Finite element modelling of skeletal muscles coupled with fatigue

In this study, Hill's muscle theory coupled with fatigue was proposed to describe mechanical behaviours of skeletal muscles. The force developed by a fatigued muscle was described by a muscle fatigue formula which was a time function of the activation α_a and the stretch λ. The modified Hill's muscle theory was hence incorporated into a three-dimensional (3D) finite element model using the PAK finite element code. In this paper, the theoretical derivation of the 3D muscle model was firstly described. After presenting the method of establishing the finite element programme, a case example of studying the mechanical response of a frog gastrocnemius muscle was used to illustrate the applicability of the proposed methodology. The effects of the muscle fatigue on the deformation as well as the stress and strain distribution of the frog muscle subject to a cyclic activation function have been determined. An experiment capturing the real-time shape change of a frog muscle was also conducted to assess the applicability of the proposed method. A comparison between the deformed shapes of the predictive model and the frog muscles was also made. It was shown that the method is capable of providing a reasonable model for describing the mechanical behaviour of skeletal muscles.     

Myosin isoforms, muscle fiber types, and transitions

Skeletal muscle is an extremely heterogeneous tissue composed of a variety of fast and slow fiber types and subtypes. Moreover, muscle fibers are versatile entities capable of adjusting their phenotypic properties in response to altered functional demands. Major differences between muscle fiber types relate to their myosin complement, i.e., isoforms of myosin light and heavy chains. Myosin heavy chain (MHC) isoforms appear to represent the most appropriate markers for fiber type delineation. On this basis, pure fiber types are characterized by the expression of a single MHC isoform, whereas hybrid fiber type express two or more MHC isoforms. Hybrid fibers bridge the gap between the pure fiber types. The fiber population of skeletal muscles, thus, encompasses a continuum of pure and hybrid fiber types. Under certain conditions, changes can be induced in MHC isoform expression heading in the direction of either fast-to-slow or slow-to-fast. Increased neuromuscular activity, mechanical loading, and hypothyroidism are conditions that induce fast-to-slow transitions, whereas reduced neuromuscular activity, mechanical unloading, and hyperthyroidism cause transitions in the slow-to-fast direction.     

Eye muscle sparing by the muscular dystrophies: lessons to be learned?

The devastating consequences of the various muscular dystrophies are even more obvious when a muscle or muscle group is spared. The study of the exceptional cell or tissue responses may prove to be of considerable value in the analysis of disease mechanisms. The small muscles responsible for eye movements, the extraocular muscles, have functional and morphological characteristics that set them aside from other skeletal muscles. Notably, these muscles are clinically unaffected in Duchenne/Becker, limb-girdle, and congenital muscular dystrophies, pathologies due to a broken mechanical or signaling linkage between the cytoskeleton and the extracellular matrix. Uncovering the strategies used by the extraocular muscles to "naturally" protect themselves in these diseases should contribute to knowledge of both pathogenesis and treatment. We propose that careful investigation of the cellular determinants of extraocular muscle-specific properties may provide insights into how these muscles avoid or adapt to the cascade of events leading to myofiber degeneration in the muscular dystrophies.     

The biomechanical effects of variation in the maximum forces exerted by trunk muscles on the joint forces and moments in the lumbar spine: a finite element analysis

The weakening of trunk muscles is known to be related to a reduction of the stabilization function provided by the muscles to the lumbar spine; therefore, strengthening deep muscles might reduce the possibility of injury and pain in the lumbar spine. In this study, the effect of variation in maximum forces of trunk muscles on the joint forces and moments in the lumbar spine was investigated. Accordingly, a three-dimensional finite element model of the lumbar spine that included the trunk muscles was used in this study. The variation in maximum forces of specific muscle groups was then modelled, and joint compressive and shear forces, as well as resultant joint moments, which were presumed to be related to spinal stabilization from a mechanical viewpoint, were analysed. The increase in resultant joint moments occurred owing to decrease in maximum forces of the multifidus, interspinales, intertransversarii, rotatores, iliocostalis, longissimus, psoas, and quadratus lumborum. In addition, joint shear forces and resultant joint moments were reduced as the maximum forces of deep muscles were increased. These results from finite element analysis indicate that the variation in maximum forces exerted by trunk muscles could affect the joint forces and joint moments in the lumbar spine.     

