Cell polarization energy and its implications for cell migration

Cells usually have a polarized shape in directional cell migration. This cell polarity may result from external cues, such as a gradient of chemo-attractants (chemotaxis), or a gradient of mechanical properties of substrate (durotaxis), and it can also arise from internal cues so that the cells self-polarize spontaneously and maintain the polar motile state for a long time. However, the mechanisms that control cell polarization have not been fully understood, and particularly, the relationship between the polarized shape and cell migration behaviors is not yet clear. In this study, we propose an energy model to study the cell polarization energy by considering the effect of matrix rigidity, cell shape, and organization of the cytoskeleton. We then propose a parameter called “motility factor” for depicting the relationship between the cell shape and the driving force of cell migration. We demonstrate that the fibroblast-like cell shape and keratocyte-like shape both have an optimal polarization angle corresponding to the most stable cell shape. Fibroblast-like cell shape also has an optimal tail length of the polarization. Furthermore, we find that the cell free energy biphasically depends on the matrix rigidity, i.e. that there is an optimum matrix rigidity for the most stable shape. And the motility factor also biphasically depends on the matrix rigidity, but the trends of the dependence are opposite to that of cell's free energy, which implies an optimum matrix rigidity for the highest speed. The optimum matrix rigidity for the most stable cell shape and that for the highest cell speed are consistent, suggesting that the most stable cell shape is favorable to the fastest cell migration. This study provides important insights into the relationship between cell polarization shape and cell migration behaviors.     

大雁塔地震可靠性分析

本文采用双参数地震破坏模型，对大雁塔的地震可靠性进行了分析研究，给出了塔体各层在不同地震烈度下的破坏指标均值和条件破坏概率，并对破坏指标均值较大的顶层计算了不同年限内的破坏概率。     

Elastic moduli of the piezoelectric cochlear outer hair cell membrane

The outer hair cell is a specialized cell in the mammalian cochlea, believed to amplify incoming sound waves. This amplification is associated with the outer hair cell's electromotility, a unique cellular phenomenon of voltage-dependent length changes. Outer hair cell properties can be described in terms of the piezoelectric relationships, and the elastic moduli are a key part of them. We revisit the problem of estimating the elastic moduli of the outer hair cell composite membrane (wall) where two methods have previously been proposed. We analyze the two methods, while taking into account experimental ranges of the measured parameters. We have shown that cell stiffness is the critical parameter that determines the difference between the method predictions, and we have found a range of stiffness where the results are reasonably close. The elastic moduli corresponding to this range can be recommended for estimation of the characteristics of the piezoelectric model.     

Coarse grained molecular dynamics and theoretical studies of carbon nanotubes entering cell membrane

Motivated by recent experimental observations that carbon nanotubes （CNT） can enter animal cells, here we conduct coarse grained molecular dynamics and theoretical studies of the intrinsic interaction mechanisms between CNT＇s and lipid bilayer. The results indicate that CNT-cell interaction is dominated by van der Waals and hydrophobic forces, and that CNT＇s with sufficiently small radii can directly pierce through cell membrane while larger tubes tend to enter cell via a wrapping mechanism. Theoretical models are proposed to explain the observed size effect in transition of entry mechanisms.     

The role of binder mobility in spontaneous adhesive contact and implications for cell adhesion

The standard view of mechanical adhesive contact is as a competition between a reduction in free energy when surfaces with bonding potential come into contact and an increase in free energy due to elastic deformation that is required to make these surfaces conform. An equilibrium state is defined by an incremental balance between these effects, akin to the Griffith crack growth criterion. In the case of adhesion of biological cells, the molecules that tend to form surface-to-surface bonds are confined to the cell wall but they are mobile within the wall, adding a new phenomenon of direct relevance to adhesive contact. In this article, the process of adhesive contact of an initially curved elastic plate to a flat surface is studied for the case in which the binders that account for adhesion are able to migrate within the plate. This is done by including entropic free energy of the binder distribution in the total free energy of the system. By adopting a constitutive assumption that binders migrate at a speed proportional to the local gradient in chemical potential, the transient growth of an adhesion zone due to binder transport is analyzed. For the case of a plate of very large extent, the problem can be solved in closed form, whereas numerical methods are invoked for the case of a plate of limited extent. Results are presented on the rate of growth of an adhesion zone in terms of system parameters, on the evolution of the distribution of binders and, in the case of a plate of limited extent, on the long-term limiting size of the adhesion zone.     

