore velar bone for impact loading applications

Rocky Mountain bighorn sheep rams (Ovis canadensis canadensis) routinely conduct intraspecific combat where high energy cranial impacts are experienced. Previous studies have estimated cranial impact forces to be up to 3400 N during ramming, and prior finite element modeling studies showed the bony horncore stores 3 × more strain energy than the horn during impact. In the current study, the architecture of the porous bone within the horncore was quantified, mimicked, analyzed by finite element modeling, fabricated via additive manufacturing, and mechanically tested to determine the suitability of the novel bioinspired material architecture for use in running shoe midsoles. The iterative biomimicking design approach was able to tailor the mechanical behavior of the porous bone mimics. The approach produced 3D printed mimics that performed similarly to ethylene–vinyl acetate shoe materials in quasi-static loading. Furthermore, a quadratic relationship was discovered between impact force and stiffness in the porous bone mimics, which indicates a range of stiffness values that prevents impact force from becoming excessively high. These findings have implications for the design of novel bioinspired material architectures for minimizing impact force.

Anisotropic and viscoelastic tensile mechanical properties of aponeurosis: Experimentation, modeling, and tissue microstructure

Aponeuroses are stiff sheath-like components of the muscle-tendon unit that play a vital role in force transmission and thus locomotion. There is clear importance of the aponeurosis in musculoskeletal function, but there have been relatively few studies of aponeurosis material properties to date. The goals of this work were to: 1) perform tensile stress-relaxation tests, 2) perform planar biaxial tests, 3) employ computational modeling to the data from 1 to 2, and 4) perform scanning electron microscopy to determine collagen fibril organization for aponeurosis tissue. Viscoelastic modeling and statistical analysis of stress-relaxation data showed that while relaxation rate differed statistically between strain levels (p = 0.044), functionally the relaxation behavior was nearly the same. Biaxial testing and associated modeling highlighted the nonlinear (toe region of ~2-3% strain) and anisotropic (longitudinal direction linear modulus ~50 MPa, transverse ~2.5 MPa) tensile mechanical behavior of aponeurosis tissue. Comparisons of various constitutive formulations showed that a transversely isotropic Ogden approach balanced strong fitting (goodness of fit 0.984) with a limited number of parameters (five), while damage modeling parameters were also provided. Scanning electron microscopy showed a composite structure of highly aligned, partially wavy collagen fibrils with more random collagen cables for aponeurosis microstructure. Future work to expand microstructural analysis and use these data to inform computational modeling would benefit this work and the field.

Differing trabecular bone architecture in dinosaurs and mammals contribute to stiffness and limits on bone strain

The largest dinosaurs were enormous animals whose body mass placed massive gravitational loads on their skeleton. Previous studies investigated dinosaurian bone strength and biomechanics, but the relationships between dinosaurian trabecular bone architecture and mechanical behavior has not been studied. In this study, trabecular bone samples from the distal femur and proximal tibia of dinosaurs ranging in body mass from 23-8,000 kg were investigated. The trabecular architecture was quantified from micro-computed tomography scans and allometric scaling relationships were used to determine how the trabecular bone architectural indices changed with body mass. Trabecular bone mechanical behavior was investigated by finite element modeling. It was found that dinosaurian trabecular bone volume fraction is positively correlated with body mass similar to what is observed for extant mammalian species, while trabecular spacing, number, and connectivity density in dinosaurs is negatively correlated with body mass, exhibiting opposite behavior from extant mammals. Furthermore, it was found that trabecular bone apparent modulus is positively correlated with body mass in dinosaurian species, while no correlation was observed for mammalian species. Additionally, trabecular bone tensile and compressive principal strains were not correlated with body mass in mammalian or dinosaurian species. Trabecular bone apparent modulus was positively correlated with trabecular spacing in mammals and positively correlated with connectivity density in dinosaurs, but these differential architectural effects on trabecular bone apparent modulus limit average trabecular bone tissue strains to below 3,000 microstrain for estimated high levels of physiological loading in both mammals and dinosaurs.

