Mathematical Model And Its Algorithm Studying For The Functional Simulation Of The Human Mitral Valve

The mitral valve is one of the most important valve tissues in human heart.Research shows that the heart valves open and close about 3×109 times in a human lifetime.Because of the highly frequent movement,the human heart valves are subject to all kinds of diseases,for example,valve regurgitation congruent disease which can lead to cardiac dysfunction.Therefore,the study of physiological structure and periodic movement is one of the key research topics in the simulation of cardiovascular system,which provides important theoretical and practical support for the production of artificial valves and valve repair.In this paper,a mathematical model that takes the mechanical properties of the heart valve into consideration and depicts the complete movement of the mitral valve is established.And the corresponding numerical method is constructed.The main contents of this paper include the following four aspects:An elastic thin shell is used to characterize the mitral leaflets on the basis of the existing statistical data of the mitral valve and combined with its geometric characteristics and material properties.That is to say,the anterior leaflet and posterior leaflet of mitral valve are regarded as two elliptical cylindrical shells respectively,and the parametric equation of front and back leaflets is given.A dynamic mathematical model of the human mitral valve is established based on elastic theory and method.Proceeding with the static model of the elastic shell,the time variable is introduced into the statics model.Thus,the elastodynamic model of the mitral valve represented by hyperbolic partial differential equation is established.And the theoretical analysis of the model is given by combining the elastic thin shell theory with the elastodynamics theory.For the proposed elastodynamic model of the mitral valve,we discrete the space variable by finite element method and discrete the time variable by finite difference method and then construct the fully discrete form of the elastodynamic model by Newmark method.Next,we calculate the stress and deformation of the mitral valve in a heartbeat cycle.And various discrete schemes are given to analyze the algorithm and verify the validity and accuracy of the model.Based on the elastodynamic Koiter model,the application of the model is extended from the medical field to the construction field.The hyperbolic parabolic shell is used as the representative of the elastic shell whose Gaussian curvature K<0 on the middle surface.The Valencia aquarium is taken as an example of the building field to simulate the displacement distribution on the middle surface.At the same time,the dynamic process of its deformation with the change of the applied force is provided.