基于解析方法和数值模拟的中耳结构动力学行为研究

发布时间：2018-07-08 15:31

本文选题：中耳结构 + 声波传导　；参考：《上海大学》2010年博士论文

【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。
[Abstract]:The twenty-first Century is a period of high development of life science. The study of mechanical and structural engineering has gradually entered the field of life science. The structure of the middle ear is a tiny and complex structure in living living body. It has transmitted vibration under the excitation of sound waves and transformed the sound energy into a mechanical energy into the inner ear. This sound process is a solid dynamics and fluid dynamics. At present, the middle ear diseases and conductive deafness caused by the middle ear diseases are still the unsolved problems in the ear medicine, and the problem of middle ear disorders in the study of simple medical treatment fails to consider the dynamic behavior characteristics of the structure in the process of sound transmission, so the curative effect is not ideal. The structure is characterized by the hyperfine and complex structure of the ossicular chain and soft tissue (tympanic membrane, ligament and tendon). Based on the principle of mechanics, the structure of the middle ear is analyzed by analytical method and numerical simulation. The equation of motion of the vibration skeleton is derived by analytical method; the middle ear of the framework and the whole system of soft tissue is numerically simulated. On the basis of the predecessors' finite element method, the new numerical method - the natural element method is introduced to simulate the element mesh distortion and entanglement in the finite element simulation of the hyperelastic deformation of the soft tissue of the organism. The viscoelastic hyperelastic ear organism can be more accurately simulated and analyzed. The main work is as follows:
1, the mechanical characteristics and physical laws of the structural vibration skeleton system of the middle ear are analyzed. The equations of motion of the drum, the ossicular chain and the artificial ossicular are derived by the variational principle, and the correctness of the equation is verified by the comparison with the experimental data. The physical law of the variation of the parameters is obtained by the motion equation, in which the modulus of elasticity is changed. It is most sensitive to the vibration information of the middle ear (the amplitude of the stapes base plate), and further lays the foundation for refining the parameters of numerical simulation.
2, using the edge elements in the Voronoi diagram instead of the body elements in the map to construct the interpolation function, the calculation efficiency of the natural element method is improved. In the integral scheme, the background grid integral is used and the minimum integral point number is determined by the method of determining the number of points in the finite element method. The method is verified by the example of piecewise test. The results show that the method is correct and reliable.
3, the discrete scheme of the dynamic problem of the three-dimensional natural element method is derived, and the first integral scheme combined with the central difference and the Newmark constant average acceleration method is used to decouple the discrete scheme, and each free decoupling recursive formula is obtained. The calculation efficiency of the natural element method in solving the dynamic problem is further improved. The correctness of the dynamic discrete scheme and the decoupling algorithm of the natural element method deduced in this paper is verified.
4, the natural element method is used to simulate the dynamic behavior of the framework and the sound conduction of the whole middle ear, including the soft tissue (the tympanic membrane, the ligament and the tendon etc.). The result shows that the natural element method can reflect the wave characteristics of the acoustic wave caused by the sound wave in the middle ear in the case of less nodes; the natural element method simulates the biology. The soft tissue, especially the super elastic (large deformation) ligament, is better than the finite element method. The calculated results are more consistent with the experimental results than the finite element method.
5, through the simulation analysis of the overall structure of the middle ear, we get a further understanding in the analysis of the analytical equation of the single component. The results obtained by the analytical equation "reduce the modulus of elasticity and increase the amplitude" are conditional and range. In the conduction motion of the auditory osseous chain of the tympanic membrane, the change of the elastic modulus of the ossicular chain is in accordance with the analytical equation. The amplitude of the stapes displacement will decrease when the elastic modulus of the tympanic membrane is small to a certain value.
6, based on the above analytical model and numerical model, in view of the common middle ear diseases in clinical medicine, such as tympanic membrane perforation, ossicular chain fracture, artificial auditory bone access and access position, the pathological mechanism of the dynamic behavior of each component in the sound conduction process is interpreted - the tympanic membrane perforation and the ossicular chain fracture appear. In the maximum position of stress or displacement, the artificial auditory ossicle is connected to the tympanic membrane and the sound transmission effect is the best.
7, using numerical simulation to analyze the mechanism of typical middle ear lesions - tympanosclerosis - induced hearing loss and the effect of surgical treatment. The hardening of soft tissue (ligaments and tendons, etc.) was characterized by increasing modulus of elasticity, and the treatment of soft tissue with the connection of the connection of the soft tissue with the temporal bone was used to remove the hardened soft tissue. The simulation results showed that some sclerosis and toughening were removed. The band can restore the ossicular movement and make the sound energy more effectively spread into the inner ear.
The analytical equation, numerical model, and theoretical analysis have provided a theoretical basis for the study of conductive deafness surgery from the perspective of the cross study of mechanical and biological structures, and a preliminary attempt in the field of mechanics and structural analysis infiltrating into living living bodies.
【学位授予单位】：上海大学
【学位级别】：博士
【学位授予年份】：2010
【分类号】：R764;R318.0

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