Constitutive modeling of menisci tissue: a critical review of analytical and numerical approaches

Menisci are fibrocartilaginous disks consisting of soft tissue with a complex biomechanical structure. They are critical determinants of the kinematics as well as the stability of the knee joint. Several studies have been carried out to formulate tissue mechanical behavior, leading to the development of a wide spectrum of constitutive laws. In addition to developing analytical tools, extensive numerical studies have been conducted on menisci modeling. This study reviews the developments of the most widely used continuum models of the meniscus mechanical properties in conjunction with emerging analytical and numerical models used to study the meniscus. The review presents relevant approaches and assumptions used to develop the models and includes discussions regarding strengths, weaknesses, and discrepancies involved in the presented models. The study presents a comprehensive coverage of relevant publications included in Compendex, EMBASE, MEDLINE, PubMed, ScienceDirect, Springer, and Scopus databases. This review aims at opening novel avenues for improving menisci modeling within the framework of constitutive modeling through highlighting the needs for further research directed toward determining key factors in gaining insight into the biomechanics of menisci which is crucial for the elaborate design of meniscal replacements.

Biological and Mechanical Predictors of Meniscus Function: Basic Science to Clinical Translation

Progressive knee joint degeneration occurs following removal of a torn meniscus. However, there is significant variability in the rate of development of post-meniscectomy osteoarthritis (OA). While there is no current consensus on the risk factors for development of knee OA in patients with meniscus tears, it is likely that both biological and biomechanical factors play critical roles. In this perspective paper, we review the mechanical and the biological predictors of the response of the knee to partial meniscectomy. We review the role of patient-based studies, in vivo animal models, cadaveric models, bioreactor systems, and statistically augmented computational models for the study of meniscus function and post-meniscectomy OA, providing insight into the important interplay between biomechanical and biologic factors. We then discuss the clinical translation of these concepts for "biologic augmentation" of meniscus healing and meniscus replacement. Ultimately, collaborative studies between engineers, biologists, and clinicians is the optimal way to improve our understanding of meniscus pathology and response to injury and/or disease, and to facilitate effective translation of laboratory findings to improved treatments for our patients. © 2019 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 38:937-945, 2020.

Three-dimensional finite-element analysis of aggravating medial meniscus tears on knee osteoarthritis

BACKGROUND

The biomechanical change during the medial meniscus damage in the process of knee osteoarthritis has not been explored. The purpose of this study was to determine the effect of aggravating medial meniscus degenerative tear on the progress of knee osteoarthritis through the finite-element simulation method.

METHODS

The three-dimensional digital model of a total-knee joint was obtained using a combination of magnetic resonance imaging and computed tomography images. Four types of medial meniscus tears were created to represent the aggravating degenerative meniscus lesions. Meniscectomy of each meniscal tear was also utilized in the simulation. The compression and shear stress of bony tissue, cartilage, and meniscus were evaluated, and meniscus extrusion of the healthy knee, postinjured knee, and postmeniscectomy knee were investigated under the posture of balanced standing.

RESULTS

Based on the results of finite-element simulation, the peak shear principal stress, peak compression principal stress, and meniscus extrusion increased gradually as the meniscus tears' region enlarged progressively (from 7.333 MPa to 15.14 MPa on medial femur and from 6 MPa to 20.94 MPa on medial tibia). The higher stress and larger meniscus extrusion displacement in all tests were observed in the flap and complex tears. The oblique tears also had a biomechanical variation of stress and meniscus extrusion in the knee joint, but their level was milder. Both the peak value of the stress and meniscus displacement increased after the meniscectomy.

CONCLUSION

In contrast to the damaged hemijoint, the stress applied on the healthy lateral hemijoint increased. The change of biomechanics was more obvious with the aggravation of meniscus injury. The advanced degenerative damage resulted in increasing stress that was more likely to cause symptomatic clinical manifestation in the knee joint and accelerate the progress of osteoarthritis. Moreover, we found that the meniscus injury caused higher stress concentration on the contralateral side of the joint. We also discovered that the meniscectomy can lead to more serious biomechanical changes, and although this technique can relieve pain over a period of time, it increased the risk of osteoarthritis (OA) occurrence.

