探讨粘弹性生物组织中波的传播规律，以求利用无创检测方法对相关疾病进行早期的诊断治疗，在临床和生物医学发展方面非常重要。本项目研究波传播与无创检测问题所驱动的本构关系建立、动力学建模、流固耦合模型分析、参数估计与检测定位等数学问题。..改进运动耦合方案、更科学地分析粘弹性性能，对克服前人研究中的适定性困难、方法精确性上缺陷十分关键。基于非线性本构理论，我们拟通过选择适当的细观结构模型与参数，建立依赖于生物组织物性参数的本构关系；通过改进或发展Canic的能量方法、先验估计技巧与均匀化思想，构建更一般化的流固耦合模型并加以分析，以反映狭窄、弯曲、分叉等应用实际；通过应用内部应变结构到拟线性本构方程中，构建更贴合实际的横波传播模型并进行计算与适定性分析，为检测和诊断动脉狭窄等疾病提供更为科学准确的方法。..开展这些问题的研究，在生物、流体、偏微分方程建模和计算等交叉研究方面具有重要的科学意义。

Discussion wave propagation in viscoelastic biological tissue is very important in the development of clinical and biomedical, due to its early diagnosis and treatment of related diseases by take advantage of non-invasive detecting method. This project intends to study some mathematical problems, such as the constitutive of relationship, dynamic modeling, analysis of fluid-structure interaction model, parameter estimation and detection location, which are given in wave propagation and noninvasive detection problem...It is very critical to improve the kinematically coupled scheme and to give more scientific analysis of the viscoelastic properties in overcoming the deficiencies of the well-posed and the method's accuracy respectively in the previous study. Based on the nonlinear constitutive theory, we intend to establish the constitutive relationship that depends on the physical parameters of biological tissue, by selecting the appropriate microstructure model and parameters; to build and analyze a more generalized fluid-structure interaction model so as to reflect narrow, curved, and bifurcated in the practical applications, by improving or developing energy method, a priori estimates and the homogenization skills due to Canic; to build a more fit the actual shear wave propagation model and to do suitable qualitative analysis, so as to provide more scientific and accurate method for the detection and diagnosis of arterial stenosis and other diseases, through the applying of the internal structure in the quasilinear stress-strain constitutive equation...This research has important scientific significance in cross-over study of biological, fluid, modeling and computing of partial differential equations.