摘要
21世纪是生命科学高度发展的时期,力学及结构工程的研究已逐步进入生命科学领域。中耳结构是生命活体中微小复杂的结构,它在声波激励下发生传导振动,将声能转化为机械能传入内耳,这一传声过程是一个集固体动力学、流体动力学于一体的复杂的动力传导过程。目前,由于中耳病变引起的中耳疾病及其传导性耳聋仍是耳科医学中的尚未解决的问题,而单纯医疗手段研究中耳疾患问题未能考虑该结构在传声过程中的动力学行为特征,因此疗效不理想。介于中耳结构的特点----听骨链及软组织(鼓膜、韧带和肌腱)为一体的超精细微小复杂结构。本论文基于力学原理,采用解析分析及数值模拟相结合的方法分析中耳结构。解析方法推导振动骨架的运动方程;数值模拟骨架及软组织整个体系的中耳结构。并在前人有限元的基础上,引入新的数值方法-----自然单元法进行数值模拟,克服了有限元模拟生物体软组织的超弹性大变形出现的单元网格畸变和缠结问题。使粘弹性超弹性的耳生物体能更为准确的模拟分析。其主要工作如下:
1、从机理上分析中耳结构振动骨架系统的力学特征及物理规律,采用变分原理,推导了鼓膜、听骨链及人工听骨的运动方程。并通过与实验数据的对比,验证了方程的正确性。通过运动方程得到参数变化的物理规律,其中以弹性模量变化对中耳振动信息(镫骨底板的振幅)影响最为敏感。进一步为数值模拟提炼参数优化打下基础。
2、采用Voronoi图中的边元素代替图中体元素构造插值函数,提高了自然单元法的计算效率。在积分方案中采用背景网格积分,并借助有限元方法中确定积分点个数方法确定最小积分点数。在布置积分点时采用内松外密的布点方案。最后采用分片试验、算例对本文方法进行验证,验证结果表明本方法正确,具有可靠的精度。
3、推导了三维自然单元法动力学问题的离散格式,并采用中心差分和Newmark常平均加速度法相结合的第一种积分格式对离散格式进行解耦,得到每个自由的解耦递推式,进一步提高了自然单元法在求解动力学问题的计算效率。通过算例验证本文推导的自然单元法的动力学离散格式和解耦算法的正确性。
4、应用自然单元法模拟骨架及包括软组织(鼓膜、韧带及肌腱等)在内的中耳整体结构的声音传导动力学行为。则结果显示:自然单元法在使用较少的结点的情况下,就可以反映出声波引起中耳结构振动的波的特性;自然单元法模拟生物软组织,特别是超弹性(大变形)的韧带优于有限元法。计算结果较有限元法更与实际(实验)吻合。
5、通过对中耳整体结构的模拟分析,得到较单个构件解析方程分析中更进一步的认识,由解析方程得到的结论“弹性模量降低,振幅增大”是有条件的和范围的。在鼓膜带动听骨链的传导运动中,听骨链的弹性模量变化符合解析方程得到的结论;但由于鼓膜刚度过小将无法带动锤骨产生有效的振动,则当鼓膜弹性模量小到一定值时,镫骨位移振幅反而会减小。
6、基于以上的解析模型及数值模型,针对临床医学常见的中耳病变问题,如鼓膜穿孔、听骨链断裂、人工听骨接入方式以及接入位置等问题,用声音传导过程中各部件的动力学行为特征诠释其病变机理------鼓膜穿孔和听骨链断裂都出现在应力或位移最大位置;人工听骨接在鼓膜凸位置其传音效果最理想。
7、应用数值模拟分析典型的中耳病变---鼓室硬化导致听力下降的机理及其手术治疗效果。采用弹性模量增大刻画软组织(韧带及肌腱等)的硬化,采用解除软组织与颞骨的连接模拟切除硬化软组织的治疗。模拟结果显示切除某些硬化韧带可以恢复听骨运动,使声能更有效传入内耳。
本课题的解析方程、数值模型、以及理论分析的研究成果从力学与生物结构交叉研究的视角为传导性耳聋手术研究提供理论基础;是力学及结构分析原理渗透到生命活体的研究领域里的一个初步尝试。
The life science is highly developped in the 21th century, the research of mechanics and structure engineering has entered in life science gradually. Middle ear structure is a fine and complex structure in life body. It generates transmission vibration in acoustic motivation, and transforms acoustic energy into kinetic energy to afferent inner ear. This is a set of power transmission process involving solid dynamics and hydrodynamics theory. At present, middle ear diseases and conduction deafness which are caused by middle ear lesions aren’t still solved in ear medical science. However, due to the dynamics behavior in the process of human hearing transmission is not taken into account when middle ear diseases are studied by medical treatment only, treatment effect isn’t fine. The paper research middle ear by analytical method and numerical simulation based on mechanics theory because middle ear structure is complex structure including ossicular chain and soft tissue(tympanic membrane, ligaments and tendons)。The motion equation of vibration framework is derived by analytical method; it is simulated by numerical method that whole system of middle ear structure includes skeleton and soft tissue. A new numerical method----- natural element method (NEM) is introduced, and overcomes the shortcomings which are element cell distortion and entanglement in simulating hyperelastic large deformation of soft tissue in living body by finite element method. Ear life body of viscoelasticity and hyperelasticity can be well simulated. Main contents of the article are as follows:
1. The mechanical vibration characteristics and physical laws of the middle ear vibration system are analyzed from the view of mechanism. the motion equations of tympanic membrane(TM) ossicular chain and artificial ossicles are derived by the variation principle. The correctness of the motion equations are verified by the comparison with experimental results. Physical laws of parameter variation are gained by the motion equations. Elastic modulus change is the most sensitive to effect of vibration information in middle ear structure (the displacement of stapes footplate). It is the basis of parameter optimization in numerical simulation.