基于卷积神经网络与扩展卡尔曼滤波的 单目视觉惯性里程计

针对单目相机采集室外图像易受环境光照影响、尺度存在不确定性的缺点,以及利用神经网络进行位姿估计不准确的问题,提出一种基于卷积神经网络(CNN)与扩展卡尔曼滤波(EKF)的单目视觉惯性里程计。采用神经网络取代传统里程计中基于几何约束的视觉前端,将单目相机输出的估计值作为测量更新,并通过神经网络优化EKF的误差协方差。利用EKF融合CNN输出的单目相机位姿和惯性测量单元(IMU)数据,优化CNN的位姿估计,补偿相机尺度信息与IMU累计误差,实现无人系统运动位姿的更新和估计。相比于使用单目图像的深度学习算法Depth-VO-Feat,所提算法融合单目图像和IMU数据进行位姿估计,KITTI数据集中09序列的平动、转动误差分别减少45.4%、47.8%,10序列的平动、转动误差分别减少68.1%、43.4%。实验结果表明所提算法能进行更准确的位姿估计,验证了算法的准确性和可行性。     

Importance of sarcomere length when determining muscle physiological cross-sectional area: a spine example

Muscle physiological cross-sectional area predicts the maximum capability of a muscle to generate isometric force. Biomechanical models often use estimates of individual muscle physiological cross-sectional area to partition internal forces among different muscles and predict joint forces and stability. In the spine literature, these physiological cross-sectional area values are generally obtained from imaging or cadaveric studies that have not accounted for a potential lengthened or shortened (and thus thinned or thickened, respectively) state of the muscles in question. Sarcomere length measurements can be used to normalize muscle lengths and correct for these length discrepancies. This article was designed to demonstrate potential effects of not accounting for instantaneous sarcomere length when calculating the physiological cross-sectional area of muscles of the spine region. Because some muscles of the spine region appear to be shortened and others lengthened in the neutral spine posture, both over- and under-estimations of physiological cross-sectional area are possible. Specifically, it is shown that the muscle physiological cross-sectional area could be over-estimated or under-estimated by as much as + 36% (multifidus) and -21% (rectus abdominis), respectively. This differential error effect poses difficulties in accurately estimating individual muscle forces and subsequent spine forces and stability that result from biomechanical models incorporating physiological cross-sectional area data obtained in the absence of sarcomere length measurements. Future work is needed to measure the dynamic range of sarcomere lengths of all spinal muscles to ensure correct inputs to biomechanical models.     

A p-type finite element solution for the simulation of O2 transport in articular cartilage tissue: heterogeneous and porous media

The partial pressure of oxygen (pO2) is suggested to have a regulatory effect on chondrocyte biosynthetic activities, and its effect during expansion is unknown. The authors hypothesize that oxygen tension due to mechanical deformation or swelling could be as important as direct mechanical effects on cell biosynthetic activities. While there are plenty of studies on measuring and/or modelling pO2 in articular cartilage (AC) for static (rest) conditions, to the best of the authors' knowledge there are very few such studies on pO2 in AC for dynamic conditions such as swelling or tissue deformation. In this study, it is attempted to develop a model to study the dynamics of oxygen transport in AC. A high-precision hybrid element is designed using the p-type finite element method, by which diffusion and convection are incorporated as a single element. A domain decomposition method is used that allows the use of a different type of discretization with independent discretization variables in non-overlapping sub-domains, for a generic three-dimensional approach to elliptic boundary value problems of order 2 or higher. The formulation developed in this study might be used in determining the necessary flow conditions to cultivate tissue constructs in tissue repair and tissue engineering.     

Leptin‐like immunoreactivity in the muscle of juvenile sea bass (Dicentrarchus labrax)

The mammalian hormone, leptin, is mainly synthesized in adipose tissue along with other tissues. Leptin plays a role in numerous processes such as in the control of food intake, homeostasis, immune function and reproduction. In this study, we detected and localized leptin immunoreactivity to the muscle of early juvenile sea bass (Dicentrarchus labrax) by Western blot analysis and immunohistochemistry. A leptin immunopositive band with a molecular weight of ～16 kDa, corresponding to mammalian leptin, was identified in trunk skeletal muscle homogenate. Furthermore, leptin immunopositive cells were detected in the endomysium of skeletal muscular fibers. These cells showed immunostained cytoplasmic granules and roundish and oval nuclei. The most intense immunostaining was observed in the endomysial space among the superficial red muscular fibers of the trunk. These findings suggest that in early juvenile sea bass, leptin is mostly produced by skeletal muscles. Therefore, during the developmental stage lacking adipose tissue, skeletal muscles can be considered an important source of leptin. As already suggested in mammals, we can hypothesize the potential roles of leptin not only in energy expenditure for muscle contraction but also during muscle differentiation and growth. Microsc. Res. Tech. 73:797–802, 2010. © 2010 Wiley‐Liss, Inc.     