轴压随机几何缺陷圆柱壳可靠性分析

轴压随机几何缺陷圆柱壳屈曲的失效函数具有较强的非线性，对于该结构已应用的可靠性分析方法不能同时满足计算精度和计算效率的要求。本文发展一个修正的ＭｏｎｔｅＣａｒｌｏ法，由两个步骤执行：应用一阶可靠性方法计算Ｈａｓｏｆｅｒ－Ｌｉｎｄ可靠性指标β；将简单ＭｏｎｔｅＣａｒｌｏ法的采样区域限制在基本随机变量构成的ｎ维β－球外部，采样点由一个χ２分布的随机半径Ｒ≥β和（－１，１）均匀分布的随机方向组成，该修正的ＭｏｎｔｅＣａｒｌｏ法用于轴压随机几何缺陷圆柱壳屈曲强度可靠性分析表明，在相同精度的情况下修正的ＭｏｎｔｅＣａｒｌｏ法的样本容量比简单ＭｏｎｔｅＣａｒｌｏ法要低３个数量级，一阶可靠性方法的计算误差随着与分支屈曲模态一致的初始几何缺陷项数的增加越来越显著     

Simultaneous measurement of viscoelastic changes and cell opening during processing of flexible polyurethane foam

A parallel-plate rheomete was constructed and used to study the development of dynamic shear modulus and cell opening under forced adiabatic conditions for a series of flexible slabstock polyurethane foams. Typical industrial formulations were used. The plates were heated to follow the adiabatic temperature profile of a real foam bun during foaming. The rheometer overcomes difficulties encountered in other methods such as heat loss and bubble damage caused by the probe.A four-stage modulus development profile was observed: initial bubble growth, bubble network, polymer stiffening and final curing. Chemical structure development was also studied under forced adiabatic conditions, using Fourier transform infrared spectroscopy. Polymer stiffening coincided with bidentate (hydrogen-bonded) urea formation.The normal force exerted by the expanding foam on the plates was found to be a function of the rate of foam expansion and the foam modulus. A sudden drop in the normal force typically coincides with the visually observed blow-off in the reacting foam bun, thus the normal force profile is a new and accurate indicator of cell opening. The normal force profile clearly shows that cell opening occurs just after the onset of polymer stiffening, thus illustrating the role of polymer rheology in the cell opening mechanism.Dedicated to the memory of Professor Tasos C. PapanastasiouPortions presented at the SPI Polyurethanes Technical/Marketing Conference, October 9–12, 1994, Boston, massachusetts, USA (Best paper award) and at the XIIth International Congress on Rheology, August 18–23, 1996, Québec City, Québec, Canada.     

A model of cell motility leading to biphasic dependence of transport speed on adhesive strength

A rolling model for cell motility is proposed here where the movement of cell is treated as a result of the continuous release and growth of adhesions at the trailing and leading edge of the cell, respectively. The appearance of actin polymerization is key in this model as it breaks the symmetry of adhesion characteristics. The cell speed predicted here is in the correct range and exhibits a biphasic relationship with the cell-substrate adhesive strength which is consistent with experimental observations. We will show that this biphasic dependence of cell speed on adhesivity is due to the interplay between the energy dissipation associated with cell movement and the thermal fluctuations of actin filaments necessary for polymerization. Our results also suggest that the mobility of adhesion molecules is not only unnecessary but may actually limit cell motility.     

可靠性敏度分析方法及其在非线性蠕变疲劳失效模型中的应用

针对非线性极限状态方程,发展了两种基本随机变量为非正态情况下的可靠性敏度分析方法:基于改进一次二阶矩的近似解析法和基于Monte-Carlo的数字模拟法.近似解析法中非正态变量首先被等价变换为正态变量,然后用正态变量的敏度分析法和隐函数求导法则来得到失效概率对非正态变量分布参数的灵敏度,求解敏度的数字模拟法是从计算失效概率的所有样本点中选取合适的抽样点,利用回归分析和隐函数求导法则来求取可靠性灵敏度的.所提方法被用于非线性蠕变疲劳失效模式的可靠性灵敏度分析,近似解析法和数字模拟法结果的一致说明了所提方法的合理可行.蠕变疲劳失效的可靠性灵敏度随参数的变化趋势分析为工程设计提供了有益指导.     