2. In order to improve the computational efficiency of natural element method, interpolating function is constructed by edge element of Voronoi figure which replaces body elements. Integration method of background cell is applied in integral scheme, and the minimum number of integral point is determined by the method which is applied on FEM. Integral points is arranged by the demand that points are close in edge of integral domain and loose in center of integral domain.Finally, examples ( patch test etc) verify the method and moreover the results prove it correct and reliable accuracy.
3. The Discrete form of dynamics problems of three-dimensional NEM is obtained, apply No 1 integral form which is composed of centered difference and Newmark average acceleration .Decoupled recursion is obtained, and furthermore improves the computational efficiency that NEM solves dynamics problems. The examples verify the currency of natural element method discrete format and decoupling algorithm.
4. Dynamics action of sound transmission in whole system of middle ear structure including skeleton and soft tissue is simulated by NEM. Results show that NEM simulates the character that sound wave leads to vibration of middle-ear structure with little points in simulation computing; NEM simulates soft tissue in life body, especially hyperelastic large deformation of ligaments is well simulated than finite element method. Calculation results are well concord of experiments than those of finite element method.
5. Because middle ear structure is simulated and analyzed, the better knowledge of analytical equation is obtained compared with that of single component, the conclusion—“elastic modulus is reducing and the displacement is increasing”which is gained by analytical equation is condition and range. Change of elastic modulus in ossicular chain is accordance with the conclusion of analytical equation in transmission motion which TM drives ossicular chain. But stiffness of TM is too little and can not drive malleus motion, displacement of stapes is reducing when elastic modulus of TM reduces fixed value.
6. Based on the above analytical model and numerical model, according to middle ear diseases of clinical medicine---- TM perforation , ossicular chain fracture, connecting method of artificial ossicular and connecting location of artificial ossicular, pathological theory is explained by dynamics action of every component in sound transmission-----location of TM perforation and ossicular chain fracture is appeared the maximum location of stress and strain, and its sound transmission is the best when artificial ossicular is connected to TM umbo.
7.Typical middle ear disease is simulated and analyzed by numerical simulation------ the mechanism and treatment outcome of which tympanosclerosis result in hearing loss is operated. Hardening of soft tissue (ligaments and tendons) is described by increasing elastic modulus, removal of Hardening tissue is described by deleting connections of soft tissue and temporal bone. The results showed ossicular motion can be recovered by resecting hardening ligaments and sound power is leaded in inner ear.
The numerical model, analytic equation and the results of theoretical analysis can provide a theoretical reference for surgical research on conductive hearing loss from the view of crossing research of mechanics and biological structure. This is the preliminary attempt which mechanics and principle of structural analysis has entered into the research field of life body.
引文
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