Interpreting principal components in biomechanics: Representative extremes and single component reconstruction

Principal component analysis is a powerful tool in biomechanics for reducing complex multivariate datasets to a subset of important parameters. However, interpreting the biomechanical meaning of these parameters can be a subjective process. Biomechanical interpretations that are based on visual inspection of extreme 5th and 95th percentile waveforms may be confounded when extreme waveforms express more than one biomechanical feature. This study compares interpretation of principal components using representative extremes with a recently developed method, called single component reconstruction, which provides an uncontaminated visualization of each individual biomechanical feature. Example datasets from knee joint moments, lateral gastrocnemius EMG, and lumbar spine kinematics are used to demonstrate that the representative extremes method and single component reconstruction can yield equivalent interpretations of principal components. However, single component reconstruction interpretation cannot be contaminated by other components, which may enhance the use and understanding of principal component analysis within the biomechanics community.     

Biomechanical profiling of Caenorhabditis elegans motility

Caenorhabditis elegans locomotion is a stereotyped behavior that is ideal for genetic analysis. We integrated video microscopy, image analysis algorithms, and fluid mechanics principles to describe the C. elegans swim gait. Quantification of body shapes and external hydrodynamics and model-based estimates of biomechanics reveal that mutants affecting similar biological processes exhibit related patterns of biomechanical differences. Therefore, biomechanical profiling could be useful for predicting the function of previously unstudied motility genes.     

Biomechanics in anthropology

Biomechanics is the set of tools that explain organismal movement and mechanical behavior and links the organism to the physicality of the world. As such, biomechanics can relate behaviors and culture to the physicality of the organism. Scale is critical to biomechanical analyses, as the constitutive equations that matter differ depending on the scale of the question. Within anthropology, biomechanics has had a wide range of applications, from understanding how we and other primates evolved to understanding the effects of technologies, such as the atlatl, and the relationship between identity, society, culture, and medical interventions, such as prosthetics. Like any other model, there is great utility in biomechanical models, but models should be used primarily for hypothesis testing and not data generation except in the rare case where models can be robustly validated. The application of biomechanics within anthropology has been extensive, and holds great potential for the future.     

Speciation through the lens of biomechanics: locomotion,prey capture and reproductive isolation

Speciation is a multifaceted process that involves numerous aspects of the biological sciences and occurs for multiple reasons. Ecology plays a major role, including both abiotic and biotic factors. Whether populations experience similar or divergent ecological environments, they often adapt to local conditions through divergence in biomechanical traits. We investigate the role of biomechanics in speciation using fish predator–prey interactions, a primary driver of fitness for both predators and prey. We highlight specific groups of fishes, or specific species, that have been particularly valuable for understanding these dynamic interactions and offer the best opportunities for future studies that link genetic architecture to biomechanics and reproductive isolation (RI). In addition to emphasizing the key biomechanical techniques that will be instrumental, we also propose that the movement towards linking biomechanics and speciation will include (i) establishing the genetic basis of biomechanical traits, (ii) testing whether similar and divergent selection lead to biomechanical divergence, and (iii) testing whether/how biomechanical traits affect RI. Future investigations that examine speciation through the lens of biomechanics will propel our understanding of this key process.     

Biomechanics in fossil plant biology

The use of biomechanics for the analysis of the form—function relationship in palaeobotany is reviewed. Four fields of application of biomechanics are discussed and illustrated, i.e. the functional analysis of plants and plant organs (examples: lianas, leaf margin types), reconstruction of fossil plants (growth habit, tree height), functional analysis of ontogeny (lianas, trees), and evolutionary pathways (evolution of early land plants). The biomechanical analysis of ontogeny and evolution is of particular interest because it not only reveals the biomechanical constraints and functional background of these processes, but also yields information concerning the underlying mechanisms. Ontogenetic and phylogenetic changes may resemble a self-organization process constrained by laws of biomechanics.     

