A mathematical model of cortical bone remodeling at cellular level under mechanical stimulus

A bone cell population dynamics model for cortical bone remodeling under mechanical stimulus is developed in this paper. The external experiments extracted from the literature which have not been used in the creation of the model are used to test the validity of the model. Not only can the model compare reasonably well with these experimental results such as the increase percentage of final values of bone mineral content (BMC) and bone fracture energy (BFE) among different loading schemes (which proves the validity of the model), but also predict the realtime development pattern of BMC and BFE, as well as the dynamics of osteoblasts (OBA), osteoclasts (OCA), nitric oxide (NO) and prostaglandin E₂ (PGE₂) for each loading scheme, which can hardly be monitored through experiment. In conclusion, the model is the first of its kind that is able to provide an insight into the quantitative mechanism of bone remodeling at cellular level by which bone cells are activated by mechanical stimulus in order to start resorption/formation of bone mass. More importantly, this model has laid a solid foundation based on which future work such as systemic control theory analysis of bone remodeling under mechanical stimulus can be investigated. The to-be identified control mechanism will help to develop effective drugs and combined nonpharmacological therapies to combat bone loss pathologies. Also this deeper understanding of how mechanical forces quantitatively interact with skeletal tissue is essential for the generation of bone tissue for tissue replacement purposes in tissue engineering.     

反演在骨生长方程参数识别中的应用

基于BFGS算法,根据自行设计的动物实验,得到在不同应力环境中,快速生长期大鼠股骨生 长与重建过程中骨密度实测数据,采用反演数值方法,获取了骨生长方程中随时间变化的 生物参数B和K. 通过正演验证,表明所建立的基于BFGS算法的参数识别方法具有较好的 稳定性和较高的识别精度,能够反演出比较切合实际的生物参数数值. 研究表明,反问 题方法是解决生命现象不可测性和未知性问题的有效手段,把反演方法应用到骨生长与重建 等生命现象的研究中,可确定、修正预设的数学模式,为数值量化骨适应生物模型的建立提 供了一条可行的途径.     

A theoretical model for surface bone remodeling under electromagnetic loads

A theoretical model for surface bone remodeling under electromagnetic loads is proposed in this paper. In the model, surface bone remodeling is assumed to be related to growth factors. Growth factors in latent form in osteocytes are released to the bone fluid after the osteocytes are absorbed by osteoclasts, and then regulate the bone formation process. At the same time, environmental loadings can influence the generation of growth factors. This paper shows how surface bone remodeling is triggered under the influence of growth factors. Based on this hypothesis, a computational model is established that simulates the bone coupling remodeling process, including internal and surface bone remodeling. The effects of various loadings, including electrical and magnetic loadings, are simulated and compared. The interactions between internal and surface bone remodeling are investigated via the numerical method. The results indicate that an electromagnetic field can strongly influence the bone remodeling process and that the remodeling process will be altered after surface bone remodeling is triggered, compared to the sole effect of the internal remodeling process.     

Effect of magnetic field on poroelastic bone model for internal remodeling

This paper studies the effects of the magnetic field and the porosity on a poroelastic bone model for internal remodeling. The solution of the internal bone remodeling process induced by a magnetic field is presented. The bone is treated as a poroelastic material by Biot’s formulation. Based on the theory of small strain adaptive elasticity, a theoretical approach for the internal remodeling is proposed. The components of the stresses, the displacements, and the rate of internal remodeling are obtained in analytical forms, and the numerical results are represented graphically. The results indicate that the effects of the magnetic field and the porosity on the rate of internal remodeling in bone are very pronounced.     

骨组织生长重建的力学生物学机制研究进展

生物力学已被证实是骨组织生长、重建及成形当中一个十分重要的因素. 骨组织的损 伤修复过程本质上是细胞的生物学过程和应力作用下的生长过程. 这虽然肯定了生物力学在 骨组织生长、重建过程中的重要地位, 但是, 人们对生物力学因素如何诱导骨生长、 重建的力学生物学机制仍不甚了解. 而骨组织工程需要更为科学完善的细胞生物学机制来研究和探 索骨组织的构建过程. 本文概述了国内外生物力学与骨组织生长重建的宏微观理论, 主要讨 论了骨组织结构及功能形成过程中的力学生物学相关问题.     

AN EFFICIENT LIQUID SLOSHING DAMPER FOR VIBRATION CONTROL

The next generation of tall structures are being designed to be lighter and more flxible, making them susceptible to wind, ocean waves and earthquake type of excitations. One approach to vibration control of such systems is through energy dissipation using a liquid sloshing damper. Such dampers are already in use for vibration control of tall structures in Japan and Australia. The present parametric study focuses on enhancing the energy dissipation efficiency of a rectangular liquid damper through introduction of a two-dimensional obstacle. A parametric free-vibration study, aimed at optimum size and location of the obstacle, is described first. Results suggest a significant increase in the energy dissipation, up to 60%, in the presence of the obstacle. An extensive wind tunnel test-program was undertaken which substantiated the effectiveness of the improved damper in suppressing both vortex resonance and galloping types of instabilities. Ability of the damper to control structural oscillations with a smaller amount liquid is quite attractive for real-life applications.     