Preparing sections of skeletal muscle for transmission electron analytical microscopy (TEAM) of diffusible elements.

Comparative morphological examination and elemental analysis were carried out in structural compartments of sections of skeletal muscles. These had been prepared either by conventional plastic embedding technique or by various methods of cryo-ultramicrotomy. The analyses were performed in a Philips EM 301 with an Edax energy-dispersive X-ray spectrometer. Spectra obtained from sections of plastic-embedded muscle depended on the reagents used for fixation and staining and were absent if these were omitted. Brief fixation with glutaraldehyde resulted in gross ionic changes, and sectioning of frozen material with trough liquid led to extraction of elements. Sections cut from unfixed and frozen muscle without trough liquid showed numerous peaks. (Mg, P, S, Cl, K, Ca). In the superficial parts of the fibres of freeze-dried sections reproducible spectral differences were found between different structures. Thus, rapid freezing of unfixed tissue, dry cutting in the frozen state, and freeze-drying should be the procedure of choice if data on diffusible ions are desired.     

Modelling of ergonomics and muscular comfort

Commercially available software packages permit to position human models of various geometries in practical scenarios while respecting the anatomical constraints of the skeletal joints and of the bulk of the bodies. Beyond such features, the PAM-Comfort^TM software has been conceived to provide direct access to the muscular forces needed by humans to perform physical actions where muscle force is required. The PAM-Comfort^TM human models are made of multi-body linked anatomical skeletons, equipped with finite elements of the relevant skeletal muscles. The hyper-static problem of determination of muscle forces is solved by optimisation techniques. Voluntary stiffening of muscles can be added to the basic contraction levels needed to perform a specific task. The calculated muscle forces obey Hill's model. The model and software have been applied in several interesting scenarios of various fields of application, such as car industry, handling of equipment and sports activities.     

Imaging and elasticity measurements of the sarcolemma of fully differentiated skeletal muscle fibres

This study aimed to describe the three-dimensional structure and the elastic properties of the sarcolemma of adult, fully differentiated, skeletal muscle fibres combining Atomic Force Microscopy (AFM) and optical microscopy. Single fibres were enzymatically dissociated from Flexor Digitorum Brevis of adult mice and were maintained in culture up to 3 weeks. On the sixth day after dissociation, the upper surface of intact fibres, either alive in solution or fixed and kept in solution or fixed and exposed in air, was analysed with AFM. The most prominent features in AFM images were periodic transversal foldings with an interval that corresponded to the sarcomere length. More detailed analysis of the topography profile showed that the depth in the folding decreased with increasing sarcomere length and that the crests of the foldings corresponded to the Z-lines. Minor periodic structures could be detected in the valleys between the major foldings. AFM images also showed deep depressions on the sarcolemma likely corresponding to openings of T tubules and caveolae. Two-dimensional elasticity maps were obtained using AFM as an indenter and showed that the crests of the transversal foldings correspond to higher stiffness regions. This study provides the first complete three-dimensional topography and mechanical characterization of intact, living skeletal muscle fibres and might form the basis for further investigations aimed to compare healthy and dystrophic muscles.     

基于三弯矩法的环曲面金刚石切削刀具路径规划及其仿真分析

为解决环曲面加工困难的问题,对环曲面金刚石切削方法进行研究。在刀具路径规划中,使用了刀触点综合离散方法,该方法结合了等角度离散与等弧长离散的优点;提出了通过控制相邻刀触点间Z向距离以减小刀具的Z向移动从而提高离散精度的方法。根据加工时刀位点插补的特点,应用三弯矩法计算插补入口参数,实现插值函数的二阶导数连续。仿真分析表明,综合离散方法能够减小离散误差,使用三弯矩法进行插补计算可将最大插值误差由Hermite插值的0.35 μm减小至0.001 2 μm,效果明显。加工试验结果表明,该路径规划方法可用于环曲面的加工,且能改善工件的加工质量。     