THE TRANSLATIONAL POTENTIAL OF THIS ARTICLE

It is clear that the meniscal lesions can cause osteoarthritic knee, but the biomechanical change during the meniscus damage period has not been explored. We have evaluated the variation of stress during the aggravating medial degenerative meniscus tears and the relationship in the process of knee OA through finite-element simulation. This study does favour to obtain a better understanding on the symptoms and pathological changes of OA. It also may provide some potential directions for the prophylaxis and treatment of OA.

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.

Biomechanical analysis of the effect of medial meniscus degenerative and traumatic lesions on the knee joint

The purpose of this study was to determine the effect of the degenerative medial meniscus and traumatic lesions on the biomechanical behavior of the knee. An elaborate three-dimensional (3D) finite element model of the total knee joint containing bones, articular cartilages, main ligaments, and menisci was developed from a combination of magnetic resonance images and computed tomography. Three types of meniscus tears were employed to represent the degenerative and traumatic lesions. The stress and meniscus extrusion of healthy and injured knees were investigated under the posture of static stance. The traumatic longitudinal tear demonstrated the highest stress and the largest meniscus extrusion displacement. The degenerative horizontal and peripheral tears also showed an irregular biomechanical balance in the knee joint. Despite the damaged hemijoint, the stress on the healthy lateral hemijoint was increased. Although the biomechanics was deteriorated in all meniscus tear models, the variation degree was diverse. The transfixion damage could potentially cause future injury in the knee joint and accelerate the progress of osteoarthritis. Moreover, the meniscus injury may cause high-stress concentration on the contralateral side of the joint. The current results revealed the cause of different clinical manifestation after meniscus tears and the risk of knee osteoarthritis through biomechanical aspects.

Effects of a viscosupplementation therapy on rabbit menisci in an anterior cruciate ligament transection model of osteoarthritis

The aim of this study was to evaluate the morphological, microstructural, and mechanical effects of a viscosupplementation therapy on rabbit menisci at an early stage of osteoarthritis (OA). Anterior cruciate ligament transection (ACLT) was performed in twelve male New-Zealand White rabbits on the right knee joint. Six of these twelve rabbits received a mono intra-articular injection of high molecular weight hyaluronic acid (HA) two weeks after ACLT. Six additional healthy rabbits served as controls. Medial menisci were removed from all right knees (n=18) six weeks after ACLT and were graded macroscopically. Indentation-relaxation tests were performed in the anterior and posterior regions of the menisci. Collagen fiber organization and glycosaminoglycan (GAG) content were assessed by biphotonic confocal microscopy and histology, respectively. Viscosupplementation significantly (p=0.002) improved the surface integrity of the medial menisci compared to the operated non-treated group. Moreover, the injection seems to have an effect on the GAG distribution in the anterior region of the menisci. However, the viscoelastic properties of both operated groups were similar and significantly lower than those of the healthy group, which was explained by their modified collagen fiber organization. They displayed disruption of the tie fibers due to structural alterations of the superficial layers from which they emanate, leading to modifications in the deep zone. To conclude, the viscosupplementation therapy prevents macroscopic lesions of the menisci, but it fails to restore their collagen fiber organization and their viscoelastic properties. This finding supports the role of this treatment in improving the lubrication over the knee.

Osteoarthritis year in review 2016: mechanics

Inappropriate biomechanics, namely wear-and-tear, has been long believed to be a main cause of osteoarthritis (OA). However, this view is now being re-evaluated, especially when examined alongside mechanobiology and new biomechanical studies. These are multiscale experimental and computational studies focussing on cell- and tissue-level mechanobiology through to organ- and whole-body-level biomechanics, which focuses on the biomechanical and biochemical environment of the joint tissues. This review examined papers from April 2015 to April 2016, with a focus on multiscale experimental and computational biomechanical studies of OA. Assessing the onset or progression of OA at organ- and whole-body-levels, gait analysis, medical imaging and neuromusculoskeletal modelling revealed the extent to which tissue damage changes the view of inappropriate biomechanics. Traditional gait analyses studies reported that conservative treatments can alter joint biomechanics, thereby improving pain and function experienced by those with OA. Results of animal models of OA were consistent with these human studies, showing interactions among bone, cartilage and meniscus biomechanics and the onset and/or progression OA. Going down size scales, experimental and computational studies probed the nanosize biomechanics of molecules, cells and extracellular matrix, and demonstrated how the interactions between biomechanics and morphology affect cartilage dynamic poroelastic behaviour and pathways to OA. Finally, integration of multiscale experimental data and computational models were proposed to predict cartilage extracellular matrix remodelling and the development of OA. Summarising, experimental and computational methods provided a nuanced biomechanical understanding of the sub-cellular, cellular, tissue, organ and whole-body mechanisms involved in OA.