Damaged-bone remodeling theory: Thermodynamical approach

The bone remodeling process is generally viewed as bone material response to functional demands and muscle attachments by continual process of growth, reinforcement and resorption which occur in living situation. Everyday activities damage bone, and this damage is normally repaired in a continuous process. When an imbalance in this remodeling process occurs, Bones may become more susceptible to fracture. An attempt to establish a relationship between induced microdamage and adaptive bone remodeling is proposed. A thermodynamic theoretical framework is provided as basis for a consistent formulation of bone remodeling involving a chemical reaction and mass transfer between two constituents in presence of microtracks.     

The influence of different loads on the remodeling process of a bone and bioresorbable material mixture with voids

A model of a mixture of bone tissue and bioresorbable material with voids was used to numerically analyze the physiological balance between the processes of bone growth and resorption and artificial material resorption in a plate-like sample. The adopted model was derived from a theory for the behavior of porous solids in which the matrix material is linearly elastic and the interstices are void of material. The specimen—constituted by a region of bone living tissue and one of bioresorbable material—was acted by different in-plane loading conditions, namely pure bending and shear. Ranges of load magnitudes were identified within which physiological states become possible. Furthermore, the consequences of applying different loading conditions are examined at the end of the remodeling process. In particular, maximum value of bone and material mass densities, and extensions of the zones where bone is reconstructed were identified and compared in the two different load conditions. From the practical view point, during surgery planning and later rehabilitation, some choice of the following parameters is given: porosity of the graft, material characteristics of the graft, and adjustment of initial mixture tissue/bioresorbable material and later, during healing and remodeling, optimal loading conditions.     

Bone remodeling I: theory of adaptive elasticity

A thermomechanical continuum theory involving a chemical reaction and mass transfer between two constituents is developed here as a model for bone remodeling. Bone remodeling is a collective term for the continual processes of growth, reinforcement and resorbtion which occur in living bone. The resulting theory describes an elastic material which adapts its structure to applied loading.

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Zusammenfassung Eine Thermo-mechanische kontinuum Theorie als Modell für die Knochenrekonstrucktion wird entwickelt, die eine chemische Reaktion und einen Massentransport zwischen zwei Komponenten behandelt. Knochenrekonstruktion ist ein Sammelbegriff für die kontinuierlichen Prozesse des Wachsens, der Verstärkung und des Abbaus wie sie im lebenden Knochen auftreten. Die Theorie beschreibt ein elastisches Material, das sich in der Form der Belastung anpasst.

     

Effect of hoisting cable elasticity on anti-sway controllers of quay-side container cranes

Oscillation frequency of crane payloads is the main and most important factor in crane anti-sway control systems design. In the summer of 2005, a Smart Sway Control system (SSC) was installed on a 65-ton quay-side container crane at Jeddah Port. During the calibration phase of the installation, it was observed that heavy payloads combined with the dynamic stretch of the hoist cables had a significant impact on the configuration of the hoisting mechanism and the pattern of oscillation. This introduced considerable change in the oscillation frequency of the payload, which resulted in a significant impact on the performance of the anti-sway control system. Empirical formulas had to be used to compensate for the change in the frequency approximation used in the controller algorithm. In this work, an analytic approximation of the oscillation frequency of the hoisting mechanism of a quay-side container crane is developed, which takes into consideration the elasticity of the hoisting cables. A parametric study is performed to investigate the extent of the effect of the hoisting cables stretch on the system behavior for a typical range of payload masses and cable lengths. The performance of the delayed feedback control system used in the SSC controller is simulated on an elastic cables model using both the elastic and rigid cable frequency approximations.     

Identification of a constitutive law for trabecular bone samples under remodeling in the framework of irreversible thermodynamics

We construct in the present paper constitutive models for bone remodeling based on micromechanical analyses at the scale of a representative unit cell (RUC) including a porous trabecular microstructure. The time evolution of the microstructure is simulated as a surface remodeling process by relating the surface growth remodeling velocity to a surface driving force incorporating a (surface) Eshelby tensor. Adopting the framework of irreversible thermodynamics, a 2D constitutive model based on the setting up of the free energy density and a dissipation potential is identified from FE simulations performed over a unit cell representative of the trabecular architecture obtained from real bone microstructures. The static and evolutive effective properties of bone at the scale of the RUC are obtained by combining a methodology for the evaluation of the average kinematic and static variables over a prototype unit cell and numerical simulations with controlled imposed first gradient rates. The formulated effective growth constitutive law at the scale of the homogenized set of trabeculae within the RUC is of viscoplastic type and relates the average growth strain rate to the homogenized stress tensor. The postulated model includes a power law function of an effective stress chosen to depend on the first and second stress invariants. The model coefficients are calibrated from a set of virtual testing performed over the RUC subjected to a sequence of loadings. Numerical simulations show that overall bone growth does not show any growth kinematic hardening. The obtained results quantify the strength and importance of different types of external loads (uniaxial tension, simple shear, and biaxial loading) on the overall remodeling process and the development of elastic deformations within the RUC.     