Multi-scale mechanics from molecules to morphogenesis

Dynamic mechanical processes shape the embryo and organs during development. Little is understood about the basic physics of these processes, what forces are generated, or how tissues resist or guide those forces during morphogenesis. This review offers an outline of some of the basic principles of biomechanics, provides working examples of biomechanical analyses of developing embryos, and reviews the role of structural proteins in establishing and maintaining the mechanical properties of embryonic tissues. Drawing on examples we highlight the importance of investigating mechanics at multiple scales from milliseconds to hours and from individual molecules to whole embryos. Lastly, we pose a series of questions that will need to be addressed if we are to understand the larger integration of molecular and physical mechanical processes during morphogenesis and organogenesis.     

The role of extracellular matrix in biomechanics and its impact on bioengineering of cells and 3D tissues

The cells and tissues of the human body are constantly exposed to exogenous and endogenous forces that are referred to as biomechanical cues. They guide and impact cellular processes and cell fate decisions on the nano-, micro- and macro-scale, and are therefore critical for normal tissue development and maintaining tissue homeostasis. Alterations in the extracellular matrix composition of a tissue combined with abnormal mechanosensing and mechanotransduction can aberrantly activate signaling pathways that promote disease development. Such processes are therefore highly relevant for disease modelling or when aiming for the development of novel therapies.In this mini review, we describe the main biomechanical cues that impact cellular fates. We highlight their role during development, homeostasis and in disease. We also discuss current techniques and tools that allow us to study the impact of biomechanical cues on cell and tissue development under physiological conditions, and we point out directions, in which in vitro biomechanics can be of use in the future.     

Finite element algorithm for frictionless contact of porous permeable media under finite deformation and sliding

This study formulates and implements a finite element contact algorithm for solid-fluid (biphasic) mixtures, accommodating both finite deformation and sliding. The finite element source code is made available to the general public. The algorithm uses a penalty method regularized with an augmented Lagrangian method to enforce the continuity of contact traction and normal component of fluid flux across the contact interface. The formulation addresses the need to automatically enforce free-draining conditions outside of the contact interface. The accuracy of the implementation is verified using contact problems, for which exact solutions are obtained by alternative analyses. Illustrations are also provided that demonstrate large deformations and sliding under configurations relevant to biomechanical applications such as articular contact. This study addresses an important computational need in the biomechanics of porous-permeable soft tissues. Placing the source code in the public domain provides a useful resource to the biomechanics community.     

A simple approach to guide factor retention decisions when applying principal component analysis to biomechanical data

The use of principal component analysis (PCA) as a multivariate statistical approach to reduce complex biomechanical data-sets is growing. With its increased application in biomechanics, there has been a concurrent divergence in the use of criteria to determine how much the data is reduced (i.e. how many principal factors are retained). This short communication presents power equations to support the use of a parallel analysis (PA) criterion as a quantitative and transparent method for determining how many factors to retain when conducting a PCA. Monte Carlo simulation was used to carry out PCA on random data-sets of varying dimension. This process mimicked the PA procedure that would be required to determine principal component (PC) retention for any independent study in which the data-set dimensions fell within the range tested here. A surface was plotted for each of the first eight PCs, expressing the expected outcome of a PA as a function of the dimensions of a data-set. A power relationship was used to fit the surface, facilitating the prediction of the expected outcome of a PA as a function of the dimensions of a data-set. Coefficients used to fit the surface and facilitate prediction are reported. These equations enable the PA to be freely adopted as a criterion to inform PC retention. A transparent and quantifiable criterion to determine how many PCs to retain will enhance the ability to compare and contrast between studies.     

Biological variability in biomechanical engineering research: Significance and meta-analysis of current modeling practices

Biological systems are characterized by high levels of variability, which can affect the results of biomechanical analyses. As a review of this topic, we first surveyed levels of variation in materials relevant to biomechanics, and compared these values to standard engineered materials. As expected, we found significantly higher levels of variation in biological materials. A meta-analysis was then performed based on thorough reviews of 60 research studies from the field of biomechanics to assess the methods and manner in which biological variation is currently handled in our field. The results of our meta-analysis revealed interesting trends in modeling practices, and suggest a need for more biomechanical studies that fully incorporate biological variation in biomechanical models and analyses. Finally, we provide some case study example of how biological variability may provide valuable insights or lead to surprising results. The purpose of this study is to promote the advancement of biomechanics research by encouraging broader treatment of biological variability in biomechanical modeling.     