Simulating the sensitivity of cell nutritive environment to composition changes within the intervertebral disc

Altered nutrition in the intervertebral disc affects cell viability and can generate catabolic cascades contributing to extracellular matrix (ECM) degradation. Such degradation is expected to affect couplings between disc mechanics and nutrition, contributing to accelerate degenerative processes. However, the relation of ECM changes to major biophysical events within the loaded disc remains unclear. A L4-L5 disc finite element model including the nucleus (NP), annulus (AF) and endplates was used and coupled to a transport-cell viability model. Solute concentrations and cell viability were evaluated along the mid-sagittal plane path. A design of experiment (DOE) was performed. DOE parameters corresponded to AF and NP biochemical tissue measurements in discs with different degeneration grades. Cell viability was not affected by any parameter combinations defined. Nonetheless, the initial water content was the parameter that affected the most the solute contents, especially glucose. Calculations showed that altered NP composition could negatively affect AF cell nutrition. Results suggested that AF and NP tissue degeneration are not critical to nutrition-related cell viability at early-stage of disc degeneration. However, small ECM degenerative changes may alter significantly disc nutrition under mechanical loads. Coupling disc mechano-transport simulations and enzyme expression studies could allow identifying spatiotemporal sequences related to tissue catabolism.     

Role of cell regularity and relative density on elasto-plastic compression response of random honeycombs generated using Voronoi diagrams

The Voronoi tessellation technique and solid modeling methods are used in this work to create virtual random structures and link cell morphology with the mechanical behavior. Their compression responses are analyzed using the finite element method. First, the effect of loading direction is analyzed for structures with different levels of randomness characterized by a regularity parameter to assess the degree of scatter in the results. Subsequently, morphological characteristics such as arrangement of cells and randomness are analyzed separately. The effect of relative density on structures with different levels of randomness is also studied. Simulations suggest that at low relative densities the arrangement of cells has a negligible effect on the compression response of random honeycombs. On the contrary, the cellular randomness has significant influence on the elastic and plastic characteristics especially when fully random structures are compared with the regular counterparts.     

Stability and resonance of micro-machined gyroscope under nonlinearity effects

Resonance frequency for a micro-gyroscope plays an extremely significant role since the driving frequency is accordingly tuned so that the best sensitivity and resolution can be achieved. In practice, the micro-gyroscope is usually driven into resonance to retain its superior angular rate detection capability. However, the embedded nonlinearity effect upon the micro-gyroscopic dynamics may not only deteriorate the stability around the vicinity of operation point, but also alter the initially-designed resonance frequencies so that the angular rate detection performance of the micro-gyroscope is dramatically degraded. Hence, the nonlinearities, mainly resulting from flexure springs and electrostatic force, are both taken into account to construct the nonlinear dynamic model of the micro-gyroscope in our work at first. Secondly, the instability region of the proposed micro-gyroscope under different driving frequency and natural frequencies, which tends to be drifted due to mechanical fatigue and temperature rise, is unveiled. In order to catch the insight of slight variation of system parameters, the nonlinear dynamic equation is analyzed by using multiple scales method to outstand the influence of the variation of driving moment. Thirdly, the external resonance and non-resonant hard excitation of the micro-gyroscope—totally five types—are both theoretically studied. It is interesting to find that the resonance frequencies and resonant magnitude are both changed accordingly if either the driving frequency or the magnitude of driving moment is tuned via control loop for the sake of considering more stability or better performance. Finally, the chaotic behavior of the micro-gyroscope is numerically inspected by bifurcation diagrams and verified that the sense mode and drive mode have the similar orbits for transitions across distinct patterns of dynamic motion of the presented micro-gyroscope.     

GPS动态定位的可靠性及精度分析

动态环境中的ＧＰＳ接收机，其伪距观测量常含有各种粗差，不同高度角的可见卫星，其伪距观测量的精度差异很大，为此，本文从可靠性与精度两个方面，分析、研究了ＧＰＳ动态定位的性能。     

非线性动力系统全局分析的变胞胞映射法与转子／轴承系统的全局稳定性

在Ｐｏｉｎｃａｒｅ映射及胞映理论的基础上，提出了一种非线性动力系统全局分析的新方法－－变胞胞映射法，这种新方法改变了原胞映射法中胞在胞空间分布的不合理性及运算逻辑的不合理性，更适用于高维、大求解域非线性动力系统的求解。应用此方法，对具有非线性油膜力的Ｊｅｆｆｃｏｔ转子轴承系统进行了全局分析，绘制了系统分岔后的全局吸引域图，解释了一些工程中常见的非线性现象。     

