Research On Elastodynamic Model And Its Algorithm For The Human Tricuspid Valve

The human tricuspid valve plays an important role in the circulatory system.It controls the one-way flow of blood from the right atrium to the right ventricle.'Every time the heart beats,the valve moves from open to closed once.Such a high frequency of movement easily causes valve lesions.Once valve disease occurs,the more common medical treatment is valve replacement.Therefore,the study of valve shape and its periodic movement become extremely important.According to the geometrical shape and mechanical properties of human heart tricuspid valve,the elastodynamic model and algorithm of tricuspid valve are studied in this thesis.The main research contents consist of the following four aspects:(1)Determination of the geometric model of tricuspid valve in human heart.Based on the existing medical images and the structure of tricuspid valve as it fully opens,the tricuspid valve is decsribed as a part of the shell of two elliptical cylinders.Concretely,the anterior,the posterior and the septal leaflets of the human tricuspid valve are assumed as portions of the union of two interfacing semi-elliptic cylindrical shells in the case of fully open.Then the parametric equations of the anterior,posterior and septal leaflets are given.(2)Establishment of statics model of tricuspid valve in human heart.Because the tricuspid valve is relatively thin and has super elasticity,the classical Koiter static model of elastic shell theory is used to study the instantaneous force on the tricuspid valve and the corresponding numerical format is given.Specifically,we have discretize the space variable,i.e.,the two displacement components of the tangent plane are discretized by the coordinated linear finite element(P1 element),and the displacement components of the normal direction are discretized by the coordinated finite element(HCT element).Then we verify efficience of the model and the stability and convergence of the numerical scheme on the tricuspid valve.(3)Establishment of a dynamic model of tricuspid valve in human heart.The time-dependent Koiter model is obtained by introducing a time variable into the established static model.Finite element method is used for spatial variables,and Newmark method is used for time variables.Numerical experiments are conducted for three valves to obtain the movement process of the valve from opening to closing to opening in the process of heartbeat.(4)Based on the dynamic model for the tricuspid valve in human heart,we study the dynamic flexural shell with the special assumption that the bending energy is dominant.Thus,the existence,uniqueness of the time-dependent flexible shell model is given.To obtain numerical solution,spatial variables are discretized by finite element method and time variables are discretized by Newmark method.The correspinding stability analysis and error estimation of numerical methods are carried out,and numerical experiments are carried out with a portion of cylindrical shells and a portion of conical shells.The stability and convergence of the numerical method are verified by numerical experiments.