Mathematical Models And Numerical Methods Of The Aortic Valve

The aortic valve,which controls blood flow to the whole body and the heart,plays a significant role in the human blood circulation system.In a human lifetime,the aortic valve will open and close approximately 3 billion times without stopping.Each time oxygenated blood passes through the aortic valve,the aortic valve will be subjected to huge pressure from the left ventricle.Therefore,the aortic valve is prone to dysfunction,which will further induce cardiovascular diseases.Currently,one of the main strategies to treat severe aortic valve disease is aortic valve replacement.Therefore,the researches on the geometry and mechanical properties of the aortic valve and its influence on hemodynamics of downstream vascular have great medical value.In this paper,the aortic valve was studied from the perspectives of solid mechanics and fluid mechanics.A geometric model of the aorta was established,a numerical algorithm was constructed,and numerical computation and numerical analyses were carried out.The main research content includes the following three parts:(1)A geometric model of the aortic valve was established,and an elastic thin shell model was used to describe the material and mechanical properties of the aortic valve.Finally,numerical computation and numerical analysis were performed with the conforming finite element method.First,the dimension data combined with the geometric shape of the aortic valve in the literature,were used to calculate the parameter equations of three leaflets of the aortic valve and establish the three-dimensional geometric model of the aortic valve.Then the Koiter shell model was used to describe the mechanical properties of the aortic valve.The shell model was discretized by the conforming finite element method,and the existence,uniqueness as well as convergence of the solution to the discrete problem were proved.At last,numerical experiments were carried out on the aortic valve.(2)The impacts of three stent-free biological aortic valve designs on the hemodynamic characteristics of the aorta were studied.First,we used medical imaging data to reconstruct the patient-specific aortic model and the computational fluid dynamics methods to calculate the models.Then,the streamlines,spiral flow and the hemodynamic parameters such as wall shear stress as well as secondary flow in the aortic model implanted with three different valves were compared.In the end,the impacts of different aortic valve designs on the hemodynamic characteristics of the aorta were clarified.(3)The impacts of three stent-free biological aortic valve designs on the hemodynamic characteristics of coronary artery were studied.For the study of the coronary arteries,we used the methods similar to that of the aortic study.We compared some hemodynamic parameters in the coronary arteries after the implantation of three aortic valves to illustrate the effect of valve design on the hemodynamic characteristics in coronary arteries.