Analytical considerations of flow boiling heat transfer in metal-foam filled tubes

Flow boiling in metal-foam filled tube was analytically investigated based on a modified microstructure model, an original boiling heat transfer model and fin analysis for metal foams. Microstructure model of metal foams was established, by which fiber diameter and surface area density were precisely predicted. The heat transfer model for flow boiling in metal foams was based on annular pattern, in which two phase fluid was composed by vapor region in the center of the tube and liquid region near the wall. However, it was assumed that nucleate boiling performed only in the liquid region. Fin analysis and heat transfer network for metal foams were integrated to obtain the convective heat transfer coefficient at interface. The analytical solution was verified by its good agreement with experimental data. The parametric study on heat transfer coefficient and boiling mechanism was also carried out.     

Parametric open-plus-closed-loop control of chaos in continuous dynamical systems

This paper presents a parametric open-plus-closed-loop control approach to controlling chaos in continuous dynamical systems. As an example, chaos in the Lorenz model is controlled to demonstrate its application. Finally, the relations between the parametric open-plus-closed-loop control and the former control methods, such as the open-plus-closed-loop control and the parametric entrainment control, are discussed.Supported by the Science Foundation of the State Education Commission for Doctorate Program, and the Applied Science Foundation of the State Ministry of Metallurgical Industry.     

Water waves in an elastic vessel

Linear and nonlinear analyses of water waves in an elastic vessel are carried out to study the dramatic phenomena of Dragon Wash as well as related controllable experiments. It is proposed that the capillary edge waves are generated by parametric resonance, which is shown to be a possible mechanism for both rectangular an circular vessels. For circular vessel, the normal geometric resonance is also operating, thus greatly enhance the dramatic effect. The mechanism of nonlinear mode-mode interaction is proposed for the generation of axisymmetric low-frequency gravity waves by the high- frequency external excitation. A simple model system is studied numerically to demonstrate explicitly this interaction mechanism.     

连续动力学系统中混沌的参数开闭环控制

针对可能呈现混沌性态的连续动力学，提出了一种参数开闭环控制方案。以控制Ｌｏｒｅｎｚ混沌为例说明该方案的应用。讨论了参数开闭环控制与输送控制、参数输送控制及开闭环控制之间的关系。     

基于应变能准则优化模型的骨骼重建数值模拟

将骨骼重建的适应性弹性理论及参考应变能理论与结构优化及有限元方法结合,建立了基于应变能准则优化模型的骨骼重建数值模拟方法,研究骨骼内部重建的机理和规律。以单元应变能密度为刺激源,由内部材料的分布变化来模拟骨重建的过程和规律。通过对股骨头重建的数值模拟,取得了与临床实验相符的结果,也证实了骨结构形态是对力学环境的最佳适应,定量地反映了力学刺激对骨骼重建的影响,得到了符合骨骼重建规律的结论。     

Equivalent inclusion solution adapted to particle debonding with a non-linear cohesive law

Starting from Eshelby’s solution of the equivalent inclusion problem, an approximate solution is proposed in order to model interface debonding of a spherical inhomogeneity isolated in a uniform matrix. Both phases are linear elastic but the interface traction-separation law is non-linear. A semi-analytical incremental model is developed which is suitable for any type of loading. For computational efficiency, the model relies on two simplifying assumptions: (i) the eigenstrain is uniform inside the inhomogeneity and (ii) the interface compliance is averaged over inhomogeneity’s surface when computing the average strain within the inhomogeneity. An extensive parametric study is conducted for three loading modes and 144 combinations of non-dimensional parameters. The predictions are assessed against full-field finite element solutions based on two error measures of the mean stress field inside the inhomogeneity. The results show that the mean error value is acceptable in all cases and indicate the parameter ranges for which the model is most accurate.     

Surface remodeling of bones induced by intra-medullary nailing

The paper is devoted to a study on the surface remodeling of bones. Anisotropy and piezoelectricity of bone tissue (as per previous experimental studies) are incorporated in the analysis. Surface remodeling induced by intra-medullary nailing is of primary concern in the study.     

On a model for the pedestrians-induced lateral vibrations of footbridges

We study the synchronization of the pedestrians motion with the lateral motion of slender footbridges, which attracted the attention of researchers mainly after the Millennium Bridge well known event. We consider a bridge-pedestrians model developed by Strogatz et al. To better understand some aspects of the underlying mechanical phenomena and to increase the agreement of the model results to the effective behaviour of the walkers (as observed during the Millennium Bridge’s opening day and during Arup’s tests on site) we have introduced some modifications to the model and we have performed extensive parametric investigations, supported by many numerical simulations. Our approach is therefore computational, by means of a self-made code. This permits to highlight the parameters which mainly affect the trigger and the development of the phenomenon of synchronous lateral excitation, thus allowing a good understanding of the physical event and an evaluation of the engineering reliability of the Strogatz et al. model.