Convergence studies of the time accurate and non-linear frequency domain methods for optimum shape design

This paper presents convergence studies of the time accurate and non-linear frequency domain (NLFD) methods for optimum shape design. The NLFD method provides an attractive alternative for aerodynamic shape optimisation for unsteady flows. It dramatically reduces the number of time steps required to resolve the periodic flow field. In this work, the convergence of the gradients are investigated as the number of time steps are increased to determine the required number of modes that is adequate for shape optimisation for unsteady flows. The formulation of the adjoint equations for both the time accurate and NLFD techniques are presented. The techniques are employed for the redesign of a pitching airfoil to reduce the time-averaged drag coefficient while maintaining the lift coefficient.     

A new three-phase algorithm for computation of reliability index and its application in structural mechanics

Computation of reliability index or probability of failure in practical problems is still a challenge. In this paper, an efficient three-phase non-gradient-based algorithm is proposed to be used in structural reliability analysis. Like approximation methods, the purpose in the proposed algorithm is to locate the position of design point. However, for this purpose, at the iterations of the phases random samples are generated based on a moving sampling density function, like what is done in adaptive importance sampling. At each phase, by representing an updating criterion, the position of the candidate of design point is updated to approach the real design point. Two criteria of the first and second phase are to reduce the initial relatively large distance between the candidate of design point and the real one. In the third phase, after introducing a new effective fitness function, the third updating criterion is represented to take the final smaller steps of approaching design point. Through various numerical examples, the accuracy and efficiency of three aforementioned phases have been shown.     

Influence of heat transfer and fluid flow on crack growth in multilayered porous/dense materials using XFEM: Application to Solid Oxide Fuel Cell like material design

An advanced numerical model is developed to investigate the influence of heat transfer and fluid flow on crack propagation in multi-layered porous materials. The fluid flow, governed by the Navier–Stokes and Darcy’s law, is discretized with the nonconforming Crouzeix–Raviart (CR) finite element method. A combination of Discontinuous Galerkin (DG) and Multi-Point Flux Approximation (MPFA) methods is used to solve the advection–diffusion heat transfer equation in the flow channel and in the fluid phase within the porous material. The crack is assumed to affect only the heat diffusion within the porous layer, therefore a time splitting technique is used to solve the heat transfer in the fluid and the solid phases separately. Thus, within the porous material, the crack induces a discontinuity of the temperature at the crack surfaces and a singularity of the flux at the crack tip. Conduction in the solid phase is solved using the eXtended Finite Element Method (XFEM) to better handle the discontinuities and singularities caused by the cracks. The XFEM is also used to solve the thermo-mechanical problem and to track the crack propagation. The multi-physics model is implemented then validated for the transient regime, this necessitated a post processing treatment in which, the stress intensity factors (SIF) are computed for each time step. The SIFs are then used in the crack propagation criterion and the crack orientation angle. The methodology seems to be robust accurate and the computational cost is reduced thanks to the XFEM.     

平面结构可靠性预测的随机边界元逆分析法

在结构可靠性计算的随机边界元理论和逆分析法基础上,用随机边界元方程结合改进的卡尔曼滤波算法来预测结构的可靠性,提出了用于平面机械结构可靠性预测的边界元逆分析法理论;并将方法应用于同时存在未知缺陷和随机边界载荷模型,进行了结构可靠性预测,在识别缺陷的同时预测出随机边界载荷的分布参数及结构体上各点的结构可靠度指标,给出了平面结构模型的数值示例。     

大型结构静强度可靠性分析程序及其应用

本文全面介绍了大型结构静强度可靠性分析程序的原理、功能特点及应用实例。     

On the frequency bandwidth change of a servo system with a gear reducer due to backlash and motor input voltage

Summary The paper analyzes how the frequency bandwidth of a servo system is affected by the input voltage of its motor and the magnitude of the total backlash. The bandwidth of the system is defined as the set of antiresonance frequencies, which appears in the frequency-response characteristic. The change in the frequency-response characteristics is investigated depending on motor input voltage and the magnitude of the total backlash. It is shown that at infinite motor input voltage, the servo system has a bandwidth equivalent to that of a backlash-free system. The amount of the systems bandwidth reduction due to the backlash changes greatly with the motor input voltage. It becomes possible then to determine the necessary maximum input voltage of the motor and the admissible magnitude of the total backlash to satisfy the desired bandwidth for a servo system with a gear reducer.