Characterization of several invertebrate muscle cell types: a comparison with vertebrate muscles

Ultrastructural classification of invertebrate muscles is complex and not always clear. The aim of the present paper was to establish some criteria that might be useful for classification of invertebrate muscles and for a better understanding of the differences between them. The procedures used were: (1) immunochemical evaluation of those proteins that differentiated striated from smooth muscle (troponin, caldesmon, and calponin), and (2) calculations of several myofilament parameters to establish differences among muscles. The muscles studied were: striated muscles from the rat, Drosophila, the crab Callinectes, and the snail Helix (heart); obliquely striated muscles from the earthworm Eisenia foetida and Helix (mouth); and smooth muscles from the rat, and Helix (retractor, body wall, and intestinal wall). Immunochemical studies revealed that troponin was only present in the striated muscles and the obliquely striated muscle from Eisenia, whereas caldesmon and calponin were only present in the smooth muscles and the obliquely striated muscle from Helix. The highest thick filament/thin filament volume ratio was found in the striated muscles, followed by the obliquely striated muscles, and the smooth muscles. This suggests the order in which the contraction strength decreases. The myofilament length is inversely related to the contraction speed, which was higher in the striated muscles than in the obliquely striated muscles. In vertebrates, the smooth muscle seems to be less rapid than the striated muscle because their myofilaments are longer. This assertion cannot be generalized for invertebrate smooth muscle, because myofilament lengths vary widely in both striated and smooth muscles. In smooth muscles, the presence of apparently unordered electron-dense bodies instead of ordered Z lines and the absence of true sarcomeres permit a certain overlapping of thin filaments increasing the range of shortening.     

Inactivation of myosin heavy chain genes in the mouse: diverse and unexpected phenotypes

Myosin heavy chain (MyHC) is a critical component of the cellular contractile apparatus. The mammalian genome contains two nonmuscle, two smooth muscle, and eight striated muscle isoforms of MyHC. Within each class of genes, there is extremely high sequence homology among different MyHC isoforms, raising the question of whether these isoforms are functionally redundant or whether they perform unique roles in cell function. Recently, strains of mice null for four different MyHC isoforms have been generated. Mice null for the nonmuscle II-B isoform experience significant prenatal lethality and surviving animals have several cardiac abnormalities [Tullio et al. (1997) Proc Natl Acad Sci USA 94:12407-12412]. Mice homozygous null for alpha cardiac MyHC are embryonic lethal, while heterozygous mice are viable but also have numerous cardiac defects [Jones et al. (1996) J Clin Invest 98:1906-1917]. Mice null for IIb or IId adult skeletal MyHC are viable but have skeletal muscle abnormalities compared to wild type mice, despite compensation of a neighboring MyHC gene [Acakpo-Satchivi et al. (1997) J Cell Biol 139:1219-1229]. Both IIb and IId null mice show significant decreases in body mass. Mean muscle mass is also significantly decreased in both null strains but the extent and the pattern of affected muscles differs between the two strains. Both strains show evidence of skeletal muscle pathology but again the pattern and extent differ between the two strains. Finally, both adult skeletal strains demonstrate distinct impairments in contractile function when compared to wild type. Together these observations support the hypothesis that the different isoforms of MyHC are functionally unique and cannot substitute for one another.     

Repercussions on sarcomeres of the myotendinous junction and the myofibrillar type adaptations in response to different trainings on vertical ladder

The myofibrillary types establish to the skeletal muscle functional and adaptive properties that influence the sarcomeric arrangement during muscle contraction and may have repercussions on an important related force transmission region of the locomotor apparatus, the myotendinous junction (MTJ). This study aimed to describe changes in myofibrillary type and sarcomeric lengths in the belly muscle and MTJ of the soleus and plantaris muscles associated with training protocols in vertical ladder. Thirty adults male Wistar rats were divided into three groups (n = 10): Control (CTR), No‐load Training (NLT), and Load Training (LT). Morphoquantitative analysis of different fibers types and sarcomere lengths were performed in distinct regions of plantaris and soleus muscles. In the plantaris muscle with both trainings, there was an increase in the cross‐sectional area (CSA) in Type I and II fibers (p < .0001) while sarcomeric lengths revealed greater lengths in the proximal and distal sarcomeres of NLT, although in the LT we found greater lengths in the belly and MTJ sarcomeres. The soleus muscle showed an increase in CSA muscle fiber only in the NLT (p < .0001) and revealed alterations in belly and MTJ sarcomere lengths with training. We concluded that plantaris muscle has an adaptive effect directly associated with training load, with hypertrophy in both trainings and sarcomere length inverse from belly and MTJ, in LT associated with increased force generation and transmission at the MTJ, although soleus muscle has a lower adaptive response to training stimuli with variation in the belly and distal sarcomere of the MTJ.     