Effects of TGF-beta1 and IGF-I on the compressibility, biomechanics, and strain-dependent recovery behavior of single chondrocytes

The responses of articular chondrocytes to physicochemical stimuli are intimately linked to processes that can lead to both degenerative and regenerative processes. Toward understanding this link, we examined the biomechanical behavior of single chondrocytes in response to growth factors (IGF-I and TGF-beta1) and a range of compressive strains. The results indicate that the growth factors alter the biomechanics of the cells in terms of their stiffness coefficient ( approximately two-fold increase over control) and compressibility, as measured by an apparent Poisson's ratio ( approximately two-fold increase over control also). Interestingly, the compressibility decreased significantly with respect to the applied strain. Moreover, we have again detected a critical strain threshold in chondrocytes at approximately 30% strain in all treatments. Overall, these findings demonstrate that cellular biomechanics change in response to both biochemical and biomechanical perturbations. Understanding the underlying biomechanics of chondrocytes in response to such stimuli may be useful in understanding various aspects of cartilage, including the study of osteoarthritis and the development of tissue-engineering strategies.     

角膜生物力学的测量及临床应用进展

摘要：角膜是重要的屈光间质,约占眼光学系统总屈光力的70％;因其特殊的生理结构,可表现出复杂的生物力学性质。随着近年来科学技术的进步,用于测量角膜生物力学的方法也在不断更新,获得的生物力学参数也更加精确。越来越多的国内外研究团队将对角膜生物力学的研究同临床相结合,发现当角膜形态发生变化时,其生物力学参数也会发生相应的改变。因此,可以通过对患者角膜生物力学的测量来判断病变的发展程度,也可以根据所测得的力学参数来进行手术设计,甚至可以初判患者的愈后情况。但在角膜生物力学方面的研究仍缺乏深度,对其与部分临床疾病的联系仍缺乏充分的认知,仍需探讨如何将角膜生物力学检查更好地服务于临床。本文将对角膜生物力学的离体、活体测量方法及其目前在圆锥角膜、青光眼、翼状胬肉、屈光不正及屈光不正的矫正等临床方面的应用研究作一综述。     

Automated Reconstruction of Three-Dimensional Fish Motion,Forces, and Torques

Fish can move freely through the water column and make complex three-dimensional motions to explore their environment, escape or feed. Nevertheless, the majority of swimming studies is currently limited to two-dimensional analyses. Accurate experimental quantification of changes in body shape, position and orientation (swimming kinematics) in three dimensions is therefore essential to advance biomechanical research of fish swimming. Here, we present a validated method that automatically tracks a swimming fish in three dimensions from multi-camera high-speed video. We use an optimisation procedure to fit a parameterised, morphology-based fish model to each set of video images. This results in a time sequence of position, orientation and body curvature. We post-process this data to derive additional kinematic parameters (e.g. velocities, accelerations) and propose an inverse-dynamics method to compute the resultant forces and torques during swimming. The presented method for quantifying 3D fish motion paves the way for future analyses of swimming biomechanics.     

兔组织工程同种异体气管支架三种制备方法的比较

目的:探讨深低温冷冻-酶洗法制备的气管支架在去除抗原性、维持生物力学及保护细胞外基质方面的效果。方法:健康新西兰兔24只随机分为气管未处理作为对照A组,深低温冷冻法处理B组,玻璃化法处理C组,深低温冷冻-酶洗法D组,各组样本数均为6。处理后将各组标本行HE染色后光镜观察,戊二醛固定后电镜扫描,并测量气管最大拉伸力、破裂力和变异率等生物力学性能。结果:组织学观察显示对照A组有大量完整的粘膜上皮细胞;B组和C组可见部分气管粘膜上皮细胞;D组标本未见气管粘膜上皮细胞,且细胞核碎裂。电镜显示A、B、C、D组气管支架可见丰富的细胞基质,未暴露胶原纤维。组间两两比较,气管支架的最大拉伸力、最大破裂力和变异率均无统计学差异。结论:综合组织学、扫面电镜和生物力学分析,应用深低温冷冻-酶洗法制备气管支架D组可以有效地去除抗原,维持生物力学性能,并具有较完整的细胞外基质。     

