小波方法及其在弹性介质特异性粘附问题中的应用

发布时间：2018-11-04 19:00

【摘要】：细胞是构成生物体的基本单元,如人体由数十万亿个细胞组成。真核细胞需要通过表面受体与配体分子键的特异性结合形成与其它细胞或者细胞外基质的粘附接触。我们称这种作用为特异性粘附以区别于基于分子间范德华力的常规粘附行为。细胞的特异性粘附是细胞识别、信号传递、肿瘤转移和伤口愈合等众多生理病理的基础,相关机理的研究由于涉及介质弹性行为与分子间化学反应的耦合因此具有重要理论意义与生物医学应用价值。细胞特异性粘附系统可抽象为软弹性介质间经由可发生化学反应的分子键形成的粘附结构。而对应的数学描述则往往涉及强非线性奇异积分微分方程初边值问题。对这类问题的精确定量求解无疑是数值分析领域的一大挑战,至今仍没有成熟的方法。定量分析方法的缺乏直接妨碍了人们对细胞特异性粘附现象的深刻认识。针对这一现状,本文基于小波理论,提出了一种针对强非线性奇异积分微分方程初边值问题的高精度求解方法,并基于该方法,在建立了弹性介质经由分子键簇群形成的特异性粘附模型的基础上,定量分析了该粘附系统的粘附强度,稳定时间等特性。主要研究成果包括:(1)基于小波理论,针对一类强非线性奇异积分微分方程初边值问题的提出统一求解方法并验证。(2)考虑粘附分子的随机动态过程和两个软弹性体接触界面间的接触力学原理,建立了弹性介质经由分子键簇群形成的特异性粘附模型。(3)基于提出的求解方法,定量分析了弹性介质经由分子键簇群形成的特异性粘附模型。且研究发现:a.粘附区域表现为两端应力集中,应力集中因子越大应力集中越明显,当外部荷载较大粘附破坏从两端向中间发展;b.接触界面形状能够明显影响界面的应力分布,我们可以通过改变界面的形状来改变应力分布;c.应力集中因子越小、单个断开分子键的重新闭合率越大粘附强度越大;d.外部荷载和接触界面夹角能显著影响特异性粘附,加载角度越大粘附强度越小且稳定时间越长;e.粘附强度和加载速率有关,粘附强度随加载速率的增大而增长但增长幅度递减。这些研究结果将有利于我们对特异性粘附认识和以后的研究工作。
[Abstract]:Cells are the basic units of an organism, such as the human body, which consists of tens of billions of cells. Eukaryotic cells need to form adhesive contact with other cells or extracellular matrix through the specific binding of surface receptors to ligand molecular bonds. We call this action specific adhesion distinct from conventional adhesion behavior based on inter-molecular van der Waals force. Cell specific adhesion is the basis of many physiological pathology, such as cell recognition, signal transduction, tumor metastasis and wound healing. The study of related mechanism has important theoretical significance and biomedical application value because of the coupling between elastic behavior of medium and intermolecular chemical reaction. Cell-specific adhesion systems can be abstracted as adhesion structures between soft elastic media via chemically reactive molecular bonds. The corresponding mathematical description often involves the initial-boundary value problem of strongly nonlinear singular integro-differential equations. The accurate quantitative solution of this kind of problem is undoubtedly a great challenge in the field of numerical analysis, and there is still no mature method to solve this kind of problem. The lack of quantitative analysis directly hinders the understanding of cell-specific adhesion. In this paper, based on wavelet theory, a new method for solving the initial-boundary value problems of strongly nonlinear singular integro-differential equations is proposed. Based on the establishment of a specific adhesion model of elastic media via molecular bond clusters, the adhesion strength and stability time of the adhesive system were quantitatively analyzed. The main research results are as follows: (1) based on wavelet theory, A unified solution method is proposed for a class of strongly nonlinear singular integro-differential equations with initial boundary value problem. (2) considering the random dynamic process of adhesion molecules and the contact mechanics principle between two soft elastomer contact interfaces, A specific adhesion model of elastic medium via molecular bond cluster is established. (3) based on the proposed solution, the specific adhesion model of elastic medium via molecular bond cluster is quantitatively analyzed. And the study found that: a. The stress concentration of the two ends of the adhesion region is obvious, and the stress concentration is more obvious with the increase of the stress concentration factor, and when the external load is large, the adhesion failure develops from the two ends to the middle. The shape of the contact interface can obviously affect the stress distribution of the interface, and we can change the stress distribution by changing the shape of the interface. The smaller the stress concentration factor is, the greater the reclosure rate of a single broken molecular bond is, and the greater the adhesion strength is. The external load and contact interface angle can significantly affect the specific adhesion, the greater the loading angle, the smaller the adhesion strength and the longer the stable time. The adhesion strength is related to the loading rate, and the adhesion strength increases with the increase of the loading rate, but the increasing amplitude decreases. These results will be helpful to our understanding of specific adhesion and future research work.
【学位授予单位】：兰州大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：Q27;O175

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