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.

Viscoelastic properties of rabbit osteoarthritic menisci: A correlation with matrix alterations

The aim of this study was to evaluate the effect of early osteoarthritis (OA) on the viscoelastic properties of rabbit menisci and to correlate the mechanical alterations with the microstructural changes. Anterior Cruciate Ligament Transection (ACLT) was performed in six male New-Zealand White rabbits on the right knee joint. Six healthy rabbits served as controls. Menisci were removed six weeks after ACLT and were graded macroscopically. Indentation-relaxation tests were performed in the anterior and posterior regions of the medial menisci. The collagen fibre organization and glycosaminoglycan (GAG) content were assessed by biphotonic confocal microscopy and histology, respectively. OA menisci displayed severe macroscopic lesions compared with healthy menisci (p=0.009). Moreover, the instantaneous and equilibrium moduli, which were 2.9±1.0MPa and 0.60±0.18MPa in the anterior region of healthy menisci, respectively, decreased significantly (p=0.03 and p=0.004, respectively) in OA menisci by 55% and 57%, respectively, indicating a global decrease in meniscal stiffness in this region. The equilibrium modulus alone decreased significantly (p=0.04) in the posterior region, going from 0.60±0.18MPa to 0.26±012MPa. This induced a loss of tissue elasticity. These mechanical changes were associated in the posterior region with a structural disruption of the superficial layers, from which the tie fibres emanate, and with a decrease in the GAG content in the anterior region. Consequently, the circumferential collagen fibres of the deep zone were dissociated and the collagen bundles were less compact. Our results demonstrate the strong meniscal modifications induced by ACLT at an early stage of OA and highlight the relationship between structural and chemical matrix alterations and mechanical properties.

Osteoarthritis year in review 2015: mechanics

Motivated by the conceptual framework of multi-scale biomechanics, this narrative review highlights recent major advances with a focus on gait and joint kinematics, then tissue-level mechanics, cell mechanics and mechanotransduction, matrix mechanics, and finally the nanoscale mechanics of matrix macromolecules. A literature review was conducted from January 2014 to April 2015 using PubMed to identify major developments in mechanics related to osteoarthritis (OA). Studies of knee adduction, flexion, rotation, and contact mechanics have extended our understanding of medial compartment loading. In turn, advances in measurement methodologies have shown how injuries to both the meniscus and ligaments, together, can alter joint kinematics. At the tissue scale, novel findings have emerged regarding the mechanics of the meniscus as well as cartilage superficial zone. Moving to the cell level, poroelastic and poro-viscoelastic mechanisms underlying chondrocyte deformation have been reported, along with the response to osmotic stress. Further developments have emerged on the role of calcium signaling in chondrocyte mechanobiology, including exciting findings on the function of mechanically activated cation channels newly found to be expressed in chondrocytes. Finally, AFM-based nano-rheology systems have enabled studies of thin murine tissues and brush layers of matrix molecules over a wide range of loading rates including high rates corresponding to impact injury. With OA acknowledged to be a disease of the joint as an organ, understanding mechanical behavior at each length scale helps to elucidate the connections between cell biology, matrix biochemistry and tissue structure/function that may play a role in the pathomechanics of OA.

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.

WITHDRAWN: Meniscus mechanics and mechanobiology

The Publisher regrets that this article is an accidental duplication of an article that has already been published, http://dx.doi.org/10.1016/j.jbiomech.2015.03.020. The duplicate article has therefore been withdrawn. The full Elsevier Policy on Article Withdrawal can be found at http://www.elsevier.com/locate/withdrawalpolicy.