Dynamic finite element implementation of nonlinear,anisotropic hyperelastic biological membranes

We present a novel method for the implementation of hyperelastic finite strain, non-linear strain-energy functions for biological membranes in an explicit finite element environment. The technique is implemented in LS-DYNA but may also be implemented in any suitable non-linear explicit code. The constitutive equations are implemented on the foundation of a co-rotational uniformly reduced Hughes-Liu shell. This shell is based on an updated-Lagrangian formulation suitable for relating Cauchy stress to the rate-of-deformation, i.e. hypo-elasticity. To accommodate finite deformation hyper-elastic formulations, a co-rotational deformation gradient is assembled over time, resulting in a formulation suitable for pseudo-hyperelastic constitutive equations that are standard assumptions in biomechanics. Our method was validated by comparison with (1) an analytic solution to a spherically-symmetric dynamic membrane inflation problem, incorporating a Mooney-Rivlin hyperelastic equation and (2) with previously published finite element solutions to a non-linear transversely isotropic inflation problem. Finally, we implemented a transversely isotropic strain-energy function for mitral valve tissue. The method is simple and accurate and is believed to be generally useful for anyone who wishes to model biologic membranes with an experimentally driven strain-energy function.     

Morphometric estimation of torsional stiffness and strength in primate mandibles

In comparative studies of masticatory function and mandibular biomechanics, the mediolateral dimension of the postcanine corpus (corpus breadth) is commonly utilized as a measure of torsional stiffness from which relative torsional strength is inferred. The use of this dimension entails certain assumptions about corpus shape and cortical bone distribution that are invalid. When corpus breadth is related to an appropriate, empirically supported measure of torsional strength, it is revealed that this dimension has limited utility for inference of biomechanical competence under torsion. The use of linear dimensions to infer structural adaptations to specific loading regimes is problematic given that bone tissue is not optimally deployed to minimize strain levels arising from isolated loads. For the inference of the masticatory biomechanical environment, the more reasonable approach is to consider overall size of the corpus (i.e., cross-sectional area) for inference of intra- and inter-specific differences in masticatory forces.     

Simulation and study of the behaviour of the transversalis fascia in protecting against the genesis of inguinal hernias

Simulating the muscular system has many applications in biomechanics, biomedicine and the study of movement in general. We are interested in studying the genesis of a very common pathology: human inguinal hernia. We study the effects that some biomechanical parameters have on the dynamic simulation of the region, and their involvement in the genesis of inguinal hernias. We use the finite element method (FEM) and current models for the muscular contraction to determine the deformed fascia transversalis for the estimation of the maximum strain. We analysed the effect of muscular tissue density, Young's modulus, Poisson's coefficient and calcium concentration in the genesis of human inguinal hernia. The results are the estimated maximum strain in our simulations, has a close correlation with experimental data and the accepted commonly models by the medical community. Our model is the first study of the effect of various biological parameters with repercussions on the genesis of the inguinal hernias.     

Humans exploit the biomechanics of bipedal gait during visually guided walking over complex terrain

How do humans achieve such remarkable energetic efficiency when walking over complex terrain such as a rocky trail? Recent research in biomechanics suggests that the efficiency of human walking over flat, obstacle-free terrain derives from the ability to exploit the physical dynamics of our bodies. In this study, we investigated whether this principle also applies to visually guided walking over complex terrain. We found that when humans can see the immediate foreground as little as two step lengths ahead, they are able to choose footholds that allow them to exploit their biomechanical structure as efficiently as they can with unlimited visual information. We conclude that when humans walk over complex terrain, they use visual information from two step lengths ahead to choose footholds that allow them to approximate the energetic efficiency of walking in flat, obstacle-free environments.