Some limitations of the use of tannic acid as a marker of damaged skeletal muscle fibres

Mouse biceps brachii muscles containing single transverse incisions were treated with low molecular weight tannic acid. In the absence of fibre degeneration, intracellular spread of tannic acid was confined to a short distance along the fibres from the damaged portions of the cell membranes. Beyond this, damaged and undamaged fibres could not be distinguished from one another. Tannic acid is not a reliable marker of localized trauma to skeletal muscle fibres.     

基于视觉的机动目标定位跟踪的滤波算法

在视觉定位系统中，由于各种噪声的影响，运动目标的三维位置和姿态的计算精度受到一定限制。为了提高运动物体的定位跟踪精度，提出了一种有效的滤波算法。和已有的方法相比，这种算法具有以下两个特点：第一，不再局限于平缓运动的物体，它对于未知运动规律的机动目标同样有效，第二，由于避免了扩展卡尔曼滤波器的使用，滤波复杂度有所下降。通过分析噪声对位姿计算误差的影响，建立了一组描述位姿测量值和真实值关系的线性测量方程。然后，分别给出了两种滤波算法：基于有限记忆的检测自适应滤波和基于数值微分模型的卡尔曼滤波。在检测自适应滤波算法中，给出了分别适用于快机动和慢机动的最优机动检测函数。一旦检测出机动发生，系统采用有限记忆滤波进行矫正。在第二种滤波算法中，系统采用数值微分技术构造出了描述机动目标运动行为的鲁棒估计模型。并且，引入了衰减因子，以防止滤波器的发散现象。该衰减因子可以根据位姿计算值自适应估计。最后，通过伪贝叶斯估计算法，将两种滤波器进行数据融合，有效的降低了机动时刻位姿估值的误差抖动，进一步提高了定位跟踪精度。仿真结果验证了本算法的有效性。     

A method for the reduction of skin marker artifacts during walking : Application to the knee

Previous studies have demonstrated the importance of joint angle errors mainly due to skin artifact and measurement errors during gait analysis. Joint angle errors lead to unreliable kinematics and kinetic analyses in the investigation of human motion. The purpose of this paper is to present the Joint Averaging Coordinate System (JACS) method for human gait analysis. The JACS method is based on the concept of statistical data reduction of anatomically referenced marker data. Since markers are not attached to rigid bodies, different marker combinations lead to slightly different predictions of joint angles. These different combinations can be averaged in order to provide a “best” estimate of joint angle. Results of a gait analysis are presented using clinically meaningful terminology to provide better communication with clinical personal. In order to verify the developed JACS method, a simple three-dimensional knee joint contact model was developed, employing an absolute coordinate system without using any kinematics constraint in which thigh and shank segments can be derived independently. In the experimental data recovery, the separation and penetration distance of the knee joint is supposed to be zero during one gait cycle if there are no errors in the experimental data. Using the JACS method, the separation and penetration error was reduced compared to well-developed existing methods such as ACRS and Spoor & Veldpaus method. The separation and penetration distance ranged up to 15 mm and 12 mm using the Spoor & Veldpaus and ACRS method, respectively, compared to 9 mm using JACS method. Statistical methods like the JACS can be applied in conjunction with existing techniques that reduce systematic errors in marker location, leading to an improved assessment of human gait.     

一种基于工具坐标系的机器人运动学参数标定方法

机器人末端执行器位姿误差在基础坐标系中表示时,误差模型中包含姿态误差与位置矢量的乘积项,影响了参数标定识别精度。以工具坐标系为参考系,给出一种基于指数积公式包含关节约束条件的机器人位姿误差标定模型,避免了姿态误差与位置矢量的乘积项对参数标定识别精度的影响。以UR5机器人为标定对象,采用LeciaAT960-MR激光跟踪仪为测量设备,进行参数标定试验。试验结果表明,经参数标定后UR5机器人位置误差模和姿态误差模的平均值分别减小了91.07